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Direct numerical simulations of hypersonic boundary-layer transition with finite-rate chemistry

Published online by Cambridge University Press:  14 August 2014

Olaf Marxen ,
Gianluca Iaccarino  and
Thierry E. Magin
Olaf Marxen*
Affiliation:
Aeronautics and Aerospace Department, von Kármán Institute for Fluid Dynamics, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse, Belgium
Gianluca Iaccarino
Affiliation:
Center for Turbulence Research, Building 500, Stanford University, Stanford, CA 94305-3035, USA
Thierry E. Magin
Affiliation:
Aeronautics and Aerospace Department, von Kármán Institute for Fluid Dynamics, Chaussée de Waterloo, 72, 1640 Rhode-St-Genèse, Belgium
*
†Present address: Department of Mechanical Engineering, Imperial College London, Exhibition Road, South Kensington, London SW7 2AZ, UK. Email address for correspondence: o.marxen@imperial.ac.uk
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Abstract

The paper describes a numerical investigation of linear and nonlinear instability in high-speed boundary layers. Both a frozen gas and a finite-rate chemically reacting gas are considered. The weakly nonlinear instability in the presence of a large-amplitude two-dimensional wave is investigated for the case of fundamental resonance. Depending on the amplitude of this two-dimensional primary wave, strong growth of oblique secondary perturbations occurs for favourable relative phase differences between the two. For essentially the same primary amplitude, secondary amplification is almost identical for a reacting and a frozen gas. Therefore, chemical reactions do not directly affect the growth of secondary perturbations, but only indirectly through the change of linear instability and hence amplitude of the primary wave. When the secondary disturbances reach a sufficiently large amplitude, strongly nonlinear effects stabilize both primary and secondary perturbations.

JFM classification

Compressible Flows: Compressible boundary layers Reacting Flows: Laminar reacting flows Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 755 , 25 September 2014 , pp. 35 - 49
Copyright
© 2014 Cambridge University Press 

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References

Chang, C.-L. & Malik, M. R. 1994 Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273, 323–360.Google Scholar
Eissler, W. & Bestek, H. 1996 Spatial numerical simulations of linear and weakly nonlinear wave instabilities in supersonic boundary layers. Theor. Comput. Fluid Dyn. 8 (3), 219–235.CrossRefGoogle Scholar
Fedorov, A. V. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95.Google Scholar
Fezer, A. & Kloker, M. 2003 DNS of transition mechanisms at Mach 6.8 – flat plate versus sharp cone. In West East High Speed Flow Fields 2002 (ed. Zeitoun, D. E., Periaux, J., Desideri, J. A. & Marini, M.), pp. 434–441. CIMNE.Google Scholar
Franko, K. J., MacCormack, R. W. & Lele, S. K.2010 Effects of chemistry modeling on hypersonic boundary layer linear stability prediction. AIAA Paper 2010-4601.Google Scholar
Fujii, K. & Hornung, H. G. 2003 Experimental investigation of high-enthalpy effects on attachment-line boundary-layer transition. AIAA J. 41 (7), 1282–1291.Google Scholar
Germain, P. D. & Hornung, H. G. 1997 Transition on a slender cone in hypervelocity flow. Exp. Fluids 22, 183–190.CrossRefGoogle Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29, 245–283.Google Scholar
Hornung, H. G. 2006 Hypersonic real-gas effects on transition. In IUTAM Symposium on One Hundred Years of Boundary Layer Research (ed. Meier, G. & Sreenivasan, K.), pp. 335–344. Springer.Google Scholar
Johnson, H. B., Seipp, T. G. & Candler, G. V. 1998 Numerical study of hypersonic reacting boundary layer transition on cones. Phys. Fluids 10 (10), 2676–2685.Google Scholar
Kawai, S., Shankar, S. K. & Lele, S. K. 2010 Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows. J. Comput. Phys. 229 (5), 1739–1762.CrossRefGoogle Scholar
Mack, L. M.1969 Boundary layer stability theory. NASA Tech. Rep. JPL-900-277-REV-A; NASA-CR-131501. Jet Propulsion Laboratory.Google Scholar
Mack, L. M.1984 Boundary-layer linear stability theory. Tech. Rep. AGARD-R-709.Google Scholar
Malik, M. R. 2003 Hypersonic flight transition data analysis using parabolized stability equations with chemistry effects. J. Spacecr. Rockets 40 (3), 332–344.Google Scholar
Malik, M. R. & Anderson, E. C. 1991 Real gas effects on hypersonic boundary-layer stability. Phys. Fluids A 3 (5), 803–821.Google Scholar
Marxen, O., Iaccarino, G. & Shaqfeh, E. S. G. 2010 Disturbance evolution in a Mach 4.8 boundary layer with two-dimensional roughness-induced separation and shock. J. Fluid Mech. 648, 435–469.Google Scholar
Marxen, O., Magin, T., Iaccarino, G. & Shaqfeh, E. S. G. 2011 A high-order numerical method to study hypersonic boundary-layer instability including high-temperature gas effects. Phys. Fluids 23 (8), 084108.Google Scholar
Marxen, O., Magin, T., Shaqfeh, E. S. G. & Iaccarino, G. 2013 A method for the direct numerical simulation of hypersonic boundary-layer instability with finite-rate chemistry. J. Comput. Phys. 255, 572–589.Google Scholar
Mayer, C. S. J., von Terzi, D. A. & Fasel, H. F. 2011a Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3. J. Fluid Mech. 674, 5–42.Google Scholar
Mayer, C. S. J., Wernz, S. & Fasel, H. F. 2011b Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer. J. Fluid Mech. 668, 113–149.Google Scholar
Mironov, S. G. & Maslov, A. A. 2000 Experimental study of secondary instability in a hypersonic shock layer on a flat plate. J. Fluid Mech. 412, 259–277.Google Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order method for large eddy simulation. J. Comput. Phys. 191, 392–419.Google Scholar
Stuckert, G. & Reed, H. L. 1994 Linear disturbances in hypersonic, chemically reacting shock layers. AIAA J. 32 (7), 1384–1393.Google Scholar
Tumin, A., Wang, X. & Zhong, X. 2007 Direct numerical simulation and the theory of receptivity in a hypersonic boundary layer. Phys. Fluids 19 (1), 014101.Google Scholar
Zhong, X. & Wang, X. 2012 Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Annu. Rev. Fluid Mech. 44 (1), 527–561.Google Scholar