Modeling airflow related to train movement in subway stations: small-scale model and numerical simulations compared to on-site measurements Brussels

Keywords: discrepancies, display

scale experimental model . . . . . . III Putting in perspective 9 Numerical versus experimental comparison 9.1 Compared velocity profiles for measurements and models at locations of interest . . . . . . . . . . . . .

Loreline Faugier

Thesis presented on August 28 th , 2023 at the Royal Military Academy of Brussels, Belgium in order to obtain the degree of Doctor in Engineering sciences from the Royal Military Academy of Brussels jointly with the University of La Rochelle and the von Karman Institute for Fluid Dynamics

Acknowledgment

Ces années de thèse ont été pour moi riches d'expériences formatrices, parfois intenses, parfois aussi pleines de doutes, mais toujours bien accompagnées. Je tiens donc à remercier sincèrement les différentes personnes qui y ont contribué ou qui m'ont sontenue dans ce projet. J'ai eu notamment la chance, pour ce travail, d'être entourée par pas moins de quatre professeur•e•s, dont l'appui scientifique, le suivi et le soutien m'ont donné suffisamment de confiance pour mener cette thèse à bien.

Benoît, je ne pourrais assez te remercier pour ta présence constante tout au long de ce travail et sur tous ses aspects: pour ta disponibilité pour lire, discuter, expliquer, et relire encore, mais aussi pour avoir veillé à garder tes troupes motivées et épanouies. Ton sens de l'organisation et de la pédagogie, toujours exercés avec rigueur et sensibilité, sont pour moi des modèles pour la suite de ma vie professionnelle.

Professeur Bosschaerts, je n'en serais pas ici aujourd'hui sans votre oeil avisé lors de vos cours à l'Université de Lille, et je suis reconnaissante pour cela. Merci aussi de m'avoir laissé une grande liberté pour aborder le sujet de la thèse, tout en veillant à me faire prendre du recul sur les résultats obtenus.

Professeur Limam, vos conseils expérimentés et vos encouragements ont su me guider, et me stimuler autant que me rassurer durant les différentes étapes du projet de thèse. Merci également de m'avoir permis de participer à l'un de vos projets scientifiques, qui était une ouverture bienvenue sur d'autres environnements et sujets de recherche.

Professeure Laboureur, merci pour vos relectures attentives du manuscript, et merci d'avoir toujours su suggérer des pistes de recherche en réponse à mes questionnements, sur les aspects liés à la PIV entre autres. Votre créativité et votre sens du détail ont été de vrais atouts pour avancer dans mon travail.

Je tiens également à remercier les rapporteur•e•s et les membres du jury, qui procèdent à une lecture approfondie de cette thèse -c'est un privilège de voir l'ensemble de son travail évalué minutieusemment.

Des personnes du département de mécanique et de l' École Royale Militaire que j'ai pu solliciter, je retiens la disponibilité et la gentillesse dont vous avez toujours fait preuve.

Jan, je dois beaucoup à ton aide pour toutes les parties expérimentales du pro-jet, et particulier pour le développement -parfois express -des codes LabView. L'efficacité (avec un peu de magic tape) et l'humilité avec lesquelles tu travailles sont pour moi exemplaires. Bart, merci pour tes dépannages informatiques en tous genres, et merci d'avoir partagé ton expérience précieuse sur les différents instruments et systèmes du laboratoire.

Werner et Matthias, je voudrais aussi vous remercier pour vos conseils avisés et astucieux au laboratoire, notamment pour la construction du modèle réduit, ainsi que pour votre constante sympathie et disponibilité. Je dois aussi à M. Vandoren, du magasin Top 1 Toys, d'avoir toujours si gentiment et efficacement réparé notre fragile et précieux petit train.

Brigitte et Yoshi, je me rappelle que vous avez été parmi les premières personnes à accompagner mon arrivée en Belgique ainsi que mes débuts dans la vie de salariée. Merci pour cela.

Nikos, Ahmed, Guido, Carlo, Matija, Tristan, Pierrette, you made coffee breaks enjoyable even when the coffee that took approximately one hour to get ready was, in the end, terrible. Through stressful times, your (dark) humor, advice (whether it is about scientific and administrative topics or about swimming techniques) and enthusiasm made my heart lighter, and I wish you courage and success in the continuation of your PhDs.

To the interns I had the chance to supervise: Abderrahmane, Maria, Quentin, Antoine, Cyril, Mikhail, thank you for contributing to various level of this research. Feeling responsible for someone's education is both a humbling experience and a great source of growth, and I am thankful for the trust you have put in me. To master students in particular: Fabio, despite the Covid outbreak hitting in the middle of your thesis and forcing you to re-think your topic, you demonstrated admirable rigor and perseverance to deliver your thesis. Isabeau and Joren, I remain impressed by your dedication, your resourcefulness, your enthusiasm and your positive mindset while conducting your thesis. Your company during the experimental campaign is for sure a good part of what remains a defining moment of the PhD for me, despite the challenges of lockdown, the demanding schedule, and freezing conditions.

To my parents, my family, my friends (if you are reading this bit, it most probably means that you are part of the close ones), I could not thank you enough for always encouraging me and sticking with me through the highs and the lows of these last years. To my friends in Brussels, I did not imagined that I would be surrounded by such kind, smart, fun and caring persons when I moved here not knowing anyone, and I am extremely grateful for having you there now. To the older ones further away, knowing that I count on you brings me joy and peace, and I am honored to have you on my side along the years.

Brussels, June 2023

Loreline Faugier F.1 Results at chosen locations for correlation and peak value of vector fields, from images processed with the subtract time filter, for different filter lengths. Filter type: subtract minimum. . . . . . . . F.2 Results at chosen locations for correlation and peak value of vector fields, from images processed with the subtract time filter and the remove background / unsteady reflections filter, in different orders. F. [START_REF]Ansys Fluent User's Guide -Release[END_REF] x, y, z

Cartesian coordinates [m]

Greek symbols

β Blokage ratio [-] δ Kronecker symbol [-] λ Wavelength [m] µ Dynamic viscosity [kg • m -1 • s -1 ] ν Kinematic viscosity [m 2 • s -1 ] ρ Density [kg • m -3 ] σ Standard deviation [-] τ or τ ij Shear stress [N • m -2 ]
Sub-and Superscripts Résumé en franc ¸ais -Summary in French-Modélisation de l'écoulement de l'air lié à la circulation des trains dans les stations de métro : modèle à échelle réduite et simulations numériques comparés aux mesures sur site La qualité de l'air intérieur des stations de métro souterraines soulève des questions liées à la santé et la sécurité des usagers, ainsi qu'à l'efficacité de la ventilation. Dans ces environnements particuliers situés à l'interface entre l'extérieur et le réseau de métro souterrain, une grande partie des mouvements d'air est attribuée à l'effet piston qui se produit lorsque les trains traversent la station. L'évolution temporelle et spatiale, à différentes échelles, de ces écoulements d'air induits par les trains n'est pas encore bien appréhendée. Étant donnée la complexité technique et logistique liée à la réalisation de mesures sur site dans une station lors de son fonctionnement, il est souvent fait appel à des modèles pour prédire et étudier ces flux d'air, bien que les différences entre les données mesurées et celles modélisées soient rarement discutées.

Cette thèse vise, à travers une étude de cas d'une station à double voie avec des quais latéraux, à explorer le développement de modèles pour les flux d'air induits par les trains sur les quais des stations de métro souterraines. Une attention particulière est accordée à la capacité des modèles à reproduire les principaux éléments de l'effet piston dans la station, conséquence des trains entrants et sortants.

Un modèle en trois dimensions de la station est créé, utilisant les techniques de Computational Fluid Dynamics (CFD) et un maillage dynamique. La longueur du tunnel nécessaire à inclure dans la géométrie pour obtenir un écoulement développé autour du train et limiter l'influence des limites géométriques du domaine est déterminée, et une tentative de simulation de la ventilation naturelle est réalisée en imposant un gradient de pression via les sorties. Le deuxième modèle consiste en une version à petite échelle de la station à l'échelle 1:95, où des images de Particle Image Velocimetry (PIV) sont acquises et traitées. Dans les deux modèles, le mouvement réaliste du train à travers la station est préservé, comprenant une phase de décélération, d'arrêt et de départ.

Afin de s'assurer de la qualité des résultats issus des modèles, une campagne extensive de mesures sur site est menée, en enregistrant la vitesse à neuf positions différentes du quai en nombre suffisant pour calculer un ensemble averaging. Afin d'évaluer quantitativement la fiabilité des modèles, il est nécessaire de disposer d'outils systématisés pour comparer les résultats de la vitesse, qui est un phénomène transitoire, à différents emplacements de la station. Comme ce flux d'air est caractérisé par des pics liés au départ et à l'arrivée du train dans la station, cette thèse propose d'évaluer la concordance entre les mesures sur site, les résultats du modèle numérique et les résultats obtenus avec le modèle à petite échelle en utilisant des paramètres de corrélation et de forme des pics. Cette comparaison approfondie permet de conclure que les modèles peuvent reproduire les principaux éléments du vent piston dans la station : les résultats numériques et expérimentaux révèlent tous deux que d'importantes différences peuvent être observées entre des emplacements même proches, en raison de l'apparition de variations dans l'écoulement à une fraction de l'échelle du quai, principalement dans le plan horizontal. De plus, des variations locales de vitesse se produisent sur de courtes périodes de temps, qui sont de l'ordre de la vitesse du train. Cependant, les prédictions plus fines de la magnitude de la vitesse sont moins fiables car elles sont limitées par des simplifications de la géométrie et des conditions aux limites, ainsi que par des considérations d'échelle. Néanmoins, les modèles sont de bons outils pour explorer les schémas d'écoulement sur le quai et sont utilisés pour étudier comment les variations du taux d'obstruction de la station ou de la vitesse du train affectent la magnitude de la vitesse et les échanges d'air dans la station.

English summary

The air quality inside underground subway station raises concerns regarding health, safety and ventilation efficiency. In these particular environments lying at the interface between the outdoors and the underground subway network, a large contribution to the air movements is attributed to the piston effect as trains are going through the station. The temporal and spatial development of this complex traininduced airflow at various scales is not fully resolved yet. On-site measurements in a station during routine operations are difficult to implement, and models are often relied on to predict and study this airflow, although the differences existing between measured and modeled data is rarely discussed.

Through a test case of a double track station with side platforms, this thesis aims to explore the development of models for train-induced airflow on the platforms of underground subway stations. Special attention is given to the ability of the models to capture the key elements of piston wind in the station due to ingoing and outgoing trains.

A three-dimensional model of the station is implemented using Computational Fluid Dynamics (CFD) and a dynamic mesh. The necessary tunnel length to include in the geometry to obtain a developed flow around the train body and limit the influence of the far-field domain boundaries is determined, and an attempt at simulating natural ventilation is realized by imposing a pressure gradient through the exits. The second model consist in a small-scale version of the station at scale 1:95, where Particle Image Velocimetry (PIV) images are acquired and processed. In both models, the realistic movement of the train through the station is preserved, including a deceleration, stop and departure phase.

To gain confidence in the outputs of the models, an extensive on-site measurement campaign is led, recording velocity magnitude at nice different positions of the platform in a sufficient number to compute an ensemble-average. In order to assess quantitatively the reliability of the models, the need arises for systematized tools to compare the results of the transient velocity magnitude at different locations. As this airflow is characterized by peaks related to the departure and the arrival of the train through the station, this thesis proposes to evaluate the match between the on-site measurements, the outputs of the numerical model and the results obtained with the small-scale model using correlation and peak shape parameters.

This in-depth comparison allows to conclude that the models can capture the key elements of piston wind in the station: both the numerical and experimental results reveal that large differences can be found between locations even if these are close to each other, that are the consequence of flow features developing at a fraction of the platform scale, mainly in the horizontal plane. Also, local velocity changes occur over short time intervals scaling with the train velocity. However, finer predictions about the value of the velocity magnitude are less reliable as they are bounded by simplifications of the geometry, of the boundary conditions and by scaling considerations. Nevertheless, the models are good tools to explore the flow patterns on the platform and are used to investigate how changes in station blockage ratio or train speed affects the velocity magnitude and air exchanges in the station.

Introduction

Context and motivation of the research

There is a growing interest in maintaining a safe and healthy environment for the millions of passengers who travel through underground public transportation infrastructures. During rush hours, large numbers of people are brought together in confined and overcrowded spaces, which can potentially lead to volatile conditions. As efforts are made to expand the subway network and alleviate traffic congestion [START_REF] Li | Does subway expansion improve air quality[END_REF], concerns arise about the concentration of particulate matter emitted from train brakes or wheel friction on the rails. Additionally, there are concerns about the transmission of infectious diseases through close person-to-person contact, as identified by Gershon et al. [START_REF] Gershon | Goldsmith. Health and Safety Hazards Associated with Subways: A Review[END_REF]. In 2020, Wen et al. [START_REF] Wen | Environmental and health effects of ventilation in subway stations: A literature review[END_REF] conducted a review of the effects of ventilation on subway station air quality, including factors such as temperature, humidity, drafts, air pollutants, and noise levels. It was noted that platforms pose the most complex challenges within subway zones, as they are isolated from the outdoor environment and directly impacted by polluted air from station halls and tunnels, while also accommodating the highest number of passengers.

INTRODUCTION

the platforms compared to inside the trains while boarding and waiting at various stations on two São Paulo subway lines. Ji et al. [START_REF] Ji | Concentration, composition, and exposure contributions of fine particulate matter on subway concourses in China[END_REF] measured PM 2.5 concentration and composition in different stations of a Chinese subway network and found that subway workers were more exposed to harmful substances compared to other types of workers. The passage of trains can also be the source of strong wind gusts, and Khayrullina et al. [START_REF] Khayrullina | CFD simulation of train aerodynamics: train-induced wind conditions at an underground railroad passenger platform[END_REF] proposed a wind speed of 5 m/s as the threshold for passenger discomfort caused by wind. Additionally, they identified a wind speed of 12 m/s with duration of 0.5 s and acceleration of 0.43 m/s 2 as the threshold for wind-related dangers. In the context of the Covid-19 pandemic, Löhner et al. [START_REF] Löhner | High-fidelity simulation of pathogen propagation, transmission and mitigation in the built environment[END_REF] conducted crowd simulations, which indicated an infection rate of 1 inside a subway train station, meaning that, on average, one person infects another commuter. Underground stations are also vulnerable to occasional fire hazards, and in such cases, Modic emphasized the critical role of smoke control through ventilation in saving lives [START_REF] Modic | Fire simulation in road tunnels[END_REF]. There have also been instances of terrorist attacks targeting these indoor environments, involving the release of toxic chemicals, as seen in the infamous Tokyo 1995 event that caused mass casualties [START_REF] Tu | Chemical Terrorism: Horrors in Tokyo Subway and in Matsumoto City[END_REF]. In such emergency situations, Policastro et al. [START_REF] Policastro | The use of technology in preparing subway systems for chemical/biological terrorism[END_REF] highlighted the importance of a rapid emergency response. Hosseini et al. [START_REF] Hosseini | CFD-based modeling of sarin gas sispersion in a subway station -A hypothetical scenario[END_REF] simulated successive train arrivals and departures through a subway station with various sarin release scenarios, demonstrating how the spread of the contaminant could be influenced by train-induced wind. Benhassine et al. [START_REF] Benhassine | Simulating the Evacuation of a Subway Station after a Sarin Release[END_REF] conducted evacuation simulations using a Gaussian puff model for inhaled sarin doses and a social force model for pedestrian trajectories to evaluate the severity of the impact on victims.

From these studies, it becomes apparent that identifying and analyzing representative scenarios are valuable tools for better designing and adapting transportation infrastructures and the various services associated with their operation. Moreover, there is a growing emphasis on the energy consumption of these systems, particularly in Western Europe where most underground transport systems were built in the last century. As a result, the renovation of ventilation systems often needs to be adapted to the existing architecture rather than integrated into the original design. Therefore, a comprehensive understanding of airflow in subway stations is essential. Subway station environments have unique climate characteristics as they are part of the built environment that interacts with both overground climate and the underground network composed of tunnels and stations. This duality, along with the computational resources required to simulate the movement of objects in a large domain, adds complexity to the development of models.

Additionally, confidence in these models can only be established through coupling them with experimental validation. The objective of the present research is to obtain a validated numerical model for air dynamics in a subway station. Computational fluid dynamics (CFD) techniques are used to simulate airflow, primarily influenced by passing trains, in two and three dimensions. The results are then compared to measurements taken by Hot Wire Anemometry (HWA) in an actual metro station during routine operations and to results obtained with Particle Image Velocimetry (PIV) in a small-scale station with a moving train.

The objectives of this thesis are stated above in a very brief way, as we will need additional information to be able to fully express their stakes and challenges. Having first surveyed the current state of the art in the field of subway climatology and train piston effect, allowing to point out the gaps in the knowledge in these areas, the research questions will be refined in Section 2.4.2. Later, after reviewing the different numerical and experimental approaches available to deal with these questions, Section 5.2 explains how the objectives will be concretely addressed.

Thesis outline

To address the topic briefly brought up in the section above, this work is structured in three parts.

Part I is focused on giving an overview of the current state of knowledge and available techniques that can be used to give insights into the flow phenomenons at stake inside an underground subway stations, aiming to provide all the necessary elements to conduct the project.

Chapter 2 consists in a literature review starting with train aerodynamics, then tackling specifically subway climatology and the flow dynamics associated with underground space, and in particular piston effect. At the end of this chapter, the limits of the literature are outlined, leading to the main research questions that will guide this project.

In Chapter 3, we present a summary of the basic definitions and equations and needed to describe the state and motion of a fluid. An introduction to CFD is also given, reviewing the most popular methods and justifying the choice of the RANS approach for our case.

Chapter 4 covers the experimental measurement techniques that will be used in this thesis. The theory behind HWA and PIV is discussed, comparing the drawbacks and advantages of each technique and how they complement each other.

Using the resources from the previous chapters, the methodology used to address the research questions can be unfolded and is detailed in Chapter 5. A reallife subway station in Brussels, where the forced ventilation is mainly realized by the piston effect, is taken as a test case: on-site measurements will be performed in this station, and both a numerical CFD model and a small-scale model will be developed based on this station. Representative scenarios are defined in order to clearly identify the object of the study and make the results comparable across measurements and model outputs.

INTRODUCTION

In Part II, these tools are implemented and developed for the three main branches of the project, discussing design choices while keeping in mind how to articulate results in order to validate the numerical model.

The large-scale field experimental campaign is firstly addressed in Chapter 6. The technical and organizational challenges associated with performing measurement in a real-life subway station during daily operation are covered. The measurement setup including notably velocity measurements with HWA and the detection of the train in the station is detailed.

Chapter 7 details the elaboration of the CFD model in ANSYS Fluent. A simplified geometry of the station is used to implement a scenario of a train passing through the station, with dynamic meshing techniques, and background wind is included in one configuration. An attempt at reproducing the results using the Immersed Boundary Method (IBM) is also reported.

Chapter 8 reports the design process to build a small-scale model of the subway station at scale 1:95 with a train moving through it in the lab of the Royal Military Academy, to perform PIV measurements in a horizontal plane in the station. The questions related to the creation of a new experimental system, both from the aspects of technical issues faced and of the scientific validity of the model, are addressed.

Part III gathers the results obtained from the previous parts, discuss them with a critical eye, and uses them to draw conclusions on train-induced station airflow.

The complete comparative results of the experimental campaign and the outputs of the numerical and small-scale models are included in Chapter 9 in the form of velocity curves. To characterize the match between the different results, peak shape parameters are brought forward and computed. The similarities and differences existing between the measured values and the outputs from the models are considered, and encapsulated in a discussion about the capabilities and limitations of the models to capture the main characteristics of train-induced airflow in an underground subway station.

With this in mind, some applications for the model are proposed in Chapter 10, both to gain knowledge about the existing situation through the models, or to predict the airflow for other simple configurations and scenarios: change of blockage ratio of the train in the station, change of train speed, or applying Background Oriented Schlieren (BOS) to visualize the spread of gas in the tunnel for instance.

The thesis concludes in Chapter 11 with a summary, highlighting key findings as well as limitations of the presented work, and presents recommendations for future research.

Being able to perform on-site measurement in a subway station while daily traffic ongoing is a rare opportunity that requires a close collaboration with public transport services. The main originality of this work therefore comes from the combination of on-site measurements, numerical model and small-scale model of the same test-case station. Special attention is given to the reproduction of realistic conditions creating the characteristic piston effect by replicating the movement of the train in both models. The quantities measured and discussed focus on the temporal and spatial variability of the airflow on the platform, within the time frame defined by the passage of a train.

Despite the parts being presented separately in this thesis, the interaction between the development of the numerical model and the experimental validations followed an iterative process. The first iterations of the numerical model made clear what type of quantities were relevant and feasible to obtain experimentally, on-site and with a small-scale model, in order to have data to validate the numerical model. On the other hand, some outputs (such as the deceleration curve of the incoming train, or the magnitude of background airflow) of the experimental campaign where used as inputs of the numerical model to make it as realistic as possible after applying the simplifications. This implies that in the time allowed to complete a doctoral research, the work had to be carried out with choices and assumptions that sometimes proven later not to be the optimal ones. Explicitly addressing the pitfalls arising in the numerical and experimental analysis along the manuscript make the thesis highly valuable from a conceptual and practical perspective when elaborating models and conducting the study.

Main related publications

Some of the results that became available during the doctoral research have been presented in various scientific contexts or published. The two main publications that have been through the peer-reviewed process are listed in this section. [START_REF] Faugier | CFD model to assess parameters influencing piston wind in a subway tunnel and station[END_REF]).

The first publication is mainly based on the elaboration of the numerical model and some of its outputs, and only an small excerpt of the on-site measurements is included in the article. A preliminary numerical study is done to determine the tunnel length necessary to obtain a stable flow around the train body before it reaches the station, for three different blockage ratios. This part is explained in Section 7.3.2 in particular.

For the simulations including the station, two different architectures and three train speeds are simulated and the effect of these configurations on the station airflow is evaluated through the air velocity and the mass flow rate at one location INTRODUCTION on the platform. Similar results are also presented and discussed in Section 10.1.

• L. Faugier, B. G. Marinus, W. Bosschaerts, D. Laboureur, K. Limam. CFD model for airflow in a subway station compared to on-site measurements: the challenges of as-built environment. Tunnelling and Underground Space Technology, 2023 (in production).

The second publication, which has been accepted and is being edited at the time of submitting this manuscript, includes the fully processed on-site measurements presented in Chapter 6 and the numerical model from Chapter 7. For these two types of outputs, numerical to experimental comparison is performed, based on the quantification of the peaks in air velocity magnitude due to ingoing and outgoing trains. These topics are extensively covered in Chapters 9.

Aeraulic effects in underground subway stations and their numerical models

In this introductory chapter, the existing research concerning flow around trains, and specifically airflow induced by trains in subway stations, is reviewed. Section 2.1 first places briefly the study in the broad context of train-induced airflow. Section 2.2 focuses on subway climatology to define the relevant concepts at stake (piston effect and background airflow in particular) and highlights the challenges of subway station ventilation. In Section 2.3, the different experimental and numerical methods used to characterize the tunnel and station airflow are reviewed, and confronted with each other. Section 2.4 finally points out the gaps in the literature and states the objectives of this thesis in order to fill those gaps.

Aerodynamics of trains

The aerodynamics related to trains at high speed (above 100 km/h) have been studied with regards to various concerns: energy losses and performance deterioration [START_REF] Raghunathan | Aerodynamics of high-speed railway train[END_REF], noise reduction [START_REF] Ricco | Nature of pressure waves induced by a high-speed train travelling through a tunnel[END_REF], or safety of persons standing on the platform subject to strong wind gusts [START_REF] Khayrullina | CFD simulation of train aerodynamics: train-induced wind conditions at an underground railroad passenger platform[END_REF], to cite only a few. Bell et al. [START_REF] Bell | Moving model analysis of the slipstream and wake of a high-speed train[END_REF] make a distinction between two flow types around a train: the accelerated regions of air, where the airflow di-rection is opposed to the train movement direction, lie in a layer close to the nose and the rear of the train; and the entrained regions of air, where the airflow direction is the same as the train movement direction, appear around the train between its front and its rear, and in the wake of the train. In his work about the dispersion of particles from train brakes in underground station, Durand [START_REF] Durand | Dispersion des particules issues du freinage des trains en stations souterraines[END_REF] pointed out that although the existing studies about high-speed trains give a good idea of the flow topology around a train, underground transportation with relatively low speed trains are characterized by different and less documented features. The flow generated by a subway train, although of lesser magnitude than for high-speed trains, will be affected by the walls of the tunnels and stations that surround it, shaping it differently than for an open-air train.

Specificities of subway climate

As Pflitsch et al. [START_REF] Pflitsch | Spatial variability and dynamic changes in air temperature distribution within different subway stations[END_REF] describe, tunnels and stations of a subway system are a very complex, vertically and horizontally expanding network that has multiple punctual connections to the surface. The air inside a subway station is therefore affected by numerous influences: natural flows from the outside, trains traveling at varying and relatively low speed through them, and other anthropogenic patterns like passengers' movement and artificial ventilation... In the past three decades, various studies have hence investigated the question of airflow in subway stations.

Waymel [START_REF] Waymel | Modélisation des effets thermiques et aérauliques dans les stations de métro[END_REF] simulated the mass flow rates through different surfaces of a Parisian subway station after 5 passages of trains in two directions to evaluate thermal comfort of the passengers and found a periodicity related to the train passage frequency. A substantial measurement campaign of particulate and gas concentrations in 10 stations in Barcelona was led by Moreno et al. [72], and evidenced the influence of train length, speed, tunnel length and station design on traininduced wind. Monitoring underground particulate concentration in a Parisian station during a week, Walther et al. [START_REF] Walther | A novel approach for the modelling of air quality dynamics in underground railway stations[END_REF] observed that the PM concentration follows closely the frequency of trains. Targino [START_REF] Targino | Spatio-temporal variability of airborne particulate matter in the São Paulo subway[END_REF] also reported that a periodicity related to the dynamics of trains serving the station was visible in the pollutants concentrations on the platforms. Consistent with Izadi et al.'s [START_REF] Izadi | Numerical analysis of the micro-particles distribution inside an underground subway system due to train piston effect[END_REF] CFD simulations results, Li et al. [START_REF] Li | Effects of traininduced unsteady airflow on air quality and air distribution in a subway station[END_REF] additionally measured on a Chinese subway platform that PM 2.5 concentration rose with the increase in air velocity at every train arrival in the station, and they proposed mitigation measures in the form of controllable vents. These works highlight piston effect and ventilation as key phenomenons affecting the dilution mechanism of particles in subway stations.

Piston effect

This phenomenon appears when a train travels through a narrow tunnel, and the air pushed by the train cannot flow freely around the train as it would in open air; a positive pressure volume is formed at the front, while a negative pressure and highly turbulent region appears behind the train [START_REF] Cross | Enhancing the piston effect in underground railway tunnels[END_REF]. In addition, because of fluid viscosity, the surface of the vehicle drags the air to flow with the vehicle. Those changing pressure differences between the front and back of the train on top of ambient wind generate flows with varying directions and intensities, which are represented schematically on Figure 2.1, where the regions drawn in blue corresponds to the characteristics of an open air train and documented by Bell [START_REF] Bell | Moving model analysis of the slipstream and wake of a high-speed train[END_REF]; the arrows in black are related to the restriction of the airflow due to the presence of the tunnel, as schematized by Khaleghi [START_REF] Khaleghi | Analysis of unsteady airflow in a subway station influenced by train movement[END_REF]. The resulting flow velocities and pressures were monitored at the entrance and the exit of a scaled tunnel by Kim and Kim [START_REF] Kim | Experimental and numerical analyses of traininduced unsteady tunnel flow in subway[END_REF] to better understand the temporal aspect of piston effect. They observed that the pressure difference reaches a maximum when the train reaches its maximum speed. When the train speed stabilizes, the pressure difference decreases before becoming constant. To provide parameters allowing comparison between various cases, velocities can be made comparable using the dimensionless velocity u/u * , where u * is a reference velocity, in this case the maximum train velocity, i.e. the cruise speed of the train in the tunnel before it brakes while arriving in the station. Bell et al. [START_REF] Bell | Moving model analysis of the slipstream and wake of a high-speed train[END_REF] have used the length-to-height ratio of the train and the Reynolds number to study the sensitivity of the airflow induced by a high-speed train to these parameters. Out of the different variables influencing the magnitude and the temporal evolution of the piston wind, the blockage ratio β can be used to compare tunnel and station design in a non-dimensional form. It compares the cross-sectional area covered by the train in the tunnel to the one of the tunnel.

Cross et al. [START_REF] Cross | A validated numerical investigation of the effects of high blockage ratio and train and tunnel length upon underground railway aerodynamics[END_REF] for instance studied the influence of blockage ratio on tunnel outlet velocities. They remarked that during acceleration and deceleration phases of the train, higher blockage ratios translate into steeper and earlier variations in the velocities, and that the maximum attained velocity is higher. During the constant velocity phase, increasing blockage ratio from 0.65 to 0.85 results in an increase of 36% in the outlet velocity. Khayrullina et al. [START_REF] Khayrullina | CFD simulation of train aerodynamics: train-induced wind conditions at an underground railroad passenger platform[END_REF] simulated two types of highspeed trains passing through a fictive station without stopping and also observed that sudden changes of blockage ratio at the beginning and the end of the platform i.e. at the transition between the station (β = 28%) and the tunnel (β = 39%) produced local maxima in the wind speeds at the extremities of the platform. At a height of 1.2 meters above the platform level, they measured maximum velocities of 0.46u * and 0.53u * for trains passing around 30 m/s. Through momentum balance equations, Brown [START_REF] Brown | Basic theory of rapid transit-tunnel ventilation[END_REF] gave a developed expression for air velocity in openair tunnels of different lengths and calculated that the air velocity in the tunnel can reach about 3 m/s for a train running at 15 m/s speed in a double-track tunnel. Jia [START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF] also notes during the arrival of the train, the peaks in the velocity magnitude are clearly progressing to the exit-side of the station and damped as the train decelerates and stops into the station (i.e. when moving forward in time). Oppositely, when the train leaves the station, the peaks are getting sharper closer from the station ends as the train accelerates (also when moving forward in time).

Background airflow

In a Newcastle upon Tyne complex station, Pflitsch et al. [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF] undertook measurements at night to assess the different contributions to airflow independently of train operation. With all fans off and doors closed, an airflow velocity of 0.5 m/s to 1.5 m/s was observed on the platforms. This phenomenon is called 'background airflow' or 'natural ventilation' [START_REF] Krasyuk | Investigation of the dynamics of air flows generated by the disturbing action of trains in the metro[END_REF], in opposition to the train-induced flow which is observable for only one or two minutes after the passage of a train. Gross [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF] also measured in a station in Hannover that a constant wind of 0.5 m/s was quickly re-established in between train runs. This observation makes the background airflow relevant for the ventilation of the station during the time a train is not near the station. Ji [START_REF] Ji | Concentration, composition, and exposure contributions of fine particulate matter on subway concourses in China[END_REF] discussed the seasonal variation of subway workers' expo-sure to harmful particles, as draft winds and ventilation conditions differ greatly in summer and in wintertime. In their case study of a station in Tehran, Khaleghi and Talaee [START_REF] Khaleghi | Analysis of unsteady airflow in a subway station influenced by train movement[END_REF] have also noted that the train-induced airflow is enhanced when the mechanical ventilation is activated during summer, compared to the non-ventilated station in winter, demonstrating the interdependence of the different contributions to station airflow. Air behavior in the station is also affected by several factors that differ with the station architecture: presence and operation of escalators, presence of ventilation shafts, activation of mechanical ventilation, position of the station gates... Fortain [START_REF] Fortain | Caractérisation des particules en gares souterraines[END_REF] has pointed out source discrimination as a limit to the measurement and modeling of particles in a Parisian subway station at night, including when a train is running. She was able to study independently the activation of the ventilation, the presence of people in the station and the passage of trains, but obtaining reproducible signals is a challenge.

Ventilation of a subway station

In summary, the effects causing airflow in the station can be divided into two categories:

-mechanical ventilation, caused by the piston effect of the trains entering and leaving the station, and by forced ventilation in the tunnels, from a far distance, due to the trains circulation all along the subway network.

-natural ventilation, caused by wind and by thermal draw due to temperature and pressure differences. In the literature, the terms 'background airflow' and 'natural airflow' are sometimes used interchangeably. In this thesis, the following definitions will be employed:

-background airflow: the flow induced by the circulation of air through the underground network. This airflow is mainly taking place through the tunnels. -natural ventilation: the flow that is not related to the passage of a train in the station. This includes background airflow and the wind blowing through the station's openings to the outside.

Experimental and numerical characterization of tunnel and station airflow 2.3.1 Numerical simulations

To estimate the aerodynamic and thermodynamic phenomena in an underground subway network, the Subway Environmental Simulation (SES) program developed by the American Public Transit Association has been widely used. Under the assumptions of being one-dimensional, unsteady and incompressible, subway airflow can be treated as pipe flow and the SES software can solve the air distribution [82] for different ventilation conditions and architecture configurations represented in the form of branched network composed of elements of different types (tunnels, shafts, stations). However, Camelli et al. [START_REF] Camelli | Modeling subway air flow using CFD[END_REF] points out that using linear equations can only roughly predict the airflow dynamics whose properties are strongly nonlinear. Researchers have subdivided the station domain to estimate contaminant dispersion in a station [START_REF] Coke | A model for the dispersion of contaminants in the subway environment[END_REF], or combined SES and CFD to simulate fans blowing in tunnels and a station [82], to investigate various ventilation or train operation modes [START_REF] Ke | Numerical simulation for optimizing the design of subway environmental control system[END_REF] or to study exchanges through shafts with the outside air related to a train run in a station [START_REF] Lin | A study on underground tunnel ventilation for piston effects influenced by draught relief shaft in subway system[END_REF].

Among others, Cross et al. [START_REF] Cross | A validated numerical investigation of the effects of high blockage ratio and train and tunnel length upon underground railway aerodynamics[END_REF], [START_REF] Cross | Enhancing the piston effect in underground railway tunnels[END_REF], Xue et al. [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF], Gross [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF] or Izadi et al. [START_REF] Izadi | 3-D numerical analysis of train-induced flow inside four ventilated underground subway stations and connecting tunnels[END_REF] have used dynamic meshing techniques in CFD models with incompressible Reynolds-Averaged Navier-Stokes (RANS) equations to simulate the flow velocities induced by train passing through stations and tunnels. Izadi [START_REF] Izadi | 3-D numerical analysis of train-induced flow inside four ventilated underground subway stations and connecting tunnels[END_REF] correlated the pressure rise in the tunnel with the magnitude of train acceleration, and observed wind speeds reaching 5 m/s on the platforms, and Gross [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF] studied the influence of station temperature, train length and speed on the outflow at station exits. Near the exits -a staircase away from the platform -of a station, Xue [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF] obtained maximal velocities of 0.8 to 1.4 m/s for a train entering the station at 20.68 m/s.

Durand's [START_REF] Durand | Dispersion des particules issues du freinage des trains en stations souterraines[END_REF] thesis focused on dispersion caused by the airflow around a train at constant speed under static conditions, and left aside the variation of train speed or the piston effect. In fact, to study these phenomenons numerically would imply to set up a dynamic mesh to simulate the train movement in an underground subway infrastructure, therefore demanding more computational resources than the static approach. The perspectives of his work note that these effects have the capacity to move large volumes of air from the tunnels to the station, and that the piston effect could influence the dispersion of particles.

Experimental measurements and use in validation of numerical models

Complementing those cited in the previous paragraphs, various work include measurements at different locations in subway stations and their surroundings. Lin et al. [START_REF] Lin | A study on underground tunnel ventilation for piston effects influenced by draught relief shaft in subway system[END_REF] compared numerically computed air velocities with experimental results obtained with a hot bulb in the draught relief shafts above a station. Although the numerical velocity magnitude is overestimated compared to the measurements, the main characteristics of piston wind are visible in both results: an increase in air velocity as the train approaches the station quickly followed by a decrease, and a re-rise in velocity as the train accelerates to leave the station. The research of Krasyuk et al. have provided in situ experimental data in a terminal subway station at 2 locations, at the extremities of the platform where the entrances are located, with continuous measurements during 5 cycles [START_REF] Krasyuk | Experimental research into air distribution in a terminal subway station[END_REF]. Their mathematical model, based on a lumped element network, provides a good estimation of this aforementioned train-induced airflow features despite being of lower time-resolution. Scale-models are also an option to observe the train-induced airflow experimentally. Using a 1/10-scale model, Bell et al. [START_REF] Bell | Dynamics of trailing vortices in the wake of a generic high-speed train[END_REF] studied unsteady vortex structures in the wake of an open-air high-speed train in a wind tunnel for speeds ranging from 25 to 48 m/s. Focusing on low-speed subway trains, Kim and Kim [START_REF] Kim | Experimental and numerical analyses of traininduced unsteady tunnel flow in subway[END_REF] conducted pressure and air velocity measurements in 1:20 scale model of a tunnel (resulting in a model of around 40 m length), with a train accelerating, then running at a constant speed and decelerating to stop at the end of the tunnel. Their highly-cited article, combined with numerical simulations also at a reduced scale, provided experimental validation data for many other studies. Durand [START_REF] Durand | Dispersion des particules issues du freinage des trains en stations souterraines[END_REF] also considered low-speed trains; in his study, a train in a double-track station with central plaftorm at scale 1:60 (825 mm long) is placed in a wind tunnel and PIV measurements are performed. Although the station is included, the movement of the train through the tunnel then the station is not implemented, and to the best of the author knowledge, no existing study discusses a scaled model that includes both a moving train and a station.

To validate their simulations and study the influence of air curtains on piston effect, Khaleghi and Talaee [START_REF] Khaleghi | Analysis of unsteady airflow in a subway station influenced by train movement[END_REF] placed their fan-type anemometer probe in a corridor close to the station entrance, separated from the platform by an escalator, and found a maximum relative error of about 30% between the experiments and the simulation for the period around arrival and stop of the train. Xue [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF] compared the numerical model with flow velocities measurements in a station in Shenyang a level away from the track and found similar profiles for the experimental data and the model. Yuan and You [START_REF] Yuan | CFD simulation and optimization of the ventilation for subway side-pletform[END_REF] compared the time-average of field measurement at 6 sections of the platform with the outputs of their simulations, and concluded in an 'acceptable' prediction of the airflow by the numerical model.

The numerical to experimental comparison given in Gross's paper [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF] consists of temperature, wind direction and wind velocity for two individual runs of trains in each direction, measured at the end of the platform and near the exits of a 100 m long station, with two tracks and 4 exits leading to the street two levels above. He mentions high uncertainties coming from the grid resolution of the model and the variability of train movements, preventing a perfect one-to-one match. Here also, the simulation over-predicts the magnitude of velocity peaks and re-establishes the background wind quicker.

For some studies and depending on the factors of interest, several adaptations of normal operation and schedule of the subway station were made possible for on-site measurements: measurements at night ( [START_REF] Brüne | Tracer gas experiments in subways using an integrated measuring and analysis system for sulfur hexafluoride[END_REF], [START_REF] Pflitsch | Natural Ventilation as a Factor Controlling the Dispersal of Airborne Toxins in Subway Systems in a Disaster Situation[END_REF], [START_REF] Charlton | Towards a dynamic evacuation system: developing methodologies to simulate the evacuation capabilities of subway stations in response to a terrorist attack with CBRNE weapons[END_REF], [START_REF] Fortain | Caractérisation des particules en gares souterraines[END_REF], [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF]) with presence of a group of people or of a train executing predefined scenarios ( [START_REF] Fortain | Caractérisation des particules en gares souterraines[END_REF]), tracer gas release in the station ( [START_REF] Brüne | Tracer gas experiments in subways using an integrated measuring and analysis system for sulfur hexafluoride[END_REF], [START_REF] Charlton | Towards a dynamic evacuation system: developing methodologies to simulate the evacuation capabilities of subway stations in response to a terrorist attack with CBRNE weapons[END_REF], [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF]) and in the train ( [START_REF] Brüne | Tracer gas experiments in subways using an integrated measuring and analysis system for sulfur hexafluoride[END_REF]), activation or deactivation of mechanical ventilation ( [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF], [72]), opening or closing the relief shafts ( [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF]) or the station's gates ( [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF])... However, the cost of these measures in terms of coordination with public services, staff involved, compliance to procedures, etc, is generally high, and the site is usually available only for a very limited time period. Depending on the case, a limited number of parameters can be controlled, or not, affecting the reproducibility of the results obtained. Since the measurements are always taking place in an already built infrastructure, Pflitsch et al. [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF] underlined that additional and extensive measurements are needed to account for the great diversity of architectures and the different factors affecting subway climate.

Relevance of the research 2.4.1 Limits of the literature

Similarly to what Durand [START_REF] Durand | Dispersion des particules issues du freinage des trains en stations souterraines[END_REF] has observed, most of the literature available around train aerodynamics concern high-speed vehicles and the associated issues. For subway systems, we are dealing with train speeds usually lower than 50 km/h; in Brussels, the operating speed of train is in the order of 30 km/h. In the past 20 years, the field of subway climatology has gained emphasis, and has seen the development of numerical models focusing on various issues and of experimental campaigns aiming to gather data on the airflow conditions and evolution in underground subway stations.

However, while there has been thorough research concerning airflow in subway tunnels and in a subway station, to the best of the author knowledge, few studies offer a direct comparison of numerical and experimental results focusing on how the airflow is perceived by a passenger standing on the platform. Experimental studies mainly focus on a few strategic locations in the station (often at station ends or at the exits), but rarely emphasize the evolution of piston effect along the entire platform as the train passes through the station. Numerical studies including a realistic movement of the train through the station, hence requiring the implementation of a dynamic mesh, are quite rare.

Despite requiring high computational resources, macro-scale and finer numerical models allow to visualize and retrieve quantitative data about airflow conditions affecting passengers comfort, health and safety, such as the air velocity distribution on a line along the platform length [START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF], contaminant dispersion into the tunnels [START_REF] Bubbico | CFD analysis of the dispersion of toxic materials in road tunnels[END_REF] and the station [START_REF] Camelli | Modeling subway air flow using CFD[END_REF], [START_REF] Coke | A model for the dispersion of contaminants in the subway environment[END_REF], and best location for draught relief shafts [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF]. Although it is hard to draw a link between the studies, as they consider very different architectures, these examples highlight the use of models to study and predict phenomenons that would be impossible, costly, or dangerous to observe in real life conditions. Lastly, when a numerical-to-experimental validation is present, it is rarely led in the same conditions. If the validation is performed, it is also often given for an individual measurement, as an average of a time-dependent variable. On the time frame of a train passage through the station -approximately 80 seconds -, the airflow on the platform in a fundamentally transient phenomenon. To compare the outputs from models and measurements obtained in real operating conditions, there is a lack of framework, making difficult to quantify the appropriate modelization of the piston effect, and to compare the results from one study to another.

Objectives of the thesis

Classical mechanics is a highly accurate framework applicable to study the motion of physical bodies for a wide range of applications for nearly 400 years. As summed up by Gibiansky [36], it effectively describes motion on scales from one picometer (10 -12 m) to 10 30 m and is generally regarded as a comprehensive and resolved set of theories. However, there is a persisting unresolved issue within classical mechanics: the solution, or even the existence of a solution, to the general case of the Navier-Stokes equations, that describes the velocity vector field that ap-plies to a fluid and will be addressed in Chapter 3, remains unknown. Therefore, we must employ alternative approaches to gain insights into fluid behavior: developing and refining models, and validating their predictions against experimental data, in one way of doing so.

A model is a partial representation of a real life case, built on minimal modeling principle, with a compromise between idealization, approximation and simplification. It is designed to capture and describe the essential aspects of the system, in particular the relationships between different variables or parameters, allowing researchers and engineers to analyze, predict, and understand its behavior. Models can be used to study a phenomenon in a less expensive, faster or simpler way, or because it is impossible to observe in real life.

Two main objectives hence emerge from the literature review and from the above discussion:

-improve the state of knowledge about the train-induced airflow, in an underground subway station, from the perspective of a passenger standing on the platform; -provide a framework based on quantitative metrics to allow the experimental validation of this transient, fundamentally unrepeatable phenomenon. In this study in particular, we will be interested in understanding the flow field in the station by observing the development of the piston airflow on the platform, carried by a train by a train performing a realistic passage in the station. The next chapters of Part I will give an overview of the techniques available to do so in Chapters 3 and 4, and how they will be articulated to obtain on-site experimental results, numerical simulations and measurements on a small-scale model in Chapter 5.

Fluid properties and governing equations

In this chapter, we present the basic concepts commonly used in the analysis of fluid flow with regards to the case of an underground subway train running through tunnels and station, and provide a short theoretical background about CFD. The consideration of all types of flow is not given here, as well as the mathematical details of the derivation of equations, but can be found for instance in the book of C ¸engel and Cimbala [START_REF] Cimbala | Fluid Mechanics: Fundamentals and Applications, Third Edition[END_REF], of Bird et al. [START_REF] Bird | Transport Phenomena -Revised Second Edition[END_REF], of Greitzer et al. [START_REF] Greitzer | Internal Flow -Concepts and Applications[END_REF] or in the courses of Marinus and Bosschaerts [START_REF] Marinus | Numerical modeling (CO 016)[END_REF], [START_REF] Marinus | Fluid dynamics & Energy conversion -Part a: Fluid Dynamics (ES312a)[END_REF].

Characterization of a flow

To characterize a flow and develop expressions allowing to analyze its dynamics, it is useful to categorize the type of flow which is the object of the study. From the characteristics, an appropriate mathematical framework for analyzing and predicting the behavior of a fluid can be provided. Dimensionless numbers, in particular, are widely used in physics and engineering problems to identify the most prominent physical effects in the fluid and the most relevant ones for our application will be given in this section.

Properties of fluids

A fluid can be characterized by its density ρ, quantifying the mass of a fluid per unit volume and hence expressed in [kg/m 3 ]. Other main quantities characterizing a flow are its pressure p, given in [Pa] or in [N/m 2 ] and referring to the forces exerted in the fluid per unit area, and its temperature T in [K] or in [°C]. The state of a fluid flow under ordinary conditions can be represented by the perfect gas law:

p = ρRT (3.1)
where R = R/M , with R the universal gas constant (R = 8.3145

J • mol -1 • K -1 )
and M the molar volume of the gas (usually taken as 0.022055 m 3 /mol at 20°C and atmospheric pressure), drawing a link from the molecular level of the fluid to its macroscopic properties. Under ordinary conditions of temperature and pressure, air behaves in a manner similar to a perfect gas. This is because the interactions between air molecules are relatively weak compared to the average kinetic energy of the molecules. For an ideal gas, the relation between the change in enthalpy de [J•kg -1 ] and the change temperature is derived from the second law of thermodynamics, and uses the specific heat at constant volume c v [J•kg -1 •K -1 ], i.e. the amount of heat that must be added to one unit of mass of the substance in order to cause an increase of one unit in temperature:

de = c v dT (3.2)
A fluid can be said incompressible to denote that the volume of fluid particle remains constant, and an incompressible flow refers to a fluid flow in which the density of the fluid remains nearly constant, regardless of changes in pressure or velocity. The limit between incompressible and compressible flows can be determined using Mach number M a, which is a dimensionless quantity that characterizes the speed of a fluid flow U relative to the speed of sound c in the surrounding medium:

M a = U c (3.3)
The flow can generally be considered as incompressible if M a < 0.25. Chapter 2 has evidenced that the speed of air in an underground subway station, with a train running at a speed in the order of 10 m/s, was rarely exceeding 10 m/s also. With these values and with c = 340 m/s in air, we obtain M a ∼ 0.03, and we can therefore safely go with the assumption of incompressible flow.

Viscosity and boundary layer flow

Viscosity is a measure of a fluid's resistance to flow. Air can be generally considered as a Newtonian fluid, meaning the shear stress within the fluid is directly proportional to the velocity gradient. The relationship between these is given by Newton's law of viscosity, introducing the proportionality coefficient µ [kg•m -1 •s -1 ]. Equation 3.10 will give the expression of the total stress tensor τ ij that combines the shear stress with the conventional pressure.

Flows can be categorized as laminar or turbulent. A laminar flow can be recognized by smooth layers sliding over each other. Turbulent flows are characterized by a highly disordered motion, often exhibiting vortices. Where laminar characteristics can be found in flows with low velocity and high viscosity, turbulent characteristics are found in high-speed flows with low viscosity. The Reynolds number, expressed by Equation 3.4, is a dimensionless quantity that gives insight into turbulent characteristics of a flow by expressing the ratio between the inertial and the viscous forces occurring in the considered fluid. Low Reynolds numbers are peculiar to laminar flows, while high Reynolds numbers are specific to turbulent flows -typically in a fully developed pipe flow (see below), the flow is considered as laminar if Re < 2300 and as turbulent if Re > 2900. In our case, Reynolds number will be calculated exactly later in Section 5.1.3 after having defined various other parameters, but it will appear that the flow is in the turbulent range.

The assumption of Newtonian fluid does however not hold true anymore near solid boundaries, such as walls. In turbulent flow regimes (Re ≫ 1), viscosity can typically be neglected, however this is only valid at distances far from solid interfaces.

Flow in pipes

Internal flow refers to a type of fluid flow that occurs within a confined space, such as within a pipe, duct, or channel. The fluid in question can be a gas or a liquid, and the flow may be driven by various mechanisms, such as pressure differences, gravity, or external forces (in the form of work for instance). Pipe flow is a type of liquid internal flow within a closed conduit, such as a pipe or tube, that can be found in many fluid mechanics cases. Contrarily to open-channel flow, pipe flow does not have a free surface, and hence does not exert direct atmospheric pressure. In the case of a subway train running through an underground network, we can use the rough approximation of a pipe flow to predict the behavior of circulating in the tunnels and other restricted areas.

When handling flow in non-circular tubes and channels in particular, the hydraulic diameter is a commonly used parameter to approximate the flow as a pipe flow, allowing to compute numerous quantities (such as Reynolds number) using the same methods as for a round conduit. Hydraulic diameter can be understood as the cross-sectional area of the channel divided by the wetted perimeter, and when the cross-section of the flow is uniform along the tube or channel length, it is defined as:

D H = 4A P (3.5)
where A [m 2 ] is the cross-sectional area of the flow, and P [m] is the wetted perimeter of the cross-section.

Navier-Stokes equations

In fluid dynamics, three fundamental conservation laws govern the behavior of fluids, and are translated to mathematical expressions. In the following, we use the approach of Euler and the basic laws of physics are applied to an infinitesimal control volume, fixed in space, through which a fluid flows. The three dimensions of space are designated by x i , x j or x k [m] and the corresponding velocity components u i , u j or u k [m/s], which in a Cartesian coordinate system can be written respectively as (x, y, z) [m] and (u, v, w) [m/s]. In the following, the Einstein summation convention is used to provide a more compact form of the equations.

• Conservation of mass The conservation of mass, or continuity equation, states that mass cannot be created or destroyed within a closed system. In fluid dynamics, this means that the total mass of a fluid remains constant as it flows. It implies that the mass entering a control volume must be equal to the mass leaving that volume, considering any possible mass changes due to sources or sinks. Equation 3.6 states that the rate of increase of mass in a the control volume is equivalent to the net rate of flow of mass into this control volume.

∂ρ ∂t + ∂(ρu j ) ∂x j = 0 (3.6)
In the case of incompressible flow, density is constant over time and uniform in space, and Equation 3.6 simplifies in:

∂(u j ) ∂x j = 0 (3.7)
• Conservation of momentum The conservation of momentum is based on Newton's second law of motion, which states that the rate of change of momentum of an object is equal to the sum of forces acting on it. These forces include both the external forces (also called volume forces or distant forces) and the contact forces (or surface forces), notably those related to the fluid viscosity through the shear stress tensor τ . Three equations (Equation 3.8), for the three dimensions in space, can hence be written:

∂(ρu i ) ∂t + ∂(ρu i u j ) ∂x j = -δ ij ∂p ∂x j + ∂τ ij ∂x j + ρg i (3.8)
where g [m•s -2 ] is the gravitational acceleration As the stress tensor on a control volume is symmetrical we have:

τ xy = τ yx , τ xz = τ zx , τ yz = τ zy (3.9)
Only six stresses are thus independent. Working with Newtonian fluids, they can be expressed as follows:

τ ij = -p δ ij + µ[ ∂u i ∂x j + ∂u j ∂x i ] -δ ij 2 3 µ ∂u k ∂x k (3.10)
• Conservation of energy The conservation of energy is derived from the first law of thermodynamics, which states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In fluid dynamics, this law states that the total energy within a closed system remains constant. It takes into account the various forms of energy present in a fluid system, such as kinetic energy (associated with fluid motion), potential energy (due to elevation changes), and internal energy (related to fluid properties like temperature and pressure).

∂(ρe) ∂t + (ρe + p) ∂u i ∂x i = ∂(τ ij u j ) ∂x i + ρf i u i + ∂( qi ) ∂x i (3.11)
For the last term of the conservation of energy equation (Equation 3.11), Fourier's law regarding heat by conduction is also introduced as an equation of transport:

qi = -λ ∂T ∂x i (3.12) with λ [W • m -1 • K -1
] the thermal conductivity of the fluid.

By applying the law of conservation of energy, ignoring compressibility (assumed when M a ≫ 0.25), viscosity (assumed when Re ≫ 1 away from solid boundaries), and thermal effects, Bernoulli's principle can be derived:

U 2 2 + p ρ = C (3.13)
where C is a constant related to a particular fluid system.

Unknowns from the system are connected by the two equations of state given in Section 3.1.1: the ideal gas law (Equation 3.1) and the change in enthalpy with temperature (Equation 3.2).

The Navier-Stokes equations hence provide a complete description of the flow, as they hold true for both its motion and all the turbulent structures, and take all the viscous effects into account. Solving non-linear partial differential equations is a difficult task and as of today, finding the solution to the Navier-Stokes equations remains a challenge for scientists. To obtain analytical solutions, it is necessary to simplify the equations -see some examples above -either by making assumptions about the fluid, about the flow or about the geometry of the problem: typical study cases are that the flow is laminar, steady, two-dimensional, incompressible, with constant properties, or between parallel plates. To study real-life, large scale, applied problems, where the introduction of hypotheses in order to simplify the system and find an analytical solution is not available to us, we need to rely on numerical solvers with computers and experimental measurement techniques. The main concepts about these techniques, limited to the ones suitable for our application, will be detailed in the following paragraphs.

Numerical methods

To solve the vast majority of flows, the only currently available choice is to discretize both the time and space and to use numerical models. Computational Fluid Dynamics is the branch of fluid mechanics that deals with the numerical analysis and simulation of fluid flows using computational methods and algorithms. In CFD, the governing equations of fluid flow -the Navier-Stokes equations given in the above section -are discretized using numerical methods. These equations, along with appropriate boundary conditions and physical models, are solved iteratively on a computational grid to obtain an approximate (yet highly accurate for most applications -CFD being sometimes called a 'high-fidelity method') solution that represents the flow field.

Discretization

The governing equations of fluid dynamics describe a continuous phenomenon in a continuous domain. When they cannot be analytically resolved, they have to be approached by algebraic relations, bound to discrete quantities. Therefore, the domain also needs to be divided into a grid (the mesh) with discrete points (the mesh points or nodes), and its elements are the cells.

To discretize the equations, one of the most prominent choices in CFD is the Finite Volume Method (FVM), which is the method used by ANSYS Fluent solver. The Finite Volume Method involves dividing the computational domain into finite volumes or control volumes. Each one of these cells is handled as a control volume. The conservation equations are integrated over each volume, and the fluxes across the control volume faces are approximated.

Each differential term in the governing equations holds a physical meaning that can be slightly altered by the chosen discretization method, and for this reason, various numerical schemes have been developed.

The accuracy of the calculation is strongly affected by the step size. If it is chosen too large, the computed solution may be quite far from the true solution of the differential equation, if too small then the calculation will become unnecessarily time-consuming, and round-off errors may build up excessively because of the numerous arithmetic operations that are being carried out. This consideration is particularly important when implementing a dynamic mesh, where the time step will also determined how much the train is moving in space. Further details on the dynamic mesh set up and requirements will be discussed in Section 7.3.1.

DNS, LES and RANS approaches and turbulence models

Recording the velocity at a particular point in the real (turbulent) fluid flow, the instantaneous velocity U would look like in Figure 3.1. In Direct Numerical Simulations (DNS), the grid is typically fine enough to resolve all the relevant scales of motion in the fluid, both in space and in time, from the largest turbulent structures down to the smallest dissipative scales, also called the Kolmogorov micro-scale. In engineering, two main approaches to modeling turbulence are used: Large-Eddy Simulation (LES) and Reynolds Averaging Navier-Stokes (RANS) models.

In terms of computational demand, LES lies between DNS and RANS, and like DNS, a 3D simulation is performed over many timesteps. This particular point is prohibitive for our case, as the implementation of the train movement through the station requires a dynamic mesh, meaning that convergence will have to be achieved at every timestep of the train motion.

In the RANS approach, physical values are averaged in time, so that the instantaneous field is defined as the sum of the mean and the fluctuating component, and equations are solved for time-averaged flow behaviour and the magnitude of turbulent fluctuations. By averaging the Navier-Stokes equations, we obtain the RANS equations:

∂ρ ∂t + ∂(ρ ūi ) ∂x i = 0 (3.14) ∂(ρ ūj ) ∂t + ∂(ρ ūi ūj ) ∂x j = ∂ p ∂x i + ∂ ∂x i µ[ ∂ ūi ∂x j + ∂baru j ∂x i -δ ij 2 3 ∂ ūk ∂x k ]+ ∂ ∂x i j (-ρu ′ i u ′ j ) (3.15)
When looking at Equation 3.15, we see that all terms are averaged in time except R ij,turb = -ρu ′ i u ′ j that expresses the fluctuations produced by the convection. R ij,turb , named the 'specific Reynolds stress tensor', is a tensor with six degrees of freedom that hence requires six more equations to solve the system. To solve the system, a 'closure' needs to be found, that should not only solve the mathematical equations but also consider the physics of the studied flow. Turbulence models allow to approximate the terms of the stress tensor.

In Eddy viscosity models, it assumed that the stress is proportional to the strain (see Equation 3.10). The only new (unknown) quantity needed by these models is an effective turbulent viscosity, or 'eddy viscosity', µ turb . This tensor is symmetrical and introduces six new variables. To solve the expanded equations, RANS turbulence models are used. These models can be divided into two categories. The low Reynolds number models, such as the 'menter shear stress transport' (SST) turbulence model and the wall function models, for example the k-ε model. The low Reynolds number models compute the boundary layer more accurately, but require more computational resources. Wall functions do not compute boundary layers, but model the result of this region based on empirical formula. The standard k-ε model is the most widely-used engineering turbulence model for industrial applications. It solves two transport equations, one for turbulent kinetic energy k and one for the dissipation rate ε.

Successful turbulence modeling requires engineering judgment of several aspects: the flow physics, the available computational resources, the outputs require-ments in terms of accuracy and computation time, and the choice of near-wall treatment. When the wall function is used correctly and one is not interested in fully resolving the boundary layer, the model will compute the effect of the boundary layer with sufficient accuracy.

In the case of an underground subway station (with a domain's unit dimension of 10 2 m), due to the wide range of turbulent scales, resolving all time and length scales to obtain an actual turbulent flow is numerically impossible. Indeed, the large amount of computational cells required to detect the small eddies, together with the short numerical time steps essential to capture the fastest turbulent structures, results in a substantial computational cost.

Currently, the most detailed approach for computing the flow field in a large space is through a RANS approach. The requirements for LES or DNS in terms of computational power are very high and therefore, the RANS approach in combination with the k-ε turbulence model is also considered the most practical option for our application.

Measurement techniques for airflow

The ability to accurately measure and analyze fluid flows is essential for understanding the complex phenomena that govern fluid motion. This chapter presents and discusses two prominent measurement techniques used in fluid dynamics research, that will be applied in this work: Section 4.1 covers Hot Wire Anemometry (HWA) and Section 4.2 addresses Particle Image Velocimetry (PIV), with a focus on Time-Resolved PIV. These techniques were used in this work to conduct field tests and lab tests.

As in the previous chapter, the concepts mentioned in this chapter are deliberately kept brief and limited to our application for low-speed airflow in the context of environment fluid dynamics, as there are many excellent sources with extended discussions of the topics covered. The course notes from the von Karman Institute [START_REF] Anthoine | Measurement techniques in fluid dynamics -An introduction[END_REF] provide a good starting point to balance theoretical and applied perspectives about measurement techniques for fluid mechanics. Exhaustive theoretical background information about PIV principle supporting the practical aspects about the implementation of this technique can be found for instance in the book of Raffel et al. [START_REF] Raffel | Particle Image Velocimetry -A Practical Guide[END_REF].

Hot Wire Anemometry

HWA is widely used for fluid mechanics measurements in research. With a frequency response from a few kHz to 220kHz depending on the wire design, and a large dynamic range (from a few cm/s up to several hundred m/s), it allows an accurate representation of velocity fluctuations even at low flow speeds and high frequencies. In this section, we explain briefly how the hot wire operates in constant temperature mode.

The sensor in the hot-wire anemometer is a thin metal wire or a film made of a material with a high temperature coefficient of resistance [START_REF] Shekhter | Hot-wire and hot-film anemometers[END_REF] -commonly tungsten or platinum -and of typical dimensions 5 µm in diameter and 1 to 3 mm in length. The wire is held by shaped supports called prongs (bent sewing needles), going to the control circuit trough a ceramic tube protected by a stainless steel tip. Due to these characteristics, the anemometer is adapted to flow measurements with a very good position precision, but one should also be cautious when manipulating it to avoid bending the prongs or breaking the wire. Depending on the medium, the flow and space conditions or the quantity to be measured, different coating, probe sizes and constructions can be used [START_REF]Probes for Hot-wire Anemometry[END_REF]. The principle of operation of the system is based on the convective heat transfer from the heated wire to the colder surrounding fluid, which is a function of the flow velocity [START_REF] Anthoine | Measurement techniques in fluid dynamics -An introduction[END_REF]. Thus, a relationship between the fluid velocity and the electrical output can be established. The electrical resistance of the wire varies with its temperature, with the following linear relationship:

Wire support

Electric current

Flow

Thin wire T hw , R hw T flow , R flow

R hw = R amb [1 + b (T hw + T amb )] (4.1)
where T amb [K] and R amb [Ω] are respectively the temperature and the resistance of the surrounding fluid, T hw [K] and R hw [Ω] are respectively the temperature and the resistance of the hot wire, and b [K -1 ] a thermal coefficient of resistance.

The probe is placed in a control circuit, generally as a branch of a Wheatstone bridge, so that it is possible to derive a relation between the output voltage of the bridge and T hw . Details about the probes, the control circuit, and the different operating modes can be found in various references, starting with the ones provided in this section, and hence will not be discussed here.

However, it should be noted that the hot wire anemometer actually measures voltage; to find the correct relationship between voltage and wind velocity, a calibration is required. This can be the source of measurement errors, as the probe is sensitive to changes in environmental conditions, such as temperature, humidity, and pressure and as it cannot necessarily be calibrated in the same conditions as the ones of the measurements. In practice, other sources of uncertainties can also arise [START_REF] Anthoine | Measurement techniques in fluid dynamics -An introduction[END_REF], for instance from the finite length of the wire and the presence of its support causing a non-uniform temperature distribution over the wire, noise due to the electronic circuitry, or variations of the flow velocity and temperature happening simultaneously.

Hot wire anemometry remains also an intrusive measurement technique, as physical probes must be inserted into the fluid, bringing potential flow disturbance. A single hot wire can also only measure flow velocity in one point, with limited directional information; the hot wire measures an absolute value of velocity and is affected by the position of the wire with regard to the flow direction. Additional techniques or multiple sensors may be necessary for complete flow characterization.

Particle Image Velocimetry

Principle and setup

Particle Image Velocimetry (PIV) is a non-intrusive optical technique used to measure the velocity field of fluids, which concept and setup are schematized on Figure 4.2. The principle of PIV involves imaging tracer particles, usually seeded in the fluid, as they move under the influence of the fluid flow. A thin laser light sheet illuminates a small section of the flow field, making the tracer particle visible as they scatter light. The motion of the particles is recorded by a camera, which captures two successive frames of the particle images separated by a small time interval, typically in the range of a few microseconds to several milliseconds.

The PIV analysis then involves processing the recorded images to extract the velocity field of the fluid, as schematized on Figure 4.3. Using cross-correlation algorithms, the displacement of the particles between the two frames is then used to calculate the local velocity vector of the fluid. Coupled with a calibration of the image with an object of known size and angle (typically, a calibration plate), the displacement in pixels can be translated in an actual distance. By analyzing the velocity vectors over a large number of particles in the illuminated section, a velocity field can be obtained. More details about PIV processing will be discussed in Section 4.2.2 below. PIV can be used in both 2D and 3D configurations, depending on the number of cameras used to capture the particle images. In 2D PIV, the laser light sheet is used to illuminate a thin slice of the flow field, and a single camera captures the particle images in that plane. In 3D PIV, multiple cameras are used to capture the particle images in three dimensions, allowing for the reconstruction of the 3D velocity field in the plane of illumination. In this thesis, 2D PIV will be used.

PIV is a non-intrusive technique as no probe is placed into the flow, but its application require sufficient optical access both for the laser to illuminate the area of interest, creating a light sheet in a relevant place for the considered flow, and for the camera to visualize that area. The flow to visualize also needs to be seeded with particles, requiring both a carefully chosen tracer (depending mainly on the studied fluid and its speed) and the presence of a seeding device. In addition, most lasers and their cooling systems are heavy and sensitive instruments that cannot be easily transported. Furthermore, when working with laser light and in particular at high power, safety regulations should be observed: wear of adapted goggles to protect the eyes, limitations of reflections that could redirect the light in uncontrolled directions, protection of materials that could heat or burn from being hit by the laser light... Health issues with regard to the seeding material can also arise. For these reasons, PIV use is mostly restricted to laboratory applications.

Image processing in Particle Image Velocimetry

During the experiments, a large quantity of image pairs is obtained, where a particle image is represented by a matrix composed by grey scales for each pixel. These have to be processed in order to extract the velocity fields, as represented schematically on Figure 4.3.

The recorded frames are divided in small cells called 'interrogation windows'. For each interrogation window, the displacement vector is retrieved using a statistical method -in this work, we will limit ourselves to cross-correlation -applied on the particles images couple by shifting one window over the other, resulting in a correlation map. The largest peak represents the most probable local displacement of the set of particles within that particular window, under the assumption that the particles have moved homogeneously between the two illuminations. Velocity can be calculated using the time between the two frames and the calibration of the cameras. The size of the interrogation windows determines the resolution of the velocity field, as for each window one displacement vector is retrieved. These windows can overlap, allowing for an increased contribution of particles near the edges. This increases the resolution without having to decrease the window size, but it should be carefully selected, as reusing the same set of particles multiple times can slow down the processing without any gain in information.

The particle image shift depends on the flow velocity, the optical magnification and the time delay between the laser pulses. Generally, a large shift is desired in order to obtain a small relative uncertainty and a large dynamic velocity range [START_REF] Raffel | Particle Image Velocimetry -A Practical Guide[END_REF], but for a given flow and optical system, increasing the delay between the laser pulses might lead to losing too many particles due to out-of-plane movement. In practice, a common guideline [START_REF] Keane | Optimization of particle image velocimeters. I. Double pulsed systems[END_REF] is to aim L ≥ 4∆d, where L is the window size and ∆d the particle displacement, meaning that the maximum displacement of the particle images should be equal to or less than one quarter of the interrogation window extend in the direction of the particle image shift.

Although 'particle' is sometimes used, it should be kept in mind that the information available to us is the particle image, in the form of light intensity per pixel. Due to the diffraction of the laser on the particles, each particle image appears on several pixels, and their presence is determined by the software by averaging the light intensity of the pixels. Sub-pixel resolution can be achieved for the value of displacement, using interpolation algorithms, usually Gaussian fitting, as provided on the example of However, the observed particles should not be too small, because there will not be enough pixels to perform the sub-pixel interpolation. This leads to a bias towards integer pixels due to undersampling, yielding once more an accuracy of 1 pixel. This phenomenon is called peak-locking. In general, good practice dictates that particle diameters should be around 2-3 pixels.

Two main metrics, listed below, can assess the quality of the correlation between successive frames:

-The correlation value, associated to a displacement (∆x, ∆y), quantifies how similar one image is from the next one; the closer to 1, the more resemblance there is. -The signal to noise ratio (SNR), or peak ratio, is the ratio of the amplitude of the highest peak of the correlation map by the amplitude of the second highest peak. If this value is too close to 1, strong noise is present in the particle images, lowering the quality of the correlation. The raw images contain in fact impurities due to reflections, noise from ambient sources or non-uniform illumination. To improve the quality of the aforementioned metrics, several operations can be applied to images. Pre-processing techniques help in accurate detection and tracking of particles, leading to more precise velocity measurements. Enhancement of the images can consist in:

-Image enhancement: techniques like contrast adjustment, noise reduction, and image filtering are applied to improve the visibility of particle images and reduce noise interference. -Background and noise removal: these can be filtered out by performing a modal decomposition of the light intensity data contained within the images, and removing the modes related to background noise. The distinction between particles and noise and static background elements is made by observing correlation, as they tend to be heavily correlated, whereas PIV particles are not. -Image masking: unwanted regions in the images, such as walls or obstacles, can be masked out to focus the analysis on the desired flow area.

During the vector field calculation, the multipass algorithm can be used to improve the accuracy and resolution of velocity measurements by iteratively analyzing the particle image pairs at different spatial scales. The basic idea is to start with a relatively large interrogation window and then successively reduce its size in subsequent passes. The initial pass is carried using the classical method with the correlation peaks, generating a first correlation map with an initial displacement found in each interrogation window. Using the refined velocity vectors from the previous pass, a predictor algorithm is applied to estimate the displacement of particles in a smaller-sized interrogation window centered on the previously estimated location. This predicted displacement is used as an initial guess for the subsequent pass.

Graphically, this means than along the different passes, the compared image will be 'deformed' according to the predictor found in the previous pass, meaning that the interrogation window from the reference frame is not at the same location as the interrogation window of the compared frame.

Applied after the correlation and displacement calculation, post-processing methods serve to enhance the quality and statistical accuracy of the velocity field. These methods can include:

-Validation and outlier rejection: inaccurate or spurious vectors are identified and removed using statistical criteria or comparison with expected flow patterns to improve the quality and reliability of the velocity field. -Interrogation window optimization: the size and shape of the interrogation windows are optimized to balance the trade-off between spatial resolution and statistical accuracy. -Interpolation of missing data: techniques like spatial interpolation or data filling algorithms are used to estimate missing velocity data in regions where particle images were not detected.

Section 8.2.4 will cover the details and the effect of the different pre-and postprocessing parameters applied to the acquired particle images and the vector fields, and additional material supporting this discussion will be provided in Appendix F.

Time-Resolved Particle Image Velocimetry

Made possible with the recent developments of high speed lasers and cameras, the principle of TR-PIV is similar to that of traditional PIV, with the main difference being that successive vector fields are therefore not averaged, but animated. The cross-correlation can be performed between successive images instead of between the frames of a single image, or between frames if a higher frequency is available to acquire image pairs. This technique allows the characterization of flow features that are short lived and unrepeatable, such as time-space dependent scenarios, or the evolution of vortices, turbulence, and instabilities, which cannot be captured by traditional PIV. The shorter the time interval between frames, the higher the temporal resolution of the measurement.

For the investigation of fluid dynamics with time-space correlation, the 'time series mode' is generally chosen [START_REF]FlowMaster -Time-Resolved Particle Image Velocimetry Systems[END_REF], and schematized on Figure 4.6 below. The camera and the laser are synchronized so that one laser pulse is fired per camera frame (multi-frame/single exposure), and a vector field is calculated from each pair of consecutive images.

For a double-cavity laser, as the rate of the pulses is being kept constant, this mean that the maximum acquisition frequency f acq is determined by half of the repetition rate of the laser, or by the camera maximum frame rate. This means that the time series mode is particularly suited for relatively low flow speeds. The transient character of the captured flow induces that averaging the obtained vector fields is not considered here. This can potentially lead to increased uncertainties in the processed results. Hence, special attention must be given to feed the correlation algorithm with good quality images, in the terms defined in Section 4.2.2 above.

One of the major challenges of TR-PIV is the need for high-speed cameras and laser systems capable of generating short laser pulses at high repetition rates. High laser power is also required when measuring a larger field of view. This can make TR-PIV more expensive and technically challenging than traditional PIV. TR-PIV also involves an increased data volume generated by the high frame rates, in the repetition of measurements to perform ensemble-averaging, for instance. For the highly transient case studied in this thesis, TR-PIV is required to acquire a sufficient amount of image. The large amount of data requires specialized processing techniques and hardware to handle and analyze the data, which can be time-consuming and computationally intensive.

In conclusion, the utilization of both HWA and PIV techniques offers significant advantages and complements each other in the context of measurements to study airflow in a subway station. HWA excels in provides highly accurate and precise point measurements of the velocity. Its ability to measure the instantaneous velocity and its excellent temporal resolution, capturing rapid flow fluctuations with ease, make it an ideal choice for detailed analyses in localized regions. PIV offers a broader perspective by providing a spatially resolved velocity field over a larger area. The non-intrusive nature of PIV and its ability to capture instantaneous flow fields make it valuable for studying overall flow dynamics within a small-scale subway station.

However, both techniques have their limitations. HWA provides localized mea-surements, limiting the spatial coverage and restricting the ability to capture global flow phenomena. It may also be affected by changes in temperature, which can introduce errors in measurements. Most problematically, HWA measures only the velocity magnitude and does not give information about the flow direction. PIV provides spatially resolved velocity fields, but is limited to 2D measurements and is unable to capture out-of-plane motion. It requires a careful experimental setup and post-processing to ensure accurate results, especially for TR-PIV where the averaging the flowfields cannot be done. The technique is also sensitive to the seeding density and the presence of optical distortions, which can impact measurement accuracy.

As this chapter has reviewed the theoretical aspects and main challenges associated with HWA and PIV, Section 5.2.2 will review how they are applied in this thesis. In particular, HWA will be used for on-site measurements in a real subway station during train operation and detailed in Chapter 6, while the implementation of the PIV technique on a small-scale model of the subway station will be addressed in Chapter 8.

Test case and methodology

In this thesis, an actual subway station where the ventilation is mainly realized by the piston effect is taken as a test case, to serve as a benchmark against which the performance or predictions of models can be compared and validated. The main architectural features of the station and the movement of the train along the platform will hence be reproduced in a numerical model and in a small-scale version in the lab. On-site data will be acquired in the actual station to be compared with the outputs of the models.

Section 5.1 introduces the station at hand, presents the simplifications made and the conventions adopted and gives the main relevant parameters that can be computed. Following this description, we can describe the methodology that will be used in this work in Section 5.2. Scenarios that will be studied in the thesis are defined, and the articulation of the different models and techniques applied is explained.

A real subway station in Brussels

Description of the station

The station taken as a case study is a double-track station in Brussels, with no separation between the tracks, and a platform on each side. Pictures of the station are given in Figure 5.1 and a simplified floor plan is available in Figure 5.2. For confidentiality reasons, the name of the station and the detailed plans are not properly disclosed in this text. All the quantities and details necessary to the understanding of the physical phenomenons at stake, and ensuring the reproducibility of this work, are however given.

The station is 100 m long and symmetrical with respect to the double-track rails, with one platform for each direction of the metro line. It is fairly parallelepipedal in its length, with a cross-shaped cross section, and the tunnels ahead of and after the station have a rectangular cross-section. Six exits, three on each side, are separated from the outdoors at street level by a straight staircase. The ceiling of the station being approximately 1.5 m below the street surface, hence the station lies not very deep. The detailed geometries and dimensions adopted for this study are given in Section 5.1.2. It is important to note that in this station, no mechanical ventilation is present, and the ventilation is only realized by the piston effect caused by the train movements and natural ventilation through the tunnels and the exits.

Two types of train are running in the station at the time of this study -M5 and M6. The most recent train, M6, is shown in Figure 5.3. For this station, the transport company indicated that the trains entered the station with a speed of 40 km/h and started braking when entering the station to stop at the mirror at the end of the platform (visible on Figure 5.1c). Measurements in the station and access to operational information were made possible, thanks to a freewill collaboration with STIB-MIVB (Brussels Intercommunal Transport Company). As Chapter 2 has highlighted the limited availability of on-site measurements in underground subway stations at a detailed scale, the possibility of designing an experimental campaign, with regards to the need for validation of the numerical model, is a great source of information for this study. The constraints associated with the realization of the measurements will be discussed further in Section 6.1.

Simplified geometry and conventions

Simplified geometries are used in physics problems to make the analysis more manageable and to focus on the fundamental principles and concepts at play. From a purely geometrical point of view, reducing the station to simplified geometrical shapes will remove complexity from the spatial discretization of the numerical domain, and the construction of the small-scale station. By using a simplified geometry, we also aim to discriminate between the many factors influencing airflow on the platform that have been brought up in Chapter 2, demonstrating the effects of the sole phenomenons chosen to be kept in the simplified test case. The station amenities are hence removed, as their impact on the results is deemed of lower magnitude than the train-induced airflow. Lastly, this geometrical simplification makes the results more easily comparable to literature and to other station architectures. This enhances reproducibility as it becomes then easier to combine outputs from different studies, promoting collaboration, verification, and validation within the field of research. the tunnels are Y t = 6.5 m wide and Z p = 4.75 m high. The length to be included in the models will be discussed notably in Section 7.3.2. The train is approximated by a rectangular cuboid (as in the works of Jia [START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF] or Camelli [START_REF] Camelli | Modeling subway air flow using CFD[END_REF] for instance), having a length of X train = 90 m, a width of Y train = 2.7 m and a height of Z train = 3.5 m. The train is separated from the tunnel vertical wall by 0.34 m, from the floor by 0.50 m and from the ceiling by 0.75 m.

The platform along which the train goes to the center of Brussels is denominated 'Platform A' (or 'left' for the exits, from Chapter 7) and all elements referring to this side are designated by the letter A (or L); the other platform, along which the train comes from the center of Brussels, is called 'Platform B' (or 'right') and elements are designated by the letter B (or R). The measurements will be carried on Platform B. The upper left corner of Platform B, at the edge of the platform and the tracks, is taken as the origin of an orthonormal basis. X is in the direction of the train movement, in the length of the station: Y is in the direction of the station width; Z is in the vertical direction (see Figures 5.2 and 5.4).

Key parameters and dimensionless numbers

Using the dimensions for the station of the train, and the speed of the train, certain parameters characterizing the flow field can already be computed. Out of the different variables influencing the magnitude and the temporal evolution of the piston wind, the blockage ratio β can be used to compare tunnel and station design in a non-dimensional form. It compares the cross-sectional area covered by the train in the tunnel to the one of the tunnel:

β = A train A tunnel (5.1)
With the above equation 5.1 and the dimensions given in Figure 5.6, we obtain the blockage ratios for one train and two trains in the station and in the tunnel, summarized in Table 5.1. In the literature, blockages ratios of 33 % [82], 41 % [START_REF] Liu | An alternative algorithm of tunnel piston effect by replacing three-dimensional model with two-dimensional model[END_REF] or 67 % [START_REF] Kim | Experimental and numerical analyses of traininduced unsteady tunnel flow in subway[END_REF] for the train in the tunnel have been for example studied. To study problems of trains running through tunnels, several authors ([52], [START_REF] Liu | An alternative algorithm of tunnel piston effect by replacing three-dimensional model with two-dimensional model[END_REF], [82], [65]) have used the hydraulic diameter of the train in the tunnel. Recalling Equation 3.5, hydraulic diameter D H is defined in our case as the ratio of four times the tunnel (resp. station) cross-sectional area to the tunnel (resp. station) perimeter. With the dimensions indicated on Figures 5.5 and 5.6, we obtain:

D H,tunnel = 4Y t Z t 2(Y t + Z t ) = 4.26 m (5.2a) D H,station = 4(2Y p Z p + Y t Z t ) 2(2Y p + Z p ) + 2(Y t + 2 × 0.75) = 5.85 m (5.2b)
Y t and Y p being the width of the tunnel and the platform, respectively, and Z t and Z p the height of the tunnel and the platform, respectively.

The values for hydraulic diameter allows to compute the Reynolds numbers for the train in the tunnel or in the station: (5.3b) with ρ air = 1.246 kg/m 3 and µ air = 1.778 × 10 -5 kg m -1 s -1 for air at atmospheric pressure and 10°C (the average temperature measured during the on-site experimental campaign) and V train = 11.11 m/s as per Section 5.1. Although V train will decrease as the train enters the station, the values of the Reynolds number allow to characterize the flow as fully turbulent for the most part of the train travel.

Re tunnel = ρ air V train D H

Methodology

Definition of scenarios and locations of interest

To obtain clear, reliable data to perform a validation, one must first define precisely what is the object of the study. The movement of the trains passing through the station can be decomposed as follows:

1. running at cruise speed in the upstream tunnel; 2. decelerating when approaching the station to reach their stop position, approximately in the middle of the platform lengthwise; 3. stopping to let the passengers outboard and board in; 4. accelerating upon departure from the station; 5. reaching again the cruise speed in the downstream tunnel.

During the daily operation of the public transportation network, trains are running in both directions and with various intervals depending on the hour of the day and potential disruptions of the normal service. Based on the observations made in the station, four scenarios are likely to happen a sufficient number of times per day and are simple enough to be able to focus on the train-induced airflow. They are defined below and visualized in Appendix A:

-'A only': a train is passing along Platform A (opposite to the measurement side). -'B only': a train is passing along Platform B (on the measurement side).

-'A then B': a train is arriving and stopping along Platform A. While the train is stopped, another train is arriving and stopping along Platform B. While this second train is stopped, the first train leaves; then the second train leaves. -'B then A': a train is arriving and stopping along Platform B. While the train is stopped, another train is arriving and stopping along Platform A. While this second train is stopped, the first train leaves; then the second train leaves.

Other scenarios, such as A and B arriving at the same time, or A (resp. B) arriving as B (resp. A) is leaving, happen a lot less frequently and were therefore not selected for this study.

Our focus in this study is the evolution of piston effect along the entire platform as the train passes through the station, displacing large amounts of air across the platform. One direct, measurable consequence of this phenomenon is the change in velocity magnitude. Therefore, we define 9 measurement locations on the platform, visualized schematically on Figure 5.7, where the velocity will be measured or sampled. These positions are allowing to make observations for the development of piston effect through both the width and the length of the platform. The X-aligned positions (2-3-4 and 6-7-8) are deliberately chosen away from the exits to limit the influence of variations in outdoor conditions.

Having established these definitions, we try to guarantee the repeatability of the results, by ensuring that they are produced at the same location, with the same measurement procedure and in the same conditions. These considerations are especially important as we wish to compare data obtained from real-life measurements with the one from models.

Overview of the techniques used

Having defined in this part what is to model and what cases will be studied, we can therefore elaborate a methodology to do so, with the tools from Chapter 3 and Chapter 4 being available to us.

In Part II, two models, replicating the station's simplified geometry from Section 5.1.2, will be developed to study the train-induced airflow on the subway platform:

-a numerical model at full scale, including a portion of the tunnel on both sides, upstream and downstream. A transient fluid dynamics simulation with RANS equations will be used to model train-induced airflow in the station. This will be the object of Chapter 7. -a plexiglass small-scale model at scale 1:95, with a moving small-scale electrical train. PIV measurements will be conducted to acquire flow fields of the velocity on the platform, detailed in Chapter 8.

The symmetry of the scenarios for both train direction listed in Section 5.2.1 above is evident, and coupled to the architectural symmetry existing in the station, they will allow to get data from both platforms with just one numerical simulation. This will be made very clear in Section 7.2.1. For the small-scale model, constraints associated with the illumination by the laser will only make possible the acquisition of data for 'B only' scenario (see Section 8.2). It should be noted that all four scenarios were recorded during the on-site experimental campaign (see Table 6.2); however in this work, only the scenarios with one train, 'A only' and 'B only', have been analyzed; the scenarios with two trains, 'A then B' and 'B then A' will not be discussed in this thesis except for future development in Chapter 11 and the data can be made available upon request.

A period of approximately 80 seconds will be studied, corresponding to the time during which one train is visible from the platform throughout its approach, stop and departure from the station. On this timescale, the train movement is considered to be the only factor affecting the flow field of the station. In most similar studies indeed, the effects of wind variations at the exits, of pedestrian behavior, or of air displacements or heating due to people on door openings are not considered. The impact of these effects is assumed to be less significant than the train-induced airflow, and it is expected that taking enough measurements will make these short-term, temporary, and irregular phenomena fade in the average. The implementation of background airflow will be discussed for the numerical model.

While numerical simulations rely on mathematical models for specific phenomenon (such as turbulence or near-wall flow), scaled models -being bounded to the measurement uncertainties -allow to observe the real behavior of the fluid at stake. The lab environment also allows to get rid of any external, uncontrolled parameters, and PIV remains a unique technique to experimentally obtain the flow field. Once the setup is built, iterative measurements are made possible without a large additional cost. However, unlike lab testing, CFD does not suffer from potentially incompatible similitude requirements because simulations can be conducted at full scale. Additionally, since a large range of flow parameters (velocity, pressure, turbulence...) are computed in the numerical simulations, it is possible to make observations about the flow field and deduce behaviors that can hardly be measured experimentally.

The two previous paragraphs highlight that both the numerical simulations and measurements on a small-scale station have advantages and drawbacks, and that assumptions will have to be made to build and implement these models. To gain confidence in their outcomes, an extensive measurement campaign over nine days, described in Chapter 6 will be conducted in the station, recording the velocity at the 9 locations and for the 4 scenarios defined above in Section 5.2.1. Some outputs from this campaign, such as the average of the train's velocity, will be used as inputs for the models, promoting a realistic reproduction of the train-induced airflow.

As there is hence no such thing as an ideal model, the ability of the latter to represent the airflow in the station needs to be assessed. This will be the topic of Part III, taking the results obtained from the measurement campaign and from the models and putting them in perspective through quantitative parameters.

Part II

Experiments, simulations and results

On-site measurements along the platform of an underground subway station

The primary goal of the experimental campaign, as stated in Chapter 5, is to use realistic experimental data to validate the numerical simulations. A measurement setup is therefore designed and applied in a subway station in Brussels. Air velocity measurements, detailed in this chapter, have been conducted at 9 locations on one platform of the station using a hot wire anemometer through a 9-days campaign, for scenarios of trains arriving, stopping and departing. The scenarios including one train, 'A only' and 'B only', are then processed to make the curves comparable to the outputs of models described in other chapters.

The first section of this chapter (Section 6.1) covers the different constraints associated with performing measurements in a real-life station, notably in terms of safety, and explains the logistical implications for the setup to obtain the desired data. Section 6.2 details the measurement setup, going through the different measurement chains associated with the quantities studied: train presence in the station, wind velocity (and direction) on the platform, and train position on side B. Section 6.3 gives an overview of the realization of the measurement campaign, while the analysis process used on the gathered data is described lastly in Section 6.4. The on-site experimental setup was developed and operated in collaboration with two students, I. Sabbe and J. Vanlaere. The work reported here follows, for the most part, the structure and content of their master thesis [START_REF] Sabbe | Experimental validation of a numerical model describing piston effect driven airflow in a subway station[END_REF].

Phasing of the campaign, environment and constraints

The difficulty of getting on-site measurements to validate a model comes from the fact that, most of the time, only a few parameters can be controlled, or even recorded. We have seen in Section 2.2 that subway climate was influenced by a wide range of parameters, and that obtaining reproducible signals is a challenge. In this context, and as we focus on the spatial and temporal development of the velocity magnitude induced by a train as it goes through the station, scenarios and locations of interest have been defined in Chapter 5. The cases and the scenarios being fixed, the experimental campaign is hence designed to maintain as much reproducibility as possible while making sure to gather all the necessary parameters to allow an averaging of the measurements and a comparison with the outputs from the models. In our case, airflow data is only useful if linked to the train's position in the station. The elaborated setup hence includes: -a wind velocity sensor; -train detection sensors, called 'trigger sensors'; -a wind direction sensor; -a distance sensor; These sensors were needed to operate inside an actual subway station and endure corresponding conditions. This means, on one hand, to not disturb the train operation and to fully respect safety considerations when operating in a busy station: keep the platform clear of too many cables and tape to the floor the unavoidable ones; limit the size and the height of the measurement devices so as not to create a visual nuisance for the train drivers and to ensure that evacuation routes remain clear in the event of an emergency; avoid blocking the circulation in the station and passenger boarding and alighting; secure all sensors to prevent anything from falling onto the tracks; wearing safety vests and staying behind the yellow safety line. To protect the costly experimental equipment from potential damage and to ensure a good information of passengers, the experimental campaign required the presence of two STIB-MIVB security staff members. On the other hand, this implies that the functioning of the entire setup should not be disturbed by the presence of trains and passengers in the station. To comply with cable-avoidance requirements, wireless means of communication must therefore be preferred, so in particular data transmission must be robust enough to operate in a busy station.

In addition, available studies (such as [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF], [START_REF] Izadi | 3-D numerical analysis of train-induced flow inside four ventilated underground subway stations and connecting tunnels[END_REF], [START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF], [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF]) have made visible that the airflow on the platform is already affected by the train before it enters the station, and thus it was needed to start the recording before the train reached the station's entrance. For an efficient data management and a clear distinction between different scenarios, continuously saving the measurements is not desired, and measurements should only be triggered when a train is approaching the station. This is achieved by placing trigger sensors in the tunnels, one for each direction of the train, ahead of the station.

The safety procedures of the STIB-MIVB state that the access to the tunnels is only possible when the power in the rails is shut down -hence only during a short period of the night when there is no train service -and always supervised by STIB-MIVB engineering and safety staff. Additionally, nighttime is also sometimes used by the STIB-MIVB to perform tests or conduct works, so the planning of power cuts must be done in collaboration with many different services of the company. Granted permissions and available dates took the form of 3 blocks of 3 days, from Tuesday to Thursday, 3 weeks in a row. On the night from Monday to Tuesday, sensors where placed in the tunnel with batteries to last for 3 days, and on the night from Thursday to Friday, tunnels were accessed again to pick up the sensor and recharge the batteries. The phasing of the tunnel sensors placement and removal is summarized in Figure 6.1. It should also be noted that the measurement campaign was carried out in February 2021, as strict COVID-19 confinement measures were in place in Brussels, including a curfew at night and a limitation of employee's presence in their offices in favor of teleworking. This context was putting even more emphasis on avoiding the creation of restricted areas on the platform that would bring people closer from each other, and on the limitation of human resources available to coordinate and carry out the experiments. It was also mandatory to wear a face mask at all times. Besides these additional considerations for setup design, this also means that the station and the train were not as densely populated as usual. It was observed that even during the rush hours of the morning, the train was never reaching its full capacity. This paragraph echoes Section 2.3.2 by highlighting the cost of these measures in terms of coordination with public services, staff involved, safety and compliance to procedures, that adds up to the technical requirements necessary to obtain the desired data. The following paragraphs will detail the different parts of the experimental setup and how they deal with the mentioned challenges.

Description of the experimental setup

Four measurement chains involving four types of sensors are installed in the station to record desired data: the presence or absence of the train in the vicinity of the station; the wind velocity and direction at the 9 locations; and the location of the train on the measurement side during its deceleration. The following paragraphs detail the sensors used with the different measurement chains that were functioning in parallel, as well as the communication means necessary for the coordination of all sensors and data recording. The data was centralized and saved using the software LabVIEW, which functioning will be described last in Section 6.2.4.

Train presence: trigger sensors

Six short-range distance sensors were implemented to automatically and accurately detect the exact arrival and departure of the trains. Three train detection modules are placed on each side (i.e. for each direction of the train), one at each extremity of the platform lengthwise, and one in the tunnel, 100 m upstream the station entrance. The modules along Platform A (resp. Platform B) are named A1, A2 and A3 (resp. B1, B2 and B3) and numbered according to the order in which the train passes them. Their arrangement is displayed in Figure 6.4. A train detection module consisted of an Arduino UNO microcontroller [START_REF]Arduino UNO R3 -Product Reference Manual[END_REF], an ultrasonic or infrared distance sensor and an HC-12 transmission module [START_REF]HC-12 Wireless Serial Porte Communication Module -User Manual version 2[END_REF] soldered together (Figure 6.2a). The HC-SR04 is an ultrasonic distance sensor [START_REF]HC-SR04 User's Manual -V1[END_REF], used to sense the presence of a train. It is combined with the HC-12 module to wirelessly transmit data to another HC-12 module connected to the central PXI. However, due to cold weather conditions during the measurement campaign (see Table 6.3), the HC-SR04 sensors became inaccurate. For this reason, they were replaced by Sharp 'GP2Y0A41SK0F' infrared sensors [START_REF] Sharp | 2Y0A02YK0F -Datasheet[END_REF] (Figure 6.2b), that were used during the last 5 days of the measurement campaign.

This combination of sensors is appropriate in its compactness which is compliant with safety requirements, and provides the advantage of being quite discrete, so passengers are not tempted to touch the modules. Furthermore, the use of jumper wires allows easy replacement if a sensor is broken. Additionally, an Arduino has a low power consumption, making it ideal to be powered by a battery. The equipment for the train detection modules is also affordable, easily accessible, wireless and provides accurate data about the train presence.

Each train detection module is placed in a 3D-printed protective casing, including a cover on the top for the sensors placed in the tunnel. The modules are powered with 12 V batteries, of 7 Ah for the station modules and 12 Ah for the tunnel modules. The combination of the battery and the sensor for a train detection module in the tunnel is shown in Figure 6.3. The sensors are set to detect the presence of a train when a distance less then a predefined threshold is measured and send a message to the central module in case of a detection. This threshold is fixed to 0.85 m: low enough to only detect when a train is passing on the track on the side where the sensor is placed, but not when a train is passing on the track on the opposite side; and high enough so that a passing train cannot stay undetected. It should also be noted that according to their datasheets, HC-SR04 ultrasonic sensors measure accurately up to 4 m, while Sharp infrared sensors only measure accurately up to 0.80 m. The width of train being of a couple of meters, the chosen threshold allows for a margin of error and a very accurate measurements is henceforth not necessary. To prevent single erroneous measurements from the ultrasonic or infrared sensors, an extra safety measure is coded on the Arduino boards: a message is only transmitted if a distance lower than 0.85 m is measured three consecutive times. The placement of sensors in the station and the communication lines are schematized on Figure 6.4. The messages sent from the sensors to the central 'C' Arduino are represented by full lines on the figure, and take the form of a string of characters consisting of several times the same letter, as listed in Table B.1 in Appendix B. This type of message is designed to enhance the resilience of the communication in case the message does not arrive at the central module in its entirety. As modules A1 and B1 are placed far away in the tunnels, trains and walls are additional obstacles that may prevent their messages to reach module C at all. To improve communication, a relay function is implemented in the Arduino code of the train detection modules, as schematized by the dashed lines on Figure 6.4.

The HC-12 communication modules have a baud rate of 5000 bps in the air. Most limiting is the update frequency of the IR distance sensor of 25Hz; the maximum error in the distance measurement from these sensors is therefore of 0.4 m for V train = 10 m/s, but is likely smaller when the train arrives in the station and V train decreases.

The sensors are hence serving as triggers to start the data recording of all sensors and to detect the defining moments of the train course through the station: 'train is approaching station', 'train is entering station', 'train is leaving', 'train has left'. To keep the amount of data reasonable, the data from all the sensors is only starting to be saved when one of the tunnel modules, A1 or B1, is activated. In case of a missed message from the tunnel modules, 8 s of buffer data is always kept by LabVIEW, and added at the beginning of the recorded data when A2 or B2 is triggered.

Wind velocity: hot wire

Velocity magnitude is the critical airflow characteristic which is studied in this thesis. To this aim, theoretical insights about hot wire anemometry have been given in Section 4.1. In the station, the velocity magnitude is measured using a ComfortSense Mini hot wire anemometer from Dantec Dynamics (Figure 6.5) [START_REF]ComfortSense Mini -Robust and compact anemometer for ventilation and draught measurements[END_REF] and the data is acquired at 1 kHz. The draft probe was designed to measure instantaneous air velocities in turbulent flow. The hot wire is calibrated in the Royal Military Academy lab, using the PIV system. The probe is placed in a wind tunnel and the voltage measured by the device are written down along with the flow velocity measured by PIV, to obtain the calibration curve in Figure 6.6. The details of the uncertainty calculation are given in Appendix C. A polynomial is then fitted through the data points to get the voltage-temperature relationship. The calibration of the probe could only be realized in the lab environment, and the impact of this limitation is discussed in Section 9.5.2. For this measurement, the choice has been made to keep a cable connection instead of wireless transfers through Arduino cards as reliable, high frequency data is desired. The PXI runs a LabVIEW script which derives velocity from voltage data using the calibrated relation between the parameters. For the on-site measurement campaign, the hot wire anemometer is mounted on a wheeled cart (Figure 6.7). As explained in Section 6.1, for safety reasons, the height of the measuring instruments should be kept reasonable; for this reason, the sensor is mounted such as the hot wire stands 0.5 m above the floor. The usage of this cart gives the opportunity to easily take measurements at different locations along the platform (see Section 6. To obtain the wind direction, not determined by the hot wire, a thread and webcam system with image processing have been installed on the cart. Additional details and pictures can be found in Appendix B. During the experimental campaign however, it quickly became clear that the angle data provided by the wind direction sensor was not accurately representing the flow direction. For this reason, the wind direction data will not be discussed further, but remain a potential topic for improving the experimental setup.

Train distance: laser sensor

On Platform B side, the position of incoming train in the station is measured accurately through the whole length of the station and saved along the data from the other sensors. This measurement is achieved by using a LiDAR system, which principle relies on sending a laser beam on a desired target and collecting the reflected laser light. LiDAR system are robust devices designed for outdoor environments, and it can hence withstand the polluted air and dirty conditions inside the station. A TF03 LiDAR from Benewake [START_REF]F03 Single-Point Long-Distance LiDAR -Product Manual V0[END_REF] is used here, and showed on Figure 6.9. As visible on Figure 6.10, the laser is placed at the end of Platform B and set to point at the B-side trains. It therefore measures the distance between the sensor and the front of the train. The LiDAR is connected to a Raspberry Pi 3 model B+ [START_REF]SCB-68 Getting Started[END_REF], which is chosen for its compact format: although this sensor is not placed directly in the station and not in a zone accessible to passengers, it lies on the floor of a small corridor along the tracks that leads to technical chambers, and the path should hence be kept relatively clear. The distance data is transmitted to the central PXI using another two Arduino and HC-12 modules, named E1 and E2 and set to communicate on a third channel. With just one LiDAR system placed at the end of the platform facing towards the tunnel on the other side of the station, the acceleration of the train was not recorded, and only the absence of train upon its exit from the station is visible in the data. If the acceleration of the train is desired as well, a second LiDAR system should be positioned at the beginning of the platform pointing towards the end.

Data centralization

As mentioned in the previous sections, all measurement data is gathered on a PXI-1042 from National Instruments (Figure 6.11) [START_REF]NI PXI-1042 User Manual[END_REF] and processed by a LabVIEW [START_REF] Bitter | LabVIEW: Advanced Programming Techniques[END_REF] script. The PXI is connected to the different receiving Arduino modules visible on Figures 6.4, 6.8 and 6.10 (C for the train position from the triggers and E2 for the distance from the laser) with USB cables and to the hot wire through a BNC cable. To avoid overcrowded communication channels, a dedicated channel was provided for each measurement chain using HC-12 modules.

During the campaign, the measurements are monitored live using a screen, keyboard and computer mouse. The control screen presented by LabVIEW is displayed in Figure 6.12. The train situation in the station is indicated by three buttons on each side, turning on whenever a train detection sensor is triggered. From the combination of activated modules, different states can be deduced: waiting, train approaching, train entering station, train fully in station, train leaving. Built-in functionalities allows LabVIEW to collect data in function of time. A new .txt file is created for each new train event, and a excerpt of the data recorded in this file can be found in Appendix B. The filenames are automatically generated consisting of date and time of the measurement, and the scenario type is added manually to the name of the file to facilitate post-processing. It should be mentioned that a train event does not always describe one of the discussed scenarios specified in Chapter 5 and described in Appendix A. The files containing desired scenarios are therefore separated from others, and only these ones will be used for post-processing the velocity data.

Measurement campaign 6.3.1 Summary of the recordings

On each day of the measurement campaign, the cart is positioned differently along the platform to study various measurement locations as discussed in Section 5.2.1. Figure 6.13 shows pictures of the sensors described in the previous section while operating in the station. Table 6.1 summarizes the actual position of the cart, defined by the hot wire, on each measurement day of the campaign. We recall here that the upper left corner of Platform B is taken as the origin of the axis (see Figure 5.2). The measurement positions are schematized on Figure 6.14. Recalling Figure 5.7 from Section 5.2.1 about the methodology, it appears that although locations should theoretically have been horizontally or vertically aligned, they were subject to on-the-spot modifications while installing the sensors each measurement day. These adjustments were necessary to adapt to the daily constraints, such as making sure the measurement cart was not right in front of a train door, a station exit, or a bench, for instance. The numerical model described in Chapter 7 takes these actual locations into account.

The daily amount of measurements performed for each scenario defined in Section 5.2.1 (and schematized in Appendix A) can be found in Table 6.2. It was desired to reach 30 measurements per scenario, so that the sample size is large enough to form sufficiently accurate average velocity curves, and to be approximated by a normal distribution, allowing to use the quantile function to find the critical values of the confidence intervals (see Section 6.4.2). However, limited time in the station and the subway train's schedule did not allow to achieve this value in every case. On the first day (position 4), it took some time to prepare the set-up and resolve some preliminary issues causing less measurements to be performed. Less data was collected for position 1 due to the malfunctioning of certain sensors, caused by cold weather conditions (see Table 6.3). Few data was collected concerning scenarios describing two trains, because they did not occur as often.

Background airflow

Background airflow was studied during five days of the measurement campaign, by recording the wind velocity with the hot wire anemometer when trains were not going through the station. A example of data recorded is given in Figure 6.15 and the data for each day is presented in Table 6.16 along with two times the standard deviations of all background airflow measurements collected that day. An overall average background velocity magnitude and corresponding two standard deviations are calculated using all background airflow data. Variations across days can be attributed to different conditions regarding pressure, temperature, and wind velocity, outside the station and in the global underground network. Although the magnitudes are in agreement with the values found by Pflitsch [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF] and Gross [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF], the spatially and temporally transient characteristics of this airflow resulted in large variations over the measurements, and the real influence of the background airflow in the experimental results is therefore difficult to distinguish. In Chapter 9, where the velocity curves will be given, each measurement location will be presented with the average background wind for the corresponding day. For the days when the background airflow was not measured, the data will be presented with the average of all the other days.

Weather data

The weather conditions during the measurement campaign can be consulted in Table 6.3. Information concerning outside weather conditions was obtained from the 'Institut Royal Météorologique de Belgique' [START_REF]Bilans climatologiques de[END_REF] for a measurement station in Uccle, about 6 kilometers from the subway station. On six measurements days, the bulk temperature of the air at the cart location was measured at 8 AM. Although this data is not modeled in the following chapters, it is useful to discuss it as one of the influencing factors on subway stations airflow or on measurement conditions, especially as the entrances of the test case station are open staircases. An estimation of the temperature in the station at the time of the recordings is also necessary to use the appropriate values, for air density or kinematic viscosity for instance, in the calculation of various quantities. This study is also a contribution to the knowledge on measured wind conditions in subway stations, it is important to report as much data as were recorded.

On-site data processing

It has been stressed that the evolution of the airflow related to train movement is a transient phenomenon, characterized by different moments. In practice, it is difficult to obtain measurements of the exact same process under the exact same conditions at several different times. The key moments have been identified and measured with the trigger sensors. To be able to study the behavior of airflow in the station with regards to the train movement in the station, the data will therefore be ensemble averaged.

To compute the average curves, alignment of the data is necessary as the measurements started at various times throughout the campaign and the train cruise speed, deceleration rate, stop time and acceleration rate could differ. To evaluate the variability within a dataset, the averaged curves are presented with a 95% confidence interval (in which the value will fall 95% of the time), which is given by two times the standard deviation (2σ) of all the recordings in the dataset.

As mentioned previously, although data was recorded for all scenarios listed in Appendix A, only scenarios with one train running along the platform, 'A only' and 'B only', are fully studied.

Train distance

Only datasets corresponding to the 'B only' scenario were analyzed for the distance, as the LiDAR system was positioned on this platform. The raw data, presented in Figure 6.17a, visualizes the distance between the sensor and the train, starting with a deceleration phase upon train entrance in the station, followed by a stabilization at a constant value as the train is stopped in the station. These curves evidence the fact that train drivers decelerate at different rates, but that the deceleration shape remain similar enough to perform averaging. The curves are therefore aligned using the time at which the first distance value measured between 114 m and 116 m, and the result is given in Figure 6.17b. The curve is cut after the average time at which the train has left the station (when B3 changes from 0 to 1), as the distance measurement is not relevant anymore while the LiDAR is only pointing at the side of the train. This curve can be displayed along the wind velocity curves for 'B only', and will be used later (see Section 7.2.2) to derive the movement of the train in the numerical model.

Wind velocity

The alignment of the wind velocity is made possible by the data collected by the train detection modules. Three triggers are defined: t enters is the time when A2 (resp. B2) changes from 0 to 1; t leaving when A3 (resp. B3) changes from 0 to 1; t lef t when A3 (resp. B3) changes from 1 to 0, i.e. when the tail of the train is not detected anymore in the station. The time is counted from the first measured value (hence when A1 or B1 is activated). The values obtained from averaging the times for the datasets are given in To evaluate how much variability there is between the datasets depending on the movement actually executed by the different trains, it is interesting to look at the standard deviation existing in t leaving with respect to t enters , and in t lef t with respect to t leaving . This is done with Figure 6.19: the grey rectangles corresponds to the confidence interval of the trigger centered on its average, after alignment has been done for t enters or for t leaving . During the experimental campaign, the time a train remained in the station varied greatly depending on the measurement, causing each velocity curve to have a different t leaving and t lef t . It is indeed observable on Figures 6.19a and 6.19b that if the data is only aligned on t enters , large variations remain in t leaving , even encompassing t lef t . When the train has started to accelerate to leave the station, less variability is present between t leaving and t lef t , as illustrated in Figures 6.19c To account for these large differences in the stop time and to better evidence the link between the train movement and the airflow, the velocity magnitude is hence aligned on t enters and on t leaving before being averaged. An example for one location and scenario of the differents steps of the alignement procedure is given in Figure 6.20. For each recording, a timestamp is put when the different triggers are activated, and the velocity data is then shifted in time by the difference between the individual trigger and the average trigger. This is allowed by omitting a part of the velocity curve during the stop time of the train, where the flow is assumed to have returned to a steady state. In fact, many events can be happening during the stop that cause the train to remain longer or shorter in the station (regulation of traffic, technical issue, safety event, either in the station studied or further away on the subway line...) that are not relevant for the airflow at stake.

In the rest of the plots in this thesis, the time stamps of the numerical triggers are adopted to align the experimental data to the numerical velocity curves: the experimental triggers will be shifted (and the wind velocity curves will be shifted accordingly) to be aligned with the triggers of the CFD, which will be given Table 7.2 (Section 7.2.2). In particular, the cut in the middle of the curves will allow the stop time to always be of 30 s. By applying this method, the numerical data will not have to be altered, and this visualization will allow an easier comparison between experimental and numerical results as well as between scenarios. In the following chapters, some of the results from this chapter will already be used, in particular to comment on the appropriate choice of models. All the curves for the two scenarios studied and for the 9 positions will be given and discussed in Chapter 9, together with the corresponding curves for the numerical model and the small-scale model. Additional arrangements of curves to evidence specific phenomenons may also be found in Chapter 10.

Numerical model of a train passing through the station

In this chapter, the station described in Chapter 5 is reproduced numerically both in a 2D as well as a 3D model. A scenario of a train passing through the station is implemented, and the numerical part of the study is covered. The airflow is solved with CFD techniques using RANS equations in ANSYS (2021 R2). A brief clarification is first given in Section 7.1 about the work methodology and how the different outputs are used to draw conclusions about the flow patterns.

The following section (Section 7.2) reviews how to best represent the existing architecture and airflow conditions in the numerical model, taking as inputs some results obtained from the on-site measurements presented in Chapter 6.

In Section 7.3, the numerical model goes through various tests of parameters: the tunnel length to include ahead of the station, the possibility to use a 2D model, the meshing features, and the solver parameters including turbulence modeling. From these simulations, we obtain the set of features that is deemed to produce the most reliable results, without sacrificing too much on computational efficiency. Airflow features specific to piston effect are succinctly discussed in Section 7.4, including a comparison with existing literature on the topic. The detailed outputs of the numerical model for the velocity at the 9 locations for 'A only' and 'B only' scenarios are not given in this chapter, but will be extensively discussed in Chapter 9. Compared to dynamic meshing techniques, the Immersed Boundary Method (IBM) is presumed to offer faster solutions since it does not require the compu-tationally expensive step of developing a new mesh for each timestep. The last section (Section 7.5) reports a study of the same model implemented in ANSYS CFX, using the IBM as an alternative to the dynamic mesh.

A note on the different configurations and on comparing their outputs

As it has been mentioned at the end of Section 1.2 while setting the outline of this thesis, some of the discussions in this chapter are based on outputs of the numerical model in its 'non final' version as obtaining results was necessary to progress in the elaboration of the numerical model. For instance, the meshing features, some geometrical details such as the platform height or the initial position of the train, the train speed, or the chosen turbulence model, might vary. As we are dealing with relatively similar configurations, it is assumed the trend found for one specific parametric study (with all other parameters being kept constant) can be generally transposed to the other cases (where the other parameters are slightly different than the ones used for the parametric study).

Additionally, the reader will notice that we sometimes use data whose method of production has not yet been discussed: for example, the 2D study from Section 7.3.3 uses a tunnel length that is only formally determined for the 3D case in Section 7.3.2 that follows. This is due to the fact that the different models were studied in parallel with the realization of the experimental campaign, and that it was not always possible to re-run the simulations given the long computation time (up to one month). In this chapter, we tried to keep a thematic structure by addressing each element that has been studied to elaborate the final model, while giving an insight on the process of thoughts that comes with the elaboration of model with all the necessary simplifications or choices that must be made and assessed. For each configuration studied, the relevant details will be provided.

We also aim in this chapter to draw conclusions from the outputs of similar simulations using different parameters. This raises the question of what indicator can be used to observe transient results that are strongly time-and spacedependent, and the need for systematized tools to compare the results of the velocity magnitude at different locations hence starts to arise. This matter is the subject of Chapter 9. In this chapter, we will limit ourselves to use the peak magnitude upon train arrival and departure as a representative quantity to compare the outputs of the different simulations performed. ANSYS Fluent is among the most common softwares used in fluid mechanics and wind engineering that uses the RANS turbulence models. The ANSYS suite provides dedicated applications for geometry creation and modification, meshing and flow solving, integrated in the ANSYS Workbench platform [START_REF]Ansys Fluent Workbench Tutorial Guide -Release 2021 R[END_REF], which has been used in this work unless specified otherwise.

The station architecture of the test case described in Chapter 5 (in particular, with the dimensions of Figures 5.5 and 5.6) is reproduced numerically both in a 2D and 3D model using the Computer Aided Design (CAD) software Autodesk Inventor [8]. Similarly to Jia's [START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF] or Camelli's [START_REF] Camelli | Modeling subway air flow using CFD[END_REF] approaches for instance, the train is approximated by a rectangular block. The geometry is then edited if needed (when changes of dimensions are studied, for instance) and formatted for CFD analysis in ANSYS SpaceClaim ([4]): the space occupied by the train body is 'suppressed' from the station body using a boolean operation, so that the fluid domain is delimited by the train walls. The train body is also marked as 'suppressed for physics' as its internal structure is not studied.

The internal domain of the station is meshed using the integrated mesher of ANSYS Workbench (2021 R2) and solved using the commercial CFD software ANSYS Fluent (2021 R2). The equations governing fluid motion and the mathematical models necessary to solve them have been introduced in Chapter 3. A comprehensive description of the numerical methods used, of the features available in the software and the associated options, is provided by ANSYS in the Ansys Fluent Theory Guide [START_REF]Ansys Fluent Theory Guide -Release[END_REF] and the Ansys Fluent User's Guide [START_REF]Ansys Fluent User's Guide -Release[END_REF]. In the following paragraphs and sections, most assumptions about the best options to select are read from these references. The vast majority of simulations are ran on the computing cluster of the Royal Military Academy using 80 Intel Xeon-Gold 6148 (2.4GHz/20 Cores) cores with 384 GB of RAM each. Because of the symmetry of the station respectively to the train tracks, we can get data both for 'A only' and 'B only' scenarios with just one numerical simulation. For scenario 'B only', we place the points exactly with the coordinates of the on-site measurements (see Section 6.3). For scenario 'A only' we add points on Platform A, allowing to read results from their perspective as a train going through the station on the other side than the measurement side. To rephrase, focusing on scenario 'A only' means that using the exact same simulation, we sample the results on Platform A, reproducing the same scenario as if we were standing on the measurement platform and a train was running along the opposite platform. The coordinates of the points used to read the results on both platforms are summarized in Table 7.1, and visualized on Figure 7.1. The height (Z) of all these positions is 1.6 m above the platform floor (this choice will be further discussed in Section 7.4.3).

Position

Platform B Platform A

x [m] y [m] x [m] y [m] 1 5.7

Train motion through the User Defined Function

To keep the simulations as close as possible from the actual train movement, the averaged distance curve of all the measurements (Figure 6.18) and the average triggers measured on site (Table 6.4) serve as an input to implement the train velocity in the numerical setup. In line with scenario 'B only', we hence consider one subway train arriving at a constant speed of 10.22 m/s through the tunnel. The deceleration is modeled using a third order polynomial fitted through the average laser distance measurement. After stopping for 30 seconds, the train is linearly accelerated at 1.05 m/s 2 for 9.75 seconds, to reach its cruising speed of 10.22 m/s upon exiting the station. The superposition of the averaged distance curve, with the described velocity sequence is visible in Figure 7.2. The triggers corresponding to this train schedule are given in Table 7.2. As mentioned in the previous chapter, this triggers are taken as the reference to align the experimentally recorded data, both on-site and in the small-scale model. The train movement through the station is controlled in Fluent by a User-Defined Function (UDF) which allows to define complex velocity profiles. The .c file given as inputs in the simulations is available in Appendix D.1. At the start of the simulation, the train is positioned inside the tunnel, its rear standing 1.4 m away from the tunnel exit (hence, its front is 108.6 m upstream the station entrance).

Boundary conditions

Boundary conditions must also be provided at the 8 openings of the station geometry. In same spirit as in Xue's work [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF], the exits located mostly behind the train (the tunnel inlet section, R1 and L1) are set to pressure inlets and the exits of the station and other exit faces (the tunnel outlet section, R2, L2, R3 and L3) are set to be pressure outlets, all at atmospheric pressure P atm = 101325 Pa. These boundary conditions are summarized in

Background airflow

To the author's knowledge, no other work that performs CFD simulations of the airflow inside a subway station, at a level of detail that allows to make observations at different positions on the platform, includes also the background airflow. In this section, an attempt is made to incorporate the background airflow that has been documented in the literature and observed during the on-site experimental campaign (see Section 6.3.2) in the CFD model. In the field experiment conducted by Gross [START_REF] Gross | Observations and numerical simulations of the train-induced air flow in a subway station[END_REF], where the station's architecture is relatively similar to the one studied in this thesis, a wind sensor positioned at street level indicated that during one day, the wind direction was constant. It makes sense, therefore, to model background wind using a one-directional pressure gradient -the wind direction chosen here is the one that would enhance the airflow following a train coming on side B of the station, from left to right.

We aim to choose boundary conditions such that the mean velocity magnitude at the measurement locations on Platform B is the average of background close to the one measured experimentally, detailed in Section 6.3.2, with a value of u bg = 0.67 m/s. The exits on the train entrance side (the tunnel inlet section, R1 and L1) are therefore set to overpressure, while the exits on the train departure side (the tunnel outlet section, R3 and L3) are set to underpressure. The values of gauge pressure are adjusted manually through an iterative approach and are given in Table 7.4 and represented schematically on Figure 7.3.

The flowfield is first initialized with a velocity of u bg in the X-direction. A simulation without train movement is then ran with a timestep of 0.05 s for 900 seconds, making sure that the flow reaches a steady state. The velocity magnitude observed at four different locations from the start of the simulation is plotted in Figure 7.4. The velocity contours obtained after 600 seconds of simulations are given in Figure 7.5. Figure 7.4: Velocity evolution after applying a pressure difference at the exits in the numerical simulation, at chosen locations on the platform.

It is noticeable that oscillations persist in the velocity magnitude several minutes after reaching its steady state. Oscillations have been observed both in our experimental data (see Figure 6.15) and in the one of Pflitsch [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF] for instance. These can be attributed to the many factors affecting the airflow for individual measurements in the station, as mentionned at the beginning of Section 2.2. These phenomenons are however not accounted for in the CFD model. Another hypothesis is that the oscillations are the manifestation of Kelvin-Helmholtz instability, that appears when there is a velocity or density difference between adjacent layers of fluids -in this case, between the flow coming from the tunnel and the wind generated through the doors on the platform -causing shearing motion and the formation of vortices or waves at the interface [START_REF] Drazin | Kelvin-Helmholtz Instability[END_REF]. This interaction may or may not exist in reality, but dedicated measurements would be required to acknowledge fluctuations both in time and in space in a real-life case. It also is observed that putting symmetrical conditions for the doors on the left side and the right side does not result in a symmetrical flow pattern. As the train stays stopped at its initial position during the simulation, the flow is deviated towards Platform A side, resulting in higher velocities on this side. For this reason, the input pressures are slightly higher on side A than on side B. Still, the magnitude remains higher on side A than on side B, as we obtain an average of 0.91 m/s for the 9 measurements locations on Platform A, and of 0.72 m/s on Platform B.

After letting the simulation establishing the background airflow run for 900 seconds, the train movement is started as described in the previous section. In an empty station without train movement, Pflitsch [START_REF] Pflitsch | Air flow measurements in the underground section of a UK light rail system[END_REF] has noted that when ventilation fans are put in service, they inhibit background airflow. For a case when a train is running through the station, it is however not clear how the background airflow and the one induced train would interact. From there, two configurations are hence studied, denominated by 'BC on' and 'BC off', where 'BC' stands for 'Boundary Conditions':

-'BC on': the boundary conditions are kept with the pressure gradient sustaining background wind, as in Table 7.4. -'BC off': the boundary conditions are changed to atmospheric pressure, as in Table 7.3, as soon as the train movement is started. The results of these two simulations will be discussed in Section 7.4.2, as well as a conclusion on which configuration is preferred to model background airflow.

Geometry, mesh and solver parameters 7.3.1 Dynamic mesh: principle and challenges

Dynamic meshing techniques are used in CFD to model and simulate fluid flows in domains where the geometry changes during the simulation. This occurs in our case due to moving boundaries of the train walls while it travels through the tunnels and the station. A grid regeneration method is used here, as opposed to a grid deformation method. In the latter, the mesh nodes are moved or deformed to match the changing geometry, involving the manipulation of the coordinates of the mesh nodes based on the displacement of the object, which is adapted to problems with moderate motion. In the grid regeneration approach, the mesh is reconstructed at each time step to account for the changing geometry, ensuring that it conforms to the current boundaries. Grid regeneration methods involve steps like mesh generation, mesh connectivity updates, and interpolation of solution variables from the old mesh to the new mesh. These methods are more computationally expensive but are necessary for cases with large deformations or complex geometry changes, as in the present study, and have been used to simulate trains moving in subway stations in Cross' [START_REF] Cross | A validated numerical investigation of the effects of high blockage ratio and train and tunnel length upon underground railway aerodynamics[END_REF], [START_REF] Cross | Enhancing the piston effect in underground railway tunnels[END_REF] and Xue's [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF] works for instance.

In Fluent, this is applied by activating the dynamic mesh, specifying the fluid zone as deforming and activating the smoothing and remeshing options, which are appropriate for tetrahedral meshes. Smoothing adjusts the mesh of an area by moving or deforming its boundaries, but the number of nodes and connections does not change. In particular, the diffusion-based smoothing is preferred for cases with large (at cell scale) motion, moving mesh nodes in response to displacement of boundaries by calculating a mesh velocity using a diffusion equation, i.e. the velocity at the boundary nodes is used as a Dirichlet boundary condition. When the displacement causes the cell quality to deteriorate, the remeshing option is selected, enabling Fluent to remesh zones with low quality locally. The settings for this parameter, i.e. the cell shape and dimensions criteria from which the remeshing should be activated, are read from the mesh scale info dialog box, so that the characteristics from the initial mesh can be conserved. By adapting remeshing parameters, divergence of the results is prevented.

The timestep chosen for the simulation is also of a great importance to preserve the mesh quality, as problems might arise due to the movement of the train resulting in extreme shapes that cannot be compensated by the adaptative mesh. In particular, if a boundary travels a distance greater than the cell's dimensions during a time step, the volume becomes negative resulting in an error. A time step size of 0.001 s is found sufficient to prevent negative cell volumes and is therefore adopted for the simulations, unless specified otherwise.

Preliminary study: tunnel length

Determining the numerical domain far-field limits is crucial when studying the airflow in the subway station to ensure a boundary independent solution. We have indeed noted that the airflow in the station is already affected several seconds before the train reaches the station entrance, and that the general circulation of trains in the underground subway network participates to background airflow. For obvious reasons of computational efficiency, simulating the whole subway network is not possible with CFD, and therefore a choice must be made of where to cut the domain. Additionally, in the CFD model, as the train starts at its beginning position, all of the air surrounding it is stationary, while in reality the airflow around the body would be completely developed as the train has been traveling long enough through the tunnel. To limit these effects, the upstream tunnel length necessary to include in the geometry is hence studied and determined.

Several cases of trains running at constant speed in a 1000 m long tunnel are therefore simulated in a 3D geometry. To make sure the results remain valid when studying slightly different geometries and scenarios, various tunnel cross sections and train speeds are considered. The dimensions of the tunnel and the train are given in Figure 7.6. The blockage ratio β of the train in the tunnel and the Reynolds number Re based on the hydraulic diameter D H of the tunnel, as per Equations 5.1, 5.2a and 5.3a, are used to characterize the different geometries and velocity inputs as defined in Table 7.5. For the β = 0.37 configuration, the closer from reality, 6 different train speeds are considered. Doing so, we also want to make sure that the same model can be used with confidence for various scenarios, as this will be done in Sections 10.1 and 10.2 for instance. For the two other configurations, with one lower and one higher blockage ratio, two simulations are ran: one with approximately the same train speed as in the real-life case, i.e. 10.22 m/s, and one with a train speed chosen such as the Reynolds number is the same than for the β = 0.37 and V train = 10.22 m/s case. The computational model is solved using the commercial CFD software AN-SYS Fluent (2021 R2), with mass conservation and RANS equations for incompressible, transient flow -the choice of models and the dynamic mesh approach will be justified in the following section. The domain is meshed using a tetrahedral unstructured grid of cell size 0.3 m, and a face refinement of 0.2 m on the train walls. The tunnel extremities are set to atmospheric pressure inlets/outlets and the initial flow velocity and turbulence intensity are set to zero.

As the train starts its movement in the tunnel, a boundary layer is formed by virtue of no-slip condition: the fluid close to the train acquires the velocity of the moving train, while the fluid close to the wall has a zero velocity, resembling to the academic case known as 'Couette flow'. Moving further in the X direction, the flow will reach a point where the velocity profile does not change with streamwise direction: this state is called 'fully developed flow'.

The time and distance required to reach this state is determined by looking at the velocity magnitude along a radial horizontal line in the tunnel, represented by dashes on Figure 7.6, placed 20 meters away from the train head and moving at the same speed as the train. The velocity profiles for the first 5 seconds of simulations and every 0.5 second are plotted on Figure 7.7. The correlation coefficient between the successive profiles is then computed and given in Figure 7.8. The flow is considered sufficiently stable when the correlation coefficient stays above 0.95. The time meeting this condition for each configuration is reported in Figure 7.9. Although no clear link with the blockage ratio or speed variation appears, it is found that 30 m of travel through the tunnel is sufficient for all configurations to achieve a fully developed flow around the moving train at constant speed. Taking the train length into account (90 m), and the fact that it is desired to start recording the velocity prior to the train entrance in the station, 200 m of tunnel are used in the rest of the simulations.

2D study of the train going through the station

In an attempt to go for the simplest model for the station, a 2D case is firstly considered. The geometry consists of a horizontal slice of the station, above platform level. 175 000 triangular elements are used to capture the geometrical details and allow more flexibility, especially as the train moves through the domain. The cell size in the station is limited to 0.5 m. To better approximate physical results, an 30 cm-thick zone is defined around the tunnel and station walls, within which the cell size is of 0.1 m. In front of and at the back of the train, this zone extends to 1.5m from the train head and rear. An inflation layer is created around the tunnel, station and train walls with a total thickness of 0.05 m. An image of the mesh around the front of the train is given in Figure 7.10. The enclosure around the train aims to preserve the mesh quality along the train motion; the smaller cells concentrated around the train can provide sufficient resolution in these regions and larger cells located far from the train will improve computational efficiency [START_REF] Cross | A validated numerical investigation of the effects of high blockage ratio and train and tunnel length upon underground railway aerodynamics[END_REF]. Both k-ε and k-ω turbulence models have been tested, yielding very similar results. The outputs from the 2D simulation at the locations of interest and scenarios 'A only' and 'B only' are plotted in Appendix G, and one curve is given in Figure 7.11 to illustrate one location and one scenario. Although not in perfect agreement, the general tendency of velocity is clearly visible and a pattern is detected. First of all, a spike in airflow velocity is observed when the train enters the station. Secondly, non-zero velocities are recorded at standstill for both simulation and on-site measurements. Lastly, when the train accelerates, a second peak is formed. An evaluation of the closeness of the magnitude of these peaks to the ones present in the data measured on-site in performed in Section 7.3.4 and the results are summarized in Table 7.6. Some noticeable differences can however be found. In a lot of cases, the spike in velocity magnitude happens earlier for the numerical data the in the experimental one. Around the departure of the train, the timing of both peaks are strongly dissimilar and the numerical and experimental velocity curves start to differ significantly after this. After the arrival peak, the numerical velocity decreases to zero in almost all cases to increase again shortly after and reach, or sometimes exceed, the experimental results. This re-rise in the numerical velocity during the stop time of the train, although it comes closer to the value given by the experimental data, should however be questioned. In the real station, background airflow is deemed to produce the non-zero values recorded while the train is stopped in the station. This phenomenon is however not modeled in the simulation at hand here. What might be causing the airflow to keep circulating on one platform in the 2D simulation however is the fact that in real life, the air can flow up and down the train body, while in the 2D case the train is almost fully blocking the air to spread towards the tracks. The agreement between the numerical and experimental data during the stop time is hence more a fortuitous effect than an accurate representation of the airflow.

We conclude from these considerations that a simplification of the case to a 2D model is not indicated to obtain a realistic simulation of the airflow. In the rest of this work, we will therefore mostly focus on a 3D simulation of the test case.

Meshing

The geometry of the 3D station model is implemented such as described in Section 5.1.2 (see in particular Figures 5.4, 5.5 and 5.6). The domain is meshed with tetrahedral elements, which are prescribed for dynamic meshes in complex geometries as they allow more deformation, and a refinement on the train faces is added. Special attention must indeed be given to the zone located between the train and the tunnel wall, separated by only 34 cm. As this volume is very thin, divergence can arise from the cells located in this space, and one must therefore ensure that sufficiently fine mesh options are selected to maintain the cell skewness below 0.85.

The mesh should be refined until a solution that is independent of the mesh is achieved. The challenge is then to generate the smallest (in number of cells) mesh possible, while still obtaining a mesh-independent solution, as this will reduce the simulation's runtime. In this research, which relies on simulation and validation through experimentation, it is important to monitor point values, but equally important is the comparison between the simulation results and the measured values.

A mesh independence study is conducted on three different mesh sizes whose dimensions are given in Table 7.6. The characteristics of the mesh called '3D middle' are the one used in the previous sections, the main meshing features of which are visible on Figure 7.12. From there, a mesh with larger cells ('3D coarse') and a mesh with smaller cells ('3D fine') are derived. To account for the smaller cells, while keeping in mind the constraints mentioned in Section 7.3.1, the timestep for the finer mesh must also be decreased to 0.5 ms. The details of the 2D mesh are included as well in the table. It should be noted here that the number of cells given here is always the one of the initial mesh. As the train moves, the domain gets remeshed at each timestep, and the number of elements might slightly evolve. The outputs of the four meshes at hand, for the locations listed in Table 7.1 and scenarios 'A only' and 'B only', are reported in Appendix G, along with the averaged experimental data is also displayed. In Table 7.7, the different meshes are compared to two reference values: the experimental data, and the outputs from the 3D simulation with an intermediate mesh size. For each half of the curves, aiming to capture the peaks around the arrival and the departure of the train, the maximum of the velocity magnitude is taken; the relative difference with the reference data ('3D middle' or experimental) is then computed. The results presented in the table correspond to the average for both halves, both scenarios and all nine locations.

Comparing the 3D meshes visually, '3D middle' and '3D fine' are similarly close to the experimental values and to one another, while it appears that the coarse mesh is most of the time a bit more off, especially during the stop time. Until the arrival peak, the outputs from all three 3D meshes are the same in almost all cases. After the arrival peak however, the results from '3D coarse' also exhibits oscillations after the arrival peak that are not present in the finer meshes, nor in the experimental data -this is particularly visible for positions 5 to 8 with 'A only' for instance. Similarly for departure, although the results for all 3D meshes are matching around the peak, '3D coarse' separates from '3D middle' and '3D fine' after -for example, for positions 6 and 7 with 'A only'. These observations are confirmed by the relative difference in peak magnitude read from Table 7.7, with a difference of more than 25% between the '3D coarse' and '3D middle' meshes. Additionally, among the 3D meshes, the coarser mesh produces the results that are the further away from the experimental values, hence leading us to rule out the coarser mesh for the numerical simulations. 2D has the lowest difference in peak magnitude compared with the experimental data. However, the discussion about the curves for the 2D mesh has already been carried out in Section 7.3.3 and evidenced that unrealistic flow features were actually modeled using the 2D simplifications. This will be discussed further in Section 9.3. For the 3D cases, given that simulating 80 seconds took around 10 days for the '3D middle' mesh and 30 days for the '3D fine', while bringing the numerical results closer to the experimental ones from less than 1%, it is decided to keep working with the middle mesh, in order to maintain a reasonable computing time.

Solver parameters and models

The airflow is simulated in Fluent with mass conservation and RANS equations for incompressible, transient flow. The k-ε turbulence model is chosen for this high Reynolds number flow, and as it was previously used for the simulation of train-induced airflow where it performed well ( [START_REF] Kim | Experimental and numerical analyses of traininduced unsteady tunnel flow in subway[END_REF], [START_REF] Xue | Numerical investigation of unsteady airflow in subway influenced by piston effect based on dynamic mesh[END_REF], [START_REF] Khaleghi | Analysis of unsteady airflow in a subway station influenced by train movement[END_REF]). As we are not interested in resolving the flow very close to the wall, the standard wall treatment is used. Other general solver properties are reported in Table 7 At time zero, it is assumed that the domain is full of air at 20°C and at atmospheric pressure (p atm = 101325 Pa); the initial values gauge pressure and of the velocity components are all equal to 0; turbulence kinetic energy and turbulence dissipation rate are left as the default suggested values of 1.35 × 10 -7 m 2 /s 2 and 2.25 × 10 -11 m 3 /s 3 , respectively.

The continuity, momentum, k and ε residuals are monitored. The adopted convergence criterion is set at 0.001 for continuity, x, y and z velocity components, k and ε. Additionally, the velocity at points on the platform corresponding to the field measurement point is recorded, for later comparison with the experimental measurement points.

Preliminary CFD results

Contours of air velocity in the station

CFD allows us to visualize the entire flow velocity field, and detailed outputs at the locations of our choice. Figures 7.13 and 7.14 display the contours of velocity magnitude in the station, in a horizontal cut 1.6 m above platform level, for selected timesteps. Velocity contours are a great tool to observe the development of the flow carried by the train and spread into the station, and in particular the increase in air velocity magnitude as the train arrives in the station and goes along the platforms. Remarkable here is also the moment at which the highest velocities are recorded. A velocity magnitude around 15 m/s (higher than the train speed) is reached upon train departure, in the wake of the train.

Several other features deserve attention, and detailed observations of this airflow will be discussed in Chapter 10 as they will also be compared to the results produced by the on-site measurements and the small-scale experimental model.

Addition of background airflow

Section 7.2.4 explained the changes made in boundary conditions at the tunnel ends and station exits aimed at simulating a constant, unidirectional, wind on the platforms on the station. Results for 'BC on' and 'BC off' configurations are displayed in Figure 7.15 (where 'background' is abbreviated by 'bg'), along with the results of the simulation without background wind and the averaged experimental results. Scenarios and locations are selected so only the most speaking results are reported here and discussed. It can be first noted that the addition of background wind improves the correspondence between the experimental and numerical curves at the beginning of the simulation and around train arrival. The flow is no longer starting from a rest state, resulting in a smoother rise in the velocity when the piston-effect flow comes into play.

In both configurations including background airflow however, unrealistic behavior is observed around the train departure: for some positions (Figures 7.15a, 7.15b or 7.15d), an 'inverse' peak with almost zero velocity appears, in an opposite pattern to the one measured experimentally. During stop time, for some positions (Figure 7.15c), the velocity monitored in the simulations with background wind exhibit a rise exceeding by far the value measured on site.

These phenomenons could be due to the interaction of the train induced airflow with the oscillations that are present in the sole background airflow, as seen in Figure 7.5. Depending on the recording location, the peaks induced by piston wind might happen at a high or at low point of the airflow due to background wind, either enhancing or counterbalancing the piston wind peaks.

These comments indicate that the implementation of background airflow would benefit from more research to be modeled accurately. For now, it still seems to improve the numerical-to-experimental match around arrival, but it is not prescribed to use the results including background airflow for the stop time and departure of the train. In Chapter 9, both the simulations with and without background wind will be compared in detail. Switching the boundary conditions back to atmospheric pressure or not when the train starts its movement seems to make little difference, as the velocity curves for 'BC on' and 'BC off' are always very close. This being noted and with the idea to keep the parameters readable across different configuration simulations, we will proceed with the 'BC off' configuration for the cases where background wind is taken into account (so that in all simulations, when the train is in movement, the BC conditions are set to atmospheric pressure).

Influence of the vertical sampling position

The chosen height (Z) for the measurements locations (see Table 7.1) is 1.6 m. This height corresponds approximately to a passenger's face height, and for similar reasons, Jia [START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF] has used 1.65m, and Izadi [START_REF] Izadi | 3-D numerical analysis of train-induced flow inside four ventilated underground subway stations and connecting tunnels[END_REF] 1.5 m for instance. However, in Section 6.2.2 about the hot wire sensor used for the on-site measurements, it is specified that the wire was standing 0.5 m above the platform floor due to safety considerations when operating in a busy station.

To evaluate what differences are brought by observing the results at Z = 0.5 m or observing them at Z = 1.6 m, the velocity is sampled at both heights and the profiles are studied, and the relative difference in the peak magnitude is displayed in Table 7.9 below (for a case without background wind). Figure 7. [START_REF] Brown | Basic theory of rapid transit-tunnel ventilation[END_REF] Upon departure, positions 4 and 5 for 'A only' and positions 1 to 4 for 'B only' exhibit non negligible difference in peak magnitude. However, observing the curves on Figures 7.16a, 7.16b and 7.16c shows that these cases suffer from a high relative difference as the peaks are low for those positions when the train leaves the station, while the profiles are still very similar. The same remark remains valid for all the cases where the relative difference is less that 20 %.

Only the curves at position 9, for scenario 'B only' upon arrival, demonstrate a noticeable discrepancy in the shape of the arrival peak as well as a large delay upon departure, as visible on Figure 7.16. We can seek explanations for this by taking a closer look with Figure 7.17 when the peak in velocity magnitude is happening around 18.5 s. The air pushed by the train and drowned toward R3 gets a straight path from the lower position, while streamlines are getting more bent as Z increases, resulting in a slight decrease in velocity. The observations made in the previous paragraphs suggest that the main displacements of air away from the doors are taking place in horizontal directions, and no real tendency of the velocity magnitude at Z = 0.5 m or Z = 1.6 m being of greater than the other one can be deduced. However, depending on their locations and whether a train is entering or leaving the station, doors can also act as sources or sinks in the numerical model, bringing turbulence and complexity to the flow in their surrounding. This explains that the differences in the velocity at different heights are more visible in Position 9, which stands closer from the exit wall.

Comparison with literature

The comparison of piston effect characteristics can be sought through existing literature by only considering the flow features in the tunnel. The study of Kim and Kim [START_REF] Kim | Experimental and numerical analyses of traininduced unsteady tunnel flow in subway[END_REF] provides useful quantitative data in this regard and have been used for instance in Camelli et al.'s [START_REF] Camelli | Modeling subway air flow using CFD[END_REF] or Izadi et al.'s [START_REF] Izadi | 3-D numerical analysis of train-induced flow inside four ventilated underground subway stations and connecting tunnels[END_REF] approaches. Kim and Kim's have conducted an experimental analysis of train-induced unsteady flow on a 1/20 scale model tunnel (i.e. 39 meters long). The pressure is monitored a several locations on the top of the inside of the tunnel, while a 3-meters-long train accelerates from the tunnel entrance during 3 seconds, then runs at a constant speed of 3m/s for 8 seconds, and decelerates during 3 seconds to stop. A picture of their experimental setup is given in Figure 7.18, and the evolution of the pressure coefficient C p = p/ 1 2 ρu * 2 from their study is reproduced in Figure 7.19. In our simulation, the pressure is sampled at points located along the tunnel in the same proportions as in Kim and Kim's study, during the first 20 s of the train run before the train reaches a stop in the station. The results for the pressure coefficient are given in Figure 7.20.

Of course, differences with their configuration are present: the scale of the model (39 m tunnel length with a 3 m long train, versus 200 m with a 90 m train here), the presence of the station after the tunnel, the double track tunnel instead of single track, and the velocity sequence that includes notably a linear acceleration until 3 m/s in their case while it is a sharp start at 10 m/s here.

This being noted, the pressure variations draw a similar pattern that is characteristic of the piston effect. During the movement of the train, positive pressure appears at the front while there is a negative pressure at the rear of the train, and both pressure rise and drop are higher when the train is at its highest speed (i.e. closer to its start position). As the train decelerates, the pressure behind the train rises again.

During the time considered in this paragraph, the train has already started to enter the station. This abrupt change of geometry might involve more complex aerodynamic phenomenons to come into play. For a perfect comparison of results, the simulation should ideally have been carried out for a case with only a tunnel and the same velocity sequence. However, the movement of a train in a tunnel is already a well documented phenomenon. The results from this section hence allows to give some confidence in the results obtained, in the sense that the piston effect is correctly modeled.

Immersed boundary model

Immersed Boundary Methods, also known as Immersed Boundary Models (IBMs), have gained popularity for their ability to handle moving or deforming bodies with complex surface geometry [START_REF] Taira | The immersed boundary method: A projection approach[END_REF]. While the dynamic meshing techniques handle moving objects by creating a void in the mesh, recreated at each time step, where the body is and forcing the fluid to move around, IBM defines the absence of fluid mathematically, telling some cells that there is no fluid there and adjusting cells around it accordingly (see Figure 7.21), thus sparing the remeshing. Lastly, in Fluent, it is required that the train is inside the domain during the simulation. In IBM, this is no longer a restriction, and it is possible to let the train start outside of the tunnel and enter the fluid domain during the simulation, potentially saving a non-negligible computational time.

A disadvantage of the technique is however a limited grid resolution control in boundary layers [START_REF] Jasak | Immersed Boundary Method in FOAM -Theory, Implementation and Use[END_REF]; unlike in Fluent, it is not possible to create a zone of refinement of the mesh around the train. Initially inspired by a YouTube tutorial [START_REF] Streamcfd On | Simulating piston effect in underground metro tunnel -ansys cfx tutorial[END_REF] that details the implementation of a train moving through a station, a study was hence conducted within the project by Birkin [START_REF] Birkin | Internship on computational and experimental fluid dynamics at MECA[END_REF] to evaluate if the IBM could simplify the meshing process and provide faster results. The CFX Solver was used to simulate the same case that had been simulated with Fluent previously. The goal of the present section is to provide a brief summary of the findings, and all the implementation details are therefore included here but can be found in the report of Birkin (including mesh and time step sensitivity analysis, parametric study of the geometry and the turbulence models). Using the same geometry as the Fluent simulation, the station is defined as the 'fluid domain' and the domain of the train is of type 'immersed solid', with the only boundary being of type 'wall', corresponding to the train walls. The station walls also use the boundary setting 'Wall', while the doors and openings use the option 'opening'. The 'mass and momentum' settings of the latter are set to 0 Pa 'Opening pres. and dim'. The same realistic movement of train as in Section 7.2.2 is implemented under 'domain motion'.

The results corresponding to two different meshings and timestep configurations are reported in Figures 7.22 The most notable deviation from the on-site experimental results of every CFX simulation is that the velocity starts rising after the train has stopped at around 27 s, instead of decreasing. Upon inspecting velocity contours, it became clear that the rise in velocity comes from the bulk of air from behind the train that enters the station while still traveling at a high velocity. This means that the airflow suffers from a too low viscosity, since in practice as shown by the Fluent simulation, and this flow tends rather to dissipate.

As explained by Taira and Colonius [START_REF] Taira | The immersed boundary method: A projection approach[END_REF], at the connection between the body geometry and the coarser mesh of the domain, the no-slip boundary condition is enforced by adding appropriate boundary forces project on the involved cells of the domain. Lauber et al. [START_REF] Lauber | Immersed Boundary Simulations of Flows Driven by Moving Thin Membranes[END_REF] have already documented that this projection step introduces a slip error onto the velocity field. Liu and Stevens [START_REF] Liu | Wall modeled immersed boundary method for high Reynolds number flow over complex terrain[END_REF] also related difficulties to accurately resolve the viscous sublayer near walls.

In our case, this limitation, known sometimes as 'boundary slip error', is not only problematic around the station walls, close to which the results are not our particular focus, but for all the boundaries defined as walls in the solver, including notably the train body. In this study, the movement of the train is indeed what drives the changes of velocity magnitude across the entire station. This shows that while the IBM using CFX seems a promising approach to ease the meshing process and reduce simulation time, tests revealed that the known limitations of the IBM make its outputs inconclusive for this particular study, where the entrainment of air by the train plays a predominant role.

Handling moving objects in a fixed domain in CFD is complex, and setting up a dynamic mesh is a costly -from a computational resources perspective -and tedious process, from which divergence can very quickly arise if not carefully implemented. Following the recommendations enunciated along this chapter, notably for the mesh quality, cell size and timestep size, is therefore crucial.

Elements of this chapter have evidenced the fact that the results of the simulations are strongly influenced by choices made along the elaboration of the model. The major assumptions made about the station geometry and the boundary conditions hence deserve to be discussed with a critical eye, as this will be done in Section 9.5.1. CFD outputs should be treated with great care, emphasizing the need for a bespoke validation of the results and a quantitative evaluation of the numerical to experimental match.

Lab-scale experiments

In Chapter 5, the advantages of using a small-scale model inside of a lab to get experimental data about the platform airflow (see Section 5.2.2 in particular) have been discussed. They include notably the ease of manipulation compared to the on-site measurements, the availability of flow fields rather than pointwise data, the reproducibility of the experiment, and the possibility to extrapolate the measurement technique to other configurations or scenarios. In this chapter, a small-scale model of the test case station is built, using a simplified geometry. As airflow related to train movement is our main focus, a model moving through the small-scale station is also included. The airflow is then investigated with Time-Resolved Particle Image Velocimetry, which principle and challenges have been explained in Section 4.2. The results are sought in such a way as to provide data comparable to the results obtained in previous chapters, i.e. in the form of velocity evolution at 9 locations spread across the station platform, during the train arrival and departure, for the 'B only' scenario. A careful selection of the optimal processing parameters will be detailed, based on a quantitative analysis of the correlation results.

The first section (8.1) justifies the design choices made for the small-scale model, details its construction, and explains how the movement of the train in the station is controlled. In Section 8.2, PIV is applied to the airflow related to train movement in the station. The experimental acquisition setup is detailed, as well as all the processing steps allowing to obtain the vector fields. Section 8.3 briefly explains how the PIV results are processed in order to make them comparable with the data obtained in Chapters 6 and 7. The last section (8.4) presents the velocity curves along time obtained with the lab-scale model. Two main constraints will determine the scaling factor for the model station: firstly, the model has to fit in the lab room where the laser is operated, hence not exceeding a couple of meters in length (including upstream and downstream rails and tunnels). Secondly, the model must be sufficiently illuminated by the laser sheetthe latter gets larger as the distance between the laser head and the region of interest increases, but the light intensity also gets more spread out -and the particles should appear with a sufficiently high definition on the camera. Here, as the model is long but also small in width, as that illumination from the long side is desired, the width of a laser sheet with an acceptable light intensity is around one meter.

In this preliminary design phase, we can make an estimation that to get the station length from an order 10 2 meters in real life to an order of one meter, the scaling factor should be at least of 1:100. The choice was made of getting an already built model train to avoid excessive complexity in designing and building all the miniature parts of a train at scale, including the railing system and the motor, while ensuring a sufficiently fine control of its movement (although this last consideration will be re-discussed later). Corresponding to the 'HO scale' in the field of miniature train models of the shelf, a scaling factor (1:87) was hence considered the most appropriate for the train. HO scale is indeed one of the most popular scale in the industry of train modeling, providing hence more choice among train models available, and making possible to choose a model that would be similar, in its shape, to the real subway trains operating in the network, of which an image is given in Figure 8.1. In particular, the front and the back of the subway trains from the test case are rather flat in comparison to high speed trains. The BRAWA 44601 (picture 8.2) was matching our expectations from these aspects, and the chosen train is therefore an exact replica of an existing train from the Deutsche Bahn -although for our study, all the little modeling details have been removed from the surface of the train to reduce its shape to its cleanest form, to ease later comparison with the parallelepipedic shape of the numerical model. The dimensions and main characteristics of the small-scale train, with the corresponding values for the real-life trains, are given in Table 8.1. The ratios of the dimensions will appear later in Table 8 When designing small-scale models to study flows, it is a common practice to match the Reynolds number in order to obtain dynamic similitude of the flow. For our case, assuming the hydraulic diameter is also divided by 87 (corresponding to the HO scale, i.e. the scale of the train used compared to its real life equivalent), we would need to have:

V train,small-scale,hypothetic = V train × 87 = 966.6 m/s (8.1)

It appears clearly that in practice, it is not possible to built a supersonic train that would run at the computed speed in the lab, and it would lead to unrealistic and undesired flow features. In this work, we focus on the relationship between the air velocity on the platform and the train position in the station. We have also seen in Section 2 that blockage ratio and the train velocity sequence are one of the most influential parameters for this problem. Rather than aiming to get dynamic similitude, the choice is therefore made to preserve the geometrical similitude, and the phases of the train movement through the station. The dimensions of the full scale model (see Figure 5.6) are scaled using the ratio of the small-scale train dimensions and the full scale train dimensions, as per Table 8.1. The scaling factors obtained, given in Table 8.2, are therefore different for each direction. Scaling the dimensions with this method allows us to preserve the blockage ratio of the train in the tunnel and in the station, compared to the full scale real-life metro station and the to the numerical case, that were given in Table 5.1. An illustration of this blockage ratio for the small-scale model is visible in Figure 8.5. The model has been designed to maintain the clearest field of view possible for the camera standing above and for the laser sheet hitting the platform wall, and to allow an easy assembling, with the ceilings resting on the vertical walls. Figure 8.3 gives a 3D visualization of the model, the tunnels being removed for clarity, with the main inner dimensions. The detailed mechanical drawing of all pieces constituting the model, including 1.2 m long tunnels on each side, can be found in Appendix E.

The dimensions of the model (Figure 8.3) and the train characteristics (Table 8.1) yield the values given below for hydraulic diameter and Reynolds number. Although it is several order of magnitude below the value for the full scale case, the Reynolds number remains in the turbulent regime range. D H,small-scale = 4(2y p z p + y t z t ) 2(2y p + z p ) + 2(y t + 12 mm + 5 mm) = 63.9 mm (8.2) y t and y p being the width of the small-scale tunnel and the small-scale station, respectively, and z t and z p the height of the small-scale tunnel and the small-scale station, respectively, in mm. Using the speed given by the model train specifications (see Table 8.1):

Re small-scale = ρ air V train,small-scale D H,small-scale µ air = 2 955.50 (8.3)

A picture of the realized model is given in Figure 8.4. Plexiglass sheets of 5 mm and 12 mm thickness are used, cut with a laser cutter. The assembled model of the station and the tunnel lies on wooden panels, that have been varnished to ensure a clean surface. The different parts are glued together, using Acrifix 192, a transparent glue that polymerizes under sunlight. The ceiling of the station above the rails is left unglued, simply resting on the ceiling of the platform, to allow access to the inside of the station. The setup in the lab also includes a total length of 7 m of rails from the brand Märklin for one direction of the train (not shown on Figure 8.4), and for more realism rails are added for the second side inside the station. The rails are screwed to the wooden support of the model.

Train control 8.1.2.a Activating the model train

As the design of the station has emphasized the preservation of blockage ratio, the other aspect of the lab-scale model consists in making the model train arriving in the station, stopping and leaving the small-scale station, executing the scenario 'B only'. The technical characteristics of the BRAWA train have been given in Table 8.1, and the motor has been changed from an AC to DC one. The train runs on metal rails through which the driving current for the electric motor of the train is provided, as visible on Figure 8.6: the wheel is in contact with the side beams of the rails, and the blade in the center with the central studs. A voltage difference is applied between the beams and the studs to activate the motor and put the train in movement. The LabVIEW script generates a pulse width modulated signal (PWM) from a NI PXI-6534 Digital I/O Module with a NI SCB-68 terminal block [75] connected to a L298N motor driver [START_REF]Dual Full Bridge Driver[END_REF]. The motor driver is connected to the train rails by crocodile clips at three different locations to ensure that the electric resistance in the rail connections would not lower the power provided to the train at certain locations. The driver itself is powered by a 18 V DC source and its power output is proportional to the PWM signal. Another digital signal from LabVIEW to the L298N controls the direction of the train.

Through this circuit, the input of when and how much to change the motor speed is therefore controlled by the LabVIEW program on the PXI, which will be explained in the following paragraph.

8.1.2.b Feedback loop for the velocity

In scenario 'B only' at a smaller scale, the train must start from one side of the station on the rails, accelerate to reach its cruise speed, then decelerate to stop in the station, and leave the station after a fixed waiting time. It was however observed that even when the same voltage commands were given to the train with fixed delays between start and decelerate, the train stop position varied up to one meter distance between multiple tests. Reasons explaining this variability could be the friction of the train on the rails or the loss of electric load in the cables for instance. The need for feedback loop to gain better control over the train velocity hence arose. In addition and to enable the reproducibility of the experiment, several requirements must also be met by the train control system in order to perform the PIV measurements properly. These requirements include detection of train position in the presence of PIV seeding, the ability to operate in the dark, the ability to operate with the high-intensity laser light, minimization of airflow modification (non-intrusive) and limitation of potential light disturbance in the PIV area of interest.

(a) Tag 1 (42.5 cm before station entrance).

(b) Tag 2 (37 cm before station exit). The trigger modules from Chapter 6 (Section 6.2.1) are meeting these requirements, as they can be placed outside of the small-scale model and detect the change in distance occurring when the train passes in front of them. Two of them, visible on Figure 8.8, are used as tags for train detection with the infrared sensors, the threshold for detection being adjusted to the small-scale model. When the train is detected, a message is sent through the wireless HC-12 to a third module connected to the PXI. The first tag 'Tag 1' is placed ahead of the station 42.5 cm from the station entrance facing the rails of the tunnels; the second tag 'Tag 2' is placed 37 cm ahead of the station exit. Both tags are used to make the train decelerate and stop in the station: when Tag 1 detects the train, a command is sent via LabVIEW to reduce the speed of the train to 70 % of its nominal value; when Tag 2 detects the train, the command is sent to stop the motor supply, so that the train would stop shortly after. The corresponding sequence of commands is summarized on Figure 8.9. The friction of the train on the rails, the signal frequencies and the variability of train cruise speed make it difficult to determine the position of the tags and the voltage analytically. It has also been noted that the change in the input voltage must be sufficient to actually result in a significant velocity change. The position of the tags, as well that the pulse width modulation value, were therefore determined through trial and error. For reasons mentioned above, some variability is still present in the movement performed by the train, as reflected in the curves in Figure 8.10. The stop position of the train corresponding to the 3 arrivals is illustrated on Figure 8.11, with the distance between the front of the train and the end of the station. Although these variations can be a challenge for reproducibility, it echoes also the fact that in the real station, the movement of the train is never exactly the same (see Figure 8.11). As a result, the measurements had to be repeated and averaged over several runs. The setup for the train control is indeed limited to two points where the train position is known, reducing the possibilities for adjusting the train velocity. Ideally, we would have liked to be able to know and control the entire course of the train in the station. However, the train has demonstrated to be quite mechanically fragile, especially at the connections between its cars, and had to be repaired several times, limiting the time available for the experiments. The availability of material has therefore been privileged to deliver a functioning setup in a reasonable delay. Before developing the setup with the infrared tags used in this work, a few other setups were however tested.

8.1.2.c Other attempts for the train control

This section summarizes briefly the possibilities that have been explored or imagined to control the train speed and movement into the station. The lessons learned from their implementation and suggestions of improvement are given, with regards to the requirements listed at the beginning of Section 8.1.2.b.

• LiDAR pointing at the train The same laser than in Chapter 6 (Section 6.2.3) is used, and placed at one of the extremities of the rail, close to the where the train departs from, pointing towards the rear of the train. The desired position (in the form of a distance from the laser) of the train along time was implemented in LabVIEW, and the measured position could then be compared to the expected one. The train was slowed down or accelerated to match the expected position at any time. This method would have allowed to know the position of the train with accuracy and in real time during its entire travel, hence allowing a more precise control on the deceleration and the stop time.

Although this setup works fine in a normal environment, we realized that the beam is refracted on the oil particles which makes any distance estimation wrong, and the train position was lost as soon as it entered a densely seeded area. The presence of seeding should therefore be kept in mind if using optical methods to track the train.

• Webcam detection with color analysis

In this setup, a webcam is placed on the same support beam as the one holding the two PIV cameras, having the upstream tunnel and the entire station in its field of view. With the live output from this webcam, the main concept is to use image processing methods to track the train during its movement.

LabVIEW offers functionalities to use of real time cameras with some image processing features. Python was also considered to video-track the train, as advanced image processing libraries are available (such as pattern detection or face detection, with the OpenCV package for instance), but the compatibility and the fast communication between LabVIEW and Python outputs should still be figured out. LabVIEW, however, does not allow to analyze the position of the subway permanently in a fast and simple way as Python does, but only to detect the position of the subway at some specific places. In particular, color analysis of parts of the image is made possible through colorimetry concepts [87]. From this constraint, the idea was developed to use tags.

Two rectangular areas of interest are defined, at similar locations than the infrared sensors from Section 8.1.2.b: one before the station in the upstream tunnel, and one towards the end of the station. The two rectangles are visible on Figure 8.12. The screenshot from the LabVIEW interface also shows the decomposition of the color spectrum in 14 columns for 7 colors, with one column for high saturation and one for low saturation successively, and 2 additional columns for black and white. Each column indicates the percentage of pixels of corresponding color in the delimited zone. The model train is equipped with a LED light at its front; the red color is chosen, ensuring that the light from the laser and from the LED do not overlap and are not detected in the same columns. When the subway, passes in a tag, LabVIEW detects it through the recognition of the spectrum previously set, and applies the same control sequence as the one given in Figure 8.9 to slow down the train, and then stop it.

In normal conditions, this setup works with a precision similar to the in-place setup with infrared sensors. At high intensity however, the brightness of the laser completely overlaps that of the LED in the webcam image, and the train passes the tags without being detected. The technique can therefore not be applied with the available devices, but remain a promising one, provided that better resolutions webcams (or cameras equipped to work in live mode) are available, or that the data transmission between Python and LabVIEW is implemented.

• Variation of electrical resistance with a third rail Another option that does not involve any optics would be to place a third control rail, electrically powered, along the existing tracks. Being connected to the model train with a small conductive brush, the displacement of the train will result in a variation of the resistance of the side circuit. By wiring the third rail as one leg of a Wheatstone bridge, it is possible to quantify the displacement of the subway according to the observed output voltage.

A PXI typically measures in a 4 to 20 mA range at 5 V, corresponding to a variation of 1000 Ω in total. As the brush needs to close the circuit, the third rail should be composed of two wires, and hence the resistance variation should be distributed over 2×6.5 m = 13 m, i.e. the third rail should be in a material of ∼ 75 Ω/m. This setup has not been tested in the lab as the adapted wire was not directly available and as the fine tuning of the circuit would have required some more time spent working on the train control, but would be a way to have control over the train during its whole trajectory.

PIV measurements

The PIV setup and the general challenges related to this technique have been explained in Section 4.2. In this section, we will apply the concepts to acquire particle images of the train going through the small-scale station, and compute the corresponding velocity fields. The setup used for the PIV measurements is given in Figure 8.13. A double-cavity Litron LD30-527 Nd:YLF laser (up to 30 mJ at 527 nm at 1 kHz) is used to illuminate the flow from the side. Two cylindrical lenses form the laser beam to a light sheet, with a focal length of f = -10 mm. The light sheets stands 12 mm above the platform level, and is focused in the center of Platform B. With this configuration, the train will block the laser sheet as in enters the station: hence, only measurements for the 'B only' scenario are possible.

The experimental images are recorded by two CMOS (Complementary Metal Oxide Semiconductor) Phantom VEO-E 340L cameras, having a resolution up to 2560×1600 pixels at 800 fps; the speed can be increased by lowering the resolution. They are combined with 50 mm objectives and placed 88 cm above the station, side by side, looking downwards.

The cameras and the laser are connected both to the computer, and to a programmable timing unit (PTU X from LaVision, also called 'synchronizer'). The software DaVis (version 10.2) from LaVision is running on the computer, and allow the control and the parameterization of the PIV acquisition, as well as the processing of the acquired images. The synchronizer is used to generate trigger pulses for the cameras and the laser under the control of DaVis, and is also receiving the trigger from the PXI controlling the train.

The placement of the cameras is designed to allow for the acquisition of the entire station while maintaining a sufficient resolution of the particle images. Using a custom calibration sheet as visible in Figure 8.14, the software can perform image stitching for multiframe images from multiple cameras. The calibration also defines the orthonormal basis and scaling factors, as well as corrects for any 'tilt' in the images.

Seeding the test section

Seeding is provided by vaporizing the oil with an oil generator. Thanks to the pressurized air network connected to the smoke machine, the oil vapor particles are released into a flexible pipe that can be placed in the test section to seed it.

The seeding concentration of a flow that one wishes to observes with PIV is a parameter that has to be selected with care. Too few particles, and the velocity vectors cannot be found everywhere in the region of interest. A situation with too many particles may lead to indistinguishable successive frames, light absorption or intruded flow. Raffel [START_REF] Raffel | Particle Image Velocimetry -A Practical Guide[END_REF] stresses that a homogeneous distribution of medium density is desired for high quality PIV recordings in order to obtain optimal quantitative evaluation, and that ideally, no structures of the flow field can be detected on a PIV recording of high quality. In our setup, the main difficulty comes from the fact that the small-scale model is open at the tunnels extremities and at the doors, allowing both the seeded air to escape and non-seeded air to come in, as illustrated in Figure 8.15. In particular, as the train comes in, it pushes non-seeded air into the station and carries it into the station. To limit this phenomenon, it was considered placing the pipe providing the particles in the station to create a continuous source seeding. However, this method was bringing to much disturbance to the flow, which is supposed to be at rest when the train starts its movement. The chosen solution is to put a cardboard box upstream of the station, as illustrated in Figure 8.16, to create an enclosure with a dense seeding.

Image acquisition procedure

When Tag 1 is activated by the train passing in front of it, a trigger is sent to the laser, via the SCB-68 interface and the synchronizer, starting also the image acquisition in DaVis. From this trigger, 600 images are acquired at 0.201 kHz, totaling almost 3 seconds of recording.

In a TR-PIV setting, a high laser intensity is required to provide sufficiently illuminated particles for every frame, as each of the frames will be used to generate a vector field. Illuminating the entire station was not providing enough intensity, especially on both sides of the station were the light intensity of the laser sheet gets weaker. For this reason, the laser was moved to illuminate the left part (on the entrance side) or the right part (on the exit side) of the station, focusing therefore on the field of view of one of the other camera (see Figure 8.13). Depending on which part the laser sheet is centered on, it will be possible to retrieve information for Positions 1 to 4 or for Positions 5 to 9.

The 'arrival' and 'departure' parts of the scenario are also acquired in two separate recordings, as both parts are anyway aligned independently during postprocessing, and as during the stop of the train, the flow is expected to come back to a resting state. This allows to limit the size of the images on the hard drive and allow easier adjusting during experimenting (for instance, making sure that the train left always from the same position) and fasten the manipulation of the datasets for the software.

This splitting results in 4 different configurations necessary to obtain data for all the positions and for completing scenario 'B only', summarized in Table 8.3. Each configuration (i.e. each line of the table) is repeated 8 times to allow later averaging. Three additional recordings are performed with the laser taken further away from the model, illuminating the whole small-scale station, to obtain flowfields with the entire train movement in one acquisition (and used for instance to plot the curves of Figure 8 The aperture setting of the camera comes with several trade offs. Firstly, a higher aperture ensures that more light reaches the particles, improving their visibility on the frames. However, too much can cause the saturation of the camera sensors, with even the risk of burning permanently some of the cells. Secondly, increasing the aperture also decreases the depth of field, which makes it more difficult to keep the focus on the edges of the frame, and more likely to loose particles due to vertical motion. In these recordings, the camera aperture is set to 4.

Figure 8.17: Small-scale station with additions to avoid reflections.

To limit the reflections, a special attention must be given to identify and remove all the model elements that could create reflections of the laser light. The edges of the plexiglass were particularly reflective and were covered by black cardboard paper -although this means that the particle information very close to the wall is lost, only this made possible to increase the laser intensity to get sufficiently good images in the rest of the station. The sensors, Plaftorm A and all the other non-interesting regions are also covered. The train was also generating a lot of reflections, especially as it was directly hit by the laser sheet on the side, and it is therefore fully covered in black adhesive tape. A picture of the resulting setup is given in Figure 8.17.

The highest resolution of the cameras, 2560×1600 pixels, is used. Details of examples of acquired images are given in Figure 8.18. It is possible to track the movement of particles with the naked eye, and the displacement of the particles in this particular windows is of approximately 6 pixels. As explained in Section 4.2.2, the particle size is around 2-3 pixels, ensuring that peak-locking is avoided.

Image acquisition results

A selection of acquired images, free of any processing, is given in Figure 8.19. A scenario of train arrival in the station is pictured, in a configuration with the laser sheet centered on the left part of the station (left column) and in a configuration with the laser sheet center on the right part (right column). It can be observed from these image that despite efforts to avoid reflections of laser light -the train being entirely covered with black adhesive tape -the train still carries reflections during its movement. The rails, although they normally are not included in the laser sheet, are also still visible. Additionally, the presence of doors and the edges of the plexiglass sheets are generating shadows, and small imperfections of the plexiglass sheets are also causing a non-uniform illumination of the area of interest. In the next section, we will try to use software methods to provide corrections for these problems.

Images pre-processing and vector field calculation

As seen in Section 4.2.2, the pre-processing of the images consists in several operations that aim to improve the quality of the pictures taken by the camera. In this section, we go through the different functions applied to the recorded images before performing the cross-correlation analysis and their parameters, as well as through the different parameters available for the PIV calculation itself.

The functions will be briefly described with regard to their interest for our application. The parameters not mentioned are left as default. For a more complete and detailed information, on the whole of the available options in particular, it is suggested to turn to the manual of the DaVis software (version 10.2) by LaVision [START_REF]2 Software[END_REF].

8.2.4.a Quantitative evaluation method

In some cases, the choice of the appropriate processing parameter is obvious when looking at the images -in particular, at the coherence of the flow pattern and at the proportion of interrogation windows for which a vector was found -or at the correlation peak and the uncertainty values; but sometimes, the difference is not clearly observable. In these instances, we use a algorithmic method to determine which parameter gives the best results, relying on correlation value and peak ratio as metrics to quantify the quality of the processing, as defined in Section 4.2.

Focusing on the frame showing the left part of the station, three 20 pixels wide and 10 pixels high rectangles are chosen at strategic locations in the station, represented on Figure 8.20, to export correlation metrics. Rectangle 1 is on the left extremity of the station, in the vicinity of door L1, where seeding quality may be lower. For Rectangle 2, in the middle of the studied frame, the challenge is to see the impact of reflections due to the movement of the train on the calculation. Rectangle 3, located at the right end of this frame, is also close to an exit door, and will specifically allow us to see if the stitching between the left and right parts of the station is done correctly. The PIV algorithm is ran (with default parameters: single pass for 24-pixels rectangular interrogation windows with 50% overlap, unless specified otherwise, and on the raw images) using the different sets of images, pre-processed with the functions and parameters to study. For each of the rectangles, the correlation value and the peak ratio are averaged for all the vectors found in the rectangle, and for all the images. This computation will be performed when needed, and the results are gathered in Appendix F and discussed below.

8.2.4.b Region of interest: geometric mask

We have already established that only scenario 'B only' will be studied in this experiment. When the train enters the station, the illumination of the platform opposite to the laser is indeed blocked by the train. Therefore, we only have data i.e. illuminated particles -on one platform, and in front of the train. As the locations of interest are all situated on the platform, the study area for the PIV measurements is therefore limited to the platform on the side of the laser only -Platform B -only by applying a mask on the acquired images. This will allow both to fasten greatly the processing, without having to bother with all the non-usable parts of the images, and to delimit the region of interest taking into account the parts hidden by the black tape (as shown on Figure 8.17).

The mask is defined by a polygon for both cameras, as visible on Figure 8.21, and will be the same for all 600 images and for all 4 configurations (Left/Right illumination and Departure/Arrival).

8.2.4.c Images pre-processing

The following filters are based on time-averaging techniques. For a steady acquisition, they are much easier to apply, as it is assumed that only the particles carried by the flow are moving -and all the non-moving parts can be distinguished from particles and characterized as background, reflections or non-uniformity of the illumination. However in this application, as visible on Figure 8.19, the movement of the train creates variability in the setup itself; and the parameters of filters must therefore be carefully selected. For each point, the image resulting from the application of the chosen 'best' parameter is given here, and the outputs from the other parameters tested are put in Appendix F.

• Subtract time filter The subtract time filter can be used to eliminate background noise specifically for transient problems, to obtain bright particles on a dark background. Since the laser light reflections typically move slower than the particles, the filter can calculate light intensity for each pixels from a number of consecutive images determined by the filter length, and subtract it from the source. The cutoff frequency is determined by the length of the filter: for instance, a filter length of 50 indicates that each image will be compared with an image separated from it by 600/50 = 12 indices.

This means that as the filter length decreases (the images compared are separated by a longer time), it will be easier to distinguish the particles from the background (especially above the rails, that are not moving), as the particles will have moved a lot. However, this comes also with considerations regarding the reflections carried by the train, as they are not steady over the whole recording. show pictures obtained after applying two different types of filters -subtracting the minimum or average intensity -, making clear the using the minimum intensity is preferable as we are mostly interested in the area on the platform. The results of using different filter lengths -600, 299, 49, 15, 5 and 3 imagesare also displayed in Figure F.1.2, for an image in which the train is entering the station. From the images, we can already rule out options where the filter length is too high, as the particles are not sufficiently visible. To determine finely which filter length to use, the algorithmic method is used with 3, 5, 15, 25 or 49 images and the results are summarized in Table F.1. A filter length of 3 is chosen as it yields the best results overall for correlation and peak ratio. The effect of applying these parameters of the subtract time filter, from a raw image, is given in Figure 8.23.

• Remove background/ unsteady reflections The remove background/ unsteady reflections filter is another filter that relies on identifying the background and then removing it from the original images. Several algorithms are available to compute the background, as documented in the DaVis manual [START_REF]2 Software[END_REF].

Two of them are ruled out, as they focus on removing reflections at edges and will not be helpful with the train reflection, or are based on interpolation with neighboring pixels, which is not appropriate here as large bright spots are present. Three types of filters therefore remain. The sliding average and sliding minimum filters calculate a local average over a specified scale length by computing the average according to an equation applied 4 times, moving from left to right, from right to left, from top to bottom and from bottom to top through the image. Directional minimum computes the background for every pixel by taking the minimum along multiple lines evenly-spaced over different spatial directions, then taking the maximum of these minima. The filter size represents the radius around each pixel in which the calculation is performed. These three filters are applied on raw images and the outputs are displayed on Figure F.3. The image obtained using the directional minimum method is of much higher quality: the number of visible particles is greater, the contrast is better and the non-negligible reflections present on the edges of the lower-left side of the platform have completely disappeared. The image obtained after applying this filter is given in Figure 8.24.

• Order of the pre-processing filters Both abovementioned filters take images as input and create images as output, so they can be applied either on the raw images or on already filtered images. Therefore, an additional comparison of the order of application of the pre-processing filters has been performed. The outputs on images of applying one filter or the other first is given in Figure F.4. The analysis of correlation and peak ratio with the algorithmic method (Table F.2) concludes that is it preferable to apply first the subtract time filter before the remove background / unsteady reflections filter.

8.2.4.d Vector field calculation: PIV

While the pre-processing parameters take images as inputs and give images as outputs, several options are also available for the vector field calculation. Similarly to the parametric study performed above, the effect of different processing parameters is tested and discussed in the following paragraphs.

• Automatic masking

The mask defined in Section 8.2.4.b stays fixed throughout the whole length of the recording. To account for the movement of the train, especially on the recordings including the entire station and for visualization purposes, it is possible to define some criteria, based on the local pixel intensity, to distinguish areas of interest from areas that should not be considered in further calculations using automatic masks. Two type of masks are proposed by DaVis: the temporal auto mask, which takes consecutive images into account to reduce the influence of temporal fluctuations in the recording series; and the spatial auto mask, which aim is to distinguish between the area in the image with seeding (high pixel count values) and without seeding (low pixel count values).

The vector fields obtained from applying the temporal automask, the spatial automask and no automask are presented in Appendix F.4.1 on Figure F.5. The temporal automask seems inappropriate as it removes vectors from a large part of the platform. Calculation without auto-mask could be adequate, since no values are lost. The spatial automask correctly detects the train, that appears as a blank zone on the left side, and removes vectors from the upper platform while keeping the vectors on the platform, which is not negligible for the calculation time. We therefore retain the latter option.

Secondly, the intensity of the automasking must be determined. In DaVis, eleven levels, ranging from 0 (low) to 10 (high), are available. The impact of setting the intensity of the mask at 0, 5, 8 and 10 is displayed in Appendix F.4.2 on Figure F.6. We find that the lower levels of masking are too strict and cannot be used, and the higher positions preserve more informations. Level 8 is selected as it offers a good delimitation between the platform and the track (which is masked by black paper -see Figure 8.17), and the results of the vector field calculation (using the raw images) using this parameter is given in Figure 8.25. • Shape of the interrogation window The shape (or 'weight') of the interrogation can be selected to match the typology of the studied flow. In our case, for this parameter, only shapes equally weighted for all directions are considered, as local displacements of the flow are happening in all directions. We therefore rule out the rectangles and ovals, and focus our comparison on squares and circles and display both resulting vector fields in Appendix F.5.1. Although the results seem to be very similar, differences are noticeable on the very left part of the platform. Relying on the algorithmic methodology which results are presented in Table F.3, we conclude that the circular shape provides the best results.

• Multipass

We have seen in Section 4.2.2 that computing the displacement several times over the same window, while shifting the windows from the predictor value for each iteration, can improve the accuracy of the results. However, this comes again with a trade-off between the quality of the results and computing time, and we will therefore limit to one or two passes. As looking at the obtained images do not allow us to choose between these two possibilities, we opt for a discrimination with the algorithmic method, synthesized in Table F.4. The results show an improvement of both correlation and peak ratio when two passes are applied, and we therefore opt for this solution.

• Size of the interrogation windows The 1/4 rule is valid for the first pass to determine the particle displacement. To account for the larger flow structures and resulting in large particle displacements, a window size of 128×128 pixels is chosen for the first pass. The window size can then be iteratively decreased as long as at least one particle can be distinguished from the background, to avoid performing the correlation on noise only. However, the minimum displacement has already been found with a given size, going for smaller interrogation window sizes will therefore not affect the results, and bring additional computation time. The velocity fields resulting from the application of four sizes (48×40, 24×24, 12×12 and 8×8 pixels) for the final pass are given in Appendix F.5.3.

We note that a large windows size lends a coarse character to the velocity field map: the result looks pixelated, and we thus miss -particularly in a study like ours -many phenomenons happening at a small scale, such as strong local fluid accelerations. Although 12×12 and 8×8 may appear similar at first, they actually show very clear differences on closer inspection, as shown in Figure 8.26. • Vector post-processing Some parameters are finally available for the post-processing of the vectors. We can specify that vectors for which the correlation values is too low are filtered out. The threshold for the correlation is deliberately set low at 0.3, knowing that we can later tighten these requirements via Matlab if needed. Lastly, when valid vectors are sufficiently present in the surrounding of a deleted vector, the missing value is filled by interpolating, as the window size is chosen quite small and that the fluid properties are continuous.

8.2.4.e Summary of image processing parameters

The processing steps of the acquired PIV images with the corresponding parameters are summarized in Table 8.4, and applied to the 32 recordings. Each line of the table corresponds to a function in the DaVis software, and the denomination from the software are also used in this table.

From a first, brief observation of the contours, it seems clear that the train entrance in the station results in an increase of air velocity magnitude both around the train head and in the areas of the platform located in front of the train. Following the passage on the train head, the flow remains disturbed in unstructured patterns. Within the defined masking, we can obtain the flow field over the illuminated platform, that will allow us to extract the velocity data at relevant locations. Some areas, however, exhibit difficulties.

Position 9, at the end of the plaftorm on the train exit side, suffers from a lower image quality, as it both stands at the edge of the laser sheet, and also at the border of the field of view of the camera, where the particles are less in focus. Combined with the reflections carried by the train as it passes this position, it is not possible to obtain vectors in this area.

Apart from these specific difficulties, from observing the raw images at the locations were the correlation is the worst, we note that most of the time, particles are still visible in these zones, and can be tracked with the naked eye in the successive frames. This indicates that rather of being a problem due to the setup and to a bad quality acquisition, the flow in these areas is actually of a complex nature, and that the processing based on the analysis of interrogation windows may not be applicable there. This happens for instance on the left side, in a area next to the platform wall. Details of this area with velocity vectors is shown on Figure 8.27, for three consecutive timesteps, showing high velocity magnitudes concentrated in small zones as well as moving vortices. In these difficult areas, other measuring techniques, such as Laser Doppler Velocimetry, which is also non intrusive and based on seeding but limited to pointwise measurements, could bring more information on the flow phenomenons taking place.

PIV data processing 8.3.1 Averaging and alignment

For each recording and each configuration, the local velocity along time is exported at the 9 locations of interest, using the on-site measurement positions given in Table 6.1 and scaled to the small-scale model. The triggers for the PIV data, counted from the first image recorded, are read on the PIV images for each recording (see Figure 8.32) and averaged, resulting in the values given in Table 8.5 below -keeping in mind that the arrival and the departure of the train are recorded separately. The processing of this data is then done in a similar way to the on-site measurements (see Section 6.4.2), with alignment based on the average triggers followed by ensemble averaging. An example for Position 5 is given in Figure 8. [START_REF] Faugier | CFD model to assess parameters influencing piston wind in a subway tunnel and station[END_REF].

For comparison with the other models, similarly to the on-site data, the t enters and t leaving triggers of the PIV are shifted to be aligned with the triggers of the CFD from Table 7.2 (Section 7.2.2). In this case, no cutting of the curve during stop time is necessary, as the acquisition is already realized in two parts.

Rescaling

However, the timescale and magnitude scale are obviously of a different order between the real-scale model or measurements and the results obtained with the small-scale model. Therefore, if we wish to compare the shape of curves for both scales, the results of the PIV measurements must be rescaled. We have seen that rather than preserving the dynamic characteristics of the airflow, we focus on the relationship between the train position through the station and the development on the airflow. Hence, we compute the following scaling factors for the PIV timescale:

for arrival:

S on-site/P IV,arrival = t stops,on-site -t enters,on-site t stops,P IV -t enters,P IV = 11.82 (8.4)

for departure:

S on-site/P IV,departure = t lef t,on-site -t leaving,on-site t lef t,P IV -t leaving,P IV = 7.37

The magnitude is scaled by the ratio of the average peak magnitude for the on-site data to the small-scale data. The low image quality around Position 9 in the PIV measurements creates outliers that bring a lot of distortion in the data; the peaks at Position 9 are hence not taken into account to compute the average. When comparing the small-scale model with the on-site data and the numerical model, noting P [m/s] the peak magnitude averaged for the departure peak and the arrival peak, the PIV data will be multiplied by a factor: P on-site/P IV,departure = P avg 1→9, on-site

P avg 1→8, P IV = 2.53 m/s 0.20 m/s = 12.74 (8.6)
Finally, as many outliers are present in the data and as we wish to observe the general tendency predicted, the PIV data is algorithmically smoothed. The smoothdata function from Matlab is used, applying a robust quadratic regression "rloess" method and a window size of 30 elements (which corresponds here to approximately 1.5 s). In Chapter 9, the curves corresponding to the PIV measurements will be presented after being rescaled and smoothed.

Velocity curves for the small-scale experimental model

The aligned and averaged (but not rescaled nor smoothed) curves of velocity magnitude at the nine locations of interested are displayed on Figures 8.34 to 8.42 with the 95% confidence interval given by ±2σ of the individual measurements. Due to the optical access permitted by this configuration, only scenario 'B only' has been studied in this chapter. If one wanted to study the 'A only' scenario, for a full comparison with the on-site measurements, one would have to place the rails close to the platform opposite the laser and to operate the train in the other direction.

As discussed in Section 8.2.5, the low image quality at Position 9 results in erroneous and noisy PIV measurements (Figure 8.42). We have also noted in this chapter that a non-negligible part of the data is not available close to the walls and at the junction of the platform ceiling and of the tracks ceiling, as they were generating too much reflections. Special care must hence be taken in the construction and handling of the model, to obtain clean, straight cuts in the plexiglass and avoid scratches.

Similarly to the on-site data, peaks in the velocity magnitude are detected following the arrival and the departure of the train. Upon the train arrival, the peak is decreasing as the train velocity also decreases when passing the sampling location (1 to 9). Upon train departure, the peak gets clearly shifted to the right when looking at positions 1 to 9. Also, this peak is always happening after the train has started to leave; from positions 6 to 9, the peak is happening after the train has left the station. This is an indication that the main air movements are taking place in the wake of the train rather than by its side. The aspects related to the flow development on the platform, confronted with the results of the on-site measurement campaign and the outputs from the numerical model, will be further discussed in Section 9.4.1.

The magnitude of the peaks obtained is, on average, 12.74 times smaller than the one measured on-site (see Equation 8.6). Counting that the real train runs at approximately 10 m/s and the small-scale train at 0.66 m/s, the scaling factor for train velocity is above 15. The air velocity magnitude hence does not scale exactly with the train velocity. This is a natural consequence of the fact that the dynamic quantities have not been preserved in the downscaling of the model.

Part III

Putting in perspective

Numerical versus experimental comparison

Three different types of results have been obtained from the three chapters composing Part II and processed keeping in mind a future comparison among them: on-site measurements of air velocity in the real station (Chapter 6), CFD outputs are the corresponding locations of a geometrically simplified model of the station with a train running through it (Chapter 7), and sampled velocity magnitude sampled from PIV recordings performed on a small-scale station with a train moving through it (Chapter 8). This present chapter will therefore compare these results, quantify the match between them, and discuss similarities and differences while re-contextualizing them in the topic of subway climatology. Section 9.1 displays the curves of velocity magnitude at the locations on the platform when a train is passing through the station. These results were obtained from the previous chapters: on-site measurements in a real subway station, CFD model of a full-scale simplified station, and PIV measurements on a small-scale simplified station in plexiglass. Quantitative parameters are then defined and used to compare the agreement between these curves in Section 9.2, and in particular to discuss how well the models can capture the peak in velocity magnitude observed around train arrival and train departure in Section 9.3. Conclusions for train-induced airflow are formulated in 9.4, using the previously defined parameters of the visualizations provided by CFD and PIV. The discrepancies existing between the three types of results are explored in Section 9.5, and either causes or further investigation directions are suggested. Conclusions about the capabilities and limitations of the models to represent the train-induced airflow on the platform of this station are then formulated in Section 9.6.

Compared velocity profiles for measurements and models at locations of interest

With Figures 9.2 to 9.11, this section presents the velocity magnitude curves along time, obtained in the three preceding chapters making up Part II: from the on-site measurements in the real, full-scale station; from the numerical CFD model of the same station; and from the PIV measurements in the small-scale station in the lab.

To help reading the figures and focusing on the airflow characteristics, the various configurations studied, the conventions used and the main processing leading to this presentation of the curves are reminded in the following paragraphs.

Scenarios 'A only' and 'B only', which corresponds to the passage of one train in the station along one platform or the other (hence in two opposed directions -see Appendix A), are being studied here for the on-site measurements and the numerical simulation. For reasons mentioned in Section 8.2, only recordings for 'B only' scenario are available for the PIV measurements and will hence only be displayed on the figures corresponding to this scenario. Section 7.2.1 has made clear how we can get data both for 'A only' and 'B only' scenarios with just one numerical simulation, using the symmetry of the station respectively to the train tracks. As a reminder, Table 7.1 contains the coordinates of the locations of interest for Platform A and Platform B, and these locations are represented schematically on Figure 9.1 reproduced here. To read the curves, we recall with Appendix A and Figure 9.1 that 'B only' means 'a train is passing through the station along the platform where the measurements are taking place', passing the measurement locations from 1 to 9, while 'A only' means 'a train is passing through the station along the opposite platform', passing the measurement locations from 9 to 1. Sections 6.4.2 and 8.3 have explained how the results obtained from the onsite measurement and the PIV measurements, respectively, are processed to be comparable with the numerical data. We also remind here that additionally to the alignment and averaging, the PIV data is also smoothed and rescaled in time by a factor 11.82 for arrival (Equation 8.4) and 7.37 for departure (Equation 8.5) and in magnitude by a factor 12.74 (Equation 8.6).

The on-site experimental data is plotted with two standard deviations. As it was already given in Section 8.4, the standard deviation for the PIV measurements is not plotted here -also to avoid overloading the graphs and keep some homogeneity between the 'A only' and 'B only' scenarios. The numerical results include two configurations described in Section 7.2.4 and discussed in Section 7.4.2: one without background wind with the air being at rest at the beginning of the simulation and one with the implementation of boundary conditions and initialization aiming to create a directional airflow of 0.7 m/s in the station. The black dot on the wind velocity curve indicates the moment the front of the train passes the measurement cart.

Five locations, situated on a line along the platform length, are displayed here. Detailed results for the X-aligned locations (2-3-4 and 6-7-8) will be given together in Section 9.4.1.

Complementing the first observations made in Section 7.3.3 when comparing the meshes, and although differences exist in the different approaches, an overall trend of velocity is clearly discernible, revealing a noticeable pattern characteristic of the piston effect. Firstly, there is a rise in airflow velocity upon the train entrance into the station. Secondly, non-zero velocities are observed during stationary periods, as evident from both the simulations and on-site measurements, but with different magnitudes being remarkable for the numerical results depending on whether background wind is included or not. Lastly, when the train accelerates, a second peak in velocity is formed.

The magnitude of the peaks and the timings at which they are occurring varies from one location to another. Focusing first on the results of full-scale approaches and progressing in the increasing X direction for both scenarios (9 to 1 for 'A only', 1 to 9 for 'B only'), the peak related to the arrival of the train occurs later in time. A general tendency is that the peak transitions from being recorded after the train head passes the measurement location (indicated by the dot on the curves) to occurring after the front of the train has passed at the level of the considered location. Similary around departure, the peak appears later as the measurement locations is being passed by the train. Even if the timing of the PIV curves differs significantly from the full-scale results, the shift in time of the peak is still observable.

The discussion about the peak magnitude and other features of the development of train-induced airflow on the platform will be carried out further in Section 9.4, as we will also rely on quantitative parameters defined hereafter.

Correlation between the different outputs

At this stage, we have highlighted numerous times that key features of the traininduced airflow observed from the platform are the peaks in velocity produced upon the arrival and the departure of the train. To estimate the difference between results obtained from Part II, these peaks are deemed more representative indicators than computing the magnitude difference over the whole curve length, as the difference during the stop time of the train can distort the results a lot. With an ideal modelization, the output velocities would be equal to the measured ones and the scatter plot of both velocities would give perfectly aligned points. How far the actual values are from this linear relationship can be studied from the square of the correlation between the modeled and the on-site experimental values, known as r-square (r²) and defined in Equation 9.1. In addition, we introduce a time delay in the experimental data, i.e. the curve is horizontally shifted to maximize the correlation coefficient in order to put focus on comparing the shape of the peaks -if the delay is positive (resp. negative), the experimental signal is ahead of (resp. late on) the numerical signal. The averaged results for both part and scenarios, with and without the background wind, are given in Table 9.1. Note : as the PIV data has been significantly processed and modified, it makes no real physical sense to compute its delay compared to the experimental curves, and the correlation is therefore not calculated for the PIV results.

r 2 = 1 T -1 T i=1 N i - N σ N E i - Ē σ E 2 (9.1)
with r the Pearson correlation coefficient, T the number of observations (every millisecond); N and E the numerical signal and the experimental signal, respectively; N and σ N the mean and standard deviation of N, respectively, and Ē and σ E the mean and standard deviation of E. The correlation value can be used as a metric to evaluate the quality of the model, taking the experimental data as reference, and as a decision-making tool to pick the best model parameters. We therefore aim for the highest r² value and the lowest delay. Table 9.1 shows that these parameters are better at the arrival peak for both platforms when background wind is added. For departure however, delay is greater and correlation smaller with the addition of background airflow.

Peak shape parameters

We have started to evaluate how much difference there was between the numerical model and the experimental data when comparing the different meshes in Section 7.3.4 by calculating the relative difference in peak shape magnitude. We have also seen from this section, as proven by the 2D case (see curves in Appendix G), that the peak magnitude only was not sufficient to conclude on an accurate representation of the flow, as unrealistic features were present in the 2D results even though the peak amplitudes were close. The numerical to experimental match was also discussed in the above Section 9.2 by taking more into account the transient character of velocity and evaluating the correlation between the curves for the peaks with an average value given for all locations.

From a more practical perspective, observing the results for the 9 locations and the 2 scenarios (18 curves to look at in total) can be cumbersome and can make it difficult to get a broad perspective. A presentation of the numerical-toexperimental comparison in a more compact way would hence support the discussion and make the outcomes of the tested models more impactful.

Definition of parameters and implementation

A transient nature of the airflow makes it indeed difficult to compare objectively the agreement between the numerical and experimental curves. It seems therefore appropriate to turn towards signal-based statistical metrics as they conserve a sense of time. Peak shape parameters can indeed serve as a reduced description of a phenomenon and therefore for the evaluation of the predictive capabilities of models, including in other domains, such as the work of Michaelis and Wegscheider [START_REF] Michaelis | Improving accuracy in graphite-furnace atomic-absorption spectrometry through peak shape monitoring[END_REF] for spectroscopical applications for instance. More specifically, peak magnitude, skewness and kurtosis are deemed to be suitable quantities to quantify the peak shape around the arrival and departure of trains. As most of the post-processing is done in Matlab, the embedded functions of the language are used; their definition and formulation are given below (see Equations 9.2, 9.3 and 9.4) and can also be found in the documentation [START_REF]Signal Features[END_REF]. It must be noted that computing these parameters on normalized values would give the same results, making them good quantities for study-to-study comparison.

Peak magnitude, or peak value, is the maximum of the velocity magnitude in each isolated part -arrival and departure. For a signal ψ where individual observations are noted ψ i , it is simply defined as:

Ψ peak = max i |ψ i | (9.2)
Skewness quantifies the asymmetry of a sample distribution around the sample mean; it therefore describes how steep each side of the peak is and could be physically interpreted as a 'damping' of the airflow. The skewness of the normal distribution (or any perfectly symmetric distribution) is zero. Positive (resp. negative) skewness traduces that the tail on the right (resp. left) side of the distribution is longer than the tail on the left (resp. right) side.

Ψ skewness = 1 T T i=1 (ψ i -ψ) 3 1 T T i=1 (ψ i -ψ) 2 3/2 (9.3)
Kurtosis is a measure of the sharpness of a peak, or of how close the signal is to a normal distribution. The kurtosis has a value of 3 for a normal distribution. Positive kurtosis indicates a distribution relatively marked by a peak; negative kurtosis indicates a relatively flat distribution. Kurtosis is also sensitive to outliers, and in that sense, it can be seen as a metric of how smooth the peak profiles are.

Ψ kurtosis = 1 T T i=1 (ψ i -ψ) 4 1 T T i=1 (ψ i -ψ) 2 2 (9.4)
For the on-site and CFD data, the arrival peak is isolated by taking the velocity between t enters and 25 seconds: for departure, the peak is delimited by t leaving and t lef t . By observing all the curves, we observe indeed that the peak falls between these values a vast majority of the time. For the PIV results, as a lot of delay is present in the data, the start time and end time for the peaks are manually written in for each location. An example of peaks isolated and used for comparison of shape is given in Figure 9.12. For clarity as we want to visualize the evolution of the airflow during the train course in the station, results are displayed for locations situated on one line along the platform in the X direction.

Results for peak shape parameters

The results of the peak shapes parameters defined are displayed in Figures 9.13 A first observation of the peak leads to clear conclusions can be made about background airflow and confirms what has been mentioned in Sections 7.4.2 and 9.2. The addition of the background airflow in the numerical simulation, in the form of a pressure gradient between the left and the right side of the domain, improves the numerical-to-experimental match for the arrival part, but brings additional discrepancies for the departure part. This is particularly striking looking at the peak magnitude on Figure 9.19b for instance.

A deeper look at these graphs allows us to draw conclusions both on about what the tendencies observed in peak shape parameters across positions and scenarios tell us and on the numerical-to-experimental match. This first aspect is discussed in the following Section 9.4.1 and the second topic is addressed in Section 9.5.

Development of piston effect on the platform

Making use of the curves and the peak shape parameters, we can make deduction about the evolution of the flow through time and space in the station as the train goes through it. What is also interesting about models is that they make visualizations of contours and streamtraces possible for instance, highlighting phenomenon that would be hardly observable in real life, especially as they are moving with the train.

9.4.1 Evolution throughout the platform 9.4.1.a In the longitudinal (X) direction

As expected for peak magnitude, when a train travels on side A, the peak magnitude upon arrival decreases when the train moves from position 9 to 1 (Figure 9.19a), which are passed at an also decreasing speed by the train. On side B, locations are passed at a decreasing speed from 1 to 9 (Figure 9.22a. The same logic is followed for departure, where the magnitude of the peaks gets greater as the train accelerates (Figures 9.13b and 9.13a). Comparing also arrival and departure at position 1, for the 'A only' scenario (Figure 9.2), the magnitude of the arrival peak (for which the measurement point is passed as the train almost reaches its stop position) is clearly smaller compared to the departure peak; whereas for the 'B only' scenario (Figure 9.7), the first peak (for which the measurement point is passed as the train just entered the station, hence at a higher speed) is larger than the second peak. For Position 9, the opposite happens (Figures 9.6 and 9.11). For PIV, the relative magnitude of the arrival and departure peaks to one another is coherent with the other results: the positions towards the entrance side measure a higher peak upon arrival than upon departure, while positions towards the exit side show a higher peak upon departure than upon arrival. These behaviors could be attributed to several effects. Firstly, as explained in Section 2.2.1, Kim and Kim [START_REF] Kim | Experimental and numerical analyses of traininduced unsteady tunnel flow in subway[END_REF] determined that the most extreme pressure difference around a train occurs when a train reached its maximum traveling speed. As the train accelerates while leaving the station, this could result in higher airflow velocities. Secondly, it has also been demonstrated that the piston effect becomes more prominent when the blockage ratio increases [START_REF] Faugier | CFD model to assess parameters influencing piston wind in a subway tunnel and station[END_REF], [START_REF] Khayrullina | CFD simulation of train aerodynamics: train-induced wind conditions at an underground railroad passenger platform[END_REF]. This caused the airflow velocities to increase as well. When a train leaves the station, β increases as the cross-sectional area of the tunnel is smaller than the cross-sectional area of the station. The opposite for the blockage ratio was true when a train entered the station. These features illustrating the piston effect are well captured by the model and confirm what many researchers have observed in various studies.

Contrary to what could be expected, the magnitude is not necessarily higher for trains passing along side B, which is the side of the measurements, than on side A. One explanation for this phenomenon could be provided by Figure 9.25, that shows that closer to the train, turbulence provided more mixing, that typically lowers the velocity magnitude; while away from the train, air was rather affected by the pressure gradients induced by the piston effect in the front and the back of the train. Mirroring tendencies can be observed in the skewness for the arrival scenario on both platforms, translating that as the train arrives and slows down in the station, the rise in velocity magnitude gets less steep. Upon train departure, the skewness stays positive, indicating that the velocity drop occurs after the rear of the train passes the measurement location. This behavior is also confirmed by Figure 7.14.

The fact that no visible tendency can be read from the kurtosis could be interpreted as a confirmation that the model performs better at capturing the global shape of the peak rather than the small fluctuations around it, as also visible on the curves from Section 9.1. Despite these differences, the airflow features listed in this section can indeed be observed both from the numerical and modeled results.

9.4.1.b In the radial (Y ) direction

Apart from the evolution of the train-induced airflow through the length of the platform (which behavior can be more intuitive as this is the direction of the train run) we can also compare this airflow from the perspective of the radial (Y ) direction. To this aim, we use the velocity recorded by the positions aligned on the X-axis at two locations on the platform: Positions 2-3-4 are approximately 25 m from the entrance tunnel, and Positions 6-7-8 lie around 75 m away from it (see Table 7.1). Displaying several locations together on one plot reveals another aspect of the modeling of airflow during the stop time of the train. While both the experimental on-site data and the PIV measurements are getting back to a constant value, the numerically recorded velocity during this period are spread, for almost all cases. When looking at Figures 9.3, 9.5, 9.8 and 9.10, we see that this effect is tempered by the addition of background airflow, which brings up the numerical velocity to a non-zero value during the stop time of the train.

Contrarily to the flow development in the X direction, the peak magnitude along the Y axis does not evolve in one single direction, and can not necessarily be related to the train distance or to the distance to the wall or the edge of the platform. This can be due both to modeling errors or to perturbations of the measurements by external factor, or to the fact that the layer of fluid around the train is restricted by the station geometry (in particular, the platform and the walls), in a typical feature of piston effect. This specific airflow around the train body will be investigated further in the following section, using the contours that the models allow to visualize. The space-dependence of the airflow is also evidenced here, as changes are occurring at a fraction of the platform scale, as the locations studied here are separated by less than one meter.

Flow field around the train

As the subway train moves through the station, it carries the characteristics of piston effect from the tunnel while being affected by the change of geometry, resulting in specific features. Figures 9.36 to 9.39 display a close up of the field of velocity magnitude around the train head, for the numerical and experimental model. At this moment in time, the train is in between of R1 and R2, starting its deceleration with a velocity just below 10 m/s for the full-scale numerical model (see Figure 7.2). Streamlines, or streamtraces, are also plotted, showing the path traced by a massless particle placed at an arbitrary location in a steady-state vector field [START_REF]Tecplot 360 User's Manual -Tecplot 360 EX[END_REF], meaning for the transient simulation that they are calculated as if the airflow was steady at that exact moment in time.

The analysis of the vectors and the streamtraces visible on the figures can be done with respect to Figure 2.1 that was adapted from the literature. The accelerated region of air is visible around the head of the train, where the air velocity is higher than the train velocity. It should however be noted that contrarily to the definition given by Bell [START_REF] Bell | Moving model analysis of the slipstream and wake of a high-speed train[END_REF] for high-speed trains, the flow in this region has the same direction as the train. Next, the entrained region of air, traveling with the direction the train is traveling with the same speed, is located between the front and the tail of the train. This region is very quickly restricted by the presence of the station walls, creating a vortex on the side of the train, next to the train head, and causing the airflow to change direction on the platform in a pattern specific to trains moving in confined spaces.

This particular behavior has consequences for the airflow on the platform. Moving on a horizontal line in the decreasing Y direction through the platform (on the figures: a vertical line from the train to the wall), we can therefore distinguish three zones for the velocity: a zone of high velocity close to the train, then a zone where the velocity magnitude approaches zero in the middle of the vortex, and a zone where velocity increases again on the wall side. The region where the two higher-velocity zones meet is indeed remarkable: the air is static at the border of the two opposing flows.

It should be noted that the relative position of this lower velocity layer is closer to the train in the full-scale numerical model than in the small-scale one. This is a logic consequence of the fact that dynamic quantities, such as Reynolds number, have not been preserved in the downsizing of the model.

What is also interesting about these visualizations, is that they highlight a phenomenon thanks to the use of models, while it would be hardly observable in real life, especially as the vortices are moving with the train. One main cause presumably affecting the differences observed between modeled and measured airflow is the geometrical simplifications of the station. Rectangular shapes have been adopted to model the tunnel and the platforms, both to make the numerical simulation more efficient and to simplify the crafting of the small-scale model, but also enhance the reproducibility of the work.

The station studied here is part of one of the oldest ones of the Brussels network. From a surface station at the end of the 1960's, it was converted in an underground one in the following decade, and has undergone various renovations since then, both from an architectural perspective, including for instance a restructuring of surface accesses, and from an technical point of view, to follow the evolution of the different generations of trains. In addition, the plans we had access to is limited to the station.

For instance, the value of 6.17 m given as tunnel width (see Figure 5.6) is the distance between the edges of the opposite platforms measured on the as-built plans. However, in the real station, the platforms disappear shortly after the end of the station, either abruptly or with a gentle slope, and various elements such as barriers of different types, platforms made of grids or concrete elevations, pipes, electric meters or cable passages appear. A picture taken inside the tunnel, in Figure 9.40, shows a few of those elements. It therefore likely that this value varies significantly in the upstream and downstream tunnels. Attempts at getting the geometry as close as possible from the reality have been researched in other studies. Notably, Qian [START_REF] Qian | Integrated evaluation of air flow and gas dispersion for undeground station safety strategies based on subway climatology[END_REF] performed a laser scanning of the metro station he studied, to produce a point cloud model that is used to produce a virtual reality representation of the station and to recreate numerically the geometry of the station including all its details. In the CFD part of his work, Qian faced difficulties to generate a good quality mesh inside the station, even without having a moving train, and therefore had to use a simplified version of the geometry, as illustrated with the example of staircases in Figure 9.41, and also to remove fine details of the station. For the same reasons than the ones mentioned in the first paragraph of this section, the station amenities were not modeled in our geometry: suspended ceiling and lamps, ticket terminals, access doors to the platform, benches, advertisements on the walls and other objects are removed. Simplifications have also been adopted for the shape of the train. In particular, in the numerical simulations, the train body is approximated by a rectangular cuboid. Rounding the edges of the train body could generate more realistic flow patterns in the station, as the volumes of air displaced are indeed originating from the movement of the train.

A more accurate representation of background airflow would also be necessary. The work of Prince [82] goes in this direction by proposing multiscale numerical modeling techniques for analysing airflow in a network of tunnels in order to combine the benefits in computational effort provided by 1D modeling (using the SES software) with the accuracy of 3D simulations in OpenFoam. His 3D cases are limited tunnels without train movement and the data exchange at the 1D-3D interfaces needs further research, but the suggested approach could help to simulate more accurately the ventilation through tunnels at the scale of the underground network. In the PIV setup, although background is not included as such, the seeding system provides a continuous supply of particles through the pipe and the cardboard box (see Section 8.2.1). This likely also generated a low-speed wind coming from the entrance tunnel and going towards the station, of which the magnitude and spread in the station could be assessed by performing measurements in the empty station.

External wind conditions are as well not modeled in this thesis. One of the purposes of building a small-scale model is to have some control of these conditions. However in our case, the model is not standing in a wind tunnel nor in a controlled chamber, but in a large room where potential variations of the conditions exist, although deemed of small amplitude. Some numerical studies, such as the one of Walther et al. [START_REF] Walther | Détermination des conditions limites en pression pour le calcul de la ventilation naturelle[END_REF], propose to use CFD to determine the natural ventilation-driven air change rates at the exits of a building to improve the thermal simulation of the latter. This is achieved by coupling the thermal simulation with a CFD case where the considered building is placed in a domain with far field limits of up to 10 times the size of the building to determine the wind load on the building openings. The ventilation model of Qian [START_REF] Qian | Integrated evaluation of air flow and gas dispersion for undeground station safety strategies based on subway climatology[END_REF] is fed by the average of experimentally measured wind and temperature conditions at each of the exits of the station. As this would require setting up a completely new case and geometry, or running additional measurements, this is left as a potential future development for the model.

Lastly, the effect of train doors openings with passengers out-boarding and boarding in is not considered in the model -and is also not included in any of the references mentioned so far. Implementing this implies indeed the use of advanced techniques for modeling wall surfaces coming in contact with each other (when the doors are opening and closing), changes of domain boundaries to take the inside of the train into account, as well as the consideration of thermal effects that cannot be neglected in the confined, potentially crowded interior of the train. For all these applications, CFD may not be the approach of choice and the interaction with the inside of the train therefore goes beyond the scope of this thesis.

Temperature correction for the hot wire measurements

Hot wire anemometry is a technique that is sensitive to changes in the ambient temperature, potentially bringing errors in the velocity measurements. Ideally, one would hence need to perform the calibration in a temperature-controlled room set at the same conditions than the experimental ones. It should however be noted that ambient lab conditions where the calibration was done, in terms of temperature notably, were quite different than the ones in the station (see Table 6.3). These great variations of temperature might induce a change the measured fluid properties affecting the voltage-temperature relationship, and resulting in a less accurate reading of temperature.

In this paragraph, we provide a rough estimation of the error brought in the velocity reading, using the temperature correction proposed by Bruun [START_REF] Bruun | Hot-wire Anemometry -Principles and Signal Analysis[END_REF] given below in Equation 9.5 This method is one of the most commonly used corrections, especially as it is easy to perform a posteriori of the measurements.

E corr = E w T w -T ref T w -T amb 1/2 (9.5)
where E corr is the voltage obtained after the temperature correction; E w is the output voltage of the hot wire; T w = 400°C is the wire temperature, taken here as the maximum operating temperature of a nickel wire [START_REF]Probes for Hot-wire Anemometry[END_REF]; T ref is the temperature at which the calibration was not performed, which was not measured but is assumed to be the one of a reasonable working environment, hence taken as 20°C; and T amb is the ambient temperature of the measurement site, which we take as the lowest of the values for T station in Table 6.3, hence T amb = 7°C. Using this equation, we derive the points displayed in grey on Figure 9.42. A discernible voltage shift is noted for points with higher velocities. In our application, air velocities rarely exceed 5 m/s, and the impact on the results is hence deemed to be quite small. However, the corrective measure suggested herein is a preliminary approximation and several parameters had to be estimated. Recently, Hultmark and Smits [40] have proposed correction a more accurate method to account for the effects of relatively large temperature changes in the heat-transfer process and on the fluid properties. Their method uses similarity variables, for which it would have been required a more precise characterization of the calibration conditions. Lastly, we could also note that most velocity recordings lie below 2-3 m/s, but only a few points were recorded in this range during the calibration. To increase the precision of the measurements, it is hence recommended to take more calibration points in the lower velocity range.

Capabilities and limitations of the models

The analysis based on the peak parameters allows to draw conclusions about CFD RANS models capacity in predicting the airflow at stake here. The numerical re-sults lie in the statistical distribution of the experimental results and can hence be considered as a plausible realization of the flow following the passage of a train in the subway station. The measurements replicated over nine days and locations provide a rigorous overview, establishing that patterns observed in the airflow evolution distribution were real and not random variations or sporadic events. With measurement locations placed along the whole length of the station, several flow features typical of piston effect can be observed in the station both in the numerical and experimental results: a higher velocity magnitude between the observed peaks, that can be correlated with the speed of the train when moving close to the measurement position and the changes in blockage ratio, and abruptly changing magnitudes when the train extremities are passing the measurement location. Both the numerical and experimental results reveal that large differences can be found between locations even if these are close to each other. These differences are the consequence of flow features developing at a fraction of the scale platform, mainly in the horizontal plane. Also, local velocity changes occur over short time intervals scaling with the train velocity. With regard to the stated objectives of the research and the current state of the art, this demonstrates two elements:

-to obtain spatially (less than a meter) and temporally (in the order of one second) precise information about the flow field on the platform while a train is running through the station, the movement of the train should be integrated in the models; -even if the model can be validated for the part where the train is still in the tunnel, the extrapolation to complex architecture, including abrupt changes of geometry and blockage ratio, and interactions with the exits, is however not straightforward and requires a bespoke validation -the latter is provided for this case, but might not be always available.

The models still allows to visualize data that would be impossible to observe on-site, such as velocity contours and streamtraces. Notably, the latter indicate that air displacement experiences changes in magnitude and direction all across the station, that will be studied further in Section 9.4. The numerical domain being limited to the station and connecting tunnels, the boundary conditions necessary to create a background wind induced by a pressure gradient can only be approximated.

With the numerical model in particular, since the flow quantities are calculated for the entire domain and during the entire time of the train run, it is possible to make a posteriori observations. These has been the object of Section 9.4 where both the numerical and experimental models are used to gain insight into the flow field inside the station and around the train; and in the following chapter, models are used to simulate scenarios that could hardly be tested in real life.

Section 5.2 has specified a number of elements that have not been considered in the study and Section 9.5 discussed these further and provided some hypothesis regarding their impacts on the results. Based on what we have learned form this project, suggestions to improve the collection of experimental data and to make the models more accurate will be formulated in Section 11.2 of the last chapter.

Applications for the models

Having developed models and assessed their reliability, they can be applied to investigate the flow behavior around the train and in the station. Depending on their application, numerical models are likely to be used on already existing stations, in order to upgrade their ventilation systems for instance. In this case, the workflow is therefore different than modeling a station to be build, as the latter is at the stage where changes are still possible to implement and all information is more easily available. In this section, uses of the model that could support design decision for building or renovating underground subway station are succinctly explored.

In Section 10.1, the effect of different blockage ratios and train speeds on the air velocity on the platform is explored using various configuration of the numerical model. The consequences on lowering the train velocity are discussed further in Section 10.2, observing the mass flow rates at the exits of the station. In Section 10.3, an experimental visualization technique, Background-Oriented Schlieren (BOS), is used on lab-scale model as a proof-of-concept of the applicability of BOS to observe vapor dispersion in a horizontal plane in the station.

Station and tunnel architecture

In the case where the numerical model can be used as a design tool prior to its construction, the influence of the tunnel's and station's structural architecture on piston effect can be taken into account. Section 7.3.2 has already considered tunnels with blockage ratios of 0.30, 0.37 and 0.46 (see Table 7.5), where it appears that as blockage ratio and train speed increases, the flow around the train gets de-veloped in less time (see Figure 7.9). This was also noted by Cross [START_REF] Cross | A validated numerical investigation of the effects of high blockage ratio and train and tunnel length upon underground railway aerodynamics[END_REF], who investigated numerically the effect of varying dimensions of a single-track tunnel, considering blockage ratio of 0.65, 0.75, 0.78 and 0.85. It was observed that during acceleration and deceleration phases, higher blockage ratios translates into steeper and earlier variations in the velocities, and that the maximum attained velocity is higher. During the constant velocity phase, increasing blockage ratio from 0.65 to 0.85 results in a 36% increase of the outlet velocity. In this section, the effect of the change of blockage ratio is studied for the station. Two geometrical configurations, with varying platform dimensions -one realistic plaftorm width, and one narrower -of our numerical model are considered, and three train speeds are implemented in each of them. The parameters of these configurations are summarized in Table 10.1, Y p and Z p being respectively the width and the height of the platform, and Re based on the hydraulic diameter of the train in the tunnel. It should be noted that as this study was carried before having developed the final numerical model, the geometry used for these three simulation exhibits a few differences: before and after the station, 250 m of upstream tunnel and 150 m of downstream tunnel are respectively included (instead of 200 m on each side); the platform is less high; the floor of the platform is separated from the floor of the tunnel by 1.15 m.

Compared to the tunnel cases (Table 7.5), there are only slight changes of blockage ratio here. As the train occupies a relatively small part of the tunnel section, almost double the platform width only results in a decrease of 4% of the blockage ratio.

The UDFs used for train movement are also simpler (as this parametric was initiated before the experimental distance data was available), with constant a deceleration of -0.68 m/s 2 (linearly fitted through the train distance measured on site) and a acceleration of 1 m/s 2 being used. The train velocity versus time specified as input is plotted in Figure 10.1. The results are given on Figure 10.2 for only one point, located close to Position 2. The velocity is normalized by the train cruise speed. The vertical lines are indicating the moment the front and the rear of the train are passing the sampling location. It is noticeable that the relative intensity of the highest peak, when the train passes the point, does not vary with the blockage ratio, but that the air circulating while the train reaches its stop position is faster when the blockage ratio increases. Similar behavior happens when the train leaves, but with less intensity: in fact, at the platform entrance, the train is at the beginning of its deceleration and therefore still fast, whereas at the end of the simulation the train starts its acceleration and is rather slow. Similar to what have been observed in the literature for tunnels and to what has been deduced from the peak shape parameters, velocities indicate that the air tends to circulate at a higher velocity and at a higher rate as blockage ratio and train speed increase.

Air exchange in the station

Although the test case station has been initially chosen for its relatively simple geometry, the direct connection of the subway platform with the street level also implies that the station's atmosphere is more dependent on outdoor winds and temperature. Hence, contrary to almost all the stations studied in the cited literature, there is no station hall that acts as buffer zone to isolate the platforms from outdoor winds, that are present in real life but not in the numerical model. In such type of stations, it is thus interesting to look at the interactions happening between the station and the outdoor environment through the exit doors.

Wen [START_REF] Wen | Environmental and health effects of ventilation in subway stations: A literature review[END_REF] has pointed out the trade-off that lies in ventilating underground subway stations: on one hand, ventilation is necessary to maintain a healthy environment by avoiding the accumulation of moisture and heat and ensuring thermal comfort; but on the other hand, ventilation enhances the spread of air pollutants (potentially from sources located inside the station), fire smoke, and biological or chemical agents. In this regard, focusing on the air exchange between the inside of the station and the outdoor environment through the exits is an crucial point to study. As natural ventilation is often unable to meet the requirement discussed in Section 1.1, air curtains and platform screen doors are some of the devices that can be used to control piston winds. However, Krasyuk et al. [START_REF] Krasyuk | Experimental research into air distribution in a terminal subway station[END_REF] have demonstrated that warm-air curtains at the entrances demand high amounts of energy when the outside temperature is below 10°C in cold regions, and they might not be able to stop cold air intrusions from the outside. In this case, regulating train speeds when they arrive and exit stations might lessen the amount of cold air that enters the stations.

Therefore, we propose a simple application of our model, by monitoring mass flow rates at two doors at the extremities of the platform. Two different scenarios are simulated: the first one is the same as in the previous parts of the study, with the train running at 10 m/s in the constant speed phase in the station, then decelerating, stopping in the station for 30 seconds, and leaving the station after accelerating. In the second scenario, the train follows the same pattern, but starts from a constant speed of 7 m/s in the tunnel and reaches that same speed upon its departure. The corresponding UDF is given in Appendix D.2. The adapted triggers for both cases are visible on Figures 10.3 to 10.8, with the mass flow rates evolution.

These graphs show again how the mass flow rates are related to the train movement in the station, with air being mostly pushed out upon train arrival, while departure exhibits a quick succession of expelled then entrained air. We can also observe how lowering the train cruise speed from 10 m/s to 7 m/s lowers the transferred air volume and dampens their rates. This observation, that does not require any change in the station's architecture, could help lowering the ventilation load and enhance energy savings or pollutant containment in case of crisis, for instance. Additional ventilation devices, such as air curtains studied, can also be installed to gain better control over ventilation conditions. Aiming to prevent piston winds from propagating throughout a subway station, Khaleghi [START_REF] Khaleghi | Analysis of unsteady airflow in a subway station influenced by train movement[END_REF] evaluated how placing air curtains above platform exits blowing air at a constant velocity can affect the air velocity in the station hall near the platform exits. Their numerical simulations show that while the system reduces the maximum air speed by 68% when the train arrives and stops in the station, the air curtain is much less effective when the train accelerates and leaves the station. Due to the unsteady nature of the flow, they recommend therefore that the air curtain should be controlled as the train arrives in the station, in order to reduce the energy consumption due to ventilation. Wen indeed concludes his review article [START_REF] Wen | Environmental and health effects of ventilation in subway stations: A literature review[END_REF] by pledging for 'a more comprehensive design, flexible adjustment, and continuous maintenance' of ventilation. In order to have a satisfying control over these rates, both in term of meeting the air quality requirements discussed in the introduction and in terms of energy efficiency, the ventilation sequence and the location of ventilation devices should be depending on the schedule of trains pulling in and out of the station.

Other uses and locations of the air curtains can also be considered. Chen et al. [START_REF] Chen | Influences of the optimized air curtain at subway entrance to reduce the ingress of outdoor airborne particles[END_REF] have for instance focused on improving the air quality by preventing outdoor airborne particles from entering the station. They advise a combined use of monitoring system to determine whether it is necessary to activate the air curtains; artificial neural network based on CFD outputs to control the air curtain velocity; and air purifiers to filter the particulate matter that have escaped the ventilation systems. In their numerical study, Juraeva et al. [START_REF] Juraeva | A computational analysis of the trainwind to identify the best position for the air-curtain installation[END_REF] aim to find the best location for an air curtain going from top to bottom in the tunnel, to separate two adjacent environments and reduces the transfers of bacteria and radioactive particles. Appropriate placement and control of ventilation devices, such as air curtains, can therefore be determined with the help of numerical models, and support air renewal in the station, or, at the contrary, limit the air movements and the exchanges with other rooms or with the outdoor environment.

Visualization of vapor dispersion with

Background-Oriented Schlieren 10.3.1 Proof-of-concept: principle and setup

The Background-Oriented Schlieren (BOS) method is an optical density visualization technique that computes local inhomogeneities of the refractive index in transparent medium. With a specially designed background, a digital camera and a correlation algorithm, this effect can be observed with very small changes in refractive index, even when it would be invisible to the naked eye. The refractive index can be affected by density changes of the air (for high-speed flows for instance), but also by changes in concentration of a dissolved gas or vapor, making BOS a potentially suitable method to study how an agent would spread in the small-scale station from Chapter 8. In BOS, the field of view where we want to observe refractive index changes is placed in between the camera and the background, as represented schematically on Figure 10.9. The background is typically a pattern of random dots, that must be as fine and as closely packed a possible, while still maintaining enough size and contrast to resolve them in the image. The background pattern used in our setup is given in Figure 10.10. Images of the field of interest are recorded, and each of them is compared to a reference image of the background, observed through the undisturbed medium (taken right before or after the recording). The evaluation of the displacement of image details in BOS is very similar to the evaluation of the movement of PIV seeding particles, computed from a single frame recorded with double exposure or from two frames recorded in a suitable time interval. Most of the existing PIV evaluation programs can be used for BOS after small adaptations [69], accounting for the sensitivity requirements since the displacement of image details in BOS is often much smaller than the motion of PIV particles. The main advantage of BOS lies in the fact that, compared to PIV for instance, few devices are required to apply the technique: a good resolution camera, a printer and a processing software. As no seeding is required, BOS is a non-intrusive method. For 2D flows or 3D flows with axial symmetry, it is possible to retrieve the density from the displacement in the image by integrating the density gradient -such as in the work of Venkatakrishnan and Meier [START_REF] Venkatakrishnan | Density measurements using the Background Oriented Schlieren technique[END_REF] or of Moumen et al. [START_REF] Moumen | A new approach for the reconstruction of axisymmetric refractive index fields from backgroundoriented schlieren measurements[END_REF]. For arbitrary 3D flows, a more sophisticated setup using twelve cameras and a tomographic algorithm is required -see for instance the study of [START_REF] Nicolas | A direct approach for instantaneous 3D density field reconstruction from background-oriented schlieren (BOS) measurements[END_REF].

Depending on the sensitivity and resolution requirements, the study volume is usually placed between 1/3 and 2/3 of the total distance between the background plane and the image plane. To study the spread of a gaseous agent in the horizontal plane of the station, this means that a background should be placed in the order of one meter below the floor of the small-scale model, and instead of a wooden panel, the floor should also be in plexiglass, hence necessitating to re-build a model with a transparent floor. This section is therefore meant as a proof-of-concept of the applicability of the BOS method in the small-scale station to study gas or vapour dispersion than as a real in-depth study of the phenomenon. For this reason, the full overview of the method and of all tested configurations and outcomes is not related, but the limitations and possibilities for further work are rather highlighted. Raffel [START_REF] Raffel | Background-oriented schlieren (BOS) techniques[END_REF] or Meier [69] for instance, have published major contributions to the field and review papers that may be consulted, as well as other references of this section, to get insights of the optical technique, of various applications and of the main associated challenges of BOS. For our case, the detailed implementation of the method in the lab as well as various considerations about the setup and the images processing can be found in the internship report of Birkin [START_REF] Birkin | Internship on computational and experimental fluid dynamics at MECA[END_REF].

In this section, the study consists in observing the spread of an agent in the tunnel in the wake of the train from the side. Acetone is used as the spreading agent, as its vapor provides the required change of refractive index, while being easily accessible and safe to handle. A small cup (about 2 cm in diameter) filled with acetone is placed of the floor of the tunnel, next to the tracks, The realized setup is shown in Figure 10.11. The distances from camera to track and from track to background, placed on a stand behind the tunnel, are both 65 cm.

To ensure a good lightning of the background especially when recording with a high-speed camera (hence with very low exposure time), a panel LED light is used, which resulted in the camera getting about 100-500 counts per pixel on the sensor. The same Phantom VEO-E 340L camera and DaVis software as in Section 8.2 are used. The camera is combined with a 105 mm focal length Nikkor lens.

Acetone dispersion in the wake of the train in the tunnel

As the train passes by the acetone cup, a recording is started at 200 Hz. To give an idea of the area visualized, as well as the train speed which is constant in the whole recording, two of the recorded images of the train passing in the field of view are given in Figure 10.12. In this configuration, it is only possible to visualize the image displacement resulting from the acetone vapour after the train has passed the cup. Preliminary tests have evidenced that best results to compute the displacements are achieved with three passes of correlation using an interrogation window of 8×8 pixels. The result of the BOS analysis with the computed displacements are given in Figure 10.13, for four different time steps after the train has passed in the field of view. On these images, the movement of the acetone vapor towards the left (in the direction of the station) appears clearly; and this observation is in line with the ones made along this study, with a pressure drop at the rear of the train entraining the air in its wake. Through this proof-of-concept, we can conclude that the BOS method is promising to qualitatively observe the effect of the train on the spread of a contaminant through the small-scale station, provided that it is built with a transparent floor. Using a more advanced camera and software setup, this effect could in theory be measured quantitatively. Measurement of gas dispersion in a real metro station is complicated, and to the best of the author's knowledge, it has only been performed using tracer gas outside of the trains operating hours. This section therefore highlights the potential of small-scale models for such applications.

General conclusions

This chapter provides an overview of the problem statement, methodology and results. In Section 11.1, conclusions are formulated for each of the previous chapters. Finally, an outlook on future research is provided in Section 11.2.

Main conclusions

In this work, we investigated the topic of the piston effect generated by the movement of a subway train during its arrival or departure in an underground station, and how to best represented it with models. The problem at stake is one for which analytical equations are hard to put in practice, and for which theoretical background and systematized tools are not widely available yet. One must therefore use assumptions and sometimes navigate in the dark to build a model, and then assess how reliable the model is.

After having established the context of the research in Chapter 1, Chapter 2 emphasized that experimental validation of models for train-induced airflow in an underground subway station is rarely done at the level of detail that is required to observe how evolves the piston wind at different locations on the platform.

Chapter 3 reviews basic concepts of fluid dynamics and the Navier-Stokes equations, as well as the RANS approach used in this study, highlighting that not all factors affecting airflow can be reproduced numerically and that there is no such ideal airflow model due to the stochastic nature of turbulent movement. Chapter 4 gives experimental measurement tools that can help us approach fluid dynamics quantities and the associated challenges with their use.

The real station on which the models are based and in which the measurements are performed is introduced in Chapter 5, and the methodology of the thesis is developed with a focus on enhancing repeatability and reproducibility. The simplified geometrical model adopted for this work is presented, and the use of the different numerical and experimental techniques is made explicit. Two main scenarios, corresponding to a train passing in each direction, and nine measurement locations spread on the platform are defined to focus our research on.

Chapter 6 has described the experimental setup that allowed to record the velocity magnitude on one platform during over 450 passages of single trains. Additionally, acquisitions of air velocity in between trains passages gave an average u bg of 0.67 m/s. To process the large amount of data collected, a way of analyzing it was found to enhance comparison between the sets: after being aligned based on the triggers (train enters, train leaving, train left) recorded by dedicated sensors, the data is ensemble averaged to give an average velocity curve for each location and each scenario.

In Chapter 7 the transient, three-dimensional air flows in the underground station have been modeled using CFD. The comparison with a 2D case, taken as a horizontal slice of the 3D model, yield very different results, indicating that this reduction is not advised to solve this complex airflow. The necessary tunnel length to include in the model to minimize the influence of the domain geometrical boundaries is studied by running cases of a train running through a tunnel only, and the flow around the train is found to be developed after 30 meters of travel. This chapter reports also an attempt at simulating the background airflow by imposing an overpressure at the tunnel inlet and station doors on the train-entrance side and an underpressure on the tunnel outlet and station doors on the train-exit side. Although this first approach brings the simulated outputs closer to the measured ones around the arrival of the train, unrealistic behavior appears after this moment. A modelization using the Immersed Boundary Method is also proposed, but the limitations of the method due to the inaccuracies occurring at the walls propagate errors in viscosity modeling and lead to unrealistic results; the implementation of this would require additional research into the near-wall models working with IBM.

Chapter 8 about the small-scale model of the simplified has evidenced that, at scale 1:95 with a moving train, it was not possible to preserve Re, hence affecting the replication of the dynamic flow characteristics in lab conditions. Both recommendations have been stated and limitations have been pointed out in this chapter, about the technical challenges of train control, the seeding and the elimination of reflections. The choice of image processing parameters is not obvious when dealing with TR-PIV, and the election of a parameters (geometric mask, time-and space-based filters, interrogation window size and refinement, vector validation) is realized using a measure of the correlation value and the SNR.

Chapter 9 synthesized all the results obtained using various formats: as curves displaying the velocity magnitude along time, as the correlation between those curves around the peaks generated at the arrival and departure of the train, and as a comparison of computed peak shape parameters (magnitude, skewness and kurtosis). These results allow to conclude on the predictive capabilities and limitations of RANS models and small-scale models. This paragraph highlights the fact that, rather than being due to the limitations of the chosen calculation or acquisition methods, existing differences are deemed to be the consequences of the chosen simplified conditions. In that sense, and also considering already existing models and studies from the literature, this work evidences the challenges that come with finding models for specific phenomenons (piston effect, background wind, interaction with the exits...) and articulating them in a simulation, while maintaining the computational time reasonable and only being able to confront the numerical outputs to measurements performed in as-built or scaled environments.

Still, Chapter 10 brings forward potential uses of the models to make deduction about the dynamic airflow characteristics: both the numerical and experimental outputs indicate that significant variations exist between locations, even when they are close to each other. These differences are attributed to the development of flow characteristics at a scale smaller than the platform's dimensions, primarily in the horizontal plane. Additionally, local velocity fluctuations occur within short time intervals that are related to the velocity of the train. The other configurations simulated confirmed that higher train speeds and blockage ratios resulted in higher velocity magnitude with steeper changes, and overall increased volumes of air displaced across the platform and through the exits. With Background-Oriented Schlieren, it was possible to visualize the spread of acetone vapor in a vertical slice in the upstream tunnel.

Rather than going into the full details of the train aerodynamics and airflow quantities, this thesis provided the tools and methods to conduct an analysis of model performances and reliability for the transient characteristics of piston wind as a train goes through a subway station. The reporting of all the design choices made can be used as a practical guide to elaborate models and avoid the main pitfalls that can, at best, be time-consuming and, at worst, lead to unrealistic or false results. In the next section, we will propose a few directions to approach the ideal modelization of subway climate and train-induced airflow.

Perspectives for future work

This section suggest directions in which future work could contribute to make models for underground subway stations more accurate, efficient and reliable. Through also addressing the limitation of this thesis, topics are proposed either in the continuity of this work, or in related areas for which more in-depth knowledge is necessary.

For the on-site experimental measurements

During the experimental campaign, the outside wind and temperature conditions have not been recorded. Recording these quantities at surface level and through the exits at platform level would bring valuable information regarding the influential sources, and would make it possible to attribute the observed variations in individual recordings of velocity to the outdoor conditions or to other sources. Especially during the stop time of the train where piston winds are less prominent, the data gathered would allow to generate realistic, time-dependent boundary conditions to input as UDFs at the exits for the numerical model.

The attempt at simulating background airflow implemented in the numerical model has exhibited oscillations due to the interactions between the wind coming from outside the station and the airflow circulating through the tunnel, but their presence is yet to verify in real life. Although measurements of natural airflow due to outdoor meteorological conditions have been published, the background airflow due to the circulation of air through the underground tunnels remains fairly undocumented from an experimental perspective, especially on the fine time scale of less than a minute. This measurement would require setting up simultaneous measurements across connected stations to obtain an overview on the wind conditions through the underground network.

The choice using the hot wire could also be reconsidered, given the difficulties of in-situ calibration, the impossibility of obtaining direction and the low velocities studied. In this work, the variability existing between individual measurement has been assessed by displaying the standard deviation with the averaged curves; but rigorous analysis of the measurements uncertainties and how they propagate when performing the data post-processing would allow to be more precise in discussing the reliability of the experimental outputs.

For the numerical model

In setting up a dynamic simulation for a domain over several hundreds of meters, one main challenge comes the difficulty of setting up a good quality mesh, that should be refined enough to capture the narrow areas of the geometry (in particular, the gap between the tunnel and the train wall). To overcome this problem, other meshing techniques, such as overset mesh, eliminate the need for frequent remeshing operations and could greatly accelerate the obtention of results. As the exemple of the Immersed Boundary Model has shown, the validation of such simulation should be conducted. With the necessary time and computational resources are made available, a finer representation of the station and train geometry could also be considered.

The implementation of natural airflow in the numerical model would benefit from additional attention. In particular, the cause of low frequency oscillations in the velocity magnitude before there is any train movement remains as a question to explore. Perspectives for this topic also include the use of coupled simulations to improve the modelization of background airflow, with one-dimensional and less costly simulation for the flow in the network, and detailed CFD simulation for the airflow in the station. The use of coupled simulations has also been raised to model the effect of external wind conditions on the opening of a building, and by these considerations, draw a link with the field of urban environment modeling. These methods can be promising in order to obtain more accurate results for the airflow in the station without sacrificing too much on computational efficiency.

Four distinct scenarios were recorded during the experimental campaign, but only scenarios 'A only' and 'B only', that include one train running at a time, have been modeled and discussed. The modelization of scenarios with two trains being present in the station at the same time, namely 'A then B' and 'B then A', remains a topic to investigate.

For the small-scale model

To overcome the low image quality due to the presence of reflections, or to investigate the areas where the correlation algorithm does not perform well -along the walls and edges of the model, or near the train head -pointwise measurement techniques such as Laser Doppler Velocimetry could provide a precise measurement of the velocity magnitude on these difficult points. This technique has the advantage that it can be applied on the already built model and with the current train control setup. In terms of data processing, focusing on the area over the rails, for example using phase-averaging based on the train position, may bring a lot of information. Another upgrade of the setup could be done by adding two cameras, at an angle with the ones in place, to perform stereo-PIV measurements and investigate the 3D flow effects related to the train movements.

Improving the repeatability of the lab-scale results could be done in various manners. Suggestions to improve the preciseness of the train control have already been listed in the corresponding chapter. Since the model has opening, placing the entire model in a temperature-and pressure-controlled chamber would make it possible both to avoid the disturbance coming from the room itself and to uniformly seed the entire volume, avoiding the penetration of non-seeded air through the exits.

If the main shape features of piston wind were reproduced, their values differ from several orders of magnitude from the recorded on-site values. Comparing the results of the PIV measurements on the small-scale model and of the corresponding numerical simulation, also at small scale, would allow to discriminates which discrepancies can arise from the scaling and the transposition of the real life problem to a laboratory setting, and which ones may be coming from uncontrolled elements in the lab itself or from the uncertainty of the measurements.

Suggestions for further studies and methodological improvements have been formulated in this section. This very last paragraph is the time to take a bit of distance to restate the broad purpose of the research: to generate useful knowledge for the field of subway climatology that can be applied to make subway environments healthier, safer and more reliable.

The work presented in this thesis identifies several interesting approaches to address the design of models for train-induced airflow in an underground subway station, assesses their validity and performances, and discussed the results from an engineering perspective. While many works have focused on modeling various specific aspects of the physics related to underground subway climate and train aerodynamics, this thesis is an effort to integrate these aspects in a semi-realistic representation of the train-induced airflow in this particular environment.

A Description of the scenarios

In the scenarios with one train, the train arrives through the tunnel from one direction, stops in the station, and leaves trough the opposite tunnel.

In the scenarios with two trains, a second train enters the station as the first train is stopped. The first train leaves as the second train is still stopped in the station, and then the second train also leaves. The sensor is mounted on the cart above the hot wire anemometer (Figure 6.7), allowing to record both wind velocity and direction at the same horizontal location. A power supply cable is also included with the cart and connected to the laptop. The angle data is wirelessly transmitted to the PXI on a dedicated channel using HC-12 module communication. The HC-12 modules are controlled by Arduino microcontrollers reading the results from the Python code.

One reason that could explain the inaccuracy of this sensor is that the flow speed was too low and the piston effect was causing too abrupt flow direction changes to overcome the inertia of the woolen thread and the friction between the thread and the vertical bar.

B.2 Messages sent by the train detection modules

B.3 Example of data recorded and saved

An example of .txt file can be found in Figure B.2. Each column consists of a certain measured parameter. The first column contains time in seconds. The distance data [cm] is saved in the second column, while the wind direction data [°] is found in the third column. Each train detection module (A1/A2/A3/B1/B2/B3) has his own column containing a binary data. By default, the value in these columns is 0; if a train is detected, the value changes to 1; when the train have completely passed the sensor, the value returns to 0. The last two columns are reserved for the hot wire anemometer data: the column 'raw speed' contains the voltage data, while the column 'speed' is velocity [m/s], converted from these voltages using the calibration.

C

Hot wire uncertainty analysis

This appendix details the calculations leading to the uncertainties displayed on Figure 6.6. This analysis was carried out by I. Sabbe and J. Vanlaere [START_REF] Sabbe | Experimental validation of a numerical model describing piston effect driven airflow in a subway station[END_REF] and is reproduced here.

During the preparations of the measurement campaign, the hot wire calibration curve was fitted using 14 measurement points obtained by PIV. It should be noted that the uncertainty of the hot wire depended on numerous factors:

-the accuracy of the instrument (δU v ); -the fit of the calibration curve (δU cal ); -the accuracy of the PIV measurements (δU P IV ); -the influence of turbulence (δU turb ).

These influencing factors were combined to calculate the overall uncertainty of the hot wire anemometer measurements. When taking into account the different influences, the following equation was formulated: This appendix presents the UDFs that have been used for the Fluent CFD simulations of the train running at a constant cruise speed in the tunnel, then decelerating to stop in the station, and accelerating to reach again its cruise speed. The movement of the train goes in the X-direction only.

δU hw = (δU v ) 2 +
The first one, with a cruise speed of 10.22 m/s is the realistic one, which deceleration curve have been derived from fitting a curve through the on-site distance measurements of the train during its arrival in the station. The acceleration coefficient was modeled linearly from the difference between the moment the train starts leaving the station and when its rear end passes the end of the station (i.e. its rear end enters the exit tunnel), observed in a first iteration of the on-site measurements, assuming the train reaches its cruise speed just when it leaves the station.

For the second one, with a cruise speed of 7 m/s, the deceleration coefficient was computed linearly from the difference between the end and the start of the deceleration for the realistic case.

The third UDF corresponds to the small-scale train movement from Chapter 8. Similarly to the first UDF, the deceleration and the acceleration have been fitted through a curve using the averaged train position, recorded on PIV images.

In all cases, the timings are adjusted so that the metro stops in the middle of the station, taking the length of the tunnel (200 m for the full-scale model, ??? mm for the small-scale model) into account. The corresponding velocity sequence resulting from each UDF is plotted with each code. The curves given here are meant to support the discussion of Chapter 7 by displaying the results obtained at the 9 locations of interest (see Table 7.1 and Figure 7.1) for different numerical simulations: a 2D geometry, a 3D geometries with a coarse, middle and fine mesh. The experimental results from Chapter 6 are also displayed here as they allow to conclude on which model is able to best represented the airflow measured in the reality.

8. 1

 1 3D sketch of the M6 train ([94]). . . . . . . . . . . . . . . . . . . 8.2 Train BRAWA 44601. . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Mechanical drawing of the small-scale model (without the tunnels), with inner dimensions specified. . . . . . . . . . . . . . . . 8.4 Small-scale model. . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 View of the model train inside the small-scale station. . . . . . . . 8.6 Details of the small-scale train and rails. . . . . . . . . . . . . . . 8.7 Schematic setup for the activation of the model train. . . . . . . . 8.8 Tags used for model train detection. . . . . . . . . . . . . . . . . 8.9 Control sequence of the velocity of the model train. . . . . . . . . 8.10 Model train position upon departure and arrival in the small-scale station, for 3 different runs. . . . . . . . . . . . . . . . . . . . . . 8.11 Pictures of the stop position of the model train, for 3 different runs. 8.12 Screenshot from the LabVIEW interface, showing (in green) the position of the two tags used for color detection and the color spectrum analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.13 PIV acquisition setup in the lab. . . . . . . . . . . . . . . . . . . 8.14 Calibration image for the PIV recordings, with the plate in the small-scale station and frames from both cameras stitched. . . . . 8.15 Seeding non-uniformity. . . . . . . . . . . . . . . . . . . . . . . 8.16 Seeding system before the upstream tunnel. . . . . . . . . . . . . 8.17 Small-scale station with additions to avoid reflections. . . . . . . . 8.18 Particle images in a window of ∼ 24×24 pixels, for 3 successive frames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.19 Raw PIV images, for 'Arrival' acquisitions, the laser illuminating the left side (left) or the right side (right). . . . . . . . . . . . . . 8.20 Location of the 3 rectangles used to analyze the effect of image processing functions. . . .

10. 1 F. 1

 11 Velocity sequence executed by the train for three different cruise speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Normalized velocity magnitude at a point (around Position 2) on the platform with a train running through a station of varying platform dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3 Mass flow rates through the door R1. . . . . . . . . . . . . . . . . 10.4 Mass flow rates through the door R2. . . . . . . . . . . . . . . . . 10.5 Mass flow rates through the door R3. . . . . . . . . . . . . . . . . 10.6 Mass flow rates through the door L1. . . . . . . . . . . . . . . . . 10.7 Mass flow rates through the door L2. . . . . . . . . . . . . . . . . 10.8 Mass flow rates through the door L3. . . . . . . . . . . . . . . . . 10.9 Schematic BOS acquisition setup (adapted from [84]). . . . . . . 10.10Close-up of speckle background used for the experiments. . . . . 10.11BOS acquisition setup in the lab. . . . . . . . . . . . . . . . . . . 10.12Raw BOS images. . . . . . . . . . . . . . . . . . . . . . . . . . . 10.13Image displacements computed from BOS images. . . . . . . . . A.1 'B only': Single train passing along side B (measurement side). . A.2 'A only': Single train passing along side A. . . . . . . . . . . . . A.3 'B then A': Train arriving on side B (measurement side), then train arriving on side A. . . . . . . . . . . . . . . . . . . . . . . . . . A.4 'A then B': Train arriving on side A, then train arriving on side B (measurement side). . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Wind direction sensor on the measurement cart. . . . . . . . . . . B.2 First lines of a text file of data recorded during the experimental campaign. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.1 Velocity sequence executed by the train with a cruise speed of 10.22 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.2 Velocity sequence executed by the train with a cruise speed of 7 m/s.219 Images processed with the subtract time filter, for different types of filters. Filter length: 600 images. Image number: 0. . . . . . . F.2 Images processed with the subtract time filter, for different filter lengths. Filter type: subtract minimum. Image number: 60. . . . . F.3 Images processed with the remove background / unsteady reflections filter, for different types of filters. Image number: 60. . . . . F.4 Images processed with the subtract time filter and the remove background / unsteady reflections filter, in different orders. Image number: 60. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.5 Vector fields processed with automasking, for different types of automasks. Image number: 60 -Color scale: 0 m/s to 0.008 m/s. . F.6 Vector fields processed with a spatial automask, for different intensities. Image number: 60 -Color scale: 0 m/s to 0.42 m/s. . . . F.7 Velocity fields processed with different interrogation window shapes. Image number: 60 -Color scale: 0 m/s to 0.30 m/s. . . . . . . . . F.8 Velocity fields processed with different interrogation window sizes.Image number: 60 -Color scale: 0 m/s to 0.70 m/s. . . . . . . . . G.1 Schematic top view of the station, with measurements locations on Platform A and Platform B (reproduced from Chapter 7). . . . . . G.2 Velocity magnitude for scenario 'A only' at Position 1. . . . . . . G.3 Velocity magnitude for scenario 'A only' at Position 2. . . . . . . G.4 Velocity magnitude for scenario 'A only' at Position 3. . . . . . . G.5 Velocity magnitude for scenario 'A only' at Position 4. . . . . . . G.6 Velocity magnitude for scenario 'A only' at Position 5. . . . . . . G.7 Velocity magnitude for scenario 'A only' at Position 6. . . . . . . G.8 Velocity magnitude for scenario 'A only' at Position 7. . . . . . . G.9 Velocity magnitude for scenario 'A only' at Position 8. . . . . . . G.10 Velocity magnitude for scenario 'A only' at Position 9. . . . . . . G.11 Velocity magnitude for scenario 'B only' at Position 1. . . . . . . G.12 Velocity magnitude for scenario 'B only' at Position 2. . . . . . . G.13 Velocity magnitude for scenario 'B only' at Position 3. . . . . . . G.14 Velocity magnitude for scenario 'B only' at Position 4. . . . . . . G.15 Velocity magnitude for scenario 'B only' at Position 5. . . . . . . G.16 Velocity magnitude for scenario 'B only' at Position 6. . . . . . . G.17 Velocity magnitude for scenario 'B only' at Position 7. . . . . . . G.18 Velocity magnitude for scenario 'B only' at Position 8. . . . . . . G.19 Velocity magnitude for scenario 'B only' at Position 9. . . . . . . List of Tables 5.1 Blockage ratios for the test case. . . . . . . . . . . . . . . . . . . 6.1 Cart positions on Platform B and corresponding days. . . . . . . . 6.2 Amount of datasets measured per scenario at every location. . . . 6.3 Weather during the measurement campaign. . . . . . . . . . . . . 6.4 Average triggers measured on-site for 'A only' and 'B only'. . . . 7.1 Measurement positions on Platform A and Platform B. . . . . . . 7.2 Triggers for base-scenario train run through the station. . . . . . . 7.3 Boundary conditions at the exits (value given as gauge pressure). 7.4 Boundary conditions at the exits, including background airflow (value given as gauge pressure). . . . . . . . . . . . . . . . . . . 7.5 Geometrical and dynamical settings for the configurations of a train running through a 1000 meters long tunnel. . . . . . . . . . . 7.6 Summary of meshing features. . . . . . . . . . . . . . . . . . . . 7.7 Relative difference in peaks magnitude for compared meshes. . . . 7.8 Numerical solver parameters. . . . . . . . . . . . . . . . . . . . . 7.9 Relative difference between peak magnitudes for Z = 0.5 m and Z = 1.6 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Main characteristics of the small-scale train and the real train. . . 8.2 Scaling factors in all three directions. . . . . . . . . . . . . . . . . 8.3 Summary of PIV configurations and amount of datasets recorded. 8.4 Summary of functions and parameters for PIV images pre-processing and vector field calculation. . . . . . . . . . . . . . . . . . . . . . 8.5 Average triggers for the PIV measurements. . . . . . . . . . . . . 9.1 Goodness of fit for the aligned numerical and on-site experimental curves, around arrival and departure time. . . . . . . . . . . . . . 10.1 Geometrical and dynamical settings for the configurations of a train running through stations of varying platform dimensions. . . B.1 Messages sent by the train detection modules. . . . . . . . . . . .

ψ

  arithmetic mean of signal ψ acq refers to the data acquisition atm refers to atmospheric conditions (at sea level) avg refers to the average H refers to the hydraulic diameter hw refers to the hot wire p refers to the platform t refers to the tunnel

Figure 2 . 1 :

 21 Figure 2.1: Schematic of airflow generated by the train movement (side view), adaptedfrom[START_REF] Khaleghi | Analysis of unsteady airflow in a subway station influenced by train movement[END_REF] and[START_REF] Bell | Moving model analysis of the slipstream and wake of a high-speed train[END_REF].

Figure 2 . 2 :

 22 Figure 2.2: Air velocity distribution on a line along the platform's length (from [46]).

Figure 2 . 3 :

 23 Figure2.3: Schematic illustration of airflow and temperature phenomena in a subway system due to topography, structural properties of the subway system and temperature differences (adapted from[START_REF] Pflitsch | Natural Ventilation as a Factor Controlling the Dispersal of Airborne Toxins in Subway Systems in a Disaster Situation[END_REF]).

  ρ [kg/m 3 ] is the fluid density, u [m/s] the flow speed, L [m] a characteristic linear dimension, and µ [kg•m -1 •s -1 ] the dynamic viscosity of the fluid. The dimension L is chosen as the one that would best represent the flow's development around an object; therefore, Reynolds numbers are particular to a specific problem.

Figure 3 . 1 :

 31 Figure 3.1: Schematized decomposition of the mean and turbulent components of fluid velocity.

Figure 4 . 1 :

 41 Figure 4.1: Schematic illustration of the hot wire sensor.

Figure 4 . 2 :

 42 Figure 4.2: Schematic illustration of a 2D PIV setup (adapted from [91]).

Figure 4 . 3 :

 43 Figure 4.3: Schematic illustration of the processing of PIV images through interrogation windows and cross correlation (adapted from LaVision [57]).

  Figure 4.4.

Figure 4 . 4 :

 44 Figure 4.4: Principle of sub-pixel interpolation (from [100].

  Figure 4.5 shows two examples of correlation maps: Figure 4.5a is what is typically aimed for, while Figure 4.5b displays a lower-quality correlation.

  (a) Sharp correlation peak and high SNR. (b) Wide correlation peak and low SNR.

Figure 4 . 5 :

 45 Figure 4.5: Example of correlation maps.

  Flow fieldsΔt = 1/f acq Image frames and laser pulses

Figure 4 . 6 :

 46 Figure 4.6: Schematic illustration of TR-PIV (adapted from LaVision [56].

  (a) Point of view from 1. (b) Point of view from 2.(c) Point of view from 3.

Figure 5 . 1 :Figure 5 . 2 :

 5152 Figure 5.1: Pictures of platforms the test case station, taken from the points of view defined in Figure 5.2.

Figure 5 . 3 :

 53 Figure 5.3: M6 train (from [25]).

Figure 5 .

 5 Figure 5.4: 3D view of the modeled station, with axis and origin.

Figures 5 .

 5 Figures 5.4 to 5.6 show the simplified geometry that is adopted for this work. The platforms' dimensions are then of X p = 100 m, Y p = 4 m and Z p = 3.25 m;the tunnels are Y t = 6.5 m wide and Z p = 4.75 m high. The length to be included in the models will be discussed notably in Section 7.3.2. The train is approximated by a rectangular cuboid (as in the works of Jia[START_REF] Jia | Numerical simulation of flow characteristics in a subway station[END_REF] or Camelli[START_REF] Camelli | Modeling subway air flow using CFD[END_REF] for instance), having a length of X train = 90 m, a width of Y train = 2.7 m and a height of Z train = 3.5 m. The train is separated from the tunnel vertical wall by 0.34 m, from the floor by 0.50 m and from the ceiling by 0.75 m.The platform along which the train goes to the center of Brussels is denominated 'Platform A' (or 'left' for the exits, from Chapter 7) and all elements referring to this side are designated by the letter A (or L); the other platform, along which the train comes from the center of Brussels, is called 'Platform B' (or 'right') and elements are designated by the letter B (or R).

Figure 5 . 5 :Figure 5 . 6 :

 5556 Figure 5.5: Schematic top view of the station, with dimensions.

Figure 5 . 7 :

 57 Figure 5.7: Schematic top view of the station, with locations of interest on Platform B.

FebruaryFigure 6 . 1 :

 61 Figure 6.1: Phasing of the measurements and of tunnel sensors placement

  (a) HC-SR04 sensor and HC-12 module. (b) SHARP infrared sensor.

Figure 6 . 2 :

 62 Figure 6.2: Sensors used for train presence detection.

Figure 6 . 3 :

 63 Figure 6.3: Module used for train presence detection in the tunnel, including the sensor and the HC-12 mounted on the Arduino card, the protective casing and the battery.

Figure 6

 6 Figure 6.4: Setup and measurement chain related to the train presence.

Figure 6 . 5 :

 65 Figure 6.5: ComfortSense Mini 54N95 (left) combined with the 54T33 draft probe (right) from Dantec Dynamics

  Uncertainty of the hot wire

Figure 6 . 6 :

 66 Figure 6.6: Calibration curve of the hot wire anemometer.

Figure 6 .

 6 Figure 6.8 gives the schematized layout of the wind velocity sensor as well as the associated connections to the PXI. The voltage measured by the hot wire is sent to the PXI using a coaxial cable with BNC (Bayonet Neill-Concelman) connectors.

  3.1) and protect the equipment. ← Laptop connected to a webcam and Arduino module ← Webcam and ring light ← Thread around a fixed bar ← Anemometer ← Power supply and coaxial cable with BNC connectors

Figure 6 . 7 :

 67 Figure 6.7: Wind velocity and direction sensors mounted on a cart.

Figure 6 . 8 :

 68 Figure 6.8: Setup and measurement chain related to the wind velocity.

Figure 6 . 9 :

 69 Figure 6.9: LiDAR laser mounted on a suspension clamp.

PXIFigure 6 . 10 :

 610 Figure 6.10: Setup and measurement chain related to the train distance.

  (a) NI PXI-1042. (b) In the station.

Figure 6 .

 6 Figure 6.11: PXI and computer for data collection.

Figure 6 . 12 :

 612 Figure 6.12: LabVIEW monitoring and control display.

  (a) Measurement cart with the hot wire. (b) LiDAR laser. (c) Trigger A1, in the tunnel. (d) Trigger A2, at the station's entrance.

Figure 6 . 13 :

 613 Figure 6.13: Sensors placed in the station.

Figure 6 . 14 :

 614 Figure 6.14: Schematic top view of the station, with actual measurements locations on Platform B.

Figure 6 . 15 :

 615 Figure 6.15: Sample of background airflow measurement on Day 6.

  Figure 6.16: Average background airflow velocity magnitude per day, with corresponding two standard deviations.

Figure 6 . 17 :Figure 6 . 18 :

 617618 Figure 6.17: Train distance measurement on site.

Figure 6 .

 6 Figure 6.18 displays the resulting averaged curve. The small bump visible both in the curve and in the standard deviation around 3 s indicates the moment where the laser beam switches from hitting the front of the train and the side of the train. The curve is cut after the average time at which the train has left the station (when B3 changes from 0 to 1), as the distance measurement is not relevant anymore while the LiDAR is only pointing at the side of the train.

  Variation of t leaving for 'A only'. Variation of t leaving for 'B only'. Variation of t lef t for 'A only'. Variation of t lef t for 'B only'.

Figure 6 . 19 :

 619 Figure 6.19: Average triggers with confidence interval ±2σ in grey.

  Wind velocity measurements aligned on tenters,on-site and t leaving,on-site . Average velocity with confidence interval ±2σ in grey and average triggers.

Figure 6 . 20 :

 620 Figure 6.20: Post-processing steps of the on-site experimental measurements, example for 'B only' at Position 5.

7. 2

 2 Inputs, models and boundary conditions 7.2.1 Station model and software

Figure 7 . 1 :

 71 Figure 7.1: Schematic top view of the station, with measurements locations on Platform A and Platform B.

Figure 7 . 2 :

 72 Figure 7.2: Averaged measured distance with fitted curve and derived velocity pattern for an average train run through the station.

Figure 7 . 3 :

 73 Figure 7.3: Schematic top view of the station, with pressure boundary conditions.

Figure 7 . 5 :

 75 Figure 7.5: Contours of air velocity magnitude in the upstream tunnel (up), station (middle) and downstream tunnel (down), 600 s after applying a pressure difference at the exits.

Figure 7 . 6 :

 76 Figure 7.6: Cross section of the train in the tunnel, with dimensions, and sampling line for the velocity profiles.

Figure 7 . 7 :Figure 7 . 8 :

 7778 Figure 7.7: Velocity profiles along a radial line 20m from the train head for the β = 0.37 and Vtrain = 10.22 m/s case

46 Figure 7 . 9 :

 4679 Figure 7.9: Time necessary to obtain a developed flow versus speed of the train, for various blockage ratios.

Figure 7 . 10 :

 710 Figure 7.10: Section and detail of the 2D mesh at t = 0s.

Figure 7 . 11 :

 711 Figure 7.11: Velocity magnitude for 2D meshes for scenario 'B only' at Position 8.

Figure 7 . 13 :

 713 Figure 7.13: Contours of air velocity magnitude in the station during train arrival at t = 11 s, 13.5 s, 16 s, 20.5 s, 26 s and 35 s.

Figure 7 . 14 :

 714 Figure 7.14: Contours of air velocity magnitude in the station during train departure at t = 58 s, 60.5 s, 64 s, 66 s, 69 s and 72.5 s.

  "BC on" bg. airflow "BC off" Experimental no bg. airflow (b) A only -Position 2.

Figure 7 . 15 :

 715 Figure 7.15: Velocity evolution for various implementations of background wind in the numerical simulation, at chosen locations on the platform.

Figure 7 . 16 :

 716 Figure 7.16: Velocity evolution for Z = 0.5 m and Z = 1.6 m in the numerical simulation, at chosen locations on the platform.

Figure 7 . 17 :

 717 Figure 7.17: Contours of air velocity magnitude in the station in two Z-slices around Position 9 at 18.5 s, with streamtraces in a vertical rake at Position 9.

Figure 7 . 18 :

 718 Figure 7.18: Photograph of experimental apparatus, in the study of Kim and Kim [52].

Figure 7 . 19 :Figure 7 . 20 :

 719720 Figure 7.19: Cp variations at different locations from the 39-meters-long-tunnel entrance, in the study of Kim and Kim [52].

Figure 7 . 21 :

 721 Figure 7.21: Schematic illustration of a mesh with an immersed body (IB) defined for IBM(from[START_REF] Jasak | Immersed Boundary Method in FOAM -Theory, Implementation and Use[END_REF]).

Figure 7 . 22 :

 722 Figure 7.22: Velocity magnitude for scenario 'B only' at Position 5, with CFX results.

Figure 7 . 23 :

 723 Figure 7.23: Velocity magnitude for scenario 'B only' at Position 8, with CFX results.

8. 1

 1 Lab-scale model of a subway station 8.1.1 Scaling and design

Figure 8 . 1 :

 81 Figure 8.1: 3D sketch of the M6 train ([94]).

Figure 8 . 2 :

 82 Figure 8.2: Train BRAWA 44601.

Figure 8 . 3 :

 83 Figure 8.3: Mechanical drawing of the small-scale model (without the tunnels), with inner dimensions specified.

Figure 8 .

 8 Figure 8.4: Small-scale model.

Figure 8 . 5 :

 85 Figure 8.5: View of the model train inside the small-scale station.

  (a) Rail with connecting cable. (b) Train bogie.

Figure 8 . 6 :

 86 Figure 8.6: Details of the small-scale train and rails.

Figure 8 . 7 :

 87 Figure 8.7: Schematic setup for the activation of the model train.

Figure 8 . 8 :

 88 Figure 8.8: Tags used for model train detection.

Figure 8 . 9 :

 89 Figure 8.9: Control sequence of the velocity of the model train.

Figure 8 . 10 :

 810 Figure 8.10: Model train position upon departure and arrival in the small-scale station, for 3 different runs.

Figure 8 . 11 :

 811 Figure 8.11: Pictures of the stop position of the model train, for 3 different runs.

Figure 8 . 12 :

 812 Figure 8.12: Screenshot from the LabVIEW interface, showing (in green) the position of the two tags used for color detection and the color spectrum analysis.

Figure 8 .

 8 Figure 8.13: PIV acquisition setup in the lab.

Figure 8 . 14 :

 814 Figure 8.14: Calibration image for the PIV recordings, with the plate in the small-scale station and frames from both cameras stitched.

Figure 8 . 15 :

 815 Figure 8.15: Seeding non-uniformity.

Figure 8 . 16 :

 816 Figure 8.16: Seeding system before the upstream tunnel.

Figure 8 . 18 :

 818 Figure 8.18: Particle images in a window of ∼ 24×24 pixels, for 3 successive frames.

  (a) Image number: 18. (b) Image number: 147. (c) Image number: 51. (d) Image number: 178. (e) Image number: 84. (f) Image number: 196. (g) Image number: 109. (h) Image number: 178.

Figure 8 . 19 :

 819 Figure 8.19: Raw PIV images, for 'Arrival' acquisitions, the laser illuminating the left side (left) or the right side (right).

3 2 1 Figure 8 . 20 :

 1820 Figure 8.20: Location of the 3 rectangles used to analyze the effect of image processing functions.

  (a) Left part. (b) Right part.

Figure 8 . 21 :

 821 Figure 8.21: Geometric mask: shape drawn on the acquired images.

Figure 8 . 22 :

 822 Figure 8.22: Geometric mask: result.

Figure 8 . 23 :

 823 Figure 8.23: Image obtained after the application of the subtract time filter (subtract minimum, filter length: 3 images).

Figure F. 1 . 1

 11 Figure F.1.1 show pictures obtained after applying two different types of filters -subtracting the minimum or average intensity -, making clear the using the minimum intensity is preferable as we are mostly interested in the area on the platform. The results of using different filter lengths -600, 299, 49, 15, 5 and 3 imagesare also displayed in Figure F.1.2, for an image in which the train is entering the station.From the images, we can already rule out options where the filter length is too high, as the particles are not sufficiently visible. To determine finely which filter length to use, the algorithmic method is used with 3, 5, 15, 25 or 49 images and the results are summarized in Table F.1. A filter length of 3 is chosen as it yields the best results overall for correlation and peak ratio. The effect of applying these parameters of the subtract time filter, from a raw image, is given in Figure8.23.

Figure 8 . 24 :

 824 Figure 8.24: Image obtained after the application of the remove background/ unsteady reflections filter (directional minimum).

Figure 8 . 25 :

 825 Figure 8.25: Vector field obtained after the application of the spatial automask (set at 8).

  (a) 12×12 pixels. (b) 8×8 pixels.

Figure 8 . 26 :

 826 Figure 8.26: Details of vector fields processed with different interrogation window sizes.

Figure 8 . 27 :

 827 Figure 8.27: Vector fields in the middle of the left part of the station, during train arrival, for 3 successive frames.

  Image number: 18. (b) Image number: 51. (c) Image number: 84. (d) Image number: 109.

Figure 8 . 28 :

 828 Figure 8.28: PIV velocity contours, for 'Arrival' acquisitions, the laser illuminating the left side.

Figure 8 . 29 :

 829 Figure 8.29: PIV correlation, for 'Arrival' acquisitions, the laser illuminating the left side (black corresponds to correlation of 1, white to a correlation of 0).

Figure 8 . 30 :

 830 Figure 8.30: PIV velocity contours, for 'Arrival' acquisitions, the laser illuminating the right side.

Figure 8 . 31 :

 831 Figure 8.31: PIV correlation, for 'Arrival' acquisitions, the laser illuminating the right side (black corresponds to correlation of 1, white to a correlation of 0).

  (a) tenters,P IV . (b) t lef t,P IV .

Figure 8 . 32 :

 832 Figure 8.32: Example of images corresponding to triggers.

  velocity with confidence interval ±2σ in grey and average triggers, for arrival.

  velocity with confidence interval ±2σ in grey and average triggers, for departure.

Figure 8 . 33 :

 833 Figure 8.33: Post-processing steps of the PIV measurements, example at Position 5.

Figure 8 . 34 :

 834 Figure 8.34: Average PIV velocity with ±2σ and average triggers, for Position 1.

Figure 8 . 35 :

 835 Figure 8.35: Average PIV velocity with ±2σ and average triggers, for Position 2.

Figure 8 .

 8 Figure 8.36: Average PIV velocity with ±2σ and average triggers, for Position 3.

Figure 8 . 37 :

 837 Figure 8.37: Average PIV velocity with ±2σ and average triggers, for Position 4.

Figure 8 . 38 :

 838 Figure 8.38: Average PIV velocity with ±2σ and average triggers, for Position 5.

Figure 8 . 39 :

 839 Figure 8.39: Average PIV velocity with ±2σ and average triggers, for Position 6.

Figure 8 .

 8 Figure 8.40: Average PIV velocity with ±2σ and average triggers, for Position 7.

Figure 8 . 41 :

 841 Figure 8.41: Average PIV velocity with ±2σ and average triggers, for Position 8.

Figure 8 . 42 :

 842 Figure 8.42: Average PIV velocity with ±2σ and average triggers, for Position 9.

Figure 9 . 1 :

 91 Figure 9.1: Schematic top view of the station, with measurements locations on Platform A (up) and Platform B (down) (reproduced from Chapter 7).

Figure 9 . 2 :Figure 9 . 3 :Figure 9 . 4 :Figure 9 . 5 :Figure 9 . 6 :Figure 9 . 7 :Figure 9 . 8 :Figure 9 . 9 :Figure 9 . 10 :Figure 9 . 11 :

 9293949596979899910911 Figure 9.2: Velocity magnitude for scenario 'A only' at Position 1.

  'B only', Position 6, departure.

  'B only', Position 9, arrival.

Figure 9 . 12 :

 912 Figure 9.12: Examples of peaks compared.

  to 9.18 for the configuration without background wind in the CFD model, and in Figures 9.19 to 9.24 for the configuration with background wind.

Figure 9 . 13 :

 913 Figure 9.13: Peak magnitude for 'A only'.

Figure 9 . 14 :

 914 Figure 9.14: Skewness for 'A only'.

Figure 9 . 15 :

 915 Figure 9.15: Kurtosis for 'A only'.

Figure 9 . 16 :

 916 Figure 9.16: Peak magnitude for 'B only'.

Figure 9 . 17 :

 917 Figure 9.17: Skewness for 'B only'.

Figure 9 . 18 :

 918 Figure 9.18: Kurtosis for 'B only'.

Figure 9 . 19 :

 919 Figure 9.19: Peak magnitude for 'A only', with background airflow.

Figure 9 . 20 :

 920 Figure 9.20: Skewness for 'A only', with background airflow.

Figure 9 . 21 :

 921 Figure 9.21: Kurtosis for 'A only', with background airflow.

Figure 9 . 22 :

 922 Figure 9.22: Peak magnitude for 'B only', with background airflow.

Figure 9 . 23 :

 923 Figure 9.23: Skewness for 'B only', with background airflow.

Figure 9 . 24 :

 924 Figure 9.24: Kurtosis for 'B only', with background airflow.

Figure 9 . 25 :

 925 Figure 9.25: Contours of air velocity magnitude and streamtraces in the back of the train at t = 66s.

Figure 9 . 26 :Figure 9 . 27 :Figure 9 . 28 :Figure 9 . 29 :Figure 9 . 30 :Figure 9 . 31 :Figure 9 . 32 :Figure 9 . 33 :Figure 9 . 34 :Figure 9 . 35 :

 926927928929930931932933934935 Figure 9.26: On-site recorded velocity magnitude for scenario 'A only' at Positions 2-3-4.

Figures 9 .

 9 Figures 9.26 to 9.35 display the velocity magnitude for the X-aligned positions, grouped for each approach. The numerical configuration here is the one with background airflow. It is also remined that in the numerical simulation, Positions 2-3-4 'B only' are passed at the time as Positions 7-8-9 'A only' (at a higher speed of the train), and Positions 6-7-8 'B only' are passed at the same time as Positions 2-3-4 'A only' (at a lower speed of the train).

Figure 9 .Figure 9 . 37 :Figure 9 . 38 :Figure 9 . 39 :

 9937938939 Figure 9.36: Numerical velocity contours with streamtraces and vectors at t = 13.5 s.

Figure 9 .

 9 Figure 9.40: Picture of the tunnel near the station.

  (a) Realistic staircase. (b) Simplified staircase.

Figure 9 . 41 :

 941 Figure 9.41: Simplification of the geometry from [83].

Figure 9 . 42 :

 942 Figure 9.42: Calibration curve of the hot wire anemometer, with correction for temperature.

Figure 10 . 1 :-Figure 10 . 2 :

 101102 Figure 10.1: Velocity sequence executed by the train for three different cruise speeds.

Figure 10 . 3 :

 103 Figure 10.3: Mass flow rates through the door R1.

Figure 10 . 4 :

 104 Figure 10.4: Mass flow rates through the door R2.

Figure 10 . 5 :

 105 Figure 10.5: Mass flow rates through the door R3.

Figure 10 . 6 :

 106 Figure 10.6: Mass flow rates through the door L1.

Figure 10 . 7 :

 107 Figure 10.7: Mass flow rates through the door L2.

Figure 10 . 8 :

 108 Figure 10.8: Mass flow rates through the door L3.

Figure 10 . 9 :

 109 Figure10.9: Schematic BOS acquisition setup (adapted from[START_REF] Raffel | Background-oriented schlieren (BOS) techniques[END_REF]).

Figure 10 .

 10 Figure 10.10: Close-up of speckle background used for the experiments.

Figure 10 .

 10 Figure 10.11: BOS acquisition setup in the lab.

  (a) Image number: 50. (b) Image number: 60.

Figure 10 . 12 :

 1012 Figure 10.12: Raw BOS images.

  Image number: 150. (b) Image number: 175. (c) Image number: 200. (d) Image number: 225.

Figure 10 . 13 :

 1013 Figure 10.13: Image displacements computed from BOS images.

Figure A. 2 :

 2 Figure A.2: 'A only': Single train passing along side A.

( a )

 a Woolen thread. (b) Webcam and ring light.

Figure B. 1 :

 1 Figure B.1: Wind direction sensor on the measurement cart.

Figure B. 2 :

 2 Figure B.2: First lines of a text file of data recorded during the experimental campaign.

D. 2 Figure D. 2 :

 22 Figure D.2: Velocity sequence executed by the train with a cruise speed of 7 m/s.

F. 2

 2 Remove background / unsteady reflections (a) Sliding average. (b) Sliding minimum. (c) Directional minimum.

Figure F. 3 :

 3 Figure F.3: Images processed with the remove background / unsteady reflections filter, for different types of filters. Image number: 60.

F. 5 . 3

 53 Size of the interrogation window (a) 48×48 pixels. (b) 24×24 pixels. (c) 12×12 pixels. (d) 8×8 pixels.

Figure F. 8 :Figure G. 1 :

 81 Figure F.8: Velocity fields processed with different interrogation window sizes. Image number: 60 -Color scale: 0 m/s to 0.70 m/s.

Figure G. 5 :Figure G. 6 :Figure G. 7 :Figure G. 8 :Figure G. 9 :Figure G. 10 :Figure G. 11 :Figure G. 12 :Figure G. 13 :Figure G. 14 :Figure G. 15 :Figure G. 16 :Figure G. 17 :Figure G. 18 :Figure G. 19 :

 5678910111213141516171819 Figure G.5: Velocity magnitude for scenario 'A only' at Position 4.

Table of Contents

 of Context and motivation of the research . . . . . . . . . . . . . . . 1 1.2 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Main related publications . . . . . . . . . . . . . . . . . . . . . .5 Aerodynamics of trains . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Specificities of subway climate . . . . . . . . . . . . . . . . . . . 10 2.2.1 Piston effect . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Background airflow . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Ventilation of a subway station . . . . . . . . . . . . . . . 13 2.3 Experimental and numerical characterization of tunnel and station airflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Numerical simulations . . . . . . . . . . . . . . . . . . . 14 2.3.2 Experimental measurements and use in validation of numerical models . . . . . . . . . . . . . . . . . . . . . . . 15 7.13 Contours of air velocity magnitude in the station during train arrival at t = 11 s, 13.5 s, 16 s, 20.5 s, 26 s and 35 s. . . . . . . . . . 7.14 Contours of air velocity magnitude in the station during train departure at t = 58 s, 60.5 s, 64 s, 66 s, 69 s and 72.5 s. . . . . . . . . 7.15 Velocity evolution for various implementations of background wind in the numerical simulation, at chosen locations on the platform. . 7.16 Velocity evolution for Z = 0.5 m and Z = 1.6 m in the numerical simulation, at chosen locations on the platform. . . . . . . . . . . 7.17 Contours of air velocity magnitude in the station in two Z-slices around Position 9 at 18.5 s, with streamtraces in a vertical rake at Position 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.18 Photograph of experimental apparatus, in the study of Kim and Kim [52]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.19 C p variations at different locations from the 39-meters-long-tunnel entrance, in the study of Kim and Kim [52]. . . . . . . . . . . . . 7.20 C p variations at different locations from the 200-meters-long-tunnel entrance, in the CFD model including the station. . . . . . . . . . 7.21 Schematic illustration of a mesh with an immersed body (IB) de-

	Acknowledgment	i
	Table of Contents	iii
	List of Figures	ix
	List of Tables	xvii
	List of Acronyms	xix
	List of Symbols	xxi
	Résumé en franc ¸ais	xxv
	English summary	xxvii
	1 Introduction	1
	1.1 I Of the tools and methods	7
	2 Aeraulic effects in underground subway stations and their numerical
	models	9
	2.1

fined for IBM (from

[START_REF] Jasak | Immersed Boundary Method in FOAM -Theory, Implementation and Use[END_REF]

). . . . . . . . . . . . . . . . . . . . . . 7.22 Velocity magnitude for scenario 'B only' at Position 5, with CFX results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.23 Velocity magnitude for scenario 'B only' at Position 8, with CFX results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  . . . . . . . . . . . . . . . . . . . . . 8.21 Geometric mask: shape drawn on the acquired images. . . . . . . 8.22 Geometric mask: result. . . . . . . . . . . . . . . . . . . . . . . . 8.23 Image obtained after the application of the subtract time filter (subtract minimum, filter length: 3 images). . . . . . . . . . . . . . . 8.24 Image obtained after the application of the remove background/ unsteady reflections filter (directional minimum). . . . . . . . . . 8.25 Vector field obtained after the application of the spatial automask (set at 8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.26 Details of vector fields processed with different interrogation window sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.27 Vector fields in the middle of the left part of the station, during train arrival, for 3 successive frames. . . . . . . . . . . . . . . . . 8.28 PIV velocity contours, for 'Arrival' acquisitions, the laser illumi-.32 Example of images corresponding to triggers. . . . . . . . . . . . 8.33 Post-processing steps of the PIV measurements, example at Position 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.34 Average PIV velocity with ±2σ and average triggers, for Position 1. 8.35 Average PIV velocity with ±2σ and average triggers, for Position 2. 8.36 Average PIV velocity with ±2σ and average triggers, for Position 3. 8.37 Average PIV velocity with ±2σ and average triggers, for Position 4. 8.38 Average PIV velocity with ±2σ and average triggers, for Position 5. 8.39 Average PIV velocity with ±2σ and average triggers, for Position 6. 8.40 Average PIV velocity with ±2σ and average triggers, for Position 7. 8.41 Average PIV velocity with ±2σ and average triggers, for Position 8. 8.42 Average PIV velocity with ±2σ and average triggers, for Position 9. 9.1 Schematic top view of the station, with measurements locations on Platform A (up) and Platform B (down) (reproduced from Chapter 7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Velocity magnitude for scenario 'A only' at Position 1. . . . . . . 9.3 Velocity magnitude for scenario 'A only' at Position 3. . . . . . . 9.4 Velocity magnitude for scenario 'A only' at Position 5. . . . . . . 9.5 Velocity magnitude for scenario 'A only' at Position 7. . . . . . . 9.6 Velocity magnitude for scenario 'A only' at Position 9. . . . . . . 9.7 Velocity magnitude for scenario 'B only' at Position 1. . . . . . . 9.8 Velocity magnitude for scenario 'B only' at Position 3. . . . . . . 9.9 Velocity magnitude for scenario 'B only' at Position 5. . . . . . . 9.10 Velocity magnitude for scenario 'B only' at Position 7. . . . . . . 9.11 Velocity magnitude for scenario 'B only' at Position 9. . . . . . . 9.12 Examples of peaks compared. . . . . . . . . . . . . . . . . . . . .30 On-site recorded velocity magnitude for scenario 'B only' at Positions 2-3-4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.31 Numerical velocity magnitude for scenario 'B only' at Positions 2-3-4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.32 PIV measured velocity magnitude for scenario 'B only' at Positions 2-3-4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.33 On-site recorded velocity magnitude for scenario 'B only' at Positions 6-7-8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.34 Numerical velocity magnitude for scenario 'B only' at Positions 6-7-8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.35 PIV measured velocity magnitude for scenario 'B only' at Positions 6-7-8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.36 Numerical velocity contours with streamtraces and vectors at t = 13.5 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.37 PIV velocity contours and vectors around the train head, image number: 71. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.38 Numerical velocity contours with streamtraces and vectors at t = 14.5 s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.39 PIV velocity contours and vectors around the train head, image number: 86. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.40 Picture of the tunnel near the station. . . . . . . . . . . . . . . . . 9.41 Simplification of the geometry from [83]. . . . . . . . . . . . . . 9.42 Calibration curve of the hot wire anemometer, with correction for temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

nating the left side. . . . . . . . . . . . . . . . . . . . . . . . . . 8.29 PIV correlation, for 'Arrival' acquisitions, the laser illuminating the left side (black corresponds to correlation of 1, white to a correlation of 0). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.30 PIV velocity contours, for 'Arrival' acquisitions, the laser illuminating the right side. . . . . . . . . . . . . . . . . . . . . . . . . 8.31 PIV correlation, for 'Arrival' acquisitions, the laser illuminating the right side (black corresponds to correlation of 1, white to a correlation of 0). . . . . . . . . . . . . . . . . . . . . . . . . . . 89.13 Peak magnitude for 'A only'. . . . . . . . . . . . . . . . . . . . . 9.14 Skewness for 'A only'. . . . . . . . . . . . . . . . . . . . . . . . 9.15 Kurtosis for 'A only'. . . . . . . . . . . . . . . . . . . . . . . . . 9.16 Peak magnitude for 'B only'. . . . . . . . . . . . . . . . . . . . . 9.17 Skewness for 'B only'. . . . . . . . . . . . . . . . . . . . . . . . 9.18 Kurtosis for 'B only'. . . . . . . . . . . . . . . . . . . . . . . . . 9.19 Peak magnitude for 'A only', with background airflow. . . . . . . 9.20 Skewness for 'A only', with background airflow. . . . . . . . . . . 9.21 Kurtosis for 'A only', with background airflow. . . . . . . . . . . 9.22 Peak magnitude for 'B only', with background airflow. . . . . . . 9.23 Skewness for 'B only', with background airflow. . . . . . . . . . . 9.24 Kurtosis for 'B only', with background airflow. . . . . . . . . . . 9.25 Contours of air velocity magnitude and streamtraces in the back of the train at t = 66s. . . . . . . . . . . . . . . . . . . . . . . . . . 9.26 On-site recorded velocity magnitude for scenario 'A only' at Positions 2-3-4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.27 Numerical velocity magnitude for scenario 'A only' at Positions 2-3-4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.28 On-site recorded velocity magnitude for scenario 'A only' at Positions 6-7-8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.29 Numerical velocity magnitude for scenario 'A only' at Positions 6-7-8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

  Results at chosen locations for correlation and peak value of vector fields, from images processed with different interrogation window shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F.4 Results at chosen locations for correlation and peak value of vector fields, from several passes. . . . . . . . . . . . . . . . . . . . . .

	xxii
	V	Object velocity		[m • s -1 ]
	X, Y, Z	Cartesian coordinates		[m]
		List of Acronyms List of Symbols
	BC Constants	Boundary Condition
	bg. R	bakground (airflow) Universal gas constant	8.3145 [J • mol -1 • K -1 ]
	CFD g	Computational Fluid Dynamics Gravitational acceleration	9.81 [m • s -2 ]
	2D Roman symbols Two-dimensional
	3D A	Three-dimensional Area		[m 2 ]
	DNS Ah	Direct Numerical Simulation Ampere-hour		[Ah]
	FVM C p	Finite Volume Methode Pressure coefficient		[-]
	HWA D	Hot Wire Anemometry or Hot Wire Anemometer Diameter	[m]
	IBM f	Immersed Boundary Method Frequency		[Hz]
	LDV I	Laser Doppler Velocimetry Electrical current		[A]
	LES L	Large Eddy Simulation Length		[m]
	MIVB M	Maatschappij voor het Intercommunaal Vervoer te Brussel Molar volume	[m 3 /kg]
	PIV M a	Particle Image Velocimetry Mach number		[-]
	PM P	Particulate Matter Perimeter		[m]
	RANS p	Reynolds-Averaged Navier-Stokes Pressure		[Pa]
	STIB R	Société des Transports Intercommunaux de Bruxelles Electrical resistance	[Ω]
	TR r	Time-Resolved Pearson correlation coefficient		-
	UDF Re	User Defined Function Reynolds number		[-]
	SNR T	Signal-to-Noise Ratio Temperature	[K] or [°C]
	U	Flow velocity		[m • s -1 ]
	u, v, w	Velocity components in Cartesian coordinates		[m • s -1 ]
	u x , u y , u z Velocity components in Cartesian coordinates		[m • s -1 ]

Table 5 .

 5 1: Blockage ratios for the test case.

		one train	two trains
	in tunnel	32 %	65 %
	in station	17 %	34 %

Table 6 .

 6

	Position	Day	Date	x [m]	y [m]
	1	4	February 9, 2021	5.7	-1.45
	2	3	February 4, 2021	25.5	-1.50
	3	2	February 3, 2021	23.5	-2.50
	4	1	February 2, 2021	23.5	-3.50
	5	5	February 10, 2021	59.0	-1.90
	6	6	February 11, 2021	69.0	-1.45
	7	9	February 18, 2021	69.0	-1.90
	8	8	February 17, 2021	69.0	-3.10
	9	7	February 16, 2021	90.1	-1.45

1: Cart positions on Platform B and corresponding days.

Table 6 . 2

 62

	Position	'A only'	'B only'	'A then B'	'B then A'
	1	13	13	1	1
	2	33	28	5	3
	3	24	25	10	7
	4	12	11	0	1
	5	38	34	6	3
	6	34	31	7	8
	7	32	31	5	1
	8	32	27	7	9
	9	28	28	6	6

: Amount of datasets measured per scenario at every location.

Table 6 . 3

 63

	Position	Tstation [°C]	T mean outside [°C] v mean outside wind [m/s]
	1	7	-6	4.2
	2	-	8	3.4
	3	-	9	4.7
	4	-	8	4.6
	5	8	-5	4.0
	6	8	-4	3.2
	7	14	8	6.2
	8	12	10	5.1
	9	13	9	5.0

: Weather during the measurement campaign.

Table 6

 6 Table 6.4: Average triggers measured on-site for 'A only' and 'B only'.

	.4.

Table 7 .

 7

			-1.45	94.3	7.95
	2	25.5	-1.50	74.5	7.0
	3	23.5	-2.50	76.5	9.0
	4	23.5	-3.50	76.5	10.0
	5	59.0	-1.90	41.0	8.40
	6	69.0	-1.45	31.0	7.95
	7	69.0	-1.90	31.0	8.40
	8	69.0	-3.10	31.0	9.60
	9	90.1	-1.45	9.9	7.95

1: Measurement positions on Platform A and Platform B.

Table 7 . 2

 72

	tenters	10.70 s
	tstops	26.75 s
	t leaving	56.75 s
	t lef t	68.75 s

: Triggers for base-scenario train run through the station.

Table 7 .

 7 [START_REF]Ansys Fluent User's Guide -Release[END_REF], where the value is given as the gauge pressure. The station and train walls are set as stationary walls respecting the no-slip condition.

	Boundary	Type	Value
	Tunnel inlet	Pressure inlet	0 Pa
	Tunnel outlet	Pressure outlet	0 Pa
	R1	Pressure inlet	0 Pa
	R2	Pressure outlet	0 Pa
	R3	Pressure outlet	0 Pa
	L1	Pressure inlet	0 Pa
	L2	Pressure outlet	0 Pa
	L3	Pressure outlet	0 Pa

Table 7 .

 7 3: Boundary conditions at the exits (value given as gauge pressure).

Table 7 .

 7

	Boundary	Type	Value
	Tunnel inlet	Pressure inlet	+2 Pa
	Tunnel outlet	Pressure outlet	-2 Pa
	R1	Pressure inlet	+0.7 Pa
	R2	Pressure outlet	0 Pa
	R3	Pressure outlet	-0.7 Pa
	L1	Pressure inlet	+0.8 Pa
	L2	Pressure outlet	0 Pa
	L3	Pressure outlet	-0.8 Pa

4: Boundary conditions at the exits, including background airflow (value given as gauge pressure).

Table 7 .

 7

	Width Yt [m] Height Zt [m]	β	DH [m]	Vtrain [m/s] Re [×10 6 ]
					3.85	1.30
					7.5	2.53
	6.17	4.1	0.37	4.93	10.22	3.45
					12.5	4.22
					15	5.06
					20.7	6.98
	6.5	4.8	0.30	5.52	9.12	3.45
					10.22	3.86
	5.0	4.1	0.46	4.50	10.22	3.15
					11.17	3.45

5: Geometrical and dynamical settings for the configurations of a train running through a 1000 meters long tunnel.

Table 7 .

 7

		3D middle Experimental
	2D	63.2%	27.5%
	3D coarse	26.2%	35.5%
	3D middle	-	31.9%
	3D fine	7.9%	32.0%

7: Relative difference in peaks magnitude for compared meshes.

  .8.

	Parameter	Setting
	Numerical algorithm	Pressure-Based
	Transient formulation	1st-Order Implicit
	Pressure-Velocity Coupling SIMPLE
	Discretization Scheme	2nd-Order Upwind
	Fluid material	Air
	Table 7.8: Numerical solver parameters.

Table 7 .

 7 displays the cases showing the most difference in peak magnitude.

	Position	A only		B only
		Arrival	Departure	Arrival	Departure
	1	0.7 %	6.2 %	7.2 %	13.2 %
	2	<0.1 %	1.7 %	1.0 %	14.0 %
	3	<0.1 %	2.1 %	0.7 %	17.3 %
	4	4.5 %	13.9 %	1.1 %	11.6 %
	5	0.2 %	17.0 %	1.5 %	0.5 %
	6	0.4 %	6.0 %	3.9 %	1.1 %
	7	0.2 %	5.4 %	1.4 %	0.3 %
	8	0.4 %	1.1 %	1.3 %	1.4 %
	9	0.1 %	6.2 %	51.0 %	3.4 %

9:

Relative difference between peak magnitudes for Z = 0.5 m and Z = 1.6 m.

Table 8 .

 8 .2.

		BRAWA 44601 Full scale train
	Length (X) [mm]	780	90 000
	Width (Y) [mm]	33.1	2 700
	Height (Z) [mm]	40.5	3 500
	Cruise speed [m/s]	0.66	10.2
	Voltage supply [V]	18	900

1: Main characteristics of the small-scale train and the real train.

Table 8 .

 8 2: Scaling factors in all three directions.

	Length (X)	115.5
	Width (Y)	81.6
	Height (Z)	87.3

Table 8 .

 8 .11). 3: Summary of PIV configurations and amount of datasets recorded.

	Laser position	Scenario	Number of datasets Positions studied
	Left side	Arrival Departure	8 8	1 to 4
	Right side	Arrival Departure	8 8	5 to 9

Table 8 . 5

 85

	tenters,P IV	0.13 s
	tstops,P IV	1.49 s
	t leaving,P IV	0.21 s
	t lef t,P IV	1.84 s

: Average triggers for the PIV measurements.

Table 9 .

 9 1: Goodness of fit for the aligned numerical and on-site experimental curves, around arrival and departure time.

	Scenario	Arrival		Departure
			Delay [s]	r²	Delay [s]	r²
	No wind	A only B only	1.48 1.60	0.34 0.41	0.26 0.54	0.75 0.64
	With wind	A only B only	1.66 1.06	0.62 0.49	0.13 0.89	0.49 0.27

Table 10 .

 10

	Width Yp [m] Height Zp [m]	β	DH [m]	Vtrain [m/s] Re [×10 6 ]
					7.5	2.53
	4	2.5	0.21	4.96	7.5	3.45
					12.5	4.22
					7.5	2.53
	2.5	2.5	0.25	4.95	7.5	3.45
					12.5	4.22

1: Geometrical and dynamical settings for the configurations of a train running through stations of varying platform dimensions.

Table B .

 B 1: Messages sent by the train detection modules.

	Sensor	Message	Meaning	Sensor	Message	Meaning
	A1 0 → 1	aaaaa	Train detected	B1 0 → 1	ggggg	Train detected
	A2 0 → 1	ccccc	Train detected	B2 0 → 1	iiiii	Train detected
	A2 1 → 0	ddddd	Train passed	B2 1 → 0	jjjjj	Train passed
	A3 0 → 1	eeeee	Train detected	B3 0 → 1	kkkkk	Train detected
	A3 1 → 0	fffff	Train passed	B3 1 → 0	lllll	Train passed

  (δU cal ) 2 + (δU P IV ) 2 + (δU turb ) 2Table C.1: Results regarding the uncertainty analysis of the hot wire anemometer D

	v [m/s]	δU v [m/s]	δU cal [m/s]	δU P IV [m/s]	δU hw [m/s]
	0.75	0.3969	0.1838	0.02	0.49
	0.81	0.3969	0.1838	0.05	0.49
	1.40	0.3969	0.1838	0.09	0.49
	2.02	0.3969	0.1838	0.16	0.51
	2.70	0.3969	0.1838	0.20	0.53
	4.05	0.3969	0.1838	0.29	0.57
	5.18	0.3969	0.1838	0.45	0.66
	6.25	0.3969	0.1838	0.53	0.72
	7.60	0.3969	0.1838	0.69	0.84
	8.55	0.3969	0.1838	0.75	0.89
	9.36	0.3969	0.1838	1.07	1.18
	10.96	0.3969	0.1838	0.97	1.09
	11.40	0.3969	0.1838	0.64	0.80
	12.03	0.3969 User Defined Functions for train 0.1838 0.85 0.98
				velocity

Part I

Of the tools and methods

Vector field calculation results

The velocity contours calculated from the raw images previously given in Figure 8. [START_REF] Bubbico | CFD analysis of the dispersion of toxic materials in road tunnels[END_REF] ) are meant to be seen side-by-side, so that the correlation map on one page corresponds to the correlation map on the opposite page.-, with coordinates being the same on each page.] Although the second frame (corresponding to the camera on the side which the laser was not centered on) is not displayed on Figure 8.19, it is still acquired and a stitching is realized between both frames during the PIV calculation, hence giving theoretically a view of the entire station. The weak illumination on one side, however, results in a poor correlation value, and hence in large areas where the vectors have been filtered. δU v The accuracy of the instrument was defined by δU v , which is equal to the product of the calibration curve slope and the resolution of the hot wire anemometer (δU v = δU δv • δV ). As the calibration curve was not linear, slopes at different points along the curve were calculated. The accuracy of the ComfortSense Mini by Dantec Dynamics is equal to 0.15 V for low airflow velocities [START_REF]ComfortSense Mini -Robust and compact anemometer for ventilation and draught measurements[END_REF]. The average uncertainty caused by the voltage measurement δU v was defined as 0.3969 m/s. δU cal It was important to consider the fitting of the calibration curve relative to the measurement points. The formula below was used to calculate the statistical error with 95 % accuracy:

Part IV

General conclusions

1448 and N = 14. δU cal was calculated to be 0.1838 m/s. δU P IV The accuracy of the PIV measurements was taken into account as well. The file including the PIV velocity results provided the standard deviation of the measurements.

δU turb

The influence of the turbulence was neglected due to its small contribution to the overall uncertainty of the hot wire.

The results of the influencing factors and the total uncertainty of the hot wire anemometer measurements are presented in Table C The discussion related to the content of this appendix is available in Section 8.2.4.

To ease the reading of the tables, the highest value of correlation and peak ratio for each rectangle is written in bold. For each parameter, the image with the caption written in bold corresponds to the chosen option.

Filter length Correlation

First filter Correlation