A new conception turbulence model with partial average.

1. Investigation ofGao-Yong turbulence model with OpenFOAM Haibin LI Haibin_Li@hotmail.com 25/05/09

2. Abtract In this talk, a relatively newturbulence model named Gao-Yongturbulence model is investigated using the open source software—OpenFOAM. A newly developed statistical partial average scheme is presented. As the ensemble average is taken on two groups of turbulent fluctuations separately, the partial average scheme able to capture the first-order statistical moment of the fluctuation field, providing valuable information in addition to what have been known in the past from the conventional Reynolds average. Without any empirical coefficients, the derived equations can be used to simulate statistical mean behaviours and coherent structures of various benchmark turbulent flows. The simulated results are in good agreement with experimental data. 5/22/2009 2 Haibin_Li@hotmail.com

4. Gao-Yong turbulence model

5. The deriving process of Gao-Yong turbulence model

6. Ensemble average

7. Partial average

8. Open source software - OpenFOAM

9. The simulated examples5/22/2009 3 Haibin_Li@hotmail.com

11. Why – the significance

12. How – the current methods5/22/2009 4 Haibin_Li@hotmail.com

14. No exact defination.

15. Renolds Experiment5/22/2009 5 Haibin_Li@hotmail.com

19. No any adjustable empirical coefficients

20. Do not need wall function

21. Some steady numerical examples5/22/2009 7 Haibin_Li@hotmail.com

22. GAO-YONG TURBULENCE EUQTIONS Define the partial average of the fluctuations as: Where 5/22/2009 8 Haibin_Li@hotmail.com

23. GAO-YONG TURBULENCE EUQTIONS Applying the partial average to fluctuation equations we will get equations Model We also have continuity equation: 5/22/2009 9 Haibin_Li@hotmail.com

24. GAO-YONG TURBULENCE EUQTIONS Suppose that the constitutive relationship still exists along the direction of mean flow velocity . In coordinate system 123 constituted by , Where operator has the same meaning of “scale” in OpenFOAM Where Suppose is orthotropic and is the principal material axes Where xyz global coordinate system, is coordinate transformation tensor. 5/22/2009 10 Haibin_Li@hotmail.com

25. GAO-YONG TURBULENCE EUQTIONS energy dissipation due to eddy viscosity is the work done by fluctuation force over L also considering the phenomenon of turbulence energy inversion, item should be subtracted from the right-hand side of the second equation , therefore 5/22/2009 11 Haibin_Li@hotmail.com

27. Bad generality, readability

28. Repeated work

29. one year for one example

30. Based on secondary development of closed source software.

31. Limited the innovation, procedure has to be changed.

32. Debug is difficult.

33. Failed

34. Based on OpenFOAM

35. Rapidly development

36. Quick investigation, one month for one example5/22/2009 12 Haibin_Li@hotmail.com

38. 80X80X1 Grid is employed

39. Gao-Yong model and K-Epsilon model is seperately used

40. Transient simulation is finished

41. Initial flow field is stationary5/22/2009 13 Haibin_Li@hotmail.com

42. Comparison of U-velocity profiles along a vertical line passing through the geometry centre of the cavity 5/22/2009 14 Haibin_Li@hotmail.com

43. U-velocity profiles along a vertical line passing through the geometry centre of the cavity from t=0s to t=6s, Gao-Yong turbulence model 5/22/2009 15 Haibin_Li@hotmail.com

44. U-velocity profiles along a vertical line passing through the geometry centre of the cavity from t=7s to t=80s, Gao-Yong turbulence model 5/22/2009 16 Haibin_Li@hotmail.com

45. Re=10,000 Grid 80X80X1, t=80s, Gao-Yong model by Erturk Comparison of Streamlines 5/22/2009 17 Haibin_Li@hotmail.com

46. Comparison of Streamlines Re=10,000 Grid 80X80X1, t=80s, K-Epsilon model by Erturk 5/22/2009 18 Haibin_Li@hotmail.com

47. Streamlines from t=0s to t=6s, Gao-Yong model 5/22/2009 19 Haibin_Li@hotmail.com

48. Streamlines from t=7s to t=80s, Gao-Yong model 5/22/2009 20 Haibin_Li@hotmail.com

49. Streamlines t=6s, DNS & Gao-Yong model 5/22/2009 21 Haibin_Li@hotmail.com

50. The Stream Function Vorticity Method by Erturk Gao-Yong turbulence model t=80s Comparison of Vorticity Contour 5/22/2009 22 Haibin_Li@hotmail.com Re=10,000 Grid 80X80X1, t=80s

51. Comparison of Vorticity Contour The Stream Function Vorticity Method by Erturk K-Epsilon Turbulence model t=80s 5/22/2009 23 Haibin_Li@hotmail.com Re=10,000 Grid 80X80X1, t=80s

53. Gao-Yong turbulence model is able to gain real viscosity field in complex flow under coarse grid and unsteady condition.

54. The existing closed source software has limitations to the users, and therefore fail in the research, especially in the innovation research.

55. There is an improvement space for OpenFOAM in some aspects, such as:

56. Function of open community.

57. Open project management.

58. Open source code management.

59. Effective bug track system.

60. User interface.5/22/2009 24 Haibin_Li@hotmail.com