圆转方非轴对称喷管无粘流动的多层网格法求解

Multigrid Solutions of 3-D inviscid Flows through Circulax-To-Rectangular Ducts

本文利用多层网格法求解三维无粘亚音和跨音速圆转方非轴对称喷管的流动,基本格式是把Ni[1]的二维有限体积积分格式推广到三维流场。边界条件采用文[2]中的“预测一修正”处理方法。为了进一步提高格式稳定性,在计算流动变量的一阶时间变化量时,采用单元体积平均法而不是文[1]中的算术平均法。引入当地时间步及多层网格方法,以加快格式的收敛速度。文中还对多层网格构造形式及其收敛效果作了讨论。通过对两种喷管模型流动的计算和与试验数据的对比,验证了该算法的精度。

The 3-D inviscid subsonic and transonic flows through circular-to-rectangular transition ducts for nonaxisymmetric nozzles are solved by using a multigrid method. The Ni's 2-D finite volume integration scheme [1] is expanded for the solution of 3-D Euler flow equations, and the 'prediction-correction' method presented in [2] is successfully employed in handling the boundary conditions of the complex 3-D nozzle flows. In order to improve the stability of the scheme, the first order time rate change of the flow variables at grid point is obtained by using cell volume average instead of arithmetic average in [1]. Convergence to a steady state is enhanced by local time stepping and the use of multiple grids. The paper also discusses the constructing forms of multigrid method as well as convergence efficiency, and results show that the better convergence rate can be obtained by updating the flow variables immediately after corrections in each coarse grid are calculated and interpolated into the finest grid. Finally, solutions to the 3-D inviscid flows in two nozzle configurations are presented (one with subsonic inlet and exit flows and the other with subsonic inlet and supersonic exit flows), and the experimental results about these cases are provided to test the accuracy of the scheme.