文章快速检索 高级检索
XY-SAS模型中不同网格尺度限制器的影响分析

Influence analysis on grid scale limiter of XY-SAS model
Zheng Weilin, Yan Chao
School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:The Xu & Yan scale adaptive simulation (XY-SAS) model is based on the introduction of the von Karman length scale into the destruction term of spalart-allmaras (SA) turbulence model, which results in a large eddy simulation (LES)-like behavior in unsteady regions of the flowfield without explicit grid dependence. Because the SAS models could not provide sufficient damping of the smallest scales, the grid spacing was introduced as the high wave number damping limitation. Three different XY-SAS models were constructed by using various grid limiters and were tested by the numerical example of circular cylinder at Re=3 900. The numerical results were compared with detached eddy simulation (DES) and experimental data. It is concluded that, the grid limiter has a strong influence on the performance of the model and the minimum grid spacing is a good limitation, under which the XY-SAS model performs as well as DES method.
Key words: XY-SAS model     von Karman length scale     grid spacing     turbulence model     separation flow

SAS(Scale Adaptive Simulation)模型最早是由Menter等人于2003年提出[3],其核心思想是将冯卡门长度尺度(von Karman length scale)引入到RANS模型的尺度方程中.冯卡门长度尺度是由Rotta K-KL模型推导而来,具体形式为当地速度的一阶导数与二阶导数的比值.它能够依据当地流动结构动态地调整模型的长度尺度,从而使模型在稳定流动区域保持原有RANS模型的性能,而在不稳定流动区域允许大尺度非定常结构猝发到湍流能谱,具有类似LES的计算性能.相比于DES(Detached Eddy Simulation)方法,SAS模型由RANS到LES计算区域的过渡不依赖于网格尺度,不存在DES类方法的RANS/LES交界面问题,开辟了计算非定常湍流的新途径.目前Menter等人已将SAS模型推广到二方程SST,k-ε,k-ω模型中并广泛应用于工程问题的计算[4,5,6,7,8].

SA模型的输运方程[10]如下:

SA模型中涡黏性系数μt由下式给定:

XY-SAS模型的三维冯卡门长度尺度定义为

Ωi表示涡量;ΔjΩi表示涡量梯度;κ为冯卡门常数. 1.3 XY-SAS模型

XY-SAS模型的核心思想是将冯卡门长度尺度引入到SA模型的湍流尺度——壁面距离d中,构造新的湍流尺度如下:

XY-SAS模型的优点在于不存在显式的RANS/LES转换开关,稳态的RANS和非稳态的LES区域过渡不依赖于网格形态,模型的湍流尺度能够根据当地流动结构自动调整.

1.3.1 XY-SAS1

1.3.2 XY-SAS2

1.3.3 XY-SAS3

Cctr设置为零,即不采用限制器,湍流尺度中完全不包含网格间距[12]. 2 结果与分析

 图 1 圆柱绕流展向截面网格 Fig. 1 Two-dimensional grid of the z-slice domain
2.1 瞬时流场

 图 2 瞬时流场结构图(Q=S2-Ω2=0.1/s2) Fig. 2 Instant turbulent structures(Q=S2-Ω2=0.1/s2)

 图 3 升力系数功率谱密度分布 Fig. 3 Power spectral density (PSD) of the lifting coefficient

 计算模型 CD St SA-DES 1.046 0.208 XY-SAS1 1.110 0.213 XY-SAS2 1.039 0.208 XY-SAS3 1.056 0.208 LES 1.04 0.208±0.01 EXP 0.98±0.05 0.208±0.02
2.2 时均结果

 图 4 壁面平均压力分布 Fig. 4 Pressure coefficients on the cylinder surface

 图 5 尾迹区中心线流向平均速度分布 Fig. 5 Streamwise mean velocity on the centreline in the wake region

 图 6 近壁面尾迹区平均速度分布 Fig. 6 Mean velocity profile in the near wake region

 图 7 近壁面尾迹区平均雷诺应力分布 Fig. 7 Mean Reynolds stress profile in the near wake region

XY-SAS3的计算结果总体与XY-SAS2相接近,但由于没有采用网格尺度限制器,XY-SAS3模型计算的雷诺应力略偏高,对应的阻力系数略偏大,回流区长度略短、回流速度偏低.因此,适当地引入网格尺度作为限制器可以改善模型在大分离区域的计算性能. 3 结 论

 [1] Fröhlich J,von Teryi D.Hybrid LES/RANS methods for the simulation of turbulent flows[J].Progress in Aerospace Sciences,2008,44(5):349-377 Click to display the text [2] 阎超,于剑,徐晶磊,等.CFD模拟方法的发展成就与展望[J].力学进展,2011,41(5):562-589 Yan Chao,Yu Jian,Xu Jinglei,et al.On the achievements and prospects for the methods of computational fluid dynamics[J].Advance in Mechanics,2011,41(5):562-589(in Chinese) Cited By in Cnki (46) [3] Menter F R,Kuntz M,Bender R.A scale-adaptive simulation model for turbulent flow predictions[C]//41st Aerospace Sciences Meeting and Exhibit.Reston,VA:American Institute of Aeronautics and Astronautics Inc,2003-0767 Click to display the text [4] Menter F R,Egorov Y.A scale-adaptive simulation model using two-equation models[C]//43rd AIAA Aerospace Sciences Meeting and Exhibit.Reston,VA:American Institute of Aeronautics and Astronautics Inc,2005:271-283 Click to display the text [5] Menter F R,Egorov Y.The scale-adaptive simulation method for unsteady turbulent flow predictions.Part 1:theory and model description[J].Flow,Turbulence and Combustion,2010,85(1):113-138 Click to display the text [6] Egorov Y,Menter F R,Lechner R,et al.The scale-adaptive simulation method for unsteady turbulent flow predictions.Part 2:application to complex flows[J].Flow,Turbulence and Combustion,2010,85(1):139-165 Click to display the text [7] Menter F R,Schütze J,Kurbatskii K A,et al.Scale-resolving simulation techniques in industrial CFD[C]//6th AIAA Theoretical Fluid Mechanics Conference.Reston,VA:American Institute of Aeronautics and Astronautics Inc,2011-3474 Click to display the text [8] Menter F R.Review of the shear-stress transport turbulence model experience from an industrial perspective[J].International Journal of Computational Fluid Dynamics,2009,23(4):305-316 Click to display the text [9] 徐晶磊,阎超.一个一方程Scale-Adaptive Simulation模型的构造[C]//第14届全国计算流体力学会议.贵阳:[s.n.],2009:113-117 Xu Jinglei,Yan Chao.A one-equation scale-adaptive simulation model[C]//14th National Conference on CFD.Guiyang:[s.n. ],2009:113-117(in Chinese) [10] Spalart P R,Allmaras S R.A one-equation turbulence model for aerodynamic flows[C]//30th AIAA Aerospace Sciences Meeting and Exhibit.Reno,NV:American Institute of Aeronautics and Astronautics Inc,1992-0439 Click to display the text [11] 高瑞泽,徐晶磊,赵瑞,等.XY-SAS模型对分离流动的性能分析[J].北京航空航天大学学报,2010,36(4):414-418 Gao Ruize,Xu Jinglei,Zhao Rui,et al.Evaluation of XY-SAS model for separated flows[J].Journal of Beijing University of Aeronautics and Astronautics,2010,36(4):414-418(in Chinese) Cited By in Cnki (1) [12] Xu J L,Hu N,Gao G.A high-fidelity turbulence length scale for flow simulation[C]//Progress in Hybrid RANS-LES Modelling.Berlin:Springer,2012:141-145 Click to display the text [13] Ong L,Wallace J.The velocity field of the turbulent very near wake of a circular cylinder[J].Exp Fluids,1996,20(6):441-453 Click to display the text [14] Kravchenko A G,Moin P.Numerical studies of flow over a circular cylinder at ReD=3 900[J].Phys Fluids,2000,12(12):403-417 Click to display the text [15] Shim Y M,Sharma R N,Richards P J.Numerical study of the flow over a circular cylinder in the near wake at Reynolds number 3 900[C]//39th AIAA Fluid Dynamics Conference.Reston,VA:American Institute of Aeronautics and Astronautics Inc,2009-4160

文章信息

Zheng Weilin, Yan Chao
XY-SAS模型中不同网格尺度限制器的影响分析
Influence analysis on grid scale limiter of XY-SAS model

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(12): 1725-1729.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0742