Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-21T02:28:26.903Z Has data issue: false hasContentIssue false

Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer

Published online by Cambridge University Press:  26 April 2006

Yibin Fu
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK
Philip Hall
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Abstract

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Görtler vortices is the temperature adjustment layer sitting at the edge of the boundary layer. This temperature adjustment layer is also the most dangerous site for Rayleigh instability. In this paper, we investigate how the existence of large-amplitude Görtler vortices affects the growth rate of Rayleigh instability. The effects of wall cooling and gas dissociation on this instability are also studied. We find that all these mechanisms increase the growth rate of Rayleigh instability and are therefore destabilizing.

Type
Research Article
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Becker, E. 1968 Gas Dynamics. Academic.
Blackaby, N., Cowley, S. & Hall, P. 1993 On the instability of hypersonic flow past a flat plate. J. Fluid Mech. 247, 369416.Google Scholar
Cowley, S. J. & Hall, P. 1990 On the instability of hypersonic flow past a wedge. J. Fluid Mech. 214, 1742.Google Scholar
Fu, Y. B. & Hall, P. 1992 Nonlinear development and secondary instability of large amplitude Görtler vortices in hypersonic boundary layers. Eur. J. Mech. B 11, 465510.Google Scholar
Fu, Y. B., Hall, P. & Blackaby, N. B. 1992 On the Görtler instability in hypersonic flows: Sutherland's law fluids and real gas effects. Phil. Trans. R. Soc. Lond. (to appear.)Google Scholar
Hall, P. 1982 On the evolution of Görtler vortices in non-parallel boundary layers. IMA J. Appl. Maths 29, 173196.Google Scholar
Hall, P. & Fu, Y. B. 1989 On the Görtler vortex instability mechanism at hypersonic speeds. Theoret. Comput. Fluid Dyn. 1, 125134.Google Scholar
Kendall, J. M. 1975 Wind tunnel experiments relating supersonic to hypersonic boundary layer transition. AIAA J. 13, 290299.Google Scholar
Lighthill, M. J. 1957 Dynamics of a dissociating gas. Part 1. Equilibrium flow. J. Fluid Mech. 2, 132.Google Scholar
Smith, F. T. & Brown, S. N. 1990 The inviscid instability of a Blasius boundary layer at large values of the Mach number. J. Fluid Mech. 219, 499518.Google Scholar
Stewartson, K. 1964 The Theory of Laminar Boundary Layers in Compressible Flows. Clarendon.
Swearingen, J. D. & Blackwelder, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255290.Google Scholar