Numerical study of the effect of droplet coagulation on the dynamics of a two-fraction aerosol in an acoustic resonator

Abstract

The study is devoted to the study of the effect of coagulation of dispersed phase droplets on aerosol oscillations in an acoustic resonator. The mathematical model of aerosol dynamics implements a continuous mathematical model of the dynamics of a multiphase medium, taking into account the velocity and thermal inhomogeneity of the mixture components. To describe the dynamics of the carrier medium, a two-dimensional unsteady system of Navier – Stokes equations for a compressible gas is used, written taking into account the interphase force interaction and interphase heat transfer. To describe the dynamics of the dispersed phase, a system of equations is solved for each of its fractions, including the continuity equation for the «average density» of the fraction, the equations for the conservation of the spatial components of the momentum and the equation for the conservation of thermal energy of the fraction of the dispersed phase of the gas suspension. The interphase force interaction included the Archimedes force, the force of the added masses and the force of aerodynamic drag. The heat exchange between the carrier medium - gas and each of the dispersed phase fractions was also taken into account. The mathematical model of the dynamics of a polydisperse aerosol was supplemented by a mathematical model of collisional aerosol coagulation. For the velocity components of the mixture components, uniform Dirichlet boundary conditions were specified. For the remaining functions of the dynamics of the multiphase mixture, homogeneous Neumann boundary conditions were specified. The equations were solved by the explicit McCormack method with a nonlinear correction scheme that allows obtaining a monotonic solution. As a result of numerical calculations, it was determined that a region with an increased content of coarse particles is formed in the vicinity of the oscillating piston. The coagulation process leads to a monotonic increase in the volumetric content of the fraction of coarse particles and a monotonic decrease in the volumetric content of fine particles.