Approximate Analytic Solution of a Self-Similar Piston Moving in an Inhomogeneous Medium

Abstract

Self-similar motion for the flow between a piston and strong shock propagating in a non uniform ideal gas at rest has been studied. The solution to the problem is similar to that of hypersonic flows past the power law bodies. The gas ahead of the shock is assumed to be uniform and at rest. This is considered as a particular case of radiative piston problem. The shock is assumed to be very strong and propagating in a medium at rest in which density obeys power laws. This problem with spherical symmetry has got importance in astrophysics. To solve the gas dynamics problem, Chernyii's expansion techniques have been used in which flow variables are expanded in a series of powers of ε, the density ratio across the strong shock. The approximate analytic solution has been obtained in closed form to the zeroth approximation. The problem discussed belongs to the self-similar motion of the first kind. The resulting analytic solution gives the flow variables distribution for plane, cylindrical, and spherical symmetry for different cases which satisfy the similarity conditions with accurate trend and values.