Comparison of Numerical Models of the Dynamics of Electrically Charged Gas Suspensions with Mass and Surface Charge Densities for Different Particles Dispersities

Abstract

The purpose of the study was to mathematically model the dynamics of inhomogeneous electrically charged media, such as that of gas suspensions, i.e., solid particles suspended in a gas. The mathematical model implemented a continuum approach to modeling the dynamics of inhomogeneous media, which implies taking into account intercomponent heat transfer and momentum exchange. The carrier medium was described as a viscous, compressible, heat-conducting gas, the equations of the model were supplemented with initial and boundary conditions, and the system of the equations was integrated by an explicit finite-difference method. To obtain a monotonic grid function, a nonlinear scheme for correcting the numerical solution was used. The mathematical model was supplemented with the Poisson equation describing the electric field, which is formed by electrically charged disperse inclusions. The Poisson equation was integrated by finite-difference methods on a gas-dynamic grid. The flow of a gas suspension caused by the motion of dispersed particles under the action of the Coulomb force was studied numerically. Flows of gas suspensions with surface and mass densities of electric charge were modeled. For the surface charge density model, the Coulomb force acting on the unit mass of the gas suspension increases with a decrease in the dispersion of particles. For the mass charge density, the dispersion of particles does not affect the specific Coulomb force acting on the particles. The intensity of the gas suspension flow increases with decreasing particle size, both for the mass and surface models of charge density. For the surface charge density model, as the particle size decreases, the intensity of the gas pressure drop in the emerging gas suspension flow increases more than when modeling the gas suspension dynamics with
a mass distribution of the electric charge density

The work was carried out within the framework of the state task of the Kazan Scientific Center of Russian Academy of Sciences

Please cite this article in English as:
Tukmakov D.A. Comparison of numerical models of the dynamics of electrically charged gas suspensions with mass and surface charge densities for different particles dispersities. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2022, no. 3 (102), pp. 43--56 (in Russ.). DOI: https://doi.org/10.18698/1812-3368-2022-3-43-56

References

[1] Nigmatulin R.I. Osnovy mekhaniki geterogennykh sred [Foundations of heterogeneous media mechanics]. Moscow, Nauka Publ., 1978.

[2] Kutushev A.G. Matematicheskoe modelirovanie volnovykh protsessov v aerodispersnykh i poroshkoobraznykh sredakh [Mathematical modeling of wave processes in aerodispersed and powdery media]. St. Petersburg, Nedra Publ., 2003.

[3] Fedorov A.V., Fomin V.M., Khmel T.A. Volnovye protsessy v gazovzvesyakh chastits metallov [Wave processes in gas suspensions of metal particles]. Novosibirsk, Parallel Publ., 2015.

[4] Semenov V.P., Timofeev A.V. Parametric resonance and energy transfer in dusty plasma. Matem. modelirovanie, 2018, vol. 30, no. 2, pp. 3--17 (in Russ.).

[5] Dikalyuk A.S., Kuratov S.E. Numerical modeling of plasma devices by the Particle-In-Cell method on unstructured grids. Math. Models Comput. Simul., 2018, vol. 10, no. 2, pp. 198--208. DOI: https://doi.org/10.1134/S2070048218020059

[6] Tadaa Y., Yoshioka S., Takimoto A., et al. Heat transfer enhancement in a gas--solid suspension flow by applying electric field. Int. J. Heat Mass Transf., 2016, vol. 93, pp. 778--787. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.063

[7] Losseva T.V., Popel’ S.I., Golub’ A.P. Dust ion-acoustic shock waves in laboratory, ionospheric, and astrophysical plasmas. Plasma Phys. Rep., 2020, vol. 46, no. 11, pp. 1089--1107. DOI: https://doi.org/10.1134/S1063780X20110045

[8] Pikalev A.A., Sysun A.V., Oleshchuk O.V. The radial distribution of plasma concentration in a positive column of glow discharge with dust particle. Izvestiya vuzov. Fizika, 2020, vol. 63, no. 7, pp. 162--170 (in Russ.). DOI: https://doi.org/10.17223/00213411/63/7/162

[9] Bastykova N.Kh., Golyatina R.I., Kodanova S.K., et al. Investigation of the evolution of Be, Ni, Mo and W dust particles in fusion plasma. Prikladnaya fizika [Applied Physics], 2020, no. 3, pp. 21--26 (in Russ.).

[10] Timofeev A.V., Nikolaev V.S., Semenov V.P. Inhomogeneity of structural and dynamical characteristics of dusty plasma in a gas discharge. J. Exp. Theor. Phys., 2020, vol. 130, no. 1, pp. 153--160. DOI: https://doi.org/10.1134/S1063776119120203

[11] Kolotinskiy D.A., Nikolaev V.S., Timofeev A.V. Influence of structural inhomogeneity and nonreciprocal effects in the interaction of macroparticles on the dynamic properties of a dusty plasma monolayer. Pis’ma v ZhETF, 2021, vol. 113, no. 7-8, pp. 514--522 (in Russ.).

[12] Paul A., Mandal G., Amin M.R., et al. Analysis of solution of damped modified-KdV equation on dust-ion-acoustic wave in presence of superthermal electrons. Plasma Phys. Rep., 2020, vol. 46, no. 1, pp. 83--89. https://doi.org/10.1134/S1063780X20010158

[13] Chekalov L.V., Guzaev V.A., Smirnov M.E. Enhancement the efficiency of electrostatic precipitators of thermal power plants by improving the electrodes volume. Elektricheskie stantsii, 2021, no. 7, pp. 48--54 (in Russ.). DOI: http://dx.doi.org/10.34831/EP.2021.1080.7.008

[14] Tukmakov A.L., Tukmakov D.A. Dynamics of a charged gas suspension with an initial spatially nonuniform distribution of the average dispersed phase density during the transition to the equilibrium state. High Temp., 2017, vol. 55, no. 4, pp. 491--495. DOI: https://doi.org/10.1134/S0018151X17030221

[15] Tukmakov A.L., Tukmakov D.A. Generation of acoustic disturbances by a moving charged gas suspension. J. Eng. Phys. Thermophy., 2018, vol. 91, no. 5, pp. 1141--1147. DOI: https://doi.org/10.1007/s10891-018-1842-8

[16] Tukmakov D.A., Akhunov A.A. Numerical study of the influence of the electric charge of a dispersed phase on the propagation of a shock wave from homogeneous gas to a dusty medium. Izv. Sarat. un-ta. Nov. ser. Ser. Fizika [Izvestiya of Saratov University. New Series. Series: Physics], 2020, vol. 20, no. 3, pp. 183--192 (in Russ.). DOI: https://doi.org/10.18500/1817-3020-2020-20-3-183-192

[17] Tukmakov D.A., Akhunov A.A. Numerical study of the propagation of a small shock wave intensity from a homogeneous gas to an electrically charged dusty environment. Chebyshevckiy sbornik, 2020, vol. 21, no. 4, pp. 257--269 (in Russ.). DOI: https://doi.org/10.22405/2226-8383-2020-21-4-257-269

[18] Tukmakov D.A. Numerical study of the influence of dispersed phase parameters on the gas flow generation formed by gravitational deposition of aerosol. Computational Continuum Mechanics, 2020, vol. 13, no. 3, pp. 279--287 (in Russ.). DOI: https://doi.org/10.7242/1999-6691/2020.13.3.22

[19] Salyanov F.A. Osnovy fiziki nizkotemperaturnoy plazmy, plazmennykh apparatov i tekhnologiy [Fundamentals of physics of low-temperature plasma, plasma devices and technologies]. Moscow, Nauka Publ., 1997.

[20] Landau L.D., Lifshits E.M. Elektrodinamika sploshnykh sred [Electrodynamics of continuous media]. Moscow, Nauka Publ., 1982.

[21] Fletcher C.A. Computation techniques for fluid dynamics 1. Fundamental and general techniques. In: Scientific Computation. Berlin, Heidelberg, Springer, 1998. DOI: https://doi.org/10.1007/978-3-642-58229-5

[22] Tukmakov A.L. Numerical simulation of acoustic flows at resonance gas oscillations in a closed tube. Aviatsionnaya tekhnika, 2006, no. 4, pp. 33--36 (in Russ.).

[23] Muzafarov I.F., Utyuzhnikov S.V. Application of compact difference schemes to investigation of unstationary gas flows. Matem. modelirovanie, 1993, vol. 5, no. 3, pp. 74--83 (in Russ.).

[24] Krylov V.I., Bobkov V.V., Monastyrnyy P.I. Vychislitel’nye metody. T. 2 [Computational methods. Vol. 2]. Moscow, Nauka Publ., 1977.