The initial stage of collapse of symmetric gaseous prisms

Abstract

An algorithm is developed for calculating the parameters of a shock-free compressible gas of symmetric tetrahedral gas prisms according to a given law of motion of a section of a piston using characteristic series. It is shown that by taking account of symmetry one can determine uniquely the parameters of the gas flow and the piston shape in a compressible prism. Three subdomains are distinguished in the domain of the perturbed gas flow, in each of which a velocity potential is constructed in the form of a characteristic series. In one subdomain, the solution is defined by the specified law of motion of the piston and, in the other two subdomains the solutions are defined by the conditions that no gas flows across the plane of symmetry and the continuity of its parameters at the boundaries along which the subdomains are joined, which are characteristics. An example of the calculation of a solution is given which, in a part of the domain, is identical to a known, self-similar exact solution when the adiabatic exponent and the magnitude of the dihedral angle of the prism are matched. An exact expression is obtained for the velocity potential and the shape of the wall of the gas prism being compressed.