Effect of heat transfer on the stability of compressible boundary layers

Abstract

The effect of heat transfer on the spatial stability of compressible boundary layers is investigated using a formulation that accounts for variable-fluid properties of both the mean-flow and stability problems as well as a constant Prandtl number formulation. It is found that heat transfer is more effective in stabilizing or destabilizing flows at low Mach numbers than at high Mach numbers. Cooling always stabilizes first-mode waves and destabilizes second-mode waves. Cooling increases the peak amplifications of second-mode waves and shifts them towards higher frequencies. The least stable second-mode wave remains two-dimensional in the presence of heat transfer. The theoretical results are in good agreement with the experimental data of Lysenko and Maslov [ J. Fluid Mech. 147, 39 (1984)] for the first mode and in reasonable agreement with their experimental data for the second mode. The theoretical results are also compared with the experimental data of Lebiga et al. Archs Mech. 31, 397 (1979)] and Kosinov et al. [ J. Fluid Mech. 219, 621 (1990)].