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Estimation of the Accuracy Obtained from CFD for industrial applications

Estimation of the Accuracy Obtained from CFD for industrial applications. Prepared by Imama Zaidi. Sources of Uncertainty. Computational Grid Grid Spacing Grid Topology Numerical Approximation User Errors Post Processing Turbulence Modelling

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Estimation of the Accuracy Obtained from CFD for industrial applications

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  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 V0=

  4. Part I Laminar Flow

  5. Flow inside Cavity

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

  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 Ra=103 n=2.33

  12. Effect of Order of Convergence Rich. Extrap. Using 102, 20, 40 Rich. Extrap. Using 202, 402, 802

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

  14. Richardson Extrapolation at Hot Wall

  15. Post Processing Error

  16. 40X40 20X20

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

  18. Effect of Changing Reference Velocity

  19. Effect of Numerical Scheme

  20. Square Grid

  21. Polyhedral Grid

  22. Skewed Grid

  23. Butterfly Type Grid

  24. 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

  25. Part II Turbulent Flow

  26. Flow inside Cavity

  27. Type of Mesh

  28. 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)

  29. Y+ from 40*40 Grid

  30. Y+ from 80*80 Grid

  31. Y+ from 160*160 Grid

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

  33. Spalart Allmaras

  34. V2f Model

  35. K-sst Model

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

  37. Near Wall Grid Dependence V2f Model

  38. 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

  39. 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.

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