Chapter 6 - Three-dimensional and meridional flows in turbomachines

Summary

Introduction

Our principal aim so far has been to lay down the foundations of surface vorticity analysis for a series of progressively more advanced turbomachinery flow problems. Although a brief outline of threedimensional flow analysis was presented in Chapter 1, specific applications have been limited to problems which are twodimensional in the strict mathematical sense. Unlike the source panel method, which has been extensively applied to threedimensional flows, serious application of the surface vorticity analysis has been limited to few such engine problems. The aim of the first part of this chapter will be to expand on the basic foundation theory for dealing with the flow past three-dimensional objects by surface vorticity modelling and to consider two such problems in turbine engines which have received some attention. These will include the prediction of engine cowl intake performance at angle of attack and the behaviour of turbine cascades exhibiting sweep.

As discussed in Chapter 3 the flow through turbomachinery blade passages is in general three-dimensional, although the design or analysis problem may be tackled in a practical way by reference to a series of superimposed equivalent interacting two-dimensional flows. The two models usually adopted, which are equivalent in some respects, are the S-1, S-2 surfaces of Wu (1952) and the superposition of blade-to-blade (S-2 type) flows upon an assumed axisymmetric meridional flow. We concluded Chapter 5 with a derivation of the meridional flow equations for ducted propellers, indicating that the blade-to-blade/meridional interactions result in vorticity production within the mainstream.