1. Estimation of the Accuracy Obtained from CFD for industrial applications Prepared by Imama Zaidi

2. Sources of Uncertainty Computational Grid –Grid Spacing –Grid Topology Numerical Approximation User Errors Post Processing Turbulence Modelling Flow complexity (multi-phase flow, combustion… etc)

3. Problem Definition Rayleigh Number Ra= Reference Velocity V 0 =

4. Part I Laminar Flow

5. Flow inside Cavity

6. Types of Grids tested Square grid Polyhedral Skewed Butterfly type

7. Numerical Schemes tested Convection schemes: Second Order Upwind First Order Upwind Central Differencing Scheme Note: Runs are carried out in steady state mode

8. Richardson Extrapolation Grid independent solution Order of convergence Exact solution Targets: Nu and Mass flow across ½ section =>

9. Second Order Upwind Square grid

10. First Order Upwind Square grid

11. Central Differencing Scheme n=2.33 Ra=10 3

12. Effect of Order of Convergence Rich. Extrap. Using 10 2, 20, 40 Rich. Extrap. Using 20 2, 402, 802

13. Effect of Order of Convergence n=1.72 n=1.96

14. Richardson Extrapolation at Hot Wall

15. Post Processing Error

17. 20X20 40X40

18. Example for user input Error Reference velocity is defined as:

19. Effect of Changing Reference Velocity

20. Effect of Numerical Scheme

21. Square Grid

22. Polyhedral Grid

23. Skewed Grid

24. Butterfly Type Grid

25. Why does error not always decrease? For square grid –Dx.Dt error > Dx2 ? But this is steady state –Residual normalisation? But increasing nb of iteration => no change For skewed grid –Error = constant, whatever h. –Need to test other “gradient reconstruction” methods for non-orthogonality

26. Part II Turbulent Flow

27. Flow inside Cavity

28. Type of Mesh

29. Low Reynolds Number Model Standard Low Reynolds Number Model (Lein et all) Abe Nagano Kondoh (ANK)Low Reynolds Model (Abe et all) V2f Model(Durbin et all) Model(Mentor) Spalart Allamaras (SA) Model (Baldwin et all)

30. Y+ from 40*40 Grid

31. Y+ from 80*80 Grid

32. Y+ from 160*160 Grid

33. Error From Different Turbulence Models For Nu Kω-sst model

34. Spalart Allmaras

35. V2f Model

36. K  -sst Model

37. Near Wall Grid Dependence Kw-sst Model Grid 80X80 and changing near-wall cell  x

38. Near Wall Grid Dependence V2f Model

39. Conclusions For distorted grids (Skewed Mesh), the refinement does not guarantee the accuracy The higher the order of scheme is, the higher will be the accuracy. Richardson extrapolation theory tested for laminar flow, seems to be in good agreement with the results for order of convergence nearly equals to 2

40. Conclusions K  SST model compared to the other models tested, seems more dependent on the grid refinement near the wall and grid independence is not reached even with 160x160 grid.