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arXiv 2012.14928physics.flu-dyn
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壁面剪应力显式公式的变量变换

Variable Transformation for Explicit Wall-Shear Stress Formula

Aleksandar Jemcov, Joseph P. Maruszewski, Ryan T. Kelly

摘要:

我们制定了一个通用的变量转换现有的壁函数,允许一个明确的壁面剪应力项。所提出的转换的目的是使一个明确的表达壁面剪应力和简化现有的壁面函数的模拟代码,通过一个简单的变量转换的实施。通过引入允许定义新的壁单元变量$(r^+)$和相应的归一化粘度$(η_t^+)$的新的速度标度来定义变换。我们还证明了新变量中的壁定律与壁法向变量$(y^+_τ)$和$(ν_t^+)$中的壁定律是等价的。新形式的法律是特别适合于在计算流体动力学代码的实施,因为它不需要一个迭代过程来评估壁面剪应力。我们将展示如何转换几个已知的和经常使用的表达式的壁函数和压力梯度,允许一个明确的壁面剪应力的表达。最后,我们说明了新形式的壁函数进行说明性的数值模拟。

英文摘要:

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.

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