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An Implicitly Consistent Formulation of a Dual-Mesh Hybrid LES/RANS Method

Part of: Turbulence

Published online by Cambridge University Press:  07 February 2017

Heng Xiao ,
Jian-Xun Wang  and
Patrick Jenny
Heng Xiao*
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA 24060, USA
Jian-Xun Wang*
Affiliation:
Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg, VA 24060, USA
Patrick Jenny*
Affiliation:
Institute of Fluid Dynamics, ETH Zürich, 8092 Zurich, Switzerland
*
*Corresponding author.Email addresses:[email protected] (H. Xiao), [email protected] (J.-X.Wang), [email protected] (P. Jenny)
*Corresponding author.Email addresses:[email protected] (H. Xiao), [email protected] (J.-X.Wang), [email protected] (P. Jenny)
*Corresponding author.Email addresses:[email protected] (H. Xiao), [email protected] (J.-X.Wang), [email protected] (P. Jenny)
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Abstract

A consistent dual-mesh hybrid LES/RANS framework for turbulence modeling has been proposed recently (H. Xiao, P. Jenny, A consistent dual-mesh framework for hybrid LES/RANS modeling, J. Comput. Phys. 231 (4) (2012)). To better enforce componentwise Reynolds stress consistency between the LES and the RANS simulations, in the present work the original hybrid framework is modified to better exploit the advantage of more advanced RANS turbulence models. In the new formulation, the turbulent stresses in the filtered equations in the under-resolved regions are directly corrected based on the Reynolds stresses provided by the RANS simulation. More precisely, the new strategy leads to implicit LES/RANS consistency, where the velocity consistency is achieved indirectly via imposing consistency on the Reynolds stresses. This is in contrast to the explicit consistency enforcement in the original formulation, where forcing terms are added to the filtered momentum equations to achieve directly the desired average velocity and velocity fluctuations. The new formulation keeps the averaging procedure for the filtered quantities and at the same time preserves the ability of the original formulation to conform with the physical differences between LES and RANS quantities. The modified formulation is presented, analyzed, and then evaluated for plane channel flow and flow over periodic hills. Improved predictions are obtained compared with the results obtained using the original formulation.

Keywords

Hybrid LES/RANS methodsturbulence modelingwall-bounded flow

MSC classification

Secondary: 76F65: Direct numerical and large eddy simulation of turbulence
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 2 , February 2017 , pp. 570 - 599
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Piomelli, U. and Balaras, E.. Wall-layer models for large-eddy simulations. Annual Review of Fluid Mechanics, 34:349–374, 2002.CrossRefGoogle Scholar
[2] Chapman, D. R.. Computational aerodynamics: development and outlook. AIAA Journal, 17: 1293–313, 1979.CrossRefGoogle Scholar
[3] Choi, H. and Moin, P.. Grid-point requirements for large eddy simulation: Chapman's estimates revisited. Physics of Fluids, 24(1):011702, 2012.CrossRefGoogle Scholar
[4] Xiao, H. and Jenny, P.. A consistent dual-mesh framework for hybrid LES/RANS modeling. Journal of Computational Physics, 231(4):1848–1865, 2012.CrossRefGoogle Scholar
[5] OpenCFD Ltd. The open source CFD toolbox. URL: http://www.openfoam.com, 2011.Google Scholar
[6] Xiao, H., Wild, M., and Jenny, P.. Preliminary evaluation and applications of a consistent hybrid LES–RANS method. In Fu, S., editor, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 117. Springer, 2012.Google Scholar
[7] Xiao, H., Sakai, Y., Heninger, R., Wild, M., and Jenny, P.. Coupling of solvers with non-conforming computational domains in a dual-mesh hybrid LES/RANS framework. Computers and Fluids, 88, 2013.CrossRefGoogle Scholar
[8] Henninger, R.. IMPACT simulation code. URL \url{http://www.ifd.mavt.ethz.ch/research/group_lk/projects/impact}. Retrieved July 2012.Google Scholar
[9] Henniger, R., Obrist, D., and Kleiser, L.. High-order accurate solution of the incompressible Navier–Stokes equations on massively parallel computers. Journal of Computational Physics, 229(10):3543–3572, 2010.CrossRefGoogle Scholar
[10] Launder, B. E. and Sharma, B. I.. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Letters in Heat andMass Transfer, 1(2):131–138, 1974.CrossRefGoogle Scholar
[11] Billard, F.. Development of a robust elliptic-blending turbulence model for near-wall, separated and buoyant flows. PhD thesis, University of Manchester, 2011. Chapter 6.Google Scholar
[12] Durbin, P. A.. A Reynolds stress model for near-wall turbulence. Journal of Fluid Mechanics, 249:465–498, 1993a.CrossRefGoogle Scholar
[13] Launder, B.E., Reece, G.J., and Rodi, W.. Progress in development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics, 68:537–566, 1975.CrossRefGoogle Scholar
[14] Manceau, R. and Hanjalic, K.. A new form of the elliptic relaxation equation to account for wall effects in RANS modeling. Physics of Fluids, 12(9):2345–2351, 2000.CrossRefGoogle Scholar
[15] Manceau, R. and Hanjalic, K.. Elliptic blending model: A new near-wall Reynolds-stress turbulence closure. Physics of Fluids, 14(2):744–754, 2002.CrossRefGoogle Scholar
[16] Wizman, V., Laurence, D., Kanniche, M., Durbin, P., and Demuren, A.. Modeling near-wall effects in second-moment closures by elliptic relaxation. International Journal of Heat and Fluid Flow, 17(3):255–266, 1996.CrossRefGoogle Scholar
[17] Pettersson, B.A. and Andersson, H.I.. Near-wall Reynolds-stress modelling in noninertial frames of reference. Fluid Dynamics Research, 19(5):251–276, 1997.CrossRefGoogle Scholar
[18] 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. In First AFOSR International Conference on DNS/LES. Greyden Press, Ruston, Louisiana, August 1997.Google Scholar
[19] Girimaji, S. S.. Partially-averaged Navier-Stokes model for turbulence: A Reynolds-averaged Navier-Stokes to direct numerical simulation bridging method. Journal of Applied Mechanics, 73(3):413, 2006.CrossRefGoogle Scholar
[20] Schiestel, R. and Dejoan, A.. Towards a new partially integrated transport model for coarse grid and unsteady turbulent flow simulations. Theoretical and Computational Fluid Dynamics, 18(6):443–468, 2004.CrossRefGoogle Scholar
[21] Fadai-Ghotbi, A., Friess, C., Manceau, R., and Boree, J.. A seamless hybrid RANS–LES model based on transport equations for the subgrid stresses and elliptic blending. Physics of Fluids, 22(5):055104, 2010.CrossRefGoogle Scholar
[22] Schiestel, R.. Multiple-time-scale modeling of turbulent flows in one-point closures. Physics of Fluids, 30(3):722, 1987.CrossRefGoogle Scholar
[23] Sagaut, P., Deck, S., and Terracol, M.. Multiscale and Multiresolution Approaches in Turbulence. Imperial College Press, 2006.CrossRefGoogle Scholar
[24] Speziale, C.. Turbulence modeling for time-dependent RANS and VLES: A review. AIAA Journal, 36:173–184, 1998.CrossRefGoogle Scholar
[25] Chen, S., Xia, Z., Pei, S., Wang, J., Yang, Y., Xiao, Z., and Shi, Y.. Reynolds-stress-constrained large-eddy simulation of wall-bounded turbulent flows. Journal of Fluid Mechanics, 703:1–28, 2012.CrossRefGoogle Scholar
[26] Shi, Y., Xiao, Z., and Chen, S.. Constrained subgrid-scale stress model for large eddy simulation. Physics of Fluids, 20(1):011701, 2008.CrossRefGoogle Scholar
[27] Fröhlich, J. and von Terzi, D.. Hybrid LES/RANS methods for the simulation of turbulent flows. Progress in Aerospace Sciences, 44(5):349–377, 2008.CrossRefGoogle Scholar
[28] Baggett, J. S.. On the feasibility of merging LES with RANS for the near-wall region of attached turbulent flows. In Annual Research Briefs, pages 267–277. Center for Turbulence Research, 1998.Google Scholar
[29] Chen, S., Chen, Y., Xia, Z., Qu, K., Shi, Y., Xiao, Z., Liu, Q., Cai, Q., Liu, F., Lee, C., et al. Constrained large-eddy simulation and detached eddy simulation of flow past a commercial aircraft at 14 degrees angle of attack. Science China: Physics, Mechanics and Astronomy, 56(2): 270–276, 2013.Google Scholar
[30] Xia, Z., Shi, Y., Hong, R., Xiao, Z., and Chen, S.. Constrained large-eddy simulation of separated flow in a channel with streamwise-periodic constrictions. Journal of Turbulence, 14(1):1–21, 2013.CrossRefGoogle Scholar
[31] Xu, Q. and Yang, Y.. Reynolds stress constrained large eddy simulation of separation flows in a U-duct. Propulsion and Power Research, 3(2):49–58, 2014.CrossRefGoogle Scholar
[32] Pope, S. B.. Turbulent Flows. Cambridge University Press, Cambridge, 2000.CrossRefGoogle Scholar
[33] Spalart, P. R. and Allmaras, S. R.. A one-equation turbulence model for aerodynamic flows. In Proceedings of the 30th Aerospace Sciences Meeting and Exibit. AIAA, January 6-9 1992. Paper number: AIAA-92-0439.CrossRefGoogle Scholar
[34] Uribe, J. C., Jarrin, N., Prosser, R., and Laurence, D.. Development of a two-velocities hybrid RANS–LES model and its application to a trailing edge flow. Flow Turbulence Combustion, 85 (2):181–197, 2010.CrossRefGoogle Scholar
[35] Weller, H. G., Tabor, G., Jasak, H., and Fureby, C.. A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in Physics, 12(6):620–631, 1998. doi: 10.1063/1.168744.CrossRefGoogle Scholar
[36] Issa, R. I.. Solution of the implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics, 62:40–65, 1986.CrossRefGoogle Scholar
[37] Rhie, C. M. and Chow, W. L.. A numerical study of the turbulent flow past an isolated airfoil with trailing edge separation. AIAA, 21(11):1525–1532, 1983.CrossRefGoogle Scholar
[38] Durbin, P.. Application of a near-wall turbulence model to boundary layers and heat transfer. International Journal of Heat and Fluid Flow, 14(4):316–323, 1993b.CrossRefGoogle Scholar
[39] Yoshizawa, A. and Horiuti, K.. A statistically-derived subgrid-scale kinetic energy model for the large-eddy-simulation of turbulent flows. Journal of Physical Society of Japan, 54:2834–2839, 1985.CrossRefGoogle Scholar
[40] Horiuti, K.. Large eddy simulation of turbulent channel flow by one-equation modeling. Journal of the Physical Society of Japan, 54:2855–2865, 1985.CrossRefGoogle Scholar
[41] Fureby, C., Tabor, G., Weller, H. G., and Gosman, A. D.. Comparative study of subgrid scale models in homogeneous isotropic turbulence. Physics of Fluids, 9(5), 1997.CrossRefGoogle Scholar
[42] Xiao, H. and Jenny, P.. Dynamic evaluation of mesh resolution in hybrid LES/RANS methods. Flow, Turbulence and Combustion, 93, 2014.CrossRefGoogle Scholar
[43] Moser, R. D., Kim, J. D., and Mansour, N.N.. Direct numerical simulation of turbulent channel flow up to Reτ =590. Physics of Fluids, 11:943–945, 1999.CrossRefGoogle Scholar
[44] Saric, S., Jakirlic, S., Breuer, M., Jaffrezic, B., Deng, G., Chikhaoui, O., Fröhlich, J., von Terzi, D., Manhart, M., and Peller, N.. Evaluation of detached eddy simulations for predicting the flow over periodic hills. In ESAIM: Proceedings, volume 16, pages 133–145, 2007. doi: 10.1051/proc:2007016.Google Scholar
[45] Breuer, M., Peller, N., Rapp, Ch., and Manhart, M.. Flow over periodic hills: Numerical and experimental study in a wide range of Reynolds numbers. Computers & Fluids, 38(2):433–457, 2009.CrossRefGoogle Scholar
[46] Frohlich, J., Mellen, C.P., Rodi, W., Temmerman, L., and Leschziner, M.A.. Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. Journal of Fluid Mechanics, 526:19–66, 2005.CrossRefGoogle Scholar
[47] Spalart, P. R.. Young person's guide to detached-eddy simulation grids. Technical Report CR-2001-211032, NASA, 2001.Google Scholar