Hostname: page-component-599cfd5f84-8nxqw Total loading time: 0 Render date: 2025-01-07T08:03:00.415Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulation of the flow over a sphere at Re = 3700

Published online by Cambridge University Press:  19 May 2011

IVETTE RODRIGUEZ ,
RICARD BORELL ,
ORIOL LEHMKUHL ,
CARLOS D. PEREZ SEGARRA  and
ASSENSI OLIVA
IVETTE RODRIGUEZ
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), 08222Spain
RICARD BORELL
Affiliation:
Termo Fluids S.L., 08222Spain
ORIOL LEHMKUHL
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), 08222Spain Termo Fluids S.L., 08222Spain
CARLOS D. PEREZ SEGARRA
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), 08222Spain
ASSENSI OLIVA*
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC), Universitat Politècnica de Catalunya (UPC), 08222Spain
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The direct numerical simulation of the flow over a sphere is performed. The computations are carried out in the sub-critical regime at Re = 3700 (based on the free-stream velocity and the sphere diameter). A parallel unstructured symmetry-preserving formulation is used for simulating the flow. At this Reynolds number, flow separates laminarly near the equator of the sphere and transition to turbulence occurs in the separated shear layer. The vortices formed are shed at a large-scale frequency, St = 0.215, and at random azimuthal locations in the shear layer, giving a helical-like appearance to the wake. The main features of the flow including the power spectra of a set of selected monitoring probes at different positions in the wake of the sphere are described and discussed in detail. In addition, a large number of turbulence statistics are computed and compared with previous experimental and numerical data at comparable Reynolds numbers. Particular attention is devoted to assessing the prediction of the mean flow parameters, such as wall-pressure distribution, skin friction, drag coefficient, among others, in order to provide reliable data for testing and developing statistical turbulence models. In addition to the presented results, the capability of the methodology used on unstructured grids for accurately solving flows in complex geometries is also pointed out.

JFM classification

Turbulent Flows: Turbulence simulation Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 263 - 287
Copyright
Copyright © Cambridge University Press 2011

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

REFERENCES

Achenbach, E. 1972 Experiments on the flow past spheres at very high Reynolds numbers. J. Fluid Mech. 54, 565–575.CrossRefGoogle Scholar
Achenbach, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62 (2), 209–221.CrossRefGoogle Scholar
Bakic, V., Schmid, M. & Stankovic, B. 2006 Experimental investigation of turbulent structures of the flow around a sphere. Intl J. Therm. Sci. 10 (2), 97–112.CrossRefGoogle Scholar
Berger, E., Cholz, D. & Schumm, M. 1990 Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations. J. Fluids Struct. 4 (3), 231–257.CrossRefGoogle Scholar
Constantinescu, G. & Squires, K. 2003 LES and DES investigations of turbulent flow over a sphere at Re = 10000. Flow Turbul. Combust. 70, 267–298.CrossRefGoogle Scholar
Constantinescu, G. & Squires, K. 2004 Numerical investigations of flow over a sphere in the subcritical and supercritical regimes. Phys. Fluids 16 (5), 1449–1466.CrossRefGoogle Scholar
Davis, P. J. 1979 Circulant Matrices. Wiley-Interscience.Google Scholar
Felten, F. N. & Lund, T. S. 2006 Kinetic energy conservation issues associated with the collocated mesh scheme for incompressible flow. J. Comput. Phys. 215 (2), 465–484.CrossRefGoogle Scholar
Gray, R. M. 2006 Toeplitz and circulant matrices: a review. Found. Trends Commun. Inform. Theory 2, 155–239.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream and convergence zones in turbulent flows. Tech. Rep. CTR-S88. Center for Turbulent Research.Google Scholar
Jang, Y. I. & Lee, S. J. 2007 Visualization of turbulent flow around a sphere at subcritical Reynolds numbers. J. Vis. 10 (4), 359–366.CrossRefGoogle Scholar
Kim, H. J. & Durbin, P. A. 1988 Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Phys. Fluids 31 (11), 3260–3265.CrossRefGoogle Scholar
Mittal, R. & Najjar, F. M. 1999 Vortex dynamics in the sphere wake. AIAA Paper 99-3806.CrossRefGoogle Scholar
Morinishi, Y., Lund, T. S., Vasilyev, O. V. & Moin, P. 1998 Fully conservative higher order finite difference schemes for incompressible flow. J. Comput. Phys. 143 (1), 90–124.CrossRefGoogle Scholar
Norberg, C. 1998 LDV-measurements in the near wake of a circular cylinder. In Advances in Understanding of Bluff Body Wakes and Vortex-Induced Vibration: Proceedings of the 1998 Conference, Washington, DC.Google Scholar
Ploumhans, P., Winckelmans, G. S., Salmon, J. K., Leonard, A. & Warren, M. S. 2002 Vortex methods for a direct numerical simulation of three-dimensional bluff body flows: applications to the sphere at Re = 300, 500 and 1000. J. Comput. Phys. 178, 427–463.CrossRefGoogle Scholar
Prasad, A. & Williamson, C. H. K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375–402.CrossRefGoogle Scholar
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21, 1525–1532.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1990 A study on vortex shedding from spheres in a uniform flow. J. Fluids Engng 112, 386–392.CrossRefGoogle Scholar
Schlichting, H. 1979 Boundary Layer Theory, 7th edn. McGraw-HillGoogle Scholar
Seidl, V., Muzaferija, S. & Peric, M. 1998 Parallel DNS with local grid refinement. Appl. Sci. Res. 59, 379–394.CrossRefGoogle Scholar
Soria, M., Pérez-Segarra, C. D. & Oliva, A. 2002 A direct parallel algorithm for the efficient solution of the pressure-correction equation of incompressible flow problems using loosely coupled computers. Numer. Heat Transfer B 41, 117–138.CrossRefGoogle Scholar
Soria, M., Pérez-Segarra, C. D. & Oliva, A. 2003 A direct Schur–Fourier decomposition for the solution of the three-dimensional Poisson equation of incompressible flow using loosely coupled parallel computers. Numer. Heat Transfer B 43 (5), 467–488.CrossRefGoogle Scholar
Swarztrauber, P. N. 1977 The methods of cyclic reduction, Fourier analysis and the FACR algorithm for the discrete solution of Poisson's equation on a rectangle. SIAM Rev. 19, 490–501.CrossRefGoogle Scholar
Taneda, S. 1978 Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106. J. Fluids Mech. 85 (1), 187–192.CrossRefGoogle Scholar
Tomboulides, A. & Orszag, S. A. 2000 Numerical investigation of transitional and weak turbulent flow past a sphere. J. Fluids Mech. 416, 45–73.CrossRefGoogle Scholar
Tomboulides, A. G., Orszag, S. A. & Karniadakis, G. E. 1993 Direct and large-eddy simulation of axisymmetric wakes. In 31st Aerospace Sciences Meeting and Exhibit, AIAA Paper 93-0546.Google Scholar
Verstappen, R. W. C. P. & Veldman, A. E. P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187, 343–368.CrossRefGoogle Scholar
Yun, G., Kim, D. & Choi, H. 2006 Vortical structures behind a sphere at subcritical Reynolds numbers. Phys. Fluids 18.CrossRefGoogle Scholar

Rodriguez et al. supplementary movie

Instantaneous vortical structures in the wake of the sphere, at Re=3700, represented by means of the Q-criterion. The flow separates from the sphere at 89.5°. The separated shear layer is laminar up to a certain distance where instabilities of the flow appear (x/D=1.0-1.2). The instabilities grow resulting in turbulent flow (x/D=1.8-2.0). Vortices are shed in random azimuthal positions at St=0.215. Even though the wake has a helical appearance, vortices move downstream without rotation.

Download Rodriguez et al. supplementary movie(Video)
Video 5 MB