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Second-order modelling of particle dispersion in a turbulent flow

Published online by Cambridge University Press:  21 April 2006

Tsan-Hsing Shih  and
J. L. Lumley
Tsan-Hsing Shih
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850
J. L. Lumley
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14850
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Abstract

A set of second-order modelled equations for the motion of particles are presented. We consider the effects of the particle inertia and the crossing-trajectories effect on the particle dispersion. A simple case of a particle mixing layer in a decaying homogeneous turbulence for light and heavy particles is calculated. The results show that the crossing-trajectories effect on particle dispersion is very significant, while inertia only has a slight effect. This behaviour has been observed in experiments (Wells & Stock 1983) and is well predicted by an asymptotic analysis (Csanady, 1963). The calculation also shows that there is a significant difference between Favre-averaged particle velocity and conventional-averaged particle velocity in the low-particle-concentration region. All calculations are in good agreement with Wells & Stock's experimental data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 349 - 363
Copyright
© 1986 Cambridge University Press

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References

Csanady, G. T. 1963 Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci. 20, 201–208.Google Scholar
Lottey, J. M., Lumley, J. L. & Shih, T. H. 1983 Inclusion of particles in second-order modeling of the atmospheric surface mixing layer. Atmospheric Dispersion of Heavy Gases and Small Particles, IVTAM Symposium, Delft 1983 (ed. G. Ooms & H. Tennekes), pp. 25–38. Springer.
Lumley, J. L. 1978a Computational modeling of turbulent flows. Advances in Applied Mechanics 18 (ed. C.-S. Yih), pp. 123–176. Academic.
Lumley, J. L. 1978b Turbulent transport of passive contaminants and particles: fundamentals and advanced methods of numerical modeling. In Pollutant Dispersal, Lecture series 1978–7. Von KaArmaAn Institute for Fluid Dynamics, Rhode-St.-Genese, Belgium.
Lumley, J. L. 1978c Two-phase and non-Newtonian flows. In Turbulence (Topics in Applied Physics, vol. 12 (ed. P. Bradshaw), pp. 290–324. Springer.
Lumley, J. L. & Shih, T. H. 1981 Modeling heat flux in a thermal mixing layer. In Refined Modeling of flows, vol. I, pp. 239–250. Paris: Presses Ponts et ChausseAes.
Meek, C. C. & Jones, B. G. 1973 Studies of the behavior of heavy particles in a turbulent fluid flow. J. Atmos. Sci. 30, 239–241.Google Scholar
Nir, A. & Pismen, L. M. 1979 The effect of a steady drift on the dispersion of a particle in turbulent fluid. J. Fluid Mech. 94, 369–381.Google Scholar
Shih, T. H. 1984 Second order modeling of scalar turbulent flows. Ph.D. thesis, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, N.Y
Shih, T. H. & Lumley, J. L. 1986 Influence of time scale ratio on scalar flux relaxation: modeling Sirivat and Warhaft's homogeneous passive scalar fluctuations. J. Fluid Mech. 162, 211–222.Google Scholar
Snyder, W. H. & Lumley, J. L. 1971 Some measurements of particle velocity autocorrelation function in a turbulent flow. J. Fluid Mech. 48, 41–71.Google Scholar
Wells, M. R. & Stock, D. E. 1983 The effects of crossing trajectories on the dispersion of particles in a turbulent fluid. J. Fluid Mech. 136, pp. 31–62.Google Scholar
Yudine, M. I. 1959 Physical considerations on heavy particle diffusion. Adv. Geophys. 6, 185.Google Scholar