Aspects of Transitional flow for External Applications

1. Aspects of Transitional flow for External Applications A review presented by Clare Turner

2. Presentation Outline • Review of T3 flat plate tests • Conclusions from the flat plate tests • Direction for transition prediction • Current and future work

3. T3 Flat Plate Tests

4. Original Simulation Set-up • Domain size taken from S. R. Likki : • S = 0.05m • L = 3.3m • H = 0.08m • Inlet conditions: • k = 0.0536 m2/s2 • ε = 1.35 m2/s3 • U = 5.08 m/s • y+ ≈ 1

5. Initial Results

6. Anomalous Results After Craft et al.:

7. Possible Areas for Error • Differencing scheme • Grid density • y+ value • Residual tolerance • Domain size • Boundary conditions • Cell distribution • Near wall treatment

8. Differencing Scheme

9. Number of Streamwise Cells

10. Y+ Value

11. Number of cross-stream cells • Grids have 23, 34 and 39 cells in the viscous layer respectively

12. Domain Height

13. Cell Distribution • Several meshes generated to compare results and convergence; largest cell distribution: • More efficient to concentrate cells at the leading edge • 39390

14. Stream-wise Growth-rate

15. Convergence To the left: growthrate=1; to the right growthrate = 1.012

16. Low Reynolds Number Models Available in Star-CD: “Standard” where

17. Low Reynolds Number Models Available in Star-CD: Suga’s where

18. Near Wall Treatment (1)

19. Near Wall Treatment (2)

20. Determination of Inlet Values • Dissipation rate originally tailored to FSTI curve

21. Re-calibration of Inlet Values • Free-stream taken to be at the edge of boundary layer • Experimentally free-stream is at approximately 3 delta • Turbulence intensities calculated with new definition

22. Effect of Chosen Free-stream boundary • Error was not in the calculation of the free-stream

23. Inlet Values in Literature • Inlet k and epsilon values differ to those in literature • Differences may arise due to choice of U_inlet • 3 different inlets are tested with U = 5 m/s: • Using a correlation for lengthscale from work of Savill and interpolating FSTI at inlet • As above but with a higher FSTI • As 2) but with a lengthscale used by Chen et al.

24. Choice of Inlet Velocity • Original velocity set to 5.08 • Velocity at leading edge should be approx 5 m/s • Turbulence model does not replicate acceleration at the leading edge

25. Effect of Chosen Inlet Values (1)

26. Effect of Chosen Inlet Values (2)

27. T3 Conclusions • Largest contributing factor is the low Reynolds number treatment • Sufficient work has been done on the grid to only require small alterations for future tests • Non-linear eddy-viscosity models improve transition onset prediction and running time is not increased dramatically but no alterations can improve transition length prediction.

28. Approaches for a Physical Solution rather than Correlation Based Models 3 possible approaches: Adaptation of low Reynolds number RANS models, eg. higher order of closure, tailored to specific application. An intermittency model derived using PDFs A model using the concept of laminar kinetic energy

29. 1) Low Reynolds Number RANS Models Advantages: Large amount of in-house knowledge Have models to develop, low risk Disadvantages: Nothing new to contribute Low Re models do not accurately represent the transition process Higher orders of closure increase computational cost

30. 2) Physical Intermittency Model Advantages: New approach Should be able to predict all modes of transition Disadvantages: No literature to refer to - risky Have little expertise in PDFs Little or no time would remain to apply to rear wing

31. 3) Concept of Laminar Kinetic Energy Advantages: Relatively new giving areas for improvement Does not rely on diffusion dominated transition Only requires one additional equation Disadvantages: Walters and Leylek model (2002) gives poor reaction to large pressure gradients Determination of the effective length-scale is only based on distance from the wall

32. Walters and Leylek Model (2003) • This is the starting point for 2k model development

33. Walters and Leylek Model (2003) • Walters and Leylek assume large scales contribute to the laminar kinetic energy and small scales to the turbulent kinetic energy. • The cut – off point is the effective length-scale : • Sveningsson uses a different definition:

34. Effective Length-scale Along the Plate At 400 mm (transitional region) : δ99 = 18.5 mm

35. Effective Length-scale Along the Plate At 800 mm (turbulent region) : δ99 = 24.1 mm

36. Current Work • Adjusting individual terms of Wilcox’s transport equations for turbulent kinetic energy and specific dissipation rate to those of Walters and Leylek • Testing code by inserting fully turbulent values from completed simulations Aiming to ... • Use code with Saturne assuming laminar kinetic energy = 0 • Create new scalar variable KL to complete Walters and Leylek Model

37. Any Questions?

38. Walters and Leylek Model 2002