机翼跨声速非定常绕流IA型反命题变域变分有限元解

以文1]提出的二维振荡机翼含激波跨声速非定常绕流I_A型反命题变分原理为基础,构建求解I_A型反命题的有限元解法。构造了三维时空可变节点有限元来捕获自由尾涡面和翼面几何形状,跨声速流中的激波用人工密度法捕获。在远场边界上采用简化的无反射边界条件,新型非定常Kutta条件被用于处理尾缘条件。用该方法,根据翼型跨声速非定常绕流翼面压力分布求解I_A型反命题,得到了NACA64A010翼型的几何形状,计算结果令人满意。

VARIABLE DOMAIN VARIATIONAL FINITE ELEMENT APPROACH TO IA INVERSE PROBLEM OF UNSTEADY TRANSONIC FLOW AROUND OSCILLATING AIRFOILS

On the basis of the variational principles developed in Ref1], a finite element method(FEM) is constituted for soluting the inverse problem of 2-D unsteady transonic flow around oscillating airfoils, incorporating the non-reflecting far-field boundary conditions and a new unsteady Kutta condition^7]. All unknown boundary(airfoil contour) and discontinuities(shocks and free trailing vortex sheets) are handled(captured) via the functional variation with variable domain and artificial density concept. For the numerical realization of variable-domain variation, a special finite element with self-adjusting nodes is also suggested herein. The numerical results show that the present method is effective for the design of unsteady airfoil.