Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-23T16:42:34.867Z Has data issue: false hasContentIssue false
  • English
  • Français

Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence

Published online by Cambridge University Press:  26 April 2006

Kyle D. Squires  and
John K. Eaton
Kyle D. Squires
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
John K. Eaton
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements of heavy particle dispersion have been made using direct numerical simulations of isotropic turbulence. The parameters affecting the dispersion of solid particles, namely particle inertia and drift due to body forces were investigated separately. In agreement with the theoretical studies of Reeks, and Pismen & Nir, the effect of particle inertia is to increase the eddy diffusivity over that of the fluid (in the absence of particle drift). The increase in the eddy diffusivity of particles over that of the fluid was between 2 and 16%, in reasonable agreement with the increases reported in Reeks, and Pismen & Nir. The effect of a deterministic particle drift is shown to decrease unequally the dispersion in directions normal and parallel to the particle drift direction. Eddy diffusivities normal and parallel to particle drift are shown to be in good agreement with the predictions of Csanady and the experimental measurements of Wells & Stock.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 226 , May 1991 , pp. 1 - 35
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K.: 1949 Diffusion in a field of homogeneous turbulence. Austral. J. Sci. Res. 2, 437–450.Google Scholar
Calabrese, R. V. & Middleman, S., 1979 The dispersion of discrete particles in aturbulent fluid field. AIChE J. 25, 1025–1035.Google Scholar
Cooley, J. W. & Tukey, J. W., 1965 An algorithm for the machine calculation of complex Fourier series. Maths Comput. 19, 297–301.Google Scholar
Corrsin, S.: 1953 Remarks on turbulent heat transfer. Proc. of the Iowa Thermodynamics Symp. University of Iowa, pp. 5–30.Google Scholar
Corrsin, S.: 1959 Progress report on some turbulent diffusion research. From Proceedings of the International Symposium on Atmospheric Diffusion and Air Pollution, Adv. Geophys. 5, 161–164.Google Scholar
Corrsin, S.: 1961 Theories of turbulent dispersion. Mécanique de la Turbulence, Colloques Internationaux du Centre National de la Recherche Scientifique, no. 108, Editions du CNRS, Paris, pp. 27–52.
Csanady, G. T.: 1963 Turbulent diffusion of heavy particles in the atmosphere. J. Atmos. Sci. 20, pp. 201–208.Google Scholar
Eswaran, V. & Pope, S. B., 1988 An examination of forcing in direct numerical simulations of turbulence. Computers Fluids 16, 257–278.Google Scholar
Elghobashi, S. E. & Truesdell, G. C., 1989 Direct simulation of particle dispersion in a decaying grid turbulence. Presented at Seventh Symp. on Turbulent Shear Flows, Stanford University, California.
Frenkiel, F. N.: 1953 Turbulent diffusion: mean concentration distribution in a flow field of homogeneous turbulence. Adv. Appl. Mech. 3, 61–107.Google Scholar
Fung, J. & Perkins, R. J., 1989 Particle trajectories in turbulent flow generated by true-varying random Fourier modes. Proc. Adv. in Turbulence 2 (ed. H. H. Fernholz & H. E. Fiedler), pp. 322–328. Springer.
Gottlieb, D. & Orszag, S. A., 1977 Numerical analysis of spectral methods: theory and applications. CBMS-NSF Regional Conference series in applied mathematics, vol. 26, SIAM, Philadelphia, Pennsylvania.
Gouesbet, G., Berlemont, A. & Picart, A., 1984 Dispersion of discrete particles by continuous turbulent motions. Extensive discussion of the Tchen's theory, using a two-parameter family of Lagrangian correlation functions. Phys. Fluids 27, 827–837.Google Scholar
Grant, H. L., Stewart, R. W. & Moilliet, A., 1962 Turbulence spectra from a tidal channel. J. Fluid Mech. 12, 241–268.Google Scholar
Hinze, J. O.: 1975 Turbulence. McGraw-Hill.
Hunt, J. C. R., Buell, J. C. & Wray, A. A., 1987 Big whorls carry little whorls. Proc. of the 1987 Summer Program, Rep. CTR-S87, Stanford University, California.
Lee, C. L., Squires, K. D., Bertoglio, J. P. & Ferziger, J. H., 1988 Study of Lagrangian characteristic times using direct numerical simulation of turbulence. Turbulent Shear Flows 6 (ed. B. E. Launder et al.), pp. 58–67. Springer.
Lee, M. J. & Reynolds, W. C., 1985 Numerical experiments on the structure of homogeneous turbulence. Dept Mech. Engng Rep. TF-24, Stanford University, California.
Lumley, J. L.: 1957 Some problems connected with the motion of small particles in turbulent fluid. Ph.D. dissertation, The Johns Hopkins University, Baltimore, Maryland.
Lumley, J. L.: 1961 The mathematical nature of the problem relating Lagrangian and Eulerian statistical functions in turbulence. Mécanique de la Turbulence, Colloques Internationaux du Centre National de la Recherche Scientifique, no. 108, Editions du CNRS, Paris, pp. 17–26.
McLaughlin, J. B.: 1989 Aerosol particle deposition in numerically simulated channel flow. Phys. Fluids 1, 1211–1224.Google Scholar
Maxey, M. R.: 1987 The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Maxey, M. R. & Riley, J. J., 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889.Google Scholar
Meek, C. C. & Jones, B. G., 1973 Studies of the behavior of heavy particles in a turbulent fluid flow. J. Atmos. Sci. 30, 239–244.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
Picart, A., Berlemont, A. & Gouesbet, G., 1986 Modeling and predicting turbulence fields and the dispersion of discrete particles transported by turbulent fields. Intl J. Multiphase Flow 12, 237–261.Google Scholar
Pismen, L. M. & Nir, A., 1978 On the motion of suspended particles in stationary homogeneous turbulence. J. Fluid Mech. 84, 193–206.Google Scholar
Press, W. H., Flannery, B. P., Eukolsky, S. A. & Vetterling, W. T., 1987 Numerical Recipes. Cambridge University Press.
Pruppacher, H. R. & Klett, J. D., 1978 Microphysics of Clouds in precipitation. Reidel.
Reeks, M. W.: 1977 On the dispersion of small particles suspended in an isotropic turbulent field. J. Fluid Mech. 83, 529–546.Google Scholar
Riley, J. J.: 1971 Computer simulations of turbulent dispersion. Ph.D. dissertation, The Johns Hopkins University, Baltimore, Maryland.
Riley, J. J. & Patterson, G. S., 1974 Diffusion experiments with numerically integrated isotropic turbulence. Phys. Fluids 17, 292–297.Google Scholar
Rogallo, R. S.: 1981 Numerical experiments in homogeneous turbulence. NASA Tech. Memo. 81315.Google Scholar
Sato, Y. & Yamamoto, K., 1987 Lagrangian measurement of fluid particle motion in an isotropic turbulent field. J. Fluid Mech. 175, 183–199.Google Scholar
Shlien, D. J. & Corrsin, S., 1974 A measurement of the Lagrangian velocity autocorrelation in approximately isotropic turbulence. J. Fluid Mech. 62, 255–271.Google Scholar
Snyder, W. H. & Lumley, J. L., 1971 Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41–71.Google Scholar
Squires, K. D. & Eaton, J. K., 1990 Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A 2, 1191–1203.Google Scholar
Squires, K. D. & Eaton, J. K., 1991 Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence. Phys. Fluids A 3, 130–143.Google Scholar
Stapountzis, H., Sawford, B. L., Hunt, J. C. R. & Britter, R. E. 1988 Structure of the temperature field downwind of a line source in grid turbulence. J. Fluid Mech. 165, 401–424.Google Scholar
Tavoularis, S., Bennett, J. C. & Corrsin, S., 1978 Velocity derivative skewness in small Reynolds number, nearly isotropic turbulence. J. Fluid Mech. 88, 63–69.Google Scholar
Taylor, G. I.: 1921 Diffusion by continuous movements. Proc. R. Soc. Lond. A 20, 196–211.Google Scholar
Taylor, G. I.: 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421–478.Google Scholar
Tchen, C. M.: 1947 Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. Ph.D. dissertation, University of Delft, The Hague.
Tennekes, H. L.: 1975 Eulerian and Lagrangian time microscales in isotropic turbulence. J. Fluid Mech. 67, 561–567.Google Scholar
Townsend, A. A.: 1954 The diffusion behind a line source in homogeneous turbulence. Proc. R. Soc. Lond. A 224, 487–512.Google Scholar
Warhaft, Z.: 1984 The interference of thermal fields from line sources in grid turbulence. J. Fluid Mech. 144, 363–387.Google Scholar
Wells, M. R. & Stock, D. E., 1983 The effects of crossing trajectories on the dispersion of particles in a turbulent flow. J. Fluid Mech. 136, 31–62.Google Scholar
Yeung, P. K. & Pope, S. B., 1988 J. Comput. Phys. 79, 373.
Yeung, P. K. & Pope, S. B., 1989 Lagrangian statistics from direct numerical simulations of isotropic turbulence. J. Fluid Mech. 207, 531–586.Google Scholar
Yudine, M. I.: 1959 Physical considerations on heavy particle diffusion. From Proceedings of the International Symposium on Atmospheric Diffusion and Air Pollution, Adv. Geophys. 6, 185–191.Google Scholar