Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-24T18:38:21.428Z Has data issue: false hasContentIssue false
  • English
  • Français

Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows

Published online by Cambridge University Press:  07 June 2012

Shiyi Chen ,
Zhenhua Xia ,
Suyang Pei ,
Jianchun Wang ,
Yantao Yang ,
Zuoli Xiao  and
Yipeng Shi
Shiyi Chen
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Zhenhua Xia
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Suyang Pei
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China
Jianchun Wang
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China
Yantao Yang
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China
Zuoli Xiao
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Yipeng Shi*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, College of Engineering and CAPT & CCSE, Peking University, Beijing 100871, PR China Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
*
†Email address for correspondence: syp@mech.pku.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In the traditional hybrid RANS/LES approaches for the simulation of wall-bounded fluid turbulence, such as detached-eddy simulation (DES), the whole flow domain is divided into an inner layer and an outer layer. Typically the Reynolds-averaged Navier–Stokes (RANS) equations are used for the inner layer, while large-eddy simulation (LES) is used for the outer layer. The transition from the inner-layer solution to the outer-layer solution is often problematic due to the lack of small-scale dynamics in the RANS region. In this paper, we propose to simulate the whole flow domain by large-eddy simulation while enforcing a Reynolds-stress constraint on the subgrid-scale (SGS) stress model in the inner layer. Both the algebraic eddy-viscosity model and the one-equation Spalart–Allmaras (SA) model have been used to constrain the Reynolds stress in the inner layer. In this way, we improve the LES methodology by allowing the mean flow of the inner layer to satisfy the RANS solution while small-scale dynamics is included. We validate the Reynolds-stress-constrained large-eddy simulation (RSC-LES) model by simulating three-dimensional turbulent channel flow and flow past a circular cylinder. Our model is able to predict mean velocity, turbulent stress and skin-friction coefficients more accurately in turbulent channel flow and to estimate the pressure coefficient after separation more precisely in flow past a circular cylinder compared with the pure dynamic Smagorinsky model (DSM) and DES using the same grid resolution. Furthermore, the computational cost of the RSC-LES is almost the same as that of DES.

JFM classification

Turbulent Flows: Turbulence control Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 1 - 28
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Achenbach, E. 1968 Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to . J. Fluid Mech. 34 (4), 625–639.Google Scholar
2. Baggett, J. S. 1998 On the feasibility of merging LES with RANS in the near-wall region of attached turbulent flows. In Annu. Res. Briefs, pp. 267–277. Stanford University: Center Turbul. Res.Google Scholar
3. Balaras, E. & Benocci, C. 1994 Subgrid-scale models in finite-difference simulations of complex wall bounded flows. In AGARD CP 551, pp. 2.1–2.5. AGARD: Neuilly-Sur-Seine.Google Scholar
4. Balaras, E., Benocci, C. & Piomelli, U. 1996 Two-layer approximate boundary conditions for large-eddy simulations. AIAA J. 34 (6), 1111–1119.CrossRefGoogle Scholar
5. Breuer, M. 1998 Large eddy simulation of the subcritical flow past a circular cylinder numerical and modeling aspects. Intl J. Numer. Meth. Fluids 28, 1281–1302.3.0.CO;2-#>CrossRefGoogle Scholar
6. Breuer, M. 2000 A challenging test case for large eddy simulation: high Reynolds number circular cylinder flow. Intl J. Heat Fluid Flow 21, 648–654.Google Scholar
7. Cabot, W. H. 1995 Large-eddy simulations with wall models. In Annu. Res. Briefs 1995, pp. 41–50. Stanford University: Center Turbul. Res.Google Scholar
8. Cabot, W. H. 1996 Near-wall models in large eddy simulations of flow behind a backward-facing step. In Annu. Res. Briefs 1996, pp. 199–210. Stanford University.Google Scholar
9. Cabot, W. H. & Moin, P. 1999 Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flows. Flow Turbul. Combust. 63, 269–291.CrossRefGoogle Scholar
10. Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.CrossRefGoogle Scholar
11. Constantinescu, G. & Squires, K. 2004 Numerical investigation of flow over a sphere in the subcritical and supercritical regimes. Phys. Fluids 16, 1449–1466.CrossRefGoogle Scholar
12. Davidson, L. & Peng, S. H. 2003 Hybrid LES-RANS modelling: a one-equation SGS model combined with a model for predicting recirculating flows. Intl J. Numer. Meth. Fluids 43 (9), 1003–1018.CrossRefGoogle Scholar
13. Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME: J. Fluids Engng 100, 215–223.Google Scholar
14. Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41 (2), 453–480.CrossRefGoogle Scholar
15. Dejoan, A. & Schiestel, R. 2002 LES of unsteady turbulence via a one-equation subgrid-scale transport model. Intl J. Heat Fluid Flow 23, 398–412.CrossRefGoogle Scholar
16. Dong, S., Karniadakis, G. E., Ekmekci, A. & Rockwell, D. 2006 A combined direct numerical simulation-particle image velocimetry study of the turbulent near wake. J. Fluid Mech. 569, 185–207.CrossRefGoogle Scholar
17. van Driest, E. R. 1956 On turbulent flow near a wall. J. Aerosp. Sci. 23, 1007–1011.Google Scholar
18. Forsythe, J. R., Hoffmann, K. A., Cummings, R. M. & Squires, K. D. 2002 Detached-eddy simulation with compressibility corrections applied to a supersonic axisymmetric base flow. Trans. ASME: J. Fluids Engng 124, 911–923.Google Scholar
19. Fröhlich, J. & von Terzi, D. 2008 Hybrid LES/RANS methods for the simulation of turbulent flows. Prog. Aerosp. Sci. 44, 349–377.CrossRefGoogle Scholar
20. Gaskell, P. H. & Lau, A. K. C. 1988 Curvature-compensated convective transport: smart, a new boundedness-preserving transport algorithm. Intl J. Numer. Meth. Fluids 8, 617–641.Google Scholar
21. Georgiadis, N. J. 2008 Introduction: large-eddy simulation current capabilities and areas of needed research. Prog. Aerosp. Sci. 44, 379–380.CrossRefGoogle Scholar
22. Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
23. Ghosal, S., Lund, T. S., Moin, P. & Akselvoll, K. 1995 A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286, 229–255.CrossRefGoogle Scholar
24. Hamba, F. 2002 An approach to hybrid RANS/LES calculation of channel flows. In Engineering Turbulence Modelling and Experiments (ed. Rodi, W. & Fueyo, N. ), vol. 5, pp. 297–306. Elsevier.CrossRefGoogle Scholar
25. Haworth, D. C. & Jansen, K. 2000 Large-eddy simulation on unstructured deforming meshes: toward reciprocating ic engines. Comput. Fluids 29, 493–524.Google Scholar
26. Hoyas, S. & Jimenez, J. 2006 Scaling of velocity fluctuations in turbulent channels up to . Phys. Fluids 18, 011702.Google Scholar
27. Kapadia, S. & Roy, S. 2003 Detached eddy simulation over a reference ahmed car model. AIAA Paper 2003-0857.CrossRefGoogle Scholar
28. Keating, A., Prisco, G. De & Piomelli, U. 2006 Interface conditions for hybrid RANS/LES calculations. Intl J. Heat Fluid Flow 27, 777–788.Google Scholar
29. Kim, J., Moin, P. & Moser, R. D. 1987 Turbulent statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.Google Scholar
30. Kraichnan, R. H. 1985 Decimated amplitude equations in turbulence dynamics. In Theoretical approaches to turbulence (ed. Dwoyer, D. L., Hussaini, M. Y. & Voigt, R. G. ), vol. 58, pp. 91–135. Springer.CrossRefGoogle Scholar
31. Kraichnan, R. H. & Chen, S. 1989 Is there a statistical mechanics of turbulence?. Physica D 37, 160–172.Google Scholar
32. Kravchenko, A. G. & Moin, P. 2000 Numerical studies of flow over a circular cylinder at . Phys. Fluids 12, 403–417.Google Scholar
33. Labourasse, E. & Sagaut, P. 2002 Reconstruction of turbulent fluctuations using a hybrid RANS/LES approach. J. Comput. Phys. 182, 301–336.Google Scholar
34. Leonard, B. P. 1991 The ultimate conservative difference scheme applied to unsteady one dimensional advection. Comput. Meth. Appl. Mech. Engng 88, 17–74.CrossRefGoogle Scholar
35. Leveque, E., Toschi, F., Shao, L. & Bertoglio, J. P. 2007 Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows. J. Fluid Mech. 570, 491–502.CrossRefGoogle Scholar
36. Lilly, D. K. 1992 A proposed modification of Germano subgrid-scale closure method. Phys. Fluids A 4, 633–635.Google Scholar
37. Loh, K. C. & Domaradzki, J. A. 1999 The subgrid-scale estimation model on nonuniform grids. Phys. Fluids 11 (12), 3786–3792.CrossRefGoogle Scholar
38. Meneveau, C. 1994 Statistics of turbulence subgrid-scale stresses: necessary conditions and experimental tests. Phys. Fluids 6 (2), 815–833.Google Scholar
39. Meneveau, C. & Katz, J. 1999 Dynamic testing of subgrid models in large eddy simulation based on Germano identity. Phys. Fluids 11, 245–247.CrossRefGoogle Scholar
40. Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
41. Meneveau, C., Lund, T. S. & Cabot, W. H. 1996 A Lagrangian dynamic subgrid-scale model turbulence. J. Fluid Mech. 319, 353–358.Google Scholar
42. Meyers, J. & Sagaut, P. 2007 Is plane-channel flow a friendly case for the testing of large-eddy simulation subgrid-scale models. Phys. Fluids 19, 048105.CrossRefGoogle Scholar
43. Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.CrossRefGoogle Scholar
44. Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to . Phys. Fluids 11 (4), 943–945.CrossRefGoogle Scholar
45. Nikitin, N. V., Nicoud, F., Wasistho, B., Squires, K. D. & Spalart, P. R. 2000 An approach to wall modeling in large-eddy simulations. Phys. Fluids 12, 1629–1632.Google Scholar
46. Norberg, C. 1987 Effects of Reynolds number and low-intensity free stream turbulence on the flow around a circular cylinder. In Publ. No. 87 :2. Gothenburg, Sweden: Department of Applied Thermoscience and Fluid Mech., Chalmers University of Technology.Google Scholar
47. van Nunen, J. W. G. 1974 Pressure and forces on a circular cylinder in a cross flow at high Reynolds numbers. In Flow Induced Structural Vibrations (ed. Naudascher, E. ), pp. 748–754. Springer.CrossRefGoogle Scholar
48. Parnaudeau, P., Carlier, J., Heitz, D. & Lamballais, E. 2008 Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900. Phys. Fluids 20, 085101.Google Scholar
49. Piomelli, U. 1993 High Reynolds number calculations using the dynamic subgrid-scale stress model. Phys. Fluids A 5, 1484–1490.CrossRefGoogle Scholar
50. Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
51. Piomelli, U., Balaras, E., Pasinato, H., Squires, K. D. & Spalart, P. R. 2003 The inner–outer layer interface in large-eddy simulations with wall-layer models. Intl J. Heat Fluid Flow 24, 538–550.Google Scholar
52. Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
53. Roshko, A. 1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10 (3), 345–356.CrossRefGoogle Scholar
54. Sagaut, P., Deck, S. & Terracol, M. 2006 Multiscale and Multiresolution approaches in turbulence. Imperial College Press.Google Scholar
55. Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404.Google Scholar
56. Shi, Y., Xiao, Z. & Chen, S. 2008 Constrained subgrid-scale stress model for large eddy simulation. Phys. Fluids 20, 011701.Google Scholar
57. Shur, M., Spalart, P. R., Strelets, M. & Travin, A. 1999 Detached-eddy simulation of an airfoil at high angle of attack. In Fourth International Symposium on Engineering Turbulence Modelling and Experiments, Corsica (ed. Rodi, W. & Laurence, D. ). Elsevier.Google Scholar
58. Shur, M., Spalart, P. R., Strelets, M. & Travin, A. 2008 A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Intl J. Heat Fluid Flow 29, 1638–1649.Google Scholar
59. Son, J. & Hanratty, T. J. 1969 Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from to . J. Fluid Mech. 35, 353–368.Google Scholar
60. Spalart, P. R. 2000 Strategies for turbulence modelling and simulations. Intl J. Heat Fluid Flow 21, 252–263.Google Scholar
61. Spalart, P. R. 2009 Detached-eddy simulation. Annu. Rev. Fluid Mech. 41, 181–202.CrossRefGoogle Scholar
62. Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. Rech. Aerosp. 1, 5–21.Google Scholar
63. Spalart, P. R., Deck, S., Shur, M., Squires, K., Strelets, M. & Travin, A. 2006 A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20, 181–195.Google Scholar
64. Spalart, P. R., Jou, W. H., Strelets, M. & Allmaras, S. R. 1997 Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach. In Advances in DNS/LES (ed. Liu, C. & Liu, Z. ), pp. 137–148. Greyden Press.Google Scholar
65. Squires, K. D. 2004 Invited lecture: detached-eddy simulation: current status and perspectives. ERCOFTAC Ser. 9, 465–480.Google Scholar
66. Squires, K. D., Forsythe, J. R., Morton, S. A., Strang, W. Z., Wurtzler, K. E., Tomaro, R. F., Grismer, M. J. & Spalart, P. R. 2002 Progress on detached-eddy simulation of massively separated flows. AIAA Paper 2002-1021.CrossRefGoogle Scholar
67. Strelets, M. 2001 Detached-eddy simulation of massively separated flows. AIAA Paper 2001-0879. Washington, DC.Google Scholar
68. Temmerman, L., Hadžiabdiæ, M., Leschziner, M. A. & Hanjaliæ, K. 2005 A hybrid two-layer URANS-LES approach for large eddy simulation at high Reynolds numbers. Intl J. Heat Fluid Flow 26, 173–190.Google Scholar
69. Tessicini, F., Temmerman, L. & Leschziner, M. A. 2006 Approximate near-wall treatments based on zonal and hybrid RANSCLES methods for LES at high Reynolds numbers. Intl J. Heat Fluid Flow 27, 789–799.CrossRefGoogle Scholar
70. Travin, A., Shur, M., Strelets, M. & Spalart, P. R. 1999 Detached-eddy simulations past a circular cylinder. Flow Turbul. Combust. 63, 293–313.Google Scholar
71. Travin, A., Shur, M., Strelets, M. & Spalart, P. R. 2002 Physical and numerical upgrades in the detached-eddy simulations of complex turbulent flows. In Advances in LES of Complex Flows (ed. Friederich, R. & Rodi, W. ), vol. 65, pp. 239–254. Kluwer.CrossRefGoogle Scholar
72. Uribe, J. C., Jarrin, N., Prosser, R. & Laurence, D. 2009 Two-velocities hybrid RANS-LES of a trailing edge flows. In IUTAM Symposium on Unsteady Separated Flows and their Control (ed. Braza, M. & Hourigan, K. ). IUTAM Bookseries , vol. 14. pp. 63–75. Springer.Google Scholar
73. Warschauer, K. A. & Leene, J. A. 1971 Experiments on mean and fluctuating pressures of circular cylinders at cross flow at very high Reynolds numbers. In Proc. Intl Conf. on Wind Effects on Buildings and Structures, Tokyo, Japan, 6–9 Sept., pp. 305–315.Google Scholar
74. Zang, Y., Street, R. L. & Coseff, J. R. 1994 A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates. J. Comput. Phys. 114, 18–33.CrossRefGoogle Scholar