1 A combined RANS-LES strategy with arbitrary interface location for near-wall flows Michael Leschziner and Lionel Temmerman Imperial College London

2 Overview 1.Motivation 2.Method Description 3.Observation from Past Work 4.Modelling practice and Methodology 5.Results for Channel Flow 6.Results for Hill Flow 7.Concluding Remarks

3 Motivation  Grid requirements for LES of wall-bounded flows:  Number of nodes rises as (Chapman (1979))  High Reynolds LES is prohibitively expensive  Cost reducing strategies: Wall functions (Schumann (1975); Werner and Wengle (1993)); Zonal approach (Balaras et al (1996)); Hybrid RANS-LES methods (DES - Spalart et al (1997); Hamba (2001)).

4 Alternative Approaches  Wall functions: Mostly based on log-law approximations; Tends to be ‘adequate’ in simple shear flows; Inadequate for separated flows (no universal behaviour).  Zonal approach: Simplified set of equations resolved near the wall (TBL equations); Saving results from the removal of the Poisson problem; Not adequate for all flows.

5 Alternative Approaches  Hybrid RANS-LES strategies: Part of the turbulence is modelled in the ‘RANS’ layer; Allow to use large aspect ratio cells – we hope! Location of the interface:  either decided by user;  or controlled by cell dimensions – compare y and  = f(  x,  y,  z) as in DES;  Interface shift done via modifications of the grid: shift away from the wall  higher  x and  z;  High streamwise/spanwise resolution required in some flows (separated) even with RANS methods  interface may be too close to the wall.

6 Method Description RANS layer prescribed by reference to the wall distance. RANS Layer LES Domain Imposed LES conditions at interface Imposed RANS conditions at interface

7 Observations from Previous Work  In the URANS region, the resolved and the modelled contributions to the motion are of equal importance.  Total is too high  need of an ad hoc modification to reduce the total motion.

8 Modelling Practice  RANS model: one-equation transport model for turbulence energy (Wolfshtein (1969));  SGS model: One-equation transport model for SGS energy (Yoshizawa and Horiuti (1985))  Assumption: RANS and LES grids are identical at the interface;  Target: Velocity: ; Viscosity: ; Modelled energy:.

9 Methodology with hence : spatial average in the homogeneous directions.

10 Methodology Function 1 Function 2

11 Channel Flow – Case Description  Periodic channel flow;  ;  RANS-LES and coarse LES: Computational domain: ; Grid: 64 x 64 x 32 cells with and ;  Dense LES: Computational domain: ; Grid: 512 x 128 x 128 cells with.

12 Channel Flow - Results Time-averaged velocity and shear stress  profiles for the LES computations. 64 x 64 x 32 cells 512 x 128 x 128 cells

13 Channel Flow - Results Time-averaged C  profiles across the RANS layer (64 x 64 x 32 cells).

14 Channel Flow - Results Time-averaged velocity profiles for the hybrid RANS-LES computations (64 x 64 x 32 cells).

15 Channel Flow - Results Time-averaged shear stress  and turbulent energy profiles for the hybrid RANS-LES computations (64 x 64 x 32 cells).

16 Channel Flow - Observations  Encouraging results.  The response to the parameters change is small.  Response to the change of location of the interface: Change in the proportion of modelled motion; Variation in the width of near-wall total turbulence energy peak.

17 Hill Flow – Case Description  Periodic channel flow with constrictions at both ends  Reynolds number based on channel height and bulk velocity is  Data from highly resolved LES computations (5 x 10 6 cells) by Temmerman et al (2003)  Domain size: 9h x h x 4.5 h (h=hill height)  Grid details: Discretisation: 112 x 64 x 56 cells (4 x 10 5 cells); Near-wall resolution: y + c (1)  1; Spanwise and streamwise resolution:  x =  z.

18 Hill Flow - Results Left: location of the RANS-LES near-wall interface. Right: Distribution of C  along the interface

19 Hill Flow - Results Averaged streamlines for the reference simulation, LES, DES and RANS-LES cases. (x/h) sep. = 0.22 (x/h) reat. = 4.72 (x/h) sep. = 0.21 (x/h) reat. = 5.30 (x/h) sep. = 0.23 (x/h) reat. = 4.64 (x/h) sep. = 0.23 (x/h) reat. = x 128 x 186 cells 112 x 64 x 56 cells

20 Hill Flow - Results Left: Distribution of C  across the lower RANS layer (right). Right: Streamwise velocity profiles in wall units at x/h = 2.0.

21 Hill Flow - Results Streamwise velocity profiles at x/h = 2.0.

22 Hill Flow - Results Turbulent viscosity profiles at two streamwise positions.

23 Hill Flow - Observations  The location of reattachment is overestimated by the hybrid RANS-LES and DES probably because of the wrong prediction of the wall shear stress.  Compared to the channel case, C  has a similar behaviour.  Overall, good agreement with the reference data.  Difficult to draw definitive conclusions; too low Reynolds number.

24 Concluding Remarks  New hybrid RANS-LES method allowing: Freedom in locating the interface; Dynamic adjustment of the RANS model to ensure continuity across the interface.  For identical grids, the results obtained with the RANS-LES approach were significantly better than those obtained with LES.  Application to a recirculating flow: Results are non-conclusive due to low Reynolds number  new test case (separated hydrofoil at Re c = 2.15 x 10 6 ); The hybrid RANS-LES approach overestimates the recirculation zone length.