ISSN 2658–5782

DOI 10.21662

DOI 10.21662

Electronic Scientific Journal

2022. Vol. 17. Issue 1, Pp. 97–112

URL: http://mfs.uimech.org/mfs2022.1.008,en

DOI: 10.21662/mfs2022.1.008

URL: http://mfs.uimech.org/mfs2022.1.008,en

DOI: 10.21662/mfs2022.1.008

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

Urmancheev S.F.

Mavlyutov Institute of Mechanics UFRC RAS, Ufa, Russia

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.

coustic scattering,

system of sound-permeable spheres,

temperature stratification,

energy separation,

cyclostrophic adaptation,

igneous ore formation,

differentiation

Present review presents some results for three problems carried out within the framework of the scientific project “Hydrodynamic effects in multiphase and thermoviscous media under wave and thermal effects”. The research program on this topic is connected with the establishment of fundamental laws in hydrodynamic processes occurring under the influence of temperature and acoustic fields. In the framework of the first problem, the scattering of acoustic waves on a set of interacting sound-permeable spheres is studied. The second problem is related to mathematical simulation of a swirling turbulent flow containing particles of a dispersed phase. The third problem is devoted to simulating the processes of differentiation of magmatic melts during the flow in subvolcanic chambers, taking into account heat exchange with surrounding rocks.

**The purpose** of the research is to determine the mutual influence of the acoustic, hydrodynamic and thermodynamic parameters of the considered systems and, at the same time, to study the patterns of distribution of particles of the dispersed phase, the physical properties of the study objects, the effects of stratification and localization.

**Methods.** To solve the first problem, the fast multipole method was expanded for the possibility of its application in the case of sound-permeable bubbles or drops arbitrarily located in space. In the framework of the second problem, 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. When solving the third problem to describe the process of magmatic ore formation, a system of equations based on the methods of mechanics of multiphase media and thermohydrodynamics was 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.

**Main results.** In the framework of first problem on the basis of addition theorems for spherical wave functions, a new formula for the total scattering cross section of the system under consideration was 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. When studying the second problem, a number of parametric studies were carried out. For a wide range of turbulent flows, the optimal, from the point of view of temperature stratification of the flow, geometric parameters of the inlet and outlet sections of the vortex tube were determined. The results for the third problem, obtained in the course of a computational experiment, indicate the possibility of a periodically inhomogeneous nature of the distribution of ore-forming fractions.

**Conclusions.**

- The results of research in solving the first problem are of interest from the point of view of identifying measurement data in acoustic diagnostics of bubble and drop systems in technological installations and for analyzing the consequences of the action of ultrasound and pressure waves on screening layers consisting of particles of the dispersed phase, if the hypotheses of the mechanics of multiphase media turn out to be inapplicable for describing the physical model of the process under consideration.
- For the second problem, the analysis of scientific literature shows that the complexity of the processes occurring in swirling flows, especially in the presence of a dispersed phase, that their description requires numerical models that could allow us to take into account with a sufficient degree of accuracy how all the design features of vortex tubes , and hydrodynamic and thermophysical features of the flow process in these pipes.
- When solving the problem of the formation of ore deposits, considered in the third problem, the methods of mathematical modeling by means of a computational experiment make it possible to improve the accuracy of predicting the localization of certain ore deposits formed during the outflow of a magmatic melt.

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