1. Fifth International Symposium on Turbulence and Shear Flow Phenomena A. Revell, The University of Manchester K. Duraisamy, The University of Glasgow G. Iaccarino, Stanford University Advanced Turbulence Modelling of Wingtip Vortices Acknowledgments: T. Craft & D. Laurence at The University of Manchester CTR Summer Program 2006 DESider FP6 EU Project EDF

2. 2 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Introduction Description of Wingtip vortices Testcase details (Chow et al., 1997) Development of Curvature Corrected v 2 -f model Validation Results with structured grid Development of Stress-Strain Lag model Validation Results with unstructured grid Conclusions

3. 3 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Wingtip vortices A wingtip vortex is set up as a result of high pressure flow under the foil escaping to the lower pressure regions above it, around the wingtip. Result is an anti-clockwise Trailing vortex in wake of wingtip (as viewed from front) Wingtip Vortices can reduce efficiency of the wing and increase drag. Accurate prediction of the downstream extent of the highly rotational motion is crucial for safe aircraft separation distances. Complex separation is a challenge for turbulence models and grid requirements are stringent.

4. 4 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Testcase details Previous work established that standard RANS models over-predict turbulence levels in a vortex, and consequently over-predict the decay rate of the vortex downstream of the wing. (Craft et al 2006) Geometry matches the experimental work by Chow et al. (1997) NACA 0012 wing section at angle of attack of 10 degrees. Reynolds number of 4.35x10 6 Transition forced at 4% chord Results from Linear and Non-linear EVM are found to exhibit a far too rapid decay of the vortex core. A Reynolds stress transport model (RSM) reproduces the principal features found in the experimental measurements. Craft et al, IJHFF 27 684-695 (2006) EXPT EVM NLEVM RSM (TCL)

5. 5 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Modified v 2 -f model To account for frame-rotation (FR) effects in the v 2 -f model, a strain sensitive version of the eddy viscosity coefficient, C , was proposed (Petterson-Reif et al., 1999). Based on equilibrium solution of homogenous plane shear under orthogonal rotation Functional form dependent upon invariants of Strain and Vorticity. A range of studies have investigated the inclusion of rotational/curvature effects into a turbulence model. emphasis on 2 or 3 equation models to conserve cost economy versus full RSM. Analytic case of a simple line vortex (Lamb-Oseen). Reduction of turbulent viscosity at vortex core. However, viscosity levels are higher outside the vortex core.

6. 6 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Modified v 2 -f model The extra curvature sensitive terms cause a further reduction of viscosity over a wider radial region. Where the anti-symmetric tensor is computed according to Wallin & Johansson (2002) as: Curvature sensitivity added to the v 2 -f model by Duraisamy et al. (2005) using an objective vorticity tensor similar to Gatski (2000) and Hellsten (2002), as: The rate of time variation of the strain rate tensor (DS/Dt) is seen to be important. (Kozolv et al 2003).

7. 7 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Modified v 2 -f model: Results Similar trend in results obtained for full wingtip case on a structured grid of ~9M cells. Plots of normalized turbulent viscosity (Duraisamy et al. 2005) Plane located downstream of trailing edge (at x/c = 0.246) Baseline model v2f (FR) v2f (FR + CC)

8. 8 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Modified v 2 -f model: Results The v 2 -f Curvature Corrected model gives a good comparison to experimental data. Influence of Curvature Correction observed downstream of trailing edge. x/c =-0.114x/c = 0.456 v 2- f v 2- f (FR) v 2- f (FR+CC) EXPT (Chow et al) Axial and vertical velocity over wingAxial and vertical velocity downstream of wing

9. 9 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino The Stress-Strain Lag model Another method is applied, initially developed for unsteady mean flows (Revell et al. 2005) The misalignment parameter is defined as: Which will be zero when and are mutually perpendicular A transport equation for a parameter that provides a measure of the misalignment of the tensors of stress anisotropy, and strain,. The implemented form of the transport equation is derived from a pressure strain model: Can be incorporated into the two equation SST model by modifying the turbulent viscosity: Leading to the 3-equation model, SST-Cas DS/Dt term

10. 10 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Model implemented into Code_Saturne - 3D unstructured finite volume code (open source) Applied to a range of unsteady flows: - homogenous cyclic strain, oscillating channel, airfoil at high incidence, around circular cylinder Third equation found to add a 10-15% cost compared to standard 2 equation EVM model. - standard RSM is around 80% more expensive than a 2-equation model – 2D Flowfield around NACA0012 at 20 o, Re= 10 5 (2-eqns) (3-eqns) (7-eqns) Reproduces similar results to Reynolds Stress Model: Development of model

11. 11 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Applied to an isolated decaying vortex, initialised from DNS data of Duraisamy et al. (2006) UU UxUx Validation of SST-Cas model RSM Black lines are DNS data at fixed time intervals after initialisation. The 2 equation SST model shows a over-predicted rate of decay as expected. The RSM and Stress-Strain Lag model ( SST-Cas) are able to capture correctly the slower decay rate of the vortex. Turbulence slightly underpredicted at core with SST-Cas model. SST SST-Cas

12. 12 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Unstructured Grid Wingtip case requires fine grid resolution of both the very thin boundary layer over the wing, and the core of the vortex in the wake. Both regions are crucial in order to correctly model the flow. Structured meshes for this case quite large: RANS: ~ 9.3 Million Duraisamy (2005) LES at 10x Lower Re: ~ 26 Million Uzun (2006) Unstructured mesh using ‘Hanging Nodes’: ~ 1.2 Million cells, using in-house mesh generator from Stanford. Run at Manchester using Code_Saturne

13. 13 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Axial velocity Results with the SST-Cas Results from Unstructured Grid: plane location x/c = 0.456 downstream of trailing edge. Standard SST RSM SST-Cas EXPT (Chow et al) Under-prediction could be a result of under-refinement at the vortex core or other grid issues. RSMEXPT SSTSST-Cas

14. 14 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Unstructured Grid Tangential velocity RSM EXPT SST SST-Cas Turbulent kinetic energy RSM EXPT SST SST-Cas Turbulence is under-predicted. Misalignment effects are too strong. Similar findings in earlier results. (Craft et al., 2006)

15. 15 Fifth International Symposium on Turbulence and Shear Flow Phenomena, TUM, Garching, Germany. Aug 27-29 2007 A. Revell, K. Duraisamy & G. Iaccarino Conclusions Further work will focus on the generalisation of the modelling work for application to other models. The Stress-Strain Lag model (SST-Cas) has been shown to give substantial improvement over the baseline two equation model. Originally developed for unsteady mean flows First validated for the decaying isolated vortex: results similar to Reynolds Stress Model. These findings suggest that the inclusion of the advection of the strain is important in these flows. Vortical flows have been examined: in particular, the case of the trailing vortex in the wake of a wingtip Standard RANS models (both EVM and NLEVM) over-predict turbulence at the vortex core, and therefore under predict the downstream extent of the vortex. The Curvature Corrected v 2 -f model has been shown to significantly improve the prediction of the downstream vortex. An unstructured mesh has been used, enabling grid economies of around 80-90% Optimisation of the unstructured mesh