Effects of passive porous walls on the first Mack mode instability of hypersonic boundary layers over a sharp cone

[摘要] Passive porous coatings have been proposed in literature as a means of delaying transition to turbulence in hypersonic boundary layers. The nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls is investigated in this study. Hypersonic flows are unstable to viscous and inviscid disturbances, and following Mack (1984) these have been called the first and second Mack modes. A weakly nonlinear analysis of the instability of the flow to axisymmetric and non-axisymmetric viscous (first Mack mode) disturbances is performed here. The attached shock and effect of curvature are taken into account. Asymptotic methods are used at large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. Various porous wall models have been incorporated into the stability analysis. The eigenrelations governing the linear stability of the problem are derived. Neutral and spatial instability results show the presence of multiple unstable modes and the destabilising effect of the porous wall models on them. The weakly nonlinear stability analysis carried out allows an equation for the amplitude of disturbances to be derived. The stabilising or destabilising effect of nonlinearity is found to depend on the cone radius. It is shown that porous walls significantly influences the effect of nonlinearity. They allow nonlinear effects to destabilise linearly unstable lower frequency modes and stabilise linearly unstable higher frequency modes.

[发布机构] University:University of Birmingham;Department:School of Mathematics

[关键词] Q Science;QA Mathematics