宇航学报

宇航学报 ›› 2021, Vol. 42 ›› Issue (6): 731-739.doi: 10.3873/j.issn.1000-1328.2021.06.006

• 飞行器设计与力学 • 上一篇    下一篇

解析壁面函数的可压缩效应修正研究

王新光，陈琦，万钊，张爱婧，陈坚强   

  1. 1. 空气动力学国家重点实验室，绵阳 621010；2. 中国空气动力研究与发展中心计算所，绵阳 621000
  • 收稿日期:2020-10-13 修回日期:2020-11-30 出版日期:2021-06-15 发布日期:2021-07-22
  • 基金资助:
    国家数值风洞NNW支持项目；国家自然科学基金（11972362）

Study on an Analytical Wall Function Approach Including Compressibility

WANG Xin guang, CHEN Qi, WAN Zhao, ZHANG Ai jing, CHEN Jian qiang   

  1. 1. State Key Laboratory of Aerodynamics, Mianyang 621010, China; 2. Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
  • Received:2020-10-13 Revised:2020-11-30 Online:2021-06-15 Published:2021-07-22

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摘要： 基于适用于不可压缩流动的解析壁面函数，针对可压缩湍流边界层特征，考虑壁面网格内对流项变化和能量方程中黏性耗散项的影响，提出一种适用于可压缩流动的解析壁面函数。基于二维超声速和高超声速激波湍流边界层干扰流动，完成了粗网格高雷诺数k ε模型加标准壁面函数、原始解析壁面函数、可压缩修正解析壁面函数和密网格低雷诺数Lauder Sharma k ε模型的对比计算。结果表明：四种湍流效应模拟策略都可以准确预测壁面压力和摩擦系数，而本文发展的考虑对流项分布和黏性耗散项影响的解析壁面函数不仅消除了原始解析壁面函数的非物理振荡，而且大幅提升了壁面函数壁面热流的预测精度，与密网格解最大差异不超过40%，预测结果接近于密网格低雷诺数模型结果，而标准壁面函数和原始解析壁面函数预测的壁面热流符号相反，且数值最大差异达500%。对于Ma 5斜激波边界层干扰算例，本文构造的壁面函数计算时间仅为低雷诺数模型的5%左右，相较于其它壁面模型，计算时间仅增加了1%。


关键词: 解析壁面函数；可压缩湍流；Launder Sharma , k ε 模型；激波边界层干扰

Abstract: Based on an anlytical wall function for the imcompressible flow, compressibility modifications inluding the variation of convection terms and viscosity diffusion terms in the energy equation have been made accouding to the characteristics of compressible turbulence boundary layers. This modified analytical wall function is tested in the prediction of supersonic and hypersonic flows which involve the 2 D shock wave/turbulent boundary layer interactions (SWTBLIs) together with the standard log law based wall function, the original analytical wall function with the  k ε  model using coarsh meshes, and the Lauder Sharma  k ε  model without wall function using fine meshes. On the whole, the four turbulence modeling strategies display good predictions of wall pressure and skin friction. However, the modified AWF approach with the distribution of convection and viscosity diffusion removes the unphysical oscillation of original AWF and improves the prediction of wall heat flux significantly (maximum deviation less than 40% compared to that of the fine mesh results) compared to the other two wall function approaches which fail to predict the wall heat flux (maximum deviation up to 500%). For the  Ma 5 case, the modified AWF consumes only 5% of CPU time of the low Re model, and only needs extra 1% of that of the other wall function approaches.


Key words: Analytical wall function, Compressible turbulent flow, Launder Sharma , k ε , model, SWTBLIs

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