Dynamic Variational Multiscale LES of Bluff Body Flows on Unstructured Grids

Authors: Carine Moussaed, Stephen Wornom, Bruno Koobus, Maria Vittoria Salvetti, Alain Dervieux,

Abstract:

The effects of dynamic subgrid scale (SGS) models are investigated in variational multiscale (VMS) LES simulations of bluff body flows. The spatial discretization is based on a mixed finite element/finite volume formulation on unstructured grids. In the VMS approach used in this work, the separation between the largest and the smallest resolved scales is obtained through a variational projection operator and a finite volume cell agglomeration. The dynamic version of Smagorinsky and WALE SGS models are used to account for the effects of the unresolved scales. In the VMS approach, these effects are only modeled in the smallest resolved scales. The dynamic VMS-LES approach is applied to the simulation of the flow around a circular cylinder at Reynolds numbers 3900 and 20000 and to the flow around a square cylinder at Reynolds numbers 22000 and 175000. It is observed as in previous studies that the dynamic SGS procedure has a smaller impact on the results within the VMS approach than in LES. But improvements are demonstrated for important feature like recirculating part of the flow. The global prediction is improved for a small computational extra cost.

Keywords: variational multiscale LES, dynamic SGS model, unstructured grids, circular cylinder, square cylinder.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1332498

References:

[1] J.D. Anderson. Fundamentals of Aerodynamics, Second Edition, McGraw-Hill, New York, 1991.
[2] S. Aradag. Unsteady turbulent vortex structure downstream of a three dimensional cylinder, J. of Thermal Science and Technology, 29(1):91- 98, 2009.
[3] H. Baya Toda, K. Truffin and F. Nicoud. Is the dynamic procedure appropriate for all SGS model. V European Conference on Computational Fluid Dynamics, ECCOMAS CFD, J.C.F. Pereira and A. Sequeira (Eds), Lisbon, Portugal, 14-17 June 2010.
[4] S. Camarri, M.V. Salvetti, B. Koobus, and A. Dervieux. A low diffusion MUSCL scheme for LES on unstructured grids. Comp. Fluids, 33:1101- 1129, 2004.
[5] C. Farhat, B. Koobus and H. Tran. Simulation of vortex shedding dominated flows past rigid and flexible structures.Computational Methods for Fluid-Structure Interaction, 1-30, 1999.
[6] C. Farhat, A. Rajasekharan, B. Koobus. A dynamic variational multiscale method for large eddy simulations on unstructured meshes. Comput. Methods Appl. Mech. Engrg., 195 (2006) 1667-1691.
[7] V. Gravemeier. Variational Multiscale Large Eddy Simulation of turbulent Flow in a Diffuser. Computational Mechanics, 39(4):477:495, 2012.
[8] M. Germano, U. Piomelli, P. Moin, W.H. Cabot. A Dynamic Subgrid- Scale Eddy Viscosity Model. Physics of Fluids, A 3, 1760-1765, 1991.
[9] S. Ghosal, T. Lund, P. Moin and K. Akselvoll. The dynamic localization model for large eddy simulation of turbulent flows. J. Fluid Mech.,286:229-255, 1995.
[10] T.J.R. Hughes, L.Mazzei, and K.E. Jansen. Large-eddy simulation and the variational multiscale method. Comput. Vis. Sci., 3:47-59, 2000.
[11] B. Koobus and C. Farhat. A variational multiscale method for the large eddy simulation of compressible turbulent flows on unstructured meshesapplication to vortex shedding. Comput. Methods Appl. Mech. Eng., 193:1367-1383, 2004.
[12] M.H. Lallemand, H. Steve, and A. Dervieux. Unstructured multigridding by volume agglomeration : current status. Comput. Fluids, 21:397-433, 1992.
[13] D. K. Lilly. A proposed modification of the Germano subgrid scale closure model. Physics of Fluids A, 4:633-635, 1992.
[14] H. Lim and S. Lee. Flow Control of Circular Cylinders with Longitudinal Grooved Surfaces, AIAA Journal, 40(10):2027-2035, 2002.
[15] Tiancheng Liu, Gao Liu, Yaojun Ge, Hongbo Wu, Wenming Wu. Extended lattice Boltzmann equation for simulation of flows around bluff bodies in high Reynolds number BBAA VI International Colloquium on Bluff Bodies Aerodynamics and Applications, Milano, Italy, July, 20-24 2008
[16] S. C. Luo and MdG. Yazdani and Y. T. Chew and T. S. Lee, Effects of incidence and afterbody shape on flow past bluff cylinders, J. Ind. Aerodyn., 53:375-399, 1994.
[17] D. A. Lyn and W. Rodi The flapping shear layer formed by flow separation from the forward corner of a square cylinder J. Fluid Mech. 261:353-316, 1994.
[18] D. A. Lyn, S. Einav, W. Rodi and J-H. Park, A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder. J . Fluid Mech. 304:285-319, 1995.
[19] R. Martin and H. Guillard. A second-order defect correction scheme for unsteady problems. Comput. and Fluids, 25(1):9-27, 1996.
[20] W. Rodi, J.H. Ferziger, M. Breuer and M. Pourqui "Status of Large Eddy Simulation: Results of a Workshop" J. Fluids Engineering, Transactions of the ASME, 119, 248-262, (1997).
[21] F. Nicoud and F. Ducros. Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow Turb. Comb., 62(3):183-200, 1999.
[22] C. Norberg. Fluctuating lift on a circular cylinder: review and new measurements. J. Fluids Struct., 17:57-96, 2003.
[23] S. Wornom, H. Ouvrard, M.-V. Salvetti, B. Koobus, A. Dervieux. Variational multiscale large-eddy simulations of the flow past a circular cylinder : Reynolds number effects. Computer and Fluids, 47(1):44-50, 2011.
[24] H. Ouvrard, B. Koobus, A. Dervieux, and M.V. Salvetti. Classical and variational multiscale LES of the flow around a circular cylinder on unstructured grids. Computer and Fluids, 39(7):1083-1094, 2010.
[25] P. L. Roe. Approximate Riemann solvers, parameters, vectors and difference schemes. J. Comp. Phys, 43:357-371, 1981.
[26] E. Salvatici and M.V. Salvetti, Large-eddy simulations of the flow around a circular cylinder: effects of grid resolution and subgrid scale modeling, Wind & Structures, 6(6):419-436, 2003.
[27] J. Smagorinsky, General circulation experiments with the primitive equations. Month. Weath. Rev., 91(3) :99-164, 1963.
[28] B. Van. Leer. Towards the ultimate conservative scheme. IV :A new approach to numerical convection. J. Comp. Phys., 23:276-299, 1977.
[29] R.W.C.P. Verstappen and A.E.P. Veldman, Direct numerical simulation of turbulence at lower costs. Journal of Engineering Mathematics 32:143159, 1997.