Perturbation Solutions for Variable Energy Blast Waves

The trajectory of and the flow field behind blast waves with time varying energy input is determined. Freeman's Lagrangean coordinate formulation is modified to include both the geometric factor, alpha, for plane, cylindrical and spherical shocks and also non-integer values of beta, the energy input parameter, in a single computational algorithm. Numerical problems associated with vanishing density at the fictitious piston face are then examined and solved. Second order perturbation solutions about the infinite strength shock are then obtained in Sakurai's inverse shock Mach number expansion parameter for 0 or = beta alpha + 1. Tables and graphs of significant numerical coefficients are presented for comparison to and extension of results of other authors. Graphs of typical shock trajectories and flow field density, pressure and velocity variations are also presented and discussed. (Author)