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Flow topology in compressible turbulent boundary layer

Published online by Cambridge University Press:  14 June 2012

Li Wang  and
Xi-Yun Lu
Li Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
†Email address for correspondence: xlu@ustc.edu.cn
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Abstract

The flow topologies of compressible turbulent boundary layers at Mach 2 are investigated by means of direct numerical simulation (DNS) of the compressible Navier–Stokes equations, and statistical analysis of the invariants of the velocity gradient tensor. We identify a preference for an unstable focus/compressing topology in the inner layer and an unstable node/saddle/saddle (UN/S/S) topology in the outer layer. The dissipation and dissipation production originate mainly from this UN/S/S topology. The enstrophy depends mainly on an unstable focus/stretching (UFS) topology, and the enstrophy production relies on a UN/S/S topology in the inner layer and on a UFS topology in the outer layer. The compressibility effect on the statistical properties of the topologies is investigated in terms of the ‘incompressible’, compressed and expanding regions. It is found that the locally compressed region tends to be more stable and the locally expanding region tends to be more dissipative. The compressibility is mainly related to unstable focus/compressing and stable focus/stretching topologies. Moreover, the features of the average dissipation, enstrophy, dissipation production and enstrophy production of the various topologies are clarified in the locally compressed and expanding regions.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 255 - 278
Copyright
Copyright © Cambridge University Press 2012

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References

1. Abe, H., Antonia, R. A. & Kawamura, H. 2009 Correlation between small-scale velocity and scalar fluctuations in a turbulent channel flow. J. Fluid Mech. 627, 1–32.CrossRefGoogle Scholar
2. Adams, N. A. 1998 Direct numerical simulation of turbulent compression ramp flow. Theor. Comput. Fluid Dyn. 12, 109–129.CrossRefGoogle Scholar
3. Andreopoulos, Y. & Honkan, A. 2001 An experimental study of the dissipative and vortical motion in turbulent boundary layers. J. Fluid Mech. 439, 131–163.CrossRefGoogle Scholar
4. Bermejo-Moreno, I., Pullin, D. I. & Horiuti, K. 2009 Geometry of enstrophy and dissipation, resolution effects and proximity issues in turbulence. J. Fluid Mech. 620, 121–166.CrossRefGoogle Scholar
5. Bijlard, M. J., Oliemans, R. V. A., Portela, L. M. & Ooms, G. 2010 Direct numerical simulation analysis of local flow topology in a particle-laden turbulent channel flow. J. Fluid Mech. 653, 35–56.CrossRefGoogle Scholar
6. Blackburn, H. M., Mansour, N. & Cantwell, B. J. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 301, 269–292.CrossRefGoogle Scholar
7. van der Bos, F., Tao, B., Meneveau, C. & Katz, J. 2002 Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements. Phys. Fluids 14 (7), 2456–2474.CrossRefGoogle Scholar
8. Buxton, O. R. H. & Ganapathisubramani, B. 2010 Amplification of enstrophy in the far field of an axisymmetric turbulent jet. J. Fluid Mech. 651, 483–502.CrossRefGoogle Scholar
9. Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4 (4), 782–793.CrossRefGoogle Scholar
10. Chacin, J. M. & Cantwell, B. J. 2000 Dynamics of a low Reynolds number turbulent boundary layer. J. Fluid Mech. 404, 87–115.CrossRefGoogle Scholar
11. Chacín, J. M., Cantwell, B. J. & Kline, S. J. 1996 Study of turbulent boundary layer structure using the invariants of the velocity gradient tensor. Exp. Therm. Fluid Sci. 13, 308–317.CrossRefGoogle Scholar
12. Chertkov, M., Pumir, A. & Shraiman, B. I. 1999 Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys. Fluids 11 (8), 2394–2410.CrossRefGoogle Scholar
13. Chevillard, L., Meneveau, C., Biferale, L. & Toschi, F. 2008 Modeling the pressure Hessian and viscous Laplacian in turbulence: comparisons with direct numerical simulation and implications on velocity gradient dynamics. Phys. Fluids 20, 101504.CrossRefGoogle Scholar
14. Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.CrossRefGoogle Scholar
15. Chong, M. S., Soria, J., Perry, A. E., Chacin, J., Cantwell, B. J. & Na, Y. 1998 Turbulence structures of wall-bounded shear flows found using DNS data. J. Fluid Mech. 357, 225–247.CrossRefGoogle Scholar
16. Diamessis, P. J. & Nomura, K. K. 2000 Interaction of vorticity, rate-of-strain, and scalar gradient in stratified homogeneous sheared turbulence. Phys. Fluids 12 (5), 1166–1188.CrossRefGoogle Scholar
17. Duan, L., Beekman, I. & Martin, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245–267.CrossRefGoogle Scholar
18. Eléna, M. & Lacharme, J. 1988 Experimental study of a supersonic turbulent boundary layer using a laser Doppler anemometer. J. Méc. Théor. Appl. 7, 175–190.Google Scholar
19. Elsinga, G. E., Adrian, R. J., van Oudheusden, B. W. & Scarano, F. 2010 Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer. J. Fluid Mech. 644, 35–60.CrossRefGoogle Scholar
20. Elsinga, G. E. & Marusic, I. 2010a Evolution and lifetimes of flow topology in a turbulent boundary layer. Phys. Fluids 22, 015102.CrossRefGoogle Scholar
21. Elsinga, G. E. & Marusic, I. 2010b Universal aspects of small-scale motions in turbulence. J. Fluid Mech. 662, 514–539.CrossRefGoogle Scholar
22. Galanti, B. & Tsinober, A. 2000 Self-amplification of the field of velocity derivatives in quasi-isotropic turbulence. Phys. Fluids 12, 3097–3099.CrossRefGoogle Scholar
23. Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2006 Large-scale motions in a supersonic turbulent boundary layer. J. Fluid Mech. 556, 271–282.CrossRefGoogle Scholar
24. Girimaji, S. S. & Pope, S. B. 1990 Material-element deformation in isotropic turbulence. J. Fluid Mech. 220, 427–458.CrossRefGoogle Scholar
25. Guala, M., Liberzon, A., Tsinober, A. & Kinzelbach, W. 2007 An experimental investigation on Lagrangian correlations of small-scale turbulence at low Reynolds number. J. Fluid Mech. 574, 405–427.CrossRefGoogle Scholar
26. Gualtieri, P. & Meneveau, C. 2010 Direct numerical simulations of turbulence subjected to a straining and destraining cycle. Phys. Fluids 22, 065104.CrossRefGoogle Scholar
27. Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic boundary layer at Mach 2.5. J. Fluid Mech. 414, 1–33.CrossRefGoogle Scholar
28. Gulitski, G., Kholmyansky, M., Kinzelbach, W., Lüthi, B., Tsinober, A. & Yorish, Y. 2007 Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 1. Facilities, methods and some general results. J. Fluid Mech. 589, 57–81.CrossRefGoogle Scholar
29. Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Rep. CTR-S88, Center for Turbulence Research. Stanford University.Google Scholar
30. Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
31. Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202–228.CrossRefGoogle Scholar
32. Khashehchi, M., Elsinga, G. E., Ooi, A., Soria, J. & Marusic, I. 2010 Studying invariants of the velocity gradient tensor of a round turbulent jet across the turbulent/nonturbulent interface using Tomo-PIV. In Laser Techniques Applied to Fluid Mechanics, 15th International Symposium., Lisbon, Portugal.Google Scholar
33. Kida, S. & Orszag, S. A. 1990 Enstrophy budget in decaying compressible turbulence. J. Sci. Comput. 5 (1), 1–34.CrossRefGoogle Scholar
34. Klewicki, J. C. 1997 Self-sustaining traits of near-wall motions underlying boundary layer stress transport. In Self-Sustaining Mechanisms of Wall Turbulence (ed. Panton, R. L. ), pp. 135–166. Computational Mechanics Publications.Google Scholar
35. Lee, K., Girimaji, S. S. & Kerimo, J. 2009 Effect of compressibility on turbulent velocity gradients and small-scale structure. J. Turbul. 10 (9), 1–18.CrossRefGoogle Scholar
36. Li, Q. & Coleman, G. N. 2003 DNS of an oblique shock wave impinging upon a turbulent boundary layer. In Direct and Large-Eddy Simulation V, pp. 387–396. Kluwer.Google Scholar
37. Li, Y., Chevillard, L., Eyink, G. & Meneveau, C. 2009 Matrix exponential-based closures for the turbulent subgrid-scale stress tensor. Phys. Rev. E 79, 016305.CrossRefGoogle ScholarPubMed
38. Li, Y. & Meneveau, C. 2005 Origin of non-Gaussian statistics in hydrodynamic turbulence. Phys. Rev. Lett. 95, 164502.CrossRefGoogle ScholarPubMed
39. Li, Y. & Meneveau, C. 2006 Intermittency trends and Lagrangian evolution of non-Gaussian statistics in turbulent flow and scalar transport. J. Fluid Mech. 558, 133–142.CrossRefGoogle Scholar
40. Lüthi, B., Holzner, M. & Tsinober, A. 2009 Expanding the space to three dimensions. J. Fluid Mech. 641, 497–507.CrossRefGoogle Scholar
41. Maekawa, H., Hiyama, T. & Matsuo, Y. 1999 Study of the geometry of flow patterns in compressible isotropic turbulence. JSME Intl J. 42, 336–343.CrossRefGoogle Scholar
42. Meneveau, C. 2011 Lagrangian dynamics and models of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 43, 219–245.CrossRefGoogle Scholar
43. Nomura, K. K. & Diamessis, P. J. 2000 The interaction of vorticity and rate-of-strain in homogeneous sheared turbulence. Phys. Fluids 12 (4), 846–864.CrossRefGoogle Scholar
44. Nomura, K. K. & Post, G. K. 1998 The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence. J. Fluid Mech. 377, 65–97.CrossRefGoogle Scholar
45. Ooi, A., Martín, J., Soria, J. & Chong, M. S. 1999 A study of the evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech. 381, 141–174.CrossRefGoogle Scholar
46. Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical point concepts. Annu. Rev. Fluid Mech. 19, 125–155.CrossRefGoogle Scholar
47. Perry, A. E. & Chong, M. S. 1994 Topology of flow patterns in vortex motions and turbulence. Appl. Sci. Res 53, 357–374.CrossRefGoogle Scholar
48. Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.CrossRefGoogle Scholar
49. Pirozzoli, S., Bernardini, M. & Grasso, F. 2010a Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation. J. Fluid Mech. 657, 361–393.CrossRefGoogle Scholar
50. Pirozzoli, S., Bernardini, M. & Grasso, F. 2010b On the dynamical relevance of coherent vortical structures in turbulent boundary layers. J. Fluid Mech. 648, 325–349.CrossRefGoogle Scholar
51. Pirozzoli, S. & Grasso, F. 2004 Direct numerical simulations of isotropic compressible turbulence: influence of compressibility on dynamics and structures. Phys. Fluids 16 (12), 4386–4407.CrossRefGoogle Scholar
52. Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at . Phys. Fluids 16 (3), 530–545.CrossRefGoogle Scholar
53. Ringuette, M. J., Wu, M. & Martin, M. P. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J. Fluid Mech. 594, 59–69.CrossRefGoogle Scholar
54. Sandham, N. D., Yao, Y. F. & Lawal, A. A. 2003 Large-eddy simulation of transonic turbulent flow over a bump. Intl J. Heat Fluid Flow 24, 584–595.CrossRefGoogle Scholar
55. Shu, C. W. & Osher, S. 1988 Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439–471.CrossRefGoogle Scholar
56. da Silva, C. B. & Pereira, J. C. F. 2008 Invariants of the velocity-gradient, rate-of-strain, and rate-of-rotation tensors across the turbulent/nonturbulent interface in jets. Phys. Fluids 20, 055101.CrossRefGoogle Scholar
57. Smith, M. W. & Smits, A. J. 1995 Visualization of the structures of supersonic turbulent boundary layers. Exp. Fluids 18, 288–302.CrossRefGoogle Scholar
58. Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow. American Institute of Physics.Google Scholar
59. Soria, J. & Cantwell, B. J. 1994 Topological visualisation of focal structures in free shear flows. Appl. Sci. Res. 53, 375–386.CrossRefGoogle Scholar
60. Soria, J., Sondergaard, R., Cantwell, B. J., Chong, M. S. & Perry, A. E. 1994 A study of the fine-scale motions of incompressible time-developing mixing layers. Phys. Fluids 6 (2), 871–884.CrossRefGoogle Scholar
61. Spina, E. F., Smits, A. J. & Robinson, S. K. 1994 The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid Mech. 26, 287–319.CrossRefGoogle Scholar
62. Suman, S. & Girimaji, S. S. 2009 Homogenized Euler equation: a model for compressible velocity gradient dynamics. J. Fluid Mech. 620, 177–194.CrossRefGoogle Scholar
63. Suman, S. & Girimaji, S. S. 2010 Velocity gradient invariants and local flow field topology in compressible turbulence. J. Turbul. 11 (2), 1–24.CrossRefGoogle Scholar
64. Taylor, G. I. 1938 Production and dissipation of vorticity in a turbulent fluid. Proc. R. Soc. Lond. A 164, 15–23.Google Scholar
65. Tsinober, A. 1998 Is concentrated vorticity that important? Eur. J. Mech. B 17 (4), 421–449.CrossRefGoogle Scholar
66. Tsinober, A. 2000 Vortex stretching versus production of strain/dissipation. In Turbulence Structure and Vortex Dynamics, pp. 164–191. Cambridge University Press.Google Scholar
67. Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence, second edition. Springer.CrossRefGoogle Scholar
68. Tsinober, A., Ortenberg, M. & Shtillman, L. 1999 On depression of nonlinearity in turbulence. Phys. Fluids 11 (8), 2291–2297.CrossRefGoogle Scholar
69. Tsinober, A., Shtilman, L. & Vaisburd, H. 1997 A study of properties of vortex stretching and enstrophy generation in numerical and laboratory turbulence. Fluid Dyn. Res. 21, 477–494.CrossRefGoogle Scholar
70. Wallace, J. M. 2009 Twenty years of experimental and direct numerical simulation access to the velocity gradient tensor: What have we learned about turbulence? Phys. Fluids 21, 021301.CrossRefGoogle Scholar
71. Wang, B. C., Bergstrom, D. J., Yin, J. & Yee, E. 2006 Turbulence topologies predicted using large eddy simulations. J. Turbul. 7 (34), 1–28.CrossRefGoogle Scholar
72. Wang, L. & Lu, X.-Y. 2011 Statistical analysis of coherent vortical structures in a supersonic turbulent boundary layer. Chin. Phys. Lett. 28, 034703.CrossRefGoogle Scholar
73. White, F. M. 1974 Viscous Fluid Flow. McGraw-Hill.Google Scholar
74. Yang, Y. & Pullin, D. I. 2011 Geometric study of Lagrangian and Eulerian structures in turbulent channel flow. J. Fluid Mech. 674, 67–92.CrossRefGoogle Scholar