An analytical/numerical method for calculating blade-to-blade transonic flow fields around blade elements of an axial compressor rotor of a turbomachine is presented. Radius variation and stream sheet convergence are included. The analysis considers the time-dependent Navier-Stokes equations in conservation-law form which allows for viscous shock wave formation. A discretized method of characteristics is used to determine the boundary conditions along the blade surface and exit plane. An explicit, time-dependent, second-order, finite difference technique is utilized to numerically solve these partial differential equations in a transformed computational plane. Comparison of numerical results with cascade and rotor data indicate good agreement for blade surface pressure distributions and mixed-out exit conditions.

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