In this paper, we investigate steady inviscid compressible flows with radial symmetry in an annulus. The major concerns are transonic flows with or without shocks. One of the main motivations is to elucidate the role played by the angular velocity in the structure of steady inviscid compressible flows. We give a complete classification of flow patterns in terms of boundary conditions at the inner and outer circle. Due to the nonzero angular velocity, many new flow patterns will appear. There exists accelerating or decelerating smooth transonic flows in an annulus satisfying one side boundary conditions at the inner or outer circle with all sonic points being nonexceptional and noncharacteristically degenerate. More importantly, it is found that besides the well-known supersonic-subsonic shock in a divergent nozzle as in the case without angular velocity, there exists a supersonic-supersonic shock solution, where the downstream state may change smoothly from supersonic to subsonic. Furthermore, there exists a supersonic-sonic shock solution where the shock circle and the sonic circle coincide, which is new and interesting.

在本文中，我们研究了环形空间中具有径向对称性的稳定无粘性可压缩流动。主要的关注点是具有或不具有冲击的跨音速流动。主要动机之一是阐明角速度在稳定的无粘性可压缩流结构中所起的作用。我们根据内圆和外圆的边界条件对流型进行了完整的分类。由于角速度非零，因此将出现许多新的流动模式。在内圆或外圆上满足一侧边界条件的环形空间中，存在着加速或减速的平稳跨音速流，所有的声波点都是非异常且非特性退化的。更重要的是，已经发现，除了在不存在角速度的情况下在发散喷嘴中众所周知的超音速-亚音速冲击之外，还存在超音速-超音波冲击解，其中下游状态可以从超音速平稳地改变为亚音速。此外，还存在一种超音速冲击解决方案，其中冲击圈和声波圈重合，这是新的且有趣的。