二维振荡机翼跨声速非定常绕流的变域变分有限元解

本文首先对文献（１－３）提出的二维振荡机翼含激波跨声速非定常绕流的变分原理进行了改造，使之能适用于时间推进法；构造了三维时空的可变节点有限元来捕获自由尾涡面，而跨声流中的激波采用人工密度法捕获。在远场边界上使用简化的无反射条件和新型非定常Ｋｕｔｔａ条件。用本文方法求解了作俯爷振荡的ＮＡＣＡ６４Ａ０１０翼型的跨声速绕流，计算结果令人满意。本文方法可以推广到三维机翼及二维和三维叶栅的同类气动力问题上去

A Variable-Domain Variational Finite Element Solution of 2-D Unsteady Transonic Flow Around Oscillating Airfoils

In this paper, the variational principle for 2-D unsteady transonic flow with shocks around oscillating airfoils developed preyiously is modified in such a way that a time-marching finite element method can be employed. Non-reflecting far-field boundary conditions and a new unsteady Kutta condition are also incorporated. Great advantage has been taken of the functional variation with variable domain and the artificial density concept in capturing all unknown discontinuities such as shocks and free vortex sheets. For numerical realization of the variable-domain variation, a special finite element with self-adjusting nodes is also suggested herein. The numerical example solved by the present method showed good agreement with the experimental results of available. The present method can be extended further to unsteady flow past 2-D cascades and 3-D airfoils and rotor blading of turbomachinery.