可压缩湍流边界层壁面函数方法综述

Overview of wall functions for compressible turbulent boundary layers

以建立工程实用的高超声速湍流边界层模拟方法为目标,从湍流壁面函数是湍流边界层方程近似解的角度,梳理了相关文献的研究工作,得到如下认识:1)壁面函数与所求定解问题数值解的相容程度决定了壁面第一层网格允许放粗的程度,在流动分离点和再附点附近区域,目前壁面函数尚需进一步完善,而“子网格”壁面函数从理论上解决了相容性问题,尽管要耗费更多计算资源,但在目前计算资源相对充裕的条件下,仍不失为一个解决问题的途径;2)对于具有强压缩性和显著气动加热的高超声速湍流边界层流动而言,常用的解析形式并未充分考虑可压缩性和传热的影响,并在文中进行了重点探讨。最后,建议基于数据驱动技术和依托“子网格”壁面函数方法来发展更加普适的壁面函数。

Related studies about wall functions,which are approximate solutions to turbulent boundary layers,are surveyed to shed light on the development of a pragmatic simulation method for hypersonic turbulent boundary layers.This overview reveals the following understandings:1)The consistency between wall functions and numerical solutions determines the mesh size of the wall-next cells.However,the consistency problem is not well solved by analytical wall functions,especially in separation and reattachment regions where the pressure gradient is strong.The sub-grid wall function,in contrast,theoretically solves this problem,which makes it to be a promising method when computational resources are abundant.2)The effects of strong compressibility and significant heat transfer in hypersonic turbulent flows need to be adequately integrated into analytical wall functions.Finally,the development of a more universal wall function based on the data-driven methods and subgrid wall functions is recommended.