QUASI-THREE-DIMENSIONAL NUMERICAL ANALYSIS OF TURBOMACHINERY FLOWS
Abstract
A quasi-three-dimensional numerical analysis method has been developed to solve the governing equations for the steady (relative), inviscid, adiabatic flow of a perfect fluid on multiple hub-to-shroud stream surfaces through turbomachinery. The numerical algorithm, based on the method of Wu, was programmed in FORTRAN to calculate the subsonic or shock-free transonic flow solution in a turbomachine blade row. The blade row may be fixed or rotating, and the blades may be twisted or leaned. Flow may be axial, mixed, or radial. Subsonic solutions are obtained by a finite difference-stream function solution. Transonic solutions are obtained by either a velocity-gradient method or velocity-scaling method, both of which use information from a finite difference-stream function solution at a reduced mass flow. The method has been implemented on the CDC 6600 computer and three typical turbomachinery flow fields have been calculated. These cases include an axial flow compressor rotor, a turbine stator vane cascade, and a radial-inflow turbine rotor. The results obtained from the quasi-three-dimensional hub-to-shroud calculation are compared with those obtained from a two-dimensional midchannel hub-to-shroud calculation and illustrate how the quasi-three-dimensional S2 stream surface shape and thickness vary from that of the midchannel blade mean-camber S2 stream surface used in the two-dimensional calculation. In some cases, the midchannel calculation method performed as well as the quasi-three dimensional approach and with considerably less computational time. In other cases, the true nature of the S1 and S2 stream surfaces preclude complete reliance on the two-dimensional technique and necessitate the use of a quasi-three-dimensional (or perhaps a full three-dimensional) calculation. The method presented in this thesis represents an intermediate step in the complete quasi-three-dimensional solution process for turbomachinery flow fields. However, the results demonstrate the ability of this technique to complement and extend the applicability of the two-dimensional method and thus aid the engineer in the analysis of this most complex flow.
Degree
Ph.D.
Subject Area
Mechanical engineering
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