用多重网格技术求解平面叶栅跨音绕流

A FINITE VOLUME METHOD AND MULTIPLE-GRID TECHNIQUE FOR TRANSONIC FLOW FIELDS THROUGH PLANE CASCADES

1982年以来,Ni、Davis等人发展了一种与多重网格技术相结合的时间相关有限体积积分方法,这是一个快速求定常解的显式推进方法。本文采用这种方法计算平面叶栅跨音绕流,阐明了Ni-Davis格式的基本思想和处理原则,在物面边界近似处理上本文作了适当改进,为适当选取人工粘性项提出了具体平滑公式,又根据数值试验对多重网格技术提出了改进算法。两个跨音叶栅绕流算例表明,数值结果的精度和计算效率是令人满意的,可以满足航空发动机气动设计的需要。在IBM 4341计算机上,求解一个65×17网格上的跨音流场大约需CPU时间15分钟,使用四层网格技术后可节省CPU时间50％到60％。

Since 1982, Ni, Davis et al.have developed a time-dependent finite volume method combined with multiple -grid technique. It is an explicit scheme by which a steady state solution can be obtained rapidly. This paper adopts the method to compute the transonic flow field through plane cascades. First, elementary ideas and treatment principles of Ni-Davis scheme are clarified. The numerical treatments on solid wall boundary are then improved. The artificial viscous terms used are stated. With numerical tests, an improved algorithm for multiple -grid technique is presented. Finally, two examples of transonic flow fields through plane cascades are described. The computational accuracy and efficiency of numerical results are acceptable for aerodynamic design of aero-engine. Computing a steady state solution on a 65 x 17 grid takes about 15 minutes CPU time on IBM 4341 computer. With multiple-grid scheme, the savings in CPU time is about 50% to 60%.