论文标题
显式壁剪应力公式的可变转换
Variable Transformation for Explicit Wall-Shear Stress Formula
论文作者
论文摘要
我们为现有壁函数制定了通用变量转换，该壁功能允许明确的壁剪应力项。所提出的转换旨在通过简单的变量简单转换来实现壁剪应力的明确表达，并简化仿真代码中现有壁函数的实现。转换是通过引入新的速度刻度来定义的，从而允许定义新的墙单元变量$（r^+）$和相应的归一化粘度$（η_t^+）$。我们还证明，新变量中墙的定律等于在壁正常变量$（y^+_τ）$和$（ν_t^+）$中表达的定律。法律的新形式特别适合在计算流体动力学代码中实现，因为它不需要迭代程序来评估壁剪应力。我们展示了如何改变有和没有压力梯度的壁功能的几种已知和经常使用的表达式，以允许明确的壁剪应力表达。最后，我们通过执行说明性数值模拟来说明墙函数的新形式。
We formulate a general variable transformation for existing wall functions that allows for an explicit wall-shear stress term. The proposed transformation aims to enable an explicit expression of wall-shear stress and simplify the implementation of existing wall functions in simulation codes through a simple transformation of variables. The transformation is defined by introducing a new velocity scale allowing the definition of the new wall unit variable $(r^+)$ and the corresponding normalized viscosity $(η_t^+)$. We also demonstrate that the law of the wall in new variables is equivalent to the one expressed in wall-normal variables $(y^+_τ)$ and $(ν_t^+)$. The new form of the law is particularly suitable for implementations in computational fluid dynamics codes as it does not require an iterative procedure to evaluate the wall shear stress. We show how to transform several known and often used expressions of wall functions with and without pressure gradients to allow for an explicit wall-shear stress expression. Finally, we illustrate the new form of wall functions by performing illustrative numerical simulations.
