WALL-MODEL FOR LARGE-EDDY SIMULATION AND ITS APPLICATIONS
WuTing1,2, ShiBeiji1,2, WangShizhao1,*,, ZhangXing1,2, HeGuowei1,2 1 LNM, Institute of Mechanics, Chinese Academy of Sciences,Beijing 100190,China2 School of Engineering Sciences, University of Chinese Academy of Sciences,Beijing 100049,China 中图分类号:O357 文献标识码:A
关键词:大涡模拟;壁模型;壁面应力模型;双层模型;周期山状流 Abstract Large-eddy simulation (LES) is an important method to investigate unsteady turbulent flows. The cost of the wall-resolved LES is comparable to that of direct numerical simulation, which prevents the applications of the LES to wall-bounded turbulences at high Reynolds numbers. The grid length would be of the order of the viscous length to resolve the near-wall flow structures, which causes the prohibitive computational cost of the wall-resolved LES. Wall-models circumvent the flow details near the wall to avoid resolving all the flow structures near the wall, which significantly reduce the computation cost and have been successfully combined with the LES for turbulent flows. We discuss the basic idea of wall-models for LES and review the wall-stress models with implementation details. The construction and characteristics of the equilibrium models and the two-layer models are discussed in detail. The limitations of the wall-stress models and their improvements to account for the non-equilibrium effects are also discussed. We review the state of the art of the wall shear stress models and provide a hierarchical diagram for the current models. Finally, we present the applications of the Werner-Wengle model to the LES of flows over periodic hills.
周期山状流是ERCOFTAC/IAHR(欧洲湍流与燃烧研究机构)设计的LES的测试算例,被广泛用于数值方法和湍流模型的研究[41,42,43,44]. 该算例所用的工况为槽道中周期性放置山状障碍,其中山的高度为 ,山状障碍的间距为 ,槽道高度为 ,槽道的展向长度为 . 雷诺数( )为10 595,其中 为山顶上的平均速度. 本文取 以及 作为特征量用于流动方程的无量纲化. 图4给出了周期山状流平均速度的流线以及不同流向位置处的平均流向速度剖面. 显示原图|下载原图ZIP|生成PPT 图4周期山状流平均速度的流线以及不同流向位置处的平均流向速度剖面 -->Fig. 4The streamlines and the profiles of the mean streamwise velocities at different streamwise locations -->
本节阐述在计算中采用WW模型 (式(8)) 的主要思路,即如何由近壁速度确定壁面切应力. 采用 与ERCOFTAC数据库中文献[49,50]相同的计算网格:其中流向、法向和展向的网格数目分别为197, 129和186. 需要注意的是, 文献[49,50]使用基于结构网格的流场求解器,而本文使用基于非结构网格的流场求解器, 因此该网格预先被处理成非结构网格的形式. 图5画出了垂直于展向的某一截面上的网格分布,下壁面近壁网格的特征尺度满足 (27) 其中,上标“+”表示用黏性长度做无量纲化, 表示近壁面的第一层网格到壁面的法向距离. 可以看到下壁面附近网格尺度是能够解析壁面层的. 上壁面近壁网格的特征尺度满足 (28) 可以看到上壁面附近网格尺度不能够解析壁面层,因此需要在上壁面使用壁模型. 显示原图|下载原图ZIP|生成PPT 图5周期山状流的大涡模拟所用的网格截面 -->Fig. 5A two-dimensional slice of the grid used for LES of the flows over periodic hills -->
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