Kinetic model of a collisional admixture in dusty gas and its application to calculating flow past bodies


Using the methods of statistical physics, the basic kinetic equation describing the dynamics of a polydisperse admixture of solid particles in a dilute dusty-gas flow is derived. Particle rotation, inelastic collisions, and interaction with the carrier gas are taken into account. The basic kinetic equation is used to obtain a Boltzmann-type equation for the one-particle distribution function, for which the boundary conditions for the problem of dusty-gas flow past a body are formulated. On the basis of the kinetic model developed, using direct statistical modeling, the flow patterns and the fields of the dispersed-phase macroparameters in a uniform crosswise dusty-gas flow past a cylinder are obtained for various free-stream particle sizes and concentrations.

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  1. 1.

    Yu. M. Tsirkunov, “Admixture flow modeling in problems of two-phase aerodynamics,”Modeling in Mechanics,7, No. 2, ITPM SO RAS, Novosibirsk (1993), p. 151–193.

    Google Scholar 

  2. 2.

    S. K. Matveev, “Mathematical description of a gas-particle flow past bodies with account for the reflected particle effect,” In:Motion of a Compressible Fluid and Non-Homogeneous Media [in Russian], Izd. LGU, Leningrad (1982), p. 189–201.

    Google Scholar 

  3. 3.

    A. Kitron, T. Elpirin, and A. Tamir, “Monte-Carlo analysis of wall erosion and direct contact heat transfer by impinging two-phase jet,”J. Thermophys. Heat Transfer,3, No. 2, 112 (1989).

    ADS  Article  Google Scholar 

  4. 4.

    V. A. Tsibarov,Kinetic Method in Gas-Particle Mixture Theory [in Russian], Izd. S-Pb University, Sankt-Peterburg (1997).

    Google Scholar 

  5. 5.

    S. K. Matveev, “Model of a particle gas with account for inelastic collisions,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 12 (1983).

  6. 6.

    Yu. E. Gorbachev and V. Yu. Kruglov, “Calculation of the parameters of a two-phase mixture flow past a sphere with account for interparticle collisions,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 93 (1989).

    Google Scholar 

  7. 7.

    A. Volkov and Yu. Tsirkunov, “Direct simulation Monte-Carlo modeling of two-phase gas-solid particle flows with inelastic particle-particle collisions,” In:Proc. 3d ECCOMAS Computational Fluid Dyn. Conf. Paris, 1996, Wiley, Urichester (1996), p. 662–668.

    Google Scholar 

  8. 8.

    R. I. Nigmatulin,Fundamentals of the Mechanics of Heterogeneous Media [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  9. 9.

    J. Happel and H. Brenner,Low Reynolds Number Hydrodynamics, Prentice-Hall, Englewood Ceiffs (1965).

    Google Scholar 

  10. 10.

    E. Yokuda and C. T. Crowe, “Effect of Reynolds number and spacing on the dispersion of particles in self-induced turbulence,” In:Turbulence Modification in Multiphase Flows,110, ASME, New York (1991), p. 7–13.

    Google Scholar 

  11. 11.

    V. P. Myasnikov, “Statistical model of the mechanical behavior of disperse systems,” In:Mechanics of Multicomponent Media in Engineering Processes [in Russian], Nauka, Moscow (1978), p. 70–101.

    Google Scholar 

  12. 12.

    Yu. L. Klimontovich, “Dissipative equations for multi-particle distribution functions,”Uspekhi Fiz. Nauk,139, No. 4, 689 (1983).

    Google Scholar 

  13. 13.

    V. Ya. Rudyak, “Basic kinetic equation of a rarefied gas,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 154 (1989).

  14. 14.

    J. E. McCune, G. Sandri, and E. A. Frieman, “A new approach to nonequilibrium statistical mechanics of gases,” In:Rarefied Gas Dynamics, V.1, Acad. Press, New York (1963).

    Google Scholar 

  15. 15.

    I. M. Vasenin, V. A. Arkhipov, V. G. Butov, et al.,Gasdynamics of Two-Phase Nozzle Flows [in Russian], Izd. Tomsk Univ., Tomsk (1986).

    Google Scholar 

  16. 16.

    M. N. Kogan,Rarefied Gas Dynamics [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  17. 17.

    G. L. Babukha and A. A. Shraiber,Interaction of Polydisperse Particles in Two-Phase Flows [in Russian], Naukova Dumka, Kiev (1972).

    Google Scholar 

  18. 18.

    V. A. Lashkov, “On the experimental determination of particle velocity restitution coefficients for surface impact in a gas-particle flow,”Inzh. Fiz. Zh.,60, No. 2, 197 (1991).

    Google Scholar 

  19. 19.

    Yu. M. Tsirkunov, S. V. Panfilov, and M. B. Klychnikov, “Semi-empirical model of impact interaction between a dispersed particle and a surface in gas-particle flow,”Inzh. Fiz. Zh.,67, No. 5–6, 379 (1994).

    Google Scholar 

  20. 20.

    S. A. Morsi and A. J. Alexander, “An investigation of particle trajectories in two-phase flow systems,”J. Fluid Mech.,55, Pt. 2, 193 (1972).

    MATH  Article  ADS  Google Scholar 

  21. 21.

    S. I. Rubinow and J. B. Keller, “The transverse force on a spinning sphere moving in viscous fluid,”J. Fluid Mech.,11, Pt. 3, 447 (1961).

    MATH  Article  ADS  MathSciNet  Google Scholar 

  22. 22.

    V. A. Naumov, A. D. Solomenko, and V. P. Yatsenko, “Influence of the Magnus force on the motion of a rigid spherical body at high angular velocity,”Inzh. Fiz. Zh.,65, No. 3, 287 (1993).

    Google Scholar 

  23. 23.

    S. C. R. Dennis, S. N. Singh, and D. B. Ingham, “The steady flow due to a rotating sphere at low and moderate Reynolds numbers,”J. Fluid. Mech.,101, Pt. 2, 257 (1980).

    MATH  Article  ADS  Google Scholar 

  24. 24.

    L. E. Sternin, B. N. Maslov, A. A. Shraiber, and A. A. Podvysotskii,Two-Phase Mono- and Poly-Disperse Gas-Particle Flows [in Russian], Mashinostroenie, Moscow (1980).

    Google Scholar 

  25. 25.

    G. A. Bird,Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford (1994).

    Google Scholar 

  26. 26.

    M. S. Ivanov and S. V. Rogazinskii, “Comparative analysis of algorithms of the direct statistical modeling method in rarefied- gas dynamics,”Zh. Vych. Mat. Mekh.,28, No. 7, 1058 (1988).

    MathSciNet  Google Scholar 

  27. 27.

    M. S. Ivanov and S. V. Rogazinskii,Efficient Schemes for Statistical Modeling of Spatially Nonuniform Rarefied-Gas Flows [in Russian], Preprint No. 29-88, ITPM, Novosibirsk (1988).

    Google Scholar 

  28. 28.

    Yu. M. Tsirkunov, A. N. Volkov, and S. V. Panfilov, “Motion of solid admixture particles and surface erosion in a dilute gas-particle flow past bodies,” In:Proc. 13-th Session Intern. School on Models in Continuum Mech. St. Petersburg, 1995 [in Russian], Izd. SPb. Univ., St. Petersburg (1996), p. 109–116.

    Google Scholar 

  29. 29.

    A. N. Osiptsov and E. G. Shapiro, “Dusty-gas flow past a sphere at high supersonic velocity,” In:Investigation of Gasdynamics and Heat Transfer in Complex Homogeneous and Multiphase Flows [in Russian], Izd. MSU, Moscow (1990), p. 89–105.

    Google Scholar 

  30. 30.

    A. N. Kraiko and S. M. Sulaimanova, “Two-fluid flows of gas-particle mixtures with “sheets” and “filaments” formed in the flow past impenetrable surfaces,”Prikl. Mat. Mekh. 47, No. 4, 619 (1983).

    Google Scholar 

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Additional information

Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 81–97, May–June, 2000.

The work received financial support from the Russian Foundation for Basic Research (projects 96-01-01467 and 99-01-00674).

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Volkov, A.N., Tsirkunov, Y.M. Kinetic model of a collisional admixture in dusty gas and its application to calculating flow past bodies. Fluid Dyn 35, 380–392 (2000).

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  • Knudsen Number
  • Particle Volume Fraction
  • Cylinder Surface
  • Restitution Coefficient
  • Magnus Force