COMPRESSOR
`COMPRESSOR
`AERODYNAMICS
`AERODYNAMICS
`
`N.A. Cumpsty
`
`UTC-2003 .001
`
`GE V. UTC
`
`IPR2018-01123
`
`

`

`Compressor
`aerodynamics
`
`N.A. Cumpsty
`Department of Engineering
`University of Cambridge
`
`KRIEGER PUBLISIIlNG COMPANY
`Malabar, Florida
`
`

`

`We are grateful to Pearson Education Limited, the original publisher of Compressor
`Aerodynamics, for permission to reproduce the typography and design of their c:dition.
`
`Original Edition 1989
`Reprinted 1996, 1997 and 1998
`Reprint Edition 2004 w/new Preface, Introduction and Updated Bibliography
`
`Printed and Published by
`KRIEGER PUBLISHING COMPANY
`KRIF.GERDRIVE
`MALABAR.,FLORIDA 32950
`
`Copyright© 1989 by Longman Group UK Limited (Pearson Education Limited)
`Transfered to Author
`Reprinted by Arrangement.
`
`All rights reserved. No part of this book may be reproduced in any fonn or by any
`means, electronic or mechanical, including information storage and retrieval systems
`without pennission in writing from the publisher.
`No liability is assumed with respect to the use of the information contained herein.
`Printed in the United States of America.
`
`FROM A DECLARATION OF PRINCIPLES JOINTLY ADOPTED BY A
`COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COM(cid:173)
`MITTEE OF PUBLISHERS:
`This publication is designed to provide accurate and authori1ative information
`in regard to the subject matter covered. It is sold with the understanding that the
`legal, accounting , or other
`in rendering
`is not engaged
`publisher
`professional service. If legal advice or other expert assistance is required, the
`services of a competent professional person should be sought.
`
`Library or Congress Cataloging-in-Publication Data
`
`Cumpsty, N. A.
`Compressor aerodynamics I N.A. Cumpsty.
`p. cm.
`Includes bibliographical references and index.
`Reprint. Originally published: Harlow, Essex, England : Longman Scientific &
`Technical, 1989.
`ISBN 1-57524-247-8 (alk. paper)
`I. Compressor-Aerodynamics. I. Title.
`
`TJ267.5.C5C86 2004
`621.5 1 l-dc22
`
`10 9 8 7 6 5
`
`2003069481
`
`

`

`-:ompressor
`>f their edition.
`
`:raphy
`
`Limited)
`
`m orby any
`~val systems
`
`edherein.
`
`l:DBYA
`ACOM-
`
`formation
`g that the
`or other
`uired, the
`
`1 Scientific &
`
`g1
`
`Contents
`
`Preface to the 2004 Krieger Reprint
`Preface
`Acknowledgements
`Notation
`Introduction to the 2004 Krieger Reprint
`
`1 Useful basic ideas
`. Introduction
`1.1
`1.2 Blades and flow
`1.3 Work input into compressors
`1.4 Dynamic scaling
`1.5
`Losses
`1.6 Efficiency
`
`2 General design considerations
`2.1
`Introduction
`2.2 The axial compressor
`2.3 The radial compressor
`2.4 The matching of multistage compressors
`
`3
`
`Throughflow on the hub-casing surface and some
`aspects of flow in three dimensions
`3.1
`Introduction
`3.2 Approximations applicable to axial compressors: simple
`radial equilibrium
`3.3 Early developments
`3.4
`Practical methods for the meridional flow
`3.5 Applications of streamline curvature methods in axial
`compressors
`3.6 Mixing in multistage axial flow compressors
`3.7 Axial compressor off-design trends
`3.8
`Flow chart - use of a streamline curvature method in
`analysis mode for an axial compressor
`
`ix
`xi
`xiii
`xv
`ixx
`
`1
`1
`1
`4
`11
`21
`34
`
`46
`46
`47
`62
`78
`
`93
`93
`
`97
`102
`106
`
`114
`121
`126
`
`129
`
`

`

`4 Blade-to-blade flow for axial compressors with
`subsonic inlet flow
`
`4.1
`Introduction
`The effect of blade shape
`4.2
`Loading limits for blade rows
`4.3
`4.4 The selection of incidence
`The prediction of deviation
`4.5
`. The determination and prediction of losses
`4.6
`The effect of Reynolds number on blade performance
`4.7
`The effect of inlet Mach number on blade performance
`4.8
`4.9 Concluding remarks
`
`5 Blade-to-blade flow for axial compressors with
`supersonic inlet flow
`
`'unique
`
`5.1
`Introduction
`5.2 Choked flow with attached shocks -
`incidence'
`5.3 Operation with detached shocks
`Shock structure and the nature of flow in supersonic
`5.4
`rotors
`5.5 Losses in supersonic blading
`5.6 The design process for supersonic blades
`
`132
`132
`140
`149
`159
`168
`171
`176
`180
`191
`
`194
`
`194
`
`198
`205
`
`209
`214
`217
`
`6
`
`.
`
`The centrifugal impeller
`
`220
`220
`6.1
`Introduction
`223
`The flow pattern in impellers
`6.2
`6.3 Calculation methods and predictions of flow in impellers 236
`245
`Slip and the estimation of slip factor
`6.4
`249
`6.5
`Loss in impellers
`254
`6.6 Design choices for the impeller
`
`7
`
`The diffuser of the centrifugal compressor
`
`7 .1
`Introduction
`7.2 The nonuniform flow from the impeller
`7.3
`The vaneless diffuser
`7.4 The vaned diffuser
`7.5 The volute or scroll
`
`8
`
`Viscous effects in compressors
`
`Introduction
`8.1
`8.2 Three-dimensional viscous flows in compressors
`
`266
`
`266
`269
`276
`285
`301
`
`310
`
`310
`314
`
`

`

`132
`132
`140
`149
`159
`168
`171
`176
`180
`191
`
`194
`194
`
`198
`205
`
`209
`214
`217
`
`1ance
`rmance
`
`:onic
`
`220
`220
`223
`impellers 236
`245
`249
`254
`
`266
`266
`269
`276
`285
`301
`
`310
`310
`314
`
`)
`
`8.3 Axial blade boundary layers
`Flow in the endwall regions of axial compressors
`8.4
`8.5 Viscous effects in centrifugal compressors
`
`9 Stall and surge
`Introduction
`9.1
`Instability and the inception of stall
`9.2
`Post stall behaviour
`9.3
`9.4 The flow in the rotating stall cell
`Stability enhancement: casing treatment
`9.5
`
`10 Vibration and noise
`10.1
`Introduction
`10.2 Vibration
`Mechanical vibration modes
`Forced vibration
`Flutter
`Supersonic unstalled flutter
`10.3 Noise
`Scales and rating of noise
`Elementary acoustics
`Compressor and fan noise
`Non-aeronautical aspects of compressor noise
`Acoustic treatment
`
`11 Design, Measurement and computation
`11.1
`Introduction
`11.2 Understanding and design
`11.3 Experimental techniques
`11.4 Mathematical techniques
`
`320
`331
`356
`
`359
`359
`369
`391
`398
`401
`
`410
`410
`410
`412
`415
`417
`422
`428
`429
`431
`440
`455
`457
`
`459
`459
`459
`461
`466
`
`Appendix Blade profile families for axial compressors 479
`
`Bibliography
`
`Additional Bibliography for the 2004 Krieger Reprint
`
`Index
`
`484
`
`505
`
`513
`
`

`

`2 General design considerations
`
`2.1
`
`Introduction
`
`In the design of any compressor the initial decisions on the layout and duty
`determine to a large extent problems to be encountered and the level of effi(cid:173)
`ciency to be achieved. It needs to be recognized that the single most important
`design decision is the choice of stage loading , usually meaning the pressure
`ris1; in relation to the number of stages and the rotational speed. If, for exam(cid:173)
`ple, unduly high loading is required of one or more components it is probable
`that no subtlety of design will render the overall perfonnance satisfactory. Great
`skill and extensive commercial databases may be involved in making the initial
`decisions , steering the choice between ambitious goals and safely realizable
`ones . Occasionally the preliminary design is not given the serious attention
`it deserves and the results may be catastrophic.
`The decision to have an axial or a radial compressor (radial compressors
`are very often termed centrifugal) is one of the basic preliminary decisions
`of this section and this excludes a potentially wide class of mixed flow machines.
`The mixed flow compressor is rarely used, probably because of the limited
`experience and data existing for it, although it would seem to have a very natural
`niche. Amongst the problems of the mixed flow compressor compared to the
`axial or radial is weight, with the mixed flow machine coming out longer than
`the radial but of similar massive construction. The diffuser downstream of
`the mixed flow impeller has also been found to be a problem, with perfonnance
`well down on what was expected of the radial machine. With sufficient effort
`and appropriate design there is reason to expect that the diffuser performance
`could be greatly improved.
`The decision to choose either an axial or a radial compressor rests on many
`factors, not least the experience of the company building the machine. For
`aircraft propulsion the high flow rate per unit area of the axial is a big advan(cid:173)
`tage but when the blade height becomes very small the advantage swings to
`the radial: helicopter engines usually employ raciial compressors and they have
`even been proposed for the later stages of large jet engines with very high
`pressure ratios. Highly loaded radial compressors seem to have generally lower
`efficiencies than axial machines , but this is not altogether clear. In cases where
`
`46
`
`

`

`The axial compressor 47
`
`the impeller can be precision cast, such as those in turbochargers for automotive
`use, the simplicity of the radial compressor means that it has a huge cost
`advantage over the axial. In the remainder of this chapter it will be assumed
`that the decision of axial versus radial has been made.
`It is a common factor with all compressors that when several stages are used
`together in series there is a serious problem of matching the stages so that
`the outlet flow from one stage is acceptable to the next. This becomes more
`acute as the overall pressure ratio across the machine increases because of
`the large density changes that result. Because the pressure ratio, and therefore
`the density ratio, is roughly proportional to the square of the rotational speed
`it is a common difficulty to match multistage machines at both the full design
`speed and at reduced speed, leading to many problems not least that of starting
`the compressor or engine. This aspect of compressors is considered in this
`chapter and is illustrated with reference to the particular problems of axial
`compressors.
`What follows in this chapter are some fairly simple ideas relating to the
`overall performance of compressors with the treatment being essentially one(cid:173)
`dimensional. This begins with the axial and then moves on to the radial com(cid:173)
`pressor. The final section of the chapter is the elementary consideration of
`stage matching for axial compressors.
`
`2.2 The axial compressor
`
`In the preliminary design calculations are usually performed at a mean radius,
`called the pitchline in some work. Refinements may be introduced to assess
`the blade loadings at hub and casing, particularly if the ratio of the hub and
`casing radii is low. (NB: This is sometimes referred to as the hub-tip ratio .
`Here the word tip will not be used because of its possible ambiguity; for a
`stator cantilevered inwards, does tip refer to the hub or the casing end of the
`blade? The word casing will be preferred instead.) Criteria have to be chosen
`for satisfactory blade loading, pressure rise at the walls and maximum Mach
`number.
`The blade loading is now usually assessed by diffusion factor or alternatively
`equivalent diffusion ratio, both derived by Lieblein and· described in Chapter
`4. Here diffusion factor will be used. Essentially this relates empirically the
`peak velocity on the suction surface of the blade to the velocity at the trailing
`edge, with one component due to the one-dimensional deceleration of the flow
`and the second due to the turning of the flow. The term related to the turning
`introduces the blade solidity. For a simple two-dimensional geometry diffu(cid:173)
`sion factor reduces to
`DF = 1 _J::J_ + A.V6
`V1
`2aV1
`where V I and V 2 are the average velocities into and out of a blade row in a
`
`(2.1)
`
`tions
`
`Jut and duty
`level of effi(cid:173)
`>st important
`the pressure
`[f, for exam(cid:173)
`J is probable
`:i.ctory. Great
`.ng the initial
`ly realizable
`)Us attention
`
`compressors
`. ry decisions
`,w machines.
`f the limited
`L very natural
`1pared to the
`t longer than
`wnstream of
`performance
`ficient effort
`performance
`
`~sts on many
`1achine. For
`a big advan(cid:173)
`ge swings to
`nd they have
`th very high
`1erally lower
`: cases where
`
`

`

`48 General design considerations
`
`frame of reference fixed to the blade, A V9 is the change in whirl velocity in
`the row and o is the solidity, equal to blade chord/blade pitch. Values of DF
`in excess of 0.6 are thought to indicate blade stall and a value of 0.45 might
`be taken as a typical design choice. Over the last few years attention has been
`focussed more on the endwall region as the limit for loading and the weight
`given to the diffusion factor has decreased.
`The criterion to be adopted for endwall loading or pressure rise is Jess clear,
`mainly because the fluid mechanics is still not understood. Methods analogous
`to that produced by de Haller (1953) are still current and this will be discussed
`more in later chapters. de Haller deduced that the velocity out of a blade should
`not be less than about 0. 75 times the inlet velocity if the perfonnance· is to
`be satisfactory. This is equivalent to requiring that the static pressure rise at
`the wall should not exceed about 0.44 times the dynamic pressure into a blade
`row. The de Haller criterion has not been found to be entirely satisfactory.
`More recently Koch (I 981) has published a method which relates stage pressure
`rise capability to the mean height (i.e. mid-span) solidity averaged over the
`stage; it is based on a large-number of measurements in multistage compressors
`and will be discussed more fully in Chapter 9. The most common method of
`assessing what is acceptable loading at the wall is probably by reference back
`to previous designs by the same manufacturer, it is now very rare for an
`organization to be designing an axial compressor for the first time! The general
`view seems to be that a stage pressure rise not exceeding about 0.4pU2 is
`reliable.
`In looking at the trends in multistage compressor design it is very helpful
`to take advantage of the results given by Wisler (1988) in a comprehensive
`set of lecture notes, relating mainly the work of his company, General Elec(cid:173)
`tric. These will be referred to many times in this chapter. ,
`The limit on maximum Mach number is flexible and depends to a large extent
`on the balance between high efficiency and high pressure ratio per stage being
`sought. The loss in efficiency with Mach number is nowhere near as serious
`as was once thought. Inlet relative Mach numbers of 1.4 are now common
`at the tips of first-stage rotors in multistage compressors for aircraft and the
`flow may even be slightly supersonic into the third stage. As the Mach number
`is increased the operating range reduces, i.e. the difference between the mass
`
`Table 2.1 Compressor developments by General Electric
`
`Year
`
`Designation
`
`late 50s
`1969
`1974
`1982
`
`CJ805/J79
`CF6-50
`CFM56
`E3 engine
`
`Design
`pressure
`ratio
`
`12.5
`13.0
`12
`23
`
`Number
`of stages
`
`Corrected
`tip speed (mis)
`
`17
`14
`9
`10
`
`291
`360
`396
`456
`
`

`

`velocity in
`lues of DF
`D.45 might
`,n has been
`the weight
`
`; less clear,
`; analogous
`e discussed
`lade should
`nance' is to
`sure rise at
`into a blade
`atisfactory .
`.ge pressure
`~ over the
`ompressors
`1 method of
`:rence back
`rare for an
`The general
`t 0.4pU 2 is
`
`·ery helpful
`1prehensive
`:neral Blee-
`
`large extent
`stage being
`r as serious
`,w common
`raft and the
`achnwnber
`en the mass
`
`!Cted
`·eed (mis)
`
`The axial compressor 49
`-r-- - -...-----.
`+ +
`/.,, r
`100 "I
`97.5%
`102.5
`Corrected
`design speed
`
`-
`-
`>ex »t'
`/
`95
`
`0.8
`
`0.7
`
`0.6
`
`.; I)
`
`1/
`
`+++
`
`1c
`
`0.9 ...------,--- ----,---- -r-----.--
`Adiabatic
`r• ft r
`t
`efficiency
`.,,,t /l 85 87.5 90 92.5
`82.5
`1 80
`70
`
`Po2 25
`Po, 20
`
`15
`
`+ Core engine test
`x Turbo-fan test
`rig test
`Solid line -
`
`Engine
`Working line
`
`4-'
`97.5
`,xx'
`, , I
`95% Corrected
`1c'
`design speed
`92.5
`
`60
`50
`40
`Inlet corrected mass flow kg/s
`Fig. 2.1 The pressure ratio and efficiency characteristics of the GeneraJ Electric E3
`compressor. (Published with permission, Courtesy of General Electric Co.)
`flow for choke and surge is reduced . An important reason for keeping the speeds
`of ihdustrial compressors down is to maintain the widest possible operating
`range. The numbers given in Table 2 .1 are taken from Wisler ( 1988) and show
`the trend for much higher tip speeds from one manufacturer of jet engines,
`General Electric, but similar trends would be found for other companies as
`well as for land-based machines.
`The pressure rise-mass flow and efficiency-mass flow characteristics for
`the compressor of the E3 engine are shown as Pig. 2.1, the solid lines being
`from tests of a compressor rig and the crosses from engine tests. Just prior
`to surge at 102.4 per cent speed the very high pressure ratio of 29:1 was
`achieved. It is interesting that the engine performance is better than the rig,
`partly because the Reynolds number was higher but mainly because the tip
`clearances were smaller for the engine. The compressor was designed with
`six variable stagger stator rows but only four were used for the performance
`map shown. The peak adiabatic efficiency corresponds to a polytropic effi(cid:173)
`ciency of 90.4 per cent, a high value, and evidently the high pressure ratio
`per stage does not have to be bought at the expense of low efficiency. A
`photograph comparing the rotors for the E3 compressor with that of the much
`earlier CJ805/J79 is shown in Fig. 2.2 from which the very much higher solidity
`and lower aspect ratio of the more recent compressor is very obvious.
`Decisions have to be taken regarding the blade chord and the nwnber of
`blades. Increasing the chord reduces the aspect ratio (height/chord) and in(cid:173)
`creases solidity (chord/pitch) for the same annulus and number of blades. Both
`
`

`

`50 General design considerations
`
`(a)
`(b/
`Fig. 2.2 Comparison of (a) CJ805/J79 rotor (late 1950s) p02/p01
`12.5; 17 stages
`and (b) E3 rotor (early 1980s), p01Jp01 = 23 ; 10 stages. Note lower aspect ratio and
`higher solidity of newer machine. (Published with permission, Courtesy of General
`Electric Co.)
`
`these trends are evident in Fig. 2.3, taken from Wisler (1988). The rise in
`solidity and fall in aspect ratio can both be attributed in the main to a rise
`in chord length. With these trends for aspect ratio and solidity there is the
`striking rise in pressure rise per stage and the increase in the overall pressure
`ratio possible and utilizable for a single compressor. It should be emphasized
`that the single most important decision in the design process is the choice of
`a realistic stage loading. An over-ambitious choice may lead to untold problems
`later with little possibility of actually achieving the combination of efficiency,
`pressure ratio, mass flow and range originally intended.
`Back in the l 950s it was believed that the trend would be towards high aspect
`ratio blades to give a short compressor, mainly, it seems, because the blade
`behaviour well away from the endwalls was comparatively well understood
`and this was the direction of development which consideration of the blades
`seems to indicate. The trend was reversed mainly because large chord blades
`are more effective in the endwall regions and it is these regions which are
`crucial in determining both the efficiency and the stall point. High aspect ratio
`blades were long and thin and had atrocious vibration problems. The change
`towards low aspect ratios was not the result of an understanding of the processes
`involved but consideration of the trends for performance of different designs.
`Wennerstrom (1986) has described the catastrophic effect of adopting high
`aspect ratio blading.
`There are several performance goals to be compared, in particular pressure
`rise, efficiency and operating range (operating range might be defined as the
`ratio of the difference between maximum and minimum mass flow to the design
`value). The evidence suggests that for a good compressor near the design point
`efficiency tends to be slightly lower if the solidity is on the high side (and
`the aspect ratio low) but the pressure rise and operating range are greater.
`The major trend over the last 30 years has shown a rise in efficiency but a
`more marked rise in overall pressure rise as Fig. 2.4, from Freeman and
`Dawson (1983), shows for Rolls-Royce compressors.
`There are special problems that arise from combining stages to form
`
`

`

`The axial compressor St
`
`stage
`average
`solidity
`
`Average
`aspect
`ratio
`
`1.6
`1.4
`1.2
`1.0 1--;......-
`5 1-e---- - - - --1
`4
`3
`2
`1
`0.5 --- ~ -~-~---1
`
`Average
`loading
`Apf(po- P);n
`
`0.4
`
`Spool
`pr~ssure
`ratio
`
`1960 1970 1980"
`Year
`
`Fig. 2.3 The trend in compressor geometry (solidity and aspect ratio) and in perform(cid:173)
`ance (stage loading and spool pressure ratio) with time. (From Wisler, 1988)
`
`0.9
`Polytropic
`efficiency
`0.8
`
`30
`
`20
`
`PR
`
`0 ' - - - -" - - --;-;:!:::-=---;-::":::-=""
`1980
`1970
`1960
`1950
`
`Fig. 2.4 The variation in overall pressure ratio and in polytropic efficiency for gas
`turbine compressors. (From Freeman and Dawson, 1983)
`
`2 .5; 17 stages
`spect ratio and
`~sy of General
`
`. The rise in
`1ain to a rise
`· there is the
`:rall pressure
`: emphasized
`:he choice of
`old problems
`,f efficiency,
`
`s high aspect
`1se the blade
`I understood
`lf the blades
`:hord blades
`1s which are
`1 aspect ratio
`The change
`he processes
`·ent designs.
`lopting high
`
`:lar pressure
`:fined as the
`to the design
`design point
`:h side (and
`are greater.
`:iency but a
`reeman and
`
`:es to form
`
`

`

`52 General design considerations
`
`multistage compressors, usually referred to as matching, and this is considered
`later in this chapter. The ability to handle the matching of compressors and
`the operation of several rows of variable stagger stator blades has made pos(cid:173)
`sible the very large increase over the years in the pressure ratio for a single
`compressor spool which is illustrated by Fig. 2.3.
`• Increasing Mach number by increasing rotational speed can lead to
`mechanical problems. The limiting condition for a compressor with large
`pressure ratio is normally reached at the rear hub; this is largely a materials
`problems connected with the high temperatures. High solidity blading exacer(cid:173)
`bates the problem because of its greater mass of blade metal. A maximum
`hub rotational speed of about 380 mis may be taken as a guide, but this is
`nut a firm boundary because the choice of more expensive materials or the
`l
`use of a heavier disc would, at a price, allow some increase.
`Increased rotational speed makes it possible to increase the flow per unit
`area; Freeman and Dawson (1983) show that it is now possible to have an
`efficient compressor giving a high stage pressure ratio while passing a flow
`approaching 90 per cent of that which would choke the empty annulus at inlet.
`With the emphasis on blade design for axial compressors it is easily over(cid:173)
`looked that the overall meridional flowpath (that is the flowpath in a longitudinal
`cross-section showing axial and radial components) has a crucial effect on the
`design and the performance of a compressor. The aerodynamic problems are,
`for example, greatly relieved if the hub radius can increase from front to back,
`whilst they are made worse if the annulus area is too large towards exit. Deci(cid:173)
`sions taken at the preliminary stage in laying down the annulus shape and
`choosing the inlet and outlet radii can effectively determine whether a com(cid:173)
`pressor will be satisfactory or not and may be far more influential than
`subsequent decisions regarding the blade shape.
`Fundamental to all of the aerodynamic design are the basic decisions of an
`aerodynamic nature. At the blade mid-height (sometimes known as the pitch(cid:173)
`line radius) a choice must be made· for the local flow coefficient <f, = VxlU and
`the stage loading ,J;=Ah 0/U 2 (or alternatively !:J.p 0/pU2). Sometimes the
`degree of reaction R=Ahroto/t:,.hstage (or the equivalent in tenns of static
`pressure rise) is treated as important too. Such decisions are separate from
`choice of solidity, blade section etc., although solidity does have a marked
`effect on the choice of loading. A fascinating report of the preliminary design
`of a multistage compressor has been published by Wisler et al. (1977). Here
`the interactions between different design decisions are demonstrated with the
`advantage of the realistic estimates and extensive database available to a large
`company.
`
`Parametric study for a repeating axial stage
`The decisions on aerodynamic design take into account amongst many other
`things the compressibility of the flow, and this will be considered in later
`chapters. However, many of the trends in most stages of a multistage
`compressor are not related to compressibility and the flow can be understood
`adequately by treating it as incompressible. In this section. some parametric
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