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`Fundamentals ofJet Propulsion
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`with Applications
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`RONALD D. FLACK
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`Univérsigi of Virginia
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`CAMBRIDGE
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`UNIVERSITY PRESS
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`GE v. UTC
`TriaI‘IPRZO‘I6‘-T)09’52
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`UTC-2020.001
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`UTC-2020.001
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`GE v. UTC
`Trial IPR2016-00952
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`CAMBRIDGE UNIVERSITY PRESS
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`Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, S50 Paulo
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`Cambridge University Press
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`40 West 20th Street, New York, NY 10011-4211, USA
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`www.cambridge.org
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`Information on this title: wwVw.cambn'dge.org/9780521819831
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`© Cambridge University Press 2005
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`This book is in copyright. Subject to statutory exception
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`and to the provisions of relevant collective licensing agreements,
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`no reproduction of any part may take place without
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`the written permission of Cambridge University Press.
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`First published 2005
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`Printed in the United States of America
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`A catalog recordfor this publication is availablefrom the British Library.
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`Library of Congress Cataloging in Publication Data
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`Flack, Ronald D., 1947»
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`Fundamentals ofjet propulsion with applications / Ronald D. Flack, Jr.
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`cm. — (Cambridge aerospace series ; 17)
`p.
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`Includes bibliographical references and index.
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`ISBN 0-521-81983-0 (hardback)
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`1. Jet engines.
`I. Title.
`II, Series.
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`TL709.F5953 2005
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`621 .43'52 — dc22
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`2004020358
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`On the cover is the PW 4000 Series — 112-inch fan (courtesy of Pratt & Whitney)
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`ISBN-13
`978—0—52l—8l983—l hardback
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`ISBN—l 0 0-521-81983-0 hardback
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`Cambridge University Press has no responsibility for
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`the persistence or accuracy of URLs for external or
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`third—party Internet Web sites referred to in this book
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`and does not guarantee that any content on such
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`Web sites is, or will remain, accurate or appropriate.
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`UTC-2020.002
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`6 / Axial Flow Compressors and Fans
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`the tip and with significant blade twist from hub to tip. Typical total pressure ratios for fans
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`are 1.3 to 1.5 per stage. However, the fimdamental thermodynamics, fluid mechanics, and
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`design methodology are the same for the fan and two compressors. Thus, for the remainder
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`of this chapter no distinctions are made in the analysis of the three stage types.
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`If one were to unwrap the blades around the periphery of the compressor and consider
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`its geometry to be planar two-dimensional when viewed from the top, a series of “cascades”
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`would be seen as shown in Figure 6.6.a. The fluid first enters the inlet guide vanes. Next,
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`it enters the first rotating passage. In Figure 6.6.a, the rotor blades are shown to be moving
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`with linear velocity U, which is found from Ra), where w is the angular speed and R is the
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`mean radius of the passage. The blades and vanes are in fact airfoils, and the pressure (+ +)
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`and suction surfaces (— —) can be defined as shown in the figure. Afier passing through the
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`cascade of rotor blades, the fluid enters the cascade of stator vanes. The fluid is turned by
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`these stationary vanes and readied to enter the second stage, beginning with the second rotor
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`blades, ideally incidence free. In general, the second stage has a slightly different design
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`than the first stage (all of the stages are different). The process is repeated for each stage. In
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`Figure 6.6.3, compressor component stations 0 through 3 are defined. It is very important
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`not to confuse these with engine station designations.
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`An important parameter in compressor design is the solidity, which is defined as C/s,
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`where s is the blade spacing, or pitch, and C is the chord. The solidity is the inverse of
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`the pitch-to-chord ratio s/ C. Both parameters are defined in Figure 6.6.a. If the solidity
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`becomes too large, frictional effects, which decrease the efficiency and total pressure ratio,
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`become large because the boundary layers dominate the passage flow. However, if the
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`solidity becomes too small, sufficient flow guidance is not attained (this phenomenon is
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`termed “slip”) and the flow thus does not adequately follow the blade shape. Separation
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`can also become a major problem. For the low—solidity case due to slip, less power is added
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`to the flow than desired; as a result, the compressor does not operate at the necessary
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`pressure ratio. Because of accompanying separation (and losses), the maximum efficiency
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`is not realized. Thus, a compromise is needed. In Section 6.11 a method is presented to
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`optimize the single-stage aerodynamic performance or maximize the efficiency. Typical
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`values of solidity for a compressor are approximately 1. The selection of solidity is partially
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`responsible for the resulting number of blades in a cascade. For example, for the Pratt &
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`Whitney JT9D turbofan, 46 blades are used on the fan rotor stage, and the number of blades
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`on the compressor stages ranges from 60 to 154. For comparison, the exit guide vanes for
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`the fan (which has an extremely large chord) have only nine blades.
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`It is very important that the number of stator vanes and rotor blades for a stage or nearby
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`stages be different. If they were equal, a resonance due to fluid dynamic blade interactions
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`could be generated, resulting in large blade, disk, and shaft vibrations accompanied by
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`noise. This would reduce the life of the blades and compromise engine safety. Often, and if
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`possible, blade or vane numbers are selected as prime numbers, but they are always chosen
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`such that common multiple resonances are not excited. Cumpsty (1977) reviews this topic
`in detail.
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`Another important parameter for blade performance is the ratio of the distance to the
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`maximum camber to the chord length of the blade a. This distance is also shown in Figure
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`6.6.a. This parameter strongly influences the lift and drag characteristics of blades, which
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`in turn have marked effects on the efficiency and pressure ratio of a stage.
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`If one examines the cross-sectional flow areas in the passages between the blades (area
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`normal to the mean flow direction), it will be seen that the areas increase from the inlet to
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`the exit of the rotor, as shown in Fig 6.6.b, and also increase from the inlet to the exit of the
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`stator. Thus, both the rotor and stator blade rows act like diffuser sections.
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