Surface instabilities in laminar compressible boundary layers with sublimation

Surface patterns on ablating materials are known to appear in both high-speed ground and flight tests, but the mechanisms behind their formation are not known. In this paper, the origins of surface patterns are investigated via a local linear stability analysis of compressible laminar boundary layers over a flat camphor plate. The effects of sublimation and conjugate heat transfer are included on both the baseflow and the linear fluctuations. This newly developed framework identifies a single mode that fully characterises the stability of the surface, and this surface mode becomes unstable under laminar conditions only when the wall temperature exceeds that of an adiabatic wall, $T_{\textit{ad}}$ . These findings are consistent with experimental observations, where laminar flow conditions at adiabatic wall temperatures are observed to be stable. The present analysis also reveals that the nature of this surface mode varies as a function of the oblique angle $\psi = \tan ^{-1}({\beta /\alpha })$ , where $\alpha$ and $\beta$ are the streamwise and spanwise wavenumbers. As the wall temperature increases, the most unstable orientation of the surface mode shifts from streamwise alignment ( $\psi = 0$ ), towards the sonic angle ( $\psi = \psi _s = \cos ^{-1}(1/M_e)$ ) and then towards spanwise alignment ( $\psi = 90^\circ$ ). Finally, a critical wavenumber is identified (i.e. one at which the temporal growth rate reaches a maximum) which implies the formation of a surface pattern of a specific wavelength and orientation.