Document Type

Dissertation - Open Access

Award Date


Degree Name

Doctor of Philosophy (PhD)

Department / School

Civil Engineering

First Advisor

Edward Lumsdaine


A new method for the calculation of the unsteady circulation distribution in axial flow compressors was developed. The classical assumption of representing the rotor by a two-dimensional infinite cascade was eliminated. Instead the more realistic case of a radial cascade with blades of finite length was studied. The blades were assumed to be thin and only slightly cambered. The flow was assumed ·to be incompressible and inviscid and the secondary flow effects were neglected. The velocity induced at an arbitrary point of a reference blade due to the bound vortices on the blade under consideration and the other blades and the shed vortices was calculated, hence the integral equation of the circulation could be obtained. The circulation function was then expanded in a Fourier series with complex coefficients; those were evaluated using Glauert method. The value of the circulation as calculated by the present method was found to reduce to the steady state solution for zero disturbance frequency. In the limiting case of a long blade, when the effects of other blades are neglected, the solution was also found to reduce to the classical two-dimensional solution for a single airfoil subject to periodic disturbances. Recent methods for the solution of unsteady flow through two-dimensional cascades were also shown to be special cases of the general solution presented here. The value of the circulation calculated using the present analysis was used in the classical theory of compressor noise prediction to study the effects of the different compressor design parameters on the noise generated under different types of inlet disturbances. The results suggest that in reaching an optimum design based on minimum noise both steady and unsteady loading effects must be taken into consideration. It was also found that in the unsteady case as in the steady case the radial distribution of the circulation has a very significant effect on the sound power level generated by the compressor and that minimum noise can be achieved when no pronounced radial fluctuations in the incoming flow upstream of the compressor are present.

Library of Congress Subject Headings





South Dakota State University