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An Improved Second-Order Finite-Volume Algorithm for Detached-Eddy Simulation Based on Hybrid Grids

Part of: Turbulence Basic methods in fluid mechanics Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  21 July 2016

Yang Zhang ,
Laiping Zhang ,
Xin He  and
Xiaogang Deng
Yang Zhang*
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China Low Speed Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China
Laiping Zhang*
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China
Xin He*
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China
Xiaogang Deng*
Affiliation:
National University of Defense Technology, Changsha Hunan 410073, China
*
*Corresponding author. Email addresses:[email protected] (Y. Zhang), [email protected] (L. Zhang), [email protected] (X. He), [email protected] (X. Deng)
*Corresponding author. Email addresses:[email protected] (Y. Zhang), [email protected] (L. Zhang), [email protected] (X. He), [email protected] (X. Deng)
*Corresponding author. Email addresses:[email protected] (Y. Zhang), [email protected] (L. Zhang), [email protected] (X. He), [email protected] (X. Deng)
*Corresponding author. Email addresses:[email protected] (Y. Zhang), [email protected] (L. Zhang), [email protected] (X. He), [email protected] (X. Deng)
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Abstract

A hybrid grid based second-order finite volume algorithm has been developed for Detached-Eddy Simulation (DES) of turbulent flows. To alleviate the effect caused by the numerical dissipation of the commonly used second order upwind schemes in implementing DES with unstructured computational fluid dynamics (CFD) algorithms, an improved second-order hybrid scheme is established through modifying the dissipation term of the standard Roe's flux-difference splitting scheme and the numerical dissipation of the scheme can be self-adapted according to the DES flow field information. By Fourier analysis, the dissipative and dispersive features of the new scheme are discussed. To validate the numerical method, DES formulations based on the two most popular background turbulence models, namely, the one equation Spalart-Allmaras (SA) turbulence model and the two equation k–ω Shear Stress Transport model (SST), have been calibrated and tested with three typical numerical examples (decay of isotropic turbulence, NACA0021 airfoil at 60° incidence and 65° swept delta wing). Computational results indicate that the issue of numerical dissipation in implementing DES can be alleviated with the hybrid scheme, the resolution for turbulence structures is significantly improved and the corresponding solutions match the experimental data better. The results demonstrate the potentiality of the present DES solver for complex geometries.

Keywords

Detached-Eddy simulationsecond order schemeself-adaptive dissipationhybrid gridfinite-volume method

MSC classification

Secondary: 76F99: None of the above, but in this section 76M12: Finite volume methods 65L80: Methods for differential-algebraic equations
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016 , pp. 459 - 485
Copyright
Copyright © Global-Science Press 2016 

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References

[1] Safaei, M.R., Togun, H. and Vafai, K. et al. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT Nano fluids. Numer. Heat Transfer, Part A, 66(12): 1321–1340, 2014.Google Scholar
[2] Jiang, Z., Xiao, Z.L. and Shi, Y.P. et al. Constrained large-eddy simulation of wall-bounded compressible turbulent flows. Phys. Fluids, 25(106102):1–28, 2013.Google Scholar
[3] Strelets, M.. Detached eddy simulation of massively separated flows. AIAA paper 2001-0879, 2001.Google Scholar
[4] Bunge, U.. Guidelines for implementing Detached-Eddy Simulation using different models. Aerospace Science and Technology, 11: 376–385, 2007.Google Scholar
[5] Spalart, P.R., Jou, W.H. and Strelets, M. et al. Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach. Proceedings of 1st AFOSR International Conference On DNS/LES. Greyden Press, Columbus, 1997.Google Scholar
[6] Travin, A., Shur, M. and Strelets, M. et al. Physical and numerical upgrades in the detached-eddy simulation of complex turbulent flows. Advances in LES of Complex Flows. Springer-Verlag, Berlin, Heidelberg, 2004.Google Scholar
[7] Spalart, P.R., Deck, S. and Shur, M. et al. A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn., 20(3): 181–195, 2006.Google Scholar
[8] Menter, F. and Kuntz, M.. Adaption of eddy-viscosity turbulence models to unsteady separated flow behind vehicles. In: The Aerodynamics of Heavy Vehicles: Trucks, Buses, and Trains. Lecture Notes in Applied and Computational Mechanics. Springer-Verlag, Berlin, Heidelberg, 2004.Google Scholar
[9] Nikitin, N., Nicoud, F. and Wasistho, B. et al. An approach to wall modeling in large-eddy simulations. Phys. Fluids, 12(7): 1629–1632, 2000.CrossRefGoogle Scholar
[10] Shur, M., Spalart, P.R. and Strelets, M. et al. A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Int. J. Heat Fluid Flow, 29(6): 1638–1649, 2008.Google Scholar
[11] Xiao, Z.X., Liu, J. and Huang, J.B. et al. Numerical dissipation effects on massive separation around tandem cylinders. AIAA J., 50(5): 1119–1136, 2012.Google Scholar
[12] Mittal, R. and Moin, P.. Suitability of upwind-biased finite difference schemes for large-eddy simulation of turbulent flows. AIAA J., 35(8): 1415–1417, 1997.Google Scholar
[13] Moin, P.. Numerical and physical issues in large eddy simulation of turbulent flows. JSME Int. J., Series B, 41(2): 454–463, 1998.Google Scholar
[14] Bui, T.T.. A parallel, finite-volume algorithm for large-eddy simulation of turbulent flow. Comput. Fluids, 2000, 29(8): 877–915.Google Scholar
[15] Roe, P.L.. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 43: 357–372, 1981.Google Scholar
[16] Xiao, L.H., Xiao, Z.X. and Duan, Z.W. et al. Improved-Delayed-Detached-Eddy simulation of cavity-Induced transition in hypersonic boundary layer. Proceedings of The Eighth International Conference on Computational Fluid dynamics. ICCFD8-2014-0247, pp. 1055–1073, Chengdu, China, 2014.Google Scholar
[17] Deng, X.B., Zhao, X.H. and Yang, W. et al. Dynamic adaptive upwind method and it's applications in RANS/LES hybrid simulations. Proceedings of The Eighth International Conference on Computational Fluid dynamics. ICCFD8-2014-0164, pp. 807–814, Chengdu, China, 2014.Google Scholar
[18] Charest, M.R.J., Groth, C.P.T. and Gauthier, P.Q.. A high-order central ENO finite-volume scheme for three-dimensional low-speed viscous flows on unstructured mesh. Commun. Comput. Phys., 17(3): 615–656, 2015.Google Scholar
[19] Hughes, T.J.R., Franca, L.P. and Hulbert, G.M.. A new finite element formulation for computational fluid dynamics VIII: The Galerkin least squares method for advective-diffusive equations. Comp. Meth. Appl. Mech. Eng., 73(2): 173-89, 1989.Google Scholar
[20] Li, Z.Z., Yu, X.J. and Zhu, J. et al. A Runge Kutta discontinuous Galerkin method for Lagrangian compressible Euler equations in two-dimensions. Commun. Comput. Phys., 15(4): 1184–1206, 2014.Google Scholar
[21] Zhang, L.P., Liu, W. and He, L.X. et al. A class of hybrid DG/FV methods for conservation laws I: Basic formulation and one-dimensional systems. J. Comput. Phys., 231(4): 1081–1103, 2012.Google Scholar
[22] Zhang, L.P., Liu, W. and He, L.X. et al. A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases. J. Comput. Phys., 231(4): 1104–1120, 2012.Google Scholar
[23] Zhang, L.P., Liu, W. and He, L.X. et al. A class of hybrid DG/FV methods for conservation laws III: Two-dimensional Euler equations. J. Comput. Phys., 12(1): 284–314, 2012.Google Scholar
[24] Wang, Z.J.. Spectral (finite) volume method for conservation laws on unstructured grids I: Basic formulation. J. Comput. Phys., 178(2): 210–251, 2002.Google Scholar
[25] Wang, Z.J. and Liu, Y.. The spectral difference method for the 2D Euler equations on unstructured grids. AIAA paper 2005-5112, 2005.CrossRefGoogle Scholar
[26] Huynh, H.T.. A reconstruction approach to high-order schemes including discontinuous Galerkin for diffusion. AIAA paper 2009-403, 2009.Google Scholar
[27] He, X., Zhang, L.P. and Zhao, Z. et al. Research and development of structured/unstructured hybrid CFD software. Transactions of Nanjing University of Aeronautics & Astronautics, 30(S): 116–120, 2013.Google Scholar
[28] He, X., He, X.Y., He, L., Zhao, Z., Zhang, L.P.. HyperFLOW: A structured/unstructured hybrid integrated computational environment for multi-purpose fluid simulation. Procedia Engineering 126: 645–649, 2015.Google Scholar
[29] Shu, C.W.. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. NASA CR-97-206253, ICASE Report No. 97-65, 1997.Google Scholar
[30] Spalart, P.R. and Allmaras, S.R.. A one-equation turbulence model for aerodynamic flows. AIAA paper 92-0439, 1992.CrossRefGoogle Scholar
[31] Menter, F.. Zonal two-equation k–ω turbulence models for aerodynamic flows. AIAA paper 93-2906, 1993.Google Scholar
[32] Gritskevich, M.S., Garbaruk, A.V. and Schütze, J. et al. Development of DDES and IDDES formulations for the k–ω shear stress transport model. Flow Turbul. Combust, 88(3): 431–449, 2012.Google Scholar
[33] Comte-Bellot, G. and Corrsin, S.. Simple Eulerian time correlation of full- and narrow-band velocity signals in grid generated “isotropic” turbulence. J. Fluid Mech., 48: 273–337, 1971.Google Scholar
[34] Li, H., Zhang, S.H.. Direct numerical simulation of decaying compressible isotropic turbulence. Chinese Journal of Theoretical and Applied Mechanics, 44(4): 673–686, 2012.Google Scholar
[35] Haase, W., Braza, M. and Revell, A.. DESider-A European effort on hybrid RANS-LES modeling. Springer-Verlag, Berlin, Heidelberg, 2009.Google Scholar
[36] Swalwell, K. E., Sheridan, J. and Melbourne, W.H.. Frequency analysis of surface pressure on an airfoil after stall. In: 21st AIAA Applied Aerodynamics Conference, AIAA paper 2003-3416, 2003.CrossRefGoogle Scholar
[37] Sforza, P.M., and Smortot, M.J.. Streamwise development of the flow over a delta wing. AIAA J., 19(7): 833–834, 1981.CrossRefGoogle Scholar
[38] Towfighi, J. and Rockwellt, D.. Instantaneous structure of vortex breakdown on a delta wing via particle image velocimetry. AIAA J., 31(6): 1160–1162, 1993.Google Scholar
[39] Mitchell, A. M., Molton, P. and Barberis, D. et al. Characterization of vortex breakdown by flow field and surface measurements. AIAA Paper 2000-0788, 2000.Google Scholar
[40] Vlahostergios, Z., Missirlis, D. and Yakinthos, K. et al. Computational modeling of vortex breakdown control on a delta wing. Int. J. Heat Fluid Flow, 39 : 64–77, 2013.Google Scholar
[41] Chu, J., Luckring, J.M.. Experimental surface pressure data obtained on 65° delta wing across Reynolds number and Mach number ranges, NASA TM 4645, 1996.Google Scholar
[42] Morton, S.A., Forsythe, J.R. and Mitchell, A.M. et al. Detached-eddy simulations and Reynolds-averaged Navier-Stokes simulations of delta wing vortical flowfields. J. Fluids Engineering, 124(4): 924–932, 2002.Google Scholar
[43] Payne, F.M., Ng, T.T. and Nelson, R.C.. Visualization and flow surveys of the leading edge vortex structure on delta wing planforms. AIAA paper 86-0330, 1986.Google Scholar