边界层转捩预测中的局部散射理论

Local scattering theory for transition prediction in boundary-layer flows

随着航空航天技术的发展,工程上对转捩预测精度的要求越来越高。由于飞行器表面经常出现如粗糙元、台阶、缝隙等局部突变,而传统的基于光滑壁面边界层建立的转捩预测模型已无法满足精度要求。因而,发展考虑壁面突变影响的转捩预测方法有重要的实际意义。对于由边界层中模态扰动的累积所触发的自然转捩,局部突变通过局部感受性与线性模态的局部散射两种机制影响转捩位置,故可以通过在传统eN转捩预测方法的基础上引入这两种机制影响的方法建立新的转捩预测模型。为了量化这两种机制的影响,作者与其合作者们提出了一套通用的理论框架--局部散射理论。该理论框架采用大雷诺数渐近理论与有限雷诺数理论相结合的分析与计算方法,定量刻画局部散射系统的两个特征参数--局部感受性系数与透射系数,以预测在局部突变影响下转捩位置的改变量。文章综述了近年来局部散射理论的研究进展,重点展示了该理论在二维层流边界层中黏性与无黏两种失稳机制下的应用。

With the development of aerospace technology,higher and higher accuracy for transition prediction is required in engineering.Because the traditional transition prediction approaches based on smooth boundary layers do not satisfy the accuracy requirement when surface imperfections,e.g.roughness,steps and gaps,are present,it is of practical importance to develop a new model to predict transition with the impacts of surface imperfections being taken into account.For natural-route transition triggered by the accumulation of the boundary-layer normal modes,the transition onset may be affected through the local receptivity and linear-mode local scattering regimes,therefore,a new transition-prediction model can be developed by adding the quantitative impacts of the two regimes to the traditional eN transition-prediction approach.In order to quantify these impacts,the author and his collaborators developed a generic theoretical framework,the local scattering theory.Through combination of large-Reynolds-number asymptotic and finite-Reynolds-number theories,this framework describes the two system characteristic parameters,i.e.the local receptivity and transmission coefficients,which are used to predict the variation of the transition onset influenced by the surface imperfections.The present paper reviews the progress of the local scattering theory in the recent years,and highlights the applications of the theory in the viscous and inviscid instability regimes in twodimensional laminar boundary layers.