Application of momentum potential theory in the study of hypersonic boundary layer instabilities

Abstract

This thesis improves the momentum potential theory (MPT) proposed by Doak to study the physical mechanism underlying high-speed boundary layer instabilities. The MPT approach decomposes random disturbances into well-defined vortical, acoustic, and thermal components and derives an energy budget equation. However, the application of the original MPT approach in the study of high-speed boundary layer instabilities in previous research is questionable. The first problem is that the effect of different source terms on different energy fluxes is not clarified. Three independent energy budget equations for each MPT component are obtained for the first time. The effect of different source terms on each energy flux is clarified and energy exchange terms between MPT components are revealed. Then, the "sound radiation" mechanism of the supersonic mode and the stabilization mechanism of the porous coating to the supersonic mode is elucidated with these independent energy budget equations. The second problem is that the growth rate of the instability mode is not related to the energy budget equation explicitly. The integral energy budget equation is thus derived to evaluate contribution of different source terms to the growth rate. The growth rate analysis is performed for the unstable S mode of a Mach 6.0 boundary layer with the adiabatic wall in the spatial LST. The result indicates that the thermal diffusion source Pdiff plays a key role in the amplification of the unstable S mode. Furthermore, the growth rate analysis is performed for DNS results of different acoustic metasurfaces to clarify the stabilization mechanism of acoustic metasurfaces.