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Comparison of Two Statistical Models for the Calculation of Collisions of Particles in Isotropic Turbulence

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Abstract

Two models are given for determining the collision rate of inertial particles in a homogeneous isotropic turbulence. The advantages and disadvantages of the known models of particle collisions are discussed. One of the models suggested by us is based on the assumption that the joint probability density function of gas and particle velocities is a Gaussian distribution. The second model follows from the kinetic equation for the probability density of the relative velocity of two particles. These two models are compared with each other and with the available data of direct numerical simulation.

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REFERENCES

  1. Squires, K.D. and Eaton, J.K., Phys. Fluids A, 1991, vol. 3, p. 1169.

    Google Scholar 

  2. Wang, L.-P. and Maxey, R.M., J. Fluid Mech., 1993, vol. 256, p. 27.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  6. Hogan, R.C. and Cuzzi, J.N., Phys. Fluids, 2001, vol. 13, p. 2938.

    Google Scholar 

  7. Fevrier, P., Simonin, O., and Legendre, D., Particle Dispersion and Preferential Concentration Dependence on Turbulent, Reynolds, Number from Direct and Large-Eddy Simulations of Isotropic Homogeneous Turbulence, Proc. 4th Int. Conf. on Multiphase Flow, New Orleans, 2001, p. 1.

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

    Google Scholar 

  9. Abrahamson, J., Chem. Eng. Sci., 1975, vol. 30, p. 1371.

    Google Scholar 

  10. Williams, J.J. and Crane, R.I., Int. J. Multiphase Flow, 1983, vol. 9, p. 421.

    Google Scholar 

  11. Kruis, F.E. and Kusters, K.A., J. Aerosol Sci., 1996, vol. 27, Suppl. 1, p. 263.

    Google Scholar 

  12. Yuu, S., AIChE J., 1984, vol. 30, p. 802.

    Google Scholar 

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

  14. Wang, L.-P., Wexler, A.S., and Zhou, Y., Phys. Fluids, 1998, vol. 10, p. 2647.

    Google Scholar 

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

    Google Scholar 

  16. Zhou, Y., Wexler, A.S., and Wang, L.-P., Phys. Fluids, 1998, vol. 10, p. 1206.

    Google Scholar 

  17. Lavieville, 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 

  18. Lavieville, J., Numerical Simulations and Modeling of Interactions between Turbulence Dragging and Interpar-ticle Collisions Applied to Gas-Solid Two-Phase Flows, These de Doctorat de l'Universite De Rouen, 1997.

  19. Simonin, O., Combustion and Turbulence in Two-Phase Flows: Continuum Modelling of Dispersed Two-Phase Flows. Lecture Series 1996–02, Von Karman Institute for Fluid Dynamics, Belgium, 1996.

  20. Fede, P., Simonin, O., and Villedieu, P., Monte Carlo Simulation of Colliding Particles in Gas-Solid Turbulent Flows from a Joint Fluid-Particle PDF Equation, Proc. 5th Int. Symp. on Numerical Methods for Multiphase Flows. ASME FEDSM 2002–31226, 2002.

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

  22. Derevich, I.V. and Zaichik, L.I., Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, 1988, no. 5, p. 96.

  23. Zaichik, L.I., Phys. Fluids, 1999, vol. 11, p. 1521.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  26. Monin, A.S. and Yaglom, A.M., Statisticheskaya gidrod-inamika. Ch. 2 (Statistical Hydrodynamics. Part 2), Moscow: Nauka, 1967.

    Google Scholar 

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

    Google Scholar 

  28. Yeung, P.K. and Pope, S.B., J. Fluid Mech., 1989, vol. 207, p. 531.

    Google Scholar 

  29. Vedula, P. and Yeung, P.K., Phys. Fluids, 1999, vol. 11, p. 1208.

    Google Scholar 

  30. Voth, G.A., Satyanarayan, K., and Bodenschatz, E., Phys. Fluids, 1998, vol. 10, p. 2268.

    Google Scholar 

  31. Yeung, P.K., Phys. Fluids, 1997, vol. 9, p. 2981.

    Google Scholar 

  32. Yeung, P.K., J. Fluid Mech., 2001, vol. 427, p. 241.

    Google Scholar 

  33. Alipchenkov, V.M. and Zaichik, L.I., Izv. Akad. Nauk Mekh. Zhidk. Gaza, no. 4, p. 93.

  34. Sawford, B.L. and Yeung, P.K., Phys. Fluids, 2001, vol. 13, p. 2627.

    Google Scholar 

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Authors and Affiliations

  1. Russian Academy of Sciences, IVTAN (Institute of High Temperatures) Scientific Association, Moscow, 125412, Russia

    L. I. Zaichik & V. M. Alipchenkov

  2. Institut de Mechanique des Fluides, Toulouse, 31400, France

    O. Simonin

Authors
  1. L. I. Zaichik
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  2. O. Simonin
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  3. V. M. Alipchenkov
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Zaichik, L.I., Simonin, O. & Alipchenkov, V.M. Comparison of Two Statistical Models for the Calculation of Collisions of Particles in Isotropic Turbulence. High Temperature 41, 646–656 (2003). https://doi.org/10.1023/A:1026196712361

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