Analytical solutions for the flow field induced by a spherical flame expanding at constant velocity

An analytical solution for predicting blast effects of explosions in deflagration regimes is outlined. The analysis gives explicit algebraic solutions (closed form solutions) for the whole flow field, provided that the spherical flame is expanding at constant velocity and that burned gases are at rest. Solutions are first obtained using matched asymptotic expansion for flame expanding at a low Mach number. Then, for larger values of the flame Mach number, solutions are obtained using a simplified mathematical formulation of the problem, derived from the exact one using assumptions based on the behavior of the numerical solution for high Mach number flames. These two set of solutions give a complete description of the whole flow field (pressure, velocity, maximum pressure effect, Mach number of the leading shock wave) in terms of the expansion ratio and Mach number of the flame front.