ABSTRACT Spalart-Allmaras (SA) model is a low Reynolds number (Re) model, which means that the first off-wall grid point should be placed in the viscous sub-layer with . This restriction of placing the first off-wall grid point so close to the wall leads to an increase in the mesh size, and thus the computation. The wall function approach is an alternative to this problem. The standard wall function method usually employed has a limitation for cases that involve high adverse pressure gradient and compressibility. This limits its use to the non-separated flows only. The present work focuses on the formulation of the generalised wall function given by Shih et al. [A generalized wall function; 1999] and applies it to the SA turbulence model, with some modification. The proposed modification was found to remove the oscillation and inaccuracy found in the result when directly using the Shih et al. model. Several flows, with zero pressure gradient to those with adverse pressure gradient leading to flow separation, are solved with the proposed wall treatment, with relatively coarse grids involving beyond 50 and up to 100 for certain cases. It is concluded that the results in each case are close to those obtained by the low-Re SA model, despite the use of much coarser meshes.

中文翻译：

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包含 Spalart-Allmaras 湍流模型的可压缩性和压力梯度项的广义壁函数

摘要 Spalart-Allmaras (SA) 模型是一个低雷诺数 (Re) 模型，这意味着第一个离壁网格点应放置在粘性子层中。将第一个离墙网格点如此靠近墙的这种限制会导致网格尺寸增加，从而导致计算量增加。壁函数方法是该问题的替代方法。通常采用的标准壁函数方法对涉及高逆压力梯度和可压缩性的情况有局限性。这将其仅用于非分离流。目前的工作重点是 Shih 等人给出的广义壁函数的公式。[一个广义的壁函数；1999] 并将其应用于 SA 湍流模型，并进行了一些修改。发现建议的修改可以消除直接使用 Shih 等人的结果中发现的振荡和不准确性。模型。几个流动，从零压力梯度到那些导致流动分离的不利压力梯度，用建议的壁处理解决了，在某些情况下，相对粗糙的网格涉及超过 50 和高达 100。得出的结论是，尽管使用了更粗的网格，但每种情况下的结果都接近于低 Re SA 模型获得的结果。