Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-30T01:49:15.041Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional flow over two spheres placed side by side

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
Get access Rights & Permissions [Opens in a new window]

Abstract

Three-dimensional flow over two identical (solid or liquid) spheres which are held fixed relative to each other with the line connecting their centres normal to a uniform I stream is investigated numerically at Reynolds numbers 50, 100, and 150. We consider the lift, moment, and drag coefficients on the spheres and investigate their dependence on the distance between the two spheres. The computations show that, for a given Reynolds number, the two spheres are repelled when the spacing is of the order of the diameter but are weakly attracted at intermediate separation distances. For small spacing, the vortical structure of the near wake is significantly different from that of the axisymmetric wake that establishes at large separations. The partially confined flow passing between the two spheres entrains the flows coming around their other sides. Our results agree with available experimental and numerical data.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 465 - 488
Copyright
© 1993 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

Anderson, D. A., Tasnehill, J. C. & Pletcher, R. H. 1984 Computational Fluid Mechanics and Heat Transfer. Hemisphere.
Chiang, C. H, & Sirignano, W. A. 1992a Numerical analysis of interacting, convecting, vaporizing fuel droplets with variable properties. Intl J. Heat Mass Transfer (in press).Google Scholar
Chiang, C. H. & Sirignano, W. A. 1992b Axisymmetric calculations of three-droplets interactions. Atomization and Sprays (in press).Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops, and Particles. Academic.
Dandy, D. S. & Dwyer, H. A. 1990 A sphere in shear flow a finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J. Fluid Mech. 216, 381– 410.Google Scholar
Goldburg, A. & Floesheim, B. H. 1966 Transition and Strouhal number for the incompressible wake of various bodies. Phys. Fluids 9, 45– 50.Google Scholar
Kim, I. & Pearlstein, A. J. 1990 Stability of the flow past a sphere. J. Fluid Mech. 211. 73– 93.Google Scholar
Nakamura, I. 1976 Steady wake behind a sphere. Phys. Fluids 19, 5– 8.Google Scholar
Patnaik, G. 1986 A numerical solution of droplet vaporization with convection. Ph.D. dissertation, Carnegie-Mellon University.
Raju, M.S. & Sirignano, W. A. 1990 Interaction between two vaporizing droplets in an intermediate-Reynolds-number flow. Phys. Fluids A 2, 1780– 1796.Google Scholar
Rivkind, V. Y. & Ryskin, G. 1976 Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds numbers. Fluid Dyn. 11, 5– 12.Google Scholar
ROOS, F. W. & Willmarth, W. W. 1971 Some experimental results on sphere and disk drag AIAA J. 9, 285– 291.Google Scholar
Rosfjord, T. J. 1974 Experimental and theoretical investigations of the recirculating flow region between two-dimensional, parallel, separated jets. Ph.D. dissertation, Princeton University.
Sirignano, W. A. 1983 Fuel droplet vaporization and spray combustion. Proa Energy Combust. Sci. 9, 291– 322.Google Scholar
Tal(thau), R., Lee, D. N. & Sirignano, W. A. 1983 Hydrodynamics and heat transfer in sphere assemblages – cylindrical cell models. Intl J. Heat Mass Transfer 26, 1265– 1273.Google Scholar
Tal(thau), R., Lee, D. N. & Sirionano, W. A. 1984 Heat and momentum transfer around a pair of spheres in viscous flow. Intl J. Heat Mass Transfer 27, 1253– 1262.Google Scholar
Taneda, S, 1956 Experimental investigation of the wake behind a sphere at low Reynolds number, J. Phys. Soc. Japan 11, 1104– 1108.Google Scholar
Tomboulides, A. G., ORSZAG, S. A, & KARNIADAKIS, G. E. 1991 Three-dimensional simulation of flow past a sphere. Intl Soc. Offshore, Polar Engng Proc. Edinburgh, Scotland.
Vinokur, M. 1983 On one-dimensional stretching functions for finite-difference calculations, J. Comput. Phys. 50, 215– 234.Google Scholar