Responsable Chimie

Jean Marc Lancelin

H Electronique

Electrotechnique

M C Havgoudoukian

Gérard Scorletti
email: gerard.scorletti@ec-lyon.fr6

H E2m2
email: e2m2@biomserv.univ-lyon1.fr9

ECOSYSTEME, MICROBIOLOGIE, MODELISATION H Evolution

H Ediss

Didier Revel
email: didier.revel@creatis.uni-lyon1.fr

M Johannes Kellendonk

Jean-Yves Buffiere

Mériem Laboune

ENERGETIQUE Mega Mecanique

Genie Civil, Acoustique

H Pr

Boisse Philippe

Secrétaire

Viviane Polsinelli

Y Toussaint

Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in an urban stormwater detention basin

Keywords: settling, resuspension, stormwater detention basin, unsteady conditions, 3D modelling, turbulent kinetic energy, bed shear stress, sediment distribution, removal efficiency, Euler/Lagrange approach

Experiments and 3D modelling of

Expérimentations et modélisations tridimensionnelles de l'hydrodynamique, du transport particulaire, de la décantation et de la remise en suspension en régime transitoire dans un bassin de retenue d'eaux pluviales urbaines

Résumé

Les bassins de retenue des eaux pluviales sont des ouvrages qui contribuent à mettre en place une gestion durable des eaux pluviales urbaines. Ces ouvrages spéciaux ont deux fonctions principales: i) lutter contre les inondations en écrêtant les pics de débit ; ii) piéger les polluants particulaires par décantation en vue de préserver la qualité des milieux récepteurs. Concernant le contrôle des polluants particulaires, les géométries et les volumes des bassins de retenue (obtenus à l'issue de la phase de dimensionnement hydraulique), ainsi que les temps de séjour associés ne sont pas toujours appropriés pour avoir des efficacités de décantation satisfaisantes. On constate que les processus de sédimentation et de remise en suspension dans ces bassins de retenue ne sont pas bien compris et modélisés. Afin de mieux comprendre ces processus dans des ouvrages in situ, cette thèse porte à la fois sur des expérimentations in situ et sur les modélisations de l'hydrodynamique et du transport particulaire dans les bassins de retenue pilotes et in situ.

Cette recherche s'est appuyée en grande partie sur le bassin ϊjango Reinhardt (BϊR) à Chassieu (volume: 32000 m 3 , surface: 11000 m 2 ) dans le cadre de l'τTHU (Observatoire de Terrain en Hydrologie Urbaine) et sur les données expérimentales obtenues par [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] et [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. Les échantillons de sédiments accumulés dans le bassin depuis 2006 ont été prélevés et leurs caractéristiques physiques ont été analysées en laboratoire dans le but de cerner leur distribution spatiale. Concernant la modélisation numérique, dans un premier temps, les simulations de l'hydrodynamique en régime permanent ont été réalisées à l'aide du logiciel CFD Ansys Fluent version 14 et ont été évaluées à partir de l'analyse de corrélation entre le comportement hydrodynamique du bassin et la distribution spatiale des caractéristiques physiques des sédiments accumulés dans le bassin depuis 2006. Les conditions limites sur le fond couramment utilisées et largement décrites dans la littérature (à partir d'études sur pilotes en laboratoire) ont été testées dans le but de représenter la distribution spatiale des sédiments et l'efficacité de décantation du BϊR. δes conditions testées sont : i) contrainte de cisaillement critique ou bed shear stress -BSS et ii) énergie cinétique turbulente critique ou bed turbulent kinetic energy -BTKE. δ'approche Euler-Lagrange dite « particle tracking » (suivi de particules) a été mise en oeuvre. En raison de l'échec de prédiction des zones de dépôt à l'aide des conditions limites disponibles (BSS et BTKE), une nouvelle relation a été proposée pour estimer le seuil BTKE. La condition à la limite obtenue en utilisant cette nouvelle relation (qui prend en compte la distribution des vitesses de chute des particules) a été testée sur un bassin pilote [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] et sur le BϊR à l'aide de l'approche Euler-Lagrange en régime permanent. Les résultats obtenus n'étaient pas très satisfaisants concernant la prédiction des zones de dépôt et l'efficacité de décantation dans le bassin BDR, même en considérant une distribution granulométrique non uniforme. En effet, les résultats des simulations montrent que les conditions BTKE et BSS jouent le même rôle et permettent surtout de représenter la distribution spatiale des particules artificielles dans les bassins pilotes. Afin de mieux prédire les zones de dépôt dans le BDR, une nouvelle méthode a été proposée en considérant le transport des particules, leur décantation et leur érosion en régime transitoire. Sur la base de la méthode proposée pour le transport des particules, la décantation et l'érosion en régime transitoire, plusieurs modélisations avec différentes conditions limites ont été réalisées dans un bassin de retenue pilote rectangulaire [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. Les prédictions des efficacités et des zones de dépôt en régime transitoire avec la méthode proposée sont satisfaisantes. Finalement, la prise Résumé H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 6 en compte des effets liés au régime transitoire améliore considérablement la simulation du transport, de la décantation et de l'érosion des polluants particulaires dans les bassins de retenue.

Mots-clés: décantation, remise en suspension, bassins de retenue des eaux pluviales, régime transitoire, modélisation 3D, énergie cinétique turbulente, contrainte de cisaillement, la distribution des sédiments, efficacité de décantation, approche Euler/Lagrange

Expérimentations et modélisations tridimensionnelles de l'hydrodynamique, du transport particulaire, de la décantation et de la remise en suspension en régime transitoire dans un bassin de retenue d'eaux pluviales urbaines

Présentation des résultats majeurs de la thèse -Résumé étendu exigé pour une thèse rédigée en anglais

Les bassins de retenue des eaux pluviales sont des ouvrages importants du système d'assainissement pour la gestion durable des eaux pluviales urbaines. Les bassins de retenue des eaux pluviales ont deux fonctions principales: i) lutter contre les inondations en écrêtant les pics de débit; ii) piéger les polluants particulaires par décantation en vue de préserver la qualité des milieux récepteurs. δe dimensionnement hydraulique est aujourd'hui maitrisé (quantifier le volume à stocker pour éviter les inondations, connaissant le débit régulé de sortie). Concernant le contrôle des polluants particulaires, les géométries et les volumes des bassins de retenue (obtenus à l'issue de la phase de dimensionnement hydraulique), ainsi que les temps de séjour associés ne sont pas toujours appropriés pour avoir des efficacités de décantation satisfaisantes. En effet, de nombreux bassins de retenue existants ont été initialement conçus exclusivement pour atténuer le débit de pointe et ainsi protéger les zones situées à l'aval du bassin. Par conséquent, l'efficacité de dépollution est très variable et peu satisfaisante. On constate que les processus de sédimentation et de remise en suspension dans ces bassins de retenue ne sont pas bien compris et modélisés. Au cours des deux dernières décennies, les recherches sur ces ouvrages ont été réalisées dans le but d'améliorer les performances de ces derniers en matière de piégeage des polluants particulaires. Au cours de ces programmes de recherche, des ouvrages complexes ont été observés in situ et des bassins rectangulaires ont été étudiés en laboratoire. En outre, les simulations numériques ont été réalisées dans des conditions contrôlées avec des géométries simples en vue de reproduire la répartition spatiale des sédiments artificiels au fond des bassins étudiés et les efficacités de décantation. Cependant, les résultats obtenus à partir des bassins pilotes restent difficilement transposables aux cas des bassins in situ, principalement pour les raisons suivantes:  Géométrie plus complexe,  Variations temporelles des flux d'eau et polluants et de l'état de l'hydrodynamique,  Variations temporelles et spatiales des caractéristiques des polluants particulaires,  Effets d'échelle de similitude surtout en ce qui concerne les caractéristiques des particules. Par conséquent, il est nécessaire de porter l'effort de recherche sur les bassins in situ avec un suivi en continu et d'y associer un travail de modélisation dans le but de mieux comprendre les processus de décantation et de remise en suspension dans des ouvrages réels, et de mieux qualifier les modèles développés à partir des études sur pilotes (application des résultats obtenus à partir d'études sur pilotes aux cas d'ouvrages in situ afin de cerner les limites et de permettre les améliorations nécessaires de ces modèles). Cette thèse porte donc à la fois sur des expérimentations in situ (analyse des caractéristiques physiques des sédiments) et sur les modélisations de l'hydrodynamique et du transport particulaire dans les bassins de retenue pilotes et in situ. Les objectifs scientifiques sont les suivants: i) contribuer à améliorer la compréhension de l'hydrodynamique et des mécanismes de sédimentation dans les bassins de retenue des eaux pluviales; ii) établir, tester et vérifier la modélisation numérique 3D de l'hydrodynamique et du transport particulaire dans les bassins de retenue des eaux pluviales; iii) contribuer à améliorer la modélisation de l'interaction entre les particules et le fond du bassin; iv) proposer une nouvelle méthode qui permet de représenter les dynamiques associées au transport des sédiments et à leur entraînement en régime transitoire avec l'approche Euler-Lagrange. Deux critères de performance ont été choisis pour évaluer les modèles: la distribution spatiale des particules sur le fond du bassin et l'efficacité de décantation (qui représente la masse des particules décantées par rapport à la masse totale des particules entrantes). Cette recherche s'est appuyée en grande partie sur le bassin Django Reinhardt -BDRà Chassieu (volume maximal: 32000 m 3 , surface au sol: 11000 m 2 ) dans le cadre de l'τTHU (Observatoire de Terrain en Hydrologie Urbaine) et sur les données expérimentales obtenues par [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] et [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. Les échantillons de sédiments accumulés dans le BDR ont été prélevés et leurs caractéristiques physiques ont été analysées en laboratoire dans le but de cerner leur distribution spatiale. Cette distribution spatiale a été utilisée pour vérifier la modélisation hydrodynamique en raison de l'insuffisance des données appropriées pour valider les résultats de la modélisation. En effet, compte tenu de la taille du bassin et des conditions opératoires qui auraient été très difficiles, il n'a pas été possible de disposer de données de champ de vitesses ou de contraintes, de mesures de la surface libre dans le bassin, de mesures de quantités turbulentes, etc. Concernant la modélisation numérique, dans un premier temps, les simulations de l'hydrodynamique en régime permanent ont été réalisées à l'aide du logiciel CFD Ansys Fluent version 14 et ont été évaluées à partir de l'analyse de corrélation entre le comportement hydrodynamique du bassin et la distribution spatiale des caractéristiques physiques des sédiments accumulés dans le bassin depuis 2006. Le lien entre le champ de vitesses (mais aussi les champs d'énergie cinétique turbulente et de contraintes de cisaillement, les zones de faibles vitesse près du fond) et la distribution spatiale des caractéristiques physiques des sédiments (en particulier leurs tailles) a été clairement établi (Figure 1). Sur cette base, un modèle hydrodynamique 3D du bassin Django Reinhardt (BDR) a été établi et a été utilisé comme référence pour l'étude du transport particulaire. Les conditions limites sur le fond couramment utilisées et largement décrites dans la littérature (à partir d'études sur pilotes en laboratoire) ont été testées dans le but de représenter la distribution spatiale des sédiments et l'efficacité de décantation du BϊR. δes conditions testées sont : i) contrainte de cisaillement critique ou bed shear stress -BSS et ii) énergie cinétique turbulente critique ou bed turbulent kinetic energy -BTKE. δ'approche Euler-Lagrange dite « particle tracking » (suivi de particules) a été mise en oeuvre. En raison de l'échec de prédiction des zones de dépôt avec ces conditions limites, une nouvelle relation a été proposée pour estimer le seuil BTKE, sachant que la turbulence près du fond influence la décantation et la remise en suspension des sédiments. La relation proposée est la suivante:

2 s c v k  
Où k c est le seuil BTKE, v s est la vitesse de chute de la particule, est un coefficient d'ajustement qui permet de prendre en compte les effets de concentration lors de la décantation, les incertitudes sur les vitesses de chute, l'aspect cohésif de certaines particules, etc. La condition limite sur le fond proposée a été testée sur un bassin pilote [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] et sur le BϊR à l'aide de l'approche Euler-Lagrange en régime permanent. Les résultats obtenus n'étaient pas très satisfaisants, même en considérant une distribution granulométrique non uniforme. En effet, les résultats des simulations ont montré que les conditions BTKE et BSS jouaient le même rôle et permettaient de prédire les zones de dépôt des particules artificielles uniquement dans les bassins pilotes. Cependant, toutes les conditions limites testées ne permettent pas de prédire les zones de dépôt dans le BDR et elles entraînent une surestimation de l'efficacité de décantation. Néanmoins, les résultats de modélisation liés à la distribution spatiale des particules sur le fond du BDR sont améliorés en considérant une distribution non uniforme des vitesses de chute à l'entrée du bassin (voir Figure 2). ω'est pourquoi ces modèles ont été améliorés dans un deuxième temps, en considérant le transport des particules, leur décantation et leur érosion en régime transitoire. La figure 3 représente schématiquement la démarche employée pour mettre au point les nouvelles conditions limites sur le fond en régime transitoire: Le traitement des particules en contact avec le fond dans le processus de suivi des particules en régime instationnaire est réalisé comme suit. τn distingue deux états à l'instant t : soit la particule est en suspension, soit elle a sédimenté. En fonction de l'état à l'instant t, la méthode de traitement de la particule à l'instant t+Δt est différente, comme décrit ci-après.

(A) : La particule qui était en mouvement peut soit entrer en contact avec le fond et sédimenter (état A1, Figure 3), soit continuer à se déplacer dans l'écoulement après une remise en suspension ou se déplacer par saltation après le contact avec le fond (état A2, Figure 3). δa détermination de l'état de la particule après contact avec le fond est fondée sur le respect ou non d'un seuil de contrainte de cisaillement (Bed Shear Stress -BSS de l'ordre de 0.03 Pa selon ϊufresne, 2008) ou d'un seuil d'énergie cinétique turbulente au fond (Bed Turbulent Kinetic Engergy -BTKE de l'ordre de 2x10 -4 m 2 /s 2 selon [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. Si les valeurs locales de BSS ou BTKE sont inférieures aux seuils, la particule sédimente. Sinon elle est remise en suspension. On peut également utiliser les courbes de Shields (contrainte de cisaillement adimensionnelle) pour calculer un seuil de contrainte de cisaillement variable selon les caractéristiques des particules. Nous avons également proposé une nouvelle fonction permettant de calculer la valeur critique d'énergie cinétique turbulente. ωette fonction fait intervenir les vitesses de chute des particules. (A1) Si la particule sédimente, on n'applique pas la condition « trap » (qui détruit l'historique de la trajectoire de la particule), mais on modifie la vitesse et les forces associées au mouvement de la particule de façon à faire rester sur place. Pour ce faire, nous avons développé des modules spécifiques ou UDF (user defined function) afin de modéliser cet état de la trajectoire.

(A2) Si la particule reste en mouvement, on applique la condition de type « reflect » (rebond de la particule dans une direction donnée avec une certaine vitesse et retour dans l'écoulement ou mouvement par saltation). Il est ainsi possible de prendre en compte les pertes d'énergie dues au frottement au fond à travers des coefficients de frottement suivant les directions normale et tangentielle. Par défaut, les coefficients suivant la normale au fond et la direction tangentielle valent 1. δe choix de l'orientation et l'intensité du vecteur vitesse lors du rebond ainsi que la prise en compte du frottement peuvent permettre de représenter la saltation. Nous avons développé une autre UDF pour modéliser ces mouvements possibles de la particule.

(B) δa particule sédimentée à l'instant t peut être entraînée et se déplacer en suspension ou par charriage à l'instant t+Δt si les caractéristiques de l'écoulement le permettent. δa contrainte de cisaillement locale est comparée à une contrainte seuil obtenue à partir de la courbe de Shields. Si la contrainte locale est supérieure à la contrainte seuil, la particule est entraînée (état B2), sinon elle reste dans son état initial (situation B1). (B1) La particule reste au même endroit. (B2) Plusieurs recherches sont menées pour modéliser le charriage à l'échelle de la particule.

La saltation est le mode dominant du mouvement par charriage. Plusieurs auteurs caractérisent la saltation par une hauteur et une longueur de saut et par la vitesse de démarrage du saut. Dans cette étude, on utilise la formule proposée par Hu et Hui (1996) pour estimer la vitesse initiale d'entraînement.

Si la particule est entraînée par le fluide, la vitesse tangentielle de la particule est considérée comme étant égale à la vitesse locale de l'écoulement près du fond projetée suivant la direction tangentielle. Nous avons développé des programmes spécifiques (UDF) qui ont été implémentés dans le code FLUENT afin de réaliser les traitements des conditions aux limites sur le fond (conditions décrites précédemment, voir Figure 3).

La modélisation du transport des particules à l'aide de l'approche Euler/δagrange avec les nouvelles conditions limites en régime transitoire a été menée dans le but de représenter les zones de dépôt et l'efficacité de décantation dans les deux bassins pilotes étudiés (ϊufresne, 2008;[START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. Sur la base de la méthode proposée pour le transport des particules, la décantation et l'érosion en régime transitoire, 12 modélisations avec différentes conditions limites (voir tableau 1) ont été réalisées dans un bassin pilote de retenue rectangulaire [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. Toutes les conditions sont rappelées au tableau 1.

Expérience [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] Zones simulées La figure 4 montre la comparaison entre les zones de dépôt observées expérimentalement et simulées.

Le tableau 2 montre les efficacités de décantation simulées. En comparant les efficacités expérimentales (minimum = 83% -maximum = 87%, [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] et simulées, on constate que presque tous les cas, à l'exception du cas 7 (sans prise en compte du module de dispersion des particules noté DRWM pour Discret Random Walk Model ou modèle de dispersion particulaire), prédisent de façon satisfaisante cette efficacité. La prédiction des efficacités et des zones de dépôt en régime instationnaire avec la méthode proposée (Figure 3) sont sensibles au nombre de particules traitées, à la constante de Lagrange notée C L , aux forces de résistance lors de la remise en suspension, à la vitesse initiale d'entrainement. Au final, les effets liés au régime instationnaire dans les bassins de retenue jouent un rôle prépondérant au regard du comportement des particules près du fond. Il est donc indispensable de les prendre en compte. En outre, la condition limite de type BTKE proposée est appropriée pour prédire les zones de dépôt alors que la condition de type BSS variable estimée à partir de la courbe de Shields reste appropriée pour représenter l'entrainement des particules dans les bassins pilotes lorsque ces particules sont considérées comme étant non cohésives.

Les perspectives de ce travail sont brièvement présentées ci-après. Concernant les expérimentations in situμ i) échantillonner les particules à l'entrée du BϊR (un dispositif de type leaping weir sera installé à l'entrée du BϊR et permettra de piéger les particules susceptibles de décanter dans le bassin), ii) collecter les sédiments dans des pièges (concevoir les pièges de façon à éviter toute perturbation des trajectoires des particules lors de la décantation ou de leur transport). Concernant la modélisation du transport solide avec les conditions aux limites proposées (Figure 3), il est envisagé d'améliorer la condition BTKE, en faisant en sorte que le coefficient d'ajustement soit fonction des caractéristiques des particules et des conditions hydrauliques près du fond. Une fonction mathématique pourrait être obtenue à partir de mesures expérimentales en laboratoire. δ'amélioration de cette condition BTKE (car elle engendre une surestimation de l'efficacité) pourrait également passer par le développement d'une relation mathématique permettant de relier les autres caractéristique physiques des particules décantées à la vitesse de chute. En effet, aucune formule mathématique viable n'existe aujourd'hui pour estimer correctement la vitesse de chute à partir des autres caractéristiques physiques des particules (taille, densité, forme, etc.). Il est également prévu de réaliser les simulations de l'hydrodynamique et du transport solide en régime transitoire (en considérant des événements courts ou une partie d'un événement pluvieux long par exemple) dans le BDR. Dans ce cas, la dynamique liée aux concentrations de sortie sera également examinée par simulation (nous disposons de mesures de turbidité à l'entrée et à la sortie du BϊR). δa collision entre particules est un élément aussi à prendre en compte. Enfin, un dispositif innovant de mesure de la surface libre en 3D et du champ de vitesse de surface dans le BϊR sera mis en place. ωe dispositif permettra enfin d'avoir des données hydrodynamiques pour la validation plus aboutie des modèles 3D développés.

Mots-clés: décantation, remise en suspension, bassins de retenue des eaux pluviales, régime transitoire, la modélisation 3D, énergie cinétique turbulente, contrainte de cisaillement, la distribution des sédiments, efficacité de décantation, approche Euler/Lagrange Chapter 1 Introduction

List of Figures

List of Tables

Background

The process of urbanization has meant an increase in the proportion of impervious surfaces such as pavement and roofs in urbanized areas. These surfaces prevent precipitation from soaking into the ground naturally. Instead, a comparable volume of stormwater is discharged rapidly from the catchments. This overload of stormwater runoff runs quickly into storm drains, sewer systems, and drainage ditches and may cause: , 1997), stormwater runoff and the discharge from stormwater drain pipes were the largest contributors to water quality problems in the ωommonwealth's rivers, streams, and marine waters.

 Downstream flooding  Stream
Traditional stormwater management has focused on collecting stormwater in pipe networks and conveying it off site safely, economically, and as quickly as possible, either directly to streams or rivers, or to large stormwater management facilities (basins), or to combined sewer systems flowing to a wastewater treatment plant. With progressive urban development, natural waterways and drain and pipe systems in urbanized catchments have been increasingly taxed in their ability to convey the significantly increased quantities, and rate, of water flow [START_REF] Wong | Modelling urban stormwater treatment -A unified approach[END_REF]. This often results in urban flooding. Furthermore, there has been a growing global trend of flooding over recent years within the context of global climate change [START_REF] Werritty | Climate change: flooding occurrence review[END_REF][START_REF] Plate | Flood risk and flood management[END_REF][START_REF] Prudhomme | Uncertainty and climate change impact on the flood regime of small UK catchments[END_REF][START_REF] Few | Floods, health and climate change: A strategic review[END_REF][START_REF] Dore | Climate change and changes in global precipitation patterns: What do we know?[END_REF]Ryu and Butler, 2008).

Urbanization leads to changes in both the quantity and quality of stormwater runoff that is delivered to urban receiving waters. Growing public awareness of environmental issues in recent times has highlighted the importance of environmental management of urban stormwater. Traditional urban drainage systems were developed to meet the community's need to minimize the threat of flooding, rather than to preserve the quality of the environment. Therefore, in this field there is a clear need for additional design and assistance with implementation, as well as a need for greater information on managing the urban water cycle, especially the quality of stormwater [START_REF] Alderson | Urban stormwater: Best practice environment management guidelines[END_REF].

Sustainable urban development has been introduced into the management of stormwater. The main goals of stormwater management are to minimize stormwater runoff and to improve stormwater discharge quality in order to protect receiving water bodies. Stormwater management technologies and concepts (e.g. Water Sensitive Urban Design-WSUD, Low Impacts Development -LID, Best Management Practices -BMPs, etc.) have been developed to achieve these purposes. Stormwater Best Management Practices (BMPs) are recognized as one of the most effective and practical measures for reducing pollutants and for preventing pollutants from reaching the receiving water bodies, thus controlling the quality of runoff from a site.

Detention/retention systems are the first approach used in stormwater management, and involve large retention or detention basins or ponds. These basins can detain and retain stormwater discharge and allow sediment and trash to be removed or separated from the water before the stormwater is released into water receiving bodies. By reducing the flow velocity and controlling discharge rates, these facilities can decrease the likelihood of flooding and help to reduce the impact that impervious surfaces and urban development can have on water quality and aquatic habitats. They are still widely used in the U.S. (USEPA, 2011).

A detention basin is a dry pond or basin designed to hold storm water for at least 24 hours to reduce local and downstream flooding and to allow solids to settle. The detention basin should be able to regulate peak flow rates of large and infrequent storms (10, 25, or 100 years) and generally they remain dry. Unlike retention basins, detention basins have a limited ability for removing soluble pollutants due to the short time that stormwater runoff is detained.

Motivation

Nowadays stormwater detention basins have increasingly been used to control both stormwater quantity and quality. Originally, detention basins were designed solely to regulate the peak flow rate. However, monitoring studies have revealed that stormwater detention basins can also provide effective pollutant removal if they are of a sufficient size and if adequant settling time is available [START_REF] Randall | Urban Runoff Pollutant Trap by Sedimentation[END_REF][START_REF] Grizzard | The Effectiveness of Extended Detention Ponds for Urban Stormwater Pollution Management[END_REF]. The idea of using stormwater detention basins for the dual purpose of flood control and mitigation of pollutant runoff loads was put forward by several researchers in the 1970s [START_REF] Ferrara | Stormwater quality characteristics in detention basins[END_REF]. Many existing stormwater detention basins fail to achieve the necessary levels of nonpoint source pollutant loading reduction. This includes those basins designed solely for stormwater runoff peak discharge magnitude mitigation as well as those detention basins designed both for quantity and quality control. Though improvements in the efficiency of detention basins have been extensively discussed in the literature over the past two decades [START_REF] Ferrara | Stormwater quality characteristics in detention basins[END_REF][START_REF] Nix | Residence time in stormwater detention basin[END_REF]Loganathan et al., 1994;Nix et al., 1988;[START_REF] Marcoon | Detention basin retrofit: optimization of water quality improvement and flood control[END_REF][START_REF] Akan | Design aid for water quality detention basins[END_REF][START_REF] Takamatsu | Alternative approach to evaluation sedimentation performance of stormwater detention basins using a nondimensionlized time scale[END_REF] and some measurements have been applied to design, retrofitting and maintenance, not enough attention has been paid to improving understanding and representation. Due to the limited possibilities for the removal of soluble pollutants, usually the focus is on improving settlement efficiency for particulate pollutants within the basin. In the absence of a good understanding of the hydrodynamics of flow and the transportation of pollutant particles, many researchers consider the detention basin's water residence time to be the main way of evaluating the removal efficiency (noted as RE hereafter) of detention basins (Nix et al., 1988;[START_REF] Persson | The hydraulic performance of ponds of various layouts[END_REF][START_REF] Marcoon | Detention basin retrofit: optimization of water quality improvement and flood control[END_REF][START_REF] Akan | Design aid for water quality detention basins[END_REF]. Detention basins are generally designed assuming steady state and plug flow conditions, however, the behaviour of stormwater detention systems is very complex due to the dynamic nature of stormwater inflow, pollutant loads, and the state of the systems (e.g., water depth, temperature, etc.). Nix et al. (1988) pointed out that steady state analyses were inappropriate for evaluating the performance of a stormwater detention basin system. In addition, the water residence time for existing detention basins is difficult to obtain. The removal rates of particulate pollutants are linked to sediments characteristic (in particular the settling velocity) and flow condition such as residence time. Over the past two decades, smallscale physical model experiments and corresponding numerical investigations have been carried out by researchers (e.g. [START_REF] Saul | Sediment deposition in storage tanks[END_REF][START_REF] Stovin | Sedimentation in storage tank structures[END_REF][START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF], 2000;[START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]Dufresne et al., 2009) to try to understand the sedimentation processes, but the results obtained remain difficult to apply to in situ basin [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF], mainly due to:

 more complicated geometry  temporal variation of flow and state of hydrodynamics  variation of the pollutant loads and their properties  Scale effect of similarity mainly regarding the particle characteristics Therefore, it is necessary to carry out research in real full-scale basins via measurement and/or modelling, in order to further understand the sedimentation processes under in situ conditions, and to account for unsteady behaviour in order to represent the multiphase flow in both full and small-scale detention basins.

Objectives

This thesis aims i) to further improve the understanding of particulate pollutant sedimentation and resuspension processes in stormwater detention basins and ii) to provide effective ways for improvements to be made to the design and management of detention basins for stormwater quality.

The scientific objectives are:

 to contribute to further improving the understanding of the hydrodynamics and sedimentation characteristics in stormwater detention basins;  to establish, test and verify the 3D numerical modelling of flow and particulate pollutants transport in stormwater detention basins;  to contribute to improving the modelling of the interaction between particulate pollutants and the basin bottom;  to develop a method which enables dynamic sediment transport, settling and entrainment under unsteady conditions to be represented using the Euler/Lagrange approach.

The investigations carried out in this thesis aim to provide ways of improving the pollutant removable performances of detention basins that may be applied in practice.

Structure of the Thesis

This thesis is organized in 6 chapters.

Chapter 1 gives a general introduction to the research undertaken.

Chapter 2 reviews relevant previous investigations on detention basins. These include research on the sediment sources, sediment characteristics, sediment transport mechanisms and investigations on detention basin performances with different methods such as scaled physical models, etc.

Chapter 3 introduces the experimental site and presents the methodology for experiments and numerical modelling.

Chapter 4 analyses the accumulated sediment's spatial distribution and its physical characteristics, such as density and particle size distribution, etc. It then presents the results of the flow modelling for the hydrodynamics in the Django Reinhardt detention basin, which are implicitly validated. The sediment transport modelling results under steady flow conditions are also analysed and discussed.

Chapter 5 mainly presents test cases for sediment transport under unsteady state conditions using the newly proposed method. The simulated results are explored and discussed.

Chapter 6 highlights general conclusions on the present work and outlines future perspectives.

Chapter 2 Literature review

This chapter begins with a general introduction to stormwater detention basins in urban drainage systems; this is followed by a presentation of experimental investigations on detention basins; finally, the numerical investigations are examined.

Global overview of stormwater detention basins

Stormwater is known to be one of the most important causes of water impairment in watercourses [START_REF] German | Modelling of different measures for improving trap in a stormwater pond[END_REF]. The main objectives of stormwater management are to minimize stormwater runoff and to improve the quality of stormwater discharge in order to prevent the pollution of receiving water bodies. [START_REF] Lawrence | Stormwater detention & BMPs[END_REF]. For the last twenty to thirty years this has often been accomplished by constructing stormwater management ponds (or basins) on the site of new developments. Initially, the focus was on managing the runoff rate from a development in order to prevent flooding and erosion. In France, the use of detention basins dates back to the 1960s when 'Villes σouvelles', or New Towns, were constructed. Such facilities have become much more widespread [START_REF] Deutsch | Pour une nouvelle maîtrise des eaux pluviales[END_REF]. Meanwhile, it was realized that such basins could also play an important role in the reduction of urban rainfall runoff pollution [START_REF] Valiron | Gestion des Eaux: Alimentation en Eau[END_REF]Hall et al., 1993). From that point on, stormwater basins were also used as settling basins to control stormwater quality. However, many existing stormwater basins have low removal efficiency for two main reasons: firstly, the majority of stormwater basins were designed solely for stormwater runoff peak discharge magnitude abatement and were enhanced later to improve pollutant removal performance through the addition of various retrofitting technologies; and, secondly, even if some stormwater basins were designed for both stormwater quantity and quality, they failed to achieve the necessary levels of pollutant load reduction due to an inadequate understanding of sedimentation processes [START_REF] Guo | Hydraulic and water quality performance of urban storm water detention basin before and after outlet modification[END_REF].

Detention basins are basins or reservoirs in which water is temporarily stored for the purpose of regulating a flood. Water can be released from the basin through its outlet which may be a weir, culvert or pipe. The storage volume may be recessed below natural ground level or above natural ground level with a road embankment acting as a dam wall. Detention basins can be classified according to both their location relative to the river channel or sewer (e.g. 'on-line' or 'off-line') and their content under dry weather flow conditions (e.g. 'dry' and 'wet') (σascimento et al., 1999). Dry and wet detention basins are often termed detention and retention facilities respectively, but for the purposes of this thesis the term 'detention basin' is used to encompass all flood storage basins in general. The general definitions are as follows:

2.1.1 Definitions Detention basins are stormwater runoff containment areas that remain dry during dry weather except after rain storms when runoff is conveyed to them. The detention basins are designed initially to reduce and delay peak flow, to prevent local and downstream flooding and have subsequently been used to enhance the trapping of pollutants thanks to observations on their effective pollutant trap performance (Randall et al.1982;[START_REF] Grizzard | The Effectiveness of Extended Detention Ponds for Urban Stormwater Pollution Management[END_REF]Loganathan et al., 1994). A detention basin often has a dry bed which is usually achieved with the use of a lowflow channel or pipe system. Thus, these basins may have multi-functional purposes and can be used for sporting activities and as open spaces. Detention basins generally provide only minimal water quality improvement (Department of Transport and Main Roads, 2013).

2.1.1.2

Wet basin (retention basin) Retention basins are stormwater basins that incorporate a permanent pool and retain some water in the basin between storm events. These basins provide flood attenuation benefits during a range of flood events and provide water quality benefits during more frequent minor flood flow and regular storms. The permanent pool within a wet basin may consist of a lake, wetland, or water quality pond (Department of Transport and Main Roads, 2013). Retention basins are covered by the term detendtion basins for the purposes of discussion of sediment transport within this thesis.

General performances

As discussed above, the effective efficiency of detention basins has not been satisfactory to date due to the lack of consideration given to runoff quality control criteria and and the lack of appropriate design methods. Table 2-1 shows the annual potential and short-term removal efficiency of detention basin recorded by [START_REF] Adler | Aperçu des techniques de traitement des eaux pluviales[END_REF] in studies conducted by the French institution CEMAGREF in separate drainage systems, together with a synthesis carried out by [START_REF] Valiron | Maitrise de la pollution urbaine par temps de pluie[END_REF]. 2-2 shows the efficiency recorded in some UK detention basins, the overall range of trap efficiency reported in the literature and experimental settling rates [START_REF] Nascimento | Using detention basins: operational experience and lessons[END_REF]. The results from 1 4 5 H Gonzalez-Merchan (2012) estimated the annual removal efficiency of TSS in the Django Reinhardt detention basin located at Lyon in France using in situ monitoring data, and found it to be between 33% and 75% during the years 2004-2010. [START_REF] Pettersson | Modelling of flow pattern and particle removal in an open stormwater detention pond[END_REF] and [START_REF] Comings | Storm Water Pollutant Removal by Two Wet Ponds in Bellevue, Washington[END_REF] also reported that the settleable solids' removal efficiencies were between 40% and 90%. In short, the removal efficiencies of the detention basin are not satisfactory or well-controlled. [START_REF] Nix | Residence time in stormwater detention basin[END_REF] stated that detention basins are normally categorized as one of three types: plug flow, completely mixed flow and intermediate flow. Detention basins are often designed based on steady state conditions, which do not represent the situation in real basins. The discrepancies between theoretical and steady state values of mean residence time in unsteady conditions in real stormwater detention basins have resulted in poor pollutant control capabilities. In fact, detention basin's rate of efficiency in reducing solid pollutants is the result of the combination of a large number of variables, which include the physical, chemical and biological characteristics of the pollutants, as well as the precipitation regimes, resident time in the basin, geometric characteristics (e.g. depth, shape, volume, and outlet configuration), the quality of maintenance services, and so on. [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF] reported that sediment, flow and basin characteristics are the main factors which influence the RE of detention basins.

Given the many parameters that influence the settling processes in detention basins, it is very difficult to predict RE in a simple manner. The most accurate predictions will be those based on theoretical relationships that incorporate all of the influencing factors [START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF]. For example, factors such as pond shape, inlet/outlet configurations and physical environment should be included since they can significantly influence both hydraulic performances of these facilities and the sedimentation process. Such factors have led to different design recommendations for improving hydraulic performances and also ultimately for improving water quality. For dry or semi-dry ponds, the presence of a vegetation cover on the bottom of the pond can have major effects on the sedimentation process. However, traditional design methods do not address hydrodynamic features of flow, and these methods cannot evaluate sedimentation performances resulting from different measures such as baffles or different inlet/outlet positions in advance [START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF][START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF].

Retrofit practices for improving water quality in detention basins

Retrofitting in existing stormwater detention facilities is of critical importance for restoring impaired watersheds. Many existing stormwater detention basins were designed solely for stormwater runoff peak discharge magnitude abatement or were designed for water quality control standards at the time of construction. With the purpose of improving the effectiveness of pollutant RE, many authors have investigated the impact factors on effectiveness, including basin geometry, inflow and outflow devices, and so on.

In order to extend detention time, [START_REF] Guo | Hydraulic and water quality performance of urban storm water detention basin before and after outlet modification[END_REF] tried retrofitting smaller outlet pipes and floating risers in the outlet of detention basins. By comparing monitoring data taken before and after retrofitting, it was found that both outlet modifications resulted in longer detention times in the basin for the same volume of runoff inflow. However, contrary to what might have been expected it was found that the TSS (total suspended solids) removal efficiency did not correlate to the detention time. The extended residence time did not result in improved TSS removal efficiency. [START_REF] Marcoon | Detention basin retrofit: optimization of water quality improvement and flood control[END_REF] evaluated the different outlet structure designs for potential improvements in water quality using 2D modelling with PondPack TM software. The analysis of hydraulic results enabled them to identify all possible design options, water quality benefits, and all potential negative impacts. [START_REF] Vega | Application of CFD modeling to study the hydrodynamics of various anaerobic pond configurations[END_REF] used MIKE21 to predict the effects of changes in sludge content, baffling, inlet-outlet positioning and basin geometry on the hydrodynamic performance of WSP. The results suggested that the provision of two baffles placed at 1/3L and 2/3L (L = length of basin) increases the pond retention factor and BOD 5 (Biological Oxygen Demand over 5 days) removal efficiency. [START_REF] Akan | Design aid for water quality detention basins[END_REF] developed a set of procedures to be used when making a quick evaluation of existing retrofitted or trial designed dry detention basins. The methodology can also be employed in the preliminary sizing of a new extended dry detention basin and of its water quality outlets. [START_REF] Guo | Retrofitting detention basin with water quality control pool[END_REF] illustrated how to retrofit existing detention basins with a perforated plate and micropool for water quality control. A designed outfall box with a slow release for micro events and a fast release for extreme events is recommended for new or existing basins. [START_REF] Bennett | Optimal design of detention and drainage channel systems[END_REF] used dynamic programming methods to find the optimal minimum cost, location and the size of detention basins. Nix et al. (1988) demonstrated an approach for estimating the long-term performance of detention basin behaviour based on SWMM. The information generated can be used to provide guidance for the planning and design of a detention basin. [START_REF] Ormsbee | Design of dual purpose detention systems using dynamic programming[END_REF] proposed dynamic programming formulations for dual purpose detention systems. These proposed formulations can be used to determine the location and the dimensions of basins and associated outlet devices. [START_REF] Akan | Storm runoff detention for pollutant removal[END_REF] presented a design aid for sizing detention basins and outlet facilities for the removal of particulate pollutants from runoff. With this design aid, one can determine the stage storage relationship for a basin, the size of outlet structure and storage volume.

The retrofit practices and methods mentioned above are mostly based on theoretical or empirical models which contribute to detention basin system design and management, either through positive practical experience or lessons from failures. Some retrofit measures can improve RE, while others have failed [START_REF] Vega | Application of CFD modeling to study the hydrodynamics of various anaerobic pond configurations[END_REF]. For example, common sense would suggest that a baffle would improve RE by decreasing the inflow velocity and increasing flow path length, but Nighman and Harhor (1997) reported that after modification using a baffle in the detention basin, the RE dramatically decreased from an average 68% to 2.7% for three storm events in four monitored cases. This shows that common sense is not always to be trusted and there is a need for further research for baffle design that will reliably increase RE for a range of flow conditions. Retrofit practices are sometimes ineffective and hard to quantify due to poor understanding of hydraulic performance and sedimentation processes. As mentioned above, many factors influence the removal efficiency of detention basins, but these factors have not all been well-examined and the sedimentation processes are not wellunderstood.

Mechanisms related to Sediment transport

Source of stormwater solids

According to [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF], the solids entering sewer systems originate from a variety of sources. Four principal sources are typically defined:

 The atmosphere, which contains fine dust and aerosols;  Surfaces in catchments, where solids accumulate during dry weather periods and are washed off during storm events: roofs, streets, parkings, highways, etc.;  The environment and processes taking place inside the drainage/sewer system: natural water body interactions, infiltration/exfiltration , decay and degradation of solids;  Industrial and commercial effluents and solids from construction sites, which typically contributes very significantly to the solid loads entering sewers.

Ashley and Crabtree (1992) argued that it is not possible to draw up universal rules to identify which sources make the greatest contributions to sediment inputs for particular catchments. Localized effects can predominate; construction activities for example, have been shown [START_REF] Broeker | Impact of depositions on sewer operation[END_REF] to increase surface wash-off loadings by up to 300%. [START_REF] Dembélé | MES, DCO et polluants prioritaires des rejets urbains de temps de pluie : mesure et modélisation des flux événementiels[END_REF] noted that the main pollutants in urban runoff primarily originate from two sources: the atmosphere and watersheds.

The sediment load is known to vary during a storm, and first flush flow rates in stormwater runoff are an example of this [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]. The finest particles and dissolved pollutants are washed off at the start of a storm and correspond to the majority of pollutants which are made up of the finest solids fractions, with particles smaller than 250 m comprising some 75% of the total solids and chemical pollutant load washed in from road surfaces [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]. [START_REF] Deletic | Modeling of storm washoff of suspended solid from impervious surface[END_REF] monitored the solid and dissolved pollutants that washed off asphalt surfaces in Belgrade and Lund to show that a deterministic model for solid washoff was applicable and accounted for non-uniform sediment build-up over the contributing surface.

The model was extended to estimate the transport of particles through grass filter strips [START_REF] Deletic | Modeling of water and sediment transport over grassed areas[END_REF].

Characteristics and quantities of particulate pollutants in drainage systems

This section aims to give an overview of particulate pollutants characteristics in urban drainage systems.

Generally, the most common pollutant types that have attracted interest in sewer systems have been BOD 5 (biological oxygen demand in 5 day), COD (chemical oxygen demand), TKN (total Kjeldahl nitrogen), metals (e.g. Cd, Cr, Cu, Fe, Mn, Ni, Pb, Zn), hydrocarbon, PAHs (polycyclic aromatic hydrocarbons) and PCBs (polychlorobyphenyls) [START_REF] Bertrand-Krajewski | Pollution des rejets urbains par temps de pluie. Synthèse génerale[END_REF], cited in Ashley et al., 2004). Table 2-3 shows general ranges for COD, heavy metals and hydrocarbon mean concentrations. More recently, microbial hazards have attracted more and more attention form researchers [START_REF] Gourmelon | Development of microbial and chemical MST tools to identify the origin of the faecal pollution in bathing and shellfish harvesting waters in France[END_REF][START_REF] Sebastian | Assessment of chemical and microbial hazards in a full-scale stormwater detention basin: Their characterization, toxicity and fate[END_REF]. Some pollutants are attached to particles rather than being dissolved in the runoff, such as phosphorus, some heavy metals, and organic pollutants such as polynuclear aromatic hydrocarbons [START_REF] Furumai | Dynamic behaviour of suspended pollutants and particle size distribution in highway runoff[END_REF][START_REF] Lee | Characterization of polycyclic aromatic hydrocarbons (PAHs) in different size fractions in deposited road particles (DRPs) from Lake Biwa area, Japan[END_REF][START_REF] Vaze | Nutrient loads associated with different sediment sizes in urban stormwater and surface pollutants[END_REF]. [START_REF] Hvitved-Jacobsen | Treatment systems for urban and highway runoff in Denmark[END_REF] also reported that 60-80% of phosphorus, 30-40% of Zn, 70-80% of Pb and 30-40% of Cu are associated with suspended solids charged in the stormwater runoff. [START_REF] Bertrand-Krajewski | Pollution des rejets urbains par temps de pluie. Synthèse génerale[END_REF], [START_REF] Chebbo | Solides des rejets pluviaux urbains caractérisation et traitabilite[END_REF] and [START_REF] Chebbo | Caractérisation physico-chimique des solides des rejets urbains par temps de pluie[END_REF] reported the percentage of pollutants attached to solids (in 1 4 9 H Table 234). It has been well-established that a diverse range of potential pollutants may attach themselves to solids and that the particulate fraction includes the largest proportion of potential pollution load [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]. Absorption capacity depends on particle size. Generally, smaller particles have a higher absorption capacity per unit mass due to their larger specific surface area [START_REF] Furumai | Dynamic behaviour of suspended pollutants and particle size distribution in highway runoff[END_REF][START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF][START_REF] Lee | Characterization of polycyclic aromatic hydrocarbons (PAHs) in different size fractions in deposited road particles (DRPs) from Lake Biwa area, Japan[END_REF]. The finest particles and dissolved pollutants are washed off at the start of a storm and the strongest pollutants are associated with the finest solids fractions, with particulates smaller than 250 micron comprising some 75% of the total solids and chemical pollutant load washed from road surfaces [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]. According to [START_REF] Ellis | Incidence of heavy metals in street surface sediment: solubility and grain size studies[END_REF], about 70% of metals were attached to particles of less than 100 m, which represent less than 15% by weight of settled solids at the sites monitored. [START_REF] Chebbo | Caractérisation physico-chimique des solides des rejets urbains par temps de pluie[END_REF] reported that fine particles (ξ100 m) with a median diameter (d 50 ) ranging from 2η m to ζζ m were dominant in suspended solid during wet weather. As shown in 1 5 0 H Table 2-5, the results of measurements taken showed about 68%-85% of TSS with a diameter of less than 100 m. Becouze-Lareure (2010) measured the grain sizes for several storm events in a storm sewer network and the results indicated that grain size was heterogeneous, with values of d 50 between 8η m and 117 m as opposed to the values of between 7 m and 17 m as reported in the literature for the same type of site [START_REF] Marsalek | In Size distribution of suspended sediments in an on-stream stormwater management pond[END_REF][START_REF] Corsi | Evaluation of the multichambered treatment train, a retrofit water-quality management device[END_REF]. [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] reported that the average d 50 for two storm events ranged from 64 m to 92 m. These measured results may imply that fine particles are dominant in TSS and that grain size is heterogeneous in spatial and temporal ranges. Density is an important property of sediment. Typically, the largest particles have the lowest density in wastewater systems [START_REF] Chocat | Encyclopédie hydrologie urbaine et assainissement[END_REF][START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]. However, lower density of finer fractions of particles in stormwater runoff has also been reported, as finer fractions of particles may contain more organic matter [START_REF] Kayhanian | Characteristics of road sediment fractionated particles captured from paved surfaces, surface run-off and detention basins[END_REF]. Hence, it seems that the density of sediment depends on the site. Generally, particle density is about 1700 kg/m 3 to 2200 kg/m 3 in a combined sewer network, lower than that (<2200 kg/m 3 ) in separate storm sewers [START_REF] Chebbo | Caractérisation physico-chimique des solides des rejets urbains par temps de pluie[END_REF][START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]. The settling velocity of particles is the most important property in sediment because it often depends on diameter, density, shape and surface roughness as well as the submerged fluid viscosity [START_REF] Loch | Settling velocity-a new approach to assessing soil and sediment properties[END_REF]. Settling velocity has been used as a parameter in most transport models. Generally, the settling velocity of suspended solids is variable and it is difficult to obtain representative results for the settlement of sewage particulates [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF]) due to the heterogeneity of suspended solids. However, the interval of settling velocity is relatively comparably similar. [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] reported average median settling velocity of between 0.2 m/h -11 m/h in combined networks and 0.6 m/h -9m/h in separated networks [START_REF] Chocat | Encyclopédie hydrologie urbaine et assainissement[END_REF][START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF][START_REF] Chocat | Eaux pluviales urbaines et rejets urbains par temps de pluie[END_REF]. Due to different measurement technologies and the complexity of sampling techniques, up to now there has been no common appropriate method agreed upon in the literature for giving the settling velocity for individual suspended solids in a drainage system. The settling velocity of suspended solids in drainage systems has often been measured in the laboratory using collected samples. The results have often been expressed as the possible maximum settling velocity for certain percentage mass with S-shaped curves as in 1 5 1 H Figure 2-2. Torres (2008) tried to find a relationship between the settling velocity (V 50 ) and other particles' properties such as the diameter (d 50 ) based on a series of storm sample measurement results with the VICAS protocol. Unfortunately, there no clear direct relationship was observed between the settling velocity and the particle sizes. Hence, it is difficult to perform a simulation to estimate the corresponding settling velocity for non-uniform particles. Sediment transport, where it refers to the motion of solid particles, usually consists of the natural processes of erosion, transportation and sedimentation. 1 5 2 H Figure 2-3 illustrates the general nature of a sediment transport process in flow [START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF]. It is one of the most important and common processes or phenomenon encountered in the fields of hydraulics, hydrology and water resource engineering. Sediment transport occurs in rivers, reservoirs, channels, and marine environment, etc. It is a very complex multiphase phenomenon which involves complex physical, chemical and biological processes. It has been active throughout time and has shaped the present landscape of our world. Today, it can cause severe engineering and environmental problems. A lot of attention is paid to this field in order to to estimate, avoid or enhance engineering processes. For example, Kantoush et al. (2008c) investigated the sedimentation in shallow reservoirs with the aim of controlling the accumulation of sediment in reservoirs which leads to the reduction of the effective storage capacity. Generally, three types of sediment transport are identified: wash load, suspended load and bed load.

Wash load is the portion of sediment that is carried by fluid flow; it is in near-permanent suspension and is transported without deposition occuring, essentially passing straight through the stream. It consists of the finest particles and can be defined as having a Rouse number of <0.8, meaning that the turbulent mixing velocity is far greater than the settling velocity.

Suspended load is the portion of the sediment that is carried by fluid flow which settles so slowly that it hardly touches the bed. It is maintained in suspension by the turbulence in flowing water. The total sediment load is the sum of the three types of load. Wash load is carried within the water column as part of the flow, and therefore moves with the mean flow velocity of the main stream. Because there is little or no interaction with the bed, the particles extract only negligible momentum from the flow. Many authors simply distinguish between bed load and Deposit suspended load, assuming that the wash load is not really a mode of solid transport (Bertrand-Krajewski, 2012).

As the real sediment transport processes are interactive and dynamic, the interface of bed load and suspended load are partly arbitrary and hard to identify, however, making this distinction is useful for theoretical and experimental approaches and work. In practice it is commonly accepted that there is a thin bed load layer above the immobile bed. The top of the thin layer is considered to be the frontier between the suspended load and the bed load (Chanson, 1999).

Modelling of sediment transport mechanisms

Sediment transport mechanism is fundamental. In this section methods for predicting the suspended load and bed load transport rates are presented. Nowadays, CFD technology is becoming more and more popular, but empirical models for calculating sediment transport in rivers, reservoirs, basins, etc. are still dominant in engineering.

a. Suspended load transport

The suspended load is described by the concentration C in mass (kg/m 3 ) or in volume (m 3 /m 3 ). The transport of suspended load material is controlled by a combination of advection, turbulent diffusion and convection. Diffusion characterizes the random motion and mixing of particles throughout the superimposed water depth along the longitudinal flow motion.

b. Advection-diffusion equation

The conservation of sediment mass in incompressible dilute suspension subject to diffusion, mixing, dispersion, and advection, is described by the advection-diffusion equation:

        term sources S terms mixing diffusive z C D y C D x C D terms advective z C u y C u x C u change mass t C z y x w y x c 2 2 m 2 2 m 2 2 m                                                            (2.1)
Where C is the concentration of suspended load, ε x , ε y and ε z are the turbulent dispersion coefficients, D m is the molecular diffusion coefficient and S c is the term of phase change sources / sinks.

In laminar flow, the turbulent mixing and dispersive coefficients vanish (ε x = ε y = ε z = 0). Conversely, in turbulent flow, the molecular diffusion coefficient D m is negligible when compared to the turbulent mixing and dispersion coefficients (D m <<ε). The advectiondiffusion equation has numerous applications in hydraulic modelling within the field of sediment and contaminant transport in open channels.

c. Vertical concentration profile

If the density of sediment is heavier than the continuous phase (normally water), the sediment concentration near the bottom is larger. [START_REF] Rouse | Modern conceptions of the mechanics of turbulence[END_REF] established the following formula to describe the vertical concentration profile C(z):

    0 R a h a z z h a C z C          (2.2) * 0 v u R s s    (2.3)
Where C(a) represents the reference sediment concentration at a reference elevation "a" above the bed elevation and h is water depth. The relative concentration C(z)/C(a) depends on the elevation z above the reference elevation as derived by [START_REF] Rouse | Modern conceptions of the mechanics of turbulence[END_REF]. The exponent R o refers to the Rouse number and reflects the ratio of sediment properties to the hydraulic characteristics of the flow. u * is shear velocity, and v s is particle settling velocity, with s = 1 and von Kármán constant κ = 0.4.

The suspended load transport rate q s (in Kg/m 2 /s) can be calculated using:

   dz z u z C q h a s   (2.4)
Where u(z) is the logarithmic velocity profile along the vertical axis. For turbulent flow regime over a smooth bed, u(z) is given by:

                  5 . 5 log 75 . 5 * *  zu u z u (2.5)
For a turbulent flow regime over a rough bed, u(z) is given by:

                    5 . 8 log 75 . 5 * s k z u z u (2.6)
Where k s is the bed sand equivalent roughness of Nikuradse: k s ≈2d 50 if the bed is flat, and k s is equal to the height of the dunes if dunes are present on the bed.

Van Rijn (1984a) proposed a method for calculating the suspended load transport rate based on data from laboratory flume and river experiments. The computation method is complex and is not relevant in this case. Further information can be found in Van Rijn (1984a).

d. Bed load transport

It is widely accepted that bed load transport generally consists of sliding, rolling and saltating motion. Initially bed load transport was a problematic issue in sediment study due to the lack of advanced measuring instruments. Therefore, instead of investigating the sediment mechanism on a particle scale, early research on sediment transport mechanisms often looked at groups of particles on a macro scale. The concept of sediment transport rate (or bed load discharge) is often used to describe sediment transport. Bed load L b refers to a quantity of sediment that is moving in the bed layer, which can be measured by volume, mass, or weight.

In SI units, bed load is usually measured using mass in metric tons (1000 kg). Since some empirical formulas were not created using SI units, unit conversions are needed.

(L 3 ) L bm (M) L bw (ML/T 2 ) Bed load discharge Q bv (L 3 /T) Q bm (M/T) Q bw (ML/T 3 ) Unit bed load discharge q bv (L 2 /T) q bm (M/LT) q bw (M/T 3 ) Note: L bw = gL bm = p L bv , L bm =ρ p L bv   w b b dW q Q 0 , T d Q L T b b   0 Table 2-6
summarizes the relationships between bed load, bed load discharge, and unit bed load discharge. In terms of notation, the first subscript, b, refers to bed load and the second subscript refers to volume, mass, or weight.

A lot of research on bed load transport has been carried out and many models have been established over the past century. Usually, these models are based on equilibrium conditions. Bertrand-Krajewski (2012) classified these bed load transport formulas in four main categories, depending on their derivation:  Formulas based on shear stress excess (τ 0 -τ c ), where τ 0 is the local bed shear stress and c is the critical bed shear stress for particle inception movement (e.g. Meyer-Peter εüller's formula);  Formulas based on probability of movement(e.g. Einstein formulas);  Formulas based on the stream power concept (e.g. Bagnold formula);  Formulas based on dimensionless variables (e.g. van Rijn formula).

Another classification by [START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF] considered that bed load transport could be treated either as a deterministic or a probabilistic problem. Deterministic methods have been proposed by Du [START_REF] Boys | Études du régime du Rhône et de l'action exercée par les eaux sur un lit à fond de graviers indéfiniment affouillable[END_REF] and [START_REF] Meyer-Peter | Formulas for bed-load transport[END_REF]; probabilistic methods were developed by [START_REF] Kalinske | Criteria for determining sand transport by surface creep and saltation[END_REF] and [START_REF] Einstein | Bedload transportation in Mountain Creek[END_REF]. Both approaches yield satisfactory estimates of bed load discharge.

e. Empirical Bedload transport formulas

Among these numerous bed load formulas, a few of them, which are widely used in engineering, are quoted below. Duboys (1879) developed a bed load formula based on the concept that sediment moves in thin layers along the bed. The applied bed shear stress 0 must exceed the critical bed shear stress τ c to initiate motion. The volume of gravel material in motion per unit width and time q bv is calculated using (adapted into SI unit form by [START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF]:

c 0 4 3 05655 . 67   d q bv  (2.7)
Where d is the particle size and 0 is the local shear stress. Note that in this formula the critical shear stress c is calculated using (adapted into SI unit form Julien, 2010):

d c 0000128693 . 0 00847 . 0    (2.8)
Meyer-Peter and Muller (1948) developed a complex bed load formula for sediment mixtures and various densities of the surface layer of the bed material.

    3 2 3 2 3 1 3 1 3 1 p 25 . 0 047 . 0 bm e p p r B e q d g hJ k k d                    (2.9)
Where q bm is bed load discharge, h is the water depth, J is the energy gradient, d e is effective diameter, calculated using the equation (2.10), k B is ripple factor according to the Manning -Strickler coefficient of bed forms, k r is particle roughness according to the Manning-Strickler coefficient of particles, given by [START_REF] Strickler | Beitraege zur Frage der Geschwindigheitsformel und der Rauhikeitszahlen fuer Stroeme Kanaele und geschlossene Leitungen[END_REF]

                   (2.12)
Where τ * is the Shields parameter (or dimensionless shear stress, τ * = τ 0 /( p -)d), and τ *c is the critical dimensionless shear stress (here equal to 0.047). Einstein (1942) introduced the idea that particles move in steps proportional to their sizes. He used probability concepts extensively to define a relationship of sediment discharge. Taking into account the correction proposed by [START_REF] Brown | Sediment transportation[END_REF], the formula can be expressed as:

                                            3 2 3 2 3 * 36 36 3 2 gd gd gd q q p p p bv bv            (2.13)
Where is the kinematic viscous coefficient, q bv* is the dimensionless rate of sediment transport, this is shown in 1 5 7 H Figure 2-6 as a function of the Shields parameter τ * , with the measurements from [START_REF] Gilbert | The transport of debris by running water[END_REF], [START_REF] Bogardi | Sediment Transport in Alluvial Streams[END_REF] and [START_REF] Wilson | Bed-load transport at high shear stress[END_REF]. For very coarse sand and gravel, q bv* can be estimated as: [START_REF] Brown | Sediment transportation[END_REF] suggested the following two relationships:

mm d if gd q q p bv bv 1 3 *               (2.14)
18 . 0 ) / 391 . 0 exp( 15 . 2 * * *      if q bv (2.15) 52 . 0 18 . 0 40 * 3 * *      if q bv (2.16)
For sediment transport at high shear rates, one obtains [START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF]:

52 . 0 15 * 5 . 1 * *     if q bv
(2.17) Van Rijn (1984b) developed a formula for calculating the bed load discharge based on the empirical experimental data.

3 50 3 . 0 1 . 2 * 053 . 0 gd D T q p p bm                (2.18)
Where D* is the dimensionless particle diameter:

3 1 2 50 *           g d D p    (2.19)
And T  is the transport parameter, calculated using:

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 53

      2 * 2 * 2 * u u u T c      (2.20)           90 * 3 12 log 18 d R U g u b (2.21)
Where U is the mean flow velocity, u *c is the critical shear velocity according to the Shields diagram (shown in 1234567u * ' is the effective bed shear velocity, R b is the hydraulic radius which has a relationship with the bed according to Einstein (1942) or [START_REF] Vanoni | Laboratory studies of the roughness and suspended load of alluvial streams[END_REF] side wall correction method. [START_REF] Yalin | An expression for bed-load transportation[END_REF] proposed the following formula for bed load transport:

              r r r gd s q bm    1 ln 1 1 635 . 0 1 * 3 (2.22) Where (2.23) c r * *    (2.24) 4 . 0 * 45 . 2 s c   
(2.25) [START_REF] Nielsen | Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention[END_REF] proposed the following formula for bed load transport:

    * * * 3 12 1    c bm gd s q    (2.26)
Generally, the empirical bed load transport models were established under conditions of equilibrium. They are not suitable to for non-equilibrium conditions. These models are often used in species modelling. These models have not been used here, because the DPM (discrete phase model) approach has been selected instead to model the sediment transport.

f. Incipient motion (entrainment)

Fluid flow around sediment particles exerts forces which tend to initiate particle motion. The resisting force of non-cohesive material is made up of particle weight and frictional resistance from the boundary. Particles tend to incipient motion when the forces from the flow exceed the resistance forces. Many authors have investigated the criteria required to represent this condition's threshold. Such criteria are typically critical values of velocity or of bed shear stress.

Table 2-7 quotes some formulas for calculating the critical velocity, V c , for incipient motion of bed load. However, in this study, these formulas were not suitable for the 3D modelling because the critical velocity was generally an integrated average velocity in the whole water depth.

Table 2-7 Formulas for entrainment velocity

Reference Formula Remarks Bogardi(1968) [START_REF] Novak | A study into the correlation of sediment motion.in pipe and open channel flow[END_REF] [START_REF] Einstein | Bedload transportation in Mountain Creek[END_REF] procedure; suitable for rough fixed bed, d is particle diameter in m

6 . 1 8 . 1 3 2 3 2 * 000044 . 0                  d h g d u V c  d is particle diameter in m
  27 . 0 61 . 0 1            h c R d d s g V R h is
  38 . 0 54 . 0 1            b c R d d s g V R b is hydraulic radius of related the bed (m) according to
The most widely used approach is based on the critical shear stress τ c . When local τ 0 exceeds the critical shear stress c, incipient motion occurs. Due to the relationship of shear stress to the Shields parameter (τ * = τ 0 /( s -)d), one often uses the critical Shields parameter τ *c to determine the incipient motion based on initial work using the Shields curve (see Figure ), which enables τ c to be estimated in relation to the dimensionless particle diameter D*. Many authors have dedicated work to establishing a formula for the relationship that fits the Shields curve. Table 2-8 summarizes some formulas for critical Shields parameter τ *c estimation.

   c   6 . 0 3 1          gd s    Van Rijn (1984b)                      
  3 1 2 1 *          g s d D s=ρ p /ρ Soulsby (1997)     * 020 . 0 exp 1 055 . 0 * 2 . 1 1 30 . 0 * D D c       Julien (2010)       * 05 . 0 exp 1 tan 06 . 0 3 * exp 3 . 0 * D D c        φ is the repose angle
Based on non-cohesive uniform spherical sediment in a steady flow, [START_REF] Ling | Criteria for Incipient Motion of Spherical Sediment Particles[END_REF] derived two threshold functions as criteria for incipient motion in spherical sediment particles: the rolling threshold function and lifting threshold function. The rolling threshold gives the minimum dimensionless shear stress required to start bed load movement in the form of rolling and the lifting threshold gives the minimum stress for suspension. The Shields curve, along with some classical representative data, lies mostly between the two thresholds.

Besides shear stress, many authors have argued that particle motion near the bottom has been found to be in close association with turbulent bursting in experiments (Sumer and Oguz 1978;[START_REF] Sumer | Particle motions near the bottom in turbulent flow in an open channel, part 2[END_REF][START_REF] Grass | The influence of boundary layer turbulence on the mechanics of sediment transport[END_REF]. It has been recognized that the intermittent bursting process plays a central role in sediment transport [START_REF] Sutherland | Proposed mechanism for sediment entrainment by turbulent flow[END_REF][START_REF] Jackson | Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flow[END_REF][START_REF] Ikeda | Sediment suspension with rippled bed[END_REF][START_REF] Dyer | Formulas for the transportation of bed load[END_REF][START_REF] Kawanisi | Measurements of turbulence and suspended sediment in tidal river[END_REF]. Based on bursting processes (such as ejection and sweep event), [START_REF] Cao | Turbulent Bursting-Based Sediment Entrainment Function[END_REF] proposed a sediment entrainment function using the averaged bursting period scaled on inner variables and the spatial scale of bursts.

The probabilistic approach to modelling sediment transport has shown some promise. Many authors have developed models that describe the entrainment of sediment [START_REF] Wu | Rolling and lifting probabilities for sediment entrainment[END_REF]. [START_REF] Sun | Statistically derived bed load formula for any fraction of nonuniform sediment[END_REF] employed rolling probability in their fractional bed load equation, whereas Paintal (1971) used sliding probability in his bed load model. [START_REF] Cheng | Pickup probability for sediment entrainment[END_REF] provided a theoretical formula to describe lifting probability for sediment entrainment, which was later modified by [START_REF] Wu | Pickup probability of sediment under log-normal velocity distribution[END_REF]. Both of these studies incorporated the probability distribution of instantaneous velocity in order to explore the relationship between lifting probability and flow condition. The Gaussian and log-normal distributions of instantaneous velocity were adopted in their analyses, respectively. [START_REF] Papanicolaou | Stochastic incipient motion criterion for spheres under various bed packing conditions[END_REF] provided a quantitative model for predicting sediment entrainment under three representative bed packing densities corresponding to the isolated, wake interference, and skimming flow regimes. However, further studies incorporating more general considerations are needed in order to modify the formulation of entrainment probability. [START_REF] Wu | Rolling and lifting probabilities for sediment entrainment[END_REF] developed theoretical components for evaluating the rolling and lifting entrainment probability in hydraulically smooth-bed and transitional open-channel flow. However, the sediment particle was assumed to be lying on a bed of closely packed particles and such a configuration represents only one of many possible situations.

Transition from bed load to suspended load is more complex than entrainment of bed load motion, and there is no simple criterion equivalent to the Shields criterion for bed load (Bertrand-Krajewski, 2012). Many authors focus on the ratio of shear velocity and settling velocity. Chanson (1999) saidμ "considering a particle in suspension, the particle motion in the direction normal to the bed is related to the balance between the particle settling velocity component and the turbulent velocity fluctuation in the direction normal to the bed." Turbulence studies have suggested that turbulent velocity fluctuation is of the same order of magnitude as shear velocity. Using this assumption, a simple criterion for the initiation of suspension is: [START_REF] Bagnold | An approach to the sediment transport problem from general physics[END_REF] suggested that u * /v s =1. Engelund (1965a[START_REF] Engelund | Turbulent Energy and Suspended Load[END_REF][START_REF] Engelund | A monograph on sediment transport in alluvial streams[END_REF] stated that the threshold is equal to 0.25. Julien suggested suspension began at a value of 0.5-2. Van Rijn (1984a) developed a formula for calculating the threshold taking into consideration particle properties:

threshold v u s  * (2.27)
10 * 4 . 0 v 10 * 1 * 4 v * *      D if u D if D u s s (2.28)
Where D* is dimensionless diameter defined in equation (2.19). [START_REF] Niño | Threshold for particle entrainment into suspension[END_REF] modified Van Rijn's formula to better fit experimental data:

        3 . 27 * 4 . 0 3 . 27 * 1 * 2 . 21 v 2 . 1 * D if D if D u s (2.29)

g. Deposition

Deposition is one of the important topics for sediment transport. But when does deposition occur? A superficial answer is: when conditions are such that flow becomes overloaded, sediment is deposited. But this does not describe conditions under which flow becomes overloaded. Furthermore, this definition is based on equilibrium conditions in sediment transport. The most straightforward process involved in deposition is settling: the downward fall of sediment particles through the surrounding fluid acted on by the pull of gravity.

Observation shows that some particles reach the bottom and keep moving as bed load rather than settling out as deposition. This is absolutely critical for a true fundamental understanding of sediment deposition. Unfortunately, not nearly enough attention has been given to such matters in the literature on sedimentation, either by hydraulic engineers or by sedimentary geologists [START_REF] Southard | Special Topics: An Introduction to Fluid Motions, Sediment Transport, and Current-generated Sedimentary Structures[END_REF][START_REF] Maa | Critical bed shear stress for cohesive sediment deposition under steady flow[END_REF]. [START_REF] Hjulström | Studies of the morphological activity of rivers as illustrated by the river Fyris[END_REF] may be the first author who used velocity to determine the deposition of particles. He published a graph called Hjulström curve (shown in 12345678) to determine whether a river will erode, transport, or deposit sediment. The graph takes sediment particle size and water velocity into account. Critical shear stress is also often used as a parameter for determining the deposition of sediment. [START_REF] Krone | Flume studies of the transport of sediment in estuarial shoaling processes[END_REF] suggested the following widely used formula for deposition rate, D b :

cd b if D     0 , 0 (2.30) cd b s b if C Pv D      0 , (2.31) P=1-τ 0 /τ cd (2.32)
Where τ 0 and τ cd are the local bed shear stress and the critical bed shear stress for deposition respectively, v s is the particle settling velocity, C b is the near bed concentration, and P represents the probability for deposition. [START_REF] Stovin | Sedimentation in storage tank structures[END_REF] carried out sediment transport experiments in a small rectangular tank and they found that the distribution of deposited sediment may be predicted from the known velocity distribution in the tank and the values of the critical bed shear stresses τ cd (0.03~0.04 Pa). It may be argued, therefore, that mathematically computed velocity distribution values may be used to predict sediment deposition in prototype storage tank designs. Based on the measurements for critical bed shear stress cd , [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] performed CFD modelling of hydrodynamics and particle tracking (Euler/Lagrange approach) to predict basin efficiency and the deposition zone. [START_REF] Maa | Critical bed shear stress for cohesive sediment deposition under steady flow[END_REF] reported results of laboratory experiments on cohesive sediment deposition behaviour. Direct observations of where and when deposition was formed suggested that deposition only occurs when the local bed shear stress 0 is less than a critical value, and this value, cd, was close to 0.042 Pa. [START_REF] Gardner | Dynamics of boundary-layer deposition: A flume investigation[END_REF] suggested that initial deposition of oceanic sediment occurs at 0.046 Pa. [START_REF] Mantz | Laboratory flume experiments on the transport of cohesionless silicon silts by water streams[END_REF] reported values of deposition shear stresses of around 0.033 Pa and 0.063 Pa for particle size distribution with median diameters of 18 m (range 6-60 m) and ζ2 m (10-80 m). [START_REF] Self | Factors controlling critical shear for deposition and erosion of individual particles[END_REF] suggested that the typical values of cd , are 0.05-0.1 Pa. There is no a single value for general conditions. The value seems to be dependent on the sediment characteristics and site.

However, using a probability function to represent the bed-shear stress distribution and excluding cd , [START_REF] Winterwerp | On the sedimentation rate of cohesive sediment. Estuarine and coastal fine sediment dynamics-INTERCOH[END_REF] was able to simulate successfully deposition experiments carried out by 8 0 H [START_REF] Krone | Flume studies of the transport of sediment in estuarial shoaling processes[END_REF] in a straight flume and sediment transport experiments in an annular flume performed by [START_REF] Mehta | An investigation of the deposition properties of flocculated fine sediment[END_REF]. He deduced from this that there was no cd at all.

Mahta and Partheniades (1975) suggested that the process of deposition of flocs appears to be controlled by stochastic turbulence in the zone near the bed. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] introduced the threshold of bed turbulent kinetic energy as a criterion for determining the deposition of sediment through CFD modelling of hydrodynamics and sediment transport. The criteria for sediment deposition are still being debated.

h. Exchange of bed load and suspended load

The exchange of sediment in the interface of bed load and suspended load is often described using the concepts of sedimentation rate and erosion rate. The net exchange is calculated as the difference between them.

The sedimentation rate D b can be estimated by [START_REF] Krone | Flume studies of the transport of sediment in estuarial shoaling processes[END_REF] the equations (2.30-2.32). To calculate the erosion rate E b , there are several equations provided in scientific literature. [START_REF] Cemagref | Logiciel Rubar 20. Notice d'emploi[END_REF] uses the following equations: 2.33) and resuspension under unsteady conditions in urban stormwater detention basin / 2013 59

ce b if E     0 , 0 (
ce ce b if M E                0 0 , 1 (2.34)
Where M is the empirical coefficient, τ 0 is the local shear stress, and τ ce is the critical shear stress calculated often using the Shields parameter. However, critical erosion bed shear stress values from experiments are also often used. For example, [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF] found that the erosion threshold was 0.06 Pa when using a small basin in the laboratory. El [START_REF] Ganaoui | The deposition and erosion of cohesive sediment determined by a multi-class model[END_REF][START_REF] Ganaoui | Erosion of the upper layer of cohesive sediment: characterization of some properties[END_REF] observed that the critical shear stresses of erosion were in the range of 0.025 Pa -0.05 Pa depending on the layer of the cohesive sediment. [START_REF] Smith | Spatially averaged flow over a wavy surface[END_REF] used the following equation for erosion rate:

                    1 1 1 65 . 0 0 0 0 0 ce ce b E       (2.35)
Where γ 0 is a coefficient equal to 0.0024. [START_REF] Garcia | Entrainment of bed sediment into suspension[END_REF] also use another equation:

3 . 0 1 5 5 AZ AZ E b   (2.36)
Where A is a parameter equal to 1.3e-7, and Z is calculated by [START_REF] Abad | 2D stream hydrodynamic, sediment transport and bed morphology model for engineering applications[END_REF] as follows:

6 . 0 *         d v v u Z s s (2.37) 2.2.3.3
Particle behaviour on a particle scale

In recent years, the development of advanced experimental equipment and methods (such as the high speed photographic techniques) have lead to a better understanding sedimentation phenomena, and many researchers have focused on the mechanical characteristics of sediment transport on a particle scale, which means observing individual particle motion mechanisms in fluids. The basic principle behind this equipment and these methods is the measurement of particle transport processes in order to analyse the balance of forces according to σewton's second law of motion. The bed load movement is the most popular area of investigation since it is not well-understood and is important for sediment transport investigation. The results obtained from experiments demonstrate that saltation is the main form of bed load movement under ordinary flow conditions (Hu and Hui, 1996). In fact, authors had already investigated the saltation phenomenon with experimental and theoretical analysis [START_REF] Gilbert | The transport of debris by running water[END_REF][START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF][START_REF] Einstein | Bedload transportation in Mountain Creek[END_REF][START_REF] Gordon | Saltation of plastic balls in 'onedimensional' flume[END_REF][START_REF] Francis | Experiments on the motion of solitary particles along the bed of a water-stream[END_REF][START_REF] Luque | Erosion and transport of bed-load sediment[END_REF][START_REF] Abbott | Saltation and suspension trajectories of solid particles in a water stream[END_REF][START_REF] White | Magnus effect in saltation[END_REF] and obtained some interesting results, although the precision of these results was not high enough due to the limitation of measuring instruments available at that time. Van Rijn (1984a[START_REF] Van Rijn | Sediment transport, Part II: Suspended load transport[END_REF], [START_REF] Bridge | Bed load grain velocities and sediment transport rates[END_REF], [START_REF] Murphy | Bed load or suspended load[END_REF], [START_REF] Wiberg | A theoretical model for saltating particles in water[END_REF], [START_REF] Anderson | Sediment transport by wind[END_REF], [START_REF] Sekine | Mechanics of saltating particles[END_REF], [START_REF] Lee | Investigation of saltating particle motions[END_REF], [START_REF] Hu | Analysis of saltation characteristics of bed load transport in flowing water[END_REF] developed theories on saltation dynamics further. More recently, Hu and Hui (1996), [START_REF] Lee | Continuous saltating process of multiple sediment particles[END_REF], Niño and Garcia (1994a[START_REF] Niño | Gravel saltation II: Modeling[END_REF], 1998a, 1998b), [START_REF] Lajeunesse | Bed load transport in turbulent flow at the grain scale: experiments and modeling[END_REF] measured the saltation trajectories of particles in flow and analysed the data using methods that combined mechanical and statistical theories for a better understanding of saltation mechanisms (e.g. the force acting on particle, jump height and length, etc.).

a. Forces acting on particle

Up to now, several kinds of forces that act on the particle near bed during the transport processes have been identified (Hu and Hui, 1996):

 Submerged weight due to the gravity and buoyancy forces  Drag force due to the relative velocity  Lift force (consisting of Magnus force due to particle rotation and Saffman force due to shear effect)  The force due to the added mass effect  The force due to the effect of fluid accelerating around a static particle  The basset force due to the effect of duration of particle accelerating  The bed impact force It is generally accepted that submerged weight and drag force are the greatest forces. Many authors only examine drag force in experiments. The importance of the other forces still remains unclear. [START_REF] Van Rijn | Sediment transport, Part II: Suspended load transport[END_REF] suggested that the Magnus force could be neglected due to its low order of magnitude compared to Saffman force, while [START_REF] White | Magnus effect in saltation[END_REF] argued that the Magnus lift force was very important. [START_REF] Murphy | Bed load or suspended load[END_REF] suggested that the Basset force and Magnus force could be neglected. [START_REF] Reizes | Numerical study of continuous saltation[END_REF] thought that the lift force could be omitted. Hu and Hui (1996) stated that the forces acting on a particle vary along the saltation trajectory, e.g. the drag and lift force in the rising and descending stages were different. They also pointed out that the impact force was bigger than the other forces.

b. Kinematic characteristics of saltation trajectories

A typical measured saltation trajectory is shown in 1 6 2 H Figure 2-9. Saltation is often described as having the following characteristics: a maximum saltation height h s and saltation length L s , average particle velocity V, lift angle and impact angle, and saltation step duration in time. Some previous results for saltation characteristics are summarized in Table 2.10. In H Table 2-9, h s and L s are very different from each other, perhaps as a result of differing experimental conditions, but they were both found to be similarly dependent on average particle velocity V p [START_REF] Lajeunesse | Bed load transport in turbulent flow at the grain scale: experiments and modeling[END_REF]:

  c p bu u a V * *   (2.38)
Where a and b are positive coefficients related to the effective friction coefficient and the effective fluid velocity at the height of the particles. [START_REF] Lajeunesse | Bed load transport in turbulent flow at the grain scale: experiments and modeling[END_REF] also developed probability density functions (refered to as PDFs hereafter) for the transverse and longitudinal velocity components of particle saltation. They found the most probable flight duration time formula that fitted the experimental data. Hu and Hui (1996) reported the measured lift off angle varies from 10 to 40 degrees, and the impact angle varies from 5 to 12 degrees, and they pointed out that saltation parameters vary with flow intensity and specific particle conditions. [START_REF] Niño | Gravel saltation-experiments[END_REF] also reported the lift off angle varies between 0 -60 and the impact angle is in the range of 5 -30. They found that the mean value of lift off and impact angles decreases with the increase of τ * .

In terms of the saltation process, initially, the particle on the bed begins to move when a threshold condition (often the flow intensity, or turbulent burst events) is met. The mode of particle transport (rolling, sliding and saltation) depends on flow intensity and specific particle characteristics. Hu and Hui (1996) illustrated that the proportion of rolling, sliding and saltation depended upon Shields parameter * . The experimental results of [START_REF] Lajeunesse | Bed load transport in turbulent flow at the grain scale: experiments and modeling[END_REF] and Hu and Hui (1996) indicated that saltation is the dominate mode of bed load transport. Successive saltation processes have been observed in experimental investigations. In relation to the initial velocity of saltation, [START_REF] Francis | Experiments on the motion of solitary particles along the bed of a water-stream[END_REF] suggested that tangential and normal velocity components are approximately equal to 2u * . [START_REF] White | Magnus effect in saltation[END_REF] stated that the value for initial saltation velocity is between u * and 2.5u * . Van Rijn (1984a) gave a value of saltation velocity as 2u * in his analysis. Hu and Hui (1996) developed formulas for the initial velocity of saltation based on the shear velocity and Shields parameter. The formulas are expressed as tangential and normal component velocities for smooth bed and rough bed configurations respectively. Some authors favour the concept of collision and rebound, whereas the others have put forward the idea that a particle does not actually rebound after collision but instead reestablishes saltation in an unsteady rolling motion. Niño and Garcia (1994a) maintained that the occurrence of modes of collision depends mainly on the local configuration of bed particles at the point of collision. Niño and Garcia (1994a) tested the collision-rebound type process, as shown in 1 6 4 H Figure 2-10, where a saltating particle approaching the bed strikes the bed. The striking particle velocity is resolved into tangential and normal components with respect to the collision surface U T | in and U N | in . it is assumed that these components are reduced after the collision:

in T out T fU U  (2.39)
and resuspension under unsteady conditions in urban stormwater detention basin / 2013 62

in N out N eU U   (2.40)
Where e and f are restitution and friction coefficients respectively.

Figure 2-10 Definition diagram for collision-rebound with the bed

The calculated value of the coefficient f appears to be almost independent of flow intensity and dimensionless particle size, with a constant value of between 0.73 and 0.89 (Niño and Garcia, 1998). However, the coefficient e appears to be linearly related to τ * , and can be described as (Niño and Garcia, 1994a

            p s d L 69 . 0 * 86 . 0 78 . 1             p s d h (rough bed) 82 . 0 * 05 . 1 67 . 3             p s d h (smooth bed)   c p u u V * * 44 . 0 9 . 11   0.07-1.67 0.001- 0.014

58-1018

15-1315

21-60

Lajeunesse et al.

(

)   d 2 70 * * g V V u u d L p s s c s             s c c s c p V V a u u a V V V 03 . 0 11 . 0 , 2 . 0 4 . 4 * *        2010
0.006-0.24 0.0017-0.12 156.9-1646 12-510 1.5-10

Note that the range of Shields parameter * , bed slope S L , setting Reynolds number R es , particle Reynolds number R ep and ration of water depth and particle size h/d explored in these experiments are also indicated in the table.

Modelling of experimental small scale stormwater basins

Empirical model of detention basins

Since detention basins can trap sediment through the settling of particulate pollutants, RE has become the most important parameter for evaluating the effectiveness of a detention basin. RE is thus one of the most significant criteria in the design and retrofit of stormwater detention basins. Removal efficiency is the property of a basin or reservoir. The basin's RE depends on the characteristics of the entering sediment and the retention time in the basin, which is controlled by the basin's geometry and flow characteristics [START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF][START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF][START_REF] Akan | Design aid for water quality detention basins[END_REF].

In order to reduce pollutants in stormwater runoff as much as possible so as to protect the receiving water body, efforts have been made to improve the RE of basins through observation, experimentation and modelling. In the past, two types of models were developed to predict RE: empirical models for predicting average RE based on a mid to long term observations and theoretical models for predicting the RE of an individual storm event for small ponds [START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF]. [START_REF] Heinemann | Reservoir trap efficiency. Erosion and sediment yield: some methods of measurement and modelling[END_REF] gave an overview of the many empirical models that could be used to predict RE. Amongst them, the models proposed by Brune (1953) and [START_REF] Churchill | Discussion of Analyses and use of reservoir sedimentation data by Gottschalk L.C[END_REF] were two of the most widely used. [START_REF] Brown | Discussion of Sedimentation in reservoirs[END_REF] linked empirical data on RE to reservoir characteristics and developed a curve relating RE to a capacity-watershed area ratio C/W (C/W: reservoir storage capacity/catchments area) based on the data from 15 reservoirs. Brune (1953) examined the model based on capacitywatershed area ratio (C/W) and found that of the predicted RE for the same C/W could be of completely different values if their catchments produced different runoff volumes due to the other hydrological characteristics. To overcome this problem, Brune (1953) used a capacityannual inflow ratio C/I (C/I: reservoir storage capacity/ annual inflow rate) to predict RE. [START_REF] Churchill | Discussion of Analyses and use of reservoir sedimentation data by Gottschalk L.C[END_REF] proposed that the amounts of sediment passing through the reservoir could be related to a sedimentation index (SI: period of retention divided by mean velocity through the reservoir). This model provided more detail on the hydraulic behaviour of a reservoir and could be more suitable for predicting RE. It was able to give more accurate RE values when compared to Brune's model, but it is difficult to obtain the input data for calculating the sedimentation index [START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF]. The empirical models were developed based on large ponds and they seem to be less applicable to small ponds and are not able to make predictions for event-based RE. To overcome these limitations, different theoretical models have been developed based on sedimentation principles. An overview of the theoretical RE models was provided by Haan et al. (199ζ). ωamp's model, ϊEPτSITS, CSTRS, BASIN, STEP and SWMM are six of the theoretical models for predicting RE. [START_REF] Camp | Sedimentation and the design of settling tanks[END_REF] studied sedimentation in an ideal rectangular continuous flow basin (shown in 1 6 5 H .This model assumes a quiescent, steady flow, complete mixing of the water and sediment, and no re-suspension. When sediment is flowing into the tank, discrete particles settle with a settling velocity of v s , which is dependent on particle size. For an ideal pond one could also define a critical settling velocity (v c ) that will allow particles (for which v s equals v c ) to settle in the pond. This critical settling velocity depends on the water depth (h) and the time that the inflow needs to flow through the pond (T):

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 65

A Q T h v c   (2.42)
Where A is the surface area of the basin, and Q is the inflow or outflow discharge.

The critical settling velocity is equal to the overflow rate of the basin. Given in an ideal rectangular basin with a discrete particle size distribution, the RE can be calculated as follows:

              n i i c si c X v v X RE 1 1 100 (2.43)
Where X c equals the fraction of particles with a settling velocity less than the critical settling velocity and ∆X i equals the fraction of particles with a settling velocity of v si .

Chen (1975) modified [START_REF] Camp | Sedimentation and the design of settling tanks[END_REF] model to take turbulent flow into account:

                 c s v v RE exp 1 100 (2.44)
Chen ( 1975) also compared his model with Brune and ωhurchill's models. He concluded that these empirical models overpredict RE for fine sediment but underpredict it for coarse sediment. It could, therefore, be misleading if one uses the empirical models for specific cases without the original data. The DEPOSITS model (Ward et al., 1977 cited in Verstraeten and[START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF] uses plugflow approximation for pollutant routing. The CSTRS model [START_REF] Wilson | A sediment detention pond model using CSTRS mixing theory[END_REF] used simple reactor theory concepts. The BASIN model [START_REF] Wilson | Modeling sediment detention ponds using reactor theory and advection-Diffusion concepts[END_REF] combines the reactor theory concepts with advection-diffusion processes. In both the CSTRS and BASIN models, a pond is divided into a series of chambers of equal volume [START_REF] Akan | Design aid for water quality detention basins[END_REF]. Although the BASIN model is more sophisticated, [START_REF] Wilson | Modeling sediment detention ponds using reactor theory and advection-Diffusion concepts[END_REF] found that the two models produced similar results. The STEP model developed by [START_REF] Verstraeten | Modeling the long-term trap efficiency of small ponds[END_REF] divides a pond into a series of chambers of equal surface area. A complete mixing formulation is used within each chamber. The widely known SWMM (Huber and Dickinson, 1988) also has a component to evaluate pollutant removal efficiencies of detention basins using the plug-flow concept. Nix and Heaney (1988) used the SWMM for a continuous simulation of flow and pollutant routing in a detention basin. Loganathan et al. (1994) used the simple physical-based equations together with probabilistic concepts to study the longterm efficiency of detention basins. Loganathan et al. (1994) developed a model to estimate overall efficiency using a probability concept. They considered pollutant removal to be dependent on settling time, and assumed retention time to be a measure of settling time. They provided a close-form, explicit equation for expected detention time, which is an effective parameter in assessing pollutant settling efficiency within a detention pond. However, [START_REF] Guo | Hydraulic and water quality performance of urban storm water detention basin before and after outlet modification[END_REF] plotted RE against the detention time for TSS and found that the RE did not correlate to detention time. [START_REF] Akan | Design aid for water quality detention basins[END_REF] developed a model for dry detention basins based on the hydrologic storage equation and a concept of complete pollutant mixing in order to provide research findings in a format that could be of benefit to engineering in practice.

Takamatsu et al ( 2010) developed a conceptual model for simulating the particle RE and outflow rate for rectangular stormwater detention basins based on ideal horizontal flow reactor theory.

These theoretical models or empirical models, however,are all limited because they are based either on plug flow or on complete mixing, both of which seldom occur in reality, and only some aspects of sediment transport processes were considered in each model [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]. [START_REF] Verstraeten | Modeling the long-term trap efficiency of small ponds[END_REF] modeled the long-term sediment RE of small pond with the empirical model STEP, DEPOSITS and CSTRS. It was found that these models were ineffective for predicting long-term efficiency, with the exception of the STEP model in small ponds. These models treated the basin like a black box, so they were unable to take into account key basin features such as its geometry, inflow and outlet patterns, flow patterns, etc.

Experimental investigations in small scale basins

Field measurement and observation may be the best and most direct way to obtain data and knowledge about detention basins, for example, [START_REF] Leclaire | Etude du fonctionnement d'un bassin de pollution en tête d'une station d'épuration, propositions de gestion[END_REF], [START_REF] Letondu | Suivi du bassin de dépollution des rejets urbains par temps de pluie de la commune de Sargé-Les-Le-Mans. Rapport de stage pour la Communauté Urbaine du Mans[END_REF], [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF], etc. As discussed in the preceeding section, these investigations in the field have led to the creation of empirical models and to retrofitting. But investigations based on field sites have their limitations [START_REF] Adamsson | Measurement and three dimensional simulation of flow in a rectangular detention tank[END_REF]:

 The research results are specific to existing detention basins  The high cost and difficulty in using them for measuring performance. It is also not possible to carry them out prior to basin creation;

 Real flow conditions during the storm events are unpredicted and uncontrollable, which implies that it is difficult to influence flow conditions.

For this reason, a number of researchers have studied basin hydraulics in the laboratory using scale models. Compared to field measurements, the scale models in laboratories have certain advantages for researchers: i) Low construction costs; ii) Easier to control and adjust; iii) More convenient for taking measurements for some specific purpose, such as PIV (particle image velocimetry) for field velocity measurement.

The work undertaken by Mangelson and Watters in the 1970s at the Utah Water Research Laboratory was one of the earliest and most extensive research projects on basin hydraulics [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]. Aimed at improving treatment effectiveness, the investigations were carried out on various factors such as the layout of basins, baffle installation, length to width ratio and the positioning of inlets and outlets. They found that the treatment effectiveness was greatly affected by these hydraulic characteristics [START_REF] Mangelson | Treatment efficiency of waste stabilization ponds[END_REF][START_REF] Watters | The Hydraulics of Waste Stabilization Ponds[END_REF]. [START_REF] Kadlec | Overland flow in wetlands: vegetation resistance[END_REF] and [START_REF] Moshiri | Constructed wetlands for water quality improvement[END_REF] investigated the influence of vegetation on hydraulic performance. [START_REF] Kadlec | Treatment Wetlands[END_REF] and [START_REF] Shaw | Flow pattern characterization in an urban stormwater detention pond and implications for water quality[END_REF] reported on the influence of wind on hydraulic performance. The influence of temperature has also been studied (Marecos de Monte and Mara 1987). [START_REF] Saul | Sediment deposition in storage tanks[END_REF] developed a laboratory computer-controlled monitoring system for the purpose of visualizing flow and making a comparative assessment of sediment deposition and removal performance for different geometric configurations of storage tanks. It was found that flow patterns governed sediment settlement, and reentrainment. It has been suggested that the length to width ratio, the longitudinal and benching gradients and the dry weather flow channel are the most significant geometrical properties for sedimentation. [START_REF] Stovin | Sedimentation in storage tank structures[END_REF] described a series of laboratory experiments in which the sedimentation efficiency of a scale model storage chamber was measured. The scale model comprised of a chamber that was 2m long, 0.972 m wide and 0.45 m deep. The base of the chamber was horizontal and the inlet (pipe diameter = 0.19 m) and outlet (pipe diameter=0.15 m) were positioned centrally along the chamber width with the invert in each positioned level with the chamber base. The sediment used was 150 m crushed olive stone with the D 50 =47 m. It was found that the velocity distribution in the storage tank was the primary factor in sedimentation and it was possible to predict the distribution of deposited sediment from knowledge of velocity distribution in the tank and the values of the critical bed shear stress (0.03~0.04 Pa). It was also concluded that in order to provide a realistic assessment of the sediment retention performance of a storage tank, it is essential to carry out the tests with time as a variable and using time series flow conditions, together with inflow suspended sediment concentrations representative of full scale conditions. [START_REF] Stovin | Efficiency prediction for storage chambers using computational fluid dynamics[END_REF] established a relationship between the inlet velocity and sedimentation efficiency for this scale model tank. [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF] tested different parameters for sediment transport in a scale model tank: the length to breadth ratio (L/B) the benching gradient (Sb), the longitudinal gradient (Sb), the dry weather flow channel (D DWF ) and also the level of surcharge (H/D). Both techniques suggested that the length to breadth ratio was the most important geometric parameter, although different conclusions were reached depending on the predictive technique employed. However, the mean inlet velocity was found to have a significant impact in both cases. Regression relationships were derived from the measurements. [START_REF] Garde | Design of settling basins[END_REF] carried out a series of experiments in a 16 m long, 0.75 m wide and 0.5 m deep rectangular flume that could be adjusted to lengths of 10~15 m. A 0.30 m wide channel was constructed in the flume. A tailgate enabled the depth of flow in the flume to be adjusted. Two kinds of sand were used for experiments: 0.082 mm and 0.106 mm. 162 experiments were conducted with different inflow rates, sand sizes, concentration and flume length. The RE was found to be greatly influenced by the length to water depth ratio and the settling velocity to shear velocity ratio. Saul et al. (1992) investigated sedimentation in a circular basin. The results were used to develop a simple theoretical model of settling. [START_REF] Kowalski | Investigations into and optimization of the performance of sewage detention tanks during storm rainfall events[END_REF] carried out sediment transport experiments in a long cylindrical basin (length 9.3 m, diameter 0.441 m) with one input pipe (0.15 m) and two outputs (a circular overflow weir of 0.15 m and a throttle pipe of 0.05 m diameter). Based on the experimental results, a simple formula was proposed for predicting cleaning efficiency in CSDTs. [START_REF] Frey | Hydrodynamics fields and solid particles transport in a settling tank[END_REF] performed sediment transport experiments in a settling tank consisting of a sloping backward facing step and an outlet weir. Experiments were carried out with different sand samples, different discharges, length, depth, and slope. The experiment results were used to access the RE and to validate simulation results. [START_REF] Luyckx | Comparison between the separating efficiency of an improved high-side weir overflow and a hydrodynamic Storm King (TM) separator[END_REF] conducted efficiency experiments in overflow chambers with 20 different geometries. The length of the plenum, discharge and storage were adjustable. Four kinds of model particles were used for this test: three sizes of bakelite particles (0.4-0.5mm, 0.5-0.63mm, 0.63-2mm) and one size of nylon particle (2mm). A formula for efficiency was established based on the experiment results. By using sediment with different grain sizes and densities, efficiency curves were found for a high side weir overflow. The efficiency for a certain sediment fractions was found to be determined by its settling velocity only. [START_REF] Kantoush | Experimental study of suspended sediment transport and deposition in a rectangular shallow reservoir[END_REF]Kantoush et al. ( , 2008aKantoush et al. ( , 2008bKantoush et al. ( , 2008c[START_REF] Kantoush | geometry effect on Flow and sediment deposition patterns in shallow basins[END_REF] and [START_REF] Dewals | Experimental and numerical analysis of flow instabilities in rectangular shallow basins[END_REF] conducted a series of experiments on sediment transport and deposition in a rectangular shallow basin, whose inner dimensions were 6.0 m long and 4.0 m in wide, with rectangular inlet and outlet channels, 0.25 m wide and 1.0 m long, and with a flap gate, 0.25 m wide and 0.30 m high, at the end of the outlet. To model suspended currents, crushed walnut shells with a median grain size weight of D 50 =η0 m and density=1500kg/m 3 were used. The water depth, inflow and outflow rate, concentration and flow velocity field were measured during the experiment. Different layouts within the shallow basin were tested. It was found that flow patterns are sensitive to boundary conditions and initial conditions. The basin's geometry influences the behaviour of large turbulence structures, and flow is sensitive to the geometric shape. Although the basin was symmetric, the flow pattern was asymmetric under certain conditions. This has also been observed by other authors [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF]Saul, 1994, 1996;[START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], Dufresne et al. (2009) carried out a series of sediment transport experiments in a rectangular pilot basin, 1.80 m long, 0.76 m wide, and 0.40 m deep, limited by an overflow weir. It was equipped with an inlet (diameter = 0.08 m) and outlet pipe (diameter = 0.08 m). Non-uniform size polystyrol particles, from 3η0 m to 1ζ00 m, with a density of 1030 kg/m 3 were used in the model as sediment. Two other kinds of particles of 1η00 m with density of 1060 Kg/m 3 and 2η00 m with the density of 1080 kg/m 3 were also used. 55 tests were carried out under various configurations: variants of inflow rate (2.0-5.0L/s), variants of outlet configuration (pipe or overflow weir), different particle types, without or with obstacles (vertical baffle or columns). It was found that the flow pattern changed with water depth. With a water depth lower than 15cm, the flow was quasi-steady and asymmetric with a single large horizontal recirculation pattern; for a water depth higher than 30 cm the flow pattern was also quasi-steady and resulted in two horizontal symmetrical recirculation patterns. For a water depth of between 15cm and 30cm, the flow patterns were unsteady with oscillation although the inflow rate was constant. The removal efficiencies were also measured. [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] performed sediment transport tests in a rectangular stormwater tank (L/W/H=3125/800/200mm) to evaluate the unsteady flow influence on sedimentation. The tank was equipped with a pipe (diameter =100 mm) as an inlet and overflow weir (discharge coefficient = 0.62) located 200 mm from the bottom of the tank. Non-uniform sized particles (300 m ~700 m, density =1020kg/m 3) were used as sediment in the model. 10 tests were carried out with a constant inflow rate. It was found that the flow patterns within the tank were highly unsteady and asymmetrical even though the inflow was constant in a fully symmetrical tank. The tracer studies of the particles showed that unsteady effects were evident due to flow patterns.

It is easier to control flow conditions in a scale model in a laboratory, but results suffer from scale effects because most of the scaled-down models cannot completely satisfy all mechanical similarities, which include geometric, kinematic and dynamic similarities. For example, ensuring similarity of the Froude number in scale models may preclude the possibility of ensuring similarity for the Reynolds number. Consequently, laboratory models may over-emphasize viscous effects [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]. Basins' real geometries, the variability of hydrodynamic features, and the heterogeneity of sediment characteristics are much more complicated than those that scale models are able to replicate. Therefore the results obtained from scale models in laboratory conditions remain difficult to transpose to a real system, not only because of the effects of scale, but also due to the much more complex features in real conditions [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF].

Numerical modelling of flow and sediment transport in detention basins

More recently, due to the limitation of field observations and the development of laboratory scale models, the potential application of Computational Fluid Dynamics (CFD) technology in storm basins has been identified as an alternative way of studying detention basins. [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF] summarizes the features of CFD that may be of benefit to the study of detention basins:

 CFD modelling makes it possible to numerically solve flow, mass and energy balances in complicated flow geometries. The results show specific flow or heat transfer patterns that are hard to obtain experimentally or with conventional modelling methods.  CFD offers an alternative way to study and evaluate the performance of existing detention ponds based upon their hydrodynamic features.  CFD is a powerful tool to help in the design of new pond systems. Unlike traditional design methods, which do not address the hydrodynamic features or problems, the CFD tool can predict flow patterns and short-circuiting problems before the pond is built, and can also predict the effects of measures such as baffles or inlet/outlet reposition in advance to improve performance, thus greatly aiding engineers during the design process.

CFD technology provides a way of taking more detailed flow and sediment characteristics into account. These features of CFD make it a very promising tool for the evaluation of existing basins and in the conception of new ones [START_REF] Wood | Two dimensional computational fluid dynamic models for waste stabilisation ponds[END_REF]. [START_REF] Jarman | Computational fluid dynamics as a tool for urban drainage system analysis: A review of application and best practice[END_REF] presented a review of CFD studies carried out on urban drainage system analysis. They concluded that CFD can be applied to gain insights into most fluid processes and associated phenomena and that they have the potential to provide values for the analysis of urban drainage systems, such as flow field performance, particle behaviours, water free surface and residence time distribution, etc. Once validated with measured data, these models can be used as tools to aid management and design processes.

Modelling the hydrodynamic behaviour of detention basins

Vertical integrated 2D and 3D modelling techniques have been used to analyse hydraulic characteristics of basins. Wood et al. (1995) used a CFD model to qualitatively investigate the hydrodynamics of four pond systems. [START_REF] Pettersson | FEM-modeling of open stormwater detention ponds[END_REF][START_REF] Pettersson | Modelling of flow pattern and particle removal in an open stormwater detention pond[END_REF] simulated flow patterns in an open stormwater detention basin with FIDAP, commercial CFD software which is limited to 2D and steady flow in a laminar flow regime. [START_REF] Walker | Modeling residence time in stormwater ponds[END_REF] developed the depth-average f low equations model HYDRA to evaluate the characteristics of incoming flow for different configurations of a stormwater detention basin. [START_REF] Persson | Hydraulics efficiency of constructed wetlands and ponds[END_REF] and [START_REF] Persson | The hydraulic performance of ponds of various layouts[END_REF] used the model Mike21 to evaluate the hydraulic performance with different basin shapes and configurations. The authors tested the hydraulic efficiency (e.g. residence time distribution, short-circuiting, effective volume, etc.) in order to simulate results with which to analyse hydraulic performance. It was found that the length to width ratio and the location of inlets and outlets have a considerable impact on hydraulic performance and a submerged baffle or manifold inlet configuration made the flow less mixed and short-circuiting was reduced. [START_REF] Vega | Application of CFD modeling to study the hydrodynamics of various anaerobic pond configurations[END_REF] used Mike21 to simulate the hydrodynamics and advection-dispersion process in a full-scale anaerobic basin with 12 different configurations including different basin shapes, baffling and inlet and outlet positions. [START_REF] Stovin | Efficiency prediction for storage chambers using computational fluid dynamics[END_REF], 1998, 2000) and [START_REF] Stovin | Field testing CFD-based predictions of storage chamber gross solids separation efficiency[END_REF] used Fluent to create 3D numerical models of the flow field and sediment transport in storage chambers in order to investigate the RE and the influence of different length to width ratios, dry channels on chambers performance. [START_REF] Stovin | Sedimentation in storage tank structures[END_REF] demonstrated that rectangular chamber efficiency varied as a function of mean inflow velocity, thus they showed that the efficiency of any particular chamber could be found with the mean inflow velocity value using a mean velocity/efficiency curve (as shown in 1 6 6 H . It was also found that chamber efficiency was directly related to the percentage of deposition coverage of the bed surface. For the deposition zones, [START_REF] Stovin | Sedimentation in storage tank structures[END_REF] found that the location of sediment depositions on the bed of a storage chamber could be predicted from the distribution of shear stress in the bed. A similar result was also found by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] found that the coverage of bed turbulent kinetic energy was lower than a threshold corresponding to the preferential sediment deposition zones. Chamber efficiency could therefore be obtained by making an estimation of the percentage of deposition coverage on the bed surface using a flow field simulation for bed shear stress lower than a certain threshold. However, this method is limited because it cannot predict efficiency greater than 60% because of the accumulation of sediment in the same locations [START_REF] Stovin | Efficiency prediction for storage chambers using computational fluid dynamics[END_REF].The method is evidently also difficult to apply to real events because storm events are generally in an unsteady state, while this method was developed based on steady state laboratory experiments. [START_REF] Kantoush | Experimental study of suspended sediment transport and deposition in a rectangular shallow reservoir[END_REF]Kantoush et al. ( , 2008aKantoush et al. ( , 2008bKantoush et al. ( , 2008c[START_REF] Kantoush | geometry effect on Flow and sediment deposition patterns in shallow basins[END_REF] Torres (2008) established 2D flow with and without sediment simulations modelling a full scale stormwater detention basin using Rubar 20 based on chosen storm events. Simulated results were validated with water depth measurements. It was found that Rubar 20 could be used to study the flow behaviour (field velocity and water depth) of basins for isolated storm events or a series of storm events. The sediment transport simulation based on a storm event s able to predict overall efficiency but does not reproduce the sediment zone within the detention basin well. A 3D model for the same basin was also established using Fluent and simulations were performed for flow and sediment transport. Both simulation results for sediment deposition zones were unable to reproduce field observations well with the "trap" bed boundary conditions under steady flow conditions.

Dufresne (2008) created 3D models for pilot basins using Fluent and reproduced asymmetric flow patterns with simulations. It was found that the experimental sediment zones correspond to simulated bed shear stress or bed turbulent kinetic energy values lower than a defined threshold. However, according to ϊusfresne's results (2008), it seems that predicting sediment deposition zones only using hydraulic simulation results is sometimes inadquate. As shown in 1 6 7 H Figure 2-13, there is no sediment deposited in the some low bed shear stress zones. This may imply that the sediment deposition zone is a process which deals with the interaction between flow and sediment, and that bed shear stress highlighted in the hydraulic simulation just demonstrated a deposited opportunity for sediment.

Experiment Simulations Bed shear stress threshold Turbulent kinetic energy threshold Bentzen (2008a) investigated the effect of wind on retention time in a highway pond. Results showed that wind shear stress should be taken into account for the modeling retention time or flow patterns in shallow detention ponds i. [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF] carried out flow pattern sediment transport simulation with different inlet and outlet configurations in a scale basin in order to predict the position of the sediment deposition zone and efficiency. [START_REF] Stamou | Improving the hydraulic efficiency of water process tanks using CFD models[END_REF] used CFD models to evaluate the guiding wall effects on hydraulic efficiency of main tanks in water networks in Greater Athens. It was found that the added guiding wall created flow fields in the tanks with significant volumes of plug flow and reduced short circuiting, creating a smaller recirculation region and thus less mixing. Schimitt et al. (2002) and Stovin et al. (2002) carried out dynamic simulation of storage chambers. These investigations indicated that it is necessary to take the characteristically time-dependent nature of inflow and outflow into account.

Mesh sensitivity

Predictions made in the flow domain are sensitive to mesh density and mesh quality if one uses mesh-based methods (e.g. finite volume method -FVM, finite element method -FEM, and finite difference method -FDM). Meshing plays an important role in CFD techniques. It has a significant impact on solution accuracy, convergence features and computational time requirements [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF][START_REF] Knupp | Remarks on Mesh Quality[END_REF].

There are two kinds of basic mesh element types: structured and unstructured mesh. Generally, a structured mesh has more effective computational efficiency because of the lower quantity of storage memory required, but an unstructured mesh has more flexible features when recreating complex geometry conditions. The choice of an unstructured, structured or hybrid mesh depends on the individual conditions of each case.

No matter what kind of mesh type is chosen, mesh density and mesh quality are the key basic considerations to take into account. There are no finite rules governing ideal mesh resolution.

Usually several meshes of different sizes are tested to see at which point the computational results become independent of mesh resolution [START_REF] Jarman | Computational fluid dynamics as a tool for urban drainage system analysis: A review of application and best practice[END_REF]. The simulators always try to find the small scale mesh possible that corresponds to the level of accuracy required in order to reduce computational time.

The appropriate mesh resolution is also dependent on the specific conditions and flow features the user requires, for example, solution accuracy. Sometimes it is also affected by the numerical solution method chosen, for instance, the treatment of the boundary layer or the discretization schemes. It should be noted that a finer mesh resolution does not necessarily deliver better results. This is due to the propagation and accumulation of numerical solution errors within the mesh. The more mesh cells there are, the larger the number of errors that may be accumulated and propagated in the computational domain.

Special attention should also be paid to the wall bound mesh for dealing with wall-bound turbulent flow. [START_REF] Salim | Wall y+ strategy for dealing with wall-bounded turbulent flows[END_REF] concluded that the wall y + strategy is an accepted critia for wall boundary meshing.

Ta and Brignal (1998) modeled a full scale storage reservoir in three dimensions using approximately 7000 hexahedral cells, and stated that a finer mesh did not provide additional information in this case. Conversely, in the analysis by [START_REF] Lau | The prediction of solute transport in surcharged manholes using CFD[END_REF], which focussed on a manhole several orders of magnitude smaller than the reservoir, the mesh sensitivity limit was found to be between 55 000 and 130 000 cells. It seems that the mesh density depends upon accuracy required. [START_REF] Momplot | Effects of computational meshes on hydrodynamics of an open channel junctions flow using CFD technique[END_REF] tested 11 different density meshes for modelling the flow in an open channel junction. By validating the model using measured data, it was found that a median refined mesh was best able to simulate hydrodynamics across a subcritical open channel junction. These results confirm that mesh resolution is largely dependent on the phenomena the modeler wishes to resolve.

In addition to mesh density, it is important to consider mesh quality when aiming to create an accurate simulation on a computer. Good quality mesh helps modelers to obtain better solutions and to speed up the computation. Low quality mesh may lead to convergence issues.

The criteria used to evaluate the mesh quality include smoothness, aspect ratio, and skewness. For example, [START_REF] Ip | The role of mesh smoothness in the convergence of higher-order methods[END_REF] investigated the influence of smoothness on CFD solutions. He found that smoother meshes are better than rough meshes. Errors associated with rough meshes were far greater than expected. Furthermore, suitable mesh resolution also depends on the hydraulic conditions and the flow features the user is aiming to resolve. It is also affected by numerical solution parameters, such as discretization schemes. For instance, [START_REF] Ip | The role of mesh smoothness in the convergence of higher-order methods[END_REF] found that higher order methods are more susceptible to mesh smoothness.

Turbulence models

In practice, many, if not most, significant engineering projects involve turbulent flow, so the turbulent flow regime is not merely of theoretical interest. Fluid engineers need access to viable tools capable of representing the effects of turbulence (Versteeg and Malalasakra, 2007). The most accurate approach to turbulence simulation aims to solve the Navier-Stokes equations directly. It is called direct numerical simulation (DNS) and is done without the use of any averaging or approximation other than numerical discretization for which errors can be estimated and controlled [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]. DNS is not often used due to its very high computational cost. In engineering practice and normal academic research, the Reynolds Averaged Navier-Stokes (RANS) equations are often used to characterize turbulence features.

The RANS system is often closed using a 'turbulence model'. Among possible turbulence models, the k -ε model and its variant models, such as the Re normalized group (RNG) k -ε model, are often used in urban drainage system for hydraulics modelling [START_REF] Jarman | Computational fluid dynamics as a tool for urban drainage system analysis: A review of application and best practice[END_REF]. The standard k -ε model is an isotropic model and is widely used and has been validated in practice by engineering [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. The Reynolds Stress Model (RSM) is an anisotropic model and is considered by many authors to be better at representing turbulence when compared to these two other equation turbulence models, but it requires much higher computational time and is less stable. Within a review of CFD technique applications and best practice by [START_REF] Jarman | Computational fluid dynamics as a tool for urban drainage system analysis: A review of application and best practice[END_REF], of the twenty-two selected studies on urban drainage systems, six used the RSM model and sixteen used the standard k -ε or RNG k -ε variant turbulence model. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] employed the standard k-turbulent model for flow field and sediment transport modelling in a stormwater detention basin. The standard k -ε model enabled the vertical recirculation in a circular basin [START_REF] Quarini | Hydrodynamic modelling of sedimentation tanks[END_REF][START_REF] Jayanti | Computational study of particle-eddy interaction in sedimentation tanks[END_REF] and horizontal recirculation in rectangular tanks [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF]Saul, 1994, 1996;[START_REF] Adamsson | Measurement and three dimensional simulation of flow in a rectangular detention tank[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]Dufresne et al., 2009) to be reproduced. Dufresne argues that the standard k -ε model was sufficiently good to reproduce the flow in a detention basin. [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] used the RNG k -ε model to simulate flow field and tracer transport rather than a standard k -ε model because the RNG k -ε model enables the user to make a number of refinements. The results showed that the RNG k -ε model reproduced the flow and observed unsteady features well. [START_REF] Hunze | Investigation of clarification tanks using 3-dimensional simulation studiespart 1 circular clarification tanks[END_REF] pointed out that the RNG k -ε model is more suitable than the standard k -ε model for the simulation of flow regimes with a low Reynolds number. Stovin et al. (2002) studied different turbulence models with the aim of exploring the extent to which turbulence models may affect the predicted flow field for sewerage structures. It was found that an RSM with quadratic pressure strain was better than the k -ε and its variant models when results were compared with laboratory observations. Hence, while there is no doubt that Reynolds stress models have better potential for representing turbulent flow phenomena more accurately than the two equation turbulent models [START_REF] Hadzic | Second-moment closure modeling of transitional and unsteady turbulent flow[END_REF], in some cases the difference is so small as to be insignificant [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]. It is not yet entirely clear which model is best for which kind of flow, partly due to the fact that in many of the attempts made to answer this question, the numerical errors have been too great to allow decisive conclusions to be drawn [START_REF] Bradshaw | Collaborative testing of turbulence models[END_REF].

Sediment transport modelling

Sediment transport phenomena are encountered in many processes in industrial operations and engineering practice. Numerous examples can be found in coast, estuary, river, agricultural, reservoir and environment engineering, etc. Due to the inherent complexity of sediment transport flow, from a physical as well a numerical point of view, "general purpose" computational fluid dynamic (CFD) codes are non-existent. Sediment transport can be of many types (gas-solid, gas-liquid, liquid-liquid, etc.). In this thesis, the focus is on sediment transport in storm water discharge in a detention basin. It is therefore relevant to discuss, the different methods that can be used to model sediment transport in water here. In addition to flow fields, it can often be necessary to model additional physical characteristics at the same time. Three kinds of methods are generally used to model material transport in water flow: the species transport (scalar transport or single phase model) method, the Euler-Euler method (multiphase flow modelling) and the Euler-Lagrange method (discrete phase model). Some authors also distinguish two further categories: concentration tracking and particle tracking [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF].

Species transport model approach

The species transport method is widely applied when examining river, estuary, reservoir and coastal problems [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF][START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF], and discussions on sediment transport often refer to the species transport method. Sediment transport modelling started in the 1950s and has been extensively developed and widely applied in practice in engineering since the 1970s [START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF]. Sediment transport modelling is usually represented by spatial formulations varying from 1D and 2D depth average models to full 3D sediment flow models. This type of modelling can also be classified according to time dependent characteristics (steady or unsteady) or sediment transport characteristics (deposition & erosion, bed load & suspended load, cohesive & noncohesive, etc.). [START_REF] Papanicolaou | Sediment transport modeling review-current and future developments[END_REF] revised the current state of the art versions and future developments in sediment transport modelling. The common procedure is to split the model into a flow model and a sediment transport model [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]. Sediment transport is then calculated from the results of the flow field simulation in a decoupled way (or with one way coupling), which means the flow movement influences the sediment transport model but sediment movement does not affect flow behaviours.

Most of the 1D models are formulated in a rectilinear coordinate system and solve the differential conservation equations of mass and momentum of flow (the Saint Venant equations) along with the sediment mass continuity equation [START_REF] Papanicolaou | Sediment transport modeling review-current and future developments[END_REF]. [START_REF] Han | A study on the non-equilibrium transportation of suspended load[END_REF], [START_REF] Chang | Mathematical model for erodible channels[END_REF], [START_REF] Karim | IALLUVIAL: A commuter based flow and sediment routing for alluvial streams and its application to the Missouri River[END_REF], [START_REF] Thomas | [END_REF], [START_REF] Holly | New numerical/physical framework for mobile-bed modeling, Part I: Numerical and physical principles[END_REF], Holly et al. (1990), [START_REF] Wu | One-dimensional channel network model CCHE1D 3.0-Technical manual[END_REF] used 1D models to calculate the long-term channel deposition and erosion under quasi-steady and unsteady flow conditions [START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF].

Since the early 1990s, many 2D and 3D sediment transport models [START_REF] Shimizu | Three-dimensional computation of flow and bed deformation[END_REF][START_REF] Spasojevic | 2-D bed evolution in natural watercourses-New simulation approach[END_REF][START_REF] Lafond | Comparaison de modèles de transport en suspension application à des ouvrages de stockage dépollution[END_REF][START_REF] Olsen | Two-dimensional numerical modeling of flushing processes in water reservoirs[END_REF]Cancio and Neves, 1999;[START_REF] Wu | 3D numerical modeling of flow and sediment transport in open channels[END_REF][START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF]Bentzen et al., 2008;Torres et al., 2008) have also been created to simulate channel evolution in complex situations, such as estuarine systems and detention basins, in more detail. Usually many of them assume local equilibrium when simulating bed-load transport. Recent studies on the spatial and temporal lag of bed load transport show that a non-equilibrium transport model for bed load is also needed in many cases. For example, it is required where there is strong erosion and strong deposition, and especially under unsteady flow conditions. Furthermore, the hiding and exposure phenomena that exist in non-uniform sediment transport play an important role in bed material sorting and channel bed armouring. 2D models are depth-averaged models (2D St. Venant equations or shallow water equations) that can provide spatially varied information about water depth and bed elevation within rivers, lakes, and estuaries, as well as depth-averaged velocities. The 3D models solve the Navier-Stokes equations. Both the 2D and 3D flow models solve the sediment mass balance equations. If both the suspended load and bed load are taken into account, the sediment transport is generally subdivided into suspended load and bed load models. The suspended load transport is governed by the advection-diffusion equations incorporating sink/sources terms. For 2D model, the advection-diffusion equation is as follows [START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF]:

  C C v y C h y x C h x y VhC x UhC t hC s s s                                   *    (2.

45)

Where h is water depth; U and V are depth-averaged flow velocities components in x and y directions; C is the depth-averaged suspended concentration of suspended load; C * is the depth-averaged suspended load concentration under equilibrium conditions or the suspended load transport capacity; s is diffusivity coefficient of sedimentν α is nonequilibrium adaptation coefficient of suspended load if necessary; and v s is settling velocity of sediment particles.

The mass balance equation in bed load for 2D model is [START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF]:

    0 1                  C C v y q x q t C t z p s b by b bx b b     (2.46)
Where is thickness of bed load zoneν ω b is the averaged concentration of bed load in bed load zone, z b is the bed elevationν α bx and α by are direction cosines of bed load movement, which are usually assumed to act along the direction of bed shear stress. q b is the actual transport rate of bed materialν p' is the porosity of bed material.

For 3D models, the advection-diffusion equation is as follows [START_REF] Wu | 3D numerical modeling of flow and sediment transport in open channels[END_REF]:

                       j c t j j s j j x c x c v u x t c    3 (2.47)
Where c is the local sediment concentration; v s is settling velocity of sediment particles; j3 is Kronecker delta with j=3 indicating the vertical directionν c the turbulent Schmidt number relating the turbulent diffusivity of the sediment to the eddy viscosity t . If the sediment settling effect is not considered, the term (v s j3 ) can be omitted. At a free surface, the vertical sediment flux is zero and hence the boundary condition is:

0     c v z c s c t   (2.48)
At the lower boundary of the suspended sediment layer, which is the interface with the bed load layer, the sediment net rate across the interface is introduced as a boundary condition, normally, the exchange of deposition rate D b and Erosion rate E b , and therefore the lower boundary condition is:

  * b b s b b c c v E D    (2.49)
Where c b is the local suspended load concentration near the interface of suspended load and bed load; c b* is equilibrium concentration at the interface location.

The mass balance equation in bed load for 3D models is [START_REF] Wu | 3D numerical modeling of flow and sediment transport in open channels[END_REF]:

    0 1                 b b b by b bx b b E D y q x q t c t z p    (2.50)
Where b c is the averaged concentration over the bed load layer thickness .

Species models incorporate a certain degree of simplification in order to be computationally feasible. However, simplified models run the risk of not arriving at a reliable solution, whereas increasing the model complexity can complicate problem formulation and therefore, mean incurring more input data preparation, calibration and verification costs [START_REF] Papanicolaou | Sediment transport modeling review-current and future developments[END_REF].

The species models developed to date have not been as universal as hydraulic engineers would like them to be. Species models are limited.

Most sediment entrainment is assumed to be triggered by the excess shear stress rather than by near bed turbulence characteristics. An increasing number of researches have shown that turbulent bursts (e.g. turbulent sweeps, ejections) are the primary triggering mechanisms of sediment entrainment [START_REF] Nelson | Role of near bed turbulence structure in bed load transport and bed form mechanics[END_REF][START_REF] Papanicolaou | The role of turbulence on the initiation of sediment motion[END_REF][START_REF] Papanicolaou | The role of near bed turbulence structure in the inception of particle motion[END_REF]Papanicolaou et al., 2001;[START_REF] Zanke | On the influence of turbulence on the initiation of sediment motion[END_REF][START_REF] Dey | Near-Bed Turbulence Characteristics at the Entrainment Threshold of Sediment Beds[END_REF].

Traditionally, species models have often calculated the transport rate for a single characteristic grain size, for example, the median [START_REF] Raudkivi | Loose boundary hydraulics, 4 th Ed[END_REF]. This type of model's weakness is its inability to account for the transport of sediment particles of different sizes (or densities). It is likely to underpredict or overpredict the transport rate of individual fractions when bimodal or multimodal distributions are present atop the bed surface [START_REF] Papanicolaou | Sediment transport modeling review-current and future developments[END_REF]. In fact, a sediment particle of a certain size or density can be carried at different transport rates.

In the advection-diffusion equation, the treatment of the dispersion and diffusion coefficients as functions of the inner and outer variables, respectively, namely, the shear velocity, depthaveraged velocity, width of channel and mean flow depth is limited. It has been shown that the spatially averaged inner and outer quantities may not be good approximations of the dispersion process in channel constrictions or expansions and of flow near submerged or unsubmerged obstacles [START_REF] Papanicolaou | Sediment transport modeling review-current and future developments[END_REF].

Most species transport models have been based on equilibrium assumptions which do not often represent realistic conditions. Some researchers have considered non-equilibrium conditions with a non-equilibrium adaptation coefficient, but the results really depend on the modelling of non-equilibrium terms and hence on the value of the non-equilibrium adaptation length [START_REF] Wu | 3D numerical modeling of flow and sediment transport in open channels[END_REF][START_REF] Wu | Depthaveraged two dimensional numerical modeling of unsteady flow and non-uniform sediment transport in open channels[END_REF]. For the purposes of evaluating bed load transport, most of the available 3D models use empirical expressions for bed load transport modelling. However, the details of the processes that control sediment transport are not fully understood.

Furthermore, when it comes to modelling high sediment concentrations in fluids, the species model approach does not seem appropriate because it neglects the momentum exchanges between the fluid flow and particles. The solid volume fraction and relative velocity between fluid and solid phase is not considered [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]. In terms of species models which examine deposition and erosion, [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] performed 2D modelling of flow and sediment transport using Rubar20 for a large stormwater detention basin based on several measured storm events. The results showed the abilty of species models to model the global efficiency of a system, but failed to reproduce the preferential sediment deposition zones.

Euler-Euler approach

Sediment transport is made up of two phases: a liquid phase and a solid phase. There are two different modelling approaches that both take a multiphase view and use the grid-based CFD method to simulate the solid transport phase: Euler-Euler and Euler-Lagrange. However, in more recent years, new particle-based methods (such as Smoothed Particle Hydrodynamics-SPH, or Lattice Boltzmann Method-LBM) have been developed to simulate the solid transport phase [START_REF] Krištof | Hydraulic erosion using smoothed particle hydrodynamics[END_REF][START_REF] Vetsch | Numerical Simulation of Sediment Transport with Meshfree Methods[END_REF][START_REF] Ladd | Lattice -Boltzmann simulation of particle-fluid suspensions[END_REF][START_REF] Joshi | Multiphase lattice Boltzmann method for particle suspensions[END_REF]. With the SPH method, both the liquid and solid phases were treated with a particlebased approach within the Lagrange framework, and with a multiphase method. This method may be classified as a Lagrange-Lagrange approach. As these new methods (SPH and LBM) are still being developed, they will not be discussed further here and for the purposes of this thesis, we will observe the traditional classification of the two different approaches outlined above.

In the Euler-Euler approach, both the continuous and dispersed phases are described by Eulerian models. In these models, the dispersed phase, like the continuous phase, is treated as a continuous phase with appropriate closures, hence one calculates only the average local volume fraction, velocity, etc. but not the properties of each individual dispersed particle.

Owing to the continuum description of the particulate suspension, Eulerian models require additional closure laws to describe the momentum transfer between the fluid phase and particle phase, which is described as viscous drag force, and to describe the momentum transfer between particle and particle phase, which is described as collision interaction.

For fluid-solid flow model based on the Euler-Euler approach, the interphase momentum transfer needs to be accounted for. Closure of the solid-phase momentum equation requires a description of the solid-phase stresses. Constitutive equations for the solid-phase stresses based on the kinetic theory can be used to describe the effective stresses in the solid phase resulting from particle streaming (kinetic contribution) and direct collisions (collision contribution) [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF]. This theory is basically an extension of the classical kinetic theory of gases for dense particulate flow. The closure models consist of a series of theoretical and empirical expressions, further description can be found in Lun et al.(1984) and van [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF]. the fluid/particle and particle/particle interactions as well as the turbulent stresses. [START_REF] Zhao | Numerical simulation of scour around pipelines using an Euler-Euler coupled two-phase model[END_REF] successfully used a Eulerian two-phase model, which implemented Euler-Euler coupled governing equations for flow and sediment phase, to simulate the scour around a long fixed pipeline placed just above a non-cohesive sandy bed. [START_REF] Zhang | Comparison of the Eulerian and Lagrangian methods for predicting particle transport in enclosed spaces[END_REF] used the Eulerian model to predict particle transport in an enclosed space. In comparison to experimental data, the numerical results showed that the Eulerian model is able to predict particle concentration under steady conditions.

In Eulerian models, the interactive forces between the sediment and fluid or the intergranular stress due to particle-particle collision are often simulated using single particle characteristics, such as the median size or density [START_REF] Hsu | A two -phase flow model of wave-induced sheet flow[END_REF], hence the models is less appropriate for modelling particle size distribution and variable particle density.

Euler-Lagrange approach

The Euler-Lagrange approach is another approach used to describe the two phases of flow (fluid and sediment). In the Euler-Lagrange approach, the fluid phase flow is treated as a continuum and solid phase flow is treated as individual particles. This is called the Discrete Element Method (DEM). The DEM was introduced by Cundall and Strack in 1979. Withing the framework of the DEM, all particles are tracked using the Lagrangian approach that is based on σewton's second law of motion during computation. Further details are available in the literature (e.g. [START_REF] Campbell | Rapid Granular Flow[END_REF][START_REF] Zhou | Rolling friction in the dynamic simulation of sandpile formation[END_REF]Mattutis et al., 2000;[START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF][START_REF] Bertrand | DEM-based models for the mixing of granular materials[END_REF].

When a DEM is coupled with the Eulerian model to simulate sediment transport in fluid flow, this is known as the Euler-Lagrange approach. This approach considers the interphase momentum transfer as well as particle-particle interaction. In order to describe particle collisions, two types of approach are possible: the hard-sphere approach and the soft-sphere approach. In the hard-sphere approach, collisions between particles are assumed to be binary and instantaneous. During collision, energy is stored in the elastic deformation associated with both the normal and the tangential displacements of the contact point relative to the centre of the sphere. In the soft-sphere approach, particle interactions are modeled using potential forces. The soft-sphere approach is based on the concept that when two particles collide they deform. This deformation is described by an overlap displacement, and the particles lose kinetic energy. The normal force and frictional force are composed of a spring, a dashpot, and a friction slider. The time step in hard-sphere collision dynamics is governed by successive measures of the time between collisions. In dense systems this time step may be very small, which results in a very long computational time. The time step in soft-sphere collision dynamics is governed by the stiffness of the normal and tangential forces. The Hertzian contact theory predicts such high stiffness that in practical cases this also leads to very small possible time steps in dense suspensions [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF][START_REF] Apostolou | Discrete element simulation of liquid-particle flow[END_REF]. [START_REF] Kloss | Comprehensive DEM-DPM-CFD Simulation-model synthesis, experimental validation and scalability[END_REF] and [START_REF] Mezhericher | Modeling of Particle Pneumatic Conveying Using DEM and DPM Methods[END_REF] reported that the time step used in their sediment transport modelling has an order of magnitude of 10 -6 s. Due to the huge computation time, the amount of discrete element models which can be used is, today and in the near future, limited [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF] and it is difficult to perform large scale simulation with a DEM without advanced computer power.

For overcoming the disadvantages of creating a complete DEM, a compromise method called a discrete phase model (DPM) has been devised. It can be considered to be a simplified DEM. In DPM each "particle" represents a parcel of particles rather than an individual particle as in standard DEM. Like the DEM, the DPM tracks each particle trajectory based on the σewton's second law of motion, but without taking the collision between particles into consideration. Hence, it is only suitable for dilute suspension systems with a particulate phase volume fraction of less than 10%. Interphase moment transfer can also be added using one-way coupling or two-way coupling depending on what is needed. For dilute systems, the momentum involved in moving from solid phase flow to fluid phase flow has often been neglected in research [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. DPM is able to use larger time steps than DEM because they do not take particle collision into consideration and since they track less particles, instead using the concept of parcels, which represent a number of particles. Hence DPM needs less computational time. Nevertheless, DPM are also less accurate because they do not take collisions between particles into consideration. [START_REF] Kloss | Comprehensive DEM-DPM-CFD Simulation-model synthesis, experimental validation and scalability[END_REF] coupled DEMs and DPM for two phase flow simulation depending on the solid phase concentration. Particle transport was sped up by switching from DEM to DPM in dilute regions where interparticle collision could be neglected. But for this method to be applied, the DPM must use single particle rather than a parcel of particles.

In recent years, a growing number of research has used DPM to investigate sediment transport problems, such as research on stormwater basins [START_REF] Lafond | Comparaison de modèles de transport en suspension application à des ouvrages de stockage dépollution[END_REF][START_REF] Harwood | CFD and novel technology in combined sewer overflow[END_REF]Cheebo et al.,1998;[START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF][START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF]Dufresne et al., 2009;[START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]Yan et al., 2011;[START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF], storage chambers [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF][START_REF] Stovin | Efficiency prediction for storage chambers using computational fluid dynamics[END_REF], 1998, 2000;[START_REF] Stovin | Field testing CFD-based predictions of storage chamber gross solids separation efficiency[END_REF], hydrodynamic separators for stormwater [START_REF] Pathapati | Calibration Testing and Modeling of a Hydrodynamic Separator for Urban Drainage Particulate Matter Separation and Scour[END_REF]Pathapati and Sansalone, 2009;[START_REF] Sansalone | Particle dynamics in a hydrodynamic separator subject to transient rainfall-runoff[END_REF], meandering river [START_REF] Shams | Computational modeling of flow and sediment transport and deposition in meandering rivers[END_REF] or Combined Sewer Overflow structures (Lipeme [START_REF] Kouyi | Expérimentations et modélisations tridimensionnelles de l'hydrodynamique et de la séparation particulaire dans les déversoirs d'orage[END_REF]Dufresne et al., 2009).

There has been considerable recent progress in computational modelling of particle transport, deposition, and resuspension processes in fields related to DPM. For stormwater basins, the RE and deposition zones are the most important applications. [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF]Saul (1996, 1998) applied the DPM approach to storage chambers in order to predict RE. [START_REF] Shams | Computational modeling of flow and sediment transport and deposition in meandering rivers[END_REF] performed a computational modelling analysis of flow and sediment transport and deposition in a meandering river. [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] used particle tracking with the Lagrange approach to model the sediment transport in rectangular chamber. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] and Dufresne et al. (2009) also used the DPM approach to predict the efficiency and deposition zone in a detention tank. [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF] tested the influence of different inlet and outlet positions in a tank to determine the efficiency and deposition zone. [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] used a DPM to evaluate the influence of unsteady behaviour on sediment transport and deposition in a detention basin. For this study, predictions of efficiency and deposition zones were found to be sensitive to particle properties and boundary conditions (it can be assumed that flow field simulation was satisfactory). [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF] found that efficiency was sensitive to physical properties (e.g. injection location, particle sizes and particle density) and boundary conditions in their test cases. The simulation results from a DPM showed that efficiency is more sensitive to the particle injection location and less sensitive to particle size.

It should be noted that bed boundary conditions did not distinguish between different particles, which means that the particles were the same for bed boundary interaction treatment. They used a density of 2500 kg/m 3 in simulation instead of a real density of 1500 kg/m 3 because the former was the closest fit to the laboratory data. Efficiency was shown to be insensitive to the parameter of step length. According to the simulation results, turbulent dispersion was also a factor which had an impact on the prediction of efficiency and sediment deposition zones.

Simulated efficiency was highly sensitive to boundary condition configurations [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF]. Stovin and Saul stated that the selection of boundary conditions should reflect an understanding of the physical processes. To describe the overall efficiency of the settling processes in storage tanks, [START_REF] Lafond | Comparaison de modèles de transport en suspension application à des ouvrages de stockage dépollution[END_REF] demonstrated that complex 2D/3D CFD models did not necessarily lead to significantly better results than simple models based on modified Hazen or Camp theories. This is mainly due to critical hypotheses (especially the bottom boundary condition treatment applied to particles which reach the tank bottom), which are needed for CFD models but are difficult to verify or to prove in a field site, because of their complexity [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF].

The basic boundary conditions of DPM, which are often used in urban drainage systems, are: trap, reflect and escape. Escape is often the inlet and outlet of a system. Reflect is often the vertical or side wall. Both trap and reflect are often used as the boundary conditions for the bottom of basin, representing particle behaviour when it reaches the bottom. The pure trap boundary condition for the bed often overestimates the efficiency and sediment deposition zone, while a pure reflect boundary condition often underestimates efficiency and deposition zones due to a bad reflection of particle transport processes such as dynamic saltation and erosion [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF]. [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF] used finite reflect times (e.g. 25) for each bottom cell in an attempt to reflect particle saltation. However, this assumption cannot represent real physical processes. [START_REF] Chebbo | A stochastic approach to modeling solid transport in settling tanks[END_REF] used a stochastic approach by linking the convection-diffusion equation to Fokker-Planck's equation to determine particle bed boundary condition treatment (the particle bounces on the bottom a random number of times then stops) for solid transport in a settling tank. This approach obtained a better efficiency prediction for a settling tank, and therefore offered an alternative method, but it did still not reflect the real dynamic physical transport processes. Bed boundary conditions were improved using a combination of trap and reflects with a bed shear stress threshold [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF]. The particle was trapped if local bed shear stresses were lower than the threshold and, therefore, ended its trajectory; otherwise the particle rebounded and continued its trajectory. A similar approach was developed using a bed turbulent kinetic energy threshold to model sediment transport in a pilot detention basin [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF].

Generally, a bed shear stress threshold or a bed turbulent kinetic energy threshold was measured in the laboratory or verified by comparing the flow simulation results with observed experimental sediment deposition zones. 0.03 -0.04 Pa was found to be the critical bed shear stress for deposition [START_REF] Stovin | Sedimentation in storage tank structures[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] and 0.06 Pa for erosion critical bed shear stress in a laboratory scale tank [START_REF] Stovin | Sedimentation in storage tank structures[END_REF]. However, [START_REF] Stovin | Sedimentation in storage tank structures[END_REF] stressed that deposition and erosion of critical bed shear stress depend on the properties of the sediment, and of the rough bed conditions. Further work is required to derive appropriate values for full scale detention basins. [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] used the Shields curve to calculate the critical deposition bed shear stress which depends on the particle properties used for modelling sediment transport in a detention basin. Lipeme Kouyi et al.

(2010) performed a 3D flow simulation in a full stormwater detention basin, and found that the critical bed turbulent kinetic energy was of a much lower value than that observed by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] in small scale tank in a laboratory. To better estimate the critical bed turbulent kinetic energy and to account for particle properties, [START_REF] Yan | Modélisation numérique 3D des écoulements turbulents a surface libre charges en polluants particulaires dans un bassin de retenue -décantation des eaux pluviales[END_REF] proposed a formula for calculating the threshold based on the settling velocity of particles.

It should be noted that almost all the modelling research on detention basins for predicting efficiency and deposition zones have been based on steady state conditions with one way coupling. [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] evaluated the unsteady flow influence on the particle settling processes. They performed unsteady flow modelling and saved each time step simulation result. Then they used the time step flow modelling results to performed steady state particle tracking under one way coupling. To a certain extent, this method accounts for the unsteady flow effect on sedimentation processes. In unsteady flow conditions, a particle that has been deposited at one moment may be entrained due to a change of local flow conditions in the next moment. However, dynamic erosion could not be taken into consideration when using this method because the modelling was disconnected. Thus it was a real unsteady particle tracking approach. However, it was an improvement on predictions made using only steady state modelling.

Over the past decade, progress has been with the use of DPM approaches for sediment transport modelling, but a lack of understanding of complex sedimentation processes is still an obstacle to adequate predictions of the efficiency and sediment deposition zones of stormwater detention basins. Many phenomena involved in sedimentation processes such as dynamic entrainment, aggregation, consolidation, particle collision due to dense concentration and so on still require further investigation.

Comparison of species model, Euler-Euler and Euler-Lagrange approaches

As mentioned above, the species model has its limitations in the modelling of sediment transport because of simplification and the usage of many empirical sediment transport formulas which were developed for very specific applications.

Without invoking a series of purely empirical sediment transport formulas, the two-phase models (the Euler-Euler and Euler-Lagrange approaches) were developed based on more fundamental dynamic principles. These two-phase models were expected to be more generally applicable to a range of problems. In Eulerian models, no empirical sediment transport formulas are required [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF]. Thanks to the inclusion of flow-particle and particleparticle interactions, a two-phase model is also capable of modelling dense flow, which is difficult for species models. [START_REF] Stovin | solute transport modeling for urban drainage structures[END_REF] modeled the residence time distribution in a storage chamber taking a DPM approach and using a species model. The results showed that the DPM approach was much faster (about 100 times faster) than the species model. Moreover, the DPM approach could more easily represent the particle size distribution of sediment.

The Euler-Euler and Euler-Lagrange approaches both have their own advantages and drawbacks. The Euler-Euler approach is less able to recover the characteristics of particles, such as particle size distribution and rotation of particle. However, the Euler-Euler approach has no a strict time step constraints like those found in a DEM collision model. DEM and DPM enable more physical particle properties to be taken into account, such as non-uniform sediment sizes, densities etc. The Euler-Lagrange approach is better at representing physical and chemical treatments such as aggregation formation during the transport processes (Lu et al., 2007;Apostolou and Hrgmak, 2008). [START_REF] Zhang | Comparison of the Eulerian and Lagrangian methods for predicting particle transport in enclosed spaces[END_REF] performed particle sediment transport and distribution in enclosed spaces with Eulerian and Lagrangian approaches respectively. For steady conditions, both the approaches were able to predict particle concentration distribution in an enclosed space reasonably. The Eulerian model needs less computing time than the Lagrangian approach, because the latter needs to track large number of particles to ensure statistical stability. Under unsteady conditions, the Eulerian model requires small time steps and needs more iteration per step to ensure the convergence. It turned out that the Eulerian model required more computational time and the particle tracking (DPM) approach was actually more computationally efficient. The particle tracking process did not significantly increase the computing time compared with that under steady state conditions. It was suggested that the DPM approach was more capable of modelling particle transport under unsteady conditions.

Multiphase flow has been modeled using a Eulerian-Eulerian approach or a Eulerian-Lagrangian approach [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF] depending on the extent of coupling between phases, with the delimiter that a Eulerian-Eulerian approach is used for flow with particulate volume fractions (PVF) greater than 10% [START_REF] Sansalone | Particle dynamics in a hydrodynamic separator subject to transient rainfall-runoff[END_REF]. [START_REF] Elghobashi | Particle laden turbulent flow: Direct simulation and closure models[END_REF] proposed a regime map for appropriating the degree of interphase coupling, by analyzing length and time scales.

Conclusions of Chapter 2

The general performance of detention basins has been examined in order to give an overview of the background for this research. This research is focused on sediment transport in a detention basin and an intial review of the scientific context of the study highlighted the importance and necessity of the removal of particulate pollutants during wet weather conditions in detention basins in order to protect the receiving water bodies, as the majority of pollutants attach themselves to solid particles in stormwater runoff. Secondly, mechanisms related to sediment transport were introduced. Traditional sediment transport mechanisms were based on the concentration concept and relied on many empirical expressions. It has proved difficult to improve understanding of sedimentation phenomena further. Some researchers have used advanced equipment to examine this subject on a particle scale with the aim of further improving understanding of sediment transport.

Storm water detention basins are widely used in urban storm water management for both storm discharges quantity and quality control. However, the hydraulic and RE performance of basins are heterogeneous for historical reasons, the complexity of flow conditions and limited understanding of sediment transport phenomena.

During the development of detention basins, different methods (field observation and measurements, scaled models experiments and CFD modelling) have been performed to investigate potential improvements in hydraulic performance and removal efficiency. Each method has its own advantages and disadvantages, however, CFD modelling seems to be used more and more for research and engineering applications thanks to its low cost and the higher level of information obtained. According to previous work on CFD modelling of fluid flow and sediment transport, the Euler-Lagrange approach seems to provide more information and have a higher potential for improving the understanding of sediment transport.

Progress has been made in the field of sediment transport modelling, but the lack of understanding of complex sedimentation processes is still an obstacle to accurately predicting the efficiency and sediment deposition zone of stormwater detention basins. Many phenomena involved in sedimentation processes such as dynamic entrainment, aggregation, consolidation, particle collision due to dense concentration and so on are not clearly defined.

In fact, the DPM method is not a new technique for modelling sedimentation phenomena in stormwater basins. As discussed above, the main problem is that no satisfactory bed boundary conditions have been established that clearly represent complex sedimentation phenomena such as dynamic settling and erosion. Furthermore, most research on efficiency and the prediction of sediment deposition zones has been based on laboratory scale models and it is difficult to apply this research to real full scale systems due to the effect of scale and the more complex conditions in real systems (geometry, surface conditions, variable inflow and outflow conditions, etc.). However, some research on full scale detention basins is available in scientific studies. In order to improve the design and management of full scale detention basins, more appropriate bed boundary conditions need to be developed and dynamic bed boundary treatment for unsteady particle tracking should be considered as a method for representing the dynamic deposition and erosion processes in real conditions.

Chapter 3 Materials and methods

Methodology of the research

As noted in chapter one, this PhD aims to contribute to the understanding of the mechanisms involved in the sedimentation processes in detention basins and to modelling sediment transport in detention basins. The results of the modelling can be used to improve the design and management of stormwater detention basins. Few researchers have directly investigated full-scale detention basin numerical modelling with DPM approach mainly due to difficulties regarding control and measurement in complex real-life conditions (complex geometry, surface condition, variable inflow/outflow and pollutant loads), and the high cost and huge requirements in terms of computational resources. Instead, most research has been carried out on scale models in laboratory conditions. However, it remains difficult to apply the results obtained from scale models to real-life systems. Therefore, this research focuses directly on a full-scale detention basin, in order to test the methods available in a full-scale basin and develop a new approach to model dynamic sedimentation processes. However, we also used the scale basins to test the newly-developed methods as they require less computational time and provide experimental data for validation.

The research strategy is as follows:

 In order to characterise the sediment accumulated in the basin, sediment samples were collected and analysed in laboratory in order to determine their physical properties; then analyses were performed to obtain the sedimentation characteristics spatial distribution in the basin.  Preliminary flow field simulation tests were carried out based on a simplified geometry of a full-scale basin. Due to the lack of available flow field data measurements (such as velocity field, flow free surface, etc.) for full-scale basins against which the flow simulation results could be checked, we instead used the accumulated sediment spatial distribution characteristics to roughly and indirectly check flow pattern. This may constitute a promising approach to model verification given the difficulties in collecting appropriate hydrodynamic data from real basins.  Based on the flow simulation results, we tested the available models (mainly the bed boundary conditions to represent the sedimentation processes) with a DPM approach in the full-scale basin in order to verify the capability of those bed boundary conditions in a real basin system.  A new formula has been proposed to calculate the threshold of bed turbulent kinetic energy (BTKE) by taking into account the particle properties in order to determine the suitable thresholds for specific pollutants. When predicting the efficiency and sediment deposition zones in a new basin design, the threshold cannot be determined by comparing simulation results with an inbuilt basin as this is unfeasible. Therefore the new method was first tested on a small-scale basin to verify its feasibility.  Then the new method was tested in the full-scale basin for sediment transport modelling.  Another novel approach has been developed to model dynamic sediment transport, settling and entrainment in detention basin. Grain scale sediment transport mechanisms were represented and tested in a small-scale detention basin. The newly developed method's potential capability for predicting efficiency and sediment deposition zone was explored.

In this chapter, the field experimental site is first briefly introduced, including the structure configurations and in situ monitoring equipment. Then the approaches used for the sampling and analysis of the sediment's physical properties are described. Finally, the numerical methods used in this research are described and discussed in detail mainly focusing on the fluid flow modelling and sediment transport modelling.

Experimental site

In situ site

Our research was carried out under the framework of OTHU (Observatoire de Terrain en Hydrologie Urbaine -Field Observatory for Urban Hydrology -8 1 H http://www.graie.org/othu/). This outdoor field observatory was set up to acquire reliable data on urban effluents during wet weather, with the aim of monitoring both the quality and quantity of stormwater from urban catchments and providing methodologies in order to assess the sustainability of the urban water system and offer support for operational decision making (OTHU - Turbidity was measured using an infra-red 880 nm nephelometric sensor Endress+Hauser CUS 1 according to the NF EN 27027 standard (1994). Its use as a surrogate to estimate TSS equivalent concentrations is described by [START_REF] Bertrand-Krajewski | TSS concentration in sewers estimated from turbidity measurements by means of linear regression accounting for uncertainties in both variables[END_REF]. The inlet and outlet discharges are calculated from simultaneous measurements of water depth and velocity in the pipes. Three water height sensors are located on the bottom of the basin (labeled as h1, h2 and h3 in Figure 34). All variables are recorded with a 2 minute time step in a S50 Sofrel data logger.

Pilot basin

As we know, it is difficult to acquire detailed hydrodynamic data in a real large detention basin. Hence we used the pilot basin experiments to test the proposed methods, since pilot basin experiments can provide much more flow and sediment information. Two pilot basins from the literature [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] were chosen for this research for their simplicity and the availability of experimental data. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] carried out a series of sediment transport experiments and performed simulations of hydrodynamics and sediment transport modelling. and2 (shown in 2 8 1 H Figure 3-7). The flow rates were then calculated using a weir law. An Acoustic Doppler Velocimeter (ADV) is used to measure the instantaneous velocities of liquid flow at different points in the tank. Each acquisition lasted for 120s, which corresponds to 6000 measurements (frequency: 50 Hz). A peristaltic pump injected white polystyrol particles over a period of 25 min. The particles were placed in the water for at least one day before each experiment. Their size is non-uniform, as shown in Table 3- *: d 10 means sieving size with 10 percent of particle mass passing through.

In this section, we will further test the proposed method for dynamic sedimentation modelling. The simulation is based on the previous work conducted by [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF].

The experimental set-up (see Polystyrene particles (P 426, manufacturer BASF) were added as the sediment in order to determine settling efficiency within the tank. The density of 1020 kg/m 3 was measured using a water pycnometer. The main particle sizes fell within the range of 300 to 700 µm with a median and maximum size of 500 µm and 800 µm respectively. The suspended particles were added by impulses through the injection mechanism in 10 steps with a volume of 100 ml injected at five-minute intervals. The volume of particles retained within the tank, as well as the volume of particles from the discharge, was determined using an Imhoff cone to calculate removal efficiency.

In situ experiments to characterise accumulated sediment

Introduction

Samples had to be collected from the inlet, outlet and inside of the basin, in order to characterise particulate pollutants from storm runoff. Previous work on sampling by [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] showed that when using a conventional sampler, it was difficult to collect samples from the inlet and outlet which were representative of the whole storm event. He analysed the limitations with the conventional sampler at inlet and outlet: i) spot sampling at specific intervals with the difficulty of integrating the entire rainfall event, ii) the limited storage capability of the automatic sampler, iii) the difficulty of ensuring representative sampling of an entrained solid (bed load) and/or a solid with high settling velocity, because the sampler is designed to collect total suspended solids. Considering all these difficulties, in this present reserch, we mainly focus on the sediment settled out at the bottom of the basin.

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 94

Sampling of accumulated sediment

Information on the characteristics of accumulated sediment are a fundamental requirement for improving our understanding of sedimentation processes in stormwater detention-settling basins. On the one hand, by analysing the properties of accumulated sediment, we can gain insights into some of the characteristics of the sedimentation process. On the other hand, the sediment characteristics (grain size distribution, density, settling velocity) constitute the input parameters required to simulate solid transport. In addition, using plastic sediment traps at the bottom of the basin may disturb settling processes due to the changes in key hydrodynamic quantities close to the bottom (turbulence kinetic energy, shear stresses, velocity distribution, etc.). Hence, sampling the accumulated sediment can also be considered as a complementary way of characterising this sediment which moves near the bottom.

Layout of sampling locations

We selected representative dispersion points for sediment sampling based on previous observations [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] and the first simulation results (Yan et al., 2011a). Several key aspects concerning the physical properties of both particles and flow related to sedimentation were taken into account:

 Thickness of cumulated sediment  Density  Diameter
 Near bed flow conditions and flow pattern (e.g., bed shear stress, turbulent kinetic energy, etc.).

In order to obtain the geometric data on the detention basin required for modelling mesh, topographic measurements were taken. About 500 points inside the basin were measured using the GPS technique and the details of some specific structures were also measured, for example, the inlet, outlet, orifices, etc. The spatial interval for themeasurement points was a 5m by 5 m square. Closer spacing of the measurement points was used in the centre of the basin and wider spacing close to the basin inlet.

Sediment sampling processes

The sediment sampling processes is summarised as follows:

 Measure the thickness of the sediment at each location indicated on 1 8 1 H As regards the sieving technology, we carried out the experiments according to the XP P 94-041 standard for wet method sieving. Standard wet method sieving usually consists of the following main steps:

 Dry the sample  Weigh the dry sample  Wash the sample  Sieving analysis with water  Dry the sample  Weigh the sample Considering the cohesive properties of storm pollutants, drying the sample before sieving may enhance the sediment consolidation process through coagulation. This may induce some uncertainty concerning the measurement of particle size distribution. A preliminary comparative experiment was performed to evaluate the influence of the drying operation before sieving analysis. The results of the comparison showed that the drying operation before sieving enhances the size ofthe finer particles. We therefore eliminated this step to try to preserve the sediment in its original condition. Furthermore, in order to reproduce conditions similar to those in the detention basin, we used the stormwater collected from the Django Reinhardt detention basin filtrated with a 0.45 m filter for the wet sieving analysis.

The present experiment used 0.08 mm, 0.2 mm, 0.5 mm, 1.0 mm, 2.0 mm and 5.0 mm sized sieves. These sieves are shown in 1 8 4 H Figure 3-14. The choice of sieve sizes was based on the preliminary tests. It should be noted that the LPS analysis is quantified in volume fractions, while the sieving analysis is quantified in weight fractions. It is therefore difficult to combine the results obtained using these two different methods even with particle size.

In situ Monitoring

In order to acquire reliable data on urban effluent during wet weather, stormwater quantity and quality are measured by monitoring stations. There are two monitoring stations located at the inlet and the outlet of the Django Reinhardt detention basin. The stormwater flow quantity was often determined by measuring velocity and water depth. With the sensors available in the station, the stormwater quality parameters measured are: turbidity, conductivity, temperature, PH (hydrogen ion concentration), UV-visible spectra. The specific equipment used to provide data for this thesis was as follows:

 Turbidity was measured by nephelometry using a 880 nm infrared sensor Endress + Hauser CUS-31 according to the NF EN 27027 standard. The sensors were installed in an experimental channel (length 2m, width 0.2m, invert and semicircular) inside the stations. Urban effluent is supplied by a peristaltic pump (flow rate of 1 L/s and suction velocity of 1 m/s) from the inlet or outlet pipe. The continuous turbidity and resuspension under unsteady conditions in urban stormwater detention basin / 2013 100 measurements are used to obtain TSS concentrations which are used to assess the RE of the basin.  An ultrasound air sensor NIVUS Nivubar Plus II and a Doppler sensor NIVUS CMO / EM were installed in the inlet pipe (circular pipe with a diameter of 1.6 m) to measure the simultaneous water depth and flow velocity respectively, in order to estimate the inflow rate. Meanwhile, a Mace Flo-Pro ultrasound air sensor and Mace Flo-Pro Doppler sensor were also installed in the outlet pipe (circular pipe with a diameter of 0.6 m) to measure the simultaneous water depth and flow velocity respectively, in order to estimate the outflow rate.  Two piezoresistive membrane sensors (NIVUS Nivubar Plus II) were installed at the bottom of basin to measure the water depth; the locations of two sensor were shown in Figure 3-4 labeled as h 1 and h 2 .

All the sensors work with a time step of two minutes, and the measured data were saved in a S50 Sofrel data logger, except for the UV-visible spectra sensor data which were saved with a time step of two minutes on a dedicated PC.

In addition, a refrigerated automatic sampler (Sigma 900R) equipped with 24 1L bottles was installed in the stations to automatically collect effluent samples in the inlet and outlet pipe. These samples are used for analyses conducted at a later stage in the laboratory. The schematic configuration of sensors is shown in 1 8 6 H 3.4 Numerical modelling strategy

Introduction

The objective of this section is to present in detail the mathematical model for single phase fluid flow / multiphase flow used in this thesis.

We choose the commercial CFD solver Anasys Fluent as the modelling tool for all the simulations. It is one of the most widely used commercial CFD solvers in industrial engineering and academic research. The RANS/URANS-based approaches integrated in Fluent CFD code have been widely tested for various hydraulic flow conditions in sewer systems [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF][START_REF] Kouyi | Expérimentations et modélisations tridimensionnelles de l'hydrodynamique et de la séparation particulaire dans les déversoirs d'orage[END_REF][START_REF] Kouyi | Use of 3D modelling and several ultrasound sensors to assess overflow rate[END_REF][START_REF] Kouyi | CFD modeling of flow in a large stormwater detention and settling basin[END_REF][START_REF] Bonakdari | εodélisation des écoulements en collecteurs d'assainissementapplication à la conception de points de measures[END_REF]Benett, 2012;etc). It provides a UDF (user defined function) interface, into which specific modules can be integrated to adapt to different requirements Fluids are substances whose molecular structure offers no resistance to external shear forces: even the smallest force causes deformation of a fluid particle [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]. In most cases of interest, a fluid can be regarded as continuum, which can be treated as being differentiable from a mathematical point of view. Based on this hypothesis, the basic equations governing fluid flow, the Navier-Stokes equations, can be derived according to the basic conservation laws:

 Mass conservation  εomentum conservation (σewton's second law of motion)  Energy conservation (if required)

It is convenient to deal with the flow within a certain spatial region, so called the control volume, rather than in a parcel of matter which quickly passes through the region of interest. This method of analysis is called the control volume approach. Here we write the continuity equation ( 3.1) and momentum equation (3.2) directly in a partial differential form. More detailed derivations can be found in a number of standard texts on fluid mechanics (e.g. [START_REF] White | Fluid mechanics[END_REF][START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF]. Throughout this thesis, we shall adopt the Einstein convention that whenever the same index appears twice in any term, summation over the range of the range of that index is implied.

  0       i i x u t   , (3.1)     i i j ij j i j i F x p x x u u t u                , ( 3.2)
Where x i (i=1, 2, 3) is the Cartesian coordinates and u i is the Cartesian components of the velocity vector, ρ is the fluid density, p is the pressure, and F i is the body force (e.g. gravity, Coriolis forces, centrifugal, etc). For Newton fluid, τ ij is the viscous stress tensor. It can be described by equation (3.3). S ij is the rate of strain (deformation) tensor, as written in equation (3.4).

l l ij ij ij x u S        3 2 2 , (3.3)               i j j i ij x u x u S 2 1 , (3.4)
Where ij is Kronecker symbol ( ij =1 if i=j and ij =0 otherwise), μ is the dynamic viscosity coefficient.

Turbulent flow

Most flow encountered in engineering practice is turbulent and therefore requires different treatment. The most accurate approach to turbulence simulation is to solve the Navier-Stokes equations without averaging or approximation other than numerical discretization where errors can be estimated and controlled [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]. This approach is called direct numerical simulation (DNS). DNS results provide very detailed information about the flow. However, it also requires high restrict grid resolution mainly depending on the Reynolds number [START_REF] Tennekes | A first course in turbulence[END_REF]. The size of grid must be no larger than a viscously determined scale, called the Kolmogoroff scale. The DNS is limited by the processing speed and memory of the machine on which it is carried out. In engineering practice, an approach called one -point closure based on averaging the equations of motion over time and which leads to a set of partial differential equation called the Reynolds-averaged-Navier-Stokes equations (RANS) is widely used [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]., These equations do not form a closed set so this method requires the introduction of approximations which is called the turbulence model.

c. Reynolds-Averaged-Navier-Stokes equations

The RANS is based on the ideas proposed by Osborne Reynolds. In statistically steady flow, every variable can be written as the sum of a time-averaged value and a fluctuation around that value:

      i i i x x t x       , , (3.5
) where

        T i T i t t x T x 0 d , 1 lim   , (3.6)
Here t is the time and T is the averaging time interval. This interval must be large compared to the typical time scale of the fluctuations. If T is large enough,  does not depend on the time at which averaging is started.

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 103

For unsteady flow, this concept is described as equation (3.7).

        N n i N T i t x N x 1 , 1 lim   , (3.7)
Where N is the number of members of the set, it must be large enough to eliminate the effect of the fluctuation. The concept is illustrated in 1 8 7 H From equation (3.6), it follows that 0    , thus averaging any linear term in the conversation equations simply gives the identical term for the averaged quantity.

  

              i i i i u u u u u , (3.8)
Applying this rule to NS equations, for incompressible flow, the continuity and momentum equations so-called RANS can be written with tensor notation and Cartesian coordinates as:

  0    i i x u  , (3.9)       i i j j i j ij i j j i F u u x x p x u u x t u                      - , (3.10)
Where the ij  is the mean viscous tress tensor component:

l l ij i j j i ij x u x u x u                    3 2 - , (3.11)
The term contained in equation 3.10 as -

i j u u   
, called the Reynolds stresses cannot be presented solely in terms of the mean quantities. The equation system is not closed because the number of unknown variables is more than the number of independent equations. Closure requires the use of some approximations, which usually take the form of prescribing the Reynolds stress tensor and turbulent scalar fluxes in terms of the mean quantities. In engineering the approximations introduced are called turbulence model.

d. Turbulence models

Standard k-ε model

It is based on an assumption that the effect of turbulence can be represented as increased viscosity. This leads to the eddy-viscosity model for Reynolds stress:

k x u x u u u ij i j j i t j i    3 2                   (3.12)
Where t  is the eddy viscosity, k is the turbulent kinetic energy per unit mass:

  z z y y x x i i u u u u u u u u k             2 1 2 1 (3.13)
In this simplest description, turbulence can be characterised by two parameters: its kinetic energy, k, and a length scale L. The dissipation rate of turbulence energy, ε, is also defined. The descriptions of k and ε are written as equations (3.13) and (3.14), more detailed information can be found in [START_REF] Wilcox | Turbulence Modelling for CFD[END_REF].

                                       k j k t j j j P x k x x k u t k , (3.14)     k C k P C x x x u t k j t j j j 2 2 1                                   , (3.15) Where       2 k C L k C t   , (3.16) j i i j j i t k x u x u x u P                  , ( 3.17)
The model based on equations (3.13) and (3.14) is called the standard k-ε model and has been widely used. There are five parameters in the standard k-ε, the most commonly used values arrived at by comprehensive data fitting for a wide range of turbulent flow are [START_REF] Launder | Lectures in Mathematical Models of Turbulence[END_REF]:

; 09 . 0   C ; 44 . 1 1   C ; 2 . 19 2   C ; 0 . 1  k  ; 3 . 1    (3.18)
Generally, the k-ε model is suitable for fully developed turbulent flow.

RNG k-ε model

The Renormalization Group (RNG) was devised by [START_REF] Yakhot | Renormalization group analysis of turbulence I: Basic theory[END_REF] for hydrodynamic turbulence. They represented the effects of small-scale turbulence by means of a random forcing function in the Navier-Stokes equations (Versteeg and Malalasakra, 2007). [START_REF] Yakhot | Development of Turbulence Models for Shear Flow by a Double Expansion Technique[END_REF] expressed the RNG k-ε model as:

      ρε S τ x k μ α x x k u ρ t ρk ij ij j eff k j j j                      , (3.19)     k C S k C x x x u t ij ij j eff j j j 2 2 1                                    , (3.20)
Where

ij t ij S   2  , (3.21)               i j j i ij x u x u S 2 1 , (3.22) 3 0 3 2 2 1 1                   C C C (3.23) ij ij S S k   2   (3.24) t eff      (3.25)
The constants in the RNG k-ε model are:

k    1  C 2  C 0    C 1.

Wilcox k-ω model

The second most commonly used model is the k-model, originally introduced by Saffmen but popularised by Wilcox [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]. The k-model uses turbulence frequency =ε/k as the second variable. Then the eddy viscosity is given by:

   k t  (3.26)
The transport equations for k and for turbulent flow are as follows [START_REF] Wilcox | Reassessment of the Scale-determining Equation for Advanced Turbulence Models[END_REF](Wilcox, , 1993a(Wilcox, , b, 1994)):

            k P x k x x k u t k k j k t j j j                               , (3.27)     2                                         k P x x x u t k j t j j j , (3.28)
The constants in the k-model areμ

    k     5/9 0.075 0.09 2.0 2.0 k   

Reynolds Stress Model

The most complex classic turbulence model is the Reynolds stress model (RSM), also called the second-order or second-moment closure model. Several major drawbacks of the kmodel emerge when it is used in attempts to predict flow with complex strain fields or significant body forces. Under such conditions the individual Reynolds stresses are poorly represented by eddy-viscosity assumption, equation (3.11), even if the turbulent kinetic energy is computed with reasonable accuracy [START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]. The exact Reynolds stress transport equation on the other hand can account for the directional effects of the Reynolds stress field. The most complex model commonly used today is the RSM which is based on dynamic equations for the Reynolds stress tensor -

                                                   ijk k j i k ij ij k i k j k j k i j j j i j i C x u u x x u u u x u u u x u u u t u u                   (3.29) Where                   ij i j j i x u x u p (3.30) k j k i ij x u x u          2 (3.31) ik j jk i k j i ijk u p u p u u u C              (3.32)
In equation (3.29), the first two terms of the right-hand side are the production terms and require no approximation. The term  ij is often called the pressure-strain term, which redistributes turbulent kinetic energy amongst the components of the Reynolds stress tensor but does not change the total kinetic energy. The next term ij  is the dissipation tensor. The last one ijk C is often called turbulent diffusion. The dissipation, pressure-strain, and turbulent diffusion terms cannot be computed exactly in terms of the other terms in the equations and therefore must be modelled. The simplest and most common model for the dissipation term treats it as isotropic:

ij ij   3 2  (3.33)
This means that a dissipation equation is needed in the RSM model. The pressure-strain term and turbulent diffusion term also need to be modelled. The simplest model for pressure-strain term is that one assumes that the function of this term is to make the turbulence more isotropic. However, it has met with great success and a number of suggestions for improvement have been made. More details can be found in the literature (Launder, 1990, Hanjalić, 199ζ, Versteeg andεalalasekera, 2007). The turbulent diffusion terms are usually modelled using the gradient diffusion type of approximation. Isotropic, anisotropic and nonlinear models have also been suggested (Ferizger, 2002).

Generally, the RSM model has the potential to more accurately represent the characteristics of turbulence flow compared to the one-equation and two-equation models. However, in some flows, there is very little difference in terms of performance. Indeed, none of the models can be expected to produce robust results for all flows. Furthermore, it is not yet clear which model is best for which kind of flow, perhaps due to numerical errors in modelling?

For three dimensions model, the RSM needs to solve seven partial differential equations excluding mean flow. More scalar equations may also need to be solved if required. Thus compared to two-equation model such as k-ε, model, the RSM requires far more computation time and memory, and the calculations usually converge more slowly.

e. Free surface modelling

The free surface (i.e. the interface between the water and air) is a key parameter when modelling hydrodynamics in stormwater detention basins. In general, researchers often use a VOF model to track the free surface, which will be a result of the simulation. Also, in some specific cases or conditions (such as when the level of flow is flat and horizontal) the free surface can be represented as symmetric surface or slip wall with zero shear stress. Both the VOF model and symmetric boundary condition are used in our work as briefly presented below..

Volume of fluid (VOF)

The VOF model can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. Typical applications include the prediction of jet breakup, the motion of large bubbles in a liquid, and the motion of liquid after a dam break, and the steady or unsteady tracking of any liquid-gas interface. In our work, we tried to use the VOF model to track the free surface in the detention basin. Early in 1975, Nichols and Hirt proposed the VOF method and presented it as beingflexible and efficient for treating complicated free boundaries. To illustrate the method, a description of an incompressible hydrodynamics code SOLA-VOF, which uses the VOF technique to track the free fluid surface [START_REF] Hirt | Volume of Fluid (VOF) method for the dynamics of free boundaries[END_REF] is provided. In the VOF method, a variable, volume fraction of each phase, α q is introduced into the computational cell.

In a cell the following three conditions are possible:

 0  q 
: the cell is empty( of the q th fluid)

 1  q 
: the cell is full ( of the q th fluid)

 1 0   q  :
The cell contains the interface between the q th fluid and one or more other fluid.

Based on the local value of α q , the appropriate properties and variables will be assigned to each control volume within the domain. The tracking interface(s) between the phases is accomplished by the solution of a continuity equation for the volume fraction of one or more of the phases. For the q th phase, the volume fraction equation for each phase is written as equation (3.35) (Ansys, 2011). In each control volume, the volume fractions of all phases sum to unity, as written in equation (3.36).

                     n p qp pq q q q q q p m m v t 1 1      (3.34)    n q q 1 1  (3.35)
Where m qp is the mass transfer from phase q to phase p and m pq is the mass transfer from p phase to phase q.

The properties featured in the transport equations are determined by the presence of the component phases in each control volume. In general, for an n-phase system, the volumefraction-averaged density takes on the following form:

  q q    (3.36)
All other properties (e.g., viscosity) are computed in this manner. For example, in a two phase air and water system, the averaged dynamic viscosity, is calculated by the water fraction α w and water dynamic viscosity μ w and air viscosity μ a :

  a w w w         1 (3.37)

Initial condition and boundary condition

All CFD problems are defined in terms of initial and boundary conditions. It is important that the user specifies these correctly and understands their role in the numerical algorithm. In unsteady problems the initial values of all the flow variables need to be specified at all solution points in the flow domain [START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF]. Here we will briefly introduce some of the boundary conditions used in this investigation:

• Inlet • τutlet • Wall • Symmetry

Inlet boundary condition

In hydraulics modelling, the velocity inlet or inflow rate is often used as the boundary condition at the inlets [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF][START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF].

The pressure inlet boundary condition is recommended for channel simulation with free surface if VOF is involved. When using the velocity inlet as the inlet boundary condition, generally, a homogeneous velocity profile is often set due to the lack of a velocity profile. However, usually the homogeneous velocity profile for a cross section does not reflect reality thus an extended inlet (such as a pipe inlet) often is required to ensure a developed velocity profile in the domain of interest [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. For the reference pressure, it is common practice to fix the absolute pressure at one inlet node and set the pressure correction to zero at that node by specifying a reference pressure value [START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF].

An estimation of turbulent kinetic energy k and dissipation rate ε at the inlet boundary is often required if a turbulent model is used. The most accurate simulations can only be achieved by supplying measured inlet values for turbulent kinetic energy k and dissipation rate ε. However, such data are often not available and in practicek and are often estimated using the approximate formula. It is possible to obtain k and ε from the turbulence intensity I (typically turbulence intensity of between 1% and 6% is used) and the characteristic length L of the equipment (equivalent pipe diameter) using the following simple assumed forms:

  2 3 2 I U k ref  (3.38) ref l k C 2 3 4 3    (3.39) L l ref 07 . 0  (3.40) 8 1 Re 16 . 0   I (3.41)
Where U ref is the velocity in the inlet face, Re is the Reynolds number.

In some specific cases, the UDF is also used to specify the velocity distribution as needed, such as the velocity profile if available or inlet velocity changes with time in unsteady condition.

Outlet boundary condition

The

Wall boundary conditions

The wall is the most common boundary encountered in confined fluid flow problems. With a solid wall parallel to the x-direction, the no-slip condition (tangential velocity component equals to zero, u=v=0) is usually the appropriate condition for the velocity components at solid walls. The normal velocity component can simply be set to zero at the boundary. For all other variables, specific source terms are constructed, according to the type of flow (laminar or turbulent flow). Obviously, the mean velocity field is affected through the no-slip condition that has to be satisfied at the wall. Due to the presence of the solid boundary, the flow behaviour and turbulence structure are considerably different from free turbulent flow. The turbulent models such as k-ε are valid only at the fully developed domain. So the near wall region needs to be treated using additional complementary models.

Very close to the wall the flow is influenced by viscous effects and does not depend on free stream parameters. The mean flow velocity only depends on the distance y from the wall, fluid density ρ and viscosity and the wall shear stress τ w , dimensional analysis shows that 3.42) is the so called law of the wall and contains the definitions of two important dimensionless groups, u + and y + , u * = (τ w /ρ) 0.5 is friction velocity.

               y f Y u f u U u   * * (3.42) Formula (
The turbulent boundary layer adjacent to a solid surface is composed of two regions: the inner region and the outer region. The outer region is free from direct viscous effects [START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF]. Within the inner region there are three zones:

 The viscous sublayer: viscous stresses dominate the flow adjacent to surface  The buffer layer : viscous and turbulent stresses are of similar magnitude  The log-law layer: turbulent stresses dominate In the viscous sublayer, the shear stress is approximately constant and equal to the wall shear stress w ,

  w y U y        (3.43)
After integration with respect to y and application of boundary condition U=0 if y=0, we obtain:

  Y U w  (3.44)
Using the definition of u + and y + , we get:

   y u (3.45)
and resuspension under unsteady conditions in urban stormwater detention basin / 2013 112

In the log law layer, the shear stress varies slowly with the distance from the wall. Schilichting (1979) derived a functional relationship between u + and y + for this layer.

          Ey B y u ln 1 ln 1   (3.46)
Where κ is the von Karman's constant κ ≈ 0.ζ and B is the additive constant B≈η.η (or E≈9.8). This relationship is valid for u + between 30 and 500. Traditionally, there are two approaches to modelling the near-wall region: the near-wall model approach and the wall function approach. For the near-wall model, the turbulence models are modified to enable the viscosity-affected region to be resolved with a mesh all the way to the wall, including the viscous sublayer. For the purposes of discussion, this will be termed the "near-wall modelling" approach. As shown in 1 9 0 H , this approach requires refined meshes near the wall region to ensure the first mesh node is in the viscous sublayer [START_REF] Salim | Wall y+ strategy for dealing with wall-bounded turbulent flows[END_REF], which are generally difficult to achieve.

For the wall function approach, the viscosity affected inner region (viscous sub layer and buffer layer) is not resolved. Instead, semi-empirical formulas called 'wall functions' are used to bridge the viscosity-affected region between the wall and the fully turbulent region (shown schematically in Figure 3-19 (right side)).

Figure 3-19 Scheme of near wall region treatment (Ansys, 2011b)

The use of wall functions obviates the need to modify the turbulence models to account for the presence of the wall. In Ansys Fluent, the wall function approach is employed by adapting equations (3.45) and (3.46). The near wall flow dimensionless velocity is defined as:

   w p p k C U U 2 1 4 1 *  (3.47)    p p y k C y 2 1 4 1 *  (3.48)
And calculated by:

              225 . 11 * * ln 1 225 . 11 * * * y if Ey y if y U  (3.49)    p p y k C y 2 1 4 1 *  (3.50)

Roughness effects

The surface roughness effects on turbulence quantities and bed shear stress are considered through the modified law-of-the-wall for roughness. The standard wall functions in Ansys Fluent are based on the work by [START_REF] Launder | The numerical computation of turbulent flow[END_REF] and have been most widely used for industrial flow (Ansys, 2011a;[START_REF] Souders | Modeling Roughness Effects in Open Channel Flow[END_REF]. Experiments in rough pipes and channels indicate that the mean velocity distribution is influenced by the near rough walls and in the usual semi-logarithmic scale, has the same slope (1/κ) but a different intercept [START_REF] Tachie | Roughness effects on the mixing properties in open channel turbulent boundary layers[END_REF][START_REF] Akinlade | Outer flow scaling of smooth and rough wall turbulent boundary layers[END_REF]. Thus, the law-of-the-wall for mean velocity impacted by rough wall has the form (Ansys, 2011b): ΔB is a roughness function that quantifies the shift of the intercept due to roughness effects. ΔB depends on the type (uniform sand, rivets, threads, ribs, mesh-wire, etc.) and size of the roughness. There is no universal roughness function valid for all types of roughness. However, for sand-grain roughness and similar types of uniform roughness elements B  has been found to be well-correlated with the non-dimensional roughness height,

B y u E u U p w p    ) ln( 1 * *      (3.51)
  / * u K K s s   ,
where K s is the physical roughness height.

The turbulent flow regime is subdivided into three regimes, and the formulas proposed by [START_REF] Cebeci | Momentum Transfer in Boundary layers[END_REF] based on Nikuradse's data were adopted to compute the roughness function, Δψ, for each regime (Ansys, 2011b).

For the smooth regime (K s + < 2.25):

0  B (3.52)
For the transitional regime (2.25 < K s + < 90):

    811 . 0 ln 4258 . 0 sin 75 . 87 25 . 2 ln 1                s s s s K K C K B  (3.53)
where C s is a roughness constant, and depends on the type of the roughness.

In the fully rough regime (K s + > 90):

      s s K C B 1 ln 1  (3.54)
In the present investigation of the Django Reinhardt detention basin, the bottom was considered to be covered in concrete and the equivalent sand grain roughness height was estimated using the following formula proposed by Hager (2010):

g k K s    5 . 6 6 1 (3.55)
Where K is Strickler coefficient and k s is equivalent grain roughness heights, g is the gravity acceleration.

Symmetric boundary condition

The symmetry boundary condition means that there is no flow through the interface. The variables of the outside domain (virtual variables) are equal to the variables (actual variables) of the inside domain. In mathematical terms, this second condition results in gradients normal to the plane of symmetry of zero for all variables [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. The symmetry boundary condition is often used for free surface for some specific horizontal flat surface cases [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]Dufresne et al., 2009;[START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF]Saul, 1994, 1996;[START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF].

Initial conditions

The initial conditions play a very important role in CFD simulations, not only in terms of computational time, but also the convergence to the physical solution and accuracy. Providing an initial data field that is close to the final solution for steady-state cases means the solver has to do less work to reach the converged result. This therefore reduces simulation time. On the contrary, poor initial conditions mean more computational time is required. Typically, many users employ standard initialisation in Ansys Fluent; some use patching for localised control, especially for moving domains or multiphase analyses [START_REF] Keating | Accelerating CFD solutions[END_REF].

Within Ansys Fluent, thealternative full multigrid initialization (FMG) method or the Hybrid solution initialization method can be used to obtain better initial conditions [START_REF] Keating | Accelerating CFD solutions[END_REF]. FMG can provide the initial and approximate solution at a minimum cost to the overall computational expense. Although the overall initialization time is longer than that using standard initialization by zone, it allows a much quicker solve. FMG solves Euler equations and provides the best guess initial solution. FMG is currently available for single phase.

Hybrid solution initialization uses a collection of recipes and boundary interpolation methods to efficiently initialize the solution based purely on simulation setup. This means the user does not need to provide any additional input for initialization. This method may improve convergence robustness many cases. Unlike FMG, this initialization method can be used for multiphase flow.

Numerical procedure

The NS or RANS equations are a group of partial differential equations for flow. Ansys Fluent uses the Finite Volume Method (FVM (Ansys, 2011b)) to convert the differential conservation equations into algebraic equations that can be solved numerically. We used the pressure-based solver. The pressure-based solver makes it possible to solve flow problems in either a segregated or coupled manner. With the segregated algorithm, each iteration consists of the steps illustrated in 1 9 1 H Figure 3-20 and outlined below:

1. Update fluid properties (e.g., density, viscosity, specific heat) including turbulent viscosity (diffusivity) based on the current solution.

2. Solve the momentum equations, one after another, using the recently updated values for pressure and face mass fluxes.

3. Solve the pressure correction equation using the recently obtained velocity field and the mass-flux.

4. Correct face mass fluxes, pressure, and the velocity field using the pressure correction obtained from step 3.

5. Solve the equations for additional scalars, if any, such as turbulent quantities, energy, species, and radiation intensity using the current values of the solution variables.

6. Update the source terms arising from the interactions among different phases (e.g., source term for the carrier phase due to discrete particles).

7. Check for the convergence of the equations.

These steps are to be repeated until the convergence criteria are met.

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 117 Fluent provides three methods for pressure-velocity coupling in the segregated solver: SIMPLE, SIMPLEC, and PISO. The SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm was proposed by [START_REF] Patankar | A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flow[END_REF]Spalding (1972, cited in Versteeg and[START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF] to ensure the correct linkage between pressure and velocity using staggered grid arrangement. Van Doormal and Rithby (1984) proposed the SIMPLEC (SIMPLE-consistent) algorithm, which omits terms in the velocity correction equations that are less significant than those in SIMPLE, in order to both simplify implementation and reduce solution costs. The PISO (Pressure Implicit with Splitting of Operators) algorithm proposed by Issa (1986, cited in Versteeg and[START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF]) is a pressure-velocity calculation procedure originally developed for the non-iterative computation of unsteady compressible flow. It has been successfully adapted for the iterative solution of steady state problems [START_REF] Versteeg | An introduction to computational fluid dynamics-the finite volume method[END_REF]. Steady-state calculations will generally use SIMPLE or SIMPLEC, while PISO is recommended for unsteady calculations. PISO is recommended for unsteady calculations on highly skewed meshes (Ansys, 2011a).

Both the standard SIMPLE algorithm and the SIMPLEC (SIMPLE-Consistent) algorithm can be used in Fluent. SIMPLE is the default, but many problems will benefit from the use of SIMPLEC, particularly because of the increased under-relaxation that can be applied, which would make the calculation converge faster.

Convergence control

All the simulated cases in the present work are based on the second upwind discretization scheme for flow and turbulent variables. The convergence criterion within each time step will strongly affect solution costs, as a low criterion will result in an increased number of iterations. It is not possible to make general recommendations, as the required residual depends on the application. Furthermore, monitoring the residual is not the only way ofto adjusting the convergence. Flux conservation also needs to be checked. Generally speaking, the simulation is considered to be converged if the residuals reach the specified threshold (criteria). In some cases, the simulation cases are judged to be converged if the iterative variables are stable for steady state simulation. For unsteady simulations, the residual should be converged by approximately four orders of magnitude per time step.

Sediment transport modelling 3.4.3.1 Introduction

Obviously, sediment transport involves two phases: the liquid phase and the solid phase.

Based on the two-phase concept, there are two different modelling approaches to simulate the sediment transport phenomenon: Euler-Euler and Euler-Lagrange [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF].

In the Euler-Euler approach, different phases (fluid and sediment) are modelled as a continuum using Navier-Stokes equations. In the past, the most common procedure for modelling sedimentation involved splitting the problem into a flow model and into a sediment transport model [START_REF] Olsen | Two-dimensional numerical modeling of flushing processes in water reservoirs[END_REF][START_REF] Wu | 3D numerical modeling of flow and sediment transport in open channels[END_REF], namely the modelling the fluid phase and the solid phase in an uncoupled way. The flow model provides the hydrodynamics (local velocities) for sediment simulation. The sediment model only affects flow in terms of the changes in bed topography and in local bed friction [START_REF] Zeng | Fully 3D non-hydrostatic model to compute flow, sediment transport and bed morphology changes for an alluvial open channel bend[END_REF]. The suspended load model and bed load models are coupled using more or less empirical formulas describing the mass exchange between suspended load, bed load and the deposited sediment itself [START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF].

Up till the early 1980s, most computational models for multiphase flow at application level describe both the continuous phase and the dispersed phase as a continuum in coupled way, the so-called Eulerian model. Owing to the continuum description of the dispersed phase, Eulerian models require additional closure laws to describe particle-particle interactions. Most recent continuum models incorporate constitutive relations according to the kinetic theory of granular flow. This theory basically extends the classical kinetic theory of gases to dense particulate flow, which considers non-ideal particle-particle collisions and particle-particle drag. In these models the dispersed phase is described as a continuous phase fluid with appropriate closures. Therefore, only the average local volume fraction (mostly concentration), velocity, etc. are calculated and it cannot represent the properties of each individual dispersed particle. For example, the solid particle size is generally defined as a unique value for the whole domain [START_REF] Cao | Sediment-laden flow in open channels from two phase flow viewpoint[END_REF].

With the increases in the computational power available, the Lagrangian approach has become a very useful and versatile tool for studying the particulate flow. In these models, the Newtonian equations of motion are solved for each individual particle, and a collision model is applied to handle particle encounters. Recently, such particle models have been combined with an Eulerian model for the continuous phase simulation, the so-called Euler-Lagrange approach. In the Euler-Lagrange approach, the solid phase is represented by tracking discrete particles, taking into account momentum, heat and mass transfer between the two phases. The Lagrange approach does not require additional closure equations for the particulate phase since it tracks the motion of each individual particle, taking into consideration collisions and external forces acting on the particles. This makes it a very convenient way of taking into account individual properties such as particle size distribution, density, settling velocity, etc. However, the amount of dispersed particles that can be tracked is, even today limited [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF] and is likely to remain so in the near future.

Multiphase flows are modelled using an Eulerian-Eulerian approach or a Eulerian-Lagrangian approach [START_REF] Van Wachem | Methods for multiphase computational fluid dynamics[END_REF] depending on the extent of coupling between phases, with the delimiter that an Eulerian-Eulerian approach is used for flow with particulate volume fractions (PVF) greater than 10%. [START_REF] Elghobashi | Particle laden turbulent flow: Direct simulation and closure models[END_REF] proposed a regime map for appropriating the degree of interphase coupling, by analysing length and time scales.

Preliminary studies focusing on the comparison between multiphase models integrated in Ansys Fluent package were carried out in order to identify the best approach. Eulerian-Granular, Mixture and uncoupled DPM models were tested for dissolved tracer transport in a rectangular channel (δa ly, 2012). Compared to the experimental observation derived from a review of the literature, the results showed that the uncoupled DPM model is better atrepresenting dispersion and mixing processes in rectangular channels. Moreover, [START_REF] Chocat | Eaux pluviales urbaines et rejets urbains par temps de pluie[END_REF] pointed out that fluid flow and solid transport in sewer systems can be modelled in an uncoupled way due to the low pollutant concentration. Subsequently, it was determined that a Lagrangian approach to tracking the solid phase is appropriate for flow with low PVF influent in stormwater detention basins.

DPM approach

The δagrangian ϊPε is derived from force balances based on σewton's law describing particle trajectory. The force balance in the x-direction (in Cartesian coordinates) can be written as (Ansys, 2011b):

    x p p x p D p F g u u F dt du         (3.56)
Where u p is the velocity of the particle, u is the instantaneous velocity of the fluid, g x is the acceleration of gravity along the x axis, ρ p is the density of the particle, ρ is the fluid density, and F x is the additional forces. The left term in equation ( 3.56) corresponds to the x direction acceleration of the particle per unit particle mass. The first term on the right-hand side corresponds to the mass force of drag per unit particle mass. The coefficient F D is expressed by equation (3.57). Where μ is the dynamic viscosity of the fluid, d is the diameter of the particle; C D is drag coefficient, and Re p is the Reynolds number of the particle. The second term comprises of forces due to gravity per unit particle mass (competition between weight and buoyancy of the particle). The third term corresponds to additional forces per unit particle mass, including the added mass force and the force due to pressure gradient. It is a dimensionless number characterising the relative velocity between fluid and particle, defined in equation ( 3.58):

  p p u u d   Re (3.58)
The drag coefficient C D depends on the flow regime. For the Reynolds number of small particles (Re p 0.1), the total drag coefficient is expressed by Stokes' law, as expressed in equation (3.η9). With an increasing particle Reynolds number, Stokes' law underestimates the drag force. Schiller and Nauman proposed an expression for the drag coefficient [START_REF] Clift | Bubbles, drops, and particles[END_REF] as written in equation (3.60).

Within Fluent, one can chose the drag coefficient expression proposed by [START_REF] Morsi | An investigation of particle trajectories in two-phase flow systems[END_REF] for spherical particles, which provides the most complete range of Re p , as written in equation (3.61). The empirical constants α 1 , α 2 and α 3 depend on the particle's Reynolds number (εorsi and Alexander, 1972) and are shown in Table 34.

Simulation of the effect of fluctuating velocity on sedimentation processes

Sediment transport phenomena in turbulent flow are more striking than in laminar flow. Some researchers [START_REF] Wilkinson | CFD and experimental studies of fluid and particle flow in horizontal primary separators[END_REF][START_REF] Pettersson | FEM-modeling of open stormwater detention ponds[END_REF] assumed that particle trajectory can be calculated with the mean flow without taking into consideration the influence of flow turbulence. Others [START_REF] Thomson | Random walk modelling of diffusion in inhomogeneous turbulence[END_REF][START_REF] Thomson | Criteria for the Selection of Stochastic Models of Particle Trajectories in Turbulent Flows[END_REF][START_REF] Stovin | Computational fluid dynamics and the design of sewage storage chambers[END_REF][START_REF] Shams | Computational modeling of flow and sediment transport and deposition in meandering rivers[END_REF][START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF][START_REF] Jayanti | Computational study of particle-eddy interaction in sedimentation tanks[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], Dufresne et al., 2009;[START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]Yan et al., 2011a) argued that the dispersion of small particles is severely affected by turbulent flow. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] tested the parameter concerned, the time scale constant value, using a discrete random walk model (DRWM) in a stormwater detention basin. The authors found that the RE and sediment deposit zone were sensitive to this parameter. Since most flow in nature is in a turbulent state and turbulent flow can be characterised by fluctuating velocity fieldsthe effect of turbulent flow field on the dispersion of particles should be taken into account to obtain more accurate results. The dispersion of particles due to turbulence in the fluid phase can be predicted using the stochastic tracking model DRWM. The stochastic tracking model in Fluent is based on the eddy interaction model and the discrete particle is assumed to interact with a succession of eddies. The DRWM includes the effect of instantaneous turbulent velocity fluctuations on particle trajectories by using stochastic methods by eddies. Each eddy is characterised by a Gaussian distributed random velocity fluctuation u', v', and w', a time scale (eddy lifetime), τ e , and a length scale (eddy size), L e . Velocity fluctuation u', v', and w' are expressed in equations ( 3.60) - (3.63), where is a normal distributed random number, and k is the turbulent kinetic energy.

2 u u    (3.60) 2 v v    (3.61) 2 w w   (3.62) 3 2 2 2 2 k w v u        (3.63)
In the DRWM, the fluctuating velocity components are discrete piecewise constant functions of time. Their random value is kept constant over an interval of time calculated from the characteristic lifetime of eddies, τ e . The lifetime scale is defined as equation (3.64):

L e T 2   (3.64)
For small particles that move with the fluid, the particle integral time becomes the fluid Lagrangian integral time, T L . This time scale can be approximated as an equation based on k-ε model (3.65):

 k C T L L  (3.65)
Where C L is the time scale constant and is the only parameter to be determined by this model k is the turbulent kinetic energy; ε is the turbulent dissipation rate. For the k-models, substitute = /k into equation (3.6η).

Another option for eddy lifetime is given by a log-normal variation:

  R T L e log    (3.66)
Where R is a uniform random number between 0 and 1.

The eddy length scale is given as:

 2 3 15 . 0 k L e  (3.67)
The particle eddy crossing time, t cross , is defined as:

                    p e cross u u L t   1 ln (3.68)
Where |u-u p | is the magnitude of the relative velocity; τ is the particle relaxation time defined as:

   18 2 d p  (3.69)
During the interaction process, the fluctuating velocities are kept as constant interaction time. The interaction time is either eddy lifetime or the crossing time, whichever is lower. When this time is reached, a new set of values for instantaneous velocities are obtained from a new random value of .

Particle dispersion prediction makes use of the concept of the integral time scale, T, defined in equation. (3.63), which describes the time spent in turbulent motion along the particle path, d s :

       0 2 ) ( ) ( ds u s t u t u T (3.70)

DPM boundary condition

The basic principles of particle trajectory are set out in the previous section. In order to implement a simulation such as flow simulation, some specific boundary conditions are required.

f. Initial condition of particles

Before injecting the particles into a flow domain, the particles' properties must be defined. The primary inputs required for the discrete phase calculations in Ansys Fluent are the initial conditions that define the starting position, velocity, density, size and other parameters for each particle stream, as well as the physical effects acting on the particle streams. The initial conditions for a particle stream are defined by creating an injection and assigning properties to it. Usually, the sediment is defined as an inert particle.

The initial conditions required depend on the injection type, while the physical effects are selected by choosing an appropriate particle type. Particle size distribution of sediment was estimated in two ways: firstly using a mean diameter to represent all particle sizes; and secondly by employing the Rosin-Rammler distribution function, a new feature to describe the granulometry of sediment in inlet injection. Using this feature the whole range of particle sizes is divided into a number of discrete intervals. Each interval is represented by a mean diameter and tracked for the particle trajectory calculation. The Rosin-Rammler distribution is an empirical distribution to describe particle sizes, proposed by [START_REF] Rosin | The laws governing the fineness of powdered coal[END_REF]. The Rosin-Rammler distribution is expressed as:

              n d d d Y exp 100 (3.71)
where Y d is cumulative mass in % retained on size d, d is the size parameter, n is distribution parameter.

Taking the logarithms two times to remove the exponent gives:

  e d n d n Y d log log log log 100 log log                    (3.72)
Where e is the nature constant. An example is shown in order to test the Rosin-Rammler model. A plot of log [log (100/Y d )] versus logd should give a straight line. The parameters of the Rosin-Rammler distribution, n and d are obtained from the slope of the straight line and the intercept at the horizontal line at Y d = 36.79, respectively. An example is given as follows. 1 9 3 H Table 3-5 andTable 3-

g. Injection types

Before tracking the particles, the particles must be added into the flow domain. In Ansys Fluent, several different types of injection are available to meet different user needs in terms of injecting the particles into the flow domain. The most commonly used injection types are listed as follows (Ansys, 2011a):

• Singleμ one particle is injected

• Groupμ injection of a group of particles

• ωone (only in 3ϊ)μ injection of a group of particles forming a cone

• Surfaceμ injection of a group of particles across the entire surface

• Fileμ specific injection defined by a file

In our case, it is assumed that the sediment is fully developed and homogenous across the whole surface. Hence we most frequently use surface injections.

h. DPM boundary condition at Inlet/Outlet

The particles are tracked through the flow domain. When a particle reaches a physical boundary (e.g., bottom of detention basin) during the trajectory calculation, the interaction between the particle and physical boundary must be processed to represent particle motion and determine the fate of the trajectory. When a particle enters the flow domain at an inlet, the calculation of its trajectory starts. When a particle leaves the flow domain at an outlet, the calculation of its trajectory ends. In Ansys Fluent the boundary condition "escaped" is used at the inlet and outlet for this function.

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 126

i. DPM boundary condition for bed and side wall of the basin

For the boundary condition at the bottom of detention basin, previous CFD modelling research has shown that these boundary treatments are vital for accurate modelling of sediment transport, settling and erosion in stormwater detention basins [START_REF] Stovin | Sedimentation in storage tank structures[END_REF][START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF], 1998;[START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. Two kinds of boundary conditions available in Fluent are often used to deal with the particle trajectory fate when hitting the bottom: trap and reflect.

The Trap boundary condition

This boundary condition terminates the trajectory calculation at the physical boundary. In other words, particles settle out when they arrive at the bed of the basin. This boundary condition excludes the possibility of particle resuspension after hitting the bed and therefore often overestimates sediment removal efficiency in detention basins [START_REF] Stovin | Efficiency prediction for storage chambers using computational fluid dynamics[END_REF].

The Reflect boundary condition

The particle rebounds off the boundary via an elastic or inelastic collision. The striking particle velocity breaks down into normal and tangential components with respect to the collision surface, v in and u in , respectively. It is assumed that these components are reduced after the collision. As shown in 1 9 7 H , 1998). The normal coefficient of restitution defines the amount of momentum in the direction normal to the wall that is retained by the particle after the collision with the boundary. A normal or tangential coefficient of restitution equal to 1 implies that the particle retains all of its normal or tangential momentum (no energy lost) after the rebound (an elastic collision). A normal or tangential coefficient of restitution equal to 0 implies that the particle retains none of its normal or tangential momentum after the rebound (particle energy lost). In Fluent the normal or tangential coefficient of restitution is equal to 1 by default. The reflect boundary condition excludes the possibility of the particle settling out when it arrives at the bed. Therefore, when it is used as the boundary condition at the bed of basin, it often underestimates sediment removal efficiency in sediment transport modelling in a stormwater detention basin [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF][START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF]. In sediment transport modelling the reflect boundary condition is used at the vertical side wall.

Combination bed boundary condition with a fixed threshold

Previous research has shown that none of the available boundary conditions is particularly good at representing sediment settling and erosion process in detention basin modelling. [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] developed a boundary condition for the bed of a basin by combining these two basic boundary conditions (trap and reflect) together with critical bed shear stress (BSS). They then implemented this boundary condition in Fluent as a user defined function (UDF). If the local bed shear stress is less than the critical value, the particle settles out as with trap, otherwise, the particle rebounds off the bed as with reflect. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] used bed turbulent kinetic energy (BTKE) as the threshold in the same way to treat particle trajectory fate when it hits the bed of basin. Using this boundary condition when modelling sediment transport in the basin bed, removal efficiency was often overestimated [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. Another notable drawback with this method is that the simulated sediment distribution shows high levels of disagreement in full scale basins compared to observations. Furthermore, [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] pointed out that this method was only valid for steady flow condition and the prediction was sensitive to the chosen threshold. [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF] argued that this critical value depends on both the characteristics of the basin (shape, roughness) and sediment properties (such as particle size, density, shape, etc.). This implies that it is vital that a suitable threshold is found when using this boundary condition for sediment transport modelling. This threshold is determined based on measurements or CFD simulation by comparing the BSS or BTKE distribution with the observation of sediment distribution at the experimental site.

Combination bed boundary condition with a varying threshold

According to the combination boundary condition with a fixed threshold, the state of the different particles on hitting the basin bed was determined under the same critical value. Obviously, different particles might settle out in different strengths of flow condition (e.g. bed shear stress strength). The results of observation (shown in chapter 4) of the Django Reinhardt detention basin support this general hypothesis. Given the large and heavy particles often settled out upstream near the basin inlet, it may suggest that when representing the nonuniform sediment characteristics, different critical values should be used for different particles. For noncohesive sediment, although there is an argument that bed shear stress may be the main factor driving particle resuspension, many researchers recognize the Shields relationship between dimensionless shear stress (or Shields parameter), τ * (defined in equation (3.77)) and grain Reynolds number, R * , as a more reliable predictor of entrainment. The curve known as the Shields Curve, which is shown in 1 9 8 H Figure 3-24, was proposed by Rouse [START_REF] Vanoni | Sedimentation Engineering, Manuals and Reports on Engineering Practice[END_REF]. The Shields curve [START_REF] Vanoni | Sedimentation Engineering, Manuals and Reports on Engineering Practice[END_REF] can be expressed as equations (3.75)-(3.76), which are very convenient for computer programming.

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 128

           gd p       (3.76)  d s       0 * (3.77)  d u R * *  (3.78)
Where τ 0 is bed shear stress, s is particle specific weight, is fluid specific weight, μ is dynamic viscosity of fluid, g is acceleration of gravity, d is particle diameter, u * is shear velocity, is the kinematic viscosity of fluid.

The critical shear stress, τ c , for a particle with a diameter, d, is then calculated using the following equation:

 d s c c       * (3.79)
Dufresne (2008) used the BTKE (like the BSS) as the boundary condition threshold to determine whether particles settled out or not. If the local BTKE is larger than the threshold when the particle hits the bed, the particle rebounds, otherwise the particle is deposited. Although not explicitly stated, BTKE is considered to be a function of the bursting process since the bursting process is also associated with fluctuation velocity. ASCE [START_REF] Vanoni | Sedimentation Engineering, Manuals and Reports on Engineering Practice[END_REF] pointed out that turbulence is the most important impact factor in sediment suspension. Using the BTKE threshold to determine particle settling implies that the turbulence factor for sediment suspension may be characterised by the turbulent kinetic energy (TKE). It is easier for the particle to settle out under weak flow turbulence condition. The BTKE is calculated by equation (3.80) according to the turbulent kinetic energy, k, in the first cell near the bed [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF].

0    n k (3.80)
The threshold used by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] for the pilot basin is between 1.0e-4 m 2 /s 2 and 3.0e-4 m 2 /s 2 . The BTKE threshold is determined by comparing the simulation results and the observed deposit zone. This method makes it difficult to determine the threshold for predicting sediment transport for the cases where no observations are available. The preliminary simulation results from the Django Reinhardt detention basin showed that the BTKE threshold is between 3e-5 m 2 /s 2 and 5e-5 m 2 /s 2 (Yan et al., 2010). It differs from the threshold used by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] in a small scale stormwater detention basin. Like the Shields curve for BSS, this may imply that the BTKE threshold for deposition depends on sediment characteristics. A formula has been proposed to provide a more convenient method for determining the BTKE threshold which takes the particle characteristics into account,. This formula is expressed as (Yan et al., 2011(Yan et al., , 2012)):

2 s v k c   (3.81)
Where k c is the BTKE threshold; v s is the particle settling velocity; is an adjustment coefficient that includes the unknown factors (e.g. concentration, particle shape, energy transferring rate, collision effects, etc.). This formula is based on the following assumptions:  Flow turbulence is an important factor for sediment suspension [START_REF] Vanoni | Sedimentation Engineering, Manuals and Reports on Engineering Practice[END_REF];  Bed turbulent kinetic energy distribution can be used to estimate the deposition zone in the same way as bed shear stress [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF];  The turbulence factor for sediment suspension may be characterised by the turbulent kinetic energy with a threshold. For a given particle, if the local turbulent kinetic energy exceeds the threshold, the particle cannot settle out, otherwise the particle settles out;  It is assumed that particle settling velocity can represent all other particle properties (such as density, size, shape, concentration, etc.) because settling velocity depends on all the other properties [START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF].

This formula considers not only the hydraulic condition, but also the properties of sediment. Thisformula makes it possible to estimate the BTKE threshold using sediment properties. The BTKE threshold does not need to be determined by comparing the simulated results with the observation sediment zone before performing the sediment transport simulation. It is therefore theoretically useful for sediment transport modelling under the unsteady flow conditions which often occur in real systems.

These combination boundary conditions were implemented using UDFs. The UDFs were coded with computer language C and compiled, then hooked into Fluent as bed boundary conditions for sediment transport modelling using a DPM model. An example of a UDF combination bed boundary condition is presented in appendix A.

Bed boundary conditions for dynamic sedimentation processes under unsteady flow condition

Previous research into the modelling of sediment transport in stormwater detention basins using the Euler-Lagrange approach have often been carried out in steady flow in an uncoupled way (also known as one-way coupling, as detailed in the next section). The modelling of particle trajectories makes sense when the flow condition and sediment discharge are stable. Furthermore, although not expressed explicitly, using the combination of bed boundary condition with threshold BSS or BTKE under steady state flow condition only makes it possible to represent whether particles settle out or not. It cannot represent the dynamic entrainment process (erosion) when the flow conditions change over time (e.g., if the shear stress or turbulence increases, etc.). That is why with this method, the model prediction often overestimates removal efficiency even for high inflow rates in scale basins [START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. In order to accurately model the dynamic sedimentation and resuspension phenomena, a new approach which makes it possible to represent the dynamic settling and entrainment of deposit under unsteady flow conditions in two-way coupling with DPM is proposed. The the approach is shown in the diagram in 1 9 9 H Figure 3-25.

Figure 3-25 Diagram of dynamic sedimentation and bed load entrainment under unsteady flow conditions

The particles in contact with the bed during the particle tracking process under unsteady conditions are processed as follows. At the grain scale, two sediment states are clearly distinguished at the moment t: it is either suspended away from the bed or it settles out as deposit. Depending on the state at the moment t, the states of particles at the moment t+Δt may be different (suspension or deposit), as well as the treatment for the particle after hitting the bed. The treatment approach for particles shown in 2 0 0 H Figure 3-25 is described as follows:

Condition A: For those particles in motion at the moment t: there are two possible states at the moment t+Δt, either settled out as deposit (condition A1 in 2 0 1 H or continuing to move as suspended load or bed load after contact with the bottom (condition A2 in 2 0 2 H . In the present investigation, determining the state of the particle after contact with the bottom is either based on the widely acceptable parameter bed shear stress (BSS) or bed turbulent kinetic energy (BTKE). If local BSS or BTKE values are lower than the thresholds, the particle settles down as deposit, or else it continues to move. A threshold can be specified for all different particles (e.g., BSS = 0.03 Pa or BTKE = 0.0002 m 2 /s 2 for a scale basin according to [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] or different thresholds can also be specified for different particles, for example using Shields curves (dimensionless shear stress) to calculate a bed shear stress threshold according to the particle characteristics . Equations (3.75)-( 3.76) show a set of fitted formula of the Shields curve.

BTKE threshold can also be calculated from equation (3.81). The settling velocity can be estimated using equations (3.82) and (3.83) [START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF]:

    1 0139 . 0 1 8 5 . 0 3 * s    D d v  (3.82)
where v s is particle settling velocity (m/s), is the kinematic viscosity of water (m 2 /s) , D * is the dimensionless particle diameter (-).

Condition A1: If the particle settles down from motion when it comes into contact with the bed, the available boundary condition 'trap' should not be applied as it will end the particle trajectory calculation. Instead, the velocity and the forces associated with particle movement should be adjusted so it remains as deposit but the trajectory tracking calculation continues. In this way the deposit can be entrained if flow conditions change.

Condition A2: If the particle continues to move after comine into contact with the bed, a variant 'reflect' boundary condition is applied (the particle rebounds with a certain velocity and returns to the flow as suspended load or bed load). This makes it possible to take into account energy losses due to friction at the bottom through the restitution normal coefficient e and tangential friction coefficients f. By default, both e and f are equal to 1. This implies that the resistance force is neglected. A value ranging from 0-1 should be used to account for friction resistance from the bed. An empirical model describing the restitution coefficient and tangential friction resistance coefficient has been proposed by Nino and Garcia (1998) as:

* 84 . 4 84 . 0    e
and f = 0.73. In the present investigation, both the value of 1 and the empirical model are tested to determine rebound particle velocity. Since the particle is dragged by the near bed flow, it is assumed that the entrained particle follows the same longitudinal direction as the fluid flow.

Condition B:

The particle settled at time t can be entrained as bed load or suspension at the moment t+Δt, flow conditions permitting. The local shear stress is compared to threshold stress obtained from the Shields curve (equations (3.75)-(3.76)) according to the particle characteristics. If the local shear stress exceeds the threshold, the particle is entrained (condition B2 in 2 0 3 H Figure 3-25); otherwise it remains in the same state (condition B2 in 2 0 4 H . Similarly, the BTKE is also used as the entrainment boundary condition. The BKTE threshold is estimated using the proposed formula (3.81).

Condition B1:

The particle remains in the same location as deposit.

Condition B2: As for the entrained particle, it is necessary to specify its initial velocity (magnitude and direction) after entrainment in order to continue tracking its trajectory. Several studies were conducted to investigate the bed load movement of the individual particle [START_REF] Bridge | Bed load grain velocities and sediment transport rates[END_REF]Van Rijn, 1984a;[START_REF] Nalpanis | Saltating particles over flat beds[END_REF]Nino and Garcia, 1994;Hu and Hui, 1996;[START_REF] Lajeunesse | Bed load transport in turbulent flow at the grain scale: experiments and modeling[END_REF]. Saltation is the dominant mode of bed load movement. Several authors have characterised saltation height and the length of jump and the jump's initial velocity. In this study, the formulas proposed by Hu and Hui (1996)

         2 . 1 , 1 . 12 2 . 1 , log 7 . 3 3 . 12 * * * * *    u u u d For rough bed (3.84)          2 . 1 , 1 . 3 2 . 1 , log 5 . 4 2 . 3 * * * * *    u u v d
For smooth and rough bed (3.85) Where: u d and v d are the tangential and normal velocity components for the particle at the hitting surface respectively (m/s), u * = (τ 0 / ρ) 0.5 is the shear velocity (m/s), τ * is the dimensionless shear stress (-), τ 0 is the local shear stress.

Simple estimations of initial entrainment velocity component, as proposed by Van Rijn (1984a) were also tested:

* 2u u d  (3.86) * 2u v d  (3.87)
Regarding the particle velocity direction, since the particle is dragged by the near bed flow, it is reasonable to assume that the entrained particle follows the same longitudinal direction as the fluid flow.

The proposed approach for dynamic sedimentation and resuspension was implemented using the UDF in C language. The UDF is compiled and hooked into Fluent as a bed boundary condition of basins under unsteady DPM modelling in two-way coupling. An example of a UDF for this proposed approach is presented in appendix B. For the Euler-Lagrange approach, Fluent offers two ways of coupling the flow and discrete phase: uncoupled and coupled DPM modelling.

One-way coupling

With the uncoupled approach (also known as one-way coupling), the discrete phase patterns can be predicted based on a fixed continuous phase flow field, in which the effects of the discrete phase on the continuous phase are not taken into account. The scheme is shown in

Two-way coupling

In the coupled approach (also known as two-way coupling), the continuous phase and discrete phase interact with each other. It means that influence of the discrete phase on the continuum phase is taken into consideration. The two-way coupling is accomplished by alternately solving the discrete and continuous phase equations until the solutions in both phases stop changing (see 2 0 6 H . The interphase exchange of heat, mass, and momentum from the particle to the continuous phase is depicted qualitatively in 2 0 7 H Figure 3-27. The influence from discrete phase to continuum phase is performed by means of integrating the source terms in the continuous phase. The mass exchange from the discrete phase to the continuous phase is computed in Fluent simply as:

0 , 0 , c p p p m m m M    (3.88)
Where ∆m is the mass lost in the control cell, m p,0 is the initial mass of particle. The momentum transfer from the continuous phase to the discrete phase is computed in Fluent by the following equation when it passes through each control volume (Ansys, 2011b).

  

             t m F u

Conclusion of Chapter 3

The objective of this chapter has been to introduce the materials and methods used in our investigation. The experimental site has been described briefly and experimental methods are also introduced. Another important part of this chapter is the numerical method used for fluid flow and sediment transport simulation in stormwater detention basins.

Regarding the solid phase modelling, after comparison between the Euler-Euler and Euler-Lagrange approach, it was decided to choose the Euler -Lagrange approach to model sediment transport in the stormwater basin.

One of the most important elements in sediment transport modelling using DPM is the boundary condition treatment for the basin bed. There is no general model available for this purpose and we have therefore had to develop the appropriate boundary condition. Both the bed shear stress (BSS) and bed turbulent kinetic energy (BTKE) for boundary condition were tested in this investigation. A new formula has been proposed to more easily estimate the BTKE threshold for different sediments.

In order to represent dynamic sediment transport, settling and entrainment in detention basins under unsteady flow conditions, a new method has been developed to deal with dynamic interactions, implemented using the UDF in Fluent for detention basins.

To account for the flow turbulence effect on the tracked particles, a stochastic method was used based on the discrete random walk model (DRWM). The influence of the parameters (Lagrangian constant time scale, C L ) of DRWM will be tested both in steady state conditions and unsteady state conditions.

Chapter 4 Sediment transport under steady state conditions

Introduction

This chapter aims to present i) the analysis of accumulated sediment in order to highlight the correlation between sediment characteristics and distribution and the hydrodynamic behaviour of the Django Reinhardt stormwater detention basin and ii) the simulated results for sediment transport and removal efficiency in both small-scale detention basins and full-scale detention basins under steady state conditions. The discussion will focus on the evaluation of the developed methods and models. This chapter is structured as follows:

 The presentation of the results related to accumulated sediment spatial distribution and physical characteristics in the full-scale basin,  Highlighting the correlation between the spatial distribution of the sediment's physical characteristics (grain size, density, organic matter content) and the hydrodynamic behaviour of the full scale basin.  The preliminary 3D modelling study of sediment transport with DPM in a full-scale detention basin in order to test the bed boundary conditions derived from literature, particularly fixed BSS (bed shear stress) and BTKE (bed turbulent kinetic energy) thresholds.  The application of the new bed boundary conditions in order to represent the interaction between particles and the beds of both small and full-scale basins under steady flow conditions, using DPM.  The application of the proposed methodology and CFD models in order to simulate dynamic sediment transport, deposition and erosion in the small-scale detention basin only, under unsteady flow conditions, using DPM .

Accumulated sediment analysis

Due to the lack of appropriate data (in term of velocity field, shear stress distribution, Residence Time Distribution, turbulence quantities, etc.) to validate both the hydrodynamic and solid transport models, the spatial distribution of sediment and its physical characteristics were analysed in order to highlight the correlation between the spatial distribution of the sediment and the hydrodynamic behaviour of the basin. Indeed, in the present study it was very difficult to obtain these types of hydrodynamic measurements due to the size of basin, the safety concerns during storm events, etc. Using this procedure (the use of sediment spatial distribution and characteristics to check hydrodynamic behaviour), the hydrodynamic modelling is assumed to be implicitly verified. This means sediment transport modelling can be done using verified hydrodynamic numerical options (turbulence models, boundary conditions, velocity field, shear stress distribution, etc.).

Large quantities of sediment have accumulated in the detention basin since its rehabilitation in 2004 (see The sediment is spread over a large area in the basin. The accumulated sediment in the basin has been seen to affect particulate pollutant removal efficiency due to the effects of erosion or bed roughness. After the basin was cleaned in 2006, efficiency was high. Four measurements of the corresponding total suspended solids (TSS) mass loads taken in June to September 2006 showed efficiencies of 93%-94 %. However, as the basin was filled with sediment the efficiency decreased to a mean value of 57 % with usual values of between 33 % and 75 % [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF]Gonzalez-Merchan, 2012). Hence a thorough understanding of the solids transport processes in the basin is important to improve design with respect to removal efficiency. Furthermore, data is also needed tovalidate the simulated sediment transport results. In order to better understand and explore the spatial characteristics of the accumulated sediment in Django Reinhardt detention basin, a field measurement of accumulated sediment was carried out on April 14 2011. The profile of the preferential sediment zone and discrete point sediment thickness were measured. The measurement points were located at a distance of 5m for the preferential sediment zone (left part of basin, The sampling process and methods used for analysis were presented in chapter 3. Generally, the heavier and larger particles often settle out in the furthest upstream. Hence, the larger particles were observed near the basin inlet. The silty deposit was observed near the side of the dry channel (see 2 2 0 H , maybe due to sediment transport during the dry period. More details are presented in Table 4-1, 2 2 1 H 2 2 In Table 4-1 the second column shows the weight fractions for all samples for sieving diameters of less than 80 µm. It was observed that the fractions in samples P04, P10 and P11 were much smaller than those from the rest of the samples (<0.5%-17% against 59% -93%) and the particle sizes were significantly larger (sample point P11 was not measured by laser diffraction analysis due to its coarseness). According to the weight fraction of less than 80 µm, the particles can be categorised in three groups: the coarse group from samples P11, P04 and P10; the median group from samples P03, P06, P01 and P02; and the finer group from samples P05, P07, P08 and P09. The significant difference between the coarse group and the other groups is due to the location of these samples, close to the basin inlet (see 2 2 7 H Figure 45) and generally the coarse particles settle out faster due to the high settling velocity. The particle size characteristics of sample points P05, P08 and P09 were all finer than those of P01, which again was finer than those of P03, P04 and P10. In short, the deposited particles gradually became finer the further the distance from the detention basin inlet [START_REF] Kayhanian | Characteristics of road sediment fractionated particles captured from paved surfaces, surface run-off and detention basins[END_REF]. According to this assumption, the finer mass fraction of sample P04 should be larger than that of P10. However, actually the opposite is true. The fraction of sample P04 (4%) is less than that of P10 (17%) according to the measurement. A similar result was also observed for P07, which is closer to the inlet than many other samples such as P05. Hence, hydrodynamic behaviour may explain those differences as demonstrated in the hydrodynamic simulations and the correlation between the hydrodynamics and the spatial distribution of the sediment's physical characteristics.

In Table 4-1 the particle size values (d 10 , d 50 and d 90 ) are the mean values of triple measurements of laser diffraction analysis (given as volume percentages). The values in brackets are from the measurements without ultrasound, in which the particle size values were slightly higher for all the measured samples, except for sample point P09. Here, the values were significantly higher (4-7 times the values with ultrasound). The sediment sample from sample point P09 was significantly drier than the other samples on which the particle size distribution was measured, either with and without ultrasound (around 20% water content compared to around 40%), suggesting that this had an effect on the measurements without ultrasound.

The results for the measurements with ultrasound generally varied little between the three measurements for the individual points with standard deviation on the particle size values of 5-10% on average. However, a few of the d 90 measurements had standard deviations of 30%. Without ultrasound, the picture was the same except for sample point P09, which yielded standard deviations of 45% on the d 50 and 21% on the d 10 particle size value.

The results correspond well to the particle size distributions found in core sediment samples by [START_REF] Jacopin | Characterization and Settling of Solids in an Open, Grassed, Stormwater Sewer Network Detention Basin[END_REF] in a grassed stormwater detention basin similar to the Django Reinhardt detention basin. In sediment core samples taken more than 175 m from the inlet, the fraction of particles less than 100 µm found was 73%-79% and the d 10 , d 50 and d 90 were 4-5, 37-40 and 230-320µm, respectively. These values are similar to those obtained in this study, except for the "odd" measurement without ultrasound at sample point P09 and the three coarse samples (P04, P10 and P11).

However, particle size distribution is somewhat different from previous measurements taken in the basin. [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] measured particle size distribution using sediment traps, and Becouze-Lareure (2010) and Sebastian (2011) measured some particle characteristics using samples from the inlet. These experiments showed d 10 values of 8-12µm (based on four different rain events) and d 50 values of 49-117 µm (based on seven different rain events). This is in between the larger values of sampling points P04, P10 and P11 and the smaller values of the rest of the sample points found in this study (disregarding the measurement of sample point P09 without ultrasound). The difference in the measurement methods and sampling locations may be responsible for this difference. Indeed, previous measurements [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF][START_REF] Becouze-Lareure | Caractérisation et estimation des flux de substances prioritaires dans les rejets urbains par temps de pluie sur deux bassins versants expérimentaux[END_REF][START_REF] Sebastian | Assessment of chemical and microbial hazards in a full-scale stormwater detention basin: Their characterization, toxicity and fate[END_REF] were performed directly on the runoff water or water collected from sediment traps, adding it to the filtrated tap water. If this does not necessarily explain the differences, either the fractioning of the sediment within the basin or a change in the particle size distribution of the sediment should account forthe difference. However, one does not preclude the other.

Particle density and organic matter content

The density of each sieved fraction was measured for samples P03 and P04, and the results can be seen in 2 2 8 H Figure 4-9 It shows that for the fractions of sieving diameters larger than 0.08 mm, the density at sample point P04 was close to that of sand (around 2600 kg/m 3 [START_REF] Kayhanian | Utility of Suspended Solid Measurements for Storm-Water Runoff Treatment[END_REF]), while the density of the fraction of sieving diameters less than 0.08 mm was somewhat lower. This was also the trend in the measurements from the sample point P03, although it was not so pronounced. The results are based on one measurement, but the uncertainty of the method was very low with standard deviations of less than 0.2 % of the mean value based on the triple measurement of one sample.

For the rest of the samples, only the density of the fraction of sieving diameters of less than 0.08 mm was measured. These results can be seen in 2 2 9 H Figure 4-10 which also shows the organic matter content of the whole samples. As the figure shows, the density of the finest fraction was between around 2250 kg/m 3 and 2500 kg/m 3 . In the three coarsest samples (P04, P10 and P11), the organic matter content was low compared to the rest of the samples, in which it was close to 15%. This value is almost identical to the organic matter content found in the core sediment samples in the previously mentioned study by [START_REF] Jacopin | Characterization and Settling of Solids in an Open, Grassed, Stormwater Sewer Network Detention Basin[END_REF].

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 145 In general, the measured densities of this study are higher compared to the results found in the literature (Jacobin et al., 1999;[START_REF] Kayhanian | Characteristics of road sediment fractionated particles captured from paved surfaces, surface run-off and detention basins[END_REF]. Jacobin et al. Since it has not been possible to obtain the actual particle density from the storm event, the data on physical sediment characteristics obtained from the experiments in this study and previous findings for the basin were used to input particle properties as realistically as possible in the CFD model and to evaluate the simulated results. Hence, for the purposes of simplicity, just three different densities 1700, 2100 and 2400 kg/m 3 were tested for sediment transport modelling in this study.

Preliminary 3D modelling of the full-scale Django Reinhardt detention basin

Having selected the Euler-Lagrange approach (DPM), the first stage of the study tested previous research results from studies carried out on small-scale detention basins or similar research studies. In terms of sediment transport modelling using DPM in stormwater detention basins, the most important aspect is the boundary condition for processing the interaction between the particles and the bed of the basin during the sedimentation /erosion processes. A preliminary meshing test was carried out by Lipeme [START_REF] Kouyi | CFD modeling of flow in a large stormwater detention and settling basin[END_REF]. The hexahedral elements cell was satisfactory in this case. Thus the hexahedral element cell is used. Three different scale meshes (650000, 850000, and 1000000) were established for the independent mesh test. Preliminary simulations revealed a convergence issue with the coarse mesh, and the median and fine meshes showed no great difference while comparing flow pattern and velocity field. The median mesh was selected for all simulations to balance computational time and accuracy. The mesh sizes are variable due to the complex geometry of the basin, balancing the cell numbers and numerical modelling requirements. The mesh had a height of around 2.5cm near to the bed, increasing to 10cm near the free surface. The max xy cell measurements were 0.4m x 0.4m. The geometry model and some of the meshing details are shown in Preliminary simulation tests indicated that it is very difficult to simulate a complete storm event for hydrodynamics and sediment transport due to the complexity of the real basin and the limited computational hardware resources available in our laboratory. Therefore, steady condition simulations were performed for this basin. As described in the 'experimental site' section in chapter 3. Characterising flow pattern by water depth against inflow rate shows a transformed 'ε'-shape curve for the storm events (Yan et al., 2011) due to the retention by the inner detention wall and the limited maximum outflow rate controlled by a hydragate at the outlet (the outflow rate against the water depth h2 is shown in 4-2 were selected as the representative flow rates for steady flow simulation. It is thought that the free surface can be approximated as a plane wall. This reduces the computational time required because there is no need to capture the surface using VOF or other models. The inlet velocity is used for the inlet boundary condition. The three orifices and overflow weir are set as pressure outlet boundary. The free surface is treated as free-slip wall boundary without consideration of friction of air above the free surface.

Correlation between hydrodynamic behaviour and the spatial distribution of the sediment's physical characteristics

Three inflow rates were usedfor the fluid flow simulation. In terms of the full-scale detention basin, it is difficult to measure field flow parameters such velocity distribution due to the large domain of the basin, the high cost of the sensors and management difficulties. The hydraulic monitoring data available are the water depths in three locations inside the basin (h1, h2 and h3, see 2 3 8 H and the inflow and outflow rates with a time step of two minutes. With a steady state simulation, the inflow rate and outflow rate are balanced after convergence, thus the flow rates cannot be used for validation. The free surface was treated as a free slip wall, i.e. the water depth is fixed and the monitoring water was used to determine the level of free surface. Therefore, the water depth data cannot be used for validation, either.

In our research, the hydraulic performance was evaluated in relation to the spatial distribution of the sediment characteristics.

The analysis is based on the following assumptions:

 Sediment settles out in the low bed shear stress zones and low velocity zone, as found by numerous researchers (e.g. Stovin and Saul, 2008).  When particles settle due to gravity, coarse particles generally settle faster than smaller ones (assuming that their density is identical and the influence of particle shape is disregarded) due to the higher settling velocity. (see 2 4 0 H , with lower BSS corresponding to higher accumulated sediment depth. In terms of the simulated results for the lower BSS zone close to the overflow weir (downstream), the deposit depth is thin. This is because the majority of sediment settles upstream. For another low BSS zone near the inlet (upstream), thin but coarse sediment was sometimes observed. This is because this low BSS zone is so close to the inlet flow jet that the sediment passes directly over this zone. There is is speculateation that just a small quantity of sediment settles in this zone. In fact, this zone is the downstream zoneaccording to the flow pattern analysis. This is one reason why so little sediment accumulates in this zone. For the higher BSS zone (>0.1 Pa, white zone in For samples P01 and P02 near the end of the flow pathway, the percentage of the fine fraction is a little lower than samples P05, P07, P08 and P09 where are also at the end of the flow pathway because some of the sediment at P1and P2 comes from the upstream pathway, as for P6 and P03. sediment depth is inversally proportional to streamline density. As pointed out by [START_REF] Stovin | Sedimentation in storage tank structures[END_REF], the final pattern of sediment deposition depended not only on the velocity distribution, but also on the supply of sediment. H Figure 4-18, shows that few streamlines arrive at locations P9 and P7, so few fine particles can arrive at these locations. This may explain why the deposit depth is thin at these locations. A lot of streamlines reach the centre of basin and are caught by the flow recirculation and therefore settle out in the region.

The flow pattern of transport obtained from the simulation result can be accurately displayed in the real basin above the accumulated sediment distribution (shown in 2 4 8 H , and seem to be as expected. [4][5][START_REF]References[END_REF][7][8][9][10][11][12][13][14][15][16][17][18][19] which suggest the sediment had accumulated for about one year and six years respectively, it is speculated that there may be a main flow pattern in the basin due to the extremely similar sediment distribution in this basin. Based on the analysis above comparing observations, with the measurement of sediment characteristics (deposit zone, sediment depth spatial distribution, and particle size spatial distribution) and simulation results (especially, the BSS, velocity distribution and flow pattern), it could be hypothesised that the flow pattern for case two is the right main flow pattern for the basin. This would be logical because, as previously stated, the maximum outflow rate is limited to 0.35m 3 /s by the hydraulic gate. the threshold of 4.5e-5 m2 /s 2 . It shows a very similar distribution profile compared to the low BSS distribution. This may imply that the BTKE has a similar function to BSS as an indicator of deposition and deposition entrainment. In fact, [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] used the constant BTKE as the threshold for the bed boundary condition in a sediment transport simulation using the DPM approach. The threshold is determined by the comparing the observation sediment zone and the simulated BTKE result. However, the threshold is different, with 4.5e-5 m 2 /s 2 in our case compared to the value of 1e-4-3e-4 m 2 /s 2 observed by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. It seems that the value is dependent on sediment characteristics. ). Hence, it seems that the inflow jet changes in a small sector zone near the inlet according to variations in the inflow. Figure 4-22 shows that the inflow jet zone has dense streamlines; hence theoretically the sediment does not settle much in this zone. This analysis is consistent with observation and measurement. Almost no accumulated sediment can be observed in this sector zone near the inlet of the basin (see 2 6 1 H Figure 4-15a and2 6 2 H Figure 4-15c).

Based on the analysis comparing observation, measurement and simulation, it was found that hydraulic simulations largely agree with the measured data. This may imply that the simplification of geometry and flow conditions (inflow rates, boundary conditions, etc.) is reasonable and acceptable. It also provides an alternative method for evaluating CFD modelling for full scale stormwater detention basins since it is difficult to obtain hydraulic measurement data. Case 2 was used to carry out the bed roughness influence test and sediment transport modelling, since it was most similar to the sediment spatial distribution and can therefore be considered as representing the main flow pattern in this basin.

Bed roughness influence on vertical bed turbulence kinetic energy profile

The effects of surface roughness on sediment distribution are of great importance as discussed by Papanicolaou et al., (2001). The Django Reinhardt basin is covered with a concrete surface. Sediment has accumulated on the bed of basin, which results in bed surface roughness. BTKE boundary conditions were used for sediment transport modelling and therefore, it was important to evaluate the influence of roughness on the BTKE.

The equivalent grain roughness height was estimated by means of a relationship given by Hager (2010). The modified law of wall was used to model the roughness effects. The method used is described in detail in chapter 3. 2 6 3 H Table 4-4 gives the series of Strickler coefficients, K, and equivalent sand grain roughness height, k s, for concrete [START_REF] Graf | Hydraulique Fluviale: écoulement et phénomènes de transport dans les canaux à géométrie simple (Fluvial Hydraulics: Flow and transport processes in channels with simple geometry)[END_REF]. 4 simulated cases for different bed roughness were performed with the same flow condition configurations of DRB case 2.

Dufresne (2008) showed that the distribution of bed turbulent kinetic energy (BTKE) below a critical value (1.0e-4 -3.0e-4 m 2 /s 2 ) corresponds well with the deposition zone in a pilot basin. Previous work in the Django Reinhardt basin (Yan et al., 2011a) suggested that particle settling velocity (V s measured with protocol VICAS -Torres, 2008) could be used to estimate the critical value to determine the particle state (e.g., deposited or resuspended) based on the assumption that near bed turbulent kinetic energy has a significant influence on the motion of particle close to the bed. In that study, the V 80 (=23.5m/h) settling velocity was used to estimate the critical value using the formula:

k c = v s 2 ,
where k c is the critical turbulent kinetic energy and is a coefficient that includes unknown factors (e.g. concentration, shape of particle, energy transferring rate, collision effect, etc.).

The simulated bed turbulent kinetic energy (BTKE) distributions with different bed surface roughness are shown in the simulations for BTKE distribution with a threshold showed similar outer contours for the preferential sediment zone except at the downstream corner near the over flow weir. This may be due to the fact tat the outer contour was slightly affected by surface roughness. It also shows that using the BTKE with an appropriate critical value makes it possible to identify the preferential sediment outer contour in the full scale detention basin. Out of all cases, Ks1 represents is most similar to observed results for the upstream blank part (shown in Figure 4-25 with trapezoid), while ks4 is most similar to observed results for the central thickness of sediment (shown in Figure 4-25 with a polygon). Assuming that a low BTKE corresponds to the thickest sediment layer, this might suggest that the sand grain roughness height for a sediment layer would be higher than that for bare concrete. There were clear differences in the outer contour zones, but the overall shape was similar. For example, all the cases showed almost the same low value BTKE zone in front of orifice 1 (see ). This might be the reason for the difference between the vertical TKE profile at point 2 and that at the other points. In fact, more vertical secondary currents above the gutter were observed when observing the gutter stream through the vertical plane. These were sensitive to the surface roughness.

The research results on the effect of roughness on BTKE suggest that modelling sediment transport in real storm water detention basin should take into account the bed surface roughness effects. The aim of sediment transport modelling in detention basins is to predict the removal efficiency and sediment deposition zones in the basins. The removal efficiency predictions aim to find a way of improving pollutant abatement and of protecting receiving water bodies. The prediction of sediment deposition zones is done in order to create better strategies for basin management and maintenance, such as finding an appropriate frequency for deposit cleaning. This makes sense because the accumulated sediment affects removal efficiency: too much sediment accumulation reduces removal efficiency due to the effects of erosion.

As mentioned in chapter 2, in terms of sediment transport modelling for detention basins using DPM, the most important element is the bed boundary condition treatment for a particle arriving on the bed. Previous investigations have been carried out in small scale detention basins [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF][START_REF] Stovin | A computational fluid dynamics (CFD) particle tracking approach to efficiency prediction[END_REF][START_REF] Chebbo | A stochastic approach to modeling solid transport in settling tanks[END_REF][START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]Dufresne et al., 2009;[START_REF] Zhang | 3D numerical modeling of hydrodynamic flow, sediment deposition and transport in stormwater ponds and alluvial channels[END_REF][START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. [START_REF] Chebbo | A stochastic approach to modeling solid transport in settling tanks[END_REF] have used a stochastic approach, and other researchers have used one BSS threshold as the boundary condition in order to determine the particle settling state. For all kinds of particles, if the local BSS is larger than the given threshold, the particles rebound, otherwise, the particles settle. [START_REF] Stovin | The prediction of sediment deposition in storage chamber based on laboratory observations and numerical simulation[END_REF], [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] and [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] said that the threshold for a scale basin is in the range of 0.03-0.05Pa, while [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] used Shields curve to estimate the BSS according to particle properties (density and diameter). Dufresne ( 2008) also used the BTKE as a boundary condition, and the critical value used for the scale basin was 1.0e-4 ~3.0e-4 m 2 /s 2 .

The final stage of the research would focus on the full scale basin, and the first step was to verify the suitability of available boundary conditions for the full scale basin.

Both the constant BSS and the constant BTKE were tested in the Django Reinhardt basin. A critical value of 0.03Pa for the BSS, as used by [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] and [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], was applied into the full scale basin. A value of 0.01Pa was also tested by comparing obseved sediment distribution and the simulated BSS distribution (see . For the BTKE, a value of 4.5e-5 m 2 /s 2 was chosen after comparing the sediment distribution with the BTKE distribution in case 2. The BSS was estimated using the Shields curve and then tested. For the critical BSS and BTKE values, uniform particles sizes were used. These were based on the measurements taken by [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] and Becouze-Lareure (2010) using samples taken from the inlet and inside the basin with sediment traps during the storm events. There was some deviation between these measurements and the measurements performed for this study using samples from the accumulated deposits. The differences may be due to differences in sampling methods and the evolution of deposits in the basin. For this study, the campaign data used by [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] and Becouze-Lareure (2010) were used. The results from [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] and Becouze-Lareure (2010), were combined to give fine, median and coarse sizes (10 m, 6η m, 100 m). These were chosen to perform simulations with critical BSS and BTKE, and a series of means particle distributions were chosen for the boundary conditions from the Shields curve. The particles sizes came from campaign measurement for a storm event (31/5/2007) collected using 15 sediment traps [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF]. The data are given in 2 7 2 H Table 45It should be noted that in D 10 here means the volume percentage, not the weight percentage. Simulations were carried out for densities of 2400 kg/m 3 and 2100 kg/m 3 based on the deposit measurement and 1700 kg/m 3 , from the literature [START_REF] Ashley | Solids in sewers: characteristics effects and control of sewer solids and associated pollutants[END_REF] for density sensitivity test.

In order to account for turbulent dispersion effect, a stochastic model DRWM was used. The time scale factors C L of 0.15 (by default in Fluent) and 2 (chosen by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] that reflected the deposition zones in a scale basin better) were tested.

Removal efficiency and deposition zones

The simulated removal efficiencies of the basin are shown in 2 7 4 H Table 4-6 andTable 4-7, which show that when using a time scale factor of 0.15, all the tested boundary conditions captured all 100 µm particles and practically all 65 µm particles. For the 10 µm particles, the efficiencies were only slightly higher for 2400 kg /m 3 than for 1700 kg /m 3 particles. The efficiency of the BTKE boundary condition was in between the two critical BSS boundary conditions, for which a τ c of 0.03 Pa gave the largest and 0.01 Pa the lowest efficiency. A density of 2100 kg /m 3 was used for simulation with the Shields boundary condition. And its simulated efficiency was 97.37% (with C L =2).

These results, however, are not surprising, as the bed shear stress distribution and the bed turbulent kinetic energy distribution were very similar. The possible sedimentation zones with the BTKE boundary conditions were also larger than the critical BSS boundary conditions when using a τ c of 0.01 Pa and smaller when using a τ c of 0.03 Pa (data not shown here). In fact, the critical BTKE and critical BSS have a similar distribution (see Figure 4-15b and Figure 4-20), hence, the critical BTKE and the critical BSS boundary conditions are very similar, and the results depend on the BSS and BTKE thresholds. Changing the time scale factor from 0.15 to 2 significantly increased the efficiency of the basin for the 10 µm particles. This was probably due to the increased time spent in turbulent fluctuations, which made more particles travel away from the general flow direction. This also caused a small amount of 65 µm and 100 µm particles to escape the basin. It implies that the removal efficiency for small particles is more sensitive to the C L than that of large particles.

As mentioned in section 2 7 6 H 4.2, four storm events in June to September 2006 showed efficiencies of 93-94 % after sediment cleaning [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF], and annual average of 57 % (2004-2010) gave normal values of between 33 % and 75 % (Gonzalez-Merchan, 2012). The lower annual average efficiency is caused by the erosion of accumulated deposits. When compared to the annual average efficiency, the modelled efficiency is much higher, but the mean modelled efficiency is close to single event efficiency measured after basin cleaning. This is reasonable because in the model, the basin is assumed to be empty and the effect of erosion is not included. However, it is not possible to determine the best simulation because the cases were modelled using steady conditions corresponding to conditions at one specific moment, while event efficiency or annual efficiency is calculated from one or many storm events.

In terms of settling zones, the boundary conditions also acted in very similar ways. From 2 7 7 H Figure 4-28 the settling zones when using BTKE boundary conditions are depicted, both for the results using a time scale factor of 0.15 and 2. The figures were ctreated by plotting the final location of each particle settled down. Only the results using particle diameters of 10 and 100 µm are shown, as the sedimentation zones of simulations done using particle sizes of 65 µm merely showed an intermediary stage between the two.

As can be seen from 2 7 8 H Figure 4-28, increasing the time scale factor increased the distribution of 100 µm particles, expanding the sediment zones. This result, however, was less significant for 10 µm particles, for which there was no deposit in the upper left corner of the basin when using the time scale factor of 2.

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 167 In the simulations, a significant amount of the particles settled in zones close to the inlet, which does not correspond to a significant deposit in the real basin. The discrepancy between the simulated deposit zones and observations may be caused by two reasons: the steady state configuration used in the simulation and limitations in the boundary conditions.

A real storm event is clearly an absolute example of unsteady conditions. The final deposition zones undergo a series of alternative processes of transport, settling and resuspension, so the deposit would probably be picked up after it had settled for the first time and and would move along the flow pathway acted on by the time-dependent effect. But in a simulation under steady conditions, this does not occur because the flow pattern is invariable and so the particle stays in the first location in which it settles. This suggests that more realistic simulations should be performed using unsteady conditions.

Furthermore, the critical BSS or BTKE boundary conditions used for all particles is overestimated in the case of small particles. It is thought that the small particles settled prematurely when transported along the flow pathway because of the use of a single value for BTKE or BSS as a settling boundary condition. Generally, this critical value derives from experimental measurements or simulations done by comparing the sediment zone with measurements or with a simulated BSS/BTKE. In actuality, this value is the upper limit for BSS or BTKE in the distribution zone. That is why in the simulated deposit zone, there is almost no particle settlement in the centre of the basin. All particles settle when they arrive at the edge of the BSS or BTKE zone, as is shown in Figure 4-15 and Figure 4-20, where particles are deposited the upstream in the flow pathway at the low BSS or BTKE zone.

As mentioned in 2 8 0 H Chapter 2, critical BSS for deposition cd is often used in species models as a constant value for special cases. Sometimes due to the lack of measurement data, this value has been used as a calibration parameter. This works sometimes because in a species model, the sediment is treated as continuous phase fraction with a median particle size. This fraction is termed concentration. Concentration combines the behaviours of a group of particles in motion. From the statistic point of view, cd is a statistic mean value for special group of particles, balancing out the higher or lower values of different particles' deposition. This value depends on the characteristics of particles. This may be the reason why there is no a universal cd that can be applied to all sediments. However, this critical value may not be true in the DPM approach. In the DPM approach, sediment is treated as an individual particle. Using a critical value for all the different particles seems to lead to overestimation or underestimation of deposition. The critical value is, in fact, the upper limit for the low BSS or BTKE distribution zone, and should correspond to the largest particles. In the previous experiments, this value was used for all particles [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF][START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]. This is why using the critical BSS or BTKE often leads to overestimation of removal efficiency. Thus, more precise values for different particles should be used.

Taking an estimated BSS from the Shields curve provides different values for different particles, and it works better than a constant BSS in small scale basin with non-cohesive sediment. However, it does not work well in full scale basin, such as in this case. The reason may be because the sediment in this case is more cohesive, and the Shields curve was developed based on experimental data with non-cohesive particles [START_REF] Shields | Anwendung der Ähnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung[END_REF].

Improvement of boundary conditions for sedimentation modelling with DPM

Introduction

As discussed in the previous section, neither the fixed BSS/BTKE values nor the varying BSS calculated from the Shields curve work well in the full scale basin. This means that the main sediment zone in the centre of basin cannot be predicted accurately. It is thought that smaller particles settle prematurely when they arrive at the edge of sediment zone. In fact, this is also observed in a scale basin. It is, therefore, necessary to develop new more appropriate boundary conditions that overcome this drawback.

Turbulence plays an important role in settling and entrainment during the sedimentation processes. Particles settled when the local BTKE is less than a corresponding threshold that depends on the particle properties. This means that large and heavy particles need more turbulent energy to maintain them in a state of suspension. Based on this hypothesis, a new formula was devised to estimate this threshold for different particles according to their settling velocities, which is able to represent all the other properties such as density and size by taking their inner relationships into account. The formula was based on the theory that, since a small particle corresponds to a small BTKE threshold, its transport is likely to be longer and it would probably settle downstream in the flow pathway. In order to apply, this formula needs to be used for non-uniform particle size. This proposed formula was tested first as a boundary condition in a scale basin, then in a full scale basin.

4.4.2 Tests carried out in a small scale basin with a steady state DPM

The proposed formula was tested using the results from experiments carried out in a scale basin by [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], primarily for their simplicity and the availability of experimental data. Steady conditions with an inflow rate of 3L/s were selected for the test. [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], showed that a tetrahedral cell mesh was better than hexahedral for this simulation, since it requires less computational cells as compared to the hexahedral cells. The tetrahedral cell elements were used. Three different scale meshes 10000, 50000 and 80000) were tested for mesh sensitivity. A 50000 tetrahedral cell mesh was then used for all the simulations, to provide the best balance between computational time and accuracy. The mesh is shown in

-33 Comparison of sediment deposits zone between experimental observation and simulated deposit zones using bed boundary condition of fixed BTKE and using the proposed BTKE formula with different C L values

2 8 8 H Table 4-8 shows the experimental and simulated efficiencies. Compared to the experimental results, all the simulation cases overestimate the removal efficiency. The time scale factor C L of DRWM appears to be a positive contribution to efficiency, the larger the C L value, the higher the simulated efficiency. However, the simulated efficiency with the proposed BTKE bed boundary conditions predicts efficiency much better than that with the fixed BTKE, when compared to the experimental data. However, both of them overestimate the removal efficiency. Hence, the proposed BTKE is better than the fixed BTKE. Another advantage of the proposed BTKE method is that it does not need to be compared with observation in order to determine a threshold for the BTKE as is required for fixed BTKE boundary conditions. This could be useful for predicting sediment transport where there is not experimental data or observed data for sediment zones to use as a reference. Due to the scale effect and the more complex conditions in a real detention system, in general, it remains difficult to apply the results obtained from small scale basin to the full scale basin.

The feasibility of the proposed BTKE boundary formula was therefore then tested in the Django Reinhardt basin based on the flow simulation results of DRB case 2.

The non-uniform particle size distribution is presented in Table 4-5, and it is the same as that used for the previous DPM modelling, i.e. it uses Shields curve boundary conditions. The density used was 2100 kg/m 3 . For the purpose of comparison, the fixed BTKE (k c =4.5e-5 m 2 /s 2 ) boundary condition was also simulated with the same configuration. Due to the lack of an appropriate settling formula for estimating a settling velocity in accordance with the sediment properties in a selected sewer system, it was difficult to use a formula to estimate the settling velocity in the detention basin. Furthermore, the available values for settling velocity, as measured with the VICAS protocol, only give the relationship of maximum velocity for values below a certain fraction of mass [START_REF] Chebbo | Vicas protocol: Measurement of TSS settling velocities in urban effluents[END_REF][START_REF] Chebbo | VICAS-An Operating Protocol to Measure the Distributions of Suspended Solid Settling Velocities within Urban Drainage Samples[END_REF]. A clear relationship between settling velocity and particle size has not yet been found. Therefore, an assumption had to be made in order to be able to use the proposed formula (equation (3.81) in 2 9 0 H Chapter 3) to estimate the BTKE corresponding to different sized particles. It was assumed that settling velocity increases with particle size over a certain density.

The measured results from the storm event on 31/05/2007 performed by [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF] were chosen due to the complete nature of the data-set for measured particle sizes and settling velocity results across the 15 sediment trap samples. Within these samples, the particle sizes were measured by the Laser diffraction analysis and settling velocities were measured with the VICAS protocol in laboratory. The non-uniform particle sizes and the corresponding settling velocities are given in Table 4-9. Here V 10 -V 100 are the mean velocity of the 15 sediment samples. In order to estimate the BTKE with the proposed formula (equation (3.81) in 2 9 2 H Chapter 3), a settling velocity was used that corresponded to the particle sizes listed in Table 4-9, for example, particle size d 10 corresponds to settling velocity V 10 . The efficiency from the simulation calculated using fixed BTKE and the proposed calculated BTKE were 99.8% and 98.45%, respectively. It should be noted that in the simulations, some particles were always suspended (reported as incomplete in the simulation results). In the simulated domain, a maximum particle iteration steps of 6e+8 was set for particle tracking. These particles are captured by recirculation and remain in suspension, thus are ultimately considered to have settled as deposits by the programme. The simulated efficiencies were higher than the annual mean efficiency of 57% and the annual range of 33%-75% during 2004-2010(Gonzalez-Merchan, 2012). However, it is close to the mean removal efficiencies of 93%-94% for single storm events after basin cleaning [START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF]. It is thought that this simulation of sediment transport with steady DPM over-predicted efficiency because it did not take the time-dependent effect of erosion into consideration. An unsteady state DPM coupled with unsteady fluid flow simulation should, therefore, be performed.

Conclusions for chapter 4

A comparative analysis of the measured and simulated sediment characteristics spatial distribution and flow shows that there may be a main flow pattern in the Django Reinhardt detention basin. This main flow pattern has a representative inflow rate equal to 0.35 m 3 /s which corresponds to the maximum outflow which is regulated by the hydro-regulator.

Where there is a lack of measured data to validate a flow simulation, the spatial distribution of sediment characteristics may provide an alternative way of checking the flow pattern.

The BTKE distribution has a similar function to BSS distribution in predicting the deposit zones in full scale detention basin. In general, in a zone with low BTKE there is a higher probability that sediment may settle. However, due to a lack of sediment transport information, the method proposed here is unable to describe the build-up of sediment. Sedimentation depends on both the flow conditions and the sediment transport characteristics. Near bed turbulence is influenced by the surface roughness.

It was not possible to predict sediment zones in the real Django Reinhardt basin using fixed BSS/BTKE boundary conditions because using a single threshold for all particle sizes allows small particles to settle too early. Fixed BSS/BTKE boundary conditions overestimate removal efficiency as they do not take the timedependent effect of erosion into consideration. The Shields curve boundary does not work well in full scale basins in sewer systems either. This is because the Shields curve was calculated based on experiments carried out with non-cohesive particles, while particulate pollutants in sewer systems are predominantly made up of cohesive materials.

The proposed formula for calculating the BTKE boundary conditions is capable of identifying the preferred deposit zones in both small scale and full scale detention basins. This proposed method for estimating the BTKE threshold for different particles should be easier to use as it is not necessary to determine the BTKE by comparing it with observation, which is required when using a fixed BSS/BTKE. However, the proposed method for establishing BTKE boundary conditions overestimates predicted efficiency. Sediment transport modelling using a transient DPM clearly shows better simulated results than modelling done using a steady state DPM even when using the same boundary conditions.

Chapter 5 Sediment transport under unsteady conditions

The available bed boundary conditions have only been developed for uncoupled steady DPM modelling. [START_REF] Adamsson | Bed shear stress boundary condition for storage tank sedimentation[END_REF] concluded that these kinds of boundary conditions are suitable for steady flow conditions. These kinds of boundary conditions cannot account for dynamic settling and erosion due to the time-dependent effect (unsteady condition), found in real basin systems. The preliminary testing of full-scale detention basin modelling using DPM suggests that the time-dependent effect should be taken into account by combining unsteady flow simulation with an unsteady DPM approach. A method was therefore developed to represent the dynamic settling and erosion processes by coupling unsteady flow simulation with unsteady DPM. The method was first tested in a small-scale basin. This both reduced the computational time consumed and made it easier to validate the method using the available experimental data.

The method for dynamic sedimentation with DPM was described in chapter 3. Details about the method developed can found in that section.

In this section, the proposed method will be applied to two scale basins from [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF] and [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. A preliminary simulation was performed to evaluate the feasibility of using the method in a pilot basin [START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF], and further model parameters were examined in a transient flow condition (variable flow pattern and variable recirculation in the basin) basin because there is more experimental data available for validation [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF].

Preliminary test in a rectangular basin with permanent recirculation

Model setup

The experiment has already been described in section 4.2. The sediment transport modelling based on the flow simulation results is presented in section 4.4. Since the flow condition is a quasi-steady state, the steady flow condition was used instead of unsteady flow condition. Thus the simulation was configured forsteady flow simulation coupled with unsteady particle tracking. The particle size distribution was defined as Rosin Rammler distribution, as described in section 4.4. A total of 144360 particles, with 10 different sizes, were injected in one injection at the inlet section of the basin. The particle time step is 5 ms, and the maximum number of particle iteration steps was 50000 for each particle time steps. The bed boundary condition for particle dynamic settling and erosion was defined using the method proposed in chapter 3 and implemented using a UDF. Four different deposit conditions were tested, as shown in 2 9 7 H Table 5-1. It should be noted that as it is a preliminary test, this simulation does not model the complete experiment process which lasts for about 20 minutes, since the flow conditions are considered to be quasi-steady.. The simulated efficiencies with different boundary conditions were shown in 3 0 2 H Table 5-2.

Modelling with the bed boundary condition 'trap' largely overestimates the efficiency of sedimentation compared to the experimental data: 88% compared to 33%. Fixed BSS and fixed BTKE also overestimate removal efficiency. However, the overestimation is much lower than with the trap condition. The varying BTKE and varying BSS boundary conditions underestimate removal efficiency. However, varying BTKE most accurately predicts efficiency (close to the lower limit of the uncertainty interval) compared to the other conditions. Furthermore, it is possible to calibrate the coefficient in equation (3.81) to obtain a better fit with the experiment data. Of the four boundary conditions (listed in Table 5-1)3 0 3 , fixed BSS and BTKE need to be determined based on the comparison between the simulation results and the experimental observations. It is unfeasible to use this method in practice as observed data is unavailable. Varying BSS and varying BTKE are determined using formula, so they are easier to use if the sediment properties are available. This simulation test demonstrated that the proposed dynamic sedimentation method is capable of representing sediment transport, settling and entrainment in unsteady flow conditions. It has showed potential capability for modelling sediment transport in detention basin over a complete storm event. The results for varying BTKE and BSS show satisfactory predictions of both deposit zones and removal efficiency. The sediment transport modelling results under unsteady DPM show that both removal efficiency and deposition zones are more accurately predicted than that under steady DPM conditions, as shown in the previous section. This may suggest that the unsteady sediment transport modelling should be used in order to accurately predict the removal efficiency and sediment zones in detention basins.

Preliminary test in a basin with variable inflow jet and recirculation zones

Numerical model setup

The model experiments showed strong turbulent behaviour in the flow field due to the timedependent effect [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] performed unsteady flow simulations and carried out uncoupled steady DPM with every time step flow simulation result, in order to evaluate the influence of unsteady flow on solids settling in stormwater tanks. Varying BSS calculated using the Shields curve was used as the bed boundary condition for DPM. However, this method cannot represent the erosion motion after settlement due to the unsteady flow condition.

Here, we will use the proposed method to represent the dynamic settling and entrainment processes, taking the time-dependent effect into account by coupling unsteady flow with unsteady particle tracking. The computational mesh was established by hexahedral element.

The independent mesh was tested by [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] with a 600000 cell mesh. The mesh is shown in The bed boundary condition used was the proposed dynamic sedimentation method. Under this method, different treatment models were selected for processes A and B, different saltation frictional resistance models and two entrainment initial velocity models were tested.

The turbulent dispersion effect defined by Discrete Random Walk model was also tested, in order to more accurately represent the sediment transport mechanism. As shown in 3 0 7 H Figure 3-25, different boundary conditions can be tested for process A (deposited) and process B (entrainment). Specific condition can be integrated to represent the sedimentation processes.

The different bed boundary setups tested are set out in 3 0 8 H Table 5-4. The bed boundary conditions were implemented using the UDFs presented in chapter 3.

Evolution of sediment transport and spatial distribution

In the physical tank, unsteady behaviour was observed even though the tank was fully symmetrical with constant inflow. Recirculation zones were observed with oscillations from the left to the right-hand side. The oscillation of the inflow stream were periodical with a wave length of about 100s. More details can be found in the paper by [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]. This unsteady behaviour was also confirmed by the unsteady simulation. Since the flow pattern is periodical, thus only the first injection and transport process were simulated, due to the significant computational time and memory required. Space constraints mean the results cannot be presented in their entirety. However, as shown in In short, the newly proposed method has demonstrated its capability to simulate unsteady sediment transport in stormwater detention basins. In the next section, we are going to explore the information from the simulated results.

3 1 8 H Figure 5-10 shows the monitoring particle concentration at the outlet of basin. We can observe that the simulated result shows the instantaneous characteristics of sediment concentration. This result provides a more accurate way of obtaining the sediment concentrations. From the figure, it would seem that the particle concentration of outlet is periodical. The simulated result makes it possible to access all the information about the sediment in the domain. Figure 5-11a shows the simulated deposits spatial distribution. These particles are marked as settled particles. In In fact, by using a specific criteria flag, the simulation results can distinguish particles in different states. The particle mass or volume concentration spatial distribution can be accessed throughout the whole simulated field. Furthermore, the simulation results with DRWM showed more reasonable sediment spatial distribution across the basin. In terms of predicting the deposit zones, this may suggest that sediment transport using unsteady DPM in detention basins should take stochastic modelling into consideration in order to more accurately represent the turbulent dispersion effect. Compared to the experimental observations, cases DPM 6 and DPM 11 appear to offer better levels of agreement for the recirculation zone, the upstream corner zone and the downstream zone. It seems that varying BSS is more accurate than BTKE as the entrainment condition. Cases DPM 9 and DPM 10 seem to over predict the sediment in the middle zone of basin. In cases DPM 9, 10, 11 and 12, the combination of BTKE with BSS is more accurate than BTKE and BTKE for sediment deposition zone prediction. The comparison of cases 9 and 11 shows no major differences for sediment zones across the basin. This may imply that for entrainment condition prediction, BTKE2 and varying BSS are almost the same if the settling condition is BTKE2. Case DPM 8 under predicts the sediment zone, perhaps because C L value is higher than the other cases. Except for case DPM 6, all other cases shows high numbers of suspended particles, this may imply that the BTKE model has high levels of sediment pickup. In the proposed method varying BSS and BTKE have been shown to be adapted for us as both the settling and entrainment conditions. Out of all the boundary condition combinations tested, varying BSS+varying BSS and BTKE2+varying BSS show the best level of agreement compared to the experimental sediment zones. In terms of experimental removal efficiency, three tests were performed according to [START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF] which found overall removal efficiencies of between 83% and 87%. 3 2 9 H Table 5-5 presents the simulated removal efficiency of sediment transport modelling using the proposed method. All the cases except for case DPM 7 without DRWM predicted reasonable removal efficiency. This suggests that turbulent dispersion effect should be taken into account in sediment transport using stochastic modelling such as DRWM. The simulated efficiency is affected by many factors. It seems that efficiency decreases as the C L value for DRWM modelling increases. Out of the four test values, the smallest C L value 0.05 seems to be show a higher level of agreement than the others. However, case3 has a larger C L value but higher levels of efficiency than case 1 with a low C L value. This difference is thought to be down to the impact factor of the number of particles injected. In our simulation 22400 particles were used, but this appeared to be insufficient. More particles were therefore injected for the subsequent simulations. From the simulation results available it would appear that between 44800 and 67200 particles are required for the present study. Cases 2 and 5 would appear to show that taking into consideration particle saltation friction resistance has a slight negative impact on the efficiency. ωases η and 6 show that van Rijn's initial entrainment velocity model has a positive impact on efficiency compared to Hu and Hui's (1996) model.

Removal efficiency

In DPM cases 9, 10, 11, 12, with appropriate particle injection, and the appropriate rebound friction resistance model and initial velocity model, the BTKE and BSS boundary condition accurately predicts removal efficiency, showing 85.02%, 85.18%, 86.06% and 85.83% against the measured range of 83%-87%. However, it should be noted that, theoretically, the proposed method using DPM underestimates removal efficiency because the hiding effect and particle-particle collisions are not taken into consideration in DPM. In the high concentration zones such as the near bed zone where the particles are in a dense state, the low layer particles might be hidden by the upper layer particles due to flow entrainment. Alternatively, the low layer entrained particle may be rejected due to inter-particle collision. However, in the proposed method, the probability of a particle being entrained is the same for all particles regardless of the accumulated layer structure. In the DPM approach, collisions are disregarded in order neglected to save calculation time. The sediment hiding effect should be taken into account to improve this method in future works.

There are a range of different parameters involved in the newly proposed method. Twelve different case studies were conducted to try to determine the optimal values or models for best predicting removal efficiency and sediment deposition zones in detention basin. However, no definitive conclusions could be drawn as the way in which these parameters combine is complex and how they interact is still unclear. More research is needed to further investigate these parameters.

Conclusion of chapter 5

The newly proposed dynamic sedimentation method was tested in two scale basins both under steady and unsteady flow conditions coupled with unsteady state DPM. With the proposed method coupled with the unsteady DPM, the simulated results under steady flow conditions demonstrated more accurate sediment zone prediction compared to steady DPM. Furthermore, the simulated results based on the proposed method under unsteady flow conditions coupled with unsteady DPM can accurately reproduce the evolution of the sediment transport processes in the scale basin. However, the different parameters involved in the proposed method influence the prediction of removal efficiency and sediment deposition zone. The optimal values still needed to be determined by carrying out more tests.

Overall, the proposed dynamic sedimentation method demonstrated its ability to represent the settling and entrainment dynamics under both steady and unsteady flow conditions. Base on the simulation cases and in light of the sediment zone and efficiency predictions obtained, the proposed BTKE boundary is suitable for use as the deposit boundary condition and Shields curve is suitable for use as the entrainment boundary condition in small-scale detention basins for non-cohesive sediment.

Chapter 6 Conclusions and perspectives

This research aims to provide a better understanding and method for the modelling of sediment transport processes in small scale and full scale detention basins. The general conclusions and perspectives are as follows.

General conclusions

Field measurement and observations

Field measurements were performed in order to obtain values for the accumulated spatial distribution and characteristics of sediment in the Django Reinhardt detention basin. 11 sediment samples were collected for and their physical properties analysed. Both Laser diffraction analyse and the wet sieving method were used for particle size distribution analysis. A pycnometer method was used to measure the density of particles.

The main sediment zone is located in the centre of the basin. The main sediment zones have remained similar from 2006 to 2012, but have increased in size and accumulated sediment depth. This implies that a main sediment deposit pattern exists in this basin. Both fine particles and gravel-like particles are present in the detention basin. Particle density was found to be between 2200 kg/m 3 and 2500 kg/m 3 . From the simulated results available, a main flow pattern for the Django Reinhardt detention basin was assumed for further analysis of the comparison between the spatial distribution of measured sediment characteristics and the flow simulations. This main flow pattern had an inflow rate of 0.35 m 3 /s, which corresponds to the maximum outflow rate regulated by the hydro-regulator. Hence, analysis of the spatial distribution and characteristics of sediment may help validate complex flow models.

Numerical Simulation

The simulated flow pattern with an inflow rate of 0.35 m 3 /s showed a good level of agreement with the measured spatial distribution of particle size. Steady flow simulation with inflow rate of 0.35 m 3 /s corresponded to the main flow pattern in the basin. Where there is a lack measured data for validating flow simulations, the spatial distribution of sediment characteristics might be an alternative way of providing a rough evaluation of flow simulation results.

BTKE distribution has a similar function to BSS distribution in predicting the deposit zone for a full scale detention basin. In general, the lower BTKE zones have a higher probability for sediment settlement. However, this distribution cannot describe the build-up of sediment due to the lack of the sediment transport information. Sedimentation depends upon both the flow conditions and the sediment transport characteristics.

Sediment transport simulations using a steady state DPM were carried out with different boundary conditions for sediment zones and efficiency predictions. The simulation results show that the boundary conditions for fixed BSS/BTKE were unable to predict the preferred sedimentation zones in the real Django Reinhardt basin due to the use of a single threshold for different sized particles, which causes small particles to settle too early. The fixed BSS/BTKE boundary conditions result in an overestimation of predicted efficiency because they do not take the time-dependent effect of erosion into account. Shields curve boundary conditions do not work well full scale basins in sewer systems either. This is because the Shields curve was derived from experiments carried out with non-cohesive particles, while the cohesive materials predominate in particulate pollutants in sewer system.

Near bed turbulence is affected by surface roughness, so clearly surface roughness should be taken into account in flow simulations for full scale basins.

Turbulence plays a keyrole in determining sedimentation processes, and the BTKE can be used to predict the sediment zones in detention basins. Hence, a new formula has been proposed here for estimating the BTKE threshold for different particles according to their settling velocity. The settling velocity is thought to represent all other properties, such as density and size due to the inner relations. The formula (equation 3.81) is given in detail in chapter 3. The proposed formula was created with the aim of overcoming the notable drawbacks of the fixed BSS/BTKE values and the Shields curve, i.e. that they are unable to predict the preferential zone in full scale basin with DPM simulations. This proposed formula was tested initially within the boundary conditions for a scale basin, then in a full scale basin.

Sediment transport simulations based on the proposed BTKE method were performed both in small scale and full scale basins using a steady state DPM. The simulated results showed that the proposed formula for calculating BTKE boundary conditions is capable of identifying the preferred sedimentation deposit zones in both small scale and full scale detention basins. The proposed formula for estimating the BTKE threshold for different particles does not determine the BTKE using comparison with observed results, as required by fixed BSS/BTKE boundary conditions. However, the proposed BTKE boundary conditions overestimate predicted efficiency.

In order to take time-dependent effects for sediment transport into consideration when modelling with a DPM approach, a new method was devised for representing the dynamic sedimentation processes under unsteady flow conditions. This method is illustrated in 3 3 0 H Figure 6-1. This method was carried out using UDF in Fluent. 12 sediment transport simulations were performed in a scale detention basin using the proposed method. The impact of different factors on efficiency and sediment zone prediction were tested. The proposed dynamic sedimentation method demonstrated a good overall ability for providing a representation of dynamic settling and entrainment under unsteady flow conditions.

The efficiency and the sediment zones predicted using DPM modelling under unsteady flow conditions based on the proposed method are sensitive to the quantity of the injected particles, the parameter of stochastic modelling, the rebound friction resistance model, the initial entrained velocity model, in particular, the settling and entrainment boundary conditions. A sufficient amount of particles are required in order to ensure statistical stability because a "particle" in ϊPε represents a parcel of physical particles. If the amounts of particles are too low, it leads to under-prediction of efficiency. Stochastic modelling is required for representing the turbulent dispersion effect of sediment transport. Out of the available test cases, a C L value of 0.05 for DRWM shows the highest level of agreement compared to experimental observations for the scale basin in terms of predictions for efficiency and those for the sediment zones. The friction resistance model seems to have a small negative effect on the prediction of efficiency. The entrained initial velocity models have an impact on the sediment zone prediction. According to the experimental and simulated results available, the van Rijn model appears to predict wider spread but denser sediment accumulated in the downstream zone, which appears to show a higher level of agreement comapred to the observations. Taking both the prediction of the sediment zones and the prediction of efficiency into account, the proposed formula for calculating BTKE boundary conditions is suitable for use for deposit boundary conditions and the Shields curve is suitable for use for entrainment boundary conditions for non-cohesive sediment transport in a small scale detention basins.

Perspectives

Gravel-like particles had never been collected and analysed in previous research carried out for the Django Reinhardt detention basin. The sediment trap sampling method cannot collect coarse particles because coarse particles are often transported along the pathway within the bed load. This can lead to uncertainty when estimating removal efficiency. Within the framework of the CABRRES national project (http://www.graie.org/cabrres/index.php), new sediment traps are to be installed in the basin and at the inlet of the basin for sediment sampling in order to provide more complete information on the characteristics of sediment.

The BSS and the BTKE have similar capacities for predicting sediment zones and are both used as the bed boundary conditions in DPM modelling. However, neither of them works perfectly for predicting efficiency and sediment zones. It has been assumed that a possible combination of BSS and BTKE might be used when simulating full scale basin sedimentation processes.

The adjusted coefficient in the new formula has been assumed to be a constant. However, this value does not work well as entrained boundary conditions within unsteady DPM modelling with the dynamic sedimentation method. It is likely that the adjusted coefficient may be a function that depends upon flow conditions and particle characteristics. This coefficient function can be obtained from a special experimental setup.

Up to now, there has been no appropriate formula for estimating the settling velocity for sewer solids. There does not appear to be a clear relationship between the measured settling velocity and particle properties. A relationship between the settling velocity and particle propterties is required by the proposed formula which allows estimating the threshold of BTKE as boundary condition in sediment transport modelling.

Unsteady sediment transport modelling coupled with unsteady flow conditions is recommended for predicting efficiency and sediment zones since sediment transport behaviours are highly affected by unsteady flow conditions. Unsteady sediment transport modelling is to be performed in the Django Reinhardt basin for complete storm events which last for a short period of time.

From a theoretical perspective it is likely that the proposed DPM method underestimates efficiency because the hiding effect and particle-particle collision are not taken into consideration. In high concentration zones, such as those areas the near bed zone, the particles are in a dense state. In these zones the lower particle layer may be hidden by upper particle layers from entrainment by the flow, or the low layer entrained particle might be rejected due to an inter-particle collision. However, in the proposed method, all particles have the same possibility of being entrained without taking the accumulated layer structure into account. In a DPM approach, collision is neglected in order to save calculation time. The hiding effect within the sediment should be taken into account in order to improve this method in future work. A possible solution might be to couple DPM and DEM to improve the method and to take into consideration the hiding effect.

Free surface measurement in Django Reinhardt basin with a camera is to be performed. The data taken from these measurements could be used to validate the numerical modelling results for the flow.

A probability method could also be introduced to the calculation of the bed boundary conditions in order to better represent the stochastic effect of the settling and entrainment processes.

  (a) champ de vitesse près du fond du BDR (b) emplacement des points de prélèvement des sédiments (c) correspondance entre la distribution spatiale des caractéristiques physiques des sédiments et les lignes de courant probables dans le BDRle tableau indique la fraction volumique des particules dont le diamètre est inférieur à 80 µm. Figure 1 Mise en évidence du lien entre la distribution spatiale des caractéristiques physiques des sédiments (expérimentations) et le comportement hydrodynamique du BDR (résultats des simulations).

Figure 2

 2 Figure 2 Zones de dépôt simulées à l'aide la condition limite BTKE en fonction des vitesses de chute des particules (nouvelle condition limite proposée)une distribution non uniforme des vitesses de chute des particules a été considérée à l'entrée du BDR

Figure 3

 3 Figure 3 Traitement de la condition limite au fond en régime transitoire

Figure 4

 4 Figure 4 Comparaisons entre les zones de dépôt observées et simuléesla recirculation apparait sur le côté gauche -résultats du cas DPM 5, résultats obtenus après (de gauche à droite) 200,215 et 230s

Figure 2 - 1 Figure 3 -Figure 4 -Figure 5 -

 21345 Figure 2-1 Main factors that influence the removal efficiency of basin .................................. 40 Figure 2-2 Sediment settling velocity measured with VICAS protocol ................................... 45 Figure 2-3 Processes of erosion, transport and sedimentation ................................................. 45 Figure 2-4 Definition of bed load and suspended load ............................................................ 46 Figure 2-5 Sketch of representation of bed load movements ................................................... 46 Figure 2-6 Dimensionless sediment discharge q bv* versus Shields parameter * . .................... 52 Figure 2-7 Modified Shields diagram with power equations fitted by Van Rijn (note, s=ρ p /ρ, from van Rijn, 1984b) ...................................................................................................... 53 Figure 2-8 Hjulström curve (from 7 9 H http://en.wikipedia.org/wiki/Hjulstr%C3%B8m_curve , originates from Hjulström, 1935) ..................................................................................... 57Figure 2-9 Saltation trajectory of sand measured by high speed camera ................................. 61 Figure 2-10 Definition diagram for collision-rebound with the bed ........................................ 62 Figure 2-11 Settling conditions in an ideal rectangular settling basin ..................................... 65 Figure 2-12 Inflow velocity/efficiency curve for a laboratory chamber .................................. 71 Figure 2-13 Comparison between the deposition zones and bed shear stress and bed turbulent kinetic energy in a rectangular detention basin ................................................................ 72 Figure 3-1 Location of OTHU experimental sites in the Lyon sewer system .......................... 87 Figure 3-2 Presentation of the Chassieu catchments ................................................................ 89 Figure 3-3 View of Django Reinhardt detention-settling and infiltration facility ................... 90 Figure 3-4 Scheme of the Django Reinhardt detention-settling basin after its retrofit in 2004 .......................................................................................................................................... 90 Figure 3-5 Outlet of Django Reinhardt detention basin equipped with regulator gate with a maximum outflow rate of 350 L/s (Hydroslide® gate) .................................................... 91 Figure 3-6 Bed elevation contour of the Django Reinhardt detention basin ............................ 91 Figure 3-7 Experimental tank and measurement devices ......................................................... 92 Figure 3-8 Experimental set-up (after Vosswinkel et al. 2012) ............................................... 93 Figure 3-9 Sediment depth distributions in the Django Reinhardt detention basin. ................ 95 Figure 3-10 A photo showing an example sediment zone in Chassieu (14/4/2011) ................ 95 Figure 3-11 Layouts of the sediment sampling locations in the Django Reinhardt detention basin ................................................................................................................................. 96 Figure 3-12 Sampling process diagram .................................................................................... 96 Figure 3-13 Laser Particle Sizer (LPS): Malvern Mastersizer 2000 equipped with the Hydro2000G sample dispersion accessory. ..................................................................... 97 Figure 3-14 Sieves with selected sizes of 0.08 mm, 0.2 mm, 0.5 mm, 1.0mm, 2.0 mm and 5.0 mm .................................................................................................................................... 98 Figure 3-15 Pycnometer and accessories (experimental supports and a vacuum pump, etc.) . 99 Figure 3-16 Diagram of the measurement stations located at the inlet and outlet of the Django Reinhardt detention basin in Chassieu ........................................................................... 100 Figure 3-17 Time averaging for a statistically steady flow (left) and an unsteady flow (right) ........................................................................................................................................ 103 Figure 3-18 Velocity distribution near a solid wall ................................................................ 112 Figure 3-19 Scheme of near wall region treatment ................................................................ 113 Figure 3-20 Overview of pressure-based solution method .................................................... 117 Figure 3-21 Cumulative size distributions of particles .......................................................... 124 Figure 3-22 Rosin-Rammler curve fit for the cumulative size distribution of particles ........ 125

1 4 7 H

 7 Figure 2-1summarizes the factors which impact the removal efficiency of basins.

Figure 2 - 1

 21 Figure 2-1 Main factors that influence the removal efficiency of basin (adapted from[START_REF] Verstraeten | Estimating trap efficiency of small reservoirs and ponds: methods and implications for the assessment of sediment yield[END_REF]

Figure 2 - 3

 23 Figure 2-3 Processes of erosion, transport and sedimentation[START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF]

Figure 2 - 4

 24 Figure 2-4 Definition of bed load and suspended load[START_REF] Julien | Erosion and sedimentation. 2 nd[END_REF]

  Bed load describes particles in a flowing fluid (usually water) that are transported along the bed. Bed load is complementary to suspended load and wash load. It often involves the motion of rolling, sliding, and/or saltating as shown in 1 5 4 H Figure 2-5.

Figure 2 - 5

 25 Figure 2-5 Sketch of representation of bed load movements

Figure 2 - 6

 26 Figure 2-6 Dimensionless sediment discharge q bv* versus Shields parameter τ * (adapted from Julien, 2010).

Figure 2 - 7

 27 Figure 2-7 Modified Shields diagram with power equations fitted by Van Rijn (note, s=ρ p /ρ, from van Rijn, 1984b)

Chapter 2 :

 2 Literature review H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 55

Figure 2 - 8

 28 Figure 2-8 Hjulström curve (from 7 9 H http://en.wikipedia.org/wiki/Hjulstr%C3%B8m_curve , originates from[START_REF] Hjulström | Studies of the morphological activity of rivers as illustrated by the river Fyris[END_REF]

Figure 2 - 9

 29 Figure 2-9 Saltation trajectory of sand measured by high speed camera(Hu and Hui, 1996)

Figure 2 -

 2 Figure 2-11 Settling conditions in an ideal rectangular settling basin(Verstraeten and poesen, 2000, from Camp, 1945)

Figure 2 -

 2 Figure 2-12 Inflow velocity/efficiency curve for a laboratory chamber[START_REF] Stovin | Efficiency prediction for storage chambers using computational fluid dynamics[END_REF]

  and Dewals et al. (2008) used CCHE2D and FLOW-3D to simulate the flow patterns and sediment transport for a rectangular shallow basin. These simulations were validated with a series of measurements from experiements. It was concluded that numerical simulation can reproduce experimental flow features. The flow patterns could be simulated numerically using a parabolic eddy viscosity model. It was found that flow patterns are quite sensitive to the boundary and initial conditions.

Figure 2 -

 2 Figure 2-13 Comparison between the deposition zones and bed shear stress and bed turbulent kinetic energy in a rectangular detention basin[START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]

Cao

  et al. (1995) carried out analysis of the flow field and sediment concentration profiles in an open channel.[START_REF] Hsu | Modeling of sediment transport a two-phase flow approach[END_REF] introduced a sediment transport model based on the twophase mass and momentum equations with appropriate closures on the near bed boundary conditions and fluid turbulence. The two-phase model is able to predict the time-averaged concentration under various combinations of maximum free-stream velocity and oscillatory period adequately. However, some discrepancies have been observed when comparing the time history of concentration profiles.[START_REF] Hsu | A two -phase flow model of wave-induced sheet flow[END_REF] presented a two phase model that simulates fluid and sediment motion in the sheet flow region under oscillatory conditions. This model is able to provide accurate estimations of sediment concentrations because it uses constant equivalent sand roughness.[START_REF] Wanker | Numerical modeling of sedimentation utilizing an Euler/Euler approach[END_REF] used a Euler-Euler two-phase model to simulate the sedimentation effects and sediment transport. The model is valid for regions of high and low concentration. Bed changes are also accounted for directly without any adaptation of the grid.[START_REF] Bakhtyar | Euler-Euler coupled twophase flow modeling of sheet flow sediment motion in the near shore[END_REF] created a Eulerian two-phase flow model for fluid-sediment sheet flow simulation, that includes all the important forces such as

8 2 H

 2 http://www.graie.org/othu/).

Figure 3 - 1

 31 Figure 3-1 Location of OTHU experimental sites in the Lyon sewer system (OTHU, 2012)

Figure 3 - 2

 32 Figure 3-2 Presentation of the Chassieu catchments

Figure 3 - 3

 33 Figure 3-3 View of Django Reinhardt detention-settling and infiltration facility (photo of 15/03/2012 from Google map)

Figure 3 - 4 Figure 3 - 5 Figure 3 - 6

 343536 Figure 3-4 Scheme of the Django Reinhardt detention-settling basin after its retrofit in 2004

  The brief introduction fromDufresne et al. (2009) is summarized below in order to better understand the simulation set-up: The experimental pilot was a rectangular basin 1.80 m long and 0.76 m wide. It is equipped with an inlet pipe (diameter 80 mm), an outlet pipe (80 mm), and an overflow limiting the water depth to 0.40 m. A pump outputting between 1 and 10 L/s replenishes the tank. A valve regulates discharge in the outlet pipe and water depth in the tank. A flowmeter measures the inflow rate while two ultrasonic sensors measure water depth in settling tanks 1

  2. The mean value equals 1034 kg/m 3 , the standard deviation is 20 kg/m 3 . The particles were recovered in two settling tanks. In this way it was possible to calculate the mass balance between the particles that are injected, and those which settled in the tank, overflow, and outflow. The experimental devices are shown in Figure3-7.

Figure 3 - 7

 37 Figure 3-7 Experimental tank and measurement devices adapted from Dufresne et al. (2009)

3 0 4 H

 4  consisted of a rectangular sedimentation tank made of glass (Length/Width/Depth = 3125/ 800/ 200 mm) plus an inlet tank to dissipate the energy in the water flow. The inflow was directed through a 100 mm diameter pipe located at the bottom of the tank. The particulate and dissolved tracers were also added to the flow. Discharge from the tank passed through a weir (discharge coefficient µ=0.62) with an upstream scum board. The inflow rate at the inlet was 2.19 L/s. and resuspension under unsteady conditions in urban stormwater detention basin / 2013 93

Figure 3 - 8

 38 Figure 3-8 Experimental set-up (after Vosswinkel et al. 2012)

Figure 3 - 9

 39 Figure 3-9 Sediment depth distributions in the Django Reinhardt detention basin.

Figure 3 -Figure 3 -

 33 Figure 3-10 A photo showing an example sediment zone in Chassieu (14/4/2011)

Figure 3

 3 Figure 3-12 Sampling process diagram

Figure 3 -

 3 Figure 3-13 Laser Particle Sizer (LPS): Malvern Mastersizer 2000 equipped with the Hydro2000G sample dispersion accessory.

Figure 3 Figure 3 -

 33 Figure 3-14 Sieves with selected sizes of 0.08 mm, 0.2 mm, 0.5 mm, 1.0mm, 2.0 mm and 5.0 mm

Figure 3

 3

Figure 3 -

 3 Figure 3-16 Diagram of the measurement stations located at the inlet and outlet of the Django Reinhardt detention basin in Chassieu(Mourad, 2000)

Figure 3

 3

Figure 3 -

 3 Figure 3-17 Time averaging for a statistically steady flow (left) and an unsteady flow (right)[START_REF] Ferziger | Computational methods for fluid dynamics[END_REF]

  the Navier-Stokes equations. The Reynolds stress transport equation is as follows:

  outlet boundary condition may be used in conjunction with the inlet boundary condition. Two kinds of outlet boundary conditions are often used in hydraulic modelling: pressureoutlet and outflow. Pressure outlet boundary conditions require static (gauge) pressure at the outlet boundary to be specified. With the pressure outlet boundary condition, all other flow quantities are extrapolated from the interior domain. Outflow boundary conditions in Ansys Fluent are used to model flow at certain points where details of the flow velocity and pressure are not known prior to solving the flow problem. No conditions are defined at the outflow boundaries (unless you are modelling radiative heat transfer, a discrete phase of particles, or split mass flow): Ansys Fluent extrapolates the required information from the interior. Note that outflow boundaries cannot be used in the following cases (Ansys, 2011b): • When a problem includes pressure inlet boundariesν use pressure outlet boundary conditions instead • When modelling compressible flow • When modelling unsteady flow with varying density, even if the flow is incompressible • With the multiphase models (Eulerian, mixture, and VτF).

  1 8 9 H Figure 3-18 shows the close agreement between theoretical equations (3.45) and (3.46) in their respective area of validity and experimental data.

Figure 3 -

 3 Figure 3-18 Velocity distribution near a solid wall (Versteeg and Malalasekera, 2007 adapted from Schilichting, 1979)

κ=

  Von Kármán constant (= 0.4187) E= empirical constant (= 9.793) U p = mean velocity of the fluid at the near-wall node P k p = turbulent kinetic energy at the near-wall node P y p = distance from point to the wall μ= dynamic viscosity of the fluid

Figure 3 -

 3 Figure 3-20 Overview of pressure-based solution method (Ansys, 2011b)

Chapter 3 :

 3 Materials and methods H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin /

  6 show the particle size distribution by mass weight and cumulative mass fraction by particle size, respectively. A plot of Y d against diameter d is shown in Figure 3-211 9 5 H .

Figure 3 -

 3 Figure 3-21 Cumulative size distributions of particles

Figure 3 -

 3 Figure 3-22 Rosin-Rammler curve fit for the cumulative size distribution of particles

Figure 3 -

 3 23, e and f indicate the restitution (or normal) and friction (or tangential) coefficients, respectively (Nino and Garacia

Figure 3 -

 3 Figure 3-23 Diagram of the reflect boundary condition

Figure 3

 3 Figure 3-24 Shields curve[START_REF] Vanoni | Sedimentation Engineering, Manuals and Reports on Engineering Practice[END_REF]

Chapter 3 :

 3 Materials and methods H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin /

2 0 5 H

 5

Figure 3 -

 3 Figure 3-26 Scheme of uncoupled DPM

  rate of injected particles.

Figure 3 -Chapter 3 :

 33 Figure 3-27 Diagram of the of two-way coupling DPM approach

Figure 3 -

 3 Figure 3-28 Heat, mass, and momentum transfer between the discrete and continuous phase (Fluent, 2011b)

  2 0 8 H Figure 4-1). The sediment had accumulated since the last clean in 2006 up until March 2013, and vegetation was growing above the sediment (see 2 0 9 H Figure 4-1 and 2 1 0 H Figure 4-4).

Chapter 4 :

 4 Sediment transport under steady state condition H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 137

  2 1 1 H Figure 4-2). The measurement points were closer together in the centre of the basin and further apart towards the basin inlet (see 2 1 2 H Figure 4-2). Meanwhile, for the physical sediment characterisation analysis, 11 reprentative samples of the accumulated sediment were collected, kept and measured in laboratory. The sediment samples were characterised in terms of particle size distribution, density, and organic matter content.

Figure 4 - 1 Figure 4 - 2

 4142 Figure 4-1 Accumulated sediment in the Django Reinhardt basin on 14/04/2011

Figure 4 - 3 Figure 4 - 4

 4344 Figure 4-3 Overhead view of the Django Reinhardt basin (from Google Earth in 2012) and the contour of sediment depths measured on 14 April 2011 -Up until the time at which the measurements were taken, the sediment had been accumulating since 2006

Figure 4 - 5 Figure 4 - 6

 4546 Figure 4-5 Layout of the sediment sampling locations in the basin, numbered according to sediment depth

2 H

 2 Figure 4-7 and 2 2 3 H Figure 4-8 . and resuspension under unsteady conditions in urban stormwater detention basin / 2013 142

Figure 4 - 7

 47 Figure 4-7 Accumulated particle size distributions of the samples from the sieving analysis. The sample names refer to the locations shown in 2 2 4 H Figure 4-5

Figure 4 - 8 5 H

 485 Figure 4-8 Particle size distributions of the sample P06 by Laser diffraction analysis

Figure 4 - 9 Figure 4 -

 494 Figure 4-9 Density of each sieved fraction from sample points P03 and P04

  (1999) measured densities of 2200-2300 kg/m3 and Kayhanian et al. (2012) obtained values of 1750-2250 kg/m 3 , both measured on sediment captured in sediment traps during storm events. This suggests that, since the sediment in the Django Reinhardt detention basin had accumulated since 2006, the organic matter content had transformed hence changing the sediment's characteristics. However, the nature of stormwater particles does vary from place to place, and the deposits in the Django Reinhardt detention basin may simply be naturally dense.

  , the Django Reinhardt detention basin is divided into two parts by an inner detention wall since the 2004 retrofit. Long-term observations have shown that there is almost no deposit in part two adjacent to the outlet. It is therefore thought that the influence on sediment settling in part two can be disregarded. In order to reduce the mesh cells, the basin simulation geometry was simplified by removing part two since the investigation aims to model sediment transport. The simplified geometry is shown in 2 3 1 H

2 3 2 H

 2

Figure 4 -Figure 4 -

 44 Figure 4-11 The geometric simplification of the Django Reinhardt detention basin

2 3 3 H

 3 Figure 4-13). An example of a storm event occurred on 31/05/2007 and is shown in 2 3 4 H Figure 4-14. As 3 5 H Figure 4-14, the curve shows a back-and-forth disturbance (marked by a rectangle in 2 3 6 H Figure 4-14) around the inflow rate of 0.35 m 3 /s (equal to the maximum outflow rate) with alsomt the same water depth at h1. It is speculated that the inflow rate of 0.35 m 3 /s dominates the main flow pattern state in the basin, therefore the three inflow rates given in 2 3 7 H Table

Figure 4 -

 4 Figure 4-13 Changes in outflow rate against water depth h2 (adapted from[START_REF] Torres | Décantation des eaux pluviales dans un ouvrage réel de grande taille : éléments de réflexion pour le suivi et la modélisation[END_REF]

Figure 4 -

 4 Figure 4-14 Inflow rate against the water depth h1 for the storm event 31/05/2007.

Figure 4 -

 4 Figure 4-15 (a) Deposit spatial distribution, (b) BSS (<0.01 Pa) distribution and (c) Overhead view of sediment distribution of the basin (from Google maps, 2012)

2 4 1 H

 1 , there is almost no accumulated sediment. The sediment was flushed as soon as it settled.

Figure 4 -Figure 4 -

 44 Figure 4-16 Velocity field of 5 cm under the free surface (top) and near bed low velocity field (<0.04 m/s) of Django Reinhardt basin (low)

Figure 4 -

 4 Figure 4-18 Deduction of simulated flow pattern on the real basin with the sediment spatial distribution

Figure 4 -

 4 Figure 4-19 Overhead view of sediment distribution on the bed of the Django Reinhardt basin from Google maps in 2007 and 2012.

Figure 4 -Figure 4 -

 44 Figure 4-20 Low bed turbulent kinetic energy (<4.5e-5) distribution of DRB case two in the basin

Figure 4 -Figure 4 -Figure 4 -Figure 4 -

 4444 Figure 4-22 present the streamline of these simulation cases with different inflow rates. Generally speaking, the flow streamlines indicate flow patterns in the basin. This means the streamline provides information on flow transport in the basin. Moreover, to a certain extent, streamline density roughly indicates the velocity of the flow field. This means that in a location with a high density of streamlines, flow velocity is high. Conversely, in locations with low streamline density, flow velocity is quite low. 2 5 3 H DRB case 3 Qin=0.45 m3/s

Figure 4 -

 4 Figure 4-24 Superposition of streamlines of cases 2 and 3.

2 5 4 H

 4 Figure 4-23 and 2 5 5 H Figure 4-24 show the superposition of streamlines for different simulated cases. Assuming that the rate of change of inflow is between 0.45 m 3 /s to 0.25 m 3 /s depending on the chosen flow condition for each case, 2 5 6 H Figure 4-24 shows that the inflow jet direction at the beginning and the end are almost the same. However, the inflow jet direction changes when the simulated results of case 1 are compared with those of case 2 or those of case 2 with those of case 3. It can be estimated from the simulated results, therefore, that if the inflow rate changes from 0.45 m 3 /s to 0.35 m 3 /s, the inflow jet (blue arrow line in 2 5 7 H Figure 4-24) changes gradually within a sector zone to the direction of case 2 (black arrow line in 2 5 8 H Figure 4-24). Similarly, if the inflow rate changes from 0.35 m 3 /s to 0.25 m 3 /s, the inflow jet (black arrow line in 2 5 9 H Figure 4-23) changes gradually within the same sector zone to the direction of case 2 (green arrow line in 2 6 0 H Figure 4-23

Figure 4 -

 4 Figure 4-25 Similarity between observed deposition zones and simulated BTKE distribution (<4.4e-5= k c ) related to different surface roughnesses.

2 6 4 H

 4 Figure 4-25Ks1, Ks2, Ks3 and Ks4 indicate the different surface roughness settings used in the simulation. Comparing the measured sediment spatial distribution found in 2011 and the overhead view observation of sediment made in 2007, all

2 6 5 H

 5 Figure 3-4 labeled with 'o1') which corresponds to observations made. In order to further understand the effects of surface roughness on near bed turbulence, local vertical TKE distribution analysis was carried out at some specific locations. The positions of the local points are shown in 2 6 6 H Figure 4-26. 2 6 7 H Figure 4-27 (point 1, point 3 and point 4) shows that the near bed turbulent kinetic energy distribution is affected by surface roughness. In general, the vertical turbulent kinetic energy distribution shows a similar profile at almost all points and for all rough surfaces. The maximum beds turbulent kinetic energy was obtained close to the bed due to the influence of rough elements on the bed (see point 1, point 3 and point 4 in 2 6 8 H Figure 4-27). 2 6 9 H Figure 4-27 shows that a similar vertical profile was also obtained in an experimental investigation carried out by Dey et al. (2011). At point 2 vertical secondary currents were observed in the simulated results (see 2 7 1 H Erreur ! Source du renvoi introuvable.b

Figure 4 Figure 4 -

 44 Figure 4-26 Vertical TKE distribution of points checked

Figure 4 -

 4 Figure 4-28 Simulated deposit zones using BTKE boundary conditions with different particle sizes and densities and using a time scale factor of C L =0.15 and C L = 2.

  The simulated zone created with Shields curve boundary conditions does not show model the deposit zone any better. As shown in 2 7 9 H Figure 4-29, the majority of particles settled in the location near the end of the inflow jet. and resuspension under unsteady conditions in urban stormwater detention basin / 2013 168

Figure 4 -

 4 Figure 4-29 Simulated deposit zones using the Shield curve boundary condition with non-uniform particles sizes, the particle are shown as yellow dots

Figure 4 -

 4 Figure 4-30 Computational tetrahedral mesh for small scale basin[START_REF] Dufresne | La modélisation 3D du transport solide dans les bassins en assainissement: du pilote expérimental à l'ouvrage réel[END_REF]

2 8 4 H 2 

 42 Figure 4-30. The k-ε turbulent model was used for turbulence modelling, as suggested by Dufresne (2008), as it had already given satisfactory results. The other boundary condition configurations used for fluid flow simulation were as follows:  Inlet: velocity inlet with a inflow rate of 3 L/s  Outlet: pressure outlet  Free surface: symmetrical boundary  Side wall and bed: no-slip condition with standard wall function The DPM modelling configurations were as follows:  Injection: surface injection at the inlet boundary with a total of 7200 particles, this is enough to ensure numerial error is low due to the number of particles injected  Particle density: 1034 kg/m 3  Non-uniform particles: defined by the Rosin-Rammler equation, according to the data in Table 3-5, the calculated parameters areμ n=ζ, d=810 m, ϊ min =3η0 m and D max =1ζ00 m. The Rosin-Rammler curve is shown in 2 8 5 H Figure 4-31  Max Number of steps: 50 000  Stochastic modelling: discrete random walk model (DRWM), with CL=0.05, 0.15, 1, Inlet and outlet boundary condition: escaped  Side wall boundary condition: reflected  Bed boundary condition: BTKE estimated using the proposed formula according to the particle properties, carried out with UDF, a fixed BTKE boundary with a value of 2e-4 m2/s2 was also tested for the purpose of comparison.

Figure 4 -

 4 Figure 4-31 Rosin-Rammler curve fit showing the cumulative size distribution of particles

Figure 4 -

 4 Figure 4-32 Comparison between (a) experimental sediment transport (Dufresne, 2008), and (b) simulated velocity field from k-ε model at the height of 9.5 cm from the bed with the inflow rate of 3L/s.

Figure 4 -

 4 Figure 4-34 Comparison between observed and simulated deposit zones using different boundary condition with non-uniform particles (shown inTable 4-10)

2 Figure 5 - 2

 252 Figure 5-1 Evolution of sediment transport with the varying BTKE boundary condition

Figure 5 - 3

 53 Figure 5-3 Comparison between (a) experimental deposit zones, (b) ~ (e) simulated deposit zones using the proposed dynamic sedimentation method with different boundary conditions, and (f) simulated deposit zones with the trap boundary condition

Figure 5 - 4

 54 Figure 5-4 Particle spatial concentration distributions in the basin by vertical cutting plane

  and resuspension under unsteady conditions in urban stormwater detention basin / 2013 181

3 0 5 H

 5

Figure 5 - 5 

 55 Figure 5-5 The computational mesh

*

  # : refer to equations (3.84)-(3.85) in chapter 3; **: definition of e and f please refer to equations (3.73)-(3.74) in chapter 3. e=0.84-ζ.8ζ *, f=0.73 are from Nino and Garcia (1994): gravel saltation. #: calculated according to Shields curve, please refer to equations (3.75)-(3.78) in chapter 3. BTKE1: =1 for equation (3.81) in chapter 3. BTKE2: =1.5 for equation (3.81) in chapter 3. Note: process A and process B are shown in Figure 3-25.

3 0 9 H

 9 Figure 5-6, 3 1 0 H Figure 5-7 and 3 1 1 H Figure 5-8, present the simulated representative pattern and characteristics of sediment transport experiments. 3 1 2 H Figure 5-6 shows the experimental and simulated evolution of sediment transport processes for the first injection with an interval of 5 seconds. The simulation results are given as volume concentrations. This figure accurately reproduces the morphology of particle jet by the water inflow jet.

Figure 5 - 6 Figure 5 - 7 Figure 5 - 8 Figure 5 - 9

 56575859 Figure 5-6 Comparison of the experimental (according to Vosswinkel et al., 2012) and simulated evolution of sediment transport after first injection at an interval of 5 seconds (results of case DPM 1, time 10s-15s-20s)

Figure 5 - 6 ,

 56 3 1 0 H Figure 5-7, Figure 5-8 and 3 1 1 H Figure 5-9, the case tested can accurately capture the typical characteristics of the sediment transport process, notably the periodical vortex evolutions.

Figure 5 -

 5 Figure 5-10 Monitoring sediment mass concentration at the basin outlet (simulation case DPM 11 from 0-300s)

Figure 5 -

 5 Figure 5-11 (a) Simulated deposits in the basin (case DPM 5 at 105s), (b) simulated deposits + moving bed load (<0.002m) (case DPM 5 at 105s) and (c) top view picture of experimental sediment spatial distribution (after[START_REF] Vosswinkel | Influence of unsteady behaviour on the settling of solids in storm water tanks[END_REF]

  3 1 9 H Figure 5-11a and 3 2 0 H Figure 5-11b, the different colours indicate the different particle sizes. This result provides more information than the species model or Eulerian model. Figure 5-11b demonstrates the deposited bed load and the near bed moving bed load, which is in the layer less than 0.002 m from the bed. The bed load motion can be observed in 3 2 1 H Figure 5-11b. It shows that the particles around the clockwise recirculation are entrained due to the strong flow motion. The trend in bed load movement is accurately represented, showing a reasonable level of agreement with the the experimental photographic observations. Similarly, the suspended particles can be represented in the same way.

3 2 2 HFigure 5 -Figure 5 - 3 H

 2553 Figure 5-12 (a) Simulated near bed particle concentration distribution, the contour shows the deposition zone, and (b) the deposition zone distribution rendering with concentration isosurface.

Figure 5 -Figure 5 -Figure 5 -Figure 5 -

 5555 Figure 5-14 Comparison of simulated particle bed concentration with different C L : case DPM 5 at 230s with C L =0.05 (above) and case DPM 1 at 230s with C L =0.15 (below)

Figure 6 - 1

 61 Figure 6-1 Sketch of dynamic sedimentation process treatment of interaction between particle and bed of basin under unsteady condition

Tableau 1 Conditions aux limites utilisées pour les 12 simulations -u* et τ* représentent respectivement la vitesse de frottement et la contrainte de cisaillement adimensionnelle

	Cas traités	Processus A: conditions de décantation	Processus B: conditions d'entraînement	Nombre de particules injectées	Coefficients de résistance e (suivant la direction normale au fond) et f (suivant la direction tangentielle) lors du rebond des particules	Composantes de la vitesse initiale d'entraînement u d (suivant la direction normale au fond) et v d (suivant la direction tangentielle) -en m/s	Prise compte du en modèle de dispersion particulaire DRWM et Valeur de la constante de Lagrange C L
	1	BSS variable	BSS variable	22400	e=1, f=1	Hu and Hui (1996)	0.15
	2	BSS variable	BSS variable	44800	e=1, f= 1	Hu and Hui (1996)	0.05
	3	BSS variable	BSS variable	44800	e=1, f=1	Hu and Hui (1996)	0.25
	4	BSS variable	BSS variable	44800	e=1, f=1	Hu and Hui (1996)	0.5
	5	BSS variable	BSS variable	44800	e=0.84-ζ.8ζτ * f=0.73	Hu and Hui (1996)	0.05
	6	BSS variable	BSS variable	67200	e=0.84-ζ.8ζτ * f=0.73	u d =2u * v d =2u *	0.05
	7	BSS variable	BSS variable	67200	e=0.84-ζ.8ζτ * f=0.73	u d =2u * v d =2u *	Sans DRWM
	8	BTKE 1	BSS variable	22400	e=1, f=1	u d =2u * v d =2u *	0.15
	9	BTKE 2	BTKE 2	67200	e=0.84-ζ.8ζτ * f=0.73	u d =2u * v d =2u *	0.05
	10	BTKE 1	BTKE 1	67200	e=0.84-ζ.8ζτ * f=0.73	u d =2u * v d =2u *	0.05
	11	BTKE 2	BSS variable	67200	e=0.84-ζ.8ζτ * f=0.73	u d =2u * v d =2u *	0.05
	12	BSS=0.03 Pa	BTKE 1	67200	e=0.84-ζ.8ζτ * f=0.73	u d =2u * v d =2u *	0.05
	Tableau 2 Efficacités

de décantation simulées pour les 12 cas avec la méthode proposée

	Cas No.

Table of contents

 of

H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013

Table 2 -

 2 1 Efficiency of detention basin ...................................................................................Table 2-2 Efficiencies of detention basins ............................................................................... Table 2-3 Mean COD, metals and hydrocarbon concentrations observed in stormwater ........ Table 2-4 Percentage of the particulate fraction for different pollutants ................................. Table 2-5 Grain size characteristics for suspended solids in urban wet weather discharges ... Table 2-6 Fundamental dimensions of bed load ...................................................................... Table 2-7 Formulas for entrainment velocity ........................................................................... Table 2-8 formulas for critical Shields parameter *c ............................................................... Table 2-9 Saltation length L S , saltation height h s and averaged particle velocity V derived from experimental investigations ..................................................................................... Table 3-1 Base elevation of inlet /outlet of Django Reinhardt detention basin ....................... Table 3-2 Particle size distribution for pilot basin experiment ................................................ Table 3-3 Turbulence model available in commercial CFD codes ........................................ Table 3-ζ Empirical constants α 1 , α 2 and α 3 for different ranges of Re p ................................

Table 3 -

 3 5 Particle size distribution by mass fraction .............................................................

Table 3 -

 3 6 Mass fractions Y d with diameter larger than d % .................................................. Table 4-1 Particle size characteristics of the samples. ...........................................................

Table 4 -

 4 2 Simulation flow condition for representative steady simulation cases .................. Table 4-3 Sediment depth of the sampling locations .............................................................

Table 4 -

 4 4 Strickler roughness coefficient K and equivalent sand grain roughness height k s

Table 4 -

 4

5 Mean particle sizes distribution (psd) of 15 trap samples from storm event 31/5/2007. .......................................................................................................................

Table 4-6 Simulated removal efficiencies with different bed boundary conditions (ρ=1700) ........................................................................................................................................ Table 4-7 Simulated removal efficiencies with different bed boundary conditions (ρ=2ζ00) ........................................................................................................................................ Table 4-8 Comparison of experimental and simulated removal efficiency using bed boundary condition fixed BTKE and proposed BTKE formula with different C L values. ............ Table 4-9 Measured settling velocities from storm event 31/5/2007 with 15 sediment trap sample. ............................................................................................................................

Table 5 -

 5 1 Bed boundary conditions configuration for test ....................................................

Table 5 -

 5 2 Experimental and simulated removal efficiency in the basin ................................

Table 5 -

 5 3 Basic configurations for DPM model except bed boundary condition ..................

Table 5 -

 5 4 DPM setup and different bed boundary condition for proposed method ..............

Table 5 -

 5 5 Simulated removal efficiency of different case setup ............................................ , Q bm , Q bwFlux of sediment per unit width moving in the bed layer by volume, or mass or weight q bv , q bm , q bw Flux of sediment per unit width moving in the bed layer by volume, or mass or weight

	Notation
	A		Surface Area
	A c	Constant coefficient
	a		Positive coefficient
	B		Additive constant
	Δψ	Roughness function
	b		Positive coefficient
	c		Local sediment concentration
	C*	Depth averaged suspended load concentration under equilibrium condition
	C, C(z)	Averaged concentration of pollutant load, sediment concentration at a reference elevation z
	C b	Bed layer concentration of sediment
	C μ , C ε1 , C εβ	Constants
	C ijk	Turbulent dissipation
	C D	Drag coefficient
	C L	Time scale constant
	C s	Roughness constant
	c d		Particle diameter
	D*	Dimensionless particle diameter
	d 50 ,D 50	Median particle size
	d 90	Sieve diameter for 90 percentage of mass
	D b	Deposition rate
	D m	Molecular diffusion coefficient
	d e	Effective diameter
	d	i	The i th class particle mean size
	d		Size parameter for Rosin-Rammler distribution
	E		Constant
	E b	Erosion rate
	e		Restitution coefficient or Constants of nature
	F i	Body force
	F D	Coefficient
	F x	Additional force on particle
	f		Friction coefficient

b Local sediment concentration near the interface of suspended load and bed load c b* equilibrium concentration at the interface location b c Averaged concentration over the bed load layer thickness Notation H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 Notation H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 28 Q bv Notation H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 29 s Constant * Constant specific weight of fluid 0 Constant p specific weight of particle ij Kronecker symbol q volume fraction of the q th phase in multiphase flow Notation H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 30 Parameter H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin /

  bank erosion  Increased turbidity (muddiness created by stirred up sediment) from erosion

 Combined sewer overflow  Infrastructure damage  Contaminated streams, rivers, and coastal water Stormwater runoff causes frequent flooding. and it also increases the load of pollutants conveyed by runoff, including nutrients, solids, metals, salt, pathogens, pesticides, hydrocarbons, etc. Generally, pollutants that have been deposited on land, streets, and motorways are scoured off and carried by runoff into nearby rivers, streams, lakes, ponds, wetlands, marine waters, groundwater, and the sewer system. This contaminated runoff significantly degrades water quality and aquatic habitats. For example, according to Massachusetts Department of Environment Protection (MDEP

  Sustainable urban development has been introduced into the management of stormwater. Stormwater management technologies and concepts (e.g. Water Sensitive Urban Design-WSUD, Low Impacts Development-LID, Best Management Practices -BMPs, etc.) have been developed for this purpose. Stormwater Best Management Practices (BMPs) are recognized as one of the most effective and practical measures for reducing and preventing pollutants from reaching water bodies and for controlling the quantity of runoff from a site

Table 2 -1 Efficiency of detention basin (Nascimento et al., 1999)

 2

			Ulis Sud a detention basin		Pollutant reduction
		Annual inflow	Annual outflow	Annual	removal	after 2 h of
		load (kg/ha imp.)	load (kg/ha imp.)	efficiency (%)	decantation (%)
	TSS	3902	387	90.1		88
	BOD 5	829	107	87.1		76
	COD	2598	521	79.9		-
	TKN	189	91	51.8		-
	P total	44	22	50.6		-
	Pb	0.893	0.054	94.0		65
	Zn	5.12	0.66	87.1		77

Table 2

 2

	-1 indicate that detention basins may perform effectively at
	removing different pollutants from stormwater columns. However, the removal efficiency of
	detention basins is not variable. H Table 2-2 indicates the pollutant removal efficiency recorded
	for some UK detention basins and compares those possessing inlet sediment control traps to
	the overall range of removal efficiencies reported in the literature and with experimental
	settling rates. From the Table 2-2, we can see that the removal efficiencies of different
	detention basins vary across a large range.

Table 2 -2 Efficiencies of detention basins (Nascimento et al., 1999)

 2

	Pollutant	Imhoff	Detention basin	Detention basin	Range	of
		settleablity(24h)	2h removal (%)	6h removal (%)	observed removal
					efficiency (%)
	TSS	68	34	84	49-91
	BOD 5	32	13	48	14-53
	P total	46	20	58	20-70
	Pb	62	30	66	46-78
	Oil/Hydrocarbons 69	18	62	20-78
	Total coliforms	71	60	72	47-73

Table 2 -3 Mean COD, metals and hydrocarbon concentrations observed in stormwater (Bertrand-Krajewski, 1993)

 2

	pollutant	Unit	Minimum Maximum
	COD Cd Cr Cu Fe Mn Ni Pb Zn	mg/L g/δ g/δ g/δ g/δ g/δ g/δ g/δ g/δ	20 0.15 0.16 0.50 0.10 1 1.5 1.6 5	160 17 14 78 300 15 50 110 800
	Hydrocarbons mg/L	0.02	0.07

Table 2 -4 Percentage of the particulate fraction for different pollutants (Bertrand-Krajewski, 1993, in Ashley et al., 2004)

 2

	pollutant	COD	BOD 5 TKN Cd	Pb	Zn	Hydrocarbons PHAs PCBs
	Particulate	83-	77-	57-	>95% 68-	>95% 80-90%	79-	90-
	fraction	90%	95%	82%		96%			97%	93%

Table 2 -5 Grain size characteristics for suspended solids in urban wet weather discharges (Chebbo, 1992)

 2

	Type of network	d 10 ( m) d 50 ( m) d 90 ( m)	%ξ 100 m
	Storm sewer networks	6-9	29-38	265-1375 76%-85%
	Combined networks	4-13	25-44	183-497	66%-82%

Figure 2-2 Sediment settling velocity measured with VICAS protocol (Torres, 2008)

		1
		0.9
		0.8
		0.7					P1
	F(Vs) (mg/mg)	0.4 0.5 0.6					P2 P3 P4 P5 P6 P7
		0.3					P8
							P9
		0.2					P10
							P11
		0.1					P12
		0	10 -2	10 -1	10 0	10 1	10 2
					Vs (m/h)
	2.2.3 Mechanisms related to sediment transport
	2.2.3.1	Description of the key mechanisms
	and resuspension under unsteady conditions in urban stormwater detention basin / 2013	45

Table 2

 2 Conversions from volume to mass involve the mass density of sediment ρ p where L bm =ρ p L bv . Similarly, conversions from mass to weight involve the gravitational acceleration g, i.e. L bw = gL bm = ρ p gL bv . The bed load discharge Q b is the flux of sediment moving in the bed layer. The fundamental dimensions of Q b by volume, mass, or weight are summarized in 1 5 5 H

	-6. The

Table 2 -6 Fundamental dimensions of bed load (Julien, 2010)

 2

		by volume By mass	By weight
	Bedload	L bv

Table 2 -8 formulas for critical Shields parameter τ *c

 2

	Reference	Formula

Table 2 -9 Saltation length L S , saltation height h s and average particle velocity V derived from experimental investigations (using formulas adapted from Lajeunesse et al., 2010)

 2

	e		84 . 0		84 . 4 

): * If friction resistance is negligible, both e and f are equal to 1. H. Yan / Experiments and 3D modelling of hydrodynamics, sediment transport, settling and resuspension under unsteady conditions in urban stormwater detention basin / 2013 63

  [START_REF] Stovin | solute transport modeling for urban drainage structures[END_REF] modeled solute transport in a storage tank using a species model and a discrete phase model (DPM) based on both the RSM and RNG k -ε models. The authors found that for predicting flow fields, the RSM was better than the RNG k -ε model, although both of them under-predicted the first arrival time and gave almost identical results for predictions for cumulative residence time distributions with particle tracking method.

However,

Dufresne et al. (2009)

and

[START_REF] Mignot | Experiments and 3D simulations of flow structures in junctions and of their influence on location of flowmeters[END_REF]

tested the standard k-ε model, the RNG k-ε model and the RSM in various urban drainage structures (three combined sewer overflow chambers for solid separation and open channel junctions) and found that the RSM model did not give significantly better results when compared to the RNG k-ε model.

Table 3

 3

-1.

Table 3 -1 Base elevation of inlet /outlet of Django Reinhardt detention basin

 3

	Location of inlet / outlet (shown	Original base elevation	Base elevation relative to the
	in Figure 3-4)	(m)	lowest point (m)
	Inlet 1	196.64	2.76
	Inlet 2	196.25	2.37
	Orifice 1	196.10	2.22
	Orifice 2	195.43	1.55
	Orifice 3	196.10	2.22
	Central settling pit	193.88	0
	Overflow weir	196.40±0.3	2.52±0.3
	outlet	195.93	2.05

Table 3 -2 Particle size distribution for the pilot basin experiment, according to Dufresne (2008)

 3

	d min	d 10 * d 20	d 30	d 40	d 50	d 60	d 70	d 80	d 90	d max
	350	535	593	642	689	738	790	851	931	1056 1400

Table 3 -3 Turbulence models available in commercial CFD codes (Versteeg and Malalasakra, 2007)

 3  shows some of the turbulence models available in CFD codes. Here we describe briefly the k-ε, k-, Reynolds stress models, which are used in drainage structure modelling.

	Number of extra transport equation	name
	Zero One Two	Mixing length model Spalart -Allmaras model k -ε model k -model
		Algebraic stress model
	Seven	Reynolds stress model
	1 8 8 H

Table 3 -4 Empirical constants α 1 , α 2 and α 3 for different ranges of Re p (Morsi and Alexander, 1972)

 3

	Re p	α 1	α 2	α 3
	Re p <0.1	0	24.0	0
	0.1<Re p <1	3.69	22.73	0.0903
	1<Re p <10	1.222	29.1667	-3.8889
	10<Re p <100	0.6167	46.5	-116.67
	100<Re p <1000	0.3644	98.33	-2778
	1000<Re p <5000	0.357	148.62	-4.75e+4
	5000<Re p <10000	0.46	-490.546	5.787e+5
	Re p >10000	0.5191	-1662.5	5.4167e+6

Table 3 -5 Particle size distribution by mass fraction (Dufresne, 2008)

 3

	d min d 10	d 20	d 30	d 40	d 50	d 60	d 70	d 80	d 90	d 100
	350 535 593 642 689 738 790 851 931 1056 1400

Table 3 -6 Mass fractions Y d with diameter larger than d %

 3

	Diameter range( m)	Mass fraction Y d with
		diameter larger
		than d %
	350	100
	535	90
	593	80
	642	70
	689	60
	738	50
	790	40
	851	30
	931	20
	1056	10
	1400	0

  described by equations (3.83)-(3.85) were used to estimate the initial entrainment velocity:

	u d 	* 9 u 0 .	For smooth bed	(3.83)

Table 4 -1 Particle size characteristics of the samples. The weight percentages of the fraction of sieving diameters less than 80 µm were obtained from the wet sieving analysis, and the d 10 , d 50 and d 90 were obtained from the laser diffraction analysis of the fraction of sieving diameters less than 1600 µm. The values in brackets are from the measurements without ultrasound.

 4

	Number of	Sieving analysis	Laser diffraction analyser
	samples	Fraction <80µm (w/w %)	d 10 (v/v %) d 50 (v/v %) d 90 (v/v %)
	P01	66	4	37	295
	P02	77	4 (5)	32 (45)	314 (467)
	P03	59	4 (6)	49 (78)	518 (626)
	P04	4	340	794	1435
	P05	86	3	26	117
	P06	63	5 (7)	39 (53)	392 (541)
	P07	90	3 (4)	21 (33)	109 (290)
	P08	93	3	22	95
	P09	93	5 (18)	32 (185)	122 (828)
	P10	17	20	507	1233
	P11	<0.5	-	-	-

Table 4 -2 Flow condition for representative steady simulation cases

 4 The renormalization group (RNG) k-ε model was employed to represent the turbulent phenomena. It is thought to be better than the standard k-ε model since it contains more refinement features. Whilst the standard k-ε model is a "high-Reynolds number model", the RNG k-ε model provides an analytically derived differential formula for effective viscosity that accounts for low-Reynolds number effects. These features make the RNG k-ε model more accurate and reliable for a wider class of flows than the standard k-model. ωompared to the standard k-ε model and the RNG k-ε model, RSM (Reynolds Stress Model) is time consuming as it needs to solve more equations.Dufresne et al. (2009) andMignot et al. (2011) tested the standard k-ε model, the RNG k-ε model and the RSM in various urban drainage structures (three combined sewer overflow chambers for solid separation and open channel junctions with low Reynolds number). They found that the RSM model did not offer any significant improvement on the results derived using the RNG k-ε model.

	Django Reinhardt Basin	DRB Case 1	DRB Case 2	DRB Case 3
	Inflow rate (m 3 /s)	0.25	0.35	0.45
	4.3.1.3	Model setup

Table 4 -

 4 3 gives the measured accumulated sediment depth. It appears that the

and resuspension under unsteady conditions in urban stormwater detention basin / 2013 154

Table 4 -3 Sediment depth at the sampling locations

 4

	Locations	1	2	3	4	5	6	7 8 9 10 11
	Sediment depth (cm)	42 30 27 9 10 12 6 3 3	3	1

Table 4 -4 Strickler roughness coefficient K and equivalent sand grain roughness height k s

 4

	Roughness values	Ks1	Ks2	Ks3	Ks4
	K(m 1/3 /s)	75	65	55	50
	k s (m)	0.00040	0.00094	0.0026	0.0045

Table 4 -5 Mean particle sizes distribution (psd) of 15 trap samples from storm event 31/5/2007, adapted from Torres (2008).( D xx = volume percentage)

 4

	v/v% ϊiameter( m)	D 10 15	D 20 26	D 30 38	D 40 50	D 50 65	D 60 82	D 70 106	D 80 146	D 90 241	D 100 923

Table 4 -6 Simulated removal efficiencies with different bed boundary conditions (ρ=1700)

 4

	Particle properties		Simulated efficiency (%)
	Density	Diameter	BSS	BSS	BTKE	BTKE
	(kg/m 3 )	(µm)	(τ c =0.03Pa,	(τ c =0.01Pa,	(k c =4.5e-5,	(k c =4.5e-5,
			C L = 0.15)	C L = 0.15)	C L = 0.15)	C L = 2)
	1700	10	85.34	74.79	78.61	98.51
	1700	65	99.99	99.99	99.98	99.74
	1700	100	100	100	100	99.98
	Means efficiency (%)	95.11	91.66	92.86	99.41

Table 4 -7 Simulated removal efficiencies with different bed boundary conditions (ρ=2400)

 4

	Particle properties	Simulated efficiency (%)
	Density	Diameter	BSS	BSS	BTKE	BTKE
	(kg/m 3 )	(µm)	(τ c = 0.03 Pa,	(τ c = 0.01 Pa,	(k c =0.000045,	(k c =0.000045,
			C L = 0.15)	C L = 0.15)	C L = 0.15)	C L = 2)
	2400	10	87.42	77.80	81.05	96.66
	2400	65	100	100	100	99.96
	2400	100	100	100	100	100
	Mean efficiency (%)	95.81	92.60	93.67	99.87

Table 4 -8 Comparison of experimental and simulated removal efficiency using bed boundary conditions of fixed BTKE and the proposed BTKE formula with different C L values.

 4

	Boundary cond.	Experimental	Simulated Efficiency (%)
		Efficiency (%)	C L =0.05	C L =0.15	C L = 1	C L = 2
	Fixed BTKE	33±5	67.61	62.88	71.52	74.19
	Proposed BTKE	33±5	53.99	54.01	53.32	64.80
	4.4.3 Tests in the full scale basin using a steady state DPM

Table 4 -9 Settling velocities measured in the storm event 31/5/2007 with 15 sediment trap samples, adapted from Torres (2008).

 4

	v/v%	V 10	V 20	V 30	V 40	V 50	V 60	V 70	V 80	V 90	V 100
	Settling	0.88	1.85	3.06	4.57	6.55	9.23	13.27 21.64 35.23 57.46
	velocity (m/h)

Table 4 -10)

 4  shows the simulated deposit zone with fixed BTKE and the proposed BTKE boundary conditions. Compared to the simulated results obtained with a fixed BTKE (shown in 2 9 4 H Figure 4-34c), the proposed BTKE boundary conditions were able to predict the main deposit zones in the centre of basin and in front of Orifice 1, as shown in 2 9 5 H Figure4-34b with dashed line ellipses. The thin deposit zone near the outlet and the inlet were also predicted, as shown in 2 9 6 H Figure4-34b and marked with the rectangules. From the point of view of sediment distribution prediction, the proposed BTKE formula is capable of identifying the most likely deposit zone in full scale basins.

	2 9 3 H

Table 5 -1 Bed boundary condition test configuration

 5

		A: settling condition	B:	entrainment	Initial entrained velocity
	Case 1: fixed BSS Case 2: varying BSS Case 3: fixed BTKE	BSS=0.03 Pa BSS=Shields curve # BTKE=0.0002 m 2 /s 2	condition Shields curve # Shields curve # Shields curve #	Hu and Hui's formula* Hu and Hui's formula* Hu and Hui's formula*
	Case 4: varying BTKE	BTKE:

Table 5 -2 Experimental and simulated removal efficiency in the basin

 5

		Experiment	Varying BTKE	Varying BSS	Fixed BSS	Fixed BTKE	Trap
	Removal Efficiency (%)	33±5	28	22	47	46	88

Table 5 -4 DPM setup and different bed boundary conditions for the proposed method

 5

	Case No.	Process A: settling	Process	B:	Total	Rebound	Initial		DRWM
		cond.	entrainment	particle	resistance	entrained	C L
			cond.		number	coefficient	velocity
						e, f**	(m/s)u d ,v d
	DPM 1	Varying BSS #	Varying		22400	e:1,	Hu	and	0.15
			BSS #			f:1	Hui *#
	DPM 2	Varying BSS #	Varying		44800	e:1,	Hu	and	0.05
			BSS #			f: 1	Hui *#
	DPM 3	Varying BSS #	Varying		44800	e:1,	Hu	and	0.25
			BSS #			f:1	Hui *#
	DPM 4	Varying BSS #	Varying		44800	e:1,	Hu	and	0.5
			BSS #			f:1	Hui *#
	DPM 5	Varying BSS #	Varying BSS #		44800	f:0.73 e:0.84-ζ.8ζ *	Hui *# Hu	and	0.05
	DPM 6	Varying BSS #	Varying BSS #		67200	f:0.73 e:0.84-ζ.8ζ *	v d =2u * u d =2u *		0.05
	DPM 7	Varying BSS #	Varying BSS #		67200	e:0.84-ζ.8ζ * f:0.73	u d =2u * v d =2u *		No DRWM
	DPM 8	BTKE 1	Varying BSS #		22400	f:1 e:1,	v d =2u * u d =2u *		0.15
	DPM 9	BTKE 2	BTKE 2		67200	e:0.84-ζ.8ζ *	u d =2u *		0.05
						f:0.73	v d =2u *
	DPM 10	BTKE 1	BTKE 1		67200	e:0.84-ζ.8ζ *	u d =2u *		0.05
						f:0.73	v d =2u *
	DPM 11	BTKE 2	Varying BSS #		67200	f:0.73 e:0.84-ζ.8ζ *	v d =2u * u d =2u *		0.05
	DPM 12	Fix BSS	BTKE 1		67200	e:0.84-ζ.8ζ *	u d =2u *		0.05
		=0.03 Pa				f:0.73	v d =2u *

Table 5 -5 Simulated removal efficiency of different case setups

 5

	Case No.	DPM 1	DPM 2	DPM 3	DPM 4	DPM 5	DPM 6
	Efficiency (%)	79.45	87.85	81.48	82.00	86.77	90.80
	Case No.	DPM 7	DPM 8	DPM 9	DPM 10	DPM 11	DPM 12
	Efficiency (%)	98.41	73.02	85.02	85.19	86.06	85.83

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2013ISAL0034/these.pdf © [H. Yan],[2013], INSA de Lyon, tous droits réservés

and resuspension under unsteady conditions in urban stormwater detention basin / 2013

6 1 H Figure

2-8 illustrates several key concepts in the relationships between erosion, transport, and deposition. However, for cohesive sediment, mostly clay but also silt, the erosion velocity increases with decreasing particle size, and the cohesive forces are relatively greater when the particles get smaller. The critical velocity for deposition, on the other hand, depends on the settling velocity which decreases with decreasing particle size. The curve was added to by Hjulström's disciple[START_REF] Sundborg | The river Klarälven. A study of fluvial processes[END_REF]. He significantly improved the level of detail in the cohesive part of the diagram, and added lines for different modes of transport. However, an exact model showing the relationship can not be found in the literature.

9 H Figure

[4][5][START_REF]References[END_REF][7][8][9][10][11][12][13][14][15] shows that the BSS (<0.01 Pa) of DRB case two has a very similar profile to the spatial distribution of sediment in the basin and the photo from Google maps. Based on the assumption that there is a higher probability of sediment settling out in the lower BSS zone, and a comparison of BSS distribution and sediment depth distribution, the simulated BSS shows reasonable agreement in the central zone and the zone in front of orifice one Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2013ISAL0034/these.pdf © [H. Yan], [2013], INSA de Lyon, tous droits réservés

4 2 H Figure 4-16 shows that the low velocity (<0.04 m/s) zone near the basin bed and close to the free surface corresponds to deposit distribution in the basin. The analysis is similar to the low BSS distribution. In fact, BSS distribution shows a similar velocity distribution profile when comparing BSS distribution with the near bed velocity distribution.

5 0 H Figure 4-20 presents the bed turbulent kinetic energy (BTKE) distribution in the basin below

5 1 H Figure 4-21 shows the low bed shear stress of the simulation results for DRB cases one and three. The profile distributions shown are quite different to the sediment spatial distribution, but still present the same lower BSS zone as in DRB case two in the zone close to the downstream overflow weir and the zone in front of orifice one for example (see 2 5 2 H Figure 4-15a). Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2013ISAL0034/these.pdf © [H. Yan], [2013], INSA de Lyon, tous droits réservés

5

H DRB case 3 Qin=0.45 m3/s

1 7 H Figure 5-9a presents the final deposit zone from the simulated sediment transport results. As we can see from the figure, the simulated sediment distribution zone shows reasonable levels of agreement compared to the preferential experimental deposit zones, such as the deposits in the downstream section of the basin and in the left and right-hand upstream corners. The almost empty zone at the middle of basin is all accurately predicted.

2 5 H Figure 5-14 and 3 2 6 H Figure 5-15 show the near bed particle concentration distribution with different DRWM modelling parameters C L . Compared with the observations shown in Figure 5-7, the simulation results with C L =0.05 seem to agree on near bed sediment distribution. Thus C L =0.05 in DRWM was chosen for the subsequent tests. Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2013ISAL0034/these.pdf © [H. Yan], [2013], INSA de Lyon, tous droits réservés

Acknowledgements

First of all, I would like to express my gratitude to my supervisors, Jean-Luc Bertrand-Krajewski and Gislain Lipeme Kouyi for their exceptional supervision of my PhD research. Over the past three and half years, G. Lipeme Kouyi offered his valuable input during discussions and his support on the subject. I am particularly grateful for his extraordinary patience during our discussions, given my level of French. J.-L. Bertrand-Krajewski gave indispensable guidance for this research, in particular on experiments. His rigorous scientific attitude and extensive knowledge have deeply influenced me.

List of Figures

H. Yan (1994).Design hydrology and sedimentology for small catchments. San Diego, CA: Academic Press.

Hager W.H. (2010). Wastewater Hydraulics: theory and practice. 2 nd , Springer, Switzerland.

Hall M.J., Hockin and Ellis J.B. (1993). Design of food storage reservations. London: Butterworth Heinemann.

Appendix