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Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect ofhigh enthalpy

Published online by Cambridge University Press:  06 September 2011

L. Duan  and
M. P. Martín
L. Duan
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
M. P. Martín*
Affiliation:
Department of Aerospace Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: pmartin@umiacs.umd.edu
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Abstract

In this paper we present direct numerical simulations (DNS) of hypersonic turbulent boundary layers to study high-enthalpy effects. We study high- and low-enthalpy conditions, which are representative of those in hypersonic flight and ground-based facilities, respectively. We find that high-enthalpy boundary layers closely resemble those at low enthalpy. Many of the scaling relations for low-enthalpy flows, such as van-Driest transformation for the mean velocity, Morkovin’s scaling and the modified strong Reynolds analogy hold or can be generalized for high-enthalpy flows by removing the calorically perfect-gas assumption. We propose a generalized form of the modified Crocco relation, which relates the mean temperature and mean velocity across a wide range of conditions, including non-adiabatic cold walls and real gas effects. The DNS data predict Reynolds analogy factors in the range of those found in experimental data at low-enthalpy conditions. The gradient transport model approximately holds with turbulent Prandtl number and turbulent Schmidt number of order unity. Direct compressibility effects remain small and insignificant for all enthalpy cases. High-enthalpy effects have no sizable influence on turbulent kinetic energy (TKE) budgets or on the turbulence structure.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulent boundary layers Reacting Flows: Turbulent reacting flows

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 25 - 59
Copyright
Copyright © Cambridge University Press 2011

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References

1. 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
2. Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9, 33–54.CrossRefGoogle Scholar
3. Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243–S252.CrossRefGoogle Scholar
4. Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.Google Scholar
5. 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
6. Dong, M. & Zhou, H. 2010 The improvement of turbulence modeling for the aerothermal computation of hypersonic turbulent boundary layers. Sci. Chin. 53, 369–379.Google Scholar
7. van Driest, E. R. 1956 The problem of aerodynamic heating. Aeronaut. Engng Rev. 15 (10), 26–41.Google Scholar
8. Duan, L., Beekman, I. & Martín, M. P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419–445.CrossRefGoogle Scholar
9. Duan, L., Beekman, I. & Martín, 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
10. Duan, L. & Martín, M.P. 2009a Effect of finite-rate chemical reactions on turbulence in hypersonic turbulent boundary layers. AIAA Paper 2009-0588.Google Scholar
11. Duan, L. & Martín, M. P. 2009b Effect of turbulence fluctuations on surface heating rate in hypersonic turbulent boundary layers. AIAA Paper 2009-4040.Google Scholar
12. Duan, L. & Martín, M. P. 2009c An effective procedure for testing the validity of DNS of wall-bounded turbulence including finite-rate reactions. AIAA J. 47 (1), 244–251.CrossRefGoogle Scholar
13. Duan, L. & Martín, M. P. 2011 Assessment of turbulence–chemistry interaction in hypersonic turbulent boundary layers. AIAA J. 49 (1), 172–184.CrossRefGoogle Scholar
14. 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
15. Gordon, S. & McBride, B. J. 1994 Computer program for calculation of complex chemical equilibrium compositions and applications. NASA RP 1311.Google Scholar
16. 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
17. Gupta, R. N., Yos, J. M., Thompson, R. A. & Lee, K. P. 1990 A review of reaction rates and thermodynamic and transport properties for 11-species air model for chemical and thermal non-equilibrium calculations to 30 000 K. NASA RP 1232.Google Scholar
18. 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
19. 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
20. 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
21. Keener, E. R. & Polek, T. E. 1972 Measurements of Reynolds analogy for a hypersonic turbulent boundary layer on a nonadiabatic flat plate. AIAA J. 10 (6), 845–846.CrossRefGoogle Scholar
22. Keyes, F. G. 1951 A summary of viscosity and heat-conduction data for He, H2, O2, CO, CO2, H2O and air. Trans. ASME 589–596.Google Scholar
23. Maeder, T. 2000 Numerical investigation of supersonic turbulent boundary layers. PhD thesis, ETH, Zürich.Google Scholar
24. 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
25. Martín, M. P. 2000 Shock-capturing in LES of high-speed flows. Tech Rep. Center for Turbulence Research, Stanford University.Google Scholar
26. Martín, M. P. 2003Exploratory studies of turbulence/chemistry interaction in hypersonic flows. AIAA Paper 2003-4055.Google Scholar
27. Martín, 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
28. Martín, M. P. & Candler, G. V. 1998 Effect of chemical reactions on decaying isotropic turbulence. Phys. Fluids 10, 1715–1724.CrossRefGoogle Scholar
29. Martín, M. P. & Candler, G. V. 1999 Subgrid-scale model for the temperature fluctuations in reacting hypersonic turbulent flows. Phys. Fluids 11.CrossRefGoogle Scholar
30. Martín, M. P. & Candler, G. V. 2001 Temperature fluctuation scaling in reacting turbulent boundary layers. AIAA Paper 2001-2717.CrossRefGoogle Scholar
31. Martín, M. P., Taylor, E. M., Wu, M. & Weirs, V. G. 2006 A bandwidth-optimized WENO scheme for the effective direct numerical simulation of compressible turbulence. J. Comput. Phys. 220, 270–289.CrossRefGoogle Scholar
32. Morkovin, M. V. 1962 Effects of compressibility on turbulent flows. In Mécanique de la Turbulence, Colloques Internationaux du Centre National de la Recherche Scientifique, 108. pp. 367–380. Editions du CNRS.Google Scholar
33. O’Farrell, C. & Martín, M. P. 2009 Chasing eddies and their wall signature in DNS data of turbulent boundary layers. J. Turbul. 10, no. 15.Google Scholar
34. Park, C. 1990 Nonequilibrium Hypersonic Aerothermodynamics, 1st edn. John Wiley & Sons.Google Scholar
35. 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
36. 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
37. Roy, C. J. & Blottner, F. G. 2006 Review and assessment of turbulence models for hypersonic flows. Prog. Aerosp. 42, 469–530.CrossRefGoogle Scholar
38. Rubesin, M. W. 1990 Extra compressibility terms for Favre-averaged two-equation models of inhomogeneous turbulent flows. Tech Rep. 177556. NASA Contractor Rep.Google Scholar
39. Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow, 2nd edn. American Institute of Physics.Google Scholar
40. Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to Re θ equals 1410. J. Fluid Mech. 187, 61–98.CrossRefGoogle Scholar
41. Taylor, E. M. & Martín, M. P. 2007 Stencil adaptation properties of a WENO scheme in direct numerical simulation of compressible turbulence. J. Sci. Comput. 30 (3), 533–554.CrossRefGoogle Scholar
42. Vreman, A. W., Sandham, N. D. & Luo, K. H. 1996 Compressible mixing layer growth rate and turbulence characteristics. J. Fluid Mech. 320, 235–258.CrossRefGoogle Scholar
43. Walz, A. 1969 Boundary Layers of Flow and Temperature. MIT.Google Scholar
44. Wilcox, D. C. 2006 Turbulence Modeling for CFD, 3rd edn. DCW Industries.Google Scholar
45. Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 48–56.CrossRefGoogle Scholar
46. Wright, M. J., White, T. & Mangini, N. 2009 Data Parallel Line Relaxation (DPLR) code User Manual; Acadia – Version 4.01.1. NASA TM 2009-215388.Google Scholar
47. Xu, S. & Martín, M. P. 2004 Assessment of inflow boundary conditions for compressible turbulent boundary layers. Phys. Fluids 16 (7), 2623–2639.CrossRefGoogle Scholar
48. Yos, J. M. 1963 Transport properties of nitrogen, hydrogen, oxygen, and air to 30,000 K. Avco. Corp. TR AD-TM-63-7.Google Scholar