Abstract
Direct numerical simulation and visualization of three-dimensional separated flows of a homogeneous incompressible viscous fluid are used to comprehensively describe different mechanisms of vortex formation behind a sphere at moderate Reynolds numbers (200 ≤ Re ≤ 380). For 200 < Re ≤ 270 a steady-state rectilinear double-filament wake is formed, while for Re > 270 it is a chain of vortex loops. The three unsteady periodic flow patterns corresponding to the 270 < Re ≤ 290, 290 < Re ≤ 320, and 320 < Re ≤ 380 ranges are characterized by different vortex formation mechanisms. Direct numerical simulation is based on the Meranzh (SMIF) method of splitting in physical factors with an explicit hybrid finite-difference scheme which possesses the following properties: secondorder approximation in the spatial variables, minimal scheme viscosity and dispersion, and monotonicity. Two different vortex identification techniques are used for visualizing the vortex structures within the wake.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F.W. Roos and W.W. Willmarth, “Some experimental results on sphere and disk drag,” AIAA J., 9, 285 (1971).
R. H. Magarvey and R. L. Bishop, “Transition ranges for three-dimensional wakes,” Canad. J. Phys., 39, 1418 (1961).
I. Nakamura, “Steady wake behind a sphere,” Phys. Fluids, 19, 5 (1976).
H. Sakamoto and H. Haniu, “A study on vortex shedding from spheres in a uniform flow,” Trans. ASME: J. Fluid Engng., 112, 386 (1990).
H. Sakamoto and H. Haniu, “The formation mechanism and shedding frequency of vortices from a sphere in uniform shear flow,” J. Fluid Mech., 287, 151 (1995).
S. Shirayama and K. Kuwahara, “Patterns of three-dimensional boundary layer separation,” AIAA Paper, No. 0461 (1987).
U. Dallmann and B. Schulte-Werning, “Topological changes of axisymmetric and non-axisymmetric vortex flows,” in: IUTAM Symposium on Topological Fluid Mechanics, August 1989, Cambridge, UK (1989).
T.A. Johnson and V. C. Patel, “Flow past a sphere up to a Reynolds number of 300,” J. Fluid Mech., 378, 19 (1999).
V.A. Gushchin, A.V. Kostomarov, P.V. Matyushin, and E.R. Pavlyukova, “Direct numerical simulation of the transitional separated fluid flows around a sphere and a circular cylinder,” J. Wind Eng. & Industr. Aerodynamics,” 90, 341 (2002).
V.A. Gushchin and P.V. Matyushin, “Classification of the patterns of separated flows around a sphere at moderate Reynolds numbers,” in: Mathematical Modeling. Problems and Results [in Russian], Nauka, Moscow (2003), p. 199.
P.V. Matyushin, “Numerical simulation of three-dimensional separated flows of a homogeneous incompressible viscous fluid around a sphere,” Thesis submitted for the degree of Candidate of Sciences, Moscow (2003).
V.A. Gushchin, A.V. Kostomarov, and P.V. Matyushin, “3D visualization of the separated fluid flows, ” J. Visualization, 7, 143 (2004).
M. S. Chong, A. E. Perry, and B. J. Cantwell, “A general classification of three-dimensional flow fields,” Phys. Fluids, A2, 765 (1990).
J. Jeong and F. Hussain, “On the identification of a vortex,” J. Fluid Mech., 285, 69 (1995).
A.G. Toumboulides, “Direct and large-eddy simulation of wake flows: flow past a sphere,” PhD Thesis, Princeton Univ. (1993).
R. Natarajan and A. Acrivos, “The instability of the steady flow past spheres and disks,” J. Fluid Mech., 254, 323 (1993).
S. Lee, “A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers,” J. Computers and Fluids, 29, 639 (2000).
R. Mittal and F. M. Najjar, “Vortex dynamics in the sphere wake,” AIAA Paper, No. 3806 (1999).
O. M. Belotserkovskii, V. A. Gushchin, and V. N. Kon’shin, “Splitting method for studying stratified flows with free surfaces,” Zh. Vychisl. Mat. Mat. Fiz., 27, 594 (1987).
V. A. Gushchin and V. N. Konshin, “Computational aspects of the splitting method for incompressible flow with a free surface,” J. Computers and Fluids, 21, 345 (1992).
O. M. Belotserkovskii, Numerical Modeling in Continuum Mechanics [in Russian], Fizmatlit, Moscow (1994).
V. A. Gushchin and P. V. Matyushin, “Numerical modeling of three-dimensional separated flows around a sphere,” Zh. Vychisl. Mat. Mat. Fiz., 37, 1122 (1997).
L. S. Pontryagin, Ordinary Differential Equations [in Russian], Nauka, Moscow (1974).
V. Karlo and T. Tezduyar, “3D computation of unsteady flow past a sphere with a parallel finite element method,” Comput. Methods Appl. Mech. Engng., 151, 267 (1998).
Additional information
__________
Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, 2006, pp. 135–151.
Original Russian Text Copyright © 2006 by Gushchin and Matyushin.
An erratum to this article is available at http://dx.doi.org/10.1134/S0015462807020196.
Rights and permissions
About this article
Cite this article
Gushchin, V.A., Matyushin, R. Vortex formation mechanisms in the wake behind a sphere for 200 < Re < 380. Fluid Dyn 41, 795–809 (2006). https://doi.org/10.1007/s10697-006-0096-x
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10697-006-0096-x