Effect of wall cooling on the stability of compressible subsonic flows over smooth humps and backward-facing steps

The effect of wall cooling on the two-dimensional linear stability of subsonic flows over two-dimensional surface imperfections is investigated. Results are presented for flows over smooth humps and backward-facing steps with Mach numbers up to 0.8. The results show that, whereas cooling decreases the viscous instability, it increases the shear-layer instability and hence it increases the growth rates in the separation region. The coexistence of more than one instability mechanism makes a certain degree of wall cooling most effective. For the Mach numbers 0.5 and 0.8, the optimum wall temperatures are about 80 pct and 60 pct of the adiabatic wall temperature, respectively. Increasing the Mach number decreases the effectiveness of cooling slightly and reduces the optimum wall temperature.