A Study of Compressible Perfect Fluid Motion in Turbomachines with Infinitely Many Blades

Citation

Monroe, Gerald Morgan (1951) A Study of Compressible Perfect Fluid Motion in Turbomachines with Infinitely Many Blades. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HQD3-G406. https://resolver.caltech.edu/CaltechETD:etd-03182009-151729

Abstract

A study is made of compressible perfect fluid motion in turbomachines having infinitely many blades and a general theory is developed. An underlying concept of the theory is that force fields which represent the action of infinitely many blades belong to a special class described as pseudo-conservative and can be expressed as the product of a scalar function and the gradient of a potential. The scalar function is simply the rate at which energy is imparted to the fluid by the blades, and the potential is simply the family of the equations for the blade surfaces. The introduction of these two functions to express the force field casts an entirely new light on problems of mixed-flow turbomachines having infinitely many blades of arbitrary shape. In the formulation of the problem the non-linear action of rotationality and compressibility is regarded as a force tending to displace the streamsurfaces from their irrotational, incompressible position. It is shown that the character of the problem is determined by a governing velocity: the velocity relative to the blades where blades are present, or the meridional velocity, where blades are not present. Where the governing velocity is subsonic the problem is essentially elliptic, where supersonic, hyperbolic. The theory and the examples lead to conclusions which are believed to explain in part the unexpected efficiencies observed for compressors having transonic governing velocities. These conclusions, which indicate that transonic compressors could perhaps be profitably developed, are as follows: The deflection of the streamsurfaces induced by a given strength of vorticity at a certain point in the flow has one sense when the governing velocity at the point is subsonic, the opposite sense when it is supersonic, and becomes zero as it becomes sonic. The deflection of the streamsurfaces brought about by a given distribution of vorticity in a region is less when the governing velocity in the region is transonic than when it is entirely subsonic or entirely supersonic. Examples of incompressible flow through a mixed flow compressor with prescribed blades, and subsonic and transonic flow through actuator disks, were solved by the method of finite differences, applying simultaneously the relaxation technique and an iteration process.

Thesis Files