Structures in the turbulent wake of an Ahmed body: LES vs Experiments using POD and some ideas about control

Transcription

1 LES vs Experiments using POD and some ideas about control Stéphanie PELLERIN and Bérengère PODVIN Laboratoire d Informatique pour la Mécanique et les Sciences de l Ingénieur Context Université Paris Sud, Université Paris Saclay, Orsay Reduction of energy consumption, environmental impact, automobile industry Wake of a square-back Ahmed body Deviation of the wake due to the bistability behavior firstly observed in experiments LES and comparisons with the experiment Control of the wake Configurations studied Flow characteristics Re = 4,8 10 4, U = 10 m/s U C H C* ~ Ahmed body with usual aspect ratios no-slip condtion slip condition 1

2 Velocity-vorticity (v-) formulation of the Navier-Stokes equations 3D uncompressible unsteady code NAPEM t Vorticity transport equation 1 v e Velocity determination v v 0 C. Tenaud, S. Pellerin, A. Dulieu and L. Ta Phuoc, C & F, 34, 2005 Large Eddy Simulation sg 1 e Filtering of the equations subgrid tensor subgrid viscosity sg Mixed scale model (LIMSI, Ta Phuoc, 1994) sg 1 2 C C k' S B Discretization M.A.C. staggered grid Discretization: second order schemes macrosopic microscopic 2

3 Computational domain y Propagation direction (x) z x Vertical direction (y): slip conditions imposed at the lower and upper surfaces Transverse (spanwise) direction (z): periodic conditions (xy) plane: side view Penalization method for solids Ahmed body z y x H (zx) plane: top-view Independence of grids, easy implementation, movement of bodies y Penalization of the computation inside the solids 0 no diffusion imposed D Dt 0 x 3

4 Some cases with different ground clearance Unsteady field: spanwise component of the vorticity z side-view median (xy) plane C* = C/H = 0.1 C* = C/H = 0.3 4

5 Some cases with different ground clearance Mean flow: <v x > and stream function (v x -v y ) side-view median (xy) plane C* = 0 C* = 0.17 C* = 0.3 slip condition 5

6 Case with a slip condition (quasi C ) Unsteady field: vertical component of the vorticity y top-view horizontal mid-height plane Mean flow: <v x > and stream function (v x -v y ) deviation of the wake 6

7 Proper Orthogonal Decomposition Lumley Solving an eigenvalue problem where the eigenfunctions method of snapshots (Sirovich), with Use POD 2D: to allow a comparison between LES and experiments 3D: to extract and to identify the most energetic modes of the flow 7

8 Comparisons LES experiment using 2-D POD Experiments O. Cadot, A. Evrard, ENSTA, IMSIA (UME) POD on PIV data Numerics 2D POD on LES 3D data, LIMSI! different velocities different bodies Horizontal plane, at mid-height of the body, at the rear end of the body 400 fields for both data Numerous switches in experiment, not in LES data symmetrized database: ADD Z-REFLECTION OF EACH SNAPSHOT TO EACH DATA SET 8

9 Symmetrized 2D POD Spectra 9

10 Symmetrized 2D POD Experiments Top-view, close to the back face of the body Numerics MODE 1 SYMMETRIC MODE 2 ANTISYMMETRIC 10

11 Symmetrized 2D POD/3D POD Experiments Top-view, close to the back face of the body Numerics (3D cross-section) MODE 1 SYMMETRIC MODE 2 ANTISYMMETRIC 11

12 Symmetrized 2D POD Experiments Top-view, close to the back face of the body Numerics MODE 3 SYMMETRIC MODE 4 ANTISYMMETRIC 12

13 Symmetrized 2D POD Experiments Top-view, close to the back face of the body Numerics MODE 5 ANTISYMMETRIC MODE 6 SYMMETRIC 13

14 Symmetrized 2D POD Experiments Numerics Is the wake switching sides? 14

15 2D POD versus 3D POD (no sign change) amplitude of the mode 2 top-view mid-height horizontal (zx) plane 15

16 3D POD versus 2D POD How numerical simulations can be useful amplitudes t complex 3D structures Mode 6 Mode 1: symmetric part of the mean mode Mode 2: anti-symmetric part of the mean mode 16

17 3D POD top-view transverse-view Mode 1: Mode 2: symmetric part of the mean modeanti-symmetric part of the mean mode 17

18 Wake quasi-steady states J. Westerwheel (oscillation of elliptical vortex rings) 18

19 3D POD shedding mode MODE 3 SYMMETRIC MODE 4 SYMMETRIC amplitudes t approximatively St =

20 3D POD shedding mode side-view top-view 20

21 3D POD amplitudes MODE 5 Mode 5 SYMMETRIC MODE 7 SYMMETRIC Mode 7 21

22 3D POD MODE 5 MODE 3 MODE 4 MODE 7 22

23 Deviation of the wake obtained with LES Comparison with the experiment via POD Control of the wake flaps with an angle top-view flaps with zero angle: cavity side-view Suction/blowing side-view preliminary studies in Codes NAPEM and SUNFLUIDH (big grids, parralel, v-p) Pseudo-penalization for solids Passive control (flaps or shape adaptation) or active control (suction/blowing) Comparisons with corresponding experiments 23

24 Flaps with an angle 6 10 Cavity at the rear of the body full body 24

25 Conclusions 2-D POD: Good agreement of LES with experiments - despite differences in geometry and limitations (no switch) thanks to extended database - BUT 2D results should be interpreted with caution 3D versus 2D: numerical simulations can be useful Future work Carry out full analysis of configuration for control (active, passive) Provide some understanding of control 25