Aircraft Propulsion Systems
`Technology and Design
`
`Edited by
`
`Gordon C. Oates
`
`University of Washington
`Seattle, Washington
`
`6 A
`
`IAA EDUCATION SERIES
`
`J. S. Przemieniecki
`
`Series Editor-in-Chief
`
`Air Force Institute of Technology
`Wright-Patterson Air Force Base, Ohio
`
`Published by
`
`American Institute of Aeronautics and Astronautics, Inc.
`370 L’Enfant Promenade, SW, Washington. DC 20024-2518
`
`UTC-2011.001
`
`UTC-2011.001
`GE v. UTC
`Trial IPR2016-00534
`Trial IPR2016_-00534
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`GE V. UTC
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`

`
`American Institute of Aeronautics and Astronautics, Inc. _
`Washington, DC
`
`Library of Congress Cataloging in Publication Data
`
`Aircraft propulsion systems technology and design/edited by Gordon C.
`Oates.
`
`p. cm.—(AIAA education series)
`The last of three texts on aircraft propulsion technology planned by
`Gordon C. Oates. Other titles: Aerothermodynamics of gas turbine and
`rocket propulsion (c1988); Aerothermodynamics of aircraft engine com-
`ponents (C1985).
`Includes bibliographical references.
`1. Aircraft gas-turbines.
`l. Oates, Gordon C.
`TL'.+'09.A44 629.134’353 — dc20
`89-17834
`ISBN O—930403—24—X
`
`II. Series.
`
`Copyright © 1989 by the American Institute of Aeronautics and Astronau-
`tics, Inc. All rights reserved. Printed in the United States. No part of this
`publication may be reproduced, distributed, or transmitted, in any form or
`by any means, or stored in a database or retrieval system, without the prior
`written permission of the publisher.
`
`UTC-2011.002
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`UTC-2011.002
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`

`
`ENGINE OPERABILITY
`
`6
`
`NOMENCLATURE
`
`AIP
`AT
`B
`BP
`BT
`DGC
`DTC
`
`EXP
`EXT
`f
`fl.
`F
`KP,
`KP,
`KER.
`KT,
`K},
`MFR,
`
`MPR-,-
`
`N 6
`P3
`PR
`P(t)
`T)
`P0)
`APC/P
`APR/P
`APRS
`RSS
`SM ,._._,ML
`ASM
`ATC/ T
`
`= aerodynamic interface plane
`= averaging time
`= recoverability parameter
`= total pressure distortion superposition function
`= total temperature distortion superposition function
`= distortion generation coefficient
`= distortion transfer coefficient
`
`= circumferential total pressure distortion extent function
`= circumferential total temperature distortion extent function
`= frequency
`= cutoff frequency
`= total pressure/total temperature superposition function
`= circumferential total pressure distortion sensitivity
`= radial total pressure distortion sensitivity
`= circumferential total temperature distortion sensitivity
`= radial total temperature distortion sensitivity
`= planar wave sensitivity
`= circumferential total pressure distortion multiple-per-
`revolution distortion descriptor
`= circumferential total temperature distortion multiple-per-
`revolution distortion descriptor
`= corrected speed
`= compressor discharge pressure
`= total pressure ratio
`= time-varying total pressure
`= time-averaged total pressure
`= time-varying spatial average of AIP total pressures
`= circumferential total pressure distortion intensity element
`= radial total pressure distortion intensity element
`= loss of stability pressure ratio
`= root-sum-square
`= available stability margin
`= loss of stability margin
`=circumferentia1 total temperature distortion intensity
`element
`
`ATR/ T
`WF
`W.
`
`= radial total temperature distortion intensity element
`= combustor fuel flow
`= corrected flow
`
`339
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`UTC-2011.003
`UTC-2011.003
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`
`
`340
`
`ill,»
`¢
`¢(f}
`Z
`t
`
`9
`3"
`
`AIRCRAFT PROPULSION SYSTEMS
`
`= pressure coefficient
`= flow coefficient
`= power spectral density function
`= sum
`= error
`
`= angle
`= angular extent of total temperature distortion
`= angular extent of total pressure distortion
`
`Siifiwripis
`i
`F1115
`0L
`SLL
`
`= ring designator
`= root-mean-square
`= operating line
`= stability limit line
`
`6.1
`
`INTRODUCTION
`
`Engine operability is the discipline that addresses all the factors having
`an impact on the installed aerodynamic operation of a gas turbine engine
`(tivhfien at is operated either in a steady-state or transient manner over the
`e ne _1_\dach numberfaltitude and maneuver envelopes. The goal of engine
`operability is to assure that the engine operates free of instability or with an
`aloceptably small number of recoverable aerodynamic instabilities during
`(tfe on-aircraft life of the engine. -I-rrany case, good design practice would
`pifilgltge
`that aerodynamic instabilities do not occur at mission critical
`_ While the discipline of engine ‘operability could be the subject ofa book
`in itself.
`it
`is the purpose of this chapter to address the major tenets of
`engine operabilityvand not
`to be all inclusive. To this end, discussion is
`focused on the major tool of engine operability —— the stability assessment,
`This method of treatment ‘highlights those factors that are the largest and
`most variable in the stability assessment and gives a logical framework to
`the treatment that follows.
`
`Engine operability as a discipline has evolved from considerations that
`were based on inletfengine compatibility. Today the spectrum of issues is
`considerably broader. Although it has long been recognized that engine
`instabilities result from local compressor blade and vane velocity triangles
`being distorted to the point that incidence angles become unacoeptab]
`large. it was found that acceptable correlations could be developed (ha);
`Felalcd 91¢ I033 0f Stability pressure ratio (based on ratios of total pressure)
`to nonuniforrnities in the entering total pressure profiles (differences in
`10l3l P7555373)» thus obviating the need to accomplish difiicult-to-make
`local \’€l0Cl‘}’ measurements. This fortuitous finding has greatly simplified
`the ‘'‘“‘k Or the engine °P°1’3bllll)' fiflgineer and made possible the significant
`advances lhfll have taken place in this discipline.
`
`ENGINE OPEFIABILITY
`
`341
`
`that unsteadiness of the total pressure as characterized by root-mean-
`square values of the total pressure contributed additionally to the loss of
`stability pressure ratio? The current state of inletfengine compatibility owes
`much to the work of Plourde and Brimelow.’ who developed the first
`methodology to quantify the effects of time-varying inlet total pressures on
`engine stability. It is from these foundations that the discipline of engine
`operability has evolved with the concomitant need to assess all
`those
`factors affecting engine stability.
`The current state of the art in engine operability to a large degree is
`based on the work of SAE S-lo. Turbine Engine Inlet Flow Distortion. an
`industry committee composed of representatives from engine manufactur~
`ers, airframe manufacturers. and civil, regulating, and defense governmen-
`tal agencies. In the material that follows. liberal use has been made of this
`committee's published works‘-5 and its soon to be published working
`documents in the areas of total temperature distortion and planar waves as
`well as the forerunner of this chapter.‘ Extensive bibliographies and
`references to the literature can be found in Refs. 7-10.
`As the reader progresses through this chapter,
`it will help him to
`understand that
`this author explicitly and often implicitly is assuming a
`two-spool turbofan engine with a fuel control using fuel flow divided by
`compressor discharge pressure [WF,iP3) acceleration schedules. This as-
`sumption by no means limits the utility of the material of this chapter and
`was implemented to prevent distracting digressions that amount
`to nu-
`ances. The techniques that are discussed are readily extendable to other gas
`turbine engine configurations and engine control modes.
`
`8.2 DEFINITIONS
`
`As a result of advances that have taken place, especially as a result of the
`nonrecoverable stall (stagnation stall) programs conducted by both Pratt
`and Whitney Aircraft and General Electric Aircraft Engines in the early
`|980’s.
`it has become necessary to clarify and sharpen the focus of the
`terminology used in engine operability studies. The definitions presented in
`this section and later in this chapter represent a more modern view and are
`consistent with current usage. It will be helpful if the reader takes the time
`to familiarize himself with the terms and their definitions as they will occur
`frequently throughout the chapter.
`When presenting definitions and terminology. it is important to deter.
`mine clearly the point of view that one is adopting. In our case, the point
`of view taken is that of an engine systems person looking at the overall
`behavior of a compression component or a compression system. This point
`of view is adopted because it is tied to those parameters that are most easily
`measured, that is, annulus average total pressure. corrected speed. corrected
`flow. and turbine or a related temperature.
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`Al FICRAFT PROPULSION SYSTEMS 342
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`ENGINE OPEFIABILITY
`
`343
`
`
`
`
`
`axial flow compression component to the point at which the compression
`component cannot sustain an increase in pressure ratio andfor decrease in
`corrected flow (loss of pumping capability) without the compression com~
`ponent incurring a sharp drop in discharge pressure. Unsteadiness within
`the compression component will accompany these aerodynamic flow insta-
`bilities. The surge and rotating stall
`instabilities are the two known
`compression component instabilities.
`
`
`
`
`
`
`
`
`Aerodynamic Stability timit Line
`The aerodynamic stability limit line is defined by the locus of points in
`
`terms of annulus average total pressure ratio vs corrected flow obtained by
`
`slowly throttling a compression component until an aerodynamic instability
`occurs.
`
`
`
`
`
`
`The aerodynamic stability limit line is generally obtained from rig or
`component
`tests by throttling the compression component at constant
`corrected speed until it loses pumping capability due to the occurrence of
`an aerodynamic instability. (See Fig. 6.1.) It should be noted that for the
`purposes of conducting stability assessments,
`the onset of undesirable
`mechanical stresses may occur prior to the occurrence of an aerodynamic
`instability in some speed ranges and would, therefore, represent the limiting
`condition.
`
`
`
`\\\\\‘%\i}o
`neromechani cal
`Instabi 1 it
`
`flierodynami c
`Stability Limit
`Line
`
`
`
` PressureRatio—PF
`
`Corrected Flow - HE
`
`Fig. 6.2 Definition of stability limit line.
`
`mously. Because either rotating stall‘ 0!’ Surge ma)’ 093"’ °r b°°a”5"
`additional constraints may set the limit
`locus of points over part of the
`speed range, it is desirable that a more encompassing and descriptive term
`he used: hence. the term aerodynamic stability limit line. (See Fig. 6.2.)
`
`S tail‘
`
`The initiation of an aerodynamic instability often is characterized by a
`drop in discharge pressure that occurs when the ccmP“335'°n ‘3°mP°“°“l
`.0535 the capability to pump flow at the immediate values of pressiireratao
`and corrected flow. This characteristic initiation of an aerodynamic "'51a'
`'l't
`'
`lled stall.
`_
`_
`_
`_
`_
`bl gsiilllslecaids to either transient or full)‘ de"°l°P°d 3°"°dy“3""° lnswbllmes
`(rotating stalls or surge cyCl€5)-
`(5176 FlB- 63-)
`
`Rotating Sta”
`
`is an aerodynamic instability characterized as a local
`Rotating 513]]
`blockage to the axial flow within a compression component that rotates
`cjrcumferemially in the direction of the rotor rotation at rotational speeds
`equal to approximately one—half of the rotor speed. Operation with fully
`developed rotating stall results in a stable annulus average operating p_0i I1!
`that lies on the stalled characteristic of the cornP°“°“l D11‘-Ssure coefficientf
`flow coefficient representation. (See Fig- 6-3-)
`1
`1
`Rotating stalls can occur as full— or part-Bl:1|ad‘t:3\;1]_.‘-130 (hub, mids1iEI1.a?;
`
`UTC-2011.005
`
`In some low—speed regions, a clearly discernible aerodynamic instability
`may not occur. but rather heavy turbulence indicative of separated flow
`may develop and a subjective decision has to be made as to the usable
`pressure ratiofcorrected flow range for the purposes of establishing the
`aerodynamic stability limit line.
`line often has been called
`In the past. the aerodynamic stability limit
`either the surge line or the stall line. with both terms being used synony-
`
`Lines of Constant /
`
`/
`
`
`
`/
`4—-—/
`
`Aerodynamic stability
`Limit Point
`
`
`
`
`
`
`
`
`unstal led
`Characteristic
`
`Increased
`Throttling
`
`I §
`
`on
`
`
`
`N,tf'B' = Constant
`
`

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` ENGlNE OPERABILITY
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`344
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`AIRCRAFT PROPULSION SYSTEMS
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`
`
`
`Fully developed rotating stalls generally occur at low speeds for high-
`pressure-ratio compressors. Low-pressure-ratio [fan and booster) compres-
`sion components often only exhibit the rotating stall instability throughout
`
`their operating speed ranges.
`
`
`
`
`
`
`Surge
`Surge is an aerodynamic instability characterized by a breakdown in the
`flow that results in more or less planar waves traveling in the axial direction
`of the compression component. Fully developed surge cycles will be
`characterized by alternate cycles of stall. depressurization. and repressuriza-
`tion (recovery). Often,
`the depressurization portion of the surge cycle
`exhibits some reverse flow. {See the component pressure coefiicientiflow
`coefficient representation in Fig. 6.3.)
`Fully developed surge generally occurs at high speeds for a high—pres-
`sure-ratio compressor. For medium and large turbofan engines. surge cycle
`frequencies will tend to lie in the 5-20 Hz frequency range.
`
`Available Stability Margin
`
`the
`is
`The available stability margin for a compression component
`difference between the pressure ratio at
`the stability limit
`line and the
`pressure ratio at
`the operating line nondimensionalized by the pressure
`ratio at the steady-state operating line. all taken at the same corrected flow.
`With reference to Fig. 6.4. the available stability margin can be written in
` "°l_!!"'9 ‘-_t.<!l_‘.
`Stall
`L.-vD;tt'.‘.l:rL*t'"‘.!‘ *°“
`
`lHpHntelim Stall
`
`Flow Eoefflclerit
`
` PressureCoefficient-up Eu-iprussiori
`
` Q
`
`DischargePressure
`
`equation form as
`
`SMAVAIL ';
`
`PRSLL — PROL
`PROL
`
`W, - coast
`
`345
`
`(GA)
`
`UTC-2011.006
`
`The available stability margin is often quoted as a percentage. In the
`past
`the terms available stall margin or available surge mafgln ha“ been
`used‘ interchangeably. The use of available stability margin removes any
`chance for ambiguity.
`
`Loss of Stability Margin
`The loss of stability margin is the difference between the PT°55“T"-_ “"0 3‘
`some assessment point AP] and another lower assessment point AP2
`nondimensionalized by a reference operating lint? PTESSH“? '’_3_“°~ 3“ 1333“ 3‘
`the same corrected airflow. Values of the loss of Stability “13T8!1'1 3'9
`generally expressed as a percentage for discussion purposes. HOWBVF:
`calculations are carried out in decimal form. In equation form and wit
`reference to Fig. 6.4, the loss of stability margin is defined as
`
`issivi = —-—-—-—
`PROL
`
`W‘ - eorist
`
`(5-2)
`
`Often the assessment point AP2 is located on the operating line and, hence.
`_
`' h t
`l
`.55 of stability margin has been known as loss of
`513111: fiflzréiialstort ‘asses? 93,33 margin. The use of the term loss of Slabllll?‘
`ma.-gin removes any ambiguity caused by the interchangeable use of t e
`words stall and surge.
`
`Aerodynamic
`Stability Limit
`Line
`aPl‘:tS or ASP!
`Depending on
`." Nonoirnensional izatian
`
`
`
` .Uperating
`
`"
`
`Line
`
`in H: :2
`
`
`
`PressureRatio—FR
`
`Corrected Flour
`
`- NC
`
`
`
`
`
`E_°_'ie9.'.~.-1I_*_er;r=3e".t.a_tl.°1|
`. - * ' ’
`
`
`
`E 0
`E J
`.. 3
`It *"
`L ..
`El L
`I‘
`.. .7
`t“
`In.
`E 1
`25
`..c.
`‘'5
`
`“T l_.s...m. cu-1.,
`
`,
`I
`r
`‘
`
`I
`
`.r
`
`l
`
`\
`
`‘.}
`"
`Ll
`i
`'-‘
`.
`..
`\)
`3
`II
`'-
`3.
`‘‘§‘
`D.
`
`

`
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`346
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`AIFICRAI-‘I’ PROPULSION SYSTEMS
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`ENGINE OPEHABILITY
`
`347
`
`Loss of Stability Pressure Ratio
`
`The loss of stability pressure ratio is the difference between the pressure
`ratio at some assessment point API and some lower assessment point AP2
`ncndimensionalized by the stability limit line pressure ratio all taken at the
`same corrected airflow. Values are generally expressed as a percentage for
`discussion purposes, but for calculational purposes, the values are used in
`decimal form. In equation fonnat and with reference to Fig. 6 4 the loss of
`stability pressure ratio is defined as
`i
`’
`
`npns : E&';P';’&%
`31. L
`
`W‘, in cons:
`
`(63)
`
`th
`
`t b']'i
`1’
`'
`'
`Often the assessment point AP! is located
`e s a try imit line and
`on
`hence’ PR”! = PR5”.
`In the past, the term loss of stability pressure ratio has been known by
`title rtlenns loss of stall pressure ratio anclfor loss of surge pressure ratio, use
`o t 'e term loss of stability pressure ratio removes any ambiguity caused by
`the interchangeable use of the words stall and surge.
`loss of
`tlghlrough use of the definitions for available ‘stability margin.
`E: I
`ity_ margin. and loss of stability pressure ratio [Eqs. (6.1-6.3)], it can
`readily shown that the three definitions are related as follows:
`
`115-M = APRSU + SMAVAIL)
`
`(6.4)
`
`This equation has particular utility when transforming stability limit line or
`operating line effects to a common base for use in conducting stability
`assessments.
`
`8.3 STABILITY ASSESSM ENT
`
`The engine designer is faced with significant dilemmas during his studies
`to provide adequate available stability margin throughout the aircraft flight
`envelope, that is. to optimally balance requirements for high thrust levels,
`low fuel consumption,
`low engine weight,
`long life, and low cost with
`adequate available stability margin. The operability engineer's too]
`for
`accounting for the factors for which he is responsible in contributing to this
`optimal balance is called the stability assessment. The stability assessment is
`a method for accounting in an orderly manner for all
`the destabilizing
`factors that consume stability margin during the operational on-aircraft ]jfi;
`of the engine at flight conditions of interest.
`the operability engineer can
`Through use of the stability assessment,
`iiChi|=V° 3" 3PP1‘°Priate balance between the available stability margin and
`the stability margin required by the destabilizing factors. If the desired
`baliincfi
`l5 3°l'1i€VBd,
`then the compression components of an engine will
`opcrzilt.‘
`instability free.
`if the destabilizing factors should require more
`
`aerodynamic instabilities should last for extended periods {approximately
`greater than 0.] s). then the mechanical life of the engine may be impaired,
`overtemperature of the turbine may occur, or llameouts may occur. Surge
`has been known to cause mechanical damage in high-pressure-ratio com-
`pressors with fiexible blades as a result of the reverse flow causing “tip
`clang." In this situation, the compressor blades elastically deform during
`the reverse flow portion of the surge cycle and impact adjacent blades
`at
`the tip, causing the inelastic deformation that gives rise to stress
`concentrations.
`The stability assessment is used during the conceptual and preliminary
`design phases of an engine program to help the cycle designer place the
`operating line of each compression component in relation to the objective
`stability limit
`line that
`the fan and compressor aerodynamic designers
`estimate will be achieved. During the development phase of the engine
`program. the stability assessment is used to ensure that adequate available
`stability margin is maintained in critical regimes of the flight envelope.
`while during the operational phase, it is used to diagnose those factors that
`may be increasing beyond the design allowance5—hencc,
`it
`is another
`element of maintaining engine quality.
`The destabilizing factors that contribute to losses of available stability
`margin are divided into two groups: internal and external factors.
`
`Internal’ Destabilizing Factors
`
`Losses of stability margin that result from features internal to the engine
`are designated as being due to internal destabilizing factors. Examples of
`these factors are engine-to—enginc manufacturing tolerances, deterioration.
`control tolerances, power laccelfldecelfbode) transients, and thermal tran-
`sients. These factors can impact both the stability limit
`line and the
`operating line.
`
`Engine-to-engine manufacturing tolerances. Blade and vane quality,
`rotor tip clearances. hub leakage paths. and buildup tolerances are consid-
`ered to be manufacturing tolerances that cause variations in the stability
`limit line of a compression component. Tolerances in exhaust and turbine
`nozzle areas and variations in component quality that affect efficiency are
`examples of manufacturing tolerances having an impact on the operating
`line of a compression component.
`
`themselves as de-
`Deterioration. Deterioration items that manifest
`graders of the stability limit line are blade and vane erosion due to sand.
`deposit buildups on blades and vanes due to dirty atmospheres. opening 0f
`hub seal clearances due to wear. and opening of tip clearances due to rubs
`during rapid acceleration and deceleration. Deterioration of the turbines
`
`UTC-2011.007
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`349
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`
`
`It should be noted that the power transient allowance is developed based
`on an engine operability philosophy such as the usage associated with a
`given power transient at the corrected How of interest or. as is the author's
`choice. to run many transients of all types and to encompass the maximum
`transient stability margin usage as a function ofcorrecled airflow by a locus
`that ensures the engine can handle any transient.
`
`Thermal’ transients. Accelerations and decelerations give rise to two
`types of thermal transients: (1) thermal mechanical expansions and contrac-
`tions that affect clearances and (2) heat transfer to the gas path that results
`in compressor rear-end stage mismatching. Modern-day compressors are
`the result of sophisticated thermal design techniques and materials match-
`ing to cause the expansion (or contraction) of the compressor case to match
`in an optimal manner the expansion (or contraction) of the rotor.
`
`External‘ Destabilizing Factors
`
`Losses of stability margin that result from the environment external to
`the engine are termed external destabilizing factors, examples of which are
`Reynolds number.
`inlet
`total pressure distortion,
`inlet
`total
`temperature
`distortion. and planar waves. The latter three items may appear in combi-
`nation and their effect is often accounted for in a combinatorial manner.
`In general. Reynolds number efiects are accounted for by cycle deck
`predictions, that is, Reynolds number effects that cause the cycle to rematch
`and cause changes in the operating lines due to changes in’ engine inlet
`conditions are handled automatically by the cycle dec_k._ Stmilarily.
`the
`stability limit
`line will be properly represented 1f_cII1P1|'1'33[ 5Ca'_3T5_3"d
`adders are included to modify the stability limit line as the engine inlet
`conditions (Reynolds numbers) change. In this manner, a cycle deck will
`provide correct estimates of the available stability margin.
`‘
`_
`Because inlet total pressure distortion. inlet total temperature distortion.
`and planar waves can consume large amounts of the available stability
`margin of compression components as functions of engine corrected
`airflow. aircraft Mach number. and aircraft attitude (angle of attack and
`angle of sideslip).
`they play a major and often a dominant role in any
`stability assessment procedure. The techniques that have been developed
`for estimating the impact of these external destabilizing influences upon the
`stability ofa compression component are reviewed later in this chapter. It
`suffices to say here that
`techniques do exist
`to permit
`the operability
`engineer to estimate values of the loss of _stability pressure ratio for a
`compression component due to these destabilizing influences.
`
`Assessment Technique
`technique that has evolved over the last We
`The stability assessment
`decades is designed to provide the engine operability engineer with an
`
`UTC-2011.008
`
`Control tolerances. Control tolerances exhibit impact on the stability
`limit
`line and operating lines through the accuracy with which variable
`geometry can be positioned and fuel schedules repeated from one time to
`the next. Examples of such variable geometry include inlet guide vanes
`(lGV‘s). ganged [GV‘s and variable stators. and booster (low-pressure
`compressor} bypass doors. Fuel schedule repeatability depends on the
`accuracy with which sensed control parameters can be measured and these
`signals then being transformed via control schedules to actuation of valves
`that control fuel flow to the main burner.
`
`Power transients. Turbofan engine power transients that result in the
`acceleration or deceleration of an engine will have their main impact upon
`the compressor operating line, while augrnenter transients (lightofi and
`zone transitions) will have their main impact upon the fan operating line.
`As an example of a compressor power transient.
`the trajectory of an
`acceleration operating line is shown in Fig. 6.5. Some of the available
`stability margin is consumed. resulting in a loss of stability margin due to
`the acceleration of the compressor from idle to intermediate power as
`depicted on the pressure ratiolcorrected flow compressor map. Since the
`steady-state operating line represents balanced torque points [the work
`produced by the turbine equals the work consumed by the compressor). an
`acceleration can be accomplished only by having the turbine produce more
`work than the compressor consumes. This is accomplished by adding excess
`fuel in the combustor. which results in an increased compressor discharge
`pressure and. hence. an increase in compressor pressure ratio as depicted by
`the dashed line labeled "acceleration path" in Fig. 6.5.
`The acceleration time of an engine can be increased by increasing the
`area bounded by the acceleration trajectory and the steady-state operating
`line. if power transient operating points should occur and cause unaccept-
`able amounts of stability margin usage. “trimming“ of the acceleration fuel
`schedule can result in more optimum usage of stability margin.
`
`Aerodynamic
`Stability Limit
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`
`
`
`ENGINE OPERABILITY
`
`351
`
` F
`
`COHDITION:
`
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`
`STABILITY iuinciii
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`NET SH REMAINING
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`Fig. 6.6 Example of ii compressor stability assessment.
`
`will have to be transformed to loss of stability pressure ratio using Eq. (6.4)
`in order to maintain the accounting in the same type of units.
`Examination of Fig. 6.6 will reveal that there are two columns for each
`destabilizing factor. The left-hand column is used for those factors that are
`deterministic in nature and are to be summed directly. The right-hand
`column is for those items that are statistically distributed and are root-sum-
`squared. Control and manufacturing tolerances fall
`into this latter cate-
`gory.
`In carrying out
`the RSS process of the right-hand column,
`it
`is
`generally assumed that each individual destabilizing factor is a Gaussianly
`distributed statistic. Hence. it
`is important to ensure that the contribution
`of each destabilizing influence represents the same number of standard
`deviations. For these purposes. two standard deviations are often used.
`If the right-hand column is root-sum-squared and the resulting value is
`added to the direct sum contribution from the left-hand column. then the
`loss of stability pressure ratio for a statistically worse case engine is
`obtained. This value. when transformed 10 Slfibllltl’ margin units.
`is then
`subtracted from the available stability m3I'8lfl- lf the result
`is zero or
`positive, then current interpretations hold that no aerodynamic instability
`
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`DIS’!DR'.l‘ION
`
`
`
`
`
`350
`
`AIFICFIAFF PROPULSION SYSTEMS
`
`is important to note that stability assessments are accomplished at
`It
`given or defined engine corrected airflow settings in keeping with the
`definitions of Sec. 6.2. Engine corrected airflow is the parameter of choice
`for correlations because it promotes communication between the airframe
`manufacturer and the engine manufacturer and because inlet distortion and
`planar waves are often primarily functions of engine corrected airflow.
`Although the engine manufacturer generally accomplishes his component
`testing as a function of corrected speed. the transition to corrected airflow
`can be made with relative ease. As a result. engine speed changes during the
`engine development program due to cycle rematching and control schedule
`changes are transparent to the inlet designer.
`With experience, the operability engineer will learn to identify the flow
`settings and Mach numberfaltitude conditions at which “pinch“ points
`occur. Pinch points are those combined engine and aircraft operating points
`at which the remaining stability margin (available stability margin less the
`stability margin consumed by the sum of the external and internal destabi-
`lizing factors} is a relative minimum. It is important to engine and aircraft
`development programs to identify the pinch points and to conduct stability
`assessments at them. in conducting a stability assessment at a pinch point.
`each compression component of the engine should be examined.
`Thus, having identified in principle the points at which stability assess—
`ments are to be conducted, we will now examine in some detail the manner
`in which a stability assessment is conducted for a given condition and for
`one compression component—a compressor. A compressor has been cho-
`sen for stability assessment because it
`illustrates most aspects of the
`instability assessment procedure. Stability assessments for other compres-
`sion components would be conducted in a similar manner.
`One approach to conducting a stability assessment is illustrated in Fig.
`6.6. First.
`important
`infonriation about
`the point selected is gathered.
`From the aircraft point of view.
`this infonriation will
`include Mach
`number, altitude. engine power setting, engine airflow, angle of attack,
`angle of sideslip, inlet recovery. and inlet distortion. From the engine point
`of view, the important information will include engine power setting. Mach
`number, altitude, customer bleed requirements. and customer horsepower
`requirements. With this information, the cycle deck can be run to provide
`the cycle operating points, component corrected speeds, component cor-
`rected flows, and the available stability margins. It is for the purposes of
`obtaining the available stability margins of each compression component
`that the information just described is tabulated at the beginning of each
`assessment.
`
`the
`Because loss of stability margin or stability pressure ratio for
`destabilizing factors is generally correlated as a function of corrected speed
`or Corrected flow.
`the cycle output data permits the engine operability
`engineer to enter his correlations, whether they are based on historic andlor
`empirical data,
`test data. or analytical studies to obtain the impact on
`stability of each destabilizing item that has been identified to be important
`
`

`
`
`
`
`
`352
`
`AIRCRAFT PROPULSION SYSTEMS
`
`ENGINE OPEHABILITY
`
`353
`
`It is interesting to note that stability assessments can be designed for a
`specific set of circumstances; that is, a new engine can be represented by
`setting the deterioration allowances to zero or to some small
`levels to
`represent break—in losses or, alternatively. fixed throttle operation can be
`represented by setting the power transient allowance to zero.
`The next subsection provides a discussion of the manner in which the
`concept of the stability assessment can be extended to broaden its utility.
`
`Probability of t'n.stab.i!:’ty Occurrence
`
`The stability assessment illustrated by Fig. 6.6 was accomplished for a
`compressor with 1.2% customer bleed taken from the compressor discharge
`and resulted in positive remaining margin.
`if a stability assessment was
`accomplished for zero customer bleed and hence a higher operating line.
`then the available stability margin is reduced and the remaining stability
`margin results in a negative amount equal to -0.6%. It is appropriate to
`ask what proportion of the number of times this combined set of flight and
`engine conditions will result in engine aerodynamic instabilities.
`The proportion of occurrences can be estimated using the assumption of
`Gaussian statistics. The procedure is illustrated by Fig. 6.7. The probability
`of the occurrence of an aerodynamic instability at these conditons is noted
`to be 4.3%.
`
`the SAE S—l6 Turbine Engine Inlet Flow
`It should be noted that
`Distortion Committee currently has a subcommittee investigating the poss