M Siroux

J.-B Bouvenot

B Latour

MODELING AND EXPERIMENTAL ANALYSIS OF MICRO COMBINED HEAT AND POWER SYSTEMS COUPLED WITH RESIDENTIAL BUILDINGS

Keywords: Energy Technologies, Micro combined heat and power, modeling, experimentations, heat storage IFHT2016-1858

The micro combined heat and power (µCHP) is a technology which produces simultaneously decentralized thermal and electrical energy at low power (electrical power lower than 50 kW el ). This technology recovers the "fatal heat" losses considered as "heat waste" produced in thermodynamics cycles for mechanic energy production. Micro-CHP technology offers significant benefits: reduced primary energy consumptions, reduced CO2 emissions, avoidance of central plant and network construction. A wood pellet steam engine and a gas Stirling engine micro-CHP devices have been tested at the Climatherm laboratory of INSA Strasbourg in order to characterize their performances in steady and unsteady states. Two dynamic models based on these experimental investigations have been developed in order to predict their energy performance. These models have been implemented in the TRNSYS's numerical environment where an optimization platform has been implemented. Thermal and electrical energy storage systems and energy management controller have been implemented in this platform which is used to optimize the coupling between buildings and the micro combined heat and power devices by considering energetic, economic and environmental criteria. This work presents the micro combined heat and power systems, the simulation platform, the energy storage systems and the control strategies possibilities. We also show how the thermal sensitivity of the French energetic mix correlates the economic, environmental and energetic performances of the micro combined heat and power systems.

INTRODUCTION

The µCHP systems are based on different technologies for power generation, the main technologies are: micro gas turbines, Stirling engines, Ericsson engines (studied but not yet used), internal combustion engines, steam engines, micro (organic or not) Rankine turbines and fuel cells [START_REF] Bianchi | Guidelines for residential micro-CHP systems design[END_REF]. The figure 1 presents a performance mapping of existing technologies and shows different "families". The most electrically efficient systems are also the less flexible systems and the less globally efficient systems because of their complexity (difficulty to recover latent heat for the internal combustion engine (ICE), reformer processing for fuell cells (FC), unburned gas for ICE, etc.). For example, some fuel cells have to continuously operate although Stirling engines can be triggered freely. In this work, we focus on "flexible" technologies and more precisely on Stirling engines and Steam engines.

EXPERIMENTAL STUDY

Among the µCHP technologies, a gas Stirling engine and a biomass steam engine have been tested at the laboratory of INSA Strasbourg in order to characterize their performances in steady and unsteady states (cf. Fig. 2 & 3) [START_REF] Bouvenot | Gas Stirling engine μCHP boiler experimental data driven model for building energy simulation[END_REF][START_REF] Bouvenot | Dynamic model based on experimental investigations of a wood pellet steam engine µCHP for building energy simulation[END_REF]. In particular, boundary conditions (inlet temperature, mass flow rate and part load ratio) influence and dynamic responses have been investigated [START_REF] Bouvenot | Gas Stirling engine μCHP boiler experimental data driven model for building energy simulation[END_REF][START_REF] Bouvenot | Dynamic model based on experimental investigations of a wood pellet steam engine µCHP for building energy simulation[END_REF].

NUMERICAL TOOL DEVELOPMENT

To study the coupling between µCHP systems and residential buildings, a numerical tool has been developed in the TRNSYS environment with realistic and dynamic criteria. This tool is presented at Fig. 4 where we distinguish the "thermal loop" at the top, the "electrical loop" at the bottom and each component with the links between the blocks. This tool is aimed to compute energy, environmental and economic calculation at low time steps (1 min).

µCHP models

The µCHP numerical models have been developed in order to be suitable with annual dynamic thermal simulations. They are based on experimental studies which led to semi physical and dynamic models [START_REF] Bouvenot | Gas Stirling engine μCHP boiler experimental data driven model for building energy simulation[END_REF][START_REF] Bouvenot | Dynamic model based on experimental investigations of a wood pellet steam engine µCHP for building energy simulation[END_REF]. In particular, the fuel power inputs and the thermal ( ) and electrical power outputs in steady state are given by the following correlations according to the inlet cooling water temperature , , to the water mass flow and to the part load ratio (the coefficients a, b, c, d, e, f, g, h and i are constant values determined from experimental studies):

• Gas Stirling engine µCHP :

= + , - , + ( - ) (1) = + " , - , + # ( - ) (2) = + $ , - , + % ( - ) (3)
• Biomass steam engine µCHP :

= & ( - ) + (4) = ℎ( - ) + (5) = ( ( - ) + (6)

Energy storage systems (ESS)

The tool integrates thermal energy storage systems (TESS) models and electrical energy storage systems (EESS) models. The TESSs are simulated by multi-nodes cylindrical vertical buffer tanks (existing type 534 on TRNSYS). The model parameters are the tank volume, the tank height, the heat loss coefficient of the walls, the number of tank nodes, the number and the location of the ports (cold water entry, heating water entry/exit, heater network entry/exit and DHW exit). The EESS are simulated by electrical batteries models which are either static (basic storage) or mobile (because embedded in electric cars). Specific models have been modelled on TRNSYS by using data from literature [START_REF] Eddahech | Modélisation du vieillissement et détermination de l'état de santé de batteries lithium-ion pour application véhicule électrique et hybride[END_REF][START_REF] Ruellan | Solutions de stockage de l'énergie pour les systèmes de production intermittente d'électricité renouvelable[END_REF][START_REF] Wiaux | The Lithium-ion battery -Service life parameters[END_REF]. EESS models parameters are the charge efficiency, the calendar losses, the depth of discharge (DOD) influence (cf. Fig. 5), the cycling losses (cf. Fig. 6) , the maximum number of cycles, the maximum specific power, the minimum state of charge and a presence scenario (if electrical car). µCHP

IFHT2016-1858

Fig. 5 Depth of discharge (DOD) influence. Fig. 6 Cycling impact on maximum state of charge (SOC).

Heating loads

The tool proposes 8 climatic zones defined in the French thermal regulation whose choice involves the use of a specific real 15 min time step meteorological file for a given year (2010 to 2014) of a city located in the climatic zone. Besides, buildings are classified according to their energetic performance and surface. We distinguish 6 energy classes defined in the French thermal regulation according to their thermal needs (see Table 1):

Table 1 Building energy classes.

class A B C D E F G
Thermal needs (kWhFE/m²) <50 <75 <150 <200 <250 <350 <500

DHW loads

There are two French standard methods for calculating the DHW needs: the AICVF method [START_REF] Aicvf | Eau chaude sanitaire : maîtriser énergie, confort, santé. Recommandation[END_REF] which gives typical bailing profiles smoothed over the day and the method described in EN 13203-2 standard [START_REF] Afnor | NF-EN 13203-2, Gas-fired domestic appliances producing hot water -Appliances not exceeding 70 kW heat input and 300 litres water storage capacity -Part 2[END_REF] which gives typical profiles of water withdrawing with are occasional at precise hours of the day (any day of the year) for 2 types of dwelling (dwelling of 3 or 5/6 inhabitants). These profiles are not appropriate here since they are not enough realistic and variable. To incorporate variability, DHW needs are calculated stochastically by a generator similar to the power generator (see § 3.5). The generator uses a "bottom up" approach by aggregating each type of withdrawing (shower, cleaning, washing, bathing, etc.) characterized by a draw-off time (variable according to a standard normal distribution around the mean time), a withdrawing temperature (constant and variable depending on the use) and a withdrawing flow rate (variable according to a standard normal distribution around the mean flow). The generator is based on the work of Jordan and Vajen [START_REF] Jordan | Influence of the DHW load profile on the fractional energy savings: a case study of a solar combi-system with TRNSYS simulations[END_REF] on the modeling of DHW needs for solar applications. The probability profiles of drawoff occurrence are derived from the profiles of the AICVF method [START_REF] Aicvf | Eau chaude sanitaire : maîtriser énergie, confort, santé. Recommandation[END_REF] and the work of Jordan and Vajen [START_REF] Jordan | Influence of the DHW load profile on the fractional energy savings: a case study of a solar combi-system with TRNSYS simulations[END_REF]. The generator offers 2 DHW consumption levels (high and low) based on data from NF EN 13203-2 [START_REF] Afnor | NF-EN 13203-2, Gas-fired domestic appliances producing hot water -Appliances not exceeding 70 kW heat input and 300 litres water storage capacity -Part 2[END_REF].

Electrical loads

The specific electrical needs (excluding any electrical heating) are a crucial factor to assess the energetic, environmental and economic relevance of µCHP solutions. There are several databases for electrical needs for countries in North America or Europe specifically dedicated to studies on µCHP or micro generation [START_REF] Knight | European and Canadian non-HVAC electric and DHW load profiles for use in simulating the performance of residential cogeneration systems[END_REF]. However, these data are not suited to our tool in the French context, especially about the time step, the level of detail and the geographic context, that's why we develop our own tool to generate random electrical needs profiles using a 1 minute time step. This generator is based on statistical profiles of frequency of use: "time of use" method (TOU). It aggregates the power consumption of each electrical appliance based on use probabilities depending on the time of the day, the type of day (week end or week days) and the season: it's a

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"bottom-up" method as described by Grandjean et al. [START_REF] Grandjean | A review and an analysis of the residential electric load curve models[END_REF]. The operating time is variable and follows a standard normal distribution around the mean duration. All statistics used come from the measurement campaign at European level: REMODECE [START_REF]Residential Monitoring to Decrease Energy Use and Carbon Emissions in Europe (REMODECE)[END_REF]. The generator creates unique profiles by separating nonshifting from the shifting part, which enables intelligent energy management according to 2 input parameters: the dwelling level of appliance based on REMODECE data [START_REF]Residential Monitoring to Decrease Energy Use and Carbon Emissions in Europe (REMODECE)[END_REF] (low, medium and high) and the electrical appliances energy class based on the European directive 92/75/ EEC [13]. Fig. 7 shows an example of the stochastic power consumption profile generated for a winter day in the case of a high appliance level and a B energy class.

DISCUSSIONS

In the European context, centralized electricity generation is marked by strong hourly-seasonal variations with temperature sensitive behavior; that is to say that the production correlates with the outside temperature. Indeed, the harsh climate in winter increases the need for heating and lighting at about 2.4 GW el /°C in 2014 in France [START_REF] Rte | [END_REF] (cf. Fig. 8) which requires the triggering of peak power plants. This thermoelectric gradient is particularly marked in France compared to the major European neighbors (cf. Fig. 8). In parallel, the electrical production of a µCHP device is also marked by a temperature-sensitive behavior. The numerical tool shows this thermal sensitivity on µCHP electrical production with a limit linked to the sizing and to the building (cf. Fig. 9). Indeed, if a µCHP system is controlled according to the heating demand, its concomitant power generation will follow the same behavior with a more frequent operation for low outside temperatures.

IFHT2016-1858

Thus, µCHP systems differently impact the grid compared to separate heat production systems. For example, a thermal gas generator consumes power only via its auxiliary devices or an electrical heater consumes electricity in proportion to the heating needs while µCHP will produce electricity in proportion to the heating needs and relieve the grid with a "natural" and well predictable production capacity. Eventually, a judicious mix of µCHP systems is a welcome solution to compensate for seasonal phenomenon and avoid the use of peak power plants.

CONCLUSIONS

2 innovative µCHP systems have been tested. A numerical tool on the coupling between µCHP systems and residential buildings has been developed. This tool is based on experimental results on these 2 µCHP systems which fed 2 numerical models. All the energy needs and all the others components are also modelled. This numerical tool is aimed to compute energetic, environmental and economic to prove and maximize the relevance of µCHP systems in the French context.

NOMENCLATURE

Fig. 1

 1 Fig. 1 Correlation between electrical, global efficiencies and technology complexity of existing systems.

Fig. 2 Fig. 3

 23 Fig. 2 Gas Stirling engine dynamic test bench. Fig. 3 Biomass steam engine dynamic test bench.

Fig. 4

 4 Fig. 4 Numerical tool principle scheme on TRNSYS.

N = 1 ,091E 7 DOD - 1

 171

Fig. 7

 7 Fig. 7 Sample of stochastic electrical loads (thermal and electrical).

Fig. 8

 8 Fig. 8 Power thermal sensitivity in Europe. Fig. 9 Thermal sensitivity of a µCHP power production


T Deloze
email: tdeloze@imft.fr

Yannick Hoarau
email: hoarau@unistra.fr

M Chinaud

Johannes Scheller

E Deri

Jean-François F Rouchon

Eric Duhayon

Marianna Braza
email: marianna.braza@imft.fr

Dynamic Effect of an Active Deformable Flat Plate on Its Turbulent Flow

Keywords: turbulence, flat plate, shape memory alloys, deformation

come

Introduction

The interest for micro and nano air vehicles is increasing in recent years. Their development open some problems in aerodynamics, as the control, with demanding constraints, such as weight. Meanwhile during the last ten years, many morphing materials have been developed and studied. These materials have opened new opportunities in fluid mechanic applications as morphing wing. The shape of an airfoil can be locally modified by this morphing technology. In this work, we focus on the dynamic effect of the deformation imposed by morphing material on a turbulent flow. The final goal is an optimised integration into the flight controls of micro airplane.

The numerical present study is based on the turbulent flow around a flat plate at incidence with untapered edges. The flat plate is equipped with Shape Memory Alloys (SAM) that allow dynamic morphing by electric power. The deformation is an camber of the plate with uniform deformation in the span direction. The first part of the study aims at the analysis of the 3-dimensional wake behind a flat plate at incidence with an attention to capture the vortex shedding and the shear layer with numerical results. This focus is motivated by the harmful effect of the both phenomena on the aerodynamic performance and on the noise production. Then the influence of the shape is examined in 2-dimensional simulations, to determine the effect of the curve shape profiled by the SAM equipment compared to the linear shape. At the last, the dynamic effect on the flow is discussed with 2-dimensional simulations.

Configuration

The configuration is defined by a previous experimental study performed at the Institut de Mécaniques des Fluides de Toulouse (E. Deri et al. [START_REF] Deri | Investigation of the threedimensional turbulent near-wake structure past a flat plate by tomographic piv at high reynolds number[END_REF]). The experiment involves a flat plate (cf. figure 1) with an aspect ratio of 20 (width (l) over thickness (h)), an angle of incident of 10 degrees and a turbulent flow characterized by the Reynolds number of 200 000 based on the freestream flow velocity (U ), the width of the plate and the kinematic viscosity (ν). The experiments (cf. figure 2) have been carried out in the S4 wind tunnel and the results are obtained by 3D tomographic PIV (E. Deri et al. 2012 [START_REF] Deri | Investigation of the threedimensional turbulent near-wake structure past a flat plate by tomographic piv at high reynolds number[END_REF]) for a rigid plate (without deformation). The Proper Orthogonal Decomposition (POD) was performed and the higher modes show the Von Karman pattern. The tomographic PIV results are obtained with a slow speed camera and do not allow a time correlation of the velocity. To complete this study, a second round of wind tunnel testing is conducted with a high speed camera and for the dynamic deformation of the plate. These results (cf. figure 5, right) are used to determine the velocity with time resolution (time resolved PIV). The images obtained were also used to characterize the displacement of the trailing edge of the plate, which is deformed by excitation of the SAM material (cf. figure 6).

Results

The numerical simulations are performed with NSMB software [START_REF] Vos | [END_REF][START_REF] Vos | Navier-Stokes solvers in European aircraft design[END_REF][START_REF] Vos | Recent Advances in aerodynamics inside the NSMB (Navier-Stokes Multiblock) Consortium[END_REF] based on the resolution of the Navier-Stokes equation (LU-SGS scheme for the implicit time discretisation and central scheme with Jameson dissipation for the space integration) and the OES turbulence modeling approach developed in the IFS2T team (Braza et al. [START_REF] Braza | Turbulence properties in the cylinder wake at high reynolds number[END_REF]). This approach is based on the splitting of the energy spectrum into two parts, the first regrouping the organised coherent motion (resolved turbulence) and the second, the chaotic random turbulence (modeled part). This OES modeling achieves to capture the thin shear-layers for the flow with coherent structures. The flow around the inclined plate hold the quasi-periodic structures (Von-Karman vortex shedding) and the shear-layer, appropriate for OES modeling.

3D simulations of the static flat plate

The first set of results is related to the static case (initial linear shape with an angle of attack equal to 10 degrees). These results provide a validation of the numerical method and shows good accuracy in the prediction of the flow with a comparison of time-averaged velocity of the flow. The Von-Karman vortex shedding appears in the wake with the Kelvin-Helmotz vortices in the shear layer (cf. figure 5). The comparison of the turbulence models (k-, k-ω-BSL-OES, k-ω-DDES-BSL-OES, k-ω-DDES-SST-Menter) was conducted. The evolution of the coefficients are similar except for the k--OES (see figure 4). The k-ω-BSL-OES model shows a good agreement with the experimental results (tomographic PIV) for the comparison of the time average of streamwise velocity (figure 4). A dominant period appears for all the cases around St = 0.72. The frequency is induced by the Von Karman vortex shedding. The DDES approach does not radically change the mean values of the coefficients although instantaneous velocity are different (see figure 3). Figure 3 (right) shows the presence of vortices arising in the leading edge and deformed to horseshoe vortices. The Von Karman vortex shedding in the wake is clearly defined for none hybrid model and this coherent structures disappear in the wake for the visualisation of

DDES model.

The representation of the streamwise velocity in the plane perpendicular to the plate present the same flow characteristics that appear in the TR-PIV measurements (figure 5), with the Kelvin Helmotz vortices in the shear layer.

2D static simulations of the several deformations

In the second step, the 2D simulations are performed for five forms of the plate during its deformation (position 1 is close to its initial position, and position 5 is close to its maximum deformation). The figure 6 shows the deformation. This deformation is obtained by activating the SAM material. To get closer to the experience, the position of the trailing edge is determined with the TR-PIV results and imposed in the numerical simulations. The deformation of the plate then follows the law of deformation of a beam. These results are compared to linear plate shape (figure 6). The frequencies calculated with the lift coefficient, characterizing vortex shedding, are close between curve and linear shapes. This result is consistent with the results of Fage [START_REF] Fage | On the flow of air behind an inclined flat plate of infinite span[END_REF], indicating that the frequency depends on the length of the projection of the plate in the cross flow direction. The coefficient of lift and drag have a much more pronounced difference. The curved shape provides higher values of the both coefficients (cf. figure 7 for the lift coefficient). For a given coefficient, the value of the required deformation is lower in the case of the curve shape. For example, for rms(C L ) = 0.5, the curve shape reaches to a position close to 3, while the linear form near the position 4. Thus for the same lift coefficient, the frequency will be higher, because the inclination of the plate will be lower. The same goes for the drag coefficient. The comparison of the instantaneous streamwise velocity between the curve and linear shape plate (figure 8) presents closed results.

2D dynamic simulations

The final step is the determination of the influence of the dynamics of the deformation. In the experiment, the deformation rate of the plateis about 1/1000 th of the freestream velocity which means that compared to the period of Von Karman instability, the maximum deformation is reached after about 50 Von Karman vortex shedding. The deformation is slow relative to the flow dynamic. This can explain the small -or negligible-difference between the forces appearing between static and dynamic cases. Thus, the dynamics can be considered as a quasi-static state succession. We have computed five deformation speed : x0.5, x1, x2, x4 and x8 and at each time step the grid is updated through a parallel Volume Spline Interpolation proposed by Spekreijse et al [START_REF] Spekreijse | A simple, robust and fast algorithm to compute deformations of multi-block structured grids[END_REF]. Figure 9 compare the time evolution of the aerodynamics coefficients regarding the different deformation velocities and we can that this deformation velocity has no influence on the final state of the system. The final evolution of the flow is the same, the drag and lift are higher than the static case and the strouhal number is lower.

Conclusions

This work has shown a good prediction of the 3D flow with URANS and hybrid turbulent models for flow around a fixed flat plate. The 2D study of the influence of the profile shape demonstrates that curved shape reached lift coefficient with less required deformation. Dynamic simulation of deformation shows that the deformation is too slow to strongly influence the vortex structures and the flow can be considered as a succession of static states. The outline is a 3D dynamic simulation of the deformation.

Figure 1 :

 1 Figure 1: Configuration 2d of the flat plate and the deformation (left) and the 3D frame of the plate (right)

Figure 2 :

 2 Figure 2: Description of the wind tunnel experiment, E. Deri et al. 2012 (left) and representation of the 3D isovalues of the average of the streamwise velocity (right)

Figure 3 :Figure 4 :

 34 Figure 3: Instatenious field of the isovalues of Y-vorticity for k--OES (left), k-ω-DDES-SST-Menter (middle) and the isovalue -1 of the criteria λ 2 for k-ω-BSL-OES (right)

Figure 5 :

 5 Figure 5: In the plane perpendicular to the plate, isovalues of the streamwise velocity (left) and a zoom on the trailing edge (middle) for k-ω-DDES-SST-Menter and the same representation for the TR-PIV (right)

Figure 6 :

 6 Figure 6: Evolution of the position of the trailing edge (left) and description of the curve and linear shapes of the plate for the position #5

Figure 7 :

 7 Figure 7: Deformation versus the root mean square of the lift coefficient (left) and versus the Strouhal number (right) for the two shapes

Figure 8 :

 8 Figure 8: Streamwise velocity for the position #5 for curve shape (left) and linear shape (right)

Figure 9 :

 9 Figure 9: Time evolution of the aerodynamics coefficients for the different deformation velocities : black (x0.5), red (x1), green (x2), ble (x4) and purple (x8)

Acknowledgements

The present work was supported by the Foundation STAE-RTRA, research programm EMMAV. The authors would like to acknowledge the following high performance computing centers for supporting this work by providing scientific support and access to computing resources : CINES/GENCI, PRACE and the Direction Informatique of the University of Strasbourg.


J C R Hunt

T Ishihara
email: ishihara@cse.nagoya-u.ac.jp

D Szubert
email: damien.szubert@imft.fr

I Asproulias
email: ioannis.asproulias@imft.fr

Y Hoarau
email: hoarau@unistra.fr

M Braza

Updated contribution "Advances in Fluid-Structure Interaction" from the

We consider well-developed inhomogeneous turbulent shear flows in the x direction that are bounded by interfaces (I ) separating regions of turbulent and non-turbulent (or weak turbulent) flows. The interfaces are approximately continuous and there is no large-scale forcing (by body forces or external turbulence) in these flows, see fig 1. The mean velocity is ū¿ with significant mean shear S=∇ ū¿ ~ΔU o / L , which is comparable with the large scale strain in the turbulence, Σ ~uo / L , where u o is the rms turbulence, which is of the order of the large scale velocity fluctuations , i.e. ΔU o ~uo .

The fluctuating interface location y I at given x, z and given time is defined by where the normal gradients of fluctuating vorticity are maximum [START_REF] Bisset | The turbulent/non-turbulent interface bounding a far wake[END_REF]. In all types (without forcing or external straining flow) there is a significant mean 'boundary entrainment velocity'

E b =dy I /dt which is of order u o . As Prandtl originally suggested, (see [START_REF] Bodenschatz | Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies[END_REF], the rms fluctuations of E b , E b ′ , relative to its mean value E b are related to the structure of the interface and the whole flow. There may or may not be a significant mean normal velocity, the 'entrainment velocity E v ', which can be comparable with u o , as found in jets.

The properties of the turbulence near the interface y= y I ( x , z ,t ) on the edge of well developed shear flows has been the object of a number of recent studies, [START_REF] Ouvrard | Capturing turbulent interfaces in wake flows by means of the OES approach[END_REF], [START_REF] Westerweel | Momentum and scalar transport at the turbulent/non-turbulent interface of a jet[END_REF], [START_REF] Eames | New developments in understanding interfacial processes in turbulent flows[END_REF], [START_REF] Hunt | Vortical interactions with interfacial shear layers[END_REF][START_REF] Hunt | Interfaces in turbulence and implications for advanced modeling methods[END_REF], [START_REF] Braza | Turbulence modelling for strongly detached unsteady high-Re flows, based on refined PIV experiments[END_REF], [START_REF] Braza | Turbulence modelling for strongly detached flows around bodies at high-Reynolds number, involving fluid-structure interaction[END_REF], and can be summarised as follows.

(a) Thin shear layers form at the continuous interface between sheared turbulent flow ( y< y I

) and the exterior region where there is weak turbulence with weak shear. There is a jump in the large-scale velocity, ΔU0, (defined conditionally relative to the interface) with fluctuations of the order of u o and a mean jump velocity ⟨ ΔU I ⟩ . The mean thickness of these sheets l I is of the order of the Taylor micro scale (  ). , to the integral length scale L of the turbulence in the shear flow depends on the type of shear flow. When Ri >~l the interface fluctuations are large and the shape of the interface is convoluted (i.e. y I may have 2 or more values). Whereas when Ri <<1, the fluctuations are smaller and the interface is single valued. In the former case external fluid is directly transported or 'engulfed' into the internal fluid, while in the latter case there is small-scale eddy transport and molecular transport at the interface, i.e. 'nibbling' (Mathews & Basu 2002). For the same range of values of Ri, dominance of 'engulfing' or 'nibbling' there is a local form of the flow near the interface. It is found that the profile of the conditionally sampled velocity field relative to the interface i.e. u ¿ ( ỹ )=⟨U ⟩ , where ỹ= y-y I , is similar near the outer edge of different shear flows [START_REF] Westerweel | Momentum and scalar transport at the turbulent/non-turbulent interface of a jet[END_REF].

(c) The main features of the dynamics of the flow outside and within the interfacial layers are as follows.

(i) Growth mechanisms and conditional profiles are affected by the inflection points in the mean conditional profile ⟨ Ũ ⟩( ỹ) . For jets, wakes and plumes these occur at the outside of the interface, i.e. d 2 ⟨ Ũ ⟩( ỹ )/d ỹ2 =0 , where ỹ=0 . For these types of shear layer the most energetic eddies are produced by the conditionally averaged shear d ⟨U ⟩/dy within the turbulent region (i.e. non-modal or `rapid distortion' or `horse shoe' eddies [START_REF] Hunt | Rapid distortion theory and the problems of turbulence[END_REF][START_REF] Ferre | Three-dimensional large-eddy motions and fine-scale activity in a plane turbulent wake[END_REF]). However in boundary layers and mixing layers the inflection point in (iii) The key external influence of the interfacial shear layers is that it 'blocks' the smaller scale eddies of the turbulent region (which move at the local mean velocity) and distorts their vorticity as they impact onto the layer [START_REF] Hunt | Perturbed vortical layers and shear sheltering[END_REF][START_REF] Turfus | A stochastic Analysis of the displacements of fluid elements in inhomogeneous turbulence using Kraichnan's method of random modes[END_REF]. The blocking leads to a decorrelation of velocity fluctuations across the interface. [START_REF] Ishihara | Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers[END_REF] Also these distortions lead to the sharp mean velocity gradients within and outside the layers [START_REF] Hunt | Vortical interactions with interfacial shear layers[END_REF]. However the larger scale eddy motions inside the interface move at the average speed across the shear flow which differs from the local speed at the interface. They are not blocked but stimulate irrotational fluctuations in the exterior region [START_REF] Carruthers | Velocity fluctuations near an interface between a turbulent region and a stably stratified layer[END_REF]Bissett et al 2002), see fig3. The combined contribution of the small and large scales leads to a jump in the Reynolds stress across the layer from zero outside to Δτ just inside the interfacial layer. (d) The above studies enable an adaptation of the Organised Eddy Simulation, OES method [START_REF] Braza | Turbulence Properties in the cylinder wake at high Reynolds number[END_REF], Braza et al 2008, Bourguet et al 2008), to better capture interfacial layers at the same time as using economic grids. In the OES method the resolved velocity field U (x , t) is the ensemble-average of the exact velocity representing all the coherent processed and the turbulent fluctuation û represents all the random turbulence processes. The second moments of this field are especially modelled by means of tensorial eddy-viscosity modelling that captures quite well the turbulence stress anisotropy. Thus

⟨ Ũ ⟩( ỹ)
u ¿ =U ( x ,t )+{ û( x ,t )} ,
where {} denotes the component that is only defined statistically.

In the Improved OES method (IOES), an intermediate random velocity field V RI is introduced, by means of the high-order POD (Proper Orthogonal Decomposition) modes [START_REF] Szubert | Shock-vortex shearlayer interaction in the transonic flow around a supercritical airfoil at high Reynolds number in buffet conditions[END_REF]. The method first requires estimating the position of the continuous interface y I ( x ,t ) from the OES field, using the dynamical criterion for the interface (e.g. max of dissipation or shear) and then computing its mean and fluctuating positions i.e.

⟨ y I ( x , z ,t )⟩ and In order to model the effects of the different types of eddies impacting on the interface, y I ( x ,t ) is filtered into 'large' and 'medium' scales. The new step in the IOES method is to introduce at each time step a random explicit intermediate velocity field {ǔ } . ǔ is calculated in terms of the OES velocity, i.e. U (x , t) near the interface, using the theory of blocking by the interfacial layer for the medium to small scales and irrotational transformation for the large scales, as explained in (iii) above (see also [START_REF] Turfus | A stochastic Analysis of the displacements of fluid elements in inhomogeneous turbulence using Kraichnan's method of random modes[END_REF]. The sharp gradients associated with the intermediate velocity field also lead to a correction to the statistically modelled Reynolds stresses (i.e. for medium and small scales).

The dynamical effect of the interaction between of the intermediate field and the OES field together with the corrected statistical Reynolds stresses, were modelled by [START_REF] Hunt | Vortical interactions with interfacial shear layers[END_REF], which showed how the interfacial layer remains sharp through the distortion of eddies near interface. The theoretical base of this model is achieved by considering higher-order POD (Proper Orthogonal Decomposition) modes for the stochastic forcing of the kinetic energy and dissipation transport equations [START_REF] Braza | Turbulence modelling for strongly detached flows around bodies at high-Reynolds number, involving fluid-structure interaction[END_REF]. This is created by a randomly fluctuating forcing term in the dissipation rate of these equations [START_REF] Braza | Physical analysis of turbulent/non-turbulent interfaces in the transonic interaction around an airfoil by stochastic forcing and Organised Eddy Simulation[END_REF] containing a kinetic-energy scale reconstructed by higher-order POD modes, as presented in the following.

This leads to a corrected value of U (x , t) .

It can be shown that the higher-order POD modes whose energy distribution is presented in Figure 4, precisely act within the shearing regions and in the separated areas, as well as between the shearing regions delimiting the wake, without 'contaminating' the irrotational regions. The present 're-injection' of turbulence in these regions characterised by the shearing mechanism and the Turbulent-Non-Turbulent (TNT) interfaces dynamics produces the "eddy-blocking effect" previously described and maintains these shear layers thin. This leads to a reduction of the wake's width and therefore to an improved drag force. 265455 (2013-2016). Fig. 5 shows the 3D buffet dynamics interacting with the shear layer and the von Kármán vortices of the near wake. Fig. 6 shows the energy of the three-dimensional POD modes as well as the signal and spectrum of the second POD temporal coefficient describing the buffet phenomenon and the spectrum of the 11-th order POD temporal coefficient beyond which the influence of the von Kármán frequency bump becomes visible.

Figure 7 shows the topology of the higher-order three-dimensional POD modes for the V2C configuration.

  Fig 2 shows the conditional profile for a turbulent boundary layer. There may be a jump in the scalar concentration of order ΔC i . (b) The locations y I of the interfaces fluctuate (in a moving frame) on time scales of order L/u o . The ratio Ri of the rms fluctuations of y I , y I ′

  occurs in the interior of the shear flow, approximately where the interface shear layer joins the internal shear layer, i.e. at ỹ=-l . Since the unstable normal modes of these profiles have a large magnitude within the turbulent region on the scale L, there are larger indentation of the interface y I ′ / L ~1 and larger fluctuations in the boundary entrainment velocity i.e. the thin interfacial shear layer, whose thickness ℓ is of order  , as small scale vortical eddies are stretched by the shear, their typical radius reduces to the Kolmogorov microscale l v ~L⋅Re -3/4 (da Silva & dos Reis 2011).

(

  iv) As the vortex sheet of the interfacial shear layer moves in the y-direction with velocity E b , there is a local acceleration (~E b ⟨ ΔU I ⟩/l I ), which is balanced by the gradient in the Reynolds stress in the layer ( Δτ /l I ). Integrating the x-component of the mean momentum equation across the layer shows how the mean product of the mean and fluctuating boundary entrainment velocity and the mean and fluctuating velocity jump ⟨ ΔU I ⟩ ′ momentum flux is balanced by the jump in shear stress, i.e.⟨E b ⟩⟨ΔU I ⟩⋅(1+Ce )=-Δτ . The entrainment coefficient Ce=⟨ E b ′ ⋅⟨ ΔU I ⟩ ′ ⟩/(⟨E b ⟩⟨ ΔU I ⟩)is of order 1 when the engulfment is greater than 'nibbling' (as DNS of turbulent boundary layers demonstrate), and small when nibbling dominates (as with wakes and jets[START_REF] Westerweel | Momentum and scalar transport at the turbulent/non-turbulent interface of a jet[END_REF].

  e.g. as in[START_REF] Deri | Capturing coherent structures and turbulent interfaces in wake flows by means of the Organised Eddy Simulation, OES and by Tomo-PIV[END_REF].

Figure 4

 4 represents the transonic interaction around a supercritical airfoil, the OAT15A configuration, obtained by the present IOES approach. The interfacial shear-layer and the von Kármán eddies which span the whole shear layer are both quite well captured, as well as the buffet frequency of 78 Hz in good agreement with the experiments by[START_REF] Jacquin | Experimental Study of Shock Oscillation over a Transonic Supercritical Profile[END_REF]. The results show in fig.4the sharper interfacial layer using the IOES method. The present test-case has been one of the test-cases of the ATAAC (Advanced Turbulence Simulations for Aerodynamic Application Challenges) European program N° 233710, coordinated by DLR (D. Schwamborn), (March 2009 -June 2012). The method is also in application in the case of the so-called V2C supercritical laminar wing designed by Dassault Aviation, in the TFAST (Transition location effect on shock-boundary layer interaction) European project N°

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. A typical interface separating turbulence in shear layers from irrotational fluctuations outside. (a) High Reynolds number experiments of a turbulent boundary layer (from "Album of Fluid Motion" by Van Dyke ). (b) Schematic diagram of the outer region of a wake or jet (when fully developed)

Fig. 4 .

 4 Fig.4. Computation of the transonic interaction over a supercritical airfoil (the OAT15A) by means of the Organised Eddy Simulation, OES. Left: iso-div(U) contours showing the wake and the production of waves outside it Right:

Fig. 5 .Fig. 6 .

 56 Fig. 5. Illustration of the three-dimensional Q criterion coloured by vorticity for two instants corresponding to the upstream and downstream shock motion and to the buffet phenomenon around the V2C supercritical wing at incidence of 7°, free-stream Mach number 0.70 and Reynolds number 3.245x10 6 .

Fig. 7 .

 7 Fig.7. Higher-order POD modes -V2C wing

Acknowledgement

Part of this study has been carried out in the context of the European programmes ATAAC and TFAST. Part of the computing hours allocation has been provided by the French supercomputing centres CINES, IDRIS, CALMIP.