绕升力机身跨音速流动的有限元素法数值分析

 <正> 本文应用全速位方程最小压强积分的有限元素法解绕升力机身的跨音速流动。机身头部可以是尖的或带有进气道的。用头部伸出无穷长圆柱来模拟头部进气。尖头机身在元素形状处理上具有一定的复杂性,从数值实验角度考虑我们分别按尖头和头部伸出无穷长细圆柱来近似尖头头部两种方法对尖头机身进行计算。采用人工密度法捕获激波,但由于绕机身流线形状比较复杂,直接采用机翼问题中的人工粘性公式,解往往不收敛。我们推导出一种较精确的,适用于复杂流动情况的人工粘性计算公式,为了加速收敛,应用网格逐次加密技术,可使收敛速度提高2～3倍。本文还给出绕升力机身跨音速流动的远场速位解析式。

FINITE ELEMENT NUMERICAL ANAIYSIS FOR TRANSONIC FLOWS AROUND LIFTING FUSELAGES

A finite element method based on the minimum pressure integral obtained by a variational principle for full potential equation, is used to calculate the transonic flows around lifting fuselages. The nose of the fuselage is either pointed or with inlet. The fuse-Sage may be with arbitrary cross section and canopy.The artificial density method is used to capture the shock wave. In contrast to wings, the streamlines on the fuselage surface are complicated, especially for the lifting fuselage. A suitable artificial density formula has been develpoed in the present paper.On the fuselage surface, Neumann boudary conditions are satisfied automatically. In addition, Dirichlet condition on the far field boundary around a lifting fuselage is imposed directly. This condition can be prescribed from the far field approximation of the full potential equation.The system of equations deduced from the finite element discretization is solved by SLOR procedure, and the density is updated after each SLOR sweep. In orde e the convergence speed, a successive grid refinement technique is employed, and that reduces the computer time considerably. number of numerically computed examples are presented and compared with experimental results.