Effect of pressure gradient on the stability of compressible boundary layers

An investigation into the influence of pressure gradient (wall shaping) on the stability of compressible boundary layers is presented. The steady, compressible, nonsimilar boundary-layer equations are solved with a potential flow velocity distribution corresponding to a power law edge Mach number distribution. The stability of the mean flow is investigated using the small-disturbance compressible linear stability theory. The results indicate that two-dimensional second-mode (Mack) waves can be stabilised with pressure gradient. However, the effectiveness of the pressure gradient on the natural laminar flow control of two-dimensional second-mode waves decreases at hypersonic speeds. The maximum growth rate varies almost linearly with the pressure gradient level. The effect of pressure gradients on stabilising three-dimensional first-mode waves is much larger than their effect on stabilising two-dimensional first-mode waves.