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Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature

Published online by Cambridge University Press:  13 May 2010

L. DUAN ,
I. BEEKMAN  and
M. P. MARTÍN
L. DUAN
Affiliation:
Aerospace Engineering Department, University of Maryland, College Park, MD 20742, USA
I. BEEKMAN
Affiliation:
Aerospace Engineering Department, University of Maryland, College Park, MD 20742, USA
M. P. MARTÍN*
Affiliation:
Aerospace Engineering Department, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: pmartin@princeton.edu
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Abstract

In this paper, we perform direct numerical simulation (DNS) of turbulent boundary layers at Mach 5 with the ratio of wall-to-edge temperature Tw/Tδ from 1.0 to 5.4 (Cases M5T1 to M5T5). The influence of wall cooling on Morkovin's scaling, Walz's equation, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, compressibility effects and near-wall coherent structures is assessed. We find that many of the scaling relations used to express adiabatic compressible boundary-layer statistics in terms of incompressible boundary layers also hold for non-adiabatic cases. Compressibility effects are enhanced by wall cooling but remain insignificant, and the turbulence dissipation remains primarily solenoidal. Moreover, the variation of near-wall streaks, iso-surface of the swirl strength and hairpin packets with wall temperature demonstrates that cooling the wall increases the coherency of turbulent structures. We present the mechanism by which wall cooling enhances the coherence of turbulence structures, and we provide an explanation of why this mechanism does not represent an exception to the weakly compressible hypothesis.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 419 - 445
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Adrian, R., Meinhart, C. & Tomkins, C. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Bakewell, H. P. & Lumley, J. L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 10 (9), 1880–1889.CrossRefGoogle Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–54.CrossRefGoogle Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243–S252.CrossRefGoogle Scholar
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.Google Scholar
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
van Driest, E. R. 1956 The problem of aerodynamic heating. Aeronaut. Engng Rev. 15 (10), 26–41.Google Scholar
Fernholz, H. H. & Finley, P. J. 1980 A critical commentary on mean flow data for two-dimensional compressible boundary layers. AGARD-AG-253.Google Scholar
Ganapathisubramani, B., Clemens, N. & Dolling, D. 2006 Large-scale motions in a supersonic turbulent boundary layers. J. Fluid Mech. 556, 1–11.CrossRefGoogle Scholar
Gatski, T. B. 1997 New Tools in Turbulence Modelling. Springer.Google Scholar
Gatski, T. B. & Erlebacher, G. 2002 Numerical simulation of a spatially evolving supersonic turbulent boundary layer. Tech. Rep. TM-211934. NASA.Google Scholar
Gaviglio, J. 1987 Reynolds analogies and experimental study of heat transfer in the supersonic boundary layer. Intl J. Heat Mass Transfer 30 (5), 911–926.CrossRefGoogle Scholar
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at mach 2.5. J. Fluid Mech. 414, 1–33.CrossRefGoogle Scholar
Hopkins, E. J. & Inouye, M. 1971 Evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic mach numbers. AIAA J. 9 (6), 993–1003.CrossRefGoogle Scholar
Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.CrossRefGoogle Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstaller, W. P. 1967 J. Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Lele, S. K. 1994 Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26, 211–254.CrossRefGoogle Scholar
Maeder, T. 2000 Numerical investigation of supersonic turbulent boundary layers. PhD thesis, ETH, Zürich.Google Scholar
Maeder, T., Adams, N. A. & Kleiser, L. 2001 Direct simulation of turbulent supersonic boundary layers by an extended temporal approach. J. Fluid Mech. 429, 187–216.CrossRefGoogle Scholar
Martin, M. P. 2004 DNS of hyersonic turbulent boundary layers. AIAA Paper 2004-2337.CrossRefGoogle Scholar
Martin, M. P. 2007 Direct numerical simulation of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments. J. Fluid Mech. 570, 347–364.CrossRefGoogle Scholar
Morinishi, Y., Tamano, S. & Nakabayashi, K. 2004 Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502, 273–308.CrossRefGoogle Scholar
Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. In Mécanique de la Turbulence (ed. Favre, A.), pp. 367–380. CNRS.Google Scholar
O'Farrell, C. & Martin, M. P. 2009 Chasing eddies and their wall signature in DNS data of turbulent boundary layers. J. Turbul. 10 (15), 1–22.CrossRefGoogle Scholar
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25. Phys. Fluids 16 (3), 530–545.CrossRefGoogle Scholar
Ringuette, M. J., Martin, M. P., Smits, A. J. & Wu, M. 2006 Characterization of the turbulence structure in supersonic boundary layers using DNS data. AIAA Paper 2006-3539.CrossRefGoogle Scholar
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
Rubesin, M. W. 1990 Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows. Tech. Rep. CR-177556. NASA.Google Scholar
Runstadler, P. S., Kline, S. J. & Reynolds, W. C. 1963 An experimental investigation of flow structure of the turbulent boundary layer. Tech. Rep. MD-8. Mechanical Engineering Department, Stanford University.Google Scholar
Smits, A. J. 1991 Turbulent boundary layer structure in supersonic flow. Phil. Trans. R. Soc. Lond. A 336 (1), 81–93.Google Scholar
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow, 2nd edn. American Institute of Physics.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Reθ equals 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
Voisinet, R. L. P. & Lee, R. E. 1972 Measurements of a mach 4.9 zero-pressure-gradient turbulent boundary layer with heat transfer. Part 1. Data compilation. Tech. Rep. 0033757. Naval Ordnance Lab, White Oak, MD.CrossRefGoogle Scholar
Walz, A. 1969 Boundary Layers of Flow and Temperature. MIT Press.Google Scholar
Xu, S. & Martin, M. P. 2004 Assessment of inflow boundary conditions for compressible turbulent boundary layers. Phys. Fluids 16 (7), 2623–2639.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar