A 2D partially-parabolic procedure for axial-flow turbomachinery cascades

Abstract

A general finite-difference procedure is presented for the calculation of steady, two-dimensional 'partially-parabolic' flows, with special reference to turbine cascade problems. It can be used for incompressible, subsonic, supersonic or transonic flows. It can be characterised as an 'iterative space-marching' method. The method is more economical in computer storage than time-marching procedures; and computer time is also low. The main distinguishing features of the method are: (a) use of a streamline coordinate system, (b) one-dimensional storage for all variables except pressure, (c) solution by repeated marching integration from upstream to downstream. The capabilities of the method are demonstrated by application to six different inviscid-flow problems. In each case, computed results are compared with the available analytical or experimental data. Good agreement is shown. The method is capable of including momentum transfer across streamlines by viscous effects; it can easily incorporate a two-equation turbulence model; and heat transfer can be simultaneously calculated.