Power-Series Solutions of the Gasdynamic Equations for Mach Reflection of a Planar Shock by a Wedge

摘要

The self-similar solutions to the problem of a planar shock with Mach number reflecting obliquely from a wedge with vertex angle are obtained to arbitrary accuracy by expanding the fluid quantities in power series in scaled variables. For single Mach reflection, there are four distinct regions, (a) the ambient gas ahead of the incident shock; (b) the gas behind the incident shock and outside the reflected (bow) shock; (c) the region bounded by the Mach stem, the wedge, and the contact surface (slip line) extending from the triple point; and (b) the doubly shocked medium bounded by the contact surface, wedge, and reflected shock. In region (b) the solution is known immediately in terms of Mach number and vertex angle and the conditions in (a). The resulting algebraic equations are solved subject to the additional relations obtained by applying the reflection conditions on the wedge, together with the jump conditions on the boundaries ac and bd, approximated by power series expansions of the F and G functions. Since all these equations are nonlinear, solutions are obtained by iteration with N increasing until convergence is obtained. The Ben-Dor equation for the fluid quantities in regions c,d, at the triple point is used to give initial values. The method generalizes readily to complex and double Mach reflections.