Free unsteady expansion of a polytropic gas: Self-similar solutions

Abstract

A new class of generalized self-similar solutions for the problem of one-dimensional unsteady outflow of a gas into a vacuum is found. It allows a unified and comprehensive description of plane, cylindrical, and spherical symmetric flows for arbitrary polytropic index. A key property is a moving inner boundary. Relative to this, subsonic and supersonic outflows are possible in certain parameter regions. Simple analytic expressions are found near the boundaries and an extensive parameter discussion is presented. The asymptotic solutions are of specific importance. As an application, it is shown that the isothermal corona of a laser-generated plasma is in part described by one of these asymptotic solutions.