基于边界层相似性解的放大因子输运模型

Amplification factor transport model based on boundary layer similarity solution

为了使二维线性稳定性理论能够适应现代CFD求解技术,通过求解Falkner-Skan边界层相似性方程获得各个形状因子下的相似速度型。基于线性稳定性理论,对各个速度型进行稳定性分析从而获得对应不同速度型的扰动放大因子包络线。最后使用标量输运方程的形式实现包络近似方法中放大因子的当地化求解,并结合原始γ-Re_(θt)转捩模型中的间歇因子输运方程,实现了自然转捩和分离泡转捩的建模。使用该输运模型对S&K平板、S809翼型、NLR7301翼型和DLR-F5机翼进行转捩预测,结果均与试验结果吻合较好,验证了该模型构建的合理性和可行性。

In order to make the linear stability theory adapt to the modern CFD solver technology,the similarity velocity profiles corresponding to various shape factors is obtained through solving the Falkner-Skan similarity equation.Then the approximate envelope lines of amplification factor can be achieved by analyzing different velocity profiles based on the linear stability theory.Finally,the amplification factor of envelope approximation method is solved locally in the form of scalar transport equation and the transport equation of intermittency factor in the originalγ-Re_（θt）transition model is combined to model the prediction of natural transition and separation bubble transition.The transport model has been applied to conducting the transition prediction on the SK plate flat,S809 airfoil,NLR7301airfoil and DLR-F5 wing.The successful results verify the rationality and feasibility of the established transport transition model.