One-Dimensional Unsteady Numerical Model of Gas Suspension Flow Caused by Gravitational Sedimentation of Particles with a Constant Velocity

Nonstationary processes in a heterogeneous medium are investigated. The dynamics of heterogeneous media is largely determined by the effects caused by the interfacial interaction, the intensity of which depends on the properties of the dispersed phase. The goal of this paper is to study the effect exerted by the volumetric content, material density, and the size of aerosol particles on the motion of the carrier (continuum) medium. The object of the study is aerosols, i.e., gas-droplet and dusty media. As a rule, the motion of the mixture is initiated by the motion of the carrier phase. This study addresses the gas flow caused by the deposition of particles from the gas suspension. The effect of the dispersed phase of the two-phase mixture on the gas motion in gravitational aerosol deposition is investigated numerically. The mathematical model consists of equations describing the dynamics of the carrier medium and equations describing the dynamics of the dispersed component. It is assumed that the dispersed component of the mixture is deposited in the Stokes regime. The system of equations governing the dynamics of the carrier medium involves continuity, momentum, and energy equations. The carrier medium is treated as a viscous, compressible, and heat-conducting gas. The interfacial interaction is determined by the Stokes force. Interfacial heat transfer is taken into account in the mathematical model. The equations of the mathematical model are integrated using the MacCormack explicit finite-difference method with a second-order error. A nonlinear correction of the grid function is used to obtain a monotone numerical solution and suppress its numerical oscillations. The equations are supplemented by initial and boundary conditions. Numerical calculations of the gravitational deposition of the dispersed phase demonstrate the formation of a gas flow and the gas pressure becomes unevenly distributed due to this flow. The numerical results also reveal that the gas flow intensity depends on the parameters of the dispersed component of the gas suspension.