ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

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, iss. 3, pp. 73-85. DOI: 10.18500/0869-6632-2019-27-3-73-85

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 138)
Language: 
Russian
Article type: 
Article
UDC: 
533:6, 533:9;519.688

Numerical simulation of oscillations of an electrically charged heterogeneous medium due to inter-component interaction

Autors: 
Tukmakov D. A., IME - Subdivision of FIC KazanSC of RAS
Abstract: 

Aim. The aim of the work is the numerical study of the oscillations of two-phase medium (a mixture of gas and a dispersed phase of solid particles) which caused by electric charge of the dispersed component, and the reciprocal effect of the dynamics of gas and solid particles, as well as the effect of linear size of dispersed particles on the dynamic processes. Methods. With the help of numerical models of electrically charged suspension was modeled in different modes of oscillatory dynamics in a dusty environment. It was assumed that electrically charged are solid particles. In the simulated process, the charge of all particles has the same sign. Dusty environment is modeled as monodisperse – all particles have the same size, it is also assumed that all particles consist of a material with the same density and heat capacity. Mathematical model assumes high-speed and temperature non-equilibrium of studied processes. The model takes into account the interphase heat transfer and interphase force interaction, which includes the Stokes force, the force of the attached masses and the dynamic force of Archimedes. The carrier medium – gas – is assumed to be viscous, compressible and heat-conducting. The system of equations is solved by an explicit second-order MacCormack finite-difference method. A scheme of nonlinear correction of the grid function is used to obtain a monotone solution. Results. Influence of the particle size of the dispersed phase on the velocity and oscillation frequency of the heterogeneous medium is revealed. The dependence between the particle size of the dispersed phase and the intensity of redistribution of the «average density» of particles of the dispersed phase is revealed, and the effect of particle size on changes in the pressure in the channel during the oscillation movements of the mixture is determined

Reference: 
  1. Nigmatulin R.I. Dynamics of Multiphase Media. Part 1. M.: Nauka, 1987. 464 p. (in Russian).
  2. Kutushev A.G. Mathematical Modeling of Wave Processes in Aero-Dispersed and Powdered Media. SPb.: Nedra, 2003, 284 p. (in Russian).
  3. Kisilev S.G., Ruev G.A., Trunev A.P., Fomin V.F., Shavaliev M.Sh. Shock-wave Processes in Two-Component and Two-Phase Media. Novosibirsk: Nauka, 1992, 261 p. (in Russian).
  4. Gelfand B.E., Gubanov A.V., Medvedev E.I., Tsyganov S.A. Shock waves during expansion of the compressed volume of a gas suspension of solid particles. Doklady Physics, Academy of Sciences of USSR, 1985, vol. 281, no. 5, pp. 1113–1116 (in Russian).
  5. Kozlov V.E., Lebedev A.B., Sekundov A.N., Yakubovskii K.Y. Simulation of turbulent homogeneous combustion using the «quasi-laminar» approach. High Temperature, 2009, vol. 47, no. 6, pp. 912–919.
  6. Ryzhkov I.I., Stepanova I.V. Group of mixture / law of vibrational mixture. Journal of Applied Mechanics and Technical Physics, 2011, vol. 52, no. 4, pp. 560–570.
  7. Zabelinskii I.E., Ibraguimova L.B., Shatalov O.P., Tunik U.V. Experimental study and numerical modeling of vibrational oxygen temperature profiles behind a strong shock wave front // Progress in Flight Physics. EUCASS book series: Advances in Aerospace Sciences. Moscow, 2011. P. 231–242.
  8. Golub V.V., Bazhenova T.V., Baklanov D.I., Ivanov K.V., Krivokorytov M.S. Using of hydrogenair mixture detonation in needle-free injection devices. High Temperature, 2013, vol. 51, no. 1, pp. 138–140.
  9. Gubaidullin D.A., Tukmakov D.A. Study of the dynamics of a two-component gas with components spatially separated at the initial moment. Problems of Energy, 2014, no. 3–4, pp. 38–43 (in Russian).
  10. Sadin D.V. TVD scheme for nonhyperbolic non-conservative type. Computational Mathematics and Mathematical Physics, 2016, vol. 56, no. 12, pp. 2068–2078.
  11. Varaksin A.Y., Protasov M.V., Yatsenko V.P. Analysis of the deposited processes of solid particles in the channel walls. High Temperature, 2013, vol. 51, no. 5, pp. 665–672.
  12. Klochkov B.N., Reiman A.M. Nonlinear models of blood supply dynamics in tissue area. Izvestiya VUZ. Applied Nonlinear Dynamics, 2010, vol. 18, no. 2, pp.131–141 (in Russian).
  13. Glazunov A.A., Dyachenko N.N., Dyachenko L.I. Solid-fuel analysis of the particles in the solid-fuel rocket engine. Thermophysics and Aeromechanics, 2013, vol. 20, no. 1, pp. 79–86.
  14. Verevkin A.A., Tsirkunov U.M. There are no two-phase hypersonic shock tunnels for the dispersed phase. Journal of Applied Mechanics and Technical Physics, 2008, vol. 49, no. 5, pp. 789–798.
  15. Nigmatulin R.I., Gubaidullin D.A., Tukmakov D.A. Shock wave dispersion of gas–particle mixtures. Doklady Physics, 2016, vol. 61, no. 2, pp. 70–73.
  16. Zhuoqing A., Jesse Z. Correlating the apparent viscosity with gas–solid suspension flow in straight pipelines // Powder Technology. 2019. Vol. 345. P. 346–351.
  17. 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 – covering statistical, nonlinear, biological, and soft matter physics. https://doi.org/10.1103/PhysRevE.96.042903
  18. 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, iss. 5, pp. 1141–1147.
  19. Zinchenko S.P., Tolmachev G.N. On the accumulation of the sputtering products of a ferroelectric target in a plasma of a glowing high-frequency discharge. Applied Physics, 2012, no. 5, pp. 53–56.
  20. Dikalyuk A.S., Surzhikov S.T. Numerical simulation of a normal glow discharge. High Temperature, 2012, vol.50, no. 5, pp. 571–578.
  21. Tadaa 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. P. 778–787.
  22. Mamun A.A., Shukla P.K., Bingham R. Plasma voids (holes) in a dusty plasma. Physics Letters A, 2002, vol. 298, no. 2–3, pp. 179–184.
  23. 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, no. 11, 113703. https://doi.org/10.1063/1.5003972.
  24. Haralson Z., Goree J. Overestimation of viscosity by the Green-Kubo method in a dusty plasma experiment. Phys. Rev. Lett., 2017, vol. 118, no. 19, 195001. https://doi.org/10.1103/PhysRevLett.118.195001. 
  25. Tukmakov A.L., Kashapov N.F., Tukmakov D.A., Fazlyyakhmatov M.G. Process of the deposition of the charged polydisperse gas suspension on the electrical field. High Temperature, July 2018, Vol. 56, iss. 4, pp. 481–485. 
  26. Tukmakov A.L., Kashapov N.F., Tukmakov D.A., Fazlyyakhmatov M.G. Numerical modeling of the powder materials spraying. IOP Conference Series: Materials Science and Engineering, 2018, vol. 412, conference 1.
  27. Salyanov F.A. Fundamentals of Low-temperature Plasma Physics, Plasma Apparatus and Technology. M.: Nauka, 1997, 240 p. (in Russian). 
  28. Fletcher C.A., Computation Techniques for Fluid Dynamics, Springer-Verlang, Berlin et al., 1988, 502 p.
  29. Muzafarov I.F., Utyuzhnikov S.V. The use of compact difference schemes for the study of unsteady compressible gas flows. Mathematical modeling, 1993, vol. 5, no. 3, pp. 74–83 (in Russian).
  30. Krylov V.I., Bobkov V.V., Monastyrny P.I. Computational Methods, T. 2, M.: Nauka, 1977, 401 p. (in Russian).
Received: 
20.03.2019
Accepted: 
23.04.2019
Published: 
20.06.2019
Short text (in English):
(downloads: 179)