一种利用正交流线坐标系求解跨音速管流的新方法

本文以正交流线坐标系为工具,采用位流模型,导出了正交流线坐标系下平面或轴对称流动的控制方程组,利用流函数与位函数的存在性,进而导出了两个首次积分。设计了一套求解匀熵管流的分凝迭代方案,模拟了管内无激波的平面或轴对称喷管的跨音速流动。数值实验表明该方法能够处理小喉道曲率半径平面或轴对称喷管跨音速流动,与已有的数值计算结果及实验结果符合较好。

A NEW METHOD FOR RESOLVING TRANSONIC NOZZLE FLOWS USING ORTHOGONAL STREAM-LINES COORDINATE SYSTEM

For resolving the problems with curved boundaries or complex configurations, body-fitted coordinate systems are commonly used in computational fluid dynamics. As a body-fitted coordinate system,stream-lines(surfaces)coordinate system possesses characteristics similar to the adaptive-grid techniqures. When it is used for solving transonic or supersonic flow problems, rotated difference algorithm is not needed and C. F. L. condition can be satisfied easily. In present paper, the governing equations for 2-D,steady,inviscid and irrotational flows based on the orthogonal stream-lines coordinate system is formulated. In addition,two first-integral formulations are deduced. A fast converging iterative procedure is developed for solving the nozzle problems having small radius of curvature on the nozzle wall at the throat,and large ratios of convergence and divergence. Nozzle flow fields are computed using the method developed in the present work and the distributions of flow parameters inside nozzles are given.