Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-18T18:16:27.335Z Has data issue: false hasContentIssue false
  • English
  • Français

The effects of crossing trajectories on the dispersion of particles in a turbulent flow

Published online by Cambridge University Press:  20 April 2006

M. R. Wells  and
D. E. Stock
M. R. Wells
Affiliation:
Department of Mechanical Engineering, Washington State University, Pullman, Washington 99164 Present address: Amoco Production Research, Tulsa, OK.
D. E. Stock
Affiliation:
Department of Mechanical Engineering, Washington State University, Pullman, Washington 99164
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of ‘crossing trajectories’ and inertia on the dispersion of particles suspended in a field of grid-generated turbulence were investigated experimentally. The effect of particle trajectories crossing the trajectories of fluid elements, under the influence of a potential field (usually gravity), is to force the particles from one region of highly correlated flow to another. In this manner, particles lose velocity correlation more rapidly than the corresponding fluid points and as a result disperse less.

A homogeneous decaying turbulent field was created behind a square biplanar grid in a wind tunnel. Particles were charged by a corona discharge then passed into the test section through a small plastic tube. A uniform electric field within the test section was used to simulate the effect of gravity, forcing the charged particles out of regions of correlated fluid at a higher than normal rate, therefore inducing the effects of crossing trajectories. Two sizes of glass beads (5 μm and 57 μm diameter) were employed in order to observe inertial effects. Laser-Doppler anemometry was used to measure particle mean-square displacement, autocorrelation coefficient, and mean-square velocity, from which dispersion coefficients were calculated.

For the two particle sizes used in the tests, it was found that the particle diffusion coefficient, after a suitably long time from their release, was influenced primarily by the effect of crossing trajectories. Only in the particle mean-square velocity was the particle inertia seen to have any effect. The ratio of the particle relaxation time to the Kolmogoroff timescale was found to be a good indicator for the effects of particle inertia.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 136 , November 1983 , pp. 31 - 62
Copyright
© 1983 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. 1952 Diffusion in a field of homogeneous turbulence, part II, the relative motion of particles Proc. Camb. Phil. Soc. 48, 345–362.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A, 193, 539–810.Google Scholar
Berlemont, A. & Gouesbet, G. 1981 Prediction of the behavior of a cloud of discrete particles released in a fully developed turbulent pipe flow, using a non-discrete dispersion approach. In Proc. 2nd Intl Conf. on Numerical Methods in Laminar and Turbulent Flow, Venice, Italy, 13–810 July, 1981.
Buchhave, P. 1979 The measurement of turbulence with the burst-type laser Doppler anemometer – errors and correction methods. PhD dissertation, State University of New York, Buffalo.
Calabrese, R. V. & Middleman, S. 1979 The dispersion of discrete particles in a turbulent fluid field AIChE J. 25, 1025–1035.Google Scholar
Chao, B. T. 1965 Turbulent transport behavior of small particles in dilute suspensions. Ostereichisches Ingenieur-Archiv., Sonderabdruck aus Bd. 18, Heft 1 und 2, p. 7.
Compte-Bellot, G. & Corrsin, S. 1966 The use of a contraction to improve the isotropy of grid-generated turbulence J. Fluid Mech. 25, 657–682.Google Scholar
Corrsin, S. 1962 Theory of turbulent dispersion. In Proc. Turbulent Diffusion Conf. Marseille, France, pp. 27–52.
Corrsin, S. 1963 Turbulence: experimental methods. In Handbuch der Physik, vol.812, pp. 115–145. Springer.
Csanady, G. T. 1963 Turbulent diffusion of heavy particles in the atmosphere J. Atmos. Sci. 20, 201–208.Google Scholar
Csanady, G. T. 1964 An atmospheric dust fall experiment J. Atmos. Sci. 21, 222–225.Google Scholar
Dryden, H. L., Schubauer, G. B., Mock, W. C. & Skramstad, H. K. 1937 Measurements of the intensity and scale of wind tunnel turbulence and their relation to the critical Reynolds number of spheres. NACA Reprint no. 581.Google Scholar
Frenzen, P. 1963 A laboratory investigation of the Lagrangian autocorrelation function in a stratified fluid. Argonne Natl Lab ANL-6794.
Fuchs, N. A. 1964 The Mechanics of Aerosols. Macmillan.
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Kármán, T. Von & Howarth, L. 1938 On the statistical theory of isotropic turbulence. Proc. R. Soc. Lond A 164, 192–215.Google Scholar
Kolmogoroff, A. N. 1941 Dissipation of energy in locally isotropic turbulence C.R. Acad. Sci. URSS 32, 16–18.Google Scholar
Week, 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
Moore, A. D. 1973 Electrostatics and Its Applications, chap. 9, pp. 194–197. Wiley.
Naudascher, E. & Farrell, C. 1970 Unified analysis of grid turbulence. J. Engng Mech. Div. ASCE 96 (EM2), 121–810.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
Pasquill, F. 1962 Atmospheric Diffusion. Von Nostrand.
Pismen, L. M. & Nir, A. 1978 On the motion of suspended particles in stationary homogeneous turbulence J. Fluid Mech. 84, 193–206.Google Scholar
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. & Patterson, G. S. 1974 Diffusion experiments with numerically integrated isotropic turbulence Phys. Fluids 17, 292–297.Google Scholar
Saffman, P. G. 1962 An approximate calculation of the Lagrangian autocorrelation coefficient for stationary homogeneous turbulence Appl. Sci. Res. 11A, 245–255.Google Scholar
Snyder, W. H. & Lumley, J. L. Some measurements of particle velocity autocorrelation functions in a turbulent flow. J. Fluid Mech. 48, 41–810.
Taylor, G. I. 1921 Diffusion by continuous movements Proc. R. Soc. Lond. A 151, 421–478.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond A 151, 421–478.Google Scholar
Uberoi, M. S. & Corrsin, S. 1952 Diffusion of heat from a line source in isotropic turbulence. NACA Rep. 1142.Google Scholar
Van, Der Hegge Zijnen 1958 Measurements of the intensity, integral scale and microscale of turbulence downstream of three grids in a stream of air Appl. Sci. Res. 7A, 149–174.Google Scholar
Wells, M. R. 1982 The effects of crossing trajectories on the diffusion of particles in a turbulent flow. PhD thesis, Washington State University.
Yudine, M. I. 1959 Physical considerations on heavy-particle diffusion. In Atmospheric Diffusion and Air Pollution: Adv. Geophys. 6, 185–810.