Dynamic Variational Multiscale LES of Bluff Body Flows on Unstructured Grids
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55450", author = "Carine Moussaed and Stephen Wornom and Bruno Koobus and Maria Vittoria Salvetti and Alain Dervieux and ", title = "Dynamic Variational Multiscale LES of Bluff Body Flows on Unstructured Grids", 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.", volume = "7", number = "5", pages = "817-8", }
