Numerical Simulation of the Interaction of a Gas Suspension With a Shock Wave by Continual Mathematical Models With Ideal and Dissipative Carrier Media
DOI:
https://doi.org/10.14529/cmse220405Keywords:
numerical simulation, finite difference scheme, multiphase media, continuum model, interfacial interaction, Euler equation, Navier—Stokes equationAbstract
This paper compares computer implementations of numerical algorithms for solving the equations of mathematical models of the dynamics of gas suspensions with viscous heat-conducting, inviscid heatconducting and ideal carrier media. Mathematical models are developed within the framework of the continuum technique for modeling the dynamics of multiphase media. In the study, the process of interaction of a shock wave moving from a homogeneous gas into a gas suspension, which is often encountered in the mining industry, was modeled. The relevance of the study of this flow of inhomogeneous media is associated with the shielding of industrial explosions by aerosol curtains. When modeling for a viscous medium, homogeneous Dirichlet boundary conditions were set, for an inviscid medium, homogeneous Neumann boundary conditions. The equations of the mathematical model were integrated by the McCormack finite difference method. To overcome numerical oscillations, a nonlinear scheme for correcting grid functions was used. The program that implements the continuum method for the dynamics of multiphase media consisted of a block for specifying boundary conditions, a block that implements a numerical solution, and a block for accounting for interfacial interaction. As a result of comparing numerical calculations of mathematical models of the dynamics of a gas suspension with an ideal, inviscid heat-conducting and viscous heat-conducting carrier media, it was found that during the movement of a gas suspension, the viscosity of the carrier medium of the gas suspension has the greatest influence on the intensity of interfacial momentum exchange.References
Loitsyansky L.G. Fluid and Gas Mechanics. Moscow: Publishing “Drofa”, 2003. 784 p. (in Russian)
Fletcher C.A. Computation Techniques for Fluid Dynamics. Berlin: Publishing Springer-Verlang, 1988. 409 p. DOI: 10.1007/978-3-642-97071-9.
Muzafarov I.F., Utyuzhnikov S.V. Application of compact difference schemes to the study of unsteady compressible gas flows. Mathematical Modeling. 1993. Vol. 5, no. 3. P. 74–83. (in Russian)
Tukmakov A.L. Dependence of the mechanism of solid particle drift in a nonlinear wave field on the time constant and wave front passage time. Journal of Applied Mechanics and Technical Physics. 2011. Vol. 52, no. 4. P. 590–598. DOI: 10.1134/S0021894411040122.
Lenskaya O.Yu., Abdullaev S.M., Prikazchikov A.I., Sobolev D.N. Numerical modeling of the characteristics of the boundary layer of the atmosphere of a large industrial city (on the example of Chelyabinsk). Bulletin of the South Ural State University. Computational Mathematics and Software Engineering. 2013. Vol. 2, no. 2. P. 65–82. (in Russian) DOI: 10.14529/cmse130206.
Volkov V.Y., Golibrodo L.A., Krutikov A.A., et al. Multiscale problems of heat and mass transfer in nuclear energy. Bulletin of the South Ural State University. Computational Mathematics and Software Engineering. 2017. Vol. 6, no. 4. P. 600073. (in Russian) DOI: 10.14529/cmse170405.
Protsenko S.V., Atayan A.M., Chistyakov A.E., et al. Experimental study of power loads on the supports of a surface structure based on a mathematical model of wave processes. Bulletin of the South Ural State University. Computational Mathematics and Software Engineering. 2019. Vol. 8, no. 3. P. 27–42. (in Russian) DOI: 10.14529/cmse190302.
Madaliev M.E. Numerical study of axisymmetric jet flows based on the turbulent model nu t-92. Bulletin of the South Ural State University. Computational Mathematics and Software Engineering. 2020. Vol. 9, no. 4. P. 670078. (in Russian) DOI: 10.14529/cmse170405.
Nigmatulin R.I. Dinamika mnogofaznyh sred.Dynamics of multiphase media. Part 1. Moscow: Publishing “Nauka”, 1987. 464 p. (in Russian)
Kutushev A.G. Mathematical modeling of wave processes in aerodisperse and powder media. St. Petersburg: Publishing “Nedra”, 2003. 284 p. (in Russian)
Fedorov A.V., Fomin V.M., Khmel T.A.Wave processes in gas suspensions of metal particles. Novosibirsk: Publishing “Parallel”, 2015. 301 p. (in Russian)
Fedorov Y.V., Panin K.A. Heat and mass transfer in the acoustics of liquid with encapsulated droplets. Lobachevskii Journal of Mathematics. 2022. Vol. 43, no. 2. P. 376–380. DOI: 10.1134/S1995080222050122.
Khachai O.A., Khachai A.Y. Modeling of a seismic field in the acoustic approximation of two-phase, hierarchically inhomogeneous media. Bulletin of the South Ural State University. Computational Mathematics and Software Engineering. 2014. Vol. 3, no. 1. P. 33–43. (in Russian) DOI: 10.14529/cmse140103.
Cherkesov L.V., Shulga T.Y. Study of the influence of stationary currents on dynamic processes and the evolution of pollution in the Sea of Azov. Bulletin of the South Ural State University. Computational Mathematics and Software Engineering. 2017. Vol. 6, no. 1. P. 56–72. (in Russian) DOI: 10.14529/cmse170104.
Ravshanov N., Kurbonov N.M. Computer modeling of the process of fluid filtration in porous media. Computational Mathematics and Software Engineering. 2015. Vol. 4, no. 2. P. 89–106. (in Russian) DOI: 10.14529/cmse150207.
Surov V.S. Hyperbolic model of a single speed, heat conductive mixture with interfractional heat transfer. High Temperature. 2018. Vol. 56, no. 6. P. 890–899. DOI: 10.1134/S0018151X1806024X.
Sadin D.V., Golikov I.O., Davidchuk V.A. Modeling the interaction of a shock wave with a limited inhomogeneous layer of a gas suspension by a hybrid method of large particles. Computational methods and programming. 2021. Vol. 22, no. 1. P. 1–13. (in Russian) DOI: 10.26089/NumMet.v22r101.
Liu C., Zhao Y., Tian Z., Zhou H. Numerical Simulation of Condensation of Natural Fog Aerosol under Acoustic Wave Action. Aerosol air and quality reserch. 2021. Vol. 21, no. 4. P. 1–21. DOI: 10.4209/aaqr.2020.06.0361.
Verevkin A.A., Tsirkunov Y.M. Flow of a dispersed phase in the laval nozzle and in the test section of a two-phase hypersonic shock tunnel. Journal of Applied Mechanics and Technical Physics. 2008. Vol. 49, no. 5. P. 789–798. DOI: 10.1007/s10808-008-0099-y.
Yeom G.S., Chang K.S. Shock wave diffraction about a wedge in a gas-microdroplet mixture. International journal of heat and mass transfer. 2010. Vol. 53. P. 5073–5088. DOI: 10.1016/j.ijheatmasstransfer.2010.07.056.
Saurel R., Boivin P., Le Metayer O. A general formulation for cavitating, boiling and evaporating flows.Computers and Fluids. 2016. Vol. 128. P. 53–64. DOI: 10.1016/j.compfluid.2016.01.004.
Kapila A.K., Schwendeman D.W., Gambino J.R., Henshaw W.D. A numerical study of the dynamics of detonation initiated by cavity collapse. Shock Waves. 2015. Vol. 25. P. 545–572. DOI: 10.1007/s00193-015-0597-9.
Watanabe H., Matsuo A., Chinnayya A., et al. Numerical analysis of the mean structure of gaseous detonation with dilute water spray. Journal of Fluid Mechanics. 2020. Vol. 887. DOI: 10.1017/jfm.2019.1018.
Tukmakov D.A. Numerical study of the dynamics of gas suspensions in nonlinear wave fields: dis. cand. physics and mathematics sciences: 01.02.05 Kazan (Volga Region) Federal University, Kazan, 2015. 135 p. URL: https://kpfu.ru/dis_card?p_id=1958 (accessed: 08.09.2022). (in Russian)
Nigmatulin R.I., Gubaidullin D.A., Tukmakov D.A. Shock Wave Dispersion of Gas-Particle Mixtures. Doklady Physics. 2016. Vol. 61, no. 2. P. 70–73. DOI: 10.1134/S1028335816020038.
Tukmakov D.A. Numerical study of the influence of the density of the material of the dispersed component on the intensity of the generation of an acoustic pulse in an electrically charged gas suspension. Mathematical notes of NEFU. 2020. Vol. 27, no. 4. P. 99–109. (in Russian) DOI: 10.25587/SVFU.2020.77.39.008.
Tukmakov D.A. Comparison of mathematical models of the dynamics of electrically charged gas suspensions for various concentrations of the dispersed component. Applied Informatics. 2022. Vol. 17, no. 1. P. 39–54. (in Russian) DOI: 10.37791/2687-0649-2022-17-1-39-54.
Tukmakov A.L., Tukmakov D.A. Numerical study of the influence of the parameters of dispersed particles on the deposition of the solid phase of an electrically charged polydisperse gas suspension. Bulletin of the Saratov University. New series. Series: Mathematics. Mechanics. Informatics. 2022. Vol. 22, no. 1. P. 90–102. (in Russian) DOI: 10.18500/1816-9791-2022-22-1-90-102.
