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A numerical technique is presented for the calculation of steady inviscid transonic flows in turbomachinery cascades, wherein both subsonic and supersonic regions co-exist. The problem is posed in the time-dependent form and the aysmptotic solution at large times provides the solution of the steady physical problems. The solutions for a hyperbolic nozzle cascade and two turbine cascades are compared with other analytical solutions and with an experimental result. The agreement appears to be very good. Some preliminary results are presented for a flow containing an oblique shock and its reflection. The computed results compare satisfactorily with the exact solution.

An important building block in the development of finite difference time dependent techniques for mixed supersonic-subsonic flow calculation is the treatment of the inlet and exit boundary conditions. For cascade computations, it is convenient to locate the planes at a finite distance from the blade and hence conditions along these planes must be allowed to vary according to the overall cascade performance. It is shown in this paper that as long as the meridional velocity is subsonic, three flow variables must be specified at the inlet and one variable at the exit. The remaining flow variables must be computed as part of the solution. The paper contains a method derived from the theory of characteristics for the computation of the remaining variables under the assumption that the flow is axisymmetric at the inlet and exit planes. The response of typical turbine and compressor cascades to back pressure variations as computed by this technique is also presented.

A numerical technique is presented for the calculation of shocked flows in compressor cascades. The problem is posed in the time-dependent form and the asymptotic solution at large times provides the solution of the steady physical problem. The solutions exhibit the formation and movement of shocks as the static pressure ratio across the cascade is varied. The resulting inlet and outlet angles and total pressure loss are also shown.