Search

Mathematical Modeling of the Turbulent Transport of the Dispersed Phases in Turbulent Flow // Tomsk State Pedagogical University Bulletin. 2004. Issue 6 (43). P. 50-54

Two different approaches are currently available for the analysis of the behaviour of the solid particles in flows. These are termed the Eulerian and Langrangian. In the Lagrangian method on the trajectories of the individual size fractions are evaluated by solving time dependent ordinary differential equations. In the Eulerian approach on the other hand, partial differential equations for the conservation of mass and momentum are written for each of the particle’s fractions, which are solved together with the equation of the liquid flow. Even in the simplest hydrocyclone model, there are two phases present, namely liquid, and monosized particles. Since particles of different diameters move with different velocity, each additional particle size represents an additional phase. An algebraic slip approach was used, with three momentum equations solved for the mixture, and relative moment of each fractions take into account in the conservations equations, in an iterative manner. The relative velocities between the particles and liquid in the hydrocyclone are evaluated by consideration of the dynamic force balance on the particle itself. The consequence of the mass conservation for the all fractions in a turbulent flow is the equation of turbulent diffusion of particles for each particle fraction mass concentration (Euler description form). The method of the determination of the diffusion coefficient of the solid phases is considered. Results allow to draw a conclusion that given formula well describes turbulent transport of solid phase flow and can be used for numerical modelling multiphase flows