Initial Behavior of a Spherical Blast

Abstract

At time t=0 a unit sphere containing a perfect gas at uniformly high pressure is allowed to expand suddenly into a homogeneous atmosphere. Solutions for short times later are sought by analytic (i.e., not numerical) methods. Viscosity and heat conduction are neglected. The particle velocity,sound speed, and entropy are developed in powers of y, which is proportional to the time (more precisely, the distance moved by the head of the rarefaction wave in time t), with coefficients depending on a slope coordinate q=(1/2N)[(2N−1) +(1−x)/y], where x is the radial coordinate, N=(½)(γ+1)/(γ−1), and γ is the ratio of specific heats. The zero‐order coefficients are the plane shock‐tube solution. First‐order corrections are derived for the various regions. Boundary conditions are approximated for small y at the surfaces of discontinuity, and the method for matching the solutions in the different regions is outlined. This matching process is carried out for the expansion of a diatomic gas into diatomic air.