Self-similar solution of the spherical detonation problem

Under polytropic equation of state and strong shock assumptions, group-theoretic methods are used to obtain a class of self-similar solutions to a one-dimensional problem in reactive shock hydrodynamics with spherical symmetry and to characterize the class of all state-dependent chemical reaction rates under which such solutions exist. In the special case that the reaction rate is proportional to the internal energy, the system of ordinary differential equations describing the self-similar solution can be reduced to a single, first-order differential equation for which a phase-plane analysis yields the nature of the solution near the equation's critical points. Further, a modeling parameter which characterizes the flow is identified.