Introduction

As early in the history of gas turbines and internal aerodynamics as 1952, C. H. Wu recognised the truly three-dimensional nature of the flow in turbomachines and proposed a remarkably sophisticated scheme for numerical analysis illustrated by Fig. 3.1. The fully three-dimensional flow was treated by the superposition of a number of two-dimensional flows which were of two types located on the so-called S-1 and S-2 stream surfaces. S-2 surfaces follow the primary fluid deflection caused by the blade profile curvature and its associated aerodynamic loading. Due to the blade-to-blade variation in static pressure the curvature of each S-2 stream surface will differ, calling for several surfaces for adequate modelling of the flow. S-1 surfaces account for consequent twist in the so-called ‘through-flow’ or ‘meridional flow’ which comprises a family of stream surfaces which approach axisymmetry close to the hub and casing and exhibit maximum departure from axisymmetry at the blade passage mid height. By solution of the flows on this mesh for successively improved estimates of the S-1 and S-2 surfaces, allowing for fluid dynamic coupling between them, an iterative approach to the fully three-dimensional flow was fairly comprehensively laid out by Wu in a paper which was truly twenty years ahead of its time.

Until relatively recently such calculation procedures have been ruled out by lack of suitable computing facilities. It was in 1966 that Marsh gave a strong impetus to computer application of Wu's method by developing the well known matrix through-flow analysis.