【摘要】 S形进气道内外流场的计算对工程设计具有重大价值,本文用有限元素法计算了S形进气道内流场。以三维的速势方程作为控制方程,用Galerkin法形成有限元方程。把有限差分解和摄动法解作为边界条件,在靠近进气道进口一段区域内嵌入有限元素法求解,修正局部计算精度比较差的区域。本文提出了有限元方程求解中的面松弛改进迭代方法,以解决非线性迭代及三维有限元方程的求解问题,使得计算机的存贮量大大降低,并加快了收敛速度。成功地运用把摄动法、有限差分法和有限元素法结合起来计算流场的思想,求解了比较复杂的流场。用本文的方法得到了良好精度的收敛解,计算结果表明此方法对于计算三维问题是有效的。更多还原

【Abstract】 S-shaped inlet design is frequently adopted in modern aircraft. The flow through such an inlet undergoes severe changes as the inlet axis is much curved. Moreover, disturbances caused by fuselage and the inlet interact with each other so that the flow field is rather complicated. A simple uniform method may not give cost-effective results for the whole three-dimensional flow field of such a combination of the inlet and fuselage. Ref. [1] uses a mixed finite difference method to solve the above internal and external flow problem in an orthogonal mesh. The geometrical complexity of the inlet-fuse- lage combination causes great difficulty in generating the appropriate mesh system and treating the boundary conditions, especially near the entrance of the inlet. The body boundary condition is usually satisfied near the body surface because the mesh is not body-fitted (a 3-D body-fitted mesh is rather difficult to generate and makes the governing equations and its solution more complex). This causes great mass flow error near the entrance of the inlet, where the duct wall is of the converging-diverging shape and has the great- est curvature. Ref. [2] provides a perturbation method to treat the internal flow of any slender ducts. While the method has proved to be very fast and accurate inside the inlet duct, it cannot cope with the flow through the con- verging-diverging duct next to the entrance either, because the "slender assumption" is violated thereabout. Considering that the finite element meth- od is extremely flexible in the choice of mesh systems and quite accurate in approximating boundary conditions, we come up with the idea to embed the finite element method into the finite difference and perturbation meth- ods in the above area. Thus, we form a hybrid method which can fully ex- ploit the advantages and eliminate the disadvantages of the three different methods. Finite element approximation to a nonlinear partial differential equa- tion leads to it set of nonlinear algebraic equations, which is generally solved by means of iteration. For a three-dimensional problem, a very large set of linear algebraic equations must be solved for each iteration. This re- quires tremendous amounts of computer memory and CPU time. Ref. [3] forms the finite element equations by using the Galerkin method and solves the nonlinear algebraic equations through a Newton-Raphson iteration. Ref. [5] uses a least-square method to deal with the nonlinearity, whereas Ref. [6] presents a line-relaxation method to solve two-dimensional problems. The present paper develops a three-dimensional finite element method which is based on the Galerkin formulation and uses a surface-relaxation iteration to solve the resulting nonlinear finite element equations. This greatly reduces the computer memory and CPU time. Moreover, the Seidal method of iter- ation is employed to speed up the convergence of the nonlinear iteration. The above method is easy to implement and we use it to do the embe- dded calculation in the troublesome converging-diverging area of the inlet next to the entrance, where the finite difference and perturbation methods in [1] and [2] fail to give accurate results. The finite element computation is carried out with the entrance boundary condition provided by the finite-difference method and the exit boundary condition provided by the perturbation method. Results obtained from the embedded calculation show that the surface-relaxation finite element method developed in this paper is of good accuracy and rate of convergence. It takes only 11～14 times of iteration for a converged solution. Although the present paper is only a preliminary attempt to combine the finite-element, finite- difference and perturbation methods, it is a success. The embedded calculations reduce the mass flow error from the 7% in [1], to a max- imum less than 2%, which is an evidence of great improvement in accuracy.更多还原