Perturbed-euler similarity profiles supporting attached shock waves

A unified hypersonic/supersonic similarity solution has been obtained based on a Perturbed Euler Formulation (PEF) according to Lighthill's wedge perturbation method. The PEF similarity is derived from a pressure-based ordinary differential equation through a quasiconical coordinate transformation. This similarity yields a complete set of shock shape and pressure field solutions in closed form and applies to either concave or convex bodies with any thickness for all shock-attached Mach numbers. It is shown that a power-law body results a power-law shock of the same order and with the power-law pressure solution one order lower. The PEF removes the previous assumptions of hypersonic small disturbance theory (HSDT), hence its similarity results a shock distance further away from the body than those of HSDT by Cole and Hui. Comparisons of PEF solutions with available test and computed results show very good agreement. In addition, Mellin transform of the PEF similarity suggests a solution of a new class of bodies. For a convex body, real gas effect is found to promote the body aerodynamic efficiency. As the PEF similarity furnishes an exact solution in closed form, it offers a rapid means for hypersonic lifting surface design optimization. Such a development is currently underway.