Progress in the development of quasi-three-dimensional and full three-dimensional numerical solutions for steady subsonic rotational flow through turbomachines is presented. An iterative calculation between the flow on a mean hub-to-tip S2 stream surface and a number of blade-to-blade S1 stream surfaces gives the quasi-three-dimensional solution, which is very easily extended to give full three-dimensional solution by merely calculating a few more S2 surface flows and relaxing the restriction that S1 surfaces are surfaces of revolution. A new S2–S1 iteration scheme has been developed and employed in the present code. The governing equations on the S1 and S2 surfaces are expressed in terms of general nonorthogonal curvilinear coordinates so that they are body-fitted without any coordinate transformation and are solved by either matrix method or line-relaxation method. An automatic computing system is used, which first computes the quasi-three-dimensional flow for blade design and then computes the full three-dimensional flow for the blade row just designed. The results obtained by applying this computing system to the design and determination of full three-dimensional flow field of a two-stage axial compressor and a high subsonic compressor stator are obtained and shows clearly the amount of the twist of the general S1 surfaces and the difference in the flow field between the quasi-three-dimensional and full three-dimensional solutions.

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