The Rotational Motion of an Ideal Fluid and Application to the Three-Dimensional Flow Through Axial Turbomachinery

Citation

Marble, Frank Earl (1947) The Rotational Motion of an Ideal Fluid and Application to the Three-Dimensional Flow Through Axial Turbomachinery. Engineer's thesis, California Institute of Technology. doi:10.7907/CJJR-H730. https://resolver.caltech.edu/CaltechETD:etd-11122003-141530

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 non-uniform shock waves. The iteration process linearizes the essentially non-linear 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 n-1th 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 non-uniform flow in a two-dimensional parallel-wall channel by means of a screen and 2) The three-dimensional flow in a multistage axial turbomachine having an infinite number of blades in each blade row. The second of these, the three-dimensional 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 non-linear in some respects, especially as to the approach to periodic solutions for a succession of similar stages.

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