Detonation waves in polydisperse gas suspensions of unitary fuel having a continuous particle size distribution function

Abstract

A. I. Ivandaev, A. G. Kutushev, and S. P. Rodionov UDC 532.529The first theoretical research on the wave dynamics of polydisperse gas suspensions was evidently carried out by Williams [1], who obtained intogrodifferential equations for the steady-state motion of a reactive collisionless mixture of a gaseous oxidizer and a sprayed liquid fuel with continuous distribution functions of drop size and velocity. Specific numerical calculations of the structure of a detonation wave in a gas-drop medium, however, were carried out in [1] using a distribution function that presumes a finite number of fractions of liquid particles. The laws of propagation of detonation waves in polydisperse sprays of fuel drops was subsequently studied within the framework of such a (multifractional) description of a collisionless disperse mixture (see, e.g., [2, 3]).A system of integrodifferential equations for the unsteady motion of a multifractional, inert, collisional gas suspension with a particle velocity distribution function was used in [4] to calculate the interaction of a shock wave with a bidisperse cloud of dusty gas. Very weak shocks in a cloud of a polydisperse, inert, collisionless gas suspension with a continuous particle size distribution function were studied theoretically in [5]. The equations of unsteady motion of a polydisperse gas suspension with a continuous particle size distribution function in a linear (acoustic) approximation were generalized in [6] to the case of phase transitions in vapor-drop media. The burning of mixtures of gaseous oxidizer with metallic inclusions in a chemical reactor was investigated in [7] within the framework of the equations of a polydisperse, reactive gas suspension with a continuous distribution function of current particle sizes.A model of the motion of a polydisperse, inert, collisionless gas suspension with a continuous particle size spectrum was developed in [8] and the adequacy of the proposed system of integrodifferential equations for describing actual shock processes in dusty gases was demonstrated, as confirmed by the satisfactory agreement between calculated and experimental data. In the present work we further develop the model of [8] for the case of a reactive, collisional gas suspension of unitary fuel with a continuous initial particle size distribution function.1. Main Assumptions and Equations. Suppose that we have a polydisperse gas suspension of unitary fuel with a continuous particle size spectrum. The usual assumptions in the mechanics of continuous disperse media [8, 9] are used to describe the motion of such a mixture: The characteristic sizes of the particles and the distances between them are considerably less than the characteristic scale of variation of the macroscopic parameters of the flow; the effects of viscosity and heat conduction are important only in the interaction between phases; the mixture is rarefied and the particles are spherical; the particles do not fragment or merge in their collisions with each other; collisions between polydisperse par...

Structure and initiation of plane detonation waves in a bidisperse gas suspension of aluminum particles

“…Thus, the dependence of the critical Mach number of the initiating SW on the mass fraction ratio is nonlinear. The fact that the critical Mach number for the mean particle size does not coincide with the mean value of the critical Mach numbers is consistent with the results of [14,15]. It was found in [15] for a polydisperse suspension of monofuel particles with a continuous particle-size distribution function that there is a certain "characteristic" diameter for which initiation in a monodisperse suspension occurs at the same Mach number (the particle concentration in the suspension was varied).…”

“…4a, 4b, and 4c). For a continuous particle-size distribution function, as was found in [15] for a suspension of monofuel particles, the profiles of parameters of the detonation structure have a smoother character.…”

“…A selfsimilar solution for the structure of a non-ideal detonation wave in a mixture containing two fractions was obtained in [13]; this solution admits the possibility of formation of a two-front detonation structure under certain conditions. A physicomathematical model developed in [14,15] offers a description of shock-wave and detonation processes in polydisperse mixtures of a monofuel with a continuous particle-size distribution function. The critical Mach numbers of the initiating sustained shock waves were determined within the framework of this model in [15] for a normal-logarithmic law of the particle-size distribution.…”

“…A physicomathematical model developed in [14,15] offers a description of shock-wave and detonation processes in polydisperse mixtures of a monofuel with a continuous particle-size distribution function. The critical Mach numbers of the initiating sustained shock waves were determined within the framework of this model in [15] for a normal-logarithmic law of the particle-size distribution. Yet, the effect of explosion waves on polydisperse mixtures and the influence of dispersion on the critical values of the initiation energy have not been studied.…”

“…Metal powders, however, rarely have only one fraction of particles, and the particles usually have different sizes. The behavior of polydisperse suspensions under shock-wave loading was studied in [13][14][15] for particles of a monofuel. A selfsimilar solution for the structure of a non-ideal detonation wave in a mixture containing two fractions was obtained in [13]; this solution admits the possibility of formation of a two-front detonation structure under certain conditions.…”