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The computational investigation of the impurity dispersal in the atmosphere // Tomsk State Pedagogical University Bulletin. 2002. Issue 2 (30). P. 17-20

A combined model where the vertical impurity dis¬persal was calculated by means of a set of differential equations, such as equations of motion, turbulent dif¬fusion and heat conduction, while the horizontal dis¬persal was computed by a Gaussian model was used. The proposed model is complemented with as¬signed semi-empirical dependences for altitude varia¬tions of wind velocity, turbulent exchange coefficient, atmospheric temperature and turbulence statistics. The calculations done allowed us to estimate the pollution level for different meteorological conditions and pollu¬tion sources and provide recommendations as to how to reduce its disastrous effect on the environment.

Numerical Investigation of the Structure of the Swirled Flow in the Cylindrical Chamber with the Porous Medium // Tomsk State Pedagogical University Bulletin. 2003. Issue 4 (36). P. 14-24

Gas flow through porous media is characterized by large vortex structures and large friction coefficients, resulting in an extensive momentum and interphase energy exchange between gas and the solid phase. The model used for flow in porous regions is at once both a generalization of the Navier-Stokes equations and of Darcy's law commonly used for flows in porous regions. The model retains both advection and diffusion terms and so can be used where such effects are important. In deriving the continium equations, it assumed that 'infinitecimal' control volumes and surfaces are large relative to the interstitutal spacing of the porous medium, through small relative to the scales that we wish to resolve. Thus, given control cells and control surfaces are assumed to contain both solid and gas regions. Based on this model, an efficient numerical technique has been developed and a numerical algorithm has been produced to study the processes in the porous medium channel.

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