Numerical simulation of a two-phase turbulent pipe-jet flow loaded with polydispersed solid admixture

Abstract

Results of the mathematical modelling of a two-phase turbulent pipe-jet flow carrying fine solid particles are presented. The numerical results are compared with experimental data obtained in our laboratory. The purpose of the joint study of these flows is connected with the efforts to explain the pinch-effect experimentally discovered by Laats and Frishman (1970) and Navoznov et al. (1979) (for the motion of fine solid particles in a jet). It is associated with the growth of particle mass concentration along the jet axis with its maximum at some distance from the outlet of the pipe. The effect of intensive scattering of large particles in the initial region of the two-phase turbulent jet was also discovered in those experimental investigations. The theoretical analysis made by Kartushinsky (1984) showed that these effects are linked not only with the properties of the motion of particles of different size in the turbulent jet, but also with the prehistory of the motion of such particles in a pipe. Our calculations of the pipe jet flow provide an opportunity to trace the development of the particle mass concentration and the velocity fields in the pipe and jet, excluding the necessity for artificially given initial boundary conditions in the jet for modelling the pinch-effect. The peculiarity of this simulation is in the closure of the equations of the motion of the dispersed phase. The inter-particle collisions in polydispersed flows are considered, since in real two-phase flows the dispersed admixture itself is a polydispersed medium and, thus, the inter-particle collisions play a significant role together with the turbulent diffusion of particles in modelling. The so-called pseudo-viscosity coefficients are introduced in the transport equations of mass, momentum and angular momentum of the dispersed phase for modelling the inter-particle collisions. The formulae for pseudo-viscosity coefficients take into account the properties of the particle motion (the linear and angular velocities and mass concentration of the dispersed phase), their relaxation features as well as collision parameters (the restitution and friction coefficients). The system of equations for the motion of each particle fraction is written and solved for a pipe jet flow. The exchange of the momentum in the fluctuating motion of the gaseous and dispersed phases is taken into account together with the inter-particle collisions. Such exchange of the momentum results to the additional force factors—the Reynolds stresses in the dispersed phase (Shraiber et al. 1990). Besides, the viscous drag force, the Magnus and Saffman lift forces and the turbophoresis force due to the velocity lag as well as non-uniform distribution of the average and the fluctuating velocities of gaseous phase are also taken into account in the model. Only due to the consideration of all these factors it has been possible to simulate the pinch-effect in a two-phase jet. The numerical results are in good agreement with the experimental data for the pipe and jet flow.