Annexes 1
197
LES – PIV comparison for air flow in a simplified cowl-box
BERGER Rémi Environmental and applied
fluid mechanics von Karman institute Rhode-Sainte-Génèse,
Belgium [email protected]
DRIA/SARA/STEV/ARCT PSA Peugeot Citroën
Vélizy-Villacoublay France
DEPARDON Sébastien DRIA/SARA/STEV/ARCT
PSA Peugeot Citroën Vélizy-Villacoublay
France
RAMBAUD Patrick Environmental and applied fluid
mechanics von Karman institute Rhode-Sainte-Génèse, Belgium
BUCHLIN Jean-Marie Environmental and applied fluid
mechanics von Karman institute Rhode-Sainte-Génèse, Belgium
ABSTRACT
A single-phase Large Eddy Simulation is performed in a simplified cowl-box model and compared to PIV data. Indeed, prior to the analysis of the interaction between a turbulent air flow and an interface of liquid, the most accurate description of the 3D flow field is required. Although the qualitative phenomena are correctly rendered (flapping motion of impinging inlet jets), quantitative differences are noticed, mainly due to non satisfactory turbulent boundary condition, which induces an overestimation of the jets core length, and modifies its interaction with the cowl box walls. Nevertheless, a qualitative analysis of the instantaneous flow shows the generation of large coherent vortical structures due to the oscillation of the impinging jets at the bottom wall. The advection of these structures in the cowl-box generates large oscillations of wall shear stress and pressure distribution, which are thought to be of great importance for further two-phase flow simulations.
INTRODUCTION
Under rainy conditions, the penetration of rainwater
through the heating ventilation and air conditioning system (HVAC) must be prevented. The air-flow and its interaction with rain water within the cowl box is very complex. CFD could be used in this purpose to take into account water penetration constraints into the early design phases. A simulation of such a highly turbulent, three dimensional air-flow and water interface
tracking requires the use of specific VOF and LES models [1].
However it is known that the VOF is incompatible with the use of a turbulent model. Several previous studies show that the incompatibility is due to the transmission of the turbulence properties of the flow to the water interface. It involves specific hypothesis of the turbulence near this interface [2], [3], [4]
(anisotropy of the near interface turbulence, damping of the
turbulence viscosity….). The VOF method is also shown to be dependent on the sub grid model [5], [6].
Development of VOF-LES coupling requires first to be able to reproduce the air flow with a good accuracy keeping in mind that we need to run the LES simulation with an acceptable computation effort because of the additional cost needed for VOF.
The cowl-box configuration under investigation is presented through the description of the experimental setup. PIV measurements performed in this specific configuration are described. The aim of this study is to assess the performance of a
“light” LES simulation by comparison and validation with PIV data.
EXPERIMENTAL SETUP
The experiments are conducted on a dedicated setup designed and built at the VKI (Figure 1). The facility is composed of three main boxes made in Plexiglas for optical access. Boxes are the main tank, the extraction duct and a secondary box, respectively.
Main tank
Extraction Duct
Secondary box
Air suction
Figure 1: experimental setup
The main tank is 1500mm long, 220mm high and 300mm wide. On its top face they are two inlets represented by slots, 50mm wide and 200mm long. The main tank height is adjusted to simulate the effect of the presence of a water layer at the bottom.
On lateral face an opening is drilled to allow air suction through the intermediary duct. This liaison duct is 250mm long, 170 mm wide and 100 mm high. This section is connected to the secondary box, which is just a buffer zone implemented with baffle.
Air at ambient temperature is sucked from atmospheric pressure by an axial blower linked to the secondary box.
The flow rate is determined by measuring the velocity profile in the extraction duct. The facility works at a Reynolds number (based on the width on the slots and the bulk velocity) equal to 3,3x104.
EXPERIMENTAL INVESTIGATION OF THE FLOW FIELD
PIV technique is applied to measure the flow field characteristics. The measurement chain is made of a two cavities N-Yag laser, a PCO camera with a resolution of 864 x 1280 pixels and the related acquisition system. The laser and the camera are synchronized at 9.9Hz by means of a Stanford signal generator.
The seeding is provided by paraffin oil based mixture and a disco smoke generator. The seeding particles diameter is about 1µm.
The coordinates used in the investigation are X (main tank length direction), Y (stream wise direction of the intermediary duct) and Z (main tank height direction). The origin is defined as the intersection of the symmetry planes of the main tank (see figure 2).
The PIV measurements are performed in 6 different planes (figure 2); mainly two of them are used for the present comparison. The first plane is located in the plane Y=0 just downstream the tank inlets. The second plane is the symmetry plane of the facility located at X=0 just at the outlet of the tank (or inlet of the extraction box).
Plane N°2 : main tank outlet
Plane N°3: vertical symmetry plane in extraction duct
Plane N°4: horizontal at extraction duct height quarter
Plane N°5: horizontal at extraction duct symmetry plane
Plane N°1 : main tank inlet Plane N°6 : Normal to main stream in extraction duct
Figure 2: Experimental measurements locations
All the PIV images are processed using the VKI WIDIMs, software developed at the VKI by Scarano [7]. All the data are obtained with a 96x96 pixels first interrogation window, two steps of window size refinement and 75% of window overlapping. Two steps of window distortion are used for each step of the refinement procedure. Finally, a Gaussian peak-fitting is adopted to perform the sub-pixel interpolation. With these settings, a minimum of 29610 vectors are defined in each measurement area with
accuracy of 0.03 m/s. For each plane, the statistic is performed on 1000 fields excepted for the plane number 1 where statistical calculations are achieved on the basis of 3000 fields. Using Lourenço analysis [8], the maximal error of the statistical results is about 3% with 95% of confidence.
The experimental campaign provides a detailed data base. The instantaneous character of the PIV measurements allows looking at detailed statistics of the flow field in terms of mean and fluctuating quantities.
NUMERICAL SETUP
The numerical simulation aims to reproduce with good accuracy the flow field in the tank on rather large physical time but with an acceptable calculation cost. Moreover such CFD simulation should highlight the important flow features to guide future two-phase flow simulation. In the present case, the LES is chosen as it is projected to yield better insight than unsteady RANS for detailed analysis of complex two-phase flow.
Computational domain and boundary conditions
Because of the size of the complete setup, the numerical domain for LES computation is reduced as presented in figure 3. It is composed of the main tank and the extraction duct. The boundary conditions applied at the inlet (slots) and outlet (extraction box) is issued from RANS simulation performed on the complete geometry [9]. Applying steady RANS profiles as boundary conditions for LES could kill the unsteadiness of the flow ([10]). However, it is expected that the present geometric configuration with air sucked (negative velocity at the inlet) would naturally initiate flow unsteadiness.
Grid considerations
The grid of the LES relies exclusively on hexahedral cells.
The mesh is fully Cartesian and structured in all the directions.
Figure 3: domain and mesh overview
The mesh is done to fix the typical distance from the wall to the cell center to about Y+=2 (wall units) for the intermediary duct walls, the bottom wall of the main tank and its lateral walls. For the other walls this distance is increased up to 10 because their weaker influence expected on the flow. The wall unit is based on the instantaneous wall shear velocity. The grid spacing of the meshing is such that ∆x+ and ∆z+ are below 200.
The extraction duct and the middle of the tank mesh are deliberately coarsened to reduce the calculation costs. The final mesh is composed of 1.9 millions cells.
Numerical method and computing strategy
The computation is performed with Fluent 6.3 software using a segregated solver with a 2nd order bounded central differencing scheme for the interpolation of the advection and the diffusion in the momentum equation.
The Smagorinsky-Lilly model with a viscosity coefficient parameter fixed at Cs=0,1 is used as sub-grid model [11].
The simulation is conduced with a time-step of 5x10-5 s. First and second order statistics are obtained on a physical time of 1 second with an ensemble average of the individual realizations at successive time-steps. The averaging time of the present simulation is equal to about twenty times the time for a particle to flow through the main tank.
RESULTS AND DISCUSSION
Simulation quality
Different quantities are checked to assess the modeling quality; the courant number (CFL) related to the numerical stability, the turbulent–laminar viscosity ratio emphasizing the sub-grid model dependency and the Y+ distribution associated to the accurate reproduction of wall turbulence.
For an implicit solver, a CFL number of several units may be handled without stability issues. Nevertheless, for accuracy reason, it is accepted in the LES community that this number should be as small as 0.3 to reproduce the temporal scales associated with the spatial scales resolved [12]. In the present simulation the CFL-value resulting from an averaging on the entire numerical domain, is 0.036. However, although the major part of the CFL number is below 0.8 which is still acceptable, some local values can higher than 4. Therefore, the time step used appears to be the maximum allowed.
The maximal value of viscosity ratio µtur/µlam reached is around 35 (figure 4). This value is below the upper limit of 100 proposed by Sagaut [13], meaning that for this criterion the mesh is sufficiently refined. However it is worthwhile to point out that this value is reached very close to the bottom wall and then to the future water interface, the motion and deformations of which will be closely linked to the sub-grid model used for the computation.
Figure 4: Viscosity ratio mapping on the bottom face, y=0 plane and middle plane of the fence
According to figure 5, the Y+ values observed on each walls of the numerical domain are in accordance with the target values (Y+ ~ 2 at the bottom and side walls and Y+ ~ 10 elsewhere.). The respect of these wall unit values should guarantee the fair reproduction of the wall turbulence phenomena.
Figure 5: Y+ mapping on bottom, side and lateral walls
Statistical results
The validation of numerical results is done by comparing PIV data to CFD simulations.
The statistical results in terms of mean and RMS values indicate that the inlet fence and the extraction duct junction are the two main regions, which look worthwhile to qualify the flow simulation.
Inlet flow at the fence
The flow coming from the outside environment goes into the box through the two slots located on each extremities of the main tank.
This zone, as an inlet region, governs the entire flow behavior in the domain.
Comparing the mean velocity field of LES simulation to PIV data in the middle plane of the jet (figure 6), two main phenomena are highlighted. The first one is the difference observed in terms of velocity magnitude. Velocity is higher in the PIV field than in the LES prediction. Moreover in the PIV field is the jet is straight, while it exhibits a bending towards the centre of the tank in LES simulation.
Figure 6: Mean ZX velocity magnitude field in plane y=0 at the inlet fence:
LES (left), PIV (right)
To propose an explanation of that discrepancy, typical velocity profile on the centerline of the jet is plotted in figure 7. The velocity is normalized by the maximal velocity obtained in the jet, and the z coordinate by the width of the slot.
Velocity profile at the jet centerline
0 0.2 0.4 0.6 0.8 1 1.2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Z/e
V/Vmax
PIV Fluent LES
Figure 7: XZ Velocity profile at inlet centerline (Z/e=4.4 is the wall location, Z/e=0 is the inlet)
Figure 7 shows that the potential core length Lc (V/Vmax ~ 1) is 55% longer in the LES prediction (Z/e=2.2) than in the PIV measurements (Z/e = 1.4).
The literature survey agrees on the fact that the turbulence intensity level affects significantly the potential core whereas no firm consensus exists on the effect of the velocity ([14], [15], [16], and [17]). For instance it is shown in the literature [18-19] that Lc decreases as the turbulence intensity, I0, of the jet increases.
Typical relation is the following [18]:
Lc = 5,39 – 0,266. I0 (eq.1)
Now calculating from LES and PIV data a 2D-turbulence characteristic defined as:
)² ' ( )² '
( RMS RMS
d v u
K2 = + (eq.2)
Where u’ and v’ are respectively the x direction and y direction fluctuating velocity components. In the middle plane of the jet, we notice that the turbulence intensity level from eq.1 is 14.7% from PIV data (in good agreement with the measured value of 13.8 %), whereas is only 2% from LES. According to eq.1 we conclude that Lc in LES should be effectively higher than in PIV field.
Figure 8: 2d turbulent kinetic energy reparation in plane y=0 at inlet fence: LES (left), PIV (right)
This over prediction of the potential core length, combined with the influence of the wall is responsible of mean jet deviation.
In future studies, because the inlet turbulence needs to be better simulated, the boundary conditions will be changed, taking into account a small part of the external environment and the thickness of the slots that should allow a proper generation of turbulence level more in agreement with the experimental observation. Such an action is currently underway.
Extraction duct and main volume junction
Complex 3D phenomena may occur at the junction between main tank and extraction duct because of the convergence of the flows coming from both inlets. In this area, the large scale turbulent motion could be crucial for water entrainment occurrence.
If figure 9, we shows that the maximal velocity predicted by LES in the extraction duct center plane is lower than in the PIV field.
However the velocity gradients are well retrieved with respect to the PIV.
It is thought that the coarse mesh used in the LES simulation does not reproduce accurately the separation at the inlet of the extraction duct. This must lead to differences in terms of velocity distribution along the extraction duct cross section. This may be also a consequence of the jet deviation at the inlet fences in the LES and therefore a difference in the 3D features of the flow.
LES PIV
LES PIV
Velocity profile
-80 -60 -40 -20 0 20 40 60 80 100 120
0 1 2 3 4 5 6 7 8 9
YZ ve locity (m /s )
Z (mm)
Fluent LES PIV
Figure 9: Velocity profile at y=140mm at the extraction duct junction
Instantaneous results
Instantaneous structures in the jet
Classical impinging jet with symmetrical boundary conditions leads to formation of wide alternate coherent Taylor-like structures. The impact these turbulent puffs on the bottom wall provoke a flapping motion of the jet ([19], [20]), which should be reveal by the flow characteristics.
Figure 10 presents an instantaneous flow field, which shows on the bottom face a succession of large high velocity areas (A, B and C) associated with streaks of high shear stress (a, b and c). These footprints are clear the sign of the presence of large coherent structures linked to the jet flapping. They seem to be progressively damped as they are advected downstream the jet towards the extraction duct.
Figure 10: Wall shear stress on bottom wall versus instantaneous velocity magnitude in plane y=0
Figure 11 shows the shear stress distribution on the bottom wall at several successive time steps. The motion of the turbulent structures is clearly highlighted by the displacement of the high shear-stress streaks.
Several studies have demonstrated that the main actuators of water interface deformation are pressure gradients [21] and shear stress ([2], [4] and [5]) in the impact area. Therefore, in the present application, specific care must be taken to simulate properly the flow in this area, as it can be the main responsible of water entrainment (figure 11).
Figure 11: time shear stress evolution on the bottom wall
Finally, it seems that, due to their large standoff distance, no synchronization mechanisms between both jets could be observed within the 1.0 second of physical time recorded. The two instantaneous velocity fields reported in Figure 11 shows indeed that the jets are either in phase (fig13-a) either few tenths of second later in opposition of phase (Fig13-b).
LES PIV
Figure 12: jets motions in instantaneous fields:
a/ jet in phase – b/ jet in opposition of phase
Conclusion
Prior to two-phase flow analysis using both LES and VOF, the present study is carried out to reproduce accurately the air flow in a cowl-box model. The main objectives of this study are twofold:
first to find a calculation strategy to reproduce the air flow on a coarse mesh because of the additional calculation cost required when VOF will be introduced. Secondly to highlight the phenomena that would be crucial for interface deformation prediction.
The present “light” LES simulation is conducted on a reduced domain and compared to PIV measurements. Good quality of the simulation in terms of CFL, Y+ and viscosity ratio is achieved.
However quantitative differences are observed between PIV data and LES predictions in the inlet and extraction region.
The steady LES boundary conditions at the inlet are not able to reproduce the level of turbulence downstream in the shear layer.
The main consequence is an overestimation of the slot jet core length, which modifies its interaction with the walls. In future simulation, it is advised to extend numerical domain to include partly external entry flow and therefore to contain turbulent fluctuations.
Nevertheless, a qualitative analysis of the instantaneous flow field indicates that the generation of large coherent vertical structures at the bottom wall, which are due to jet flapping. The advection of these structures in the main tank generate large oscillations of wall shear stress and pressure distribution, which will be of great importance for water interface behavior.
Future work will be dedicated to improvement of the simulation (domain, mesh and boundary conditions) to better capture the features of the flow inside the tank for a deeper analysis of the flow/wall interaction phenomena and a conclusive validation..
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