基于非结构/混合网格的脱体涡模拟算法
收稿日期: 2014-10-10
修回日期: 2014-12-10
网络出版日期: 2015-01-30
基金资助
国家自然科学基金 (91016001, 11272339)
Detached-eddy simulation based on unstructured and hybrid grid
Received date: 2014-10-10
Revised date: 2014-12-10
Online published: 2015-01-30
Supported by
National Natural Science Foundation of China (91016001, 11272339)
为了提高二阶精度有限体积算法的湍流数值模拟能力,在原始Roe格式基础上建立了与脱体涡模拟(DES)方法相匹配的二阶混合耗散自适应格式,根据流场信息自动调节格式耗散,并分别基于Spalart-Allmaras一方程湍流模型和k-ω剪切应力输运(SST)两方程湍流模型,发展了基于非结构/混合网格的DES方法。采用该方法计算了雷诺数为3 900的圆柱绕流和NACA 0021翼型60°大迎角分离流两个典型算例,通过与试验数据以及其他数值结果的对比验证了该方法的可行性。同时开展了不同数值格式、湍流模型的对比分析,研究结果表明:采用混合格式的DES算法能够解析更小尺度的湍流涡结构、计算数据更接近试验值;本文的DES类算法受其基准湍流模型影响较小。
张扬 , 张来平 , 赫新 , 邓小刚 . 基于非结构/混合网格的脱体涡模拟算法[J]. 航空学报, 2015 , 36(9) : 2900 -2910 . DOI: 10.7527/S1000-6893.2014.0342
To improve the turbulence simulation ability of the second order finite-volume algorithm based on unstructured and hybrid grid, a hybrid second order scheme is established by modifying the dissipation term of the standard Roe flux-difference splitting scheme and the numerical dissipation of the scheme can be self-adapted according to the detached-eddy simulation (DES) flow field information. The credibility of the approach is supported by two typical numerical examples of its application: Re=3 900 circular cylinder and NACA 0021 airfoil at high angle of attack (60°), and the DES predictions are compared with experimental data and with other numerical solutions. The DES methods based on both the one equation Spalart-Allmaras turbulence model and the two equation k-ω shear stress transport (SST) model are used in the computation. The effects of numerical schemes and turbulence models are also discussed in the study, which shows that the scale of turbulence structure resolved by the hybrid scheme is smaller than that resolved by the standard Roe scheme and the corresponding flow field is better; meanwhile the DES methods used in this paper are little affected by their RANS-based models.
[1] Jiang Z, Xiao Z L, Shi Y P, et al. Constrained large-eddy simulation of wall-bounded compressible turbulent flows[J]. Physics of Fluids, 2013, 25(10): 106102.
[2] Spalart P R, Jou W H, Strelets M, et al. Comments on the feasibility of LES for wings and on a hybrid RANS/LES approach[C]//Proceedings of 1st AFOSR International Conference On DNS/LES. Columbus: Greyden Press, 1997: 137-147.
[3] Travin A, Shur M, Strelets M, et al. Physical and numerical upgrades in the detached-eddy simulation of complex turbulent flows[C]//Advances in LES of Complex Flows. Berlin: Springer, 2004: 239-254.
[4] Haase W, Braza M, Revell A. DESider-A European effort on hybrid RANS-LES modeling[M]. Berlin: Springer, 2009: 19-139.
[5] Menter F, Kuntz M. Adaption of eddy-viscosity turbulence models to unsteady separated flow behind vehicles. In: The aerodynamics of heavy vehicles: trucks, buses, and trains[C]//Lecture Notes in Applied and Computational Mechanics. Berlin: Springer, 2004.
[6] Spalart P R, Deck S, Shur M L, et al. A new version of detached-eddy simulation, resistant to ambiguous grid densities[J]. Theory Computation Fluid Dynamics, 2006, 20(3): 181-195.
[7] Nikitin N, Nicoud F, Wasistho B, et al. An approach to wall modeling in large-eddy simulations[J]. Physics of Fluids, 2000, 12(7): 1629-1632.
[8] Shur M L, Spalart P R, Strelets M K, et al. A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities[J]. International Journal of Heat and Fluid Flow, 2008, 29(6): 1638-1649.
[9] Bui T T. A parallel, finite-volume algorithm for large-eddy simulation of turbulent flow[J]. Computers & Fluids, 2000, 29(8): 877-915.
[10] Deng X B, Zhao X H, Yang W, et al. Dynamic adaptive upwind method and it's applications in RANS/LES hybrid simulations[C]//The Eighth International Conference on Computational Fluid dynamics. Mianyang: China Aerodynamics Research and Development Center, 2014: 807-814.
[11] Frink N T. Recent progress toward a three dimensional unstructured Navier-Stokes flow solver, AIAA-1994-0061[R]. Reston: AIAA, 1994.
[12] Hughes T J R, Franca L P, Hulbert G M. A new finite element formulation for computational fluid dynamics VIII: The Galerkin least squares method for advective- diffusive equations[J]. Computer Methods in Applied Mechanics and Engineering, 1989, 73(2): 173-189.
[13] Bassi F, Crivellini A, Rebay S, et al. Discontinuous Galerkin solutions of the Reynolds-averaged Navier-Stokes and k-ω turbulence model equations[J]. Computers & Fluids, 2005, 34(4-5): 507-540.
[14] Zhang L P, Liu W, He L X, et al. A class of hybrid DG/FV methods for conservation laws I: Basic formulation and one-dimensional systems[J]. Journal of Computational Physics, 2012, 231(4): 1081-1103.
[15] Zhang L P, Liu W, He L X, et al. A class of hybrid DG/FV methods for conservation laws II: Two-dimensional cases[J]. Journal of Computational Physics, 2012, 231(4): 1104-1120.
[16] Zhang L P, Liu W, He L X, et al. A class of hybrid DG/FV methods for conservation laws III: Two-dimensional Euler equations[J]. Journal of Computational Physics, 2012, 12(1): 284-314.
[17] Wang Z J. Spectral (finite) volume method for conservation laws on unstructured grids: basic formulation[J]. Journal of Computational Physics, 2002, 178(2): 210-251.
[18] Wang Z J, Liu Y. The spectral difference method for the 2D Euler equations on unstructured grids, AIAA-2005-5112[R]. Reston: AIAA, 2005.
[19] Huynh H T. A reconstruction approach to high-order schemes including discontinuous Galerkin for diffusion, AIAA-2009-0403[R]. Reston: AIAA, 2009.
[20] Zhang L P, Wang Z J. A block LU-SGS implicit dual time-stepping algorithm for hybrid dynamic meshes[J]. Computers & Fluids, 2004, 33(7): 891-916.
[21] Zhang L P, Zhao Z, Chang X H, et al. A 3D hybrid grid generation technique and multigrid/parallel algorithm based on anisotropic agglomeration approach[J]. Chinese Journal of Aeronautics, 2013, 26(1): 47-62.
[22] Spalart P R, Allmaras S R. A one-equation turbulence model for aerodynamic flows, AIAA-1992-0439[R]. Reston: AIAA, 1992.
[23] Menter F R. Zonal two-equation k-ω turbulence models for aerodynamic flows, AIAA-1993-2906[R]. Reston: AIAA,1993.
[24] Gritskevich M S, Garbaruk A V, Schütze J, et al. Development of DDES and IDDES formulations for the k-ω shear stress transport model[J]. Flow Turbulence Combust, 2012, 88(3): 431-449.
[25] Lourenco L M, Shih C. Characteristics of the plane turbulent near wake of a circular cylinder, a particle image velocimetry study, CTR Annual Research Briefs[R]. Washington, D.C. : NASA, 1994.
[26] Parnaudeau P, Carlier J, Heitz D, et al. Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900[J]. Physics of Fluids, 2008, 20(8): 085101.
[27] Norberg C. Experimental investigation of the flow around a circular cylinder: influence of aspect ratio[J]. Journal of Fluid Mechanics, 1994, 258: 287-316.
[28] Ma X, Karamanos G S, Karniadakis G E. Dynamics and low-dimensionality of a turbulent near wake[J]. Journal of Fluid Mechanics, 2000, 410: 29-65.
[29] Kravchenko A G, Moin P. Numerical studies of flow over a circular cylinder at Re=3900[J]. Physics of Fluids, 2000, 12(2): 403-417.
[30] Li D, Jiao Y Q, Igor M, et al. Detached eddy simulation for airfoil stall[J]. Acta Aeronautica et Astronautica Sinica, 2005, 26(4): 406-410 (in Chinese). 李栋, 焦予秦, Igor Men'shov, 等. Detached-Eddy Simulation方法模拟不同类型翼型的失速特性[J]. 航空学报, 2005, 26(4): 406-410.
[31] Swalwell K E, Sheridan J, Melbourne W H. Frequency analysis of surface pressure on an airfoil after stall, AIAA-2003-3416[R]. Reston: AIAA, 2003.
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