Linear Stability Theory and the Problem of Supersonic Boundary- Layer Transition

TLDR: In this paper, the amplitude ratio of constant-frequency disturbances as a function of Reynolds number for insulated and cooled-wall flat-plate boundary layers between Mach numbers 1.3 and 5.8 is calculated.

Abstract: Compressible linear stability theory is first reviewed and then used to calculate the amplitude ratio of constant-frequency disturbances as a function of Reynolds number for insulated and cooled-wall flat-plate boundary layers between Mach numbers 1.3 and 5.8. These results are used to examine the consequences of using a fixed disturbance amplitude of the most unstable frequency as a transition criterion. The effect of the freestream Mach number M1 on the transition of insulated-wall boundary layers is calculated using two different assumptions concerning the initial boundary-layer disturbance amplitude A0. It is found that the shape of the transition Reynolds number Ret vs MI curve observed in wind tunnels can be closely duplicated. As a second example, the effect of wall cooling at MI = 3.0 is calculated. A much faster increase of Re, with cooling is obtained than is observed experimentally. However, when A0 is determined from the forced response of the boundary layer to irradiated sound and from the measured freestream power spectrum, a rise in Re, similar to what is observed is obtained for a certain amplitude criterion.