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Unsteady flow interactions between an advected cylindrical vortex tube and a spherical particle

Published online by Cambridge University Press:  26 April 2006

Inchul Kim ,
Said Elghobashi  and
William A. Sirignano
Inchul Kim
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717, USA
Said Elghobashi
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717, USA
William A. Sirignano
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717, USA
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Abstract

The unsteady, three-dimensional, incompressible, viscous flow interactions between a vortical (initially cylindrical) structure advected by a uniform free stream and a spherical particle held fixed in space is investigated numerically for a range of particle Reynolds numbers 20 ≤ Re ≤ 100. The counter-clockwise rotating vortex tube is initially located ten sphere radii upstream from the sphere centre. The finite-difference computations yield the flow properties and the temporal distributions of lift, drag, and moment coefficients of the sphere. Initially, the lift force is positive owing to the upwash on the sphere, then becomes negative owing to the downwash as the vortex tube passes the sphere. Varying the size of the vortex core (σ) shows that the r.m.s. lift coefficient is linearly proportional to the circulation of the vortex tube at small values of σ. At large values of σ, the r.m.s. lift coefficient is linearly proportional to the maximum fluctuation velocity (vmax) induced by the vortex tube but independent of σ. For intermediate values of σ, the r.m.s. lift coefficient depends on both σ and vmax (or equivalently both σ and the circulation). We observe some interesting flow phenomena in the near wake as a function of time owing to the passage of the vortex tube.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 288 , 10 April 1995 , pp. 123 - 155
Copyright
© 1995 Cambridge University Press

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References

Anderson, D. A., Tannehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. Hemisphere.
Basset, A. B. 1988 A Treatise on Hydrodynamics, vol. 2, p. 285. Dover.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, p. 201. Cambridge University Press.
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic.
Houghton, G. 1963 The behaviour of particles in a sinusoidal velocity field accelerating in a viscous fluid. Proc. R. Soc. Lond. 272, 33–43.Google Scholar
Ingebo, R. D. 1956 Drag coefficient and relative velocity in bubbly, droplet, or particulate flows. NASA TN 3762.
Kim, I., Elghobashi, S. & Sirignano, W. A. 1993 Three-dimensional flow over two spheres placed side by side. J. Fluid Mech. 246, 465–488.Google Scholar
McLaughlin, J. B. 1991 Inertial migration of a small sphere in linear shear flow. J. Fluid Mech. 224, 261–274.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
Odar, F. 1966 Verification of the proposed equation for calculation of the forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 25, 591–592.Google Scholar
Patnaik, G. 1986 A numerical solution of droplet vaporization with convection. PhD dissertation, Carnegie-Mellon University.
Patnaik, G., Sirignano, W. A., Dwyer, H. A. & Sanders, B. R. 1986 A numerical technique for the solution of a vaporizing fuel droplet. Prog. Astro. Aero. 105, 253–266.Google Scholar
Rubinow, S. I. & Keller, J. B. 1961 The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 12, 447–459.Google Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400.Google Scholar
Saffman, P. G. 1968 The lift on a small sphere in a slow shear flow – Corrigendum. J. Fluid Mech. 31, 624.Google Scholar
Schöneborn, P. R. 1975 The interaction between a single particle and an oscillating fluid. Int. J. Multiphase Flow 2, 307–317.Google Scholar
Spalart, P. R. 1982 Numerical simulation of separated flows. PhD thesis, Stanford University.
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds number. J. Phys. Soc. Japan 11, 1104–1108.Google Scholar
Vinokur, M. 1983 On one-dimensional stretching functions for finite-difference calculations. J. Comput. Phys. 50, 215–234.Google Scholar