Particle Kinetics of Gas-Solid Particle Mixtures

Abstract

In this thesis the interaction of a normal gas dynamic shock wave with a gas containing a distribution of small solid spherical particles of two distinct radii, σ 1 and σ 2 , is studied (1) to demonstrate that the methods of kinetic theory can be extended to treat solid particle collision phenomena in multidimensional gas-particle flows; (2) to elucidate some of the essential physical characteristics associated with particle-particle collision processes; and (3) to give some indication regarding the importance of particle collisions in particle-laden gas flows. It is assumed that upstream of the shock wave particles σ 1 are uniformly distributed while particles σ 2 are non-uniformly distributed parallel to the shock face and in much smaller numbers than particles σ 1 . Under these conditions the gas-particle σ 1 flow downstream of the shock wave is very nearly one-dimensional and independent of the presence of particles σ 2 . The usual shock relaxation zone is established by the interaction of particles σ and the gas downstream of the shock wave. The collisional model pro- posed by Marble 3 is then extended and used with a modified form of the mean free path method of kinetic theory to calculate the macroscopic distribution and velocity of particles σ 2 as determined by the particle σ 1 - particle σ 2 and particle σ 2 -gas interactions. Within the condition that the random velocity imparted to a particle σ 2 by a collision is damped by its viscous interaction with the gas before it suffers another collision, the kinetic theory method established here may be extended to include more general particle-particle and particle-gas interaction laws than those used by Marble. However, the collisional model employed is particularly important because the criteria for its application are easy to establish and because it admits a wide class of physically interesting situations. Within the restrictions of this collision model, it is possible to analyze the macroscopic motion of particles σ 2 in three important limiting cases: (σ 2 /σ 1 ) 2 >> ⊥,(σ 2 /σ 1 ) 2 << ⊥ and (σ 2 /σ 1 ) 2 ~ ⊥. It is found that when (σ 2 /σ 1 ) 2 >> ⊥ there is essentially no redistribution of particles σ 2 normal to the gas flow. The only effect of particle σ 1 -particle σ 2 encounters is a drag force acting to slow down particles σ 2 . When (σ 2 /σ 1 ) 2 << ⊥ it is found that particles σ 2 . may have many collisions during their passage through the shock relaxation zone. As a consequence there may be a substantial redistribution of particles σ 2 downstream of the shock wave. The physical features of this process are studied in detail together with the range of validity of this diffusion model. The case (σ 2 /σ 1 ) 2 ~ ⊥ is analyzed under the condition particles σ 2 have at most one collision during their passage through the shock relaxation zone. It is found that when the gas or particle σ 1 density is low, the single collision effects may be important even when σ 2 /σ 1 differs significantly from unity and the particles are not very small. Under most conditions of practical significance, because there is invariably a distribution of particles sizes present in a dusty gas, the calculation of the particle distribution in the shock relaxation zone should account for the effects of particle-particle encounters. It is suggested that an experimental observation of particle size distribution in a shock relaxation zone can yield significant information on particle-particle and particle-gas interaction laws.