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Higher Order Approximate Solutions for the Flow in Axial Turbomachines


Monroe, Gerald Morgan (1949) Higher Order Approximate Solutions for the Flow in Axial Turbomachines. Engineer's thesis, California Institute of Technology. doi:10.7907/8BJW-AE38.


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.

Item Type:Thesis (Engineer's thesis)
Subject Keywords:Aeronautics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marble, Frank E.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1949
Record Number:CaltechETD:etd-01282009-092006
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:391
Deposited By: Imported from ETD-db
Deposited On:28 Jan 2009
Last Modified:28 Mar 2023 22:20

Thesis Files

PDF (Monroe_gm_1949.pdf) - Final Version
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