Stability Theory for Cross Hatching. Part I. Linear Stability Theory

Abstract

A linear instability theory was developed which couples small perturbations in surface shape of a subliming surface and resulting perturbations in aerodynamic heat-transfer rates. Equations governing compressible turbulent boundary layers were linearized for small perturbations whose streamwise scale lengths are comparable with the undisturbed boundary layer thickness. For turbulent shear stress, the mixing-length approximation was employed, and the turbulent Prandtl number was assumed to be unity for turbulent heat flux. Heat conduction within the ablating solid was analyzed by linearizing the boundary condition for small amplitude. Sample computations were made for a teflon surface ablating under turbulent boundary layer at Mach 2. 6, and the results indicate that the small surface perturbations are unstable within certain regions in the wave number - wave angle space.