Transonic Flow Along Arbitrary Stream Filament of Revolution Solved by Separate Computations With Shock Fitting

The transonic flow field in a cascade of blades lying on an S1 stream surface of revolution is solved by separate computations in the supersonic and the transonic region. The characteristics method is used to solve the supersonic flow upstream of the passage shock and the direct matrix method is used to solve the transonic flow downstream of the passage shock. The transonic stream-function equation in weak conservative form was discretized with respect to general non-orthogonal curvilinear coordinates. Using the artificial density technique and a new iteration scheme between the stream function and the density, the set of algebraic equations was solved by the direct matrix method. A computer program has been developed and is applied to compute the flow field on several S1 stream surfaces of revolution for the DFVLR transonic axial compressor rotor. It is found that the thickness of the S1 stream filament and the variation of entropy along the streamlines have strong influence on calculation. The calculated result agrees with the experimental data fairly well.