On the equation for spherical-particle motion: Effect of Reynolds and acceleration numbers

Journal of Fluid Mechanics

Volumn 367, Issue , 1998, Pages 221-253

  Kim, Inchul ^a   Elghobashi, Said ^a   Sirignano, William A ^a  

^a University of California at Irvine   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; COMPUTATIONAL FLUID DYNAMICS; DRAG; REYNOLDS NUMBER; UNSTEADY FLOW; WAKES;

AXISYMMETRIC FLOW; SPHERICAL PARTICLE MOTION;

NAVIER STOKES EQUATIONS;

EID: 0032119654     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112098001657     Document Type: Article

References (29)

1. BASSET, A. B. 1888 A Treatise on Hydrodynamics, vol. 2, p. 285. Dover.
2. BEREZIN, I. S. & ZHIDKOV, N. P. 1965 Computing Methods, p. 299. Addison-Wesley.
3. BERLEMONT, A., DESJONQUERES, P. & GOUESBET, G. 1990 Particle Lagrangian simulation in turbulent flows. Intl. J. Multiphase Flow 16, 19-34.
4. BOUSSINESQ, J. 1903 Theorie Analytique de la Chaleur (L'École Polytechnique, Paris), vol. 2, p. 224.
5. CHANG, E. J. & MAXEY, M. R. 1994 Accelerated motion of rigid spheres in unsteady flow at low to moderate Reynolds numbers. Part 1. Oscillatory motion. J. Fluid Mech. 277, 347-379.
6. CHANG, E. J. & MAXEY, M. R. 1995 Unsteady flow about a sphere at low to moderate Reynolds numbers. Part 2. Accelerated motion. J. Fluid Mech. 303, 133-153.
7. CHUNG, J. N. 1982 The motion of particles inside a droplet. Trans. ASME C: J. Heat Transfer 104, 438-445.
8. CLIFT, R., GRACE, J. R. & WEBER, M. E. 1978 Bubbles, Drops, and Particles. Academic.
9. FORNBERG, B. 1988 Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech. 190, 471-489.
10. KIM, I., ELGHOBASHI, S. & SIRIGNANO, W. A. 1993 Three-dimensional flow over two spheres placed side by side. J. Fluid Mech. 246, 465-488.
11. KIM, I., ELGHOBASHI, S. & SIRIGNANO, W. A. 1995 Unsteady flow interactions between an advected cylindrical vortex tube and a spherical particle. J. Fluid Mech. 288, 123-155.
12. KIM, I., ELGHOBASHI, S. & SIRIGNANO, W. A. 1996 The motion of a spherical particle in unsteady flows at moderate Reynolds numbers. AIAA Paper 96-0081.
13. KIM, I., ELGHOBASHI, S. & SIRIGNANO, W. A. 1997 Unsteady flow interactions between a pair of advected vortex tubes and a rigid sphere. Intl J. Multiphase Flow 23, 1-23.
14. LAWRENCE, C. J. & MEI, R. 1995 Long-time behaviour of the drag on a body in impulsive motion. J. Fluid Mech. 283, 307-327.
15. LOVALENTI, P. M. & BRADY, J. F. 1993a The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256, 561-605.
16. LOVALENTI, P. M. & BRADY, J. F. 1993b The force on a sphere in a uniform flow with small-amplitude oscillations at finite Reynolds number. J. Fluid Mech. 256, 607-614.
17. LOVALENTI, P. M. & BRADY, J. F. 1995 The temporal behaviour of the hydrodynamic force on a body in response to an abrupt change in velocity at small but finite Reynolds number. J. Fluid Mech. 293, 33-46.
18. MAXEY, M. R. 1993 The equation of motion for a small rigid sphere in a nonuniform or unsteady flow. Gas-Solid Flows. ASME/FED, Vol. 166, pp. 57-62.
19. MAXEY, M. R. & RILEY, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883-889.
20. MEI, R. 1994 Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number. J. Fluid Mech. 270, 133-174.
21. MEI, R. & ADRIAN, R. J. 1992 Flow past a sphere with an oscillation in the free-stream and unsteady drag at finite Reynolds number. J. Fluid Mech. 237, 323-341 (referred to herein as MA).
22. MEI, R., LAWRENCE, C. J. & ADRIAN, R. J. 1991 Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity. J. Fluid Mech. 233, 613-631.
23. 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.
24. ODAR, F. & HAMILTON, W. S. 1964 Forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 18, 302-314 (referred to herein as OH).
25. OSEEN, C. W. 1927 Hydrodynamik. Leipzig: Akademische Verlagsgesellschaft.
26. RIVERO, M., MAGNAUDET, J. & FABRE, J. 1991 Quelques resultants nouveaux concernant les forces exercees sur une inclusion spherique par en ecoulement accelere. C.R. Acad. Sci. Paris 312(II), 1499-1506.
27. SANO, T. 1981 Unsteady flow past a sphere at low Reynolds number. J. Fluid Mech. 112, 433-441.
28. TANEDA, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds number. J. Phys. Soc. Japan 11 1104-1108.
29. VINOKUR, M. 1983 On one-dimensional stretching functions for finite-difference calculations. J. Comput. Phys. 50, 215-234.