Dispersed media: scattering of sound waves, stratification in swirling flows and sedimentation processes

Abstract

A brief review on three problems from the multiphase media mechanics area related to the study of the dynamic behavior of disperse systems under various conditions and methods of interaction with external fields or the environment is presented. The problems are an integral part of the scientific project “Hydrodynamic effects in multiphase and thermoviscous media under wave and thermal effects”. The review is carried out in the context of the vector of development of modern research in the relevant areas. As a part of solving the problem of acoustic wave scattering by a set of spherical bubbles or drops, taking into account their sound permeability, the fast multipole method was developed to expand the possibilities of its application in the considered cases. On the basis of addition theorems for spherical wave functions, a new formula for the total scattering cross section for a set of interacting sound-permeable spheres arbitrarily located in space is obtained. An important aspect of the research was the estimation of the region in the parameter space of the problem, in which the effects of multiple scattering are significant. The second problem is related to mathematical modeling of a swirling turbulent flow containing particles of a dispersed phase. For numerical studies of temperature stratification in a vortex tube, an algorithm and a computer code were created using an orthogonalized finite-volume mesh with separation of the near-wall layer. A number of parametric studies have been carried out, in particular, the dependence of the temperature of the outgoing air in the cold diaphragm channel depending on the diameter of the diaphragm has been considered. In order to increase the efficiency of geological exploration in solving the third problem for describing the process of magmatic ore formation, a system of equations based on the methods of mechanics of multiphase media and thermohydrodynamics is proposed. The mathematical model provides for the heat exchange of the magmatic melt flow with the surrounding host rocks, as well as the release of heavy and light fractions from basaltic magma during its cooling. The results obtained in the course of the computational experiment indicate the possibility of a periodically inhomogeneous nature of the distribution of ore-forming fractions.