zbMATH — the first resource for mathematics

Hydrodynamic forces acting on a rigid fixed sphere in early transitional regimes. (English) Zbl 1093.76014
Summary: A spectral element code is used to investigate the hydrodynamic forces acting on a fixed sphere placed in a uniform flow in the Reynolds number interval 10–320 covering the early stages of transition, i.e. the steady axisymmetric regime with detached flow, and the steady non-axisymmetric and unsteady periodic regimes of sphere wake. The mentioned changes of regimes, shown by several authors to be related to regular Hopf bifurcations in the wake, result in significant changes of hydrodynamic action of the flow on the sphere. We show that the loss of axisymmetry is accompanied not only by an onset of lift, but also of a torque, and we give accurate values of drag, lift and torque in the whole interval of investigated Reynolds numbers. Among other results we show, moreover, that each bifurcation is accompanied also by a change of the trend of the drag versus Reynolds number, the overall qualitative effect of instabilities being an increase in drag.

76D05 Navier-Stokes equations for incompressible viscous fluids
76M22 Spectral methods applied to problems in fluid mechanics
Full Text: DOI
[1] Kim, I.; Pearlstein, A.J., Stability of the flow past a sphere, J. fluid mech., 211, 73-93, (1990) · Zbl 0686.76029
[2] Natarajan, R.; Acrivos, A., The instability of the steady flow past spheres and disks, J. fluid mech., 254, 323-344, (1993) · Zbl 0780.76027
[3] A.G. Tomboulides, S.A. Orszag, G.E. Karniadakis, Direct and large-eddy simulation of axisymmetric wakes, in: AIAA - 31st Aerospace Sciences Meeting & Exhibit, 1993, pp. 1-12
[4] Johnson, T.A.; Patel, V.C., Flow past a sphere up to a Reynolds number of 300, J. fluid mech., 378, 19-70, (1999)
[5] Ghidersa, B.; Dušek, J., Breaking of axisymmetry and onset of unsteadiness in the wake of a sphere, J. fluid mech., 423, 33-69, (2000) · Zbl 0977.76028
[6] D. Ormières, Etude expérimentale et modélisation du sillage d’une sphère à bas nombre de Reynolds, PhD thesis, Université de Provence, 1999
[7] Panton, L., Incompressible flow, (1996) · Zbl 1275.76001
[8] Clift, R.; Grace, J.R.; Weber, M.E., Bubbles, drops and particules, (1978)
[9] Tsuji, Y.; Morikawa, Y.; Mizuno, O., Experimental measurement of the Magnus force on a rotating sphere at low Reynolds numbers, Trans. ASME J. fluids engrg., 107, 484-488, (1985)
[10] Magnaudet, J.; Rivero, M.; Fabre, J., Accelerated flows past a rigid sphere or a spherical bubble. part 1. steady straining flow, J. fluid mech., 284, 97-135, (1995) · Zbl 0848.76063
[11] Patera, A., A spectral element method for fluid dynamics: laminar flow in a channel expansion, J. comput. phys., 54, 3, 468-488, (1984) · Zbl 0535.76035
[12] Karniadakis, G.E., Spectral element-Fourier methods for incompressible turbulent flows, Comput. methods appl. mech. engrg., 80, 3, 367-380, (1990) · Zbl 0722.76053
[13] Mittal, R., A fourier – chebyshev spectral collocation method for simulating flow past spheres and spheroids, Int. J. numer. methods fluids, 30, 921-937, (1999) · Zbl 0957.76060
[14] Orszag, S.A.; Patera, A.T., Secondary instability of wall bounded shear flows, J. fluid mech., 128, 347-385, (1983) · Zbl 0556.76039
[15] Magarvey, R.H.; Bishop, R.L., Transition ranges for three-dimensional wakes, Canad. J. phys., 39, 1418-1422, (1961)
[16] Levi, E., Three-dimensional wakes: origin and evolution, J. engrg. division, 659-676, (1980)
[17] Dennis, S.C.R.; Walker, J.D.A., Calculation of the steady flow past a sphere at low and moderate Reynolds numbers, J. fluid mech., 48, 771-789, (1971) · Zbl 0266.76023
[18] Rimon, Y.; Cheng, S.I., Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers, Phys. fluids, 12, 5, 949-959, (1969) · Zbl 0181.54801
[19] Taneda, S., Experimental investigation of the wake behind a sphere at low Reynolds numbers, J. phys. soc. Japan, 11, 10, 1104-1108, (1956)
[20] Nakamura, I., Steady wake behind a sphere, Phys. fluids, 19, 1, 5-8, (1976)
[21] A.G. Tomboulides, S.A. Orszag, G.E. Karniadakis, Direct and large-eddy simulation of the flow past a sphere, in: Second International Conference on Turbulence Modeling and Experiments, 1993, pp. 1-10
[22] Bagchi, P.; Balachandar, S., Steady planar straining flow past a rigid sphere at moderate Reynolds number, J. fluid mech., 466, 365-407, (2002) · Zbl 1062.76015
[23] Roos, F.W.; Willmarth, W.W., Some experimental results on sphere and disk drag, Aiaa j., 9, 2, 285-291, (1971)
[24] K.R. Sreenivasan, P.J. Strykowski, D.J. Olinger, Hopf bifurcation, Landau equation and vortex shedding behind circular cylinders, in: Proc. Forum on Unsteady Flow Separation, ASME Applied Mechanics, Bio Engineering Conference, Cincinnati, Ohio, June 11-17, ASME FED, 52, 1987
[25] Zielinska, B.J.A.; Goujon-Durand, S.; Dušek, J.; Wesfreid, J.E., A strongly nonlinear effect in unstable wakes, Phys. rev. lett., 79, 3893-3896, (1997)
[26] Goldburg, A.; Florsheim, B.H., Transition and Strouhal number for the incompressible wake of various bodies, Phys. fluids, 9, 1, 45-50, (1966)
[27] Magarvey, R.H.; Bishop, R.L., Wakes in liquid – liquid systems, Phys. fluids, 4, 7, 800-804, (1961)
[28] Sakamoto, H.; Haniu, H., A study on vortex shedding from spheres in a uniform flow, Trans. ASME, 112, 386-392, (1990)
[29] Tomboulides, G.A.; Orszag, S.A., Numerical investigation of transitional and weak turbulent flow past a sphere, J. fluid mech., 416, 45-73, (2000) · Zbl 1156.76419
[30] Mittal, R., Planar symmetry in the unsteady wake of a sphere, Aiaa j., 37, 3, 388-390, (1999)
[31] Jenny, M.; Bouchet, G.; Dušek, J., Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, J. fluid mech., 508, 201-239, (2004) · Zbl 1065.76068
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.