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Numerical simulation of oscillations of a monodisperse gas-particle mixture in a nonlinear wave field

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Abstract

This paper presents a numerical simulation procedure for the dynamics of a monodisperse gas-particle mixture in the nonlinear wave field of an acoustic resonator using a two-temperature two-velocity model ignoring phase transitions, particle collision, and possible coagulation. It is assumed that viscosity is present only in the carrier medium described by the Navier-Stokes equations for a compressible gas. The dispersed phase is described by the equation of conservation of mass, momentum, and energy. A monotonic solution is obtained by solving the equations of motion for the carrier medium and dispersed phase in generalized moving coordinates using the explicit McCormack method with splitting in the spatial directions and a conservative correction scheme. The method can be used to study nonlinear oscillations of two-phase mixtures in the vicinity of the first three eigenfrequencies in a flat channel.

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References

  1. E. P. Mednikov, Acoustic Coagulation and Precipitation of Aerosols [in Russian], Izd. Akad. Nauk USSR, Moscow (1963).

    Google Scholar 

  2. L. K. Zarembo and V. I. Timoshenko, Nonlinear Acoustics [in Russian], Izd. Mosk. Univ., Moscow (1984).

    Google Scholar 

  3. Kh. A. Rakhmatulin, “Fundamentals of gas dynamics of interpenetrating motions of compressible media,” Prikl. Mat. Mekh., 20, No. 2, 184–195 (1956).

    Google Scholar 

  4. A. G. Kutushev, Mathematical Modeling of Wave Processes in Aerodisperse and Powder Media [in Russian], Nedra, St. Petersburg (2003).

    Google Scholar 

  5. A. I. Ivandaev, A. G. Kutushev, and R. I. Nigmatulin, Gas Dynamics of Multiphase Media. Shock and Detonation Waves in Gas-Particle Mixtures [in Russian], VINITI, Moscow (1981), pp. 209–287. (Itogi Nauki Tekhniki, Ser. Mekh. Zhidk., Vol. 16.)

    Google Scholar 

  6. E. L. Sternin, Two-Phase Monodiperse and Polydisperse Gas Flows with Particles [in Russian], Mashinostroenie, Moscow (1980).

    Google Scholar 

  7. C. A. J. Fletcher, Computational Techniques for Fluid Dynamics, Springer-Verlag, Berlin-Heidelberg-New York (1991).

    Book  MATH  Google Scholar 

  8. J. L. Steger, “Implicit finite-difference simulation of flow about arbitrary two-dimensional geometries,” AIAA J., 16, No. 7, 679–686 (1978).

    Article  ADS  MATH  Google Scholar 

  9. A. L. Tukmakov, “Numerical simulation of the wave separation of solid particles in resonance oscillations of a gas in a closed tube,” Akust. Zh., 55, No. 3, 342–349 (2009).

    Google Scholar 

  10. A. I. Zhmakin and A. A. Fursenko, “On a monotonic difference scheme of through calculation,” Zh. Vychisl. Mat. Mat. Fiz., 20, No. 4, 1021–1031 (1980).

    MathSciNet  Google Scholar 

  11. M. A. Ilgamov, R. G. Zaripov, R. G. Galiullin, and V. B. Repin, “Nonlinear oscillations of a gas in a tube,” Appl. Mech. Rev., 49, No. 3, 137–154 (1996).

    Article  ADS  Google Scholar 

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Correspondence to A. L. Tukmakov.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 2, pp. 36–43, March–April, 2011.

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Tukmakov, A.L. Numerical simulation of oscillations of a monodisperse gas-particle mixture in a nonlinear wave field. J Appl Mech Tech Phy 52, 186–192 (2011). https://doi.org/10.1134/S0021894411020040

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  • DOI: https://doi.org/10.1134/S0021894411020040

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