Transition from convective combustion to detonation for an aerocolloidal suspension of a unitary fuel

Abstract

The need to investigate the transition of aerocolloidal suspensions of unitary fuels {solid propellants and high explosives) from convective combustion to detonation has been recognized lately in connection with safety-engineeri ng problems. Various techniques exist for the initiation of combustion and detonation of aerocolloidal suspensions. In this article we discuss the initiation of combustion by ignition without an increase in the pressure. A distinctive feature of unitary-fuel systems is the liberation of a large quantity of gaseous reaction products during the combustion process. These products form a convection front, which moves under the action of the pressure drop created in the gas liberation process, entraining new particles in the combustion process. We have previously [ 1, 2] developed an asymptotic theory of the initial stage of propagation of convective combustion in aerocolloidal suspensions, during which time the velocity of motion is strongly subsonic and the particles are still unable to be entrained in the motion of the gas. In this case the condition of uniformity of the pressure p =p(t) (or homobaricity) holds in the region of the hot gases, and the gas flow is a simple Riemann wave ahead of the convection front. Within the framework of this approach it is possible to determine the law governing the motion of the convective combustion front up to the time of formation of a weak shock in the flow. In this study we obtain a numerical solution of the problem of transition from convective combustion to detonation for act.colloidal suspensions within the framework of the complete system of equations of the mechanics of multiphase reacting media [3]. We describe the evolution of convective combustion of aerocolloidal suspensions up to the formation of a strong shock in the flow, behind which particle combustion takes place, followed by the transition of this shock into the steady Chapman-Jouguet detonation regime [4]. We note a recent attempt [5] to analyze the combustion-to-de tonation transition in a porous solid propellant under shock excitation and an investigation [6] of the transition to steady detonation in a gas-droplet medium as the result of a point explosion. Fundamental Equations; Statement of the Problem. Let us consider the planar one-dimensional motion of a monodisperse aerocolloid in the presence of a heterogeneous chemical reaction. We assume for simplification that the chemical reaction is initiated by heating of the particle surface to the dissociation temperature T s (p) and continues as an equilibrium process at a temperature equal to T s, so that all the heat admitted to the particle is used for its gasification and the chemical reaction obeys the simple equation A---B, where A and B are the symbols for the chemical elements; the thermodynamic properties of the reaction products and the gas carrier are the same, the gas is calorically ideal, and the particles are incompressible. The equations of motion of the aerocolloids under the stated assumptions have the form [2, 3]