Higher Order Approximate Solutions for the Flow in Axial Turbomachines

Author: Monroe, Gerald Morgan

Year: 1949

Degree: Engineer's thesis

Advisor: Marble, Frank E.

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/8BJW-AE38

Abstract

The theory of the three-dimensional rotational flow of an incompressible and inviscid fluid through an axial turbomachine is described and the hydrodynamical equations are simplified by considering an infinite number of blades in each row. The forces of the blades on the fluid are treated as non-conservative body forces distributed uniformly about the axis.

Formulation of the mathematical problem leads to one non-linear partial differential equation and two integral equations for the three velocity components. A linearized solution of these simultaneous equations for any prescribed blade loading is based on the consideration that the vorticity generated by the blades is transported downstream by the mean axial velocity. An iteration process which leads to solutions of greater accuracy is developed by considering for each iteration that the vorticity is transported by the velocities found by the previous iteration.

The Bessel's functions which occur in the Green's function solution are replaced by their asymptotic values and the infinite series is summed to express the solution in closed form. The iteration process is then adapted to mechanical calculations by dividing the region of vorticity into small rings of rectangular cross-section and determining the influence on the velocity of a unit change of vorticity in each of these rings. Once this influence is established it is relatively easy to calculate the velocities in any axial flow machine with any prescribed blade loading.

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