Application of Radial-Equilibrium Condition to Axial-Flow Compressor and Turbine Design

Basic general equations governing the three-dimensional compressible flow of gas through a compressor or a turbine are given in terms of velocity components, total enthalpy, and entropy. These equations are used to determine the radial motion of gas through an axial-flow compressor or a turbine and the corresponding effects on the radial variations of the state of gas between successive blade rows in the case of steady, axially symmetrical flow. The aspects ratio of the blade row is found to be an important factor in the calculation when the effect of radial motion is included. The usual method, which neglects the effect of radial motion, is shown to be good only for the limiting case of zero blade-row aspect ratio, that is for the case where the axial length of the blade row is much larger than the radial length of the blade row. A sinusoidal radial-flow path is found to give the effect of radial motion on the radial variation of gas state between blade rows as small as likely without any discontinuity in the curvature of the streamline and is suggested for use in design calculations. The equations are applied to investigate the maximum compatible number of the radial variations of the gas properties between successive blade rows that a designer is free to specify. The various ways of taking up these degrees of freedom and the different types of design obtained are discussed. A general procedure is given to calculate the characteristics of a compressor or turbine of any given type of design, taking into account the effect of radial motion of gas. Numerical calculations made for two types of compressor and one type of turbine show that even in the case of nontapered passage, these is appreciable radial motion and that the corresponding effects are of significant magnitude and should be taken into account in design.