Fluid Dynamics

, Volume 31, Issue 2, pp 249–260 | Cite as

Particle collisions in a turbulent flow

  • I. V. Derevich
Article

Abstract

An equation for the two-point probability density function of the two-particle the coordinate and velocity distribution is obtained. A closed system of equations for the first and second two-point moments of the velocity fluctuations of a pair of particles with allowance for the turbulent flow inhomogeneity is given. Boundary conditions for the equations of the particle concentration and the intensity of the relative random velocity during particle collision are obtained. A unified formula describing the interparticle collision process as a result of turbulent motion and the average relative particle velocity slip is obtained for the kernel of the coagulation equation. The effect of the average velocity slip of the particles and the carrier phase on the parameters of motion of the dispersed admixture and its coagulation is investigated on the basis of a two-point two-time velocity fluctuation autocorrelation function with two time and space scales representing the energy-bearing and small-scale motion of the fluid phase.

Keywords

Probability Density Function Velocity Fluctuation Velocity Slip Carrier Phase Turbulent Motion 

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References

  1. 1.
    E. Ya. Lapiga and V. I. Loginov, “The kernels of the kinetic coalescence equation,”Izv. Akad. Nauk SSSR, Mekh. Zhidk, Gaza, No. 2, 32 (1980).Google Scholar
  2. 2.
    É. G. Sinaiskii, “Droplet coagulation in a turbulent viscous fluid flow,”Kolloid. Zh.,55, No. 4, 91 (1993).Google Scholar
  3. 3.
    S. Kumar, R. Kumar, and K. S. Gandhi, “A new model for coalescence efficiency of drops in stirred dispersions,”Chem. Eng. Sci.,48, 2025 (1993).CrossRefGoogle Scholar
  4. 4.
    P. G. Saffman and J. S. Turner, “On the collision of drops in turbulent clouds,”J. Fluid Mech.,1, 16 (1956).Google Scholar
  5. 5.
    M. A. Delichatsios and R. F. Probstein, “Coagulation in turbulent flow: Theory and experiment,”J. Colloid Interface Sci.,51, 394 (1975).CrossRefGoogle Scholar
  6. 6.
    M. M. R. Williams, “A unified theory of aerosol coagulation,”J. Phys. D: Appl. Phys.,21, 875 (1988).CrossRefGoogle Scholar
  7. 7.
    A. L. Dushkin, “Turbulent condensate droplet coagulation in a cylindrical channel,”Teplofyz. Vysok. Temp.,27, 335 (1989).Google Scholar
  8. 8.
    P. W. Rambo and J. Denavit, “Time-implicit fluid simulation of collisional plasma,”J. Computat. Phys.,98, 317 (1992).CrossRefGoogle Scholar
  9. 9.
    J. Abrahamson, “Collision rates of small particles in a vigorously turbulent fluid,”Chem. Eng. Sci.,30, 1371 (1975).CrossRefGoogle Scholar
  10. 10.
    S. Yuu, “Collision rate of small particles in a homogeneous and isotropic turbulence,”AIChe J.,30, 802 (1984).CrossRefGoogle Scholar
  11. 11.
    I. V. Derevich and V. M. Eroshenko, “Calculation of the average phase velocity slip in turbulent multiphase disperse channel flow,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 69 (1990).Google Scholar
  12. 12.
    I. V. Derevich and V. M. Eroshenko, “Boundary conditions for the equations of heat and mass transport of coarsely dispersed aerosols in a turbulent flow,”Inzh.-Fiz. Zh.,61, 546 (1991).Google Scholar
  13. 13.
    I. V. Derevich, “Statistical description of the turbulent flow of a gas suspension of large particles colliding with channel walls,”Inzh.-Fiz. Zh.,66, 387 (1994).Google Scholar
  14. 14.
    E. P. Mednikov,Turbulent Transport and Deposition of Aerosols [in Russian], Nauka, Moscow (1981).Google Scholar
  15. 15.
    M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover (1964).Google Scholar
  16. 16.
    B. L. Sawford, “Reynolds number effects in Lagrangian stochastic models of turbulent dispersion,”Phys. Fluids. A,3, 1577 (1991).CrossRefGoogle Scholar
  17. 17.
    F. N. Frenkiel and P. S. Klebanoff, “Statistical properties of velocity derivatives in a turbulent field,”J. Fluid Mech.,48, 183 (1971).Google Scholar
  18. 18.
    M. R. Wells and D. E. Stock, “The effects of crossing trajectories on the dispersion of particles in turbulent flow,”J. Fluid Mech.,136, 31 (1983).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

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  • I. V. Derevich

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