Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Gubajdullin D. A., Tukmakov D. A. Numerical simulation of aerosol oscillations in a narrow closed resonator. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2026, vol. 26, iss. 2, pp. 198-210. DOI: 10.18500/1816-9791-2026-26-2-198-210, EDN: IBKYED

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
532.534
DOI: 
10.18500/1816-9791-2026-26-2-198-210
EDN: 
IBKYED

Numerical simulation of aerosol oscillations in a narrow closed resonator

Autors: 
Gubajdullin Damir A., Federal Research Center "Kazan Scientific Center of the Russian Academy of Sciences"
Tukmakov Dmitry A., Federal Research Center "Kazan Scientific Center of the Russian Academy of Sciences"
Abstract: 

This work is devoted to the numerical simulation of gas suspension oscillations in an acoustic resonator. The mathematical model utilizes a continuum technique for simulating the dynamics of multiphase media in Euler coordinates, accounting for the interaction between the gas and the dispersed phase. The dynamics of the carrier medium are described by a system of Navier – Stokes equations for a compressible, heat-conducting gas, taking into account interphase heat and momentum exchange between the mixture phases. The interphase momentum exchange forces included the aerodynamic drag force, the added mass force, and the dynamic Archimedes force. The dispersed phase dynamics are described by a system of equations including the continuity equation for the mean density, the conservation equations for the spatial components of the dispersed phase momentum, and the thermal energy conservation equation, all written taking into account interphase thermal interaction and momentum exchange between the phases. The system of equations for the dynamics of a multi-velocity, multi-temperature, monodisperse system was integrated using an explicit, second-order finite-difference method. A spatial-direction splitting scheme was used to implement the finite-difference method. A nonlinear correction scheme ensured the monotonicity of the solution. Using a numerical model, the oscillations of a gas suspension in a closed acoustic resonator were studied for various piston stroke amplitudes at a frequency close to the first linear resonance frequency. The numerical results were compared with the physical experiment. The comparison showed acceptable agreement between the numerical solution and the physical experiment data. Furthermore, within the framework of the monodisperse approximation of the mathematical model of gas suspension dynamics, the effect of particle dispersion on the intensity of change in the longitudinal component of the dispersed phase velocity and fluctuations in the dispersed phase concentration was studied. Larger dispersed inclusions have a lower velocity, and it was also found that smaller dispersed inclusions result in smaller amplitudes of carrier medium pressure fluctuations.

Key words: 
numerical modeling
multiphase media
continuum model
interphase interaction
Navier – Stokes equation
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Received: 
29.12.2025
Accepted: 
06.03.2026
Published: 
01.06.2026
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