In this paper novel unified wall function formulations for large eddy simulation of complex turbulent flows and heat transfer are presented. In contrast to existing wall functions, the proposed analytical expressions for velocity and temperature are: (1) valid over the whole range of dimensionless wall distance $y^{+}$, (2) applicable to complex flow situations that include local non-equilibrium effects, (3) suitable for a wide range of molecular Prandtl numbers, (4) thermodynamically consistent with the second law of thermodynamics, and (5) easily extendable to account for contributions of additional source term e.g. gravity, radiation, chemical reactions. Such an universal and consistent wall function formulation is particularly useful for computational fluid dynamics applications in providing appropriate wall boundary conditions for complex high Reynolds number flows. The accuracy and thermodynamic consistency of the proposed wall treatment is first testified by comparison with experimental and direct numerical simulation data. Second, in order to highlight the applicability and performance of the proposed wall functions for computational fluid dynamics, results of large eddy simulations of various complex turbulent flows including heat transfer relevant to internal combustion engine applications are presented and evaluated. It turns out that the suggested wall function approach features a superior physics modeling accuracy in terms of well-known key parameters in near-wall bounded flows in comparison to state-of-the-art wall functions.

在本文中，提出了新颖的统​​一壁函数公式，用于复杂湍流和传热的大涡模拟。与现有的墙函数相反，建议的速度和温度解析表达式为：（1）在整个无量纲墙距离范围内有效${ÿ}^{+}$，（2）适用于包含局部非平衡效应的复杂流动情况，（3）适用于各种分子的Prandtl数，（4）热力学与热力学第二定律一致，并且（5）易于扩展以解决用于附加源项的贡献，例如重力，辐射，化学反应。在为复杂的高雷诺数流提供适当的壁边界条件时，这种通用且一致的壁函数公式对于计算流体动力学应用特别有用。通过与实验和直接数值模拟数据进行比较，首先证明了所提出的壁处理的准确性和热力学一致性。其次，为了强调所提出的壁函数在计算流体动力学中的适用性和性能，提出并评估了各种复杂湍流的大涡模拟，包括与内燃机应用相关的热传递。事实证明，与最新的墙函数相比，建议的墙函数方法在近墙边界流中众所周知的关键参数方面具有出色的物理建模精度。