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Effect of carbon content on supersonic shear-layer instability

Published online by Cambridge University Press:  16 January 2012

Luca Massa
Luca Massa*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019, USA
*
†Email address for correspondence: [email protected]
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Abstract

Carbon chemistry and the endothermic reactions it supports were previously shown to delay hypersonic boundary-layer instability and transition. The present analysis addresses the analogous problem in free shear layers and arrives at the conclusion that the lack of the acoustic trapping mechanism implies that endothermic chemistry can lead to stabilization or destabilization of the shear layer depending on the free-stream temperature. This study identifies three mechanisms by which carbon chemistry affects instability and transition. The first is rooted in the changes to the inflectional profiles caused by the visco-chemical interaction. The second is due to damping of the perturbation by finite-rate chemistry. The third is linked to streamwise relaxation which delays the onset of secondary instability of vortical structures generated by a saturated primary instability wave. Linear analysis predicts changes in growth rate lower than 30 % for Mach numbers below 5. Nonlinear parabolized stability analysis predicts significantly larger differences, depending on whether the primary or secondary instability triggers the transition onset.

JFM classification

Boundary Layers: Free shear layers Aerodynamics: High-speed flow Instability: Nonlinear instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 693 , 25 February 2012 , pp. 261 - 296
Copyright
Copyright © Cambridge University Press 2012

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References

1. Arnal, D. 1994 Boundary layer transition: predictions based on linear theory. Progress in transition modelling. AGARD Rep. No. 709.Google Scholar
2. Bayly, B. J., Orszag, S. A. & Herbert, T. 1988 Instability mechanisms in shear-flow transition. Annu. Rev. Fluid Mech. 20 (1), 359–391.CrossRefGoogle Scholar
3. Bernal, LP & Roshko, A. 1986 Streamwise vortex structure in plane mixing layers. J. Fluid Mech. 170, 499–525.CrossRefGoogle Scholar
4. Bertolotti, F. P. 1998 The influence of rotational and vibrational energy relaxation on boundary-layer stability. J. Fluid Mech. 372, 93–118.CrossRefGoogle Scholar
5. Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2004 Transport Phenomena. Wiley.Google Scholar
6. Chang, C. L. 2004 Langley stability and transition analysis code (LASTRAC) version 1.2 user manual. NASA TM 213233, NASA Langley Research Center.Google Scholar
7. Chang, C. L. & Malik, M. R. 1994 Oblique-mode breakdown and secondary instability in supersonic boundary layers. J. Fluid Mech. 273, 323–360.CrossRefGoogle Scholar
8. Cheng, H. K. 1993 Perspectives on hypersonic viscous flow research. Annu. Rev. Fluid Mech. 25 (1), 455–484.CrossRefGoogle Scholar
9. Criminale, W. O., Jackson, T. L. & Joslin, R. D. 2003 Theory and Computation in Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
10. Curran, E. T., Heiser, W. H. & Pratt, D. T. 1996 Fluid phenomena in scramjet combustion systems. Annu. Rev. Fluid Mech. 28 (1), 323–360.CrossRefGoogle Scholar
11. Day, M. J., Mansour, N. N. & Reynolds, W. C. 2001 Nonlinear stability and structure of compressible reacting mixing layers. J. Fluid Mech. 446, 375–408.CrossRefGoogle Scholar
12. Doraiswamy, S., Kelley, J. D. & Candler, G. V. 2010 Vibrational modelling of CO2 in high-enthalpy nozzle flows. J. Thermophys. Heat Transfer 24 (1), 9–17.CrossRefGoogle Scholar
13. Edney, B. 1968 Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. Tech. Rep. Flygtekniska Forsoksanstalten, Stockholm.CrossRefGoogle Scholar
14. Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95.CrossRefGoogle Scholar
15. Fridman, A. 2008 Plasma Chemistry. Cambridge University Press.CrossRefGoogle Scholar
16. Fujii, K. & Hornung, H. G. 2003 Experimental investigation of high-enthalpy effects on attachment-line boundary-layer transition. AIAA J. 41 (7), 1282–1291.CrossRefGoogle Scholar
17. Giovangigli, V. 1999 Multicomponent Flow Modelling. Birkhäuser.CrossRefGoogle Scholar
18. Grasso, F., Purpura, C., Chanetz, B. & Delery, J. 2003 Type III and type IV shock/shock interferences: theoretical and experimental aspects. Aerosp. Sci. Technol. 7 (2), 93–106.CrossRefGoogle Scholar
19. Gutmark, E. J., Schadow, K. C. & Yu, K. H. 1995 Mixing enhancement in supersonic free shear flows. Annu. Rev. Fluid Mech. 27 (1), 375–417.CrossRefGoogle Scholar
20. Haynes, T. S. & Reed, H. L. 2000 Simulation of swept-wing vortices using nonlinear parabolized stability equations. J. Fluid Mech. 405, 325–349.CrossRefGoogle Scholar
21. Herbert, T. 1997 Parabolized stability equations. Annu. Rev. Fluid Mech. 29 (1), 245–283.CrossRefGoogle Scholar
22. Horvath, T. J., Berry, S. A & Merski, N. R. 2004 Hypersonic boundary/shear layer transition for blunt to slender configurations: a NASA Langley experimental perspective. Tech. Rep. RTO-MP-AVT-111, NATO Research and Technology Organisation (RTO).Google Scholar
23. Huang, L. S. & Ho, C. M. 1990 Small-scale transition in a plane mixing layer. J. Fluid Mech. 210, 475–500.CrossRefGoogle Scholar
24. Hudson, M. L., Chokani, N. & Candler, G. V. 1997 Linear stability of hypersonic flow in thermochemical non-equilibrium. AIAA J. 35 (6), 958–964.CrossRefGoogle Scholar
25. Jackson, T. L. & Grosch, C. E. 1989 Inviscid spatial stability of a compressible mixing layer. J. Fluid Mech. 208, 609–637.CrossRefGoogle Scholar
26. Jackson, T. L. & Grosch, C. E. 1990 Absolute/convective instabilities and the convective Mach number in a compressible mixing layer. Phys. Fluids A 2 (6), 949–954.CrossRefGoogle Scholar
27. Johnson, H. B., Seipp, T. G. & Candler, G. V. 1998 Numerical study of hypersonic reacting boundary layer transition on cones. Phys. Fluids 10, 2676–2685.CrossRefGoogle Scholar
28. Kiefer, J. H. & Lutz, R. W. 1967 The effect of oxygen atoms on the vibrational relaxation of oxygen. Proc. Combust. Inst. 11, 57–75.CrossRefGoogle Scholar
29. Kustova, E. V. & Nagnibeda, E. A. 1998 Transport properties of a reacting gas mixture with strong vibrational and chemical non-equilibrium. Chem. Phys. 233 (1), 57–75.CrossRefGoogle Scholar
30. Lees, L. & Lin, C. C. 1946 Investigation of the stability of the laminar boundary layer in a compressible fluid. National Advisory Committee for Aeronautics (NACA), TN No. 1115. Washington, DC, USA.Google Scholar
31. Luchini, P. & Bottaro, A. 1998 Görtler vortices: a backward-in-time approach to the receptivity problem. J. Fluid Mech. 363, 1–23.CrossRefGoogle Scholar
32. Mack, L. M. 1969 Boundary-layer stability theory. Jet Propulsion Laboratory Internal Document No. 900-277, Rev. A; also NASA Contractor Report No. 131591.Google Scholar
33. Mack, L. M. 1990 On the inviscid acoustic-mode instability of supersonic shear flows. Theor. Comput. Fluid Dyn. 2 (2), 97–123.CrossRefGoogle Scholar
34. Majda, A. & Rosales, R. 1983 A theory for spontaneous Mach stem formation in reacting shock fronts, i. The basic perturbation analysis. SIAM J. Appl. Math. 43 (6), 1310–1334.CrossRefGoogle Scholar
35. Malik, M. R. & Anderson, J. D. 1991 Real gas effects on hypersonic boundary layer stability. Phys. Fluids A 3 (5), 803–821.CrossRefGoogle Scholar
36. Massa, L. & Austin, J. M. 2008 Spatial linear stability of a hypersonic shear layer with non-equilibrium thermochemistry. Phys. Fluids 20, 084104.CrossRefGoogle Scholar
37. Mathur, S., Tondon, P. K. & Saxena, S. C. 1967 Thermal conductivity of binary, ternary and quaternary mixtures of rare gases. Mol. Phys. 12 (6), 569–579.CrossRefGoogle Scholar
38. Millikan, R. C. & White, D. R. 1963 Systematics of vibrational relaxation. J. Chem. Phys. 39, 3209–3213.CrossRefGoogle Scholar
39. Palle, S., Nolan, C. & Miller, R. S. 2005 On molecular transport effects in real gas laminar diffusion flames at large pressure. Phys. Fluids 17, 103601.CrossRefGoogle Scholar
40. Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197, 453–477.CrossRefGoogle Scholar
41. Rogers, M. M. & Moser, R. D. 1993 Spanwise scale selection in plane mixing layers. J. Fluid Mech. 247, 321–337.CrossRefGoogle Scholar
42. Rothman, L. S., Gordon, I. E., Barber, R. J., Dothe, H., Gamache, R. R., Goldman, A., Perevalov, V. I., Tashkun, S. A. & Tennyson, J. 2010 HITEMP, the high-temperature molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transfer 111 (15), 2139–2150.CrossRefGoogle Scholar
43. Rothman, L. S., Hawkins, R. L., Wattson, R. B. & Gamache, R. R. 1992 Energy levels, intensities, and linewidths of atmospheric carbon dioxide bands. J. Quant. Spectrosc. Radiat. Transfer 48 (5–6), 537–566.CrossRefGoogle Scholar
44. Sandham, N. D., Adams, N. A. & Kleiser, L. 1995 Direct simulation of breakdown to turbulence following oblique instability waves in a supersonic boundary layer. Appl. Sci. Res. 54 (3), 223–234.CrossRefGoogle Scholar
45. Schlichting, H. & Gersten, K. 2000 Boundary-Layer Theory. Springer.CrossRefGoogle Scholar
46. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
47. Schwartz, R. N., Slawsky, Z. I. & Herzfeld, K. F. 1952 Calculation of vibrational relaxation times in gases. J. Chem. Phys. 20, 1591.CrossRefGoogle Scholar
48. Wangard, W. et al. 2001 A numerically stable method for integration of the multicomponent species diffusion equations. J. Comput. Phys. 174, 460–472.CrossRefGoogle Scholar