Divergence free synthetic eddy method for embedded LES inflow boundary condition

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1 R. Poletto*, A. Revell, T. Craft, N. Jarrin for embedded LES inflow boundary condition University TSFP Ottawa 28-31/07/2011 * 1 / 19

2 SLIDES OVERVIEW 1 Introduction 2 SEM methodology 3 DF-SEM description 4 Results 5 Conclusions 2 / 19

3 Large Eddy Simulation (LES) MOTIVATION Enables instantaneous information to be obtained Expensive (in particular for industrial needs) Reynolds Averaged Navier Stokes (RANS) Needs extensive closure modelling No information about the instantaneous flow EMBEDDED LES is a practical compromise: use LES where you really need it use RANS in other regions BOUNDARY CONDITIONS RANS/LES Current work addresses the creation of inlet condition for embedded LES from a RANS field The whole LES domain might be affected by the inlet!! 3 / 19

4 SYNTHETIC TURBULENCE METHOD CLASS. SHORT DESCRIPTION Random Numbers 0D Random generated fluctuations Vortex Method (Sergeant 2002) 2D Vorticity used to define the v-w inlet fluctuating components Spectral Method (Batten 2004) 3D Fluctuations are generated according to a modified von Karman spectrum Turb. Fluctuations (Davidson 2006) 2.5D SEM (Jarrin 2006) 3D As spectral but with different time relation A distribution of eddies defines the fluctuations None of the mentioned method is able to generate a divergence free velocity field in case of anisotropic turbulence!! Current approach is based on the Synthetic Eddy Method (SEM), and generates a divergence-free velocity field. 4 / 19

5 SEM METHODOLOGY Eddies are convected through a 3D box Each eddy represents a fluctuation of the mean velocity field Flow field is taken at each time step and used as LES inlet Mean flow information are used to define: 1 mean velocity 2 turbulence magnitude and stress anisotropy 3 eddy length scales 5 / 19

6 SEM the ck Lund coefficients reconstruction of the Reynolds stresses fσ is a shape function velocity distribution around the eddy centres xk - The LES generates high pressure fluctuations close to the inlet in order to satisfy local continuity. - A divergence-free inlet velocity field should remove these. 2D velocity field + time development = 3D problem Divergence free constraint 6 / 19

7 DF-SEM DEFINITION Vorticity rotor The second term vanishes since the velocity field is divergence free The DF-SEM applies the SEM fluctuations to the vorticity field and then obtains the divergence free velocity field Vb = Eddy box volume N = Eddy number Greens Function σ = Eddy lengh scale α = Eddy intensity gσ = Eddy shape function 7 / 19

8 SEM the ck Lund coefficients reconstruction of the Reynolds stresses DF-SEM the cross product divergence free Lund coefficients cannot be used (would not be more divergence free) Modify the eddy intensity α to give desired stress anisotropy 8 / 19

9 DFSEM REPRODUCING STRESS ANISOTROPY In the local principal axes of the Reynolds stress - k' turbulent kinetic energy - λ is the Reynolds stress eigenvalue Mathematical limitation!! random numbers taken from any distribution wit: - zero mean - unit variance Eddies are then transformed from the principal axes back to the global reference frame 9 / 19

10 NORMAL STRESS ANISOTROPY Lumley triangle Limitation on λ < k' means the DF-SEM cannot reproduce all possible turbulence states. Inlet Anisotropy Clipping - Some clipping has to be applied to inlet stress field. - Overall turbulence level is retained. 10 / 19

11 DF-SEM REPRODUCED REYNOLDS STRESS (Channel Flow REт=395) 1 - <u'v'> is always underestimated 2 - y+>75 the error is relatively small 11 / 19

12 CHANNEL FLOW - Synthetic turbulence used as inlet conditions for LES channel flow. - Inlet stress field from DNS by Moser (1999) CHANNEL FLOW REτ=395 Size: 20π x 2 x 2π Resolution: 500 x 46 x 82 Wall cell: y+ = 1 22 Vel 0 DFSEM SEM LES Visual comparison of the velocity fields generated at the inlet: SEM performs poorly in the centre of the channel Structures generated by the DFSEM are closer to the LES Small structures close to the wall are not perfectly captured 12 / 19

13 PERFORMANCES COMPARISON The friction coefficient development along the channel gives a measure of the quality of the inlet DF-SEM has a quite high drop close to the inlet, but has the quickest recovery among the schemes tested 13 / 19

14 UV COMPARISON DF-SEM VORTEX DF-SEM: very good convergence for y+ > 250 SEM: quick convergence for for y+ < 20 VORTEX: very low generated Shear Stress SEM 14 / 19

15 K COMPARISON DF-SEM SEM VORTEX DF-SEM: inlet turbulence level is more flat than periodic one VORTEX: underestimation of the <u'u'> component returns a low turbulent kinetic energy 15 / 19

16 VV PREDICTION <v'v'> is suddenly dissipated along the channel <v'v'> [constant k' case] <v'v'>, over predicted by the DF-SEM, is suddenly dissipated and then quickly recovered. This behaviour explains the energy drop showed earlier Causes: 1 Overestimation of <v'v'> 2 Underestimation of <u'v'> and <u'u'> 16 / 19

17 INLET PRESSURE FLUCTUATIONS 1 Most of the synthetic turbulence are not divergence free 2 Velocity field is forced to be divergence free by LES 3 Pressure fluctuation are generated downstream the inlet 4 DF-SEM reduces the problem by more then an order of magnitude! DFSEM SEM NOTE: spikes seem at edges of DF-SEM domain are due to periodic boundary condition implementation, not the DF-SEM itself. 17 / 19

18 FURTHER DEVELOPMENTS - Anisotropy clip degrades the DF-SEM performance for y+< In high Re flows this may only correspond to a rather thin near-wall region. - SEM recovers very quickly for y+<50. HYBRID SEM-DFSEM DF-SEM spherical eddy structures SEM possibility of ellipsoid structures (suitable close to the wall) 18 / 19

19 CONCLUSIONS DF-SEM provides a promising inlet condition for embedded LES Inlet pressure fluctuations are reduced, and a relatively short flow development length is needed Better knowledge of the mechanisms in the transition zone required to further reduce the development length FUTURE WORK Anisotropy reproducibility improvement Industrial test cases 19 / 19