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A statistical model for the calculation of the frequency of turbulent collisions of particles of arbitrary density

  • Heat and Mass Transfer and Physical Gasdynamics
  • Published:
High Temperature Aims and scope

Abstract

A statistical model is given for determining the kernel of collisions of inertial particles (droplets, bubbles) in the entire range of variation of the density ratio between the dispersed and continuous phases. The model is based on the assumption that the joint probability density function of velocities of continuous medium and particles is a Gaussian distribution. The ranges of variation of bubble sizes are determined, in which the decisive part is played by the “inertial” and “spatial” collision mechanisms.

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References

  1. Saffman, P.G. and Turner, J.S., J. Fluid Mech., 1956, vol. 1, part 1, p. 16.

    Article  MATH  ADS  Google Scholar 

  2. Abrahamson, J., Chem. Eng. Sci., 1975, vol. 30, no. 11, p. 1371.

    Article  Google Scholar 

  3. Williams, J.J. and Crane, R.I., Int. J. Multiphase Flow, 1983, vol. 9, no. 4, p. 421.

    Article  MATH  Google Scholar 

  4. Derevich, I.V., Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 1996, no. 2, p. 104.

  5. Alipchenkov, V.M. and Zaichik, L.I., Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2001, no. 3, p. 93.

  6. Wang, L.-P., Wexler, A.S., and Zhou, Y., J. Fluid Mech., 2000, vol. 415, p. 117.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Zaichik, L.I., Simonin, O., and Alipchenkov, V.M., Teplofiz. Vys. Temp., 2003, vol. 41, no. 5, p. 734 (High Temp. (Engl. transl.), vol. 41, no. 5, p. 646).

    Google Scholar 

  8. Zaichik, L.I., Simonin, O., and Alipchenkov, V.M., Phys. Fluids, 2003, vol. 15, no. 10, p. 2995.

    Article  MathSciNet  ADS  Google Scholar 

  9. Zaichik, L.I., Simonin, O., and Alipchenkov, V.M., Teplofiz. Vys. Temp., 2005, vol. 43, no. 3, p. 408 (High Temp. (Engl. transl.), vol. 43, no. 3, p. 404).

    Google Scholar 

  10. Coulaloglu, C.A. and Tavlarides, L.L., Chem. Eng. Sci., 1977, vol. 32, no. 3, p. 1289.

    Article  Google Scholar 

  11. Prince, M.J. and Blanch, H.W., AIChE J., 1990, vol. 36, no.10, p. 1485.

    Article  Google Scholar 

  12. Tsouris, C. and Tavlarides, L.L., AIChE J., 1994, vol. 40, no.3, p. 395.

    Article  Google Scholar 

  13. Colin, C., Kamp, A.M., and Chesters, A.K., Measurements and Prediction of Bubble Coalescence in Turbulent Pipe Flow, Proc. 3rd Int. Conf. on Multiphase Flow, Lyon, 1998, p. 1.

  14. Kamp, A.M., Chesters, A.K., Colin, C., and Fabre, J., Proc. Int. J. Multiphase Flow, 2001, vol. 27, p. 1363.

    Article  Google Scholar 

  15. Reade, W.C. and Collins, L.R., Phys. Fluids, 2000, vol. 12, p. 2530.

    Article  ADS  Google Scholar 

  16. Alipchenkov, V.M. and Zaichik, L.I., Izv. Ross. Akad. Nauk Mekh. Zhidk. Gaza, 2003, no. 3, p. 91.

  17. Zaichik, L.I. and Alipchenkov, V.M., Phys. Fluids, 2003, vol. 15, no. 6, p. 1776.

    Article  MathSciNet  ADS  Google Scholar 

  18. Laviéville, J., Deutsch, E., and Simonin, O., Large Eddy Simulation of Interactions between Colliding Particles and a Homogeneous Isotropic Turbulence Field, Proc. 6th Int. Symp. on Gas-Particle Flows. ASME FED, 1995, vol. 228, p. 347.

    Google Scholar 

  19. Laviéville, J., Numerical Simulations and Modeling of Interactions between Turbulence Dragging and Interparticle Collisions Applied to Gas-Solid Two-Phase Flows, Thèse de Doctorat de l’Université de Rouen, 1997.

  20. Reeks, M.W., J. Fluid Mech., 1977, vol. 83, p. 529.

    Article  MATH  ADS  Google Scholar 

  21. Wang, L.-P. and Stock, D.E., J. Atmos. Sci., 1993, vol. 50, p. 1897.

    Article  ADS  Google Scholar 

  22. Sawford, B.L., Phys. Fluids A, 1991, vol. 3, p. 1577.

    Article  ADS  Google Scholar 

  23. Hinze, J.O., Turbulence, New York: McGraw-Hill, 1975.

    MATH  Google Scholar 

  24. Monin, A.S. and Yaglom, A.M., Statisticheskaya gidrodinami ka. Ch. 2 (Statistical Hydrodynamics. Part 2), Moscow: Nauka, 1967.

    Google Scholar 

  25. Sreenivasan, K.R., Phys. Fluids, 1995, vol. 7, no. 11, p. 2778.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Sundaram, S. and Collins, L.R., J. Fluid Mech., 1997, vol. 335, p. 75.

    Article  MATH  ADS  Google Scholar 

  27. Zhou, Y, Wexler, A.S., and Wang, L.-P., Phys. Fluids, 1998, vol. 10, no. 5, p. 1206.

    Article  ADS  Google Scholar 

  28. Chen, M., Kontomaris, K., and McLaughlin, J.B., Int. J. Multiphase Flow, 1998, vol. 24, no. 7, p. 1105.

    Article  Google Scholar 

  29. Zhou, Y, Wexler, A.S., and Wang, L.-P., J. Fluid Mech., 2001, vol. 433, p. 77.

    MATH  ADS  Google Scholar 

  30. Labuntsov, D.A. and Yagov, V.V., Mekhanika dvukhfaznykh system (Mechanics of Two-Phase Systems), Moscow: Izd. MEI (Moscow Inst. of Power Engineering), 2000.

    Google Scholar 

  31. Borgas, M.S. and Yeung, P.K., J. Fluid Mech., 2004, vol. 503, p. 125.

    Article  MATH  ADS  Google Scholar 

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Translated from Teplofizika Vysokikh Temperatur, Vol. 44, No. 5, 2006, pp. 717–725.

Original Russian Text Copyright © 2006 by L. I. Zaichik and V. M. Alipchenkov.

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Zaichik, L.I., Alipchenkov, V.M. A statistical model for the calculation of the frequency of turbulent collisions of particles of arbitrary density. High Temp 44, 711–719 (2006). https://doi.org/10.1007/s10740-006-0086-z

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  • DOI: https://doi.org/10.1007/s10740-006-0086-z

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