Applicability of a Chemical-Equilibrium Model to Explosion Products

Abstract

Composition of explosion products changes during the course of their expansion. The chemical equilibrium hypothesis allows closure of the gasdynamic conservation equations and calculations of the product composition without invoking the chemical kinetics equations. The rate of the change in concentrations of the reaction products depends on instantaneous values of the thermodynamic parameters of a flowing gas, its finiteness implies a certain deviation of the product composition and, consequently, of the heat released in the gas from their equilibrium counterparts. The chemical equilibrium model may be applied only in the case when this deviation is small. This defines the sufficient condition for model applicability to explosion products. It is shown that for the explosion products of fuel oxygen mixtures this condition is met at each instant during their expansion, provided the initial radius of an expanding unconfined spherical mixture volume exceeds 5 cm. In fuel-air explosive mixtures the equilibrium model applies only to clouds of a radius greater than 10 m. If the initial radius of a cloud exceeds 1 m it can be assumed that the expanding products remain equilibrated until a certain temperature is reached that depends on the initial cloud size. At this temperature nitrogen oxides in the products become frozen, whereas the explosion products containing C, H, and O atoms remain equilibrated during further expansion. Unconfined explosions of acetylene-oxygen and propaneair mixtures were modeled numerically using a kinetic scheme consisting of 18 elementary steps in order to verify the above estimates. Explosions of unconfined gaseous clouds generate a complicated flow pattern in which expansion of the combustion products play an important part. Since the combustion products are initially at a very high temperature, one has naturally to allow for a change in both the specific heats of the components and their concentrations when performing gasdynamic calculations. There are several ways how to take into account variation in the physical and chemical properties of expanding explosion products.