Three-Dimensional-Flow Theories for Axial Compressors and Turbines

Abstract

It has long been known that the energy losses occurring in an axial compressor or turbine cannot be fully accounted for by the skin-friction losses on the blades and annulus walls. The difference, usually termed secondary loss, is attributed to miscellaneous secondary flows which take place in the blade row. These flows both cause losses in themselves and modify the operating conditions of the individual blade sections, to the detriment of the overall performance. This lecture analyses the three-dimensional flow in axial compressors and turbines, so that, by appreciation of the factors involved, possible methods of improving the performance can readily be investigated. The origin of secondary flow is first examined for the simple case of a straight cascade. The physical nature of the flow, and theories which enable quantitative estimates to be made, are discussed at some length. Following this, the three-dimensional flow in an annulus with a stationary blade row is examined, and, among other things, the influence of radial equilibrium on the flow pattern is noted. All physical restrictions are then removed, and the major factors governing the three-dimensional flow in an actual machine are investigated as far as is possible with existing information, particular attention being paid to the influence of a non-uniform velocity profile, tip clearance, shrouding, and boundary layer displacement. Finally the various empirical factors used in design are discussed, and the relationships between them established.

Principles of Turbomachinery

“…This lends itself to computer-based design, as is well illustrated by Railly [95] and Railly and Howard [96]. He showed that for constant stagger angle the maximum efficiency occurred at a Table 7.1 Steps in the calculation of optimum performance, following Carter [38]. McKenzie [29] used a low speed four-stage compressor with a hub : tip ratio of 0.8, provided with constant section blades with C5 profiles on circular arc camber lines.…”

“…The well known plots of m against stagger angle for circular arc and parabolic camber lines due to Carter [38] are shown in Fig. 3.21.…”

“…The problem of designing profiles, or of applying known information to a given situation, has not yet been covered, so that the classical English approaches due to Howell [36] and Carter [38] will be introduced, and Howell's correlation applied to a sample compressor problem. Other matters of fundamental interest are the blade profiles used and their behaviour, the numbers in successive rows, the axial spacing between sets of blades and the interaction of the flow leaving one cascade on the pattern of flow at inlet to the next.…”

“…Carter's correlation [38] proceeded to relate the optimum lift: drag ratio to the deflection, gas incidence angle and outlet angle. A design following his approach would be as in Table 7.1.…”

“…(4) Find the optimum incidence i oPt for an isolated aerofoil (see Carter [34,38]). (4) Find the optimum incidence i oPt for an isolated aerofoil (see Carter [34,38]).…”