Calculation of blade-to-blade flow in a turbomachine by streamline curvature

Abstract

The object of a blade-to-blade method is to calculate the blade surface velocity distribution and the outlet angle for a given three-dimensional cascade. These give the heat drop or work done and indicate whether shock waves are likely to occur. A boundary layer calculation can then also be done to estimate the profile loss and to see if separation is likely and how much laminar flow there might be. Most methods available at present can only deal with special cases such as two-dimensional compressible flow or three-dimensional incompressible flow. The nearest alternative approach to a complete method, using a through flow method, has a longer run time and cannot find the outlet angle. A new method is described in this report for calculating the compressible flow in a three-dimensional cascade of blades. This uses the 'stream line curvature' technique with tangential quasi-orthogonals, and the shapes of the stagnation streamlines are determined iteratively to satisfy the condition of periodicity in the tangential direction. This condition is also sufficient to determine the outlet angle. The calculation includes all effects of compressibility, change of annulus area and change of radius, enabling deviations due to velocity ratio and Coriolis forces to be found. Comparisons of theoretical predictions with those of other theories and with experiment for particular cases show good agreement. A new design method for calculating the blade shape required for a prescribed velocity distribution is also outlined as a simple extension to the analysis method. These methods can be applied to cascades in steam, gas and water turbines, gas circulators, compressors and pumps with axial, mixed or radial flow.