Citation
Marble, Frank E. (1947) The rotational motion of an ideal fluid and application to the threedimensional flow through axial turbomachinery. Engineer's thesis, California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd11122003141530
Abstract
The present paper discusses the principles and applications of an iteration method for solving certain problems involving rotational motion of an ideal fluid, such as occur in the presence of heat transfer, combustion, mechanical work processes, and nonuniform shock waves. The iteration process linearizes the essentially nonlinear equations for rotational fluid motion by assuming a process for the vorticity transport, namely: the nth approximation is linearized by assuming the vorticity to be transported by the n1th velocity field. In some important cases, the first order solutions seem to offer considerable accuracy.
Two applications of the procedure are discussed in some detail, namely: 1) The process of straightening a nonuniform flow in a twodimensional parallelwall channel by means of a screen and 2) The threedimensional flow in a multistage axial turbomachine having an infinite number of blades in each blade row. The second of these, the threedimensional flow through a turbomachine, is given detailed analysis bearing some analogy to the Prandtl theory of finite wings. The results for the first order solution of velocity and enthalpy distributions are given explicitly and are shown to be defined by four relatively simple integrals. The cases of rotating and stationary single blade rows are evaluated completely. The general iteration process for obtaining higher approximations, utilizing the method of Green's functions, is given in some detail.
The calculations of the flow field generated by a blade row of given geometry is illustrated by the problem of a "vortex" turbomachine operating off the design condition. The problem is found to be essentially nonlinear in some respects, especially as to the approach to periodic solutions for a succession of similar stages.
Item Type:  Thesis (Engineer's thesis) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  1 January 1947 
Record Number:  CaltechETD:etd11122003141530 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd11122003141530 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4519 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  12 Nov 2003 
Last Modified:  26 Dec 2012 03:09 
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