Based on the basic aerothermodynamic equations in the differential and integral forms on an arbitrary stream surface in an arbitrary nonorthogonal curvilinear coordinate system derived in this paper, the relations between gas parameters ahead of and behind a shock on such a stream surface are established. These relations are greatly different from the relations for a plane shock because they contain the normal direction of the spatial shock, and the correlations between the stream surfaces are closer. Assuming the location and shape of the shock and using the above relations, calculations on the generalized surfaces of revolution are made, and the iterations between these calculations and the calculation on the central S2 stream surface are completed. These computational results and comparison with those of the conventional throughflow calculation demonstrate some important features of the three-dimensional shock and the tranconic flow in an axial compressor rotor. They are also useful for the aerothermodynamic design of compressors.

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