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On the basis of a model of the collisions of solid particles, the specific features of gasparticle flows in vertical pipes are numerically simulated. The model treats the dispersed phase as a continuum (Eulerian description) consisting of N particle fractions moving with different linear and angular velocities, which result in the particle collisions. The effective viscosity coefficients introduced serve for the closure of the transport equations for the momentum, the angular momentum, and the mass of the different particle fractions. It is shown that taking the collisions of the particles of different fractions into account ensures a satisfactory description of the specific features of the distribution of the particle concentration and the mean and fluctuation velocities of the carrier phase in upward and downward pipe flows.

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A model of the motion of an admixture of polydisperse solid particles in a horizontal plane channel with account for particle deposition on the bottom wall is presented. The dispersed phase, consisting of six particle fractions characterized by the particle size and the mass concentration, is modeled in Eulerian form. Interparticle collisions occur due to the difference in the velocities of average motion of the fractions and to particle velocity fluctuations. It is important to take interparticle collisions into account for flows with a high particle mass loading (in the model, up to 50 kg per kg of gas) and because of the gravity-induced particle accumulation on the bottom wall. To ensure a correct description of the particle-wall collisions, impinging and rebounding particle streams with the corresponding restitution coefficients for the normal and tangential particle velocities and friction are introduced. The calculations are compared with experiments [1]. upper signs of "∓" and "±" refer to the impinging stream and the lower ones to the rebounding stream. Equations (2.1) and (2.2) are the projections of the equation of