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Nonlinear stability of hypersonic flow over a cone with passive porous walls

Published online by Cambridge University Press:  22 October 2012

Vipin Michael  and
Sharon O. Stephen
Vipin Michael*
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
Sharon O. Stephen
Affiliation:
School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK
*
†Email address for correspondence: michaelv@maths.bham.ac.uk
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Abstract

This study investigates the nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls. The attached shock and effect of curvature are taken into account. Asymptotic methods are used for large Reynolds number and large Mach number to examine the viscous modes of instability (first Mack mode), which may be described by a triple-deck structure. A weakly nonlinear stability analysis is carried out allowing an equation for the amplitude of disturbances to be derived. The coefficients of the terms in the amplitude equation are evaluated for axisymmetric and non-axisymmetric disturbances. The stabilizing or destabilizing effect of nonlinearity is found to depend on the cone radius. The presence of porous walls significantly influences the effect of nonlinearity, and results for three types of porous wall (regular, random and mesh microstructure) are compared.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Compressible boundary layers Instability: Instability Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 713 , 25 December 2012 , pp. 528 - 563
Copyright
©2012 Cambridge University Press

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