Calculation of the shock wave parameters from the detonation of combustible gas mixtures of variable composition

Abstract

as a function of the composition of the mixture is of great practical interest. The validity of the calculation is determined by the correct choice of assumptions allowing a mathematical model of the process to be constructed, and by comparison of the results of the numerical analysis with the experimental results. Until recently, the calculations were performed using the assumption that the detonation products (DP) are a nonreacting gas with a constant adiabatic index [1-3]. It is shown in [4-5] that this assumption leads to errors in the calculation of the parameters of shock waves generated in air. At high temperatures, complex chemical reactions can take place in the actual detonation products. It can be supposed that the DP during the whole process of expansion have an equilibrium chemical composition. In this case the molecular mass, chemical composition, and other parameters of state of the DP differ from those determined on the assumption that the DP are a gas mixture--an inert gas with constant adiabatic index. In [4, 5] in order to calculate the equilibrium state of the DP an approximate procedure is used [6], in which the dependence of the specific heat of the individual components of the mixture on the temperature is not taken completely into consideration. In this paper, the processes of propagation of the air shock wave formed from the detonation of propane--air mixtures of different composition are investigated numerically, including mixtures with a space-variable composition. Formulation of the Problem. We shall consider a spherical region of radius ro, filled with a mixture of propane and air (of constant or variable composition). A one-dimensional spherical detonation wave is propagating through the mixture. The propane--air mixtures will be studied with a fuel to oxidant ratio given by the stoichiometric ratios ~ = 0.5, 1 and 2. Significantly different initiation energies are required for excitation of the detonation. The mixture with ~ = 0.5 is limiting in composition for initiation of a detonation. However, the mixtures chosen allow the effect of their composition on the parameters of the air shock waves to be analyzed. The combustible mixture with a composition which varies with distance represents a layer of combustible of fixed composition, the coordinates of which are determined by the relation q, Q, M~/kg