Modeling the dynamics of a two-phase gas mixture and solid dispersed particles

M. Yu. Nemtsev

Matematičeskoe modelirovanie, Tome 35 (2023) no. 7, pp. 97-117.

Résumé

The mathematical model and numerical method for solving problems of the flow of two-phase mixtures of gas and fine solid particles are considered. The particles are assumed to be absolutely rigid, incompressible and non-deformable. As the initial model, the continuum model of R.I. Nigmatulin is considered. The model has two drawbacks, namely: it is not strictly hyperbolic (i.e., it degenerates into an elliptical one under certain flow regimes) and has non-conservative form, which makes it difficult to solve numerically. The paper proposes the method for regularization of the R.I. Nigmatulin model at a discrete level, which makes it possible to eliminate these shortcomings and develop a numerical model that is well-conditioned for evolutionary problems of the flow of gas-dispersed mixtures with non-deformable solid particles. The regularization method is based on splitting the original system into two subsystems, each of which is strictly hyperbolic and has conservative form. Difference schemes of the Godunov type have been developed for the numerical solution of these subsystems. Testing of the proposed model and implemented methods includes checking the preservation of a homogeneous solution, the formation of shock waves and rarefaction waves in a gas, compaction and decompaction waves in the particle phase. The results of numerical simulation of the interaction of a shock wave in gas with a near-wall layer of particles are also presented.

Détail

Keywords: two-phase disperse media, regularization of the Nigmatulin model, Godunov's numerical method.
Mots-clés : continuum model of an ensemble of solid particles

Bibliographie

[1] H. Arastoopour, D. Gidaspow, R. W. Lyczkowski, Transport Phenomena in Multiphase Systems, Springer, 2022

[2] D. Gao et al., “CFD investigation on gas-solid two-phase flow of dust removal characteristics for cartridge filter: a case study”, Environmental Sci. and Pollution Res., 28 (2021), 13243–13263 | DOI

[3] Khomenko Y.P., Ischenko A.N., Kasimov V.Z., Matematicheskoe modelirovanie vnutriballisticheskikh protsessov v stvol'nykh sistemakh, Izd-vo SO RAN, Novosibirsk, 1999

[4] C. K. Man, M. L. Harris, “Participation of large particles in coal dust explosions”, J. of Loss Prevention in the Process Industries, 27 (2014), 49–54 | DOI

[5] F. E. Marble, Dynamics of a gas containing small solid particles, 1963

[6] Kraiko A.N., Sternin L.E., “Theory of flows of a two-velocity continuous medium containing solid or liquid particles”, J. of Applied Math. Mechanics, 29:3 (1965), 482–496 | DOI

[7] R. I. Nigmatulin, Dinamika mnogofaznykh sred, v. 2, Nauka, 1987

[8] D. Gidaspow, Multiphase flow and fluidization: continuum and kinetic theory descriptions, Academic Press, 1994 | MR | Zbl

[9] M. Baer, J. Nunziato, “A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials”, Intern. J. of Multiphase Flow, 12 (1986), 861–889 | DOI | MR | Zbl

[10] Ya. E. Poroshina, P. S. Utkin, “Chislennoe modelirovanie vzaimodeistviya normalno padayuschei udarnoi volny so sloem chastits v ramkakh uravnenii Baera-Nuntsiato”, Gorenie i vzryv, 13:1 (2020), 95–104

[11] Rodionov A.V., “Monotonic scheme of the second order of approximation for the continuous calculation of non-equilibrium flows”, USSR CM, 27:2 (1987), 175–180 | MR | MR | Zbl

[12] B. Einfeldt et al, “On Godunov-type methods near low densities”, Journal of Computational Physics, 92:2 (1991), 273–295 | DOI | MR | Zbl

[13] M. Y. Nemtsev, I. S. Menshov, I. V. Semenov, “Numerical Simulation of Dynamic Processes in a Medium of Fine-Grained Solid Particles”, Math. Mod. Comp. Simul., 15:2 (2023), 210–226 | DOI | DOI | MR

[14] S. Clain, D. Rochette, “First-and second-order finite volume methods for the one-dimensional nonconservative Euler system”, J. of Comput. Phys., 228:22 (2009), 8214–8248 | DOI | MR | Zbl