横流不稳定性转捩预测模型

由于Langtry和Menter提出的γ-Re_θt边界层转捩模型只能预测流向的边界层转捩现象,因此继续改进该转捩模型使其具有横流不稳定性转捩的预测能力显得非常必要。通过对经典Falkner-Skan-Cooke (FSC)三维边界层相似解的理论分析和数值求解,结合Thwaites压力梯度因子与当地后掠角构建的函数关系来求解复杂构型的当地Hartree压力梯度因子β_H以及形状因子H₁₂,采用由试验数据标定的C1准则关系式获得横流转捩位移厚度雷诺数,从而建立能够对复杂构型进行横流不稳定性转捩预测的转捩判据。应用所建模型对30°前缘后掠角的ONERA-M6机翼和变前缘后掠角的DLR-F5机翼以及标准6:1椭球标模进行了横流不稳定转捩数值模拟,计算结果显示转捩位置均与试验数据吻合较好,证明了该模型的合理性和实用性。

Transition model for predicting crossflow instabilities

As the γ-Re_θt boundary layer transition model proposed by Langtry and Menter could only predict the transition along the streamwise, it is necessary to develop a γ-Re_θt transition model so that it could conduct the numerical simulation of crossflow instabilities transition. With the theoretical analysis and numerical solution of Falkner-Skan-Cooke (FSC) three-dimensional boundary layer, combining the Thwaites pressure gradient factor with local swept angle to build the relationships for solving the Hartree pressure gradient factor β_H and the shape factor H₁₂, using the C1 criterion calibrated by the test data to get the crossflow instabilities transition displacement thickness Reynolds number, the crossflow transition criterion is established for complex configuration by solving the equations and data fitting. The model has been applied to conducting the numerical simulation of crossflow instabilities transition on the ONERA-M6 wing with 30° swept angle of leading edge, the DLR-F5 wing with variational swept angle of leading edge and the 6:1 prolate spheroids standard model. The numerical results show that the improved transition model could predict the location of crossflow instabilities transition of swept wing in good agreement with the test data. Therefore, the results indicate that the crossflow instabilities transition criterion built is reasonable and practical.