旋转坐标系下三维MUSCL格式的构成

MUSCL格式是近年来新发展的许多高分辨率格式之一，但直接将该格式应用到旋转坐标系时，会使计算发散或得到非物理解，不能计算旋转机械的内部流场。本文在原有MUSCL格式的基础上，根据旋转坐标系下雷诺平均N－S方程，重新构成了MUSCL格式，并且与原有MUSCL格式进行了比较，分析了两者相同与不同之处，利用该格式对两个典型算例（旋转直管和跨音速压气机）进行了计算，通过与试验结果对比表明，重新构成的MUSCL格式能够计算包括跨音速气机在内的复杂旋转机械流场，从而扩展了MUSCL格式的应用范围。

Construction of MUSCL Scheme in Moving Reference Frame

Monotonic upwind scheme for conservation law (MUSCL) scheme is one of the developing high-resolution schemes. It cannot be used for calculating the flow field in the moving reference frame directly, otherwise the results will be diverged and the non-physical results will be got. To solve this problem, based on the original one in the stationary frame and the full three-dimensional N-S equation in the moving reference frame, an MUSCL scheme is reconstructed. Compared with the original one, the new scheme has two steps, one is interpolation step, and the other is upwind step. The form of the expressions is similar to the original one. But there are some differences between two schemes, such as the transfer matrix coefficient and the expression of energy. Two typical benchmarks are calculated by using the new scheme, one is a rotating duct and the other is an axial-flow transonic compressor rotor. The detailed flow-field structures, the secondary flows, and vortex development in the blade passage can also be obtained from these results. Comparison of the computational and the experimental results shows that the scheme can predict the complex turbulent flow. The scheme is robust and reliable. The using range of the MUSCL scheme is extended.