Моделирование волн давления при дефлаграционном горении облаков топливно- воздушных смесей

Abstract

The paper examines the assumptions underlying a whole group of methods for estimating the parameters of shock waves (pressure waves) during the combustion of spherical fuel-air clouds - the so-called parametric formulas. The formulas allow to determine the parameters of pressure waves from the given energy release and combustion rate. To do this, a complete system of gas-dynamic equations is solved using high-precision numerical simulation. In this case, the combustion front is explicitly distinguished in the form of an infinitely thin discontinuity, on which the laws of conservation of mass, momentum, and energy are satisfied. The results of such a numerical calculation are compared with calculations using the corresponding parametric formulas. Clouds of a stoichiometric mixture hydrogen-air are considered. It is shown that the parametric formulas describe the expansion of clouds of hot products with a good degree of accuracy. Here, there is complete agreement with the direct numerical simulation. It is also shown that the parameters of pressure waves are satisfactorily described both in the calculation by parametric formulas and in direct numerical simulation. In this case, within the cloud, there is a greater increase in pressure than the parametric formulas predict. This is explained by the fact that the assumptions used in the formulas regarding the behavior of the flame front as an impenetrable piston do not fully reflect the physical processes: the combustion front is a semipermeable piston, and some of the mass of the initial mixture still penetrates through it. The third factor considered, which determines the achieved pressures, is the rarefaction wave that occurs in the air after the cloud burns out. This wave propagates in combination with the leading pressure front formed during combustion initiation. The extent of this complex remains practically constant, and its attenuation during spherical propagation is adequately described by the parametric formulas.