Analytical Investigation of Some Three-Dimensional Flow Problems in Turbomachines

One problem encountered in the theory of turbomachines is that of calculating the fluid velocity components when the inner and outer boundaries of the machine as well as the shape of or forces imparted by the blade row are given. The present paper discusses this problem under the restrictions that the fluid is inviscid and incompressible and that the blade rows consist of an infinite number of infinitely thin blades so that axially symmetric flow is assumed. It is shown, in general, that the velocity components in a plane through the turbomachine axis may be expressed in terms of the angular momentum and the leading-edge blade force normal to the stream surfaces. The relation is a nonlinear differential equation to which analytic solutions may be obtained conveniently only after the introduction of linearizing assumptions. A quite accurate linearization is effected through assuming an approximate shape of the stream surfaces in certain nonlinear terms. The complete linearized solution for the axial turbomachine is given in such form that blade loading, blade shape, distribution of angular momentum, or distribution of total head may be prescribed. Calculations for single blade rows of aspect ratio 2 and 2/3 are given for a radius ratio of 0.6. They indicate that the process of formation of the axial velocity profile may extend both upstream and downstream of a high-aspect-ratio blade row, while for low aspect ratios the major portion of the three-dimensional flow occurs within the blade row itself. When the through-flow velocity varies greatly from its mean value, the simple linearized solution does not describe the flow process adequately and a more accurate solution applicable to such conditions is suggested. The structure of the first-order linearized solution for the axial turbomachine suggested a further approximation employing a minimizing operation. The simplicity of this solution permits the discussion of three interesting problems: Mutual interference of neighboring blade rows in a multistage axial turbomachine, solution for a single blade row of given blade shape, and the solution for this blade row operating at a condition different from the design condition. It is found that the interference of adjacent blade rows in the multistage turbomachine may be neglected when the ratio of blade length to the distance between centers of successive blade rows is 1.0 or less. For values of this ratio in excess of 3.0, the interference may be an important influence. The solution for the single blade row indicated that, for the blade shape considered, the distortion of the axial velocity profile caused by off-design operation is appreciably less for low- than for high-aspect-ratio blades. To obtain some results for a mixed-flow turbomachine comparable with those for the axial turbomachine as well as to indicate the essential versatility of the method of linearizing the general equations, completely analogous theoretical treatment is given for a turbomachine whose inner and outer walls are concentric cones with common apex and whose flow is that of a three-dimensional source or sink. A particular example for a single rotating blade row is discussed where the angular momentum is prescribed similarly to that used in the examples for the axial turbomachine

George MacDonald and J.R.R. Tolkien on Faerie and Fairy Stories

The paper discusses the ideas of George MacDonald and J.R.R. Tolkien on Faërie and Fairy Stories, based on an analysis of MacDonald\u27s essay The Fantastic Imagination, Tolkien\u27s On Fairy-Stories, Tolkien\u27s correspondence, and Tolkien\u27s unpublished introduction to MacDonald\u27s The Golden Key

The Development of J.R.R. Tolkien\u27s Ideas on Fairy-stories

The paper is an analysis of how Tolkien\u27s thought on fairy-stories evolved between his 1939 St. Andrews Andrew Lang Lecture Fairy Stories, through his contribution On Fairy-Stories to the 1947 Essays Presented to Charles Williams, and concluding with his 1967 essay on the nature of Faërie. Time permitting, the paper will also include a discussion on how Tolkien\u27s Smith of Wooton Major illustrates his concepts

Overcoming Communism\u27s Dysfunctional Legacy: The Romanian Case

The paper develops the idea that post-communist societies are dysfunctional societies and applies this analysis to a study of contemporary Romania, 1989-2011. It looks at how the historical experiences of Romania both before and during communist rule created such a society, the development of Romania as a dysfunctional society between 1989 and 2002, and assesses the progress Romania has made in dealing with its legacy between 2002 and 2011 on the basis of several international indices

Design and optimization of Fugu's user communication unit

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1996.Includes bibliographical references (leaves 45-46).by Jonathan E. MIchelson.M.Eng

Relativity tests by complementary rotating Michelson-Morley experiments

We report Relativity tests based on data from two simultaneous Michelson-Morley experiments, spanning a period of more than one year. Both were actively rotated on turntables. One (in Berlin, Germany) uses optical Fabry-Perot resonators made of fused silica; the other (in Perth, Australia) uses microwave whispering-gallery sapphire resonators. Within the standard model extension, we obtain simultaneous limits on Lorentz violation for electrons (5 coefficients) and photons (8) at levels down to $10^{-16}$, improved by factors between 3 and 50 compared to previous work.Comment: 5 pages revtex, 2 figure