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Modeling the hydrodynamics of a spouting layer


We have developed a multizone hydrodynamic model of a conic spouting layer, consisting of averaged differential mass, momentum and angular momentum equations and accounting for the radial flow of the dispersed phase. We have obtained a numerical solution of the system of equations for the case in which the layer is divided into two zones, which is consistent with experimental data.

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equivalent diameter of the particles, m


diameter of the inlet opening of the device, m


cross-sectional area of the layer, m2

ffr :

coefficient taking into account the force of particle friction against the device wall and the viscous force of the particles, ffr=2.4–2.6 was taken


acceleration by gravity, m/sec2


initial height of the layer, m


mass flow rate of the gas, kg/sec


gas pressure, Pa

P0 :

gas pressure on the device axis, Pa

r, ϕ:

coordinates of the spherical system

v, w:

velocities of the gas and dispersed phases, m/sec


angle of taper of the device, deg


coefficient equal to κ=1–2.2


layer porosity

μr :

dynamic viscosity of the gas, Pa sec

ρr, ρM :

gas and particle pressure, kg/m3


zone number

1≤i≤n, r, ϕ:

projection on the coordinate axis


zone number pertaining to the boundary of the spout core


value at the point of entry into the layer

−, +:

values at the inner and outer boundaries of the zone, respectively


average over the cross section

1, 2:

values corresponding to the spout core and the peripheral zone

Literature Cited

  1. 1.

    K. Matur and N. Epstein, Spouting Layer [Russian translation], Leningrad (1978).

  2. 2.

    P. G. Romankov and N. B. Rashkovskaya, Drying in Suspension [in Russian], 3rd edition, Leningrad (1979).

  3. 3.

    V. F. Frolov, Modeling of Drying of Dispersed Materials [in Russian], Leningrad (1987).

  4. 4.

    A. E. Gorshtein, “Scientific principles of improving the technology of ultramarine and other inorganic substances using a spouting layer,” Engineering Sciences Doctor Dissertation, Leningrad (1983).

  5. 5.

    U. Mann and E. J. Crosby, Ind. Chem. PDD.,11, 314–318 (1972).

  6. 6.

    V. E. Babenko, A. A. Oigenblik, and É. M. Zhiganova, Teor. Osn. Khim. Tekhnol.,11, No. 5, 728–735 (1975).

  7. 7.

    V. V. Shectopalov, V. V. Men'shikov and V. V. Kafarov, Khim. Neft. Mashinostr., No. 6, 14–15 (1978).

  8. 8.

    V. V. Kafarov, I. N. Dorokhov, and É. M. Kol'tsova, Systematic Analysis of the Processes of Chemical Engineering [in Russian], Moscow (1988).

  9. 9.

    V. V. Kafarov, I. N. Dorokhov, É. M. Kol'tsova, and N. V. Men'shutina, Teor. Osn. Khim. Tekhnol.,20, No. 1, 44–50 (1986).

  10. 10.

    L. M. Galieva and Yu. P. Gupalo, Teor. Osn. Khim. Tekhnol.,23, 449–454 (1989).

  11. 11.

    Yu. V. Vasil'yev and V. F. Frolov, Zh. Prikl. Khim.,57, No. 2, 314–319 (1984).

  12. 12.

    V. E. Kutsakova, L. I. Logimov, and S. F. Demidov, Zh. Prikl. Khim.,11, No. 11, 2519–2524 (1979).

  13. 13.

    R. I. Nigmatulin, Dynamics of Multiphase Media [in Russian], Part 1, Moscow (1987).

  14. 14.

    M. É. Aérov and O. M. Todes, Hydraulic and Thermal Bases of Operation of Devices with Stationary and Boiling Granular Layer [in Russian], Leningrad (1968).

  15. 15.

    V. D. Mikhailik, N. V. Antonishin, et al., Izv. AN BSSR, Ser. Fiz.-Tékh. Navuk, No. 3, 81–86 (1967).

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Additional information

Academic Scientific Complex “A. V. Lyukov Heat and Mass Transfer Institute, Belorussian Academy of Sciences, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 350–356, March, 1993

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Akulich, P.V., Kuts, P.S. & Akulich, A.V. Modeling the hydrodynamics of a spouting layer. J Eng Phys Thermophys 64, 284–289 (1993).

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  • Experimental Data
  • Statistical Physic
  • Angular Momentum
  • Disperse Phase
  • Momentum Equation