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# articles

The author: Tukmakov D.     Published in № 1(97) 31 january 2022 year
Rubric: Models and althorithms

## Comparison of mathematical models of the dynamics of electrically charged gas suspensions for various concentrations of the dispersed component

This work is devoted to mathematical modeling of the dynamics of inhomogeneous electrically charged media. A dusty environment - solid particles suspended in a gas – was considered as an inhomogeneous medium. The mathematical model implemented a continuous approach to modeling the dynamics of inhomogeneous media. The complete hydrodynamic system of equations was solved for each component. The system of equations for the dynamics of each component included the equations of mass continuity, momentum components, and the energy conservation equation for the mixture component. Intercomponent interaction took into account momentum exchange and intercomponent heat transfer. The carrier medium was described as a viscous compressible heat-conducting gas. The flow was described as a flow with a two- dimensional geometry. The equations of the mathematical model were supplemented with initial and boundary conditions. The mathematical model took into account the wall viscosity in the channel. The system of equations of the mathematical model was integrated by McCormack's explicit finite-difference method. To obtain a monotonic grid function, a nonlinear scheme for correcting the numerical solution was used. The mathematical model was supplemented by the Poisson equation describing the electric field formed by charged dispersed particles. Poisson's equation was integrated by finite-difference methods on a gas-dynamic grid. Such a choice of the computational grid was necessary to calculate the concentration of particles required both for solving the electric field equation and for calculating the physical fields of the dynamics of inhomogeneous media. The reciprocal motion of a gas suspension caused by the movement of dispersed particles under the action of the Coulomb force was numerically investigated. The values of the surface and mass densities are determined, at which the models of the surface and mass densities of charges in the simulation of such a process are the same. It is revealed that the surface and mass models of charges are identical with respect to the volumetric content.

#### Key words

computational experiments, numerical modeling, finite-difference methods, inhomogeneous media, electro hydrodynamics

#### Tukmakov D.

##### Degree:

Cand. Sci. (Phys.-Math.), Researcher, Federal State Budgetary Institution of Sciences "Kazan Scientifi Center of Russian Academy of Sciences"

Kazan, Russia