Effect of heat transfer on the subharmonic instability of compressible boundary layers

Abstract

The effect of heat transfer on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate is analyzed using the Floquet model. The resulting problem is solved numerically by using both finite differences and the computer code suport. Results are presented for different Mach numbers. For supersonic flows, results for the first and second modes are presented. The results for an adiabatic flat plate are in good agreement with the results of the numerical simulations of Thumm et al. [in Laminar-Turbulent Transition, edited by D. Arnal and R. Michel (Springer-Verlag, Berlin, 1990), p. 271; (private communication)]. When the wall temperature is decreased and the primary wave is a second-mode wave, it is found that the subharmonic instability is shifted to higher frequencies and downstream locations. When the primary wave is a first-mode wave, the effect of cooling might be stabilizing or destabilizing depending on the frequency. When the primary wave is a first mode, cooling stabilizes the subharmonic wave at low spanwise wave numbers and destabilizes it at higher spanwise wave numbers. When the primary wave is either a first- or a second-mode wave, the most amplified subharmonic mode shifts toward a higher spanwise wave number as the cooling level increases.