7.3.4 Wall Models 壁面模型[cfd-7-3-4]

对高雷诺数（ $$Re > 10^6$$ ）有壁流动做LES的计算代价对工程应用而言仍然过高，原因在于恰当解析壁面层需要过多的网格点（单元）。为了降低代价，可以通过指定外流速度与壁面应力之间的关联来对壁面层建模。这一做法与RANS模拟中使用壁面函数相当类似。其基本假设是近壁区与外区之间只有弱的相互作用，文献[144]和[145]的研究支持这一假设。en

The computational costs of LES of wall-bounded flows at high Reynolds numbers ( $$Re > 10^6$$ ) are still too high for engineering purposes. The reason is the excessively large number of grid points (cells) required to resolve the wall layer appropriately. In order to reduce the costs, it is possible to model the wall layer by specifying a correlation between the velocity in the outer flow and the stress at the wall. This approach is quite similar to using wall functions in RANS simulations. The basic assumption is that there is only a weak interaction between the near-wall and the outer region, which is supported by the investigations in [144] and [145].

早期的壁面模型基于这样一种假设：壁面层的动力学是普适的，因而可以用广义壁面律来近似。这些模型基本上利用对数律（见[77]和[146]-[148]）。Balaras等[149]最近提出了一种新的分区（zonal）方法。在两层模型中，滤波后的Navier-Stokes方程(7.81)一直求解到壁面上方第一个网格点；从该点到壁面之间，则在加密的嵌入网格上求解二维边界层方程。嵌入网格上的解随后用于给定壁面剪切应力，作为LES的边界条件。Balaras等[149]的分区方法允许把第一个点放在 $20 < y^{+} < 100$ 的区域内，从而显著减小网格规模并缩短计算时间。该方法已成功应用于平面槽道、方形管道和旋转槽道中的湍流流动；后来又被用于分离流动的LES，结果令人鼓舞[150]-[153]。en

Earlier implementations of the wall models were based on the assumption that the dynamics of the wall layer are universal and hence they can be approximated by a generalised law-of-the-wall. Basically, the models utilised the logarithmic law (see [77] and [146]-[148]). Balaras et al. [149] proposed recently a new zonal approach. Within the two-layer model, the filtered Navier-Stokes equations (7.81) are solved up to the first grid point above the wall. From this point to the wall 2-D boundary layer equation are solved on a refined embedded grid. The solution on the embedded grid is then used to prescribe the wall shear stress as a boundary condition for the LES. The zonal approach of Balaras et al. [149] allows it to place the first point in a region $20 < y^{+} < 100$ , which leads to significantly reduced grid size and hence computational time. The methodology was applied with success to turbulent flows in a plane channel, square duct and rotating channel. Later on, it was also employed for the LES of separated flows with encouraging results [150]-[153].