Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-21T11:35:30.282Z Has data issue: false hasContentIssue false

Stratified flow past a sphere

Published online by Cambridge University Press:  26 April 2006

Q. Lin
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA
W. R. Lindberg
Affiliation:
Department of Mechanical Engineering, University of Wyoming, Laramie, Wyoming 82071-3295, USA
D. L. Boyer
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA
H. J. S. Fernando
Affiliation:
Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA

Abstract

The flow of a linearly stratified fluid past a sphere is considered experimentally in the Froude number Fi, Reynolds number Re, ranges 0.005 ≤ Fi ≤ 20 and 5 ≤ Re ≤ 10000. Flow visualization techniques and density measurements are used to describe the rich range of characteristic flow phenomena observed. These different flow patterns are mapped on a detailed Fi against Re flow regime diagram. In most instances the flow patterns were found to be very different from those observed in homogeneous fluids. Vortex shedding characteristics, for example, were found to be dramatically affected by the presence of stratification. Where possible, the results are compared with available analytical and numerical models.

Type
Research Article
Copyright
© 1992 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

Achenbach, E. 1972 Experiments on the flow past spheres at a very high Reynolds numbers. J. Fluid Mech. 54, 565575.Google Scholar
Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209221.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Berger, E. & Wille, R. 1972 Periodic flow phenomena. Ann. Rev. Fluid Mech. 4, 313340.Google Scholar
Boyer, D. L. 1968 Flow past a right circular cylinder in a rotating frame. J. Basic Engng 92, 430436.Google Scholar
Boyer, D. L., Davies, P. A., Fernando, H. J. S. & Zhang, X. 1989 Linearly stratified flow past a horizontal circular cylinder.. Phil. Trans. R. Soc. Lond. A 328, 501528.Google Scholar
Brighton, P. W. M. 1978 Strongly stratified flow past three dimensional obstacles. Q. J. R. Met. Soc. 104, 289307.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1959 Conduction of Heat in Solids, 2nd edn. Oxford University Press.
Castro, I. P., Snyder, W. H. & Baines, P. G. 1990 Obstacle drag in stratified flow. Proc. R. Soc. Lond. A429, 119140.Google Scholar
Castro, I. P., Snyder, W. H. & Marsh, G. L. 1983 Stratified flow over three-dimensional ridges. J. Fluid Mech. 135, 261282.Google Scholar
Chashechkin, Y. D. 1989 The hydrodynamics of a sphere in a stratified liquid. Isv. Akad. Nauk SSSR Mekh. Zhid. i Gaza, No. 1, 3–9.Google Scholar
Chashechkin, Y. D. & Sysoeva, E. I. 1988 Fine structure and symmetry of the wake past a sphere in a stratified liquid. Proc. Sci. and Methodol. Seminar on Ship Hydrodyn., vol. 1, 17th session, Bulgarian Ship Hydrodynamics Centre, 10, 1.
Chomaz, J. M., Bonneton, P., Butet, A. & Perrier, M. 1990 Froude 4 transition in the wake of a sphere in a stratified fluid. Bull. Am. Phys. Soc. 35, 2338.Google Scholar
Churchill, S. W. 1988 Viscous Flows, the Practical Use of Theory. Stoneham, MA: Butterworths.
Crapper, G. D. 1959 A three-dimensional solution for waves in the lee of mountains. J. Fluid Mech. 6, 5176.Google Scholar
Debler, W. 1973 The towing of bodies in a stratified fluid. Intl Symp. on Stratified Flows, Novosibirsk, 1972, ASCE, pp. 194220.
Debler, W. & Fitzgerald, P. 1971 Shadowgraphic observations of the flow past a sphere and a vertical cylinder in a density stratified liquid. Tech. Rep. EM-71–3, Dept of Mech. Engng, University of Michigan.Google Scholar
Drazin, P. G. 1961 On the steady flow of a fluid of variable density over an obstacle. Tellus 8, 239251.Google Scholar
Gad-El-Hak, M. 1987 The water towing tank as an experimental facility. Exps Fluids 5, 289297.Google Scholar
Hanazaki, H. 1988 A numerical study of three-dimensional stratified flow past a sphere. J. Fluid Mech. 192, 393419.Google Scholar
Honji, H. 1987 Near wakes of a sphere in stratified fluid. Fluid Dyn. Res. 2, 7576.Google Scholar
Hopfinger, E. J. 1987 Turbulence in stratified fluids: a review. J. Geophys. Res. 92 (C5), 52875303.Google Scholar
Hunt, J. C. R., Abell, C. J., Peterka, J. A. & Woo, H. 1978 Kinematical studies of the flows around free or surface-mounted obstacles; applying topology to flow visualization. J. Fluid Mech. 86, 179200.Google Scholar
Hunt, J. C. R. & Snyder, W. H. 1980 Experiments on stably and neutrally stratified flow over a model three-dimensional hill. J. Fluid Mech. 96, 671704.Google Scholar
Kim, H. J. & Durbin, P. A. 1988 Observations of the frequency in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 31, 32603265.Google Scholar
Lighthill, M. J. 1963 In Laminar Boundary Layers (ed. L. Rosenhead), pp. 4888. Oxford University Press
Lin, J. T. & Pao, Y. H. 1979 Wakes in stratified fluids: a review. Ann. Rev. Fluid Mech. 11, 317338.Google Scholar
Lofquist, K. & Purtell, P. 1984 Drag on a sphere moving horizontally through a stratified liquid. J. Fluid Mech. 148, 271284.Google Scholar
Magarvey, R. H. & MacLatchy, C. S. 1965 Vortices in sphere wakes. Can. J. Phys. 43, 16491656.Google Scholar
Mason, P. J. 1977 Forces on spheres moving horizontally in a rotating stratified fluid. Geophys. Astrophys. Fluid Dyn. 8, 137154.Google Scholar
Nakamura, I. 1976 Steady wake behind a sphere. Phys. Fluids 19, 58.Google Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213, 7076.Google Scholar
Pao, H. P. & Kao, T. W. 1977 Vortex structure in the wake of a sphere. Phys. Fluids 20, 187191.Google Scholar
Rosenhead, L. 1953 Vortex systems in wakes. Adv. Appl. Mech. 3, 185195.Google Scholar
Roshko, A. 1953 On the development of turbulent wakes from vortex streets. NACA Tech. Note 2913.Google Scholar
Sheppard, P. A. 1956 Air flow over mountains. Q. J. R. Met. Soc. 82, 528529.Google Scholar
Snyder, W. H., Thompson, R. S., Eskridge, R. E., Lawson, R. E., Castro, I. P., Lee, J. T., Hunt, J. C. R. & Ogawa, Y. 1985 The structure of strongly stratified flow over hills: dividing-streamline concept. J. Fluid Mech. 152, 249288.Google Scholar
Sysoeva, H. J. & Chashechkin, Y. D. 1988 The spatial structure of the path behind a sphere in a stratified liquid. Z. Prik. Mekh. i Tekh. Fiz. 5, 5965.Google Scholar
Taneda, S. 1956 Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Japan 11, 11041108.Google Scholar
Taneda, S. 1978 Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106. J. Fluid Mech. 85, 187192.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1959 Fundamental aspects of solids—gas flow. Part I: Introductory concepts and idealized sphere motion in viscous regime. Can. J. Chem. Engng 37, 129141.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1959 Fundamental aspects of solids—gas flow. Part II: The sphere wake in steady laminar fluids. Can. J. Chem. Engng 37, 167176.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1959 Fundamental aspects of solids—gas flow. Part III: Accelerated motion of a particle in a fluid. Can. J. Chem. Engng 37, 224236.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1960 Fundamental aspects of solids—gas flow. Part IV: The effects of particle rotation, roughness and shape. Can. J. Chem. Engng 38, 142153.Google Scholar
Torobin, L. B. & Gauvin, W. H. 1960 Fundamental aspects of solids—gas flow. Part V: The effects of fluid turbulence on the particle drag coefficient. Can. J. Chem. Engng 38, 189200.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.