Skip to main content
SpringerLink
Log in

LES and DES Investigations of Turbulent Flow over a Sphere at Re = 10,000

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

Large Eddy Simulation (LES) using a dynamic Smagorinsky type subgridstress (SGS) model and Detached Eddy Simulation (DES) are applied toprediction and investigation of the flow around a sphere at a Reynoldsnumber of 104 in the subcritical regime. In this regime the boundarylayers at separation are laminar, and transition to turbulence occursfarther downstream in the separated shear layers via Kelvin–Helmholtz(K–H) instabilities. The dynamic eddy viscosity model of Germano et al.(Physics of Fluids 3 (1991) 1760–1765) is used in the LES, while the current implementation of the DESemploys a formulation based on the Spalart–Allmaras (S–A) model. DES isa hybrid approach in which the closure is a modification to theproduction/destruction term of the original Reynolds-AveragedNavier–Stokes (RANS) model, reducing to RANS in the attached regions,and to LES away from the wall. In the present work where we simulate theflow over a sphere in the subcritical regime in which the boundarylayers at separation are laminar, DES can be viewed as LES with adifferent SGS model. Effects of the discretization scheme used toapproximate the convective terms are considered, along with sensitivityof predictions to changes in the additional model coefficient, C DES, in the DES formulation. DES and LES yield similar predictions of the wakestructure, large-scale vortex shedding and the Strouhal numberassociated with the low frequency mode in the wake. Predictions ofquantities such as the drag coefficient, wake frequencies, position oflaminar separation on the sphere, and the mean pressure andskin-friction distributions along the sphere are in good agreement withthe measurements of Achenbach (Journal of Fluid Mechanics 54 (1972) 565–575). Predictions of the primaryReynolds shear stress, turbulent kinetic energy, eddy viscosity, andturbulent dissipation for the two models are also similar. In addition,both models successfully resolve the formation of the vortex tubes inthe detached shear layers along with the value of the Strouhal numberassociated with the high frequency instability mode, provided that thelevel of numerical dissipation introduced by the discretization schemeremains sufficiently low. Flow physics investigations are focused onunderstanding the wake structure in the subcritical regime.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Achenbach, E., Experiments on the flow past spheres at very high Reynolds numbers. Journal of Fluid Mechanics 54 (1972) 565–575.

    Google Scholar 

  2. Achenbach, E., Vortex shedding from spheres. Journal of FluidMechanics 62 (1974) 209–221.

    Google Scholar 

  3. Aliabadi, S.K. and Tezduyar, T.E., Parallel fluid dynamics computations in aerospace applications. International Journal of Numerical Methods in Fluids 21 (1995) 783–805.

    Google Scholar 

  4. Arnone, A., Liou, M.S. and Povinelli, L.A., Integration of the Navier-Stokes equations using dual time stepping and a multigrid method. AIAA Journal 33 (1995) 985–990.

    Google Scholar 

  5. Bakic, V., Experimental investigation of turbulent flows around a sphere. Ph.D. Thesis, TUHH Hamburg, Germany (2002).

    Google Scholar 

  6. Ballaras, E, Benocci, C. and Piomelli, U., Two layer approximate boundary conditions for large-scale simulation. AIAA Journal 34 (1996) 1111–1119.

    Google Scholar 

  7. Chomaz, J.M., Bonneton, P. and Hopfinger, E.J., The structure of the near wake of a sphere moving horizontally in a stratified fluid. Journal of Fluid Mechanics 254 (1993) 1–21.

    Google Scholar 

  8. Constantinescu, G.S. and Patel, V.C., A numerical model for simulation of pump-intake flow and vortices. Journal of Hydraulic Engineering 124 (1998) 123–134.

    Google Scholar 

  9. Constantinescu, G.S. and Patel, V.C., Numerical simulation of flow in pump-bays using nearwall turbulence models. IIHR Report No. 394, Iowa Institute of Hydraulic Research, University of Iowa, Iowa City, IA (1998).

    Google Scholar 

  10. Drikakis, D., Development and implementation of parallel high-resolution schemes in 3D flows over bluff bodies. In: Proceedings of the Parallel CFD Conference Implementation and Results Using Parallel Computers. Elsevier Science Publishers, Amsterdam (1995) pp. 191–198.

    Google Scholar 

  11. Gebing, H., Numerische Simulation und topologish-physikalische Analyse der instationären, dreidimensionalen, abgelösten Wirbelströmungen an einer Kugel und an Rotationsellipsoiden. Ph.D. Thesis, Georg-August-Universität, Göttingen, Germany (1994).

    Google Scholar 

  12. Germano, M., Piomelli, U., Moin, P. and Cabot, W.H., A dynamic sub grid scale eddy viscosity model. Physics of Fluids 3 (1991) 1760–1765.

    Google Scholar 

  13. Ghosal, S. and Moin, P., The basic equations for the large eddy simulation of turbulent flows in complex geometry. Journal of Computational Physics 118 (1995) 24–37.

    Google Scholar 

  14. Hadzic, I., Bakic, V. and Peric, M., Numerical and experimental analysis of flow around sphere at subcritical Reynolds number. Paper presented at 10–STAB Workshop, Göttingen, Germany (2001).

  15. Jeong, J. and Hussain, F., On the identification of a vortex. Journal of Fluid Mechanics 285 (1995) 69–94.

    Google Scholar 

  16. Johnson, T.A., Numerical and experimental investigation of the flow past a sphere up to a Reynolds number of 300. Ph.D. Dissertation, Department of Mechanical Engineering, The University of Iowa, Iowa City, IA (1996).

    Google Scholar 

  17. Johnson, T.A. and Patel, V.C., Flow past a sphere up to a Reynolds number of 300. Journal of Fluid Mechanics 378 (1999) 19–70.

    Google Scholar 

  18. Kalro, V. and Tezduyan, T., 3D computation of unsteady flow past a sphere with a parallel finite element method. Computer Methods in Applied Mechanics and Engineering 151 (1998) 267–276.

    Google Scholar 

  19. Kim, D., Choi, H., Large eddy simulation of turbulent flow over a sphere using an immersed boundary method. Paper presented at the Third AFSOR International Conference on Direct Numerical Simulations and Large Eddy Simulations, University of Texas Arlington, TX (2001).

  20. Kim, H.J. and Durbin, P.A., Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation. Physics of Fluids A 31 (1988) 3260–3265.

    Google Scholar 

  21. Koschel, W., Lotzerich, M. and Vornberger, A., Solution on unstructured grids for the Euler and Navier-Stokes equations. AGARD Conference Proceedings 437 (1988) 26–1.

    Google Scholar 

  22. Lilly, D.K., A proposed modification of the Germano sub-grid scale closure method. Physics of Fluids A 4 (1992) 633–635.

    Google Scholar 

  23. Mansoorzadeh, S., Pain, C.C., Oliveira, C.R.E. and Goddard, A.J.H., Finite element simulations of flow past a heated/cooled sphere. International Journal of Numerical Methods in Fluids 28 (1998) 903–915.

    Google Scholar 

  24. Mittal, R., Planar symmetry in the unsteady wake of a sphere. AIAA Journal 37 (1999) 388–390.

    Google Scholar 

  25. Mittal, R. and Moin, P., Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows. AIAA Journal 35 (1997) 1415–1417.

    Google Scholar 

  26. Provansal, M., From the double vortex street behind a cylinder to the wake of a sphere. In: Hourigan, K., Leweke, T., Thompson, M.C. and Williamson, C.H. (eds), Proceedings of the Conference on Bluff Body Wakes and Vortex-Induced Vibration (BBVIV3), Port Douglas, Queensland, December 17–20 (2002).

  27. Roos, F.W. and Willmarth, W.W., Some experimental results on sphere and disk drag. AIAA Journal 9 (1979) 285–291.

    Google Scholar 

  28. Sakamoto, H. and Haniu, H., A study of vortex shedding from spheres in an uniform flow. Journal of Fluids Engineering 112 (1990) 386–392.

    Google Scholar 

  29. Schlichting, H., Boundary-Layer Theory, seventh edition. McGraw-Hill, New York (1979).

    Google Scholar 

  30. Schmid, M., Grobstruktursimulation turbulenter Strömungen auf unstrukturierten Gittern mit einer parallelen Finite-Volumen Methode. Ph.D. Thesis, TUHH Hamburg, Germany (2001).

    Google Scholar 

  31. Seidl, V., Muzaferija, S. and Peric, M., Parallel DNS with local grid refinement. Applied Scienctific Research 59 (1998) 379–394.

    Google Scholar 

  32. Shen, W.Z. and Loc, T.P., Numerical method for unsteady 3D Navier-Stokes equations in velocity-vorticity form. Computers & Fluids 26 (1997) 193–216.

    Google Scholar 

  33. Shirayama, S., Flow past a sphere: Topological transitions in the vorticity field. AIAA Journal 30 (1992) 349–358.

    Google Scholar 

  34. Shur, M.L., Spalart, P.R., Strelets, M.K. and Travin, A.K., Detached-eddy simulation of an airfoil at high angle of attack. Paper presented at the Fourth International Symposium on Engineering Turbulence Modelling and Measurements, Corsica, France (1999).

  35. Spalart, P.R. and Allmaras, S.R., A one-equation turbulence model for aerodynamic flows. La Recherche Aerospatiale 1 (1994) 5–21.

    Google Scholar 

  36. Spalart, P.R., Jou, W.H., Strelets, M. and Allmaras, S.R., Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. Paper presented at the First AFOSR International Conference on DNS/LES, Rouston, LA (1997).

  37. Strelets, M., Detached Eddy Simulation of massively separated flows. AIAA Paper 2001–0879 (2001)

  38. Taneda, S., Experimental investigations of the wake behind a sphere at low Reynolds numbers. Journal Physical Society, Japan 11 (1956) 1104–1108.

    Google Scholar 

  39. Taneda, S., Visual observations of the flow past a sphere at Reynolds numbers between 104 and 106. Journal of Fluid Mechanics 85 (1978) 187–192.

    Google Scholar 

  40. Tomboulides, A.G., Orszag, S.A. and Karniakidis, G.E., Direct and large-eddy simulations of axisymmetric wakes. AIAA Paper 93–0546 (1993)

  41. Tomboulides, A.G. and Orszag, S.A., Numerical investigation of transitional and weak turbulent flow past a sphere. Journal of Fluid Mechanics 416 (2000) 45–73.

    Google Scholar 

  42. Travin, A., Shur, M., Strelets, M. and Spalart, P., Detached-Eddy Simulations past a circular cylinder. Flow, Turbulence, and Combustion 63 (2000) 293–313.

    Google Scholar 

  43. Travin, A., Shur, M., Strelets, M. and Spalart, P., Physical and numerical upgrades in the Detached-Eddy Simulations of complex turbulent flows. Paper presented at the 412th Euromech Colloquium on LES and Complex Transitional and Turbulent Flows, Munich, Germany (2000).

Download references

Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, 94305-3030, U.S.A.

    G.S. Constantinescu

  2. Mechanical and Aerospace Engineering Department, Arizona State University, Box 876106, Tempe, AZ, 85287-6106, U.S.A

    K.D. Squires

Authors
  1. G.S. Constantinescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K.D. Squires
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Constantinescu, G., Squires, K. LES and DES Investigations of Turbulent Flow over a Sphere at Re = 10,000. Flow, Turbulence and Combustion 70, 267–298 (2003). https://doi.org/10.1023/B:APPL.0000004937.34078.71

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:APPL.0000004937.34078.71

Search

Navigation