Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-25T00:00:56.569Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-eddy simulation of the zero-pressure-gradient turbulent boundary layer up to Reθ = O(1012)

Published online by Cambridge University Press:  29 September 2011

M. Inoue  and
D. I. Pullin
M. Inoue*
Affiliation:
Graduate Aerospace Laboratories, 205-45, California Institute of Technology, Pasadena, CA 91125, USA
D. I. Pullin
Affiliation:
Graduate Aerospace Laboratories, 205-45, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: minoue@caltech.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A near-wall subgrid-scale (SGS) model is used to perform large-eddy simulation (LES) of the developing, smooth-wall, zero-pressure-gradient flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. Large-eddy simulations of the turbulent boundary layer are reported at Reynolds numbers based on the free-stream velocity and the momentum thickness in the range . Results include the inverse square-root skin-friction coefficient, , velocity profiles, the shape factor , the von Kármán ‘constant’ and the Coles wake factor as functions of . Comparisons with some direct numerical simulation (DNS) and experiment are made including turbulent intensity data from atmospheric-layer measurements at . At extremely large , the empirical Coles–Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that LES is suggestive of the asymptotic, infinite Reynolds number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger could be achieved with quad- or higher-precision arithmetic.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 507 - 533
Copyright
Copyright © Cambridge University Press 2011

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. Anderson, A. & Meneveau, C. 2011 Dynamic roughness model for large-eddy simulation of turbulent flow over multiscale, fractal-like rough surfaces. J. Fluid Mech. 679, 288–314.CrossRefGoogle Scholar
2. Araya, G., Castillo, L., Meneveau, C. & jansen, K. 2011 A dynamic multi-scale approach for turbulent inflow boundary conditions in spatially developing flows. J. Fluid Mech. 670, 581–605.CrossRefGoogle Scholar
3. Brasseur, J. G. & Wei, T. 2010 Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys. Fluids 22, 021303.CrossRefGoogle Scholar
4. Cabot, W. & Moin, P. 1999 Approximate wall boundary conditions in the large-eddy simulation of high Reynolds number flow. Flow Turbul. Combust. 63, 269–291.CrossRefGoogle Scholar
5. Chung, D. & McKeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341–364.CrossRefGoogle Scholar
6. Chung, D. & Pullin, D. I. 2009 Large-eddy simulation and wall-modelling of turbulent channel flow. J. Fluid Mech. 631, 281–309.CrossRefGoogle Scholar
7. Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.CrossRefGoogle Scholar
8. DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
9. Erm, L. P. & Joubert, P. N. 1991 Low-Reynolds-number turbulent boundary layers. J. Fluid Mech. 230, 1–44.CrossRefGoogle Scholar
10. Fasel, H. 1976 Investigation of the stability of boundary layers by a finite-difference model of the Navier–Stokes equations. J. Fluid Mech. 78.CrossRefGoogle Scholar
11. Ferrante, A. & Elghobashi, S. E. 2004 A robust method for generating inflow conditions for direct simulations of spatially-developing turbulent boundary layers. J. Comput. Phys. 198 (1), 372–387.CrossRefGoogle Scholar
12. Ferrante, A. & Elghobashi, S. E. 2005 Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J. Fluid Mech. 543, 93–106.CrossRefGoogle Scholar
13. Gottlieb, D. & Shu, C. W. 1997 On the Gibbs phenomenon and its resolution. SIAM Rev. 39 (4), 644–668.CrossRefGoogle Scholar
14. Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
15. Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
16. Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.CrossRefGoogle ScholarPubMed
17. Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
18. Jewkes, J. W., Chung, Y. M. & Carpenter, P. W. 2011 Modification to a turbulent inflow generation method for boundary-layer flows. AIAA J. 49 (1), 247–250.CrossRefGoogle Scholar
19. Jiménez, J. 2003 Computing high Reynolds number turbulence: will simulations ever replace experiments? J. Turbul. 4, 0227.CrossRefGoogle Scholar
20. Keating, A., Piomelli, U., Balaras, E. & Kaltenbach, H. J. 2004 A priori and a posteriori tests of inflow conditions for large-eddy simulation. Phys. Fluids 16, 4696.CrossRefGoogle Scholar
21. Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.CrossRefGoogle Scholar
22. Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177 (1), 133–166.CrossRefGoogle Scholar
23. Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA TN 3178.Google Scholar
24. Lesieur, M. & Metais, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 45–82.CrossRefGoogle Scholar
25. Liu, K. & Pletcher, R. H. 2006 Inflow conditions for the large-eddy simulation of turbulent boundary layers: a dynamic recycling procedure. J. Comput. Phys. 219 (1).CrossRefGoogle Scholar
26. Lu, H. & Porté-Agel, F. 2010 A modulated gradient model for large-eddy simulation: application to a neutral atmospheric boundary layer. Phys. Fluids 22, 015109.CrossRefGoogle Scholar
27. Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comput. Phys. 140 (2), 233–258.CrossRefGoogle Scholar
28. Lundgren, T. S. 1982 Strained spiral vortex model for turbulent fine structure. Phys. Fluids 25, 2193–2203.CrossRefGoogle Scholar
29. Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 2461.CrossRefGoogle Scholar
30. Marusic, I., Mathis, R. & Hutchins, N. 2010a Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193.CrossRefGoogle ScholarPubMed
31. Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010b Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
32. Marusic, I., Uddin, A. K. M. & Perry, A. E. 1997 Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 9, 3718.CrossRefGoogle Scholar
33. Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
34. Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32, 1–32.CrossRefGoogle Scholar
35. Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13, 692–701.CrossRefGoogle Scholar
36. Metzger, M., McKeon, B. J. & Holmes, H. 2007 The near-neutral atmospheric surface layer: turbulence and non-stationarity. Phil. Trans. R. Soc. A 365, 859–876.CrossRefGoogle ScholarPubMed
37. Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9, 2443–2454.CrossRefGoogle Scholar
38. Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101.CrossRefGoogle Scholar
39. Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143 (1), 90–124.CrossRefGoogle Scholar
40. Morrison, J. F., McKeon, B. J., Jiang, W. & Smits, A. J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99–131.CrossRefGoogle Scholar
41. Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. A Math. Phys. Engng Sci. 365 (1852), 755.CrossRefGoogle Scholar
42. Nickels, T. B., Marusic, I., Hafez, S., Hutchins, N. & Chong, M. S. 2007 Some predictions of the attached eddy model for a high Reynolds number boundary layer. Phil. Trans. R. Soc. A 365, 807–822.CrossRefGoogle ScholarPubMed
43. O’Gorman, P. A. & Pullin, D. I. 2003 The velocity-scalar cross spectrum of stretched spiral vortices. Phys. Fluids 15, 280–291.CrossRefGoogle Scholar
44. Österlund, J. M. 1999 Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, KTH, Mechanics.Google Scholar
45. Perot, J. B. 1993 An analysis of the fractional step method. J. Comput. Phys. 108 (1), 51–58.CrossRefGoogle Scholar
46. Piomelli, U. 2008 Wall-layer models for large-eddy simulation. Prog. Aeronaut. Sci. 44, 437–446.CrossRefGoogle Scholar
47. Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34, 349–374.CrossRefGoogle Scholar
48. Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
49. Pope, S. B. 2004 Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35.CrossRefGoogle Scholar
50. Porté-Agel, F., Meneveau, C. & Parlange, M. C. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
51. Pullin, D. I. 2000 A vortex-based model for the subgrid flux of a passive scalar. Phys. Fluids 12, 2311–2319.CrossRefGoogle Scholar
52. Pullin, D. I. & Lundgren, T. S. 2001 Axial motion and scalar transport in stretched spiral vortices. Phys. Fluids 13, 2553–2563.CrossRefGoogle Scholar
53. Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
54. Sagaut, P. 2002 Large-eddy Simulation for Incompressible Flow: An Introduction. Springer.CrossRefGoogle Scholar
55. Schlatter, P., Li, Q., Brethouwer, G., Johansson, A. V. & Henningson, D. S. 2010 Simulations of spatially evolving turbulent boundary layers up to . Intl J. Heat Fluid Flow 31 (3), 251–261.CrossRefGoogle Scholar
56. Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
57. Simens, M. P. 2008 The study and control of wall-bounded flows. PhD thesis, Aeronautics, Universidad Politécnica de Madrid, http://oa.upm.es/1047/.Google Scholar
58. Simens, M. P., Jiménez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228 (11), 4218–4231.CrossRefGoogle Scholar
59. Spalart, P. R 1988 Direct simulation of a turbulent boundary layer up to . J. Fluid Mech. 187, 61.CrossRefGoogle Scholar
60. Spalart, P. R., Moser, R. D. & Rogers, M. M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297–324.CrossRefGoogle Scholar
61. Templeton, J. A., Medic, G. & Kalitzin, G. 2005 An eddy-viscosity based near-wall treatment for coarse grid large-eddy simulation. Phys. Fluids 17, 105101.CrossRefGoogle Scholar
62. Templeton, J. A., Wang, M. & Moin, P. 2008 A predictive wall model for large-eddy simulation based on optimal control techniques. Phys. Fluids 20, 065104.CrossRefGoogle Scholar
63. Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
64. Voelkl, T., Pullin, D. I. & Chan, D. C. 2000 A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation. Phys. Fluids 12, 1810–1825.CrossRefGoogle Scholar
65. Wang, M. & Moin, P. 2002 Dynamic wall modelling for large-eddy simulation of complex turbulent flows. Phys. Fluids 14, 2043–2051.CrossRefGoogle Scholar
66. Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar