Numerical Representation of Inlet and Exit Boundary Conditions in Transient Cascade Flow

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.