Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

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

For citation:

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. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 1, pp. 90-102. DOI: 10.18500/1816-9791-2022-22-1-90-102, EDN: DJLRDK

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
Full text:
(downloads: 1805)
Article type: 

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

Tukmakov Aleksey L., Federal Research Center "Kazan Scientific Center of the Russian Academy of Sciences"
Tukmakov Dmytry A., Federal Research Center "Kazan Scientific Center of the Russian Academy of Sciences"

The work is devoted to the study of the laws governing the deposition of particles of the dispersed phase of an electrically charged dusty medium moving in a channel onto an electrode plate. The aim of the study is to reveal the influence of the size of dispersed inclusions and the density of the material of particles on the process of settling of fractions of a polydisperse gas suspension on the surface of the electrode plate. When modeling the dynamics of a gas suspension, a mathematical model of the motion of a multi-speed and multi-temperature polydisperse two-phase medium was used, taking into account the interphase force interaction and interphase heat transfer. When describing the force interaction, the Stokes force was taken into account. The mathematical model of the dynamics of a two-phase medium was supplemented with boundary conditions. The system of equations was solved by the McCormack explicit finite-difference method having the second order of accuracy. To obtain a monotonic numerical solution, a grid function correction scheme was applied. For the potential of the electric field on the lateral surfaces, the values of the potential were determined; at the open ends of the channel for the potential of the electric field, uniform Neumann boundary conditions were assumed. The paper considered gas suspension, the dispersed phase of which contains three fractions. At the same size, the gas suspension fractions differed in the material density of the particles of the fractions. At the same density of the material of particles, the fractions of the solid phase of the gas suspension had different sizes of dispersed inclusions. As a result of numerical modeling, it was revealed how the density of the material of the dispersed phase and the size of the particles affect the process of precipitation of fractions of the dispersed phase of the two-component mixture. From calculations it follows that with the same particle size, particles with a higher density of the material are deposited more intensively, and with the same density of the particle material, particles with a large linear size are deposited more intensively.

The mathematical model of the dynamics of an electrically charged aerosol in the channel was developed within the framework of the state assignment of the FRC KazanSC of RAS, calculations of the effect of the properties of the dispersed phase on the deposition of aerosol in the channel were carried out at the expense of the grant of the President of the Russian Federation No. MK-297.2020.1.
  1. Nigmatulin R. I. Osnovy mekhaniki geterogennykh sred [Fundamentals of the Mechanics of Heterogeneous Media]. Moscow, Nauka, 1978. 336 p. (in Russian).
  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, 2003. 284 p. (in Russian).
  3. Fedorov A. V., Fomin V. M., Khmel T. A. Volnovye protsessy v gazovzvesyakh chastits metallov [Wave Processes in Gas-suspension of Metal Particles]. Novosibirsk, Parallel’, 2015. 301 p. (in Russian).
  4. Tukmakov A. L. Numerical model of the electro-gas-dynamics of a gas–particle system based on the equations of motion of a two-velocity two-temperature gas–particle mixture. Journal of Applied Mechanics and Technical Physics, 2015, vol. 56, no. 4, pp. 636–643. https://doi.org/10.1134/S0021894415040112
  5. Hayakawa H., Takada S., Garzo V. Kinetic theory of shear thickening for a moderately dense gas-solid suspension: From discontinuous thickening to continuous thickening. Physical Review E, 2017, vol. 96, iss. 4, 042903. https://doi.org/10.1103/PhysRevE.96.042903
  6. Zinchenko S. P., Tolmachev G. N. Accumulation of sputtering products of a ferroelectric target in the high-frequency glow discharge plasma. Prikladnaya fizika, 2012, no. 5, pp. 53–56 (in Russian).
  7. Dikalyuk A. S., Surzhikov S. T. Numerical simulation of rarefied dusty plasma in a normal glow discharge. High Temperature, 2012, vol. 50, no. 5, pp. 571–578. https://doi.org/10.1134/S0018151X12040050
  8. Arutyunyan R. V. Simulation of the temperature and electric fields by high-current pulse to the electrode. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 138–144 (in Russian). https://doi.org/10.18500/1816-9791-2016-16-2-138-144
  9. Kosarev N. P., Makarov V. N., Ugolnikov A. V., Makarov N. V., Dyldin G. P. Mine aerology of dust aerosols under conditions of hydro-vortex coagulation. News of the Ural State Mining University, 2020, iss. 4 (60), pp. 155–165 (in Russian). https://doi.org/10. 21440/2307-2091-2020-4-155-165
  10. Kirsh A. A., Makaveev P. Yu., Kirsh V. A. Collection of metal aerosol nanoparticles at high temperature. Colloid Journal, 2020, vol. 82, no. 2, pp. 122–129. https://doi.org/10.1134/S1061933X20020052
  11. Balashov A. M. A way to increase the efficiency of electrostatic precipitators for cleaning emissions from metallurgical complex enterprises. Tendentsii razvitiya nauki i obrazovaniya [Trends in the Development of Science and Education], 2020, no. 58–5, pp. 88–91 (in Russian). https://doi.org/10.18411/lj-02-2020-108
  12. Tada Y., Yoshioka S., Takimoto A., Hayashi Y. Heat transfer enhancement in a gas–solid suspension flow by applying electric field. International Journal of Heat and Mass Transfer, 2016, vol. 93, pp. 778–787. https://doi.org/10.1016/j.ijheatmasstransfer.2015.09.063
  13. Jaiswal S., Hall T., LeBlanc S., Mukherjee R., Thomas E. Effect of magnetic field on the phase transition in a dusty plasma. Physics of Plasmas, 2017, vol. 24, iss. 11, 113703. https://doi.org/10.1063/1.5003972
  14. Shagapov V. Sh., Galimzyanov M. N., Agisheva U. O. Solitary waves in a gas-liquid bubble mixture. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2020, vol. 20, iss. 2, pp. 232–240 (in Russian). https://doi.org/10.18500/1816-9791-2020-20-2-232-240
  15. Varaksin A. Yu. Effect of particles on carrier gas flow turbulence. High Temperature, 2015, vol. 53, no. 3, pp. 423–444. https://doi.org/10.1134/S0018151X15030207
  16. Vatuzov D. N., Puring S. M. Method of selection and calculation devices air cleaning from condensed aerosols. Urban Construction and Architecture, 2016, vol. 6, no. 2 (23), pp. 14–18 (in Russian). https://doi.org/10.17673/Vestnik.2016.02.3
  17. Meshalkina M. N., Tsvetkov V. A., Popov B. I. Detection of fire situations by control of gassing and aerosol nanoparticles. Natural and Technological Risks (Physics-Mathematical and Applied Aspects), 2015, no. 2 (14), pp. 27–33 (in Russian).
  18. Kutushev A. G., Rodionov S. P. Interaction of weak shock waves with a layer of a powdered medium. Combustion, Explosion, and Shock Waves, 2000, vol. 36, no. 3, pp. 405–413.
  19. Kharitonov V. P. Dynamics of convective thermal waves in a porous continuum. Fluid Dynamics, 2013, vol. 48, pp. 283–290. https://doi.org/10.1134/S0015462813030010
  20. Mikhailenko K. I., Kuleshov V. S. Numerical modelling of inhomogeneity scale of a flow rate behind the porous barrier. Vychislitel’nye tekhnologii [Computational Technologies], 2015, vol. 20, no. 6, pp. 46–58 (in Russian).
  21. Fomin V. M., Fedorov A. V. Research in mechanics of reacting homogeneous and heterogeneous media at the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences. Combustion, Explosion, and Shock Waves, 2015, vol. 51, no. 2, pp. 223–231. https://doi.org/10.1134/S0010508215020069
  22. Moiseeva K. M., Krainov A. Yu. The influence of the coal dust composition on the propagation speed of the combustion front of the coal dust with an inhomogeneous particle distribution in the air. Computer Research and Modeling, 2018, vol. 10, no. 2, pp. 221–230 (in Russian). https://doi.org/10.20537/2076-7633-2018-10-2-221-230
  23. Krivenko I. V., Smirnova M. A. Modeling the effects of electromagnetic radiation on natural aerosols. Matematicheskaya fizika i komp’yuternoe modelirovanie [Mathematical Physics and Computer Simulation], 2019, vol. 22, no. 4, pp. 64–79 (in Russian). https://doi.org/10.15688/mpcm.jvolsu.2019.4.5
  24. Dmitrieva O. S., Madyshev I. N., Dmitriev A. V. Determination of the heat and mass transfer efficiency at the contact stage of a jet-film facility. Journal of Engineering Physics and Thermophysics, 2017, vol. 90, no. 3, pp. 651–656. https://doi.org/10.1007/ s10891-017-1612-z
  25. 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 Temperature, 2017, vol. 55, no. 4, pp. 491–495. https://doi.org/10.1134/S0018151X17030221
  26. Tukmakov A. L., Tukmakov D. A. Generation of Acoustic Disturbances by a Moving Charged Gas Suspension. Journal of Engineering Physics and Thermophysics, 2018, vol. 91, no. 5, pp. 1141–1147. https://doi.org/10.1007/s10891-018-1842-8
  27. Tukmakov A. L., Tukmakov D. A., Kashapov N. F., Fazlyyyakhmatov M. G. Process of the Deposition of Charged Polydisperse Gas Suspension on the Plate Surface in an Electrical Field. High Temperature, 2018, vol. 56, no. 4, pp. 481–485. https://doi.org/10.1134/S0018151X18040193
  28. Tukmakov D. A. Numerical simulation of oscillations of an electrically charged heterogeneous medium due to inter-component interaction. Izvestiya VUZ. Applied Nonlinear Dynamics, 2019, vol. 27, no. 3, pp. 73–85 (in Russian). https://doi.org/10. 18500/0869-6632-2019-27-3-73-85
  29. Tukmakov D. A. Numerical investigation of the influence of properties of the gas component of a suspension of solid particles on the spreading of a compressed gas-suspension volume in a binary medium. Journal of Engineering Physics and Thermophysics, 2020, vol. 93, no. 2, pp. 291–297. https://doi.org/10.1007/s10891-020-02120-9
  30. Salyanov F. A. Osnovy fiziki nizkotemperaturnoy plazmy, plazmennykh apparatov i tekhnologij [Fundamentals of Low-Temperature Plasma Physics, Plasma Devices and Technologies]. Moscow, Nauka, 1997. 240 p. (in Russian).
  31. Fletcher C. A. Computation Techniques for Fluid Dynamics. Berlin etc., Springer-Verlang, 1988. 502 p.
  32. Tukmakov A. L. Numerical simulation of the process of wave separation of solid particles in resonance gas vibrations in the closed pipe. Acoustical Physics, 2009, vol. 55, no. 3, pp. 345–352. https://doi.org/10.1134/S1063771009030099
  33. Muzafarov I. F., Utyuzhnikov S. V. Application of compact difference schemes to the study of unsteady flows of a compressible gas. Matematicheskoe modelirovanie, 1993, vol. 5, no. 3, pp. 74–83 (in Russian).
  34. Krylov V. I., Bobkov V. V., Monastyrnyi P. I. Vychislitel’nye metody [Computational Methods: in 2 vols.]. Moscow, Nauka, 1977. Vol. 2. 401 p. (in Russian).