能量耗散湍流模型的光滑壁边界条件

D. Hunsaker, W. Phillips, R. Spall
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引用次数: 0

摘要

结果表明,常用的基于耗散的湍流模型所规定的光滑壁边界条件在数学上是不正确的。结果表明,当使用这些传统的壁面边界条件时,所得到的公式要么允许无穷多个解,要么不允许解。此外,这些解决方案不执行能量守恒,它们不能适当地执行光滑表面的防滑条件。这对于所有基于耗散的湍流模型都是正确的,包括k- {\epsilon}, k- {\omega}和k- {\zeta}模型。物理上正确的壁面边界条件必须使k及其梯度在光滑壁面上都为零。对k施加这两个边界条件足以确定微分输运方程耦合系统的唯一解。在光滑表面上,不需要对{\epsilon}、{\omega}或{\zeta}施加任何壁面边界条件,这样做是不正确的。{\epsilon}, {\omega}或{\zeta}接近光滑表面的行为需要满足微分方程并迫使k及其梯度在壁上为零。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Smooth-Wall Boundary Conditions for Energy-Dissipation Turbulence Models#
It is shown that the smooth-wall boundary conditions specified for commonly used dissipation-based turbulence models are mathematically incorrect. It is demonstrated that when these traditional wall boundary conditions are used, the resulting formulations allow either an infinite number of solutions or no solution. Furthermore, these solutions do not enforce energy conservation and they do not properly enforce the no-slip condition at a smooth surface. This is true for all dissipation-based turbulence models, including the k-{\epsilon}, k-{\omega}, and k-{\zeta} models. Physically correct wall boundary conditions must force both k and its gradient to zero at a smooth wall. Enforcing these two boundary conditions on k is sufficient to determine a unique solution to the coupled system of differential transport equations. There is no need to impose any wall boundary condition on {\epsilon}, {\omega}, or {\zeta} at a smooth surface and it is incorrect to do so. The behavior of {\epsilon}, {\omega}, or {\zeta} approaching a smooth surface is that required to satisfy the differential equations and force both k and its gradient to zero at the wall.
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