N65-23345
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`AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS
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`National Aeronautics and Space Administration
`Washington, DC
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`1965
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`UTC-2019.001
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`GE v. UTC
`Trial IPR2016-00952
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`N65-23345
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`NASA SP-36
`
`AERODYNA IC DESIGN OF
`AXIAL-FLOW COMPRESSORS
`
`REVISED
`
`Prepared- bN members of the staff of Lewis Research Center, Cleveland, Ohio.
`Edited bg h m . ~ A. Jo-
`and ROBERT 0. BULLOCK. This publication supersedes
`decassified NACA Memorandum E56B03, E56BOa, and E56BO3b, 1956
`
`S&i@ d Tecbnuul Information Division
`1 9 6 5
`NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
`warbington, D.C.
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`NOTIC_E
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`T H I S D O C U M E N T H A S B E E N R E P R O D U C E D F R O M T H E
`THIS DOCUMENT HAS BEEN REPRODUCED FROM THE
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`B E S T C O P Y F U R N I S H E D US BY T H E S P O N S O R I N G
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`A L T H O U G H I T I S R E C O G N I Z E D T H A T C E R -
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`AS MUCH INFORMATION AS POSSIBLE.
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`FOREWORD
`, This work is based substantially on a three-volume Confidential
`Research Memorandum f h t issued by the National Advisory
`Committee for Aeronautics in 1956 and declassified in .1958 for re-
`lease to the general public. The material, which was of a funda-
`mental character, has been updated for the present edition in the
`light of subsequent developments in the field and*hr.s been carefully
`reexamined for current validity by members of the staff of the NASA
`Lewis Research Center, Cleveland, Ohio. It is now published for
`the first time in a single volume to meet continuing demand for the
`information and to make it readily available in convenient form to
`the engineering community both within and outside the National
`Aeronautics and Space Administration.
`
`- - - -.
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`CONTENTS
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`'^"T J
`
`CHAPTER
`I. OBJECTIVES AND SCOPE ________________________________________---
`IRVING A. JOHNSEN
`AND ROBERT 0. BULLOCK
`II. COMPRESSOR DESIGN REQUIREMENTS _________ - _ - _ - ___ - - _ - __ __ - - - -
`9
`ROBERT 0. BULLOCK AND ERNST I. PRASSE
`53 - */
`III. COMPBESSOR DESIGN SYSTEM ____________________________________
`ROBERT 0. BULLOCK AND IRVING A. JOHNSEN
`101 J
`IV. POTENTIAL FLOW IN TWO-DIMENSIONAL CASCADES:- __ - - - - - - - - - _ _
`15 1 Ir'
`WILLIAM H. ROUDEBUSH
`V. VISCOUS FLOW IN TWO-DIMENSIONAL CASCADES _ _ _ _ _ _ - _ - _ _ _ - _ _ _ - -
`183 J
`WILLIAM H. ROUDEBUSE AND SEYMOUR LIEBLEIN
`VI. EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES-----------
`227 I/
`SEYMOUR LIEBLEIN
`VII. BLADE-ELEMENT FLOW IN ANNULAR CASCADES--- - - - - - - - - - - - - - - - - -
`255 J
`WILLIAM H. ROBBINS, ROBEFJT J. JACKSON, AND SEYMOUR LIEBLEIN
`VIII. DESIGN VELOCITY DISTRIBUTION IN MERIDIONAL PLANE_----_- -- -
`CHARLES C. GIAMATI, JR., AND HAROLD B. FINGER
`IX. CHART PROCEDURES FOR DESIGN VELOCITY DISTRIBUTION---_ - - -
`ARTHUR A. MEDEIROS AND BETTY JANE HOOD
`X. PREDICTION OF OFF-DESIGN PERFORMANCE OF MULTISTAGE
`If
`297 J
`C O M P R E S S O R S _ _ _ _ _ _ _ - _ _ _ - - - - - - - _ - - - _ - _ _ _ _ _ - _ - _ - - - - _ _ - - - - - - _ _
`WILLIAM H. ROBBINS AND JAMES F. DUGAN, JR.
`XI. COMPRESSOR STALL AND BLADE VIBRATION _______________________
`311
`ROBERT W. GRAHAM AND ELEANOP COSTILOW GUENTERT
`XII. COMPRESSOR SURGE ________________________________________---_---
`4/
`331
`MERLE C. HUPPERT
`i/
`XIII. COMPRESSOR OPERATION WITH ONE OR MORE BLADE ROWS
`STALLED ________________________________________--___--__--_-_
`341
`WILLIAM A. B~NSER
`64'
`XIV. THREE-DIMENSIONAL COMPRESSOR FLOW THEORY AND REAL
`FLOW EFFECTS ________________________________________-----_-
`J
`365
`HOWAED 2. HEEZIG AND ARTHUR G. HANSEN
`XV. SECONDARY FLOWS AND THREE-DIMENSIONAL BOUNDARY-
`LAYER EFFECTS ________________________________________-----_-
`385
`ARTHUR G. HANSEN AND HOWARD 2. HERZIG
`XVI. EFFECTS OF DESIGN AND MEASUREMENT ERRORS ON COMPRES-
`SOR PERFORMANCE ________________________________________-
`-
`
`ROBEET J. JACKSON AND PEGGY L. YOHNEII
`____________
`XVII. COMPRESSOR AND TURBINE MATCHING _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .
`REFERENCES ______ __ __ __ _______ __ ___ _________ __ ____ ___________ - __ __ _____ _
`JAMES F. DUBAN, JE.
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`CONTENTS
`CONTENTS
`DETAILED CONTENTS
`DETAILED CONTENTS
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`casrmn
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`I. OBJECTIVES AND SCOPE ........................................ --
`INTRODUCTION............................................. --
`DESCRIPTION OF AXIAL-FLOW COMPRESSOR............. --
`HISTORICAL BACKGROUND ............... -_'. .............. --
`COMPRESSOR DESIGN APPROACH ..... --'. .................. _.
`OBJECTIVES OF DESIGN REPORT .......................... --
`SCOPE OF DESIGN REPORT................................ _-‘
`CONCLUDING REMARKS.................................... _-
`
`II. COMPRESSOR DESIGN REQUIREMENTS......................... --
`INTRODUCTION ............................................. --
`SYMBOLS.................................................... --
`EFFECTS OF ENGINE CHARACTERISTICS ON AIRPLANE
`PERFORMANCE ____________________________ -, ......... --
`Engine Weight.................................. -1 ......... --
`Engine Efl‘iciency ........................................... _ -
`Thrust per Unit Frontal Area................................ --
`Other Engine Requirements ................................. --
`EFFECTS OF COMPRESSOR PRESSURE RATIO, COMPRESSOR
`EFFICIENCY, AND FLIGHT CONDITIONS ON ENGINE
`PERFORMANCE ....................................... --
`Assumptions Used in Cycle Analyses.......................... --
`Efiects of Compressor Pressure Ratio and Flight Conditions on
`Turboprop-engine Performance............................. __
`Effects of Compressor Pressure Ratio and Flight Conditions on
`Turbojet-Engine Performance__________________________ --
`Subsonic flight _________________________________________ __
`Supersonic flight _______________________________________ _-
`Other Engine Cycles________________________________________ -_
`Effects of Compressor Efliciency on Engine Performance ........ _-
`Turboprop engine ______________________________________ __
`Turbojet engine________________________________________ _ _
`EFFECTS OF COMPRESSOR PRESSURE RATIO, FLOW CAPAC—
`ITY, AND EFFICIENCY ON FRONTAL AREA OF OTHER
`ENGINE COMPONENTS________________________________ __
`Comparison of Frontal Areas for Subsonic Flight............... __
`Engine inlet___________________________________________ __
`Combustor............................................ -_
`Turbine _______________________________________________ __
`Afterburner____________________________________________ -_
`Nozzle ................................................ __
`Comparison of Frontal Areas for Supersonic Flight _____________ __
`Efiects of Compressor Etficiency on Size of Components Downstream-
`FACTORS DETERMINING COMPRESSOR FLOW CAPACITY
`AND WEIGHT__________________________________________ _ _
`Flow Capacity _____________________________________________ _ _
`layout and Weight_________________________________________ -_
`' COMPRESSOR REQUIREMENTS _____________________________ _ _
`Design Point_______________________________________________ _ _
`OE-Design Considerations ___________________________________ _ _
`One-Spool Turbojet Engine __________________________________ __
`Engine acceleration_____________________________________ __
`Varying flight speeds.................................... _-
`Reynolds number effects ________________________________ -_
`Inlet flow distortions.................................... __
`Inlet matching problem_________________________________ __‘
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`CONTENTS
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`cusp-ran
`II. COMPRESSOR DESIGN REQUIREMENTS—Continued
`\
`COMPRESSOR REQUIREMENTS—Continued
`Two-Spool Turbojet Engine _________________________________ __
`Outer compressor....................................... _-
`Inner compressor_______________________________________ __
`Turboprop Engine.......................................... --
`CONCLUDING REMARKS AND SUMMARY OF COMPRESSOR
`DESIGN OBJECTIVES...................................... _-
`
`III. COMPRESSOR DESIGN SYSTEM ................................. _-
`INTRODUCTION............................................. __
`SYMBOLS .................................................... -_
`FUNDAMENTAL CONCEPTS UNDERLYING DESIGN SYSTEM-
`Equations of Thermodynamics ............................... --
`Flow through stators.................................... _-
`Flow through rotors .................................... --
`Analysis of Time-Steady and Inviscid Flow____________________ __
`Equations ignoring radial velocity ________________________ _-
`Causes of radial flows ___________________________________ __
`Effect of radial flows on stream surface configuration________ __
`Experimental data required______________________________ __
`Analysis of Viscosity Problem________________________________ __
`Two-dimensional-cascade elements _______________________ __
`Hub and easing boundary layers in compressor blade rows_-_-_
`Loading limits ______________________________ _ _' _________ _ -
`Experimental data required______________________________ _-
`Treatment of Time-Unsteady Flows __________________________ __
`REPRESENTATIVE EXPERIMENTAL DATA SUPPORTING
`DESIGN CONCEPTS ___________________________________ __
`Two-Dimensional Cascades __________________________________ - -
`Aerodynamic behavior __________________________________ _-
`Types of experimental data observed______________________ _-
`Inlet Guide Vanes __________________________________________ -_
`Free-vortex flow________________________________________ -_
`Non-free-vortex flow____________________________________ _-
`Rotors and Single-Stage Compressors _________________________ __
`Free-vortex rotor blade rows_____________________________ -_
`Non—free-vortex blade rows ______________________________ --
`Transonic blade rows ___________________________________ --
`Multistage Compressors_____________________________________ __
`Performance of fifth stage _______________________________ __
`Performance of tenth rotor______________________________ --
`Significance of Results ______________________________________ -_
`Main-flow region _______________________________________ _-
`Viscous-flow region _____________________________________ __
`Accuracy of estimate of state of air_______________________ ..
`SYSTEM ADOPTED FOR DESIGN AND RESEARCH __________ __
`Design-Point Solution in Meridoinal Plane_____________________ __
`Over-all specifications___________________________________ --
`Velocity diagrams ______________________________________ ..
`Design equations _______________________________________ -_
`Average values of energy addition for entire blade row ______ --
`Blade loading__________________________________________ __
`Relative Mach number.................................. -_
`Reynolds number_______________________________________ _-
`Axial velocity__________________________________________ __
`Hub and tip contours ___________________________________ _-
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`CONTENTS
`CONTENTS
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`III. COMPRESSOR DESIGN SYSTEM—Continued
`SYSTEM ADOPTED FOR DESIGN AND RESEARCH—Continued
`Blade Selection_____________________________________________ -_
`Blade profile___________________________________________ --
`Blade-element data_____________________________________ --
`Chord length and number of blades_______________________ --
`OE-Design Analysis_________________________________________ --
`REQUIRED IMPROVEMENTS IN ANALYSES................. -_
`Radial Distribution of Flow_________________________________ -_
`Hub and Casing Boundary Layers____________________________ ._
`Secondary flows of blade boundary layer and wakes......... __
`Cross-channel flows and passage vortex formation __________ __
`Flow in blade end regions with clearance __________________ ..
`Mixing of hub and casing boundary layers with main flow_--_-
`Loading Limits_____________________________________________ __
`CONCLUDING REMARKS____________________________________ _ _
`
`IV. POTENTIAL FLOW IN TWO-DIMENSIONAL CASCADES___________ __
`INTRODUCTION_____________________________________________ --
`SYMBOLS____________________________________________________ _-
`GENERAL CONSIDERATIONS............................... _-
`LOW-SOLIDITY CASCADES__________________________________ -_
`The Direct Problem ________________________________________ __
`Isolated airfoils_________________________________________ __
`Cascades______________________________________________ __
`Solution of low-solidity direct problem ____________________ -_
`The Inverse Problem _______________________________________ _-
`Isolated airfoils ________________________________________ _ _
`Cascades ______________________________________________ _ _
`Solution of low-solidity inverse problem ___________________ __
`Compressibility Considerations _______________________________ __
`Hodograph method_____________________________________ --
`Small-perturbation method ______________________________ __
`HIGH SOLIDITY CASCADES_________________________________ __
`The Direct Problem ________________________________________ __
`Stream-filament method _________________________________ _ _
`Relaxation and matrix solutions__________________________ __
`The Inverse Problem _______________________________________ __
`Approximate method ___________________________________ -_
`Exact method__________________________________________ _ _
`
`ANALOG TECHNIQUES______________________________________ _-
`Hydraulic Analog __________________________________________ __
`Mechanical Analogs ________________________________________ _ _
`Electrical Analogs __________________________________________ __
`CONCLUDING REMARKS____________________________________ _ _
`APPENDICES ________________________________________________ __
`A——VELOCITY DISTRIBUTION AT ARBITRARY ANGLE
`OF INCIDENCE______________________________________ __
`B—-CASCADE MAPPING FUNCTION_____________________ -_
`C—RELAXATION CONSIDERATIONS.................... _-
`D——MATRIX CONSIDERATIONS_________________________ _-
`
`V. VISCOUS FLOW IN TWO-DIMENSIONAL CASCADES______________ -- i
`INTRODUCTION_____________________________________________ __
`SYMBOLS ____________________________________________________ __
`QUALITATIVE BOUNDARY-LAYER THEORY________________ -_
`General Considerations___________ _-. ________________________ __
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`CONTENTS
`CONTENTS
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`ix
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`CHAPTER
`CHAPTEB
`V. VISCOIIS FLOW IN TWO-DIMENSIONAL CASCADES—Continued
`
`PAGE
`PAGE
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`QUALITATIVE BOUNDARY-LAYER THEORY-Continued
`Boundary-Layer Concepts___________________________________ _ -
`Types of boundary layers________________________________ --
`Boundary-layer parameters______________________________ _ -
`Loss parameters........................................ _ _
`Laminar Boundary Layer____________________________________ _-
`Turbulent Boundary Layer_______________ - _- _________________ _ _
`Transition................................................. _ _
`Infinitesimal-disturbance theory__________________________ _ -
`Finite-disturbance theory________________________________ __
`Flow about spheres _____________________________________ -_
`Boundary-layer reattachment____________________________ _ ..
`Composite Loss Variations___________________________________ __
`Zero loading____________________________________________ _ _
`Low loading____________________________________________ _ -
`Moderate loading_- __ _ ; _________________________________ _ _
`High loading___________________________________________ - _
`Summary______________________________________________ _ -
`QUANTITATIVE BOUNDARY-LAYER THEORY______________ __
`General Considerations______________________________________ _ _
`Laminar Boundary Layer___________________________________ __
`Thwaites’ method ______________________________________ __
`Loitsianskii’s method____________________________________ _ _
`Turbulent Boundary Layer__________________________________ __
`Approach______________________________________________ __
`Momentum thickness____________________________________ _ _
`Form factor____________________________________________ _ _
`Initial conditions _______________________________________ _ _
`Evaluation_____________________________________________ __
`Transition_________________________________________________ _ _
`Circulation Defect__________________________________________ __
`Calculation of Total-Pressure Loss ____________________________ __
`CONCLUDING REMARKS____________________________________ __
`
`VI. EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES______ _-
`INTRODUCTION_____________________________________________ _ _
`SYMBOLS____________________________________________________ __
`PRELIMINARY CONSIDERATIONS___________________________ __
`Description of Cascade______________________________________ _-
`Performance Parameters_____________________________________ __
`Data Selection__________ _ _-__________________________________ _ _
`Two-dimensionality_____________________________________ _ _
`Reynolds number and turbulence_________________________ _-
`Approach__________________________________________________ _-
`INCIDENCE-ANGLE ANALYSIS ______________________________ _ _
`Preliminary Analysis________________________________________ _ -
`Data Correlations __________________________________________ _ _
`Form of correlation_____________________________________ __
`NACA 65-(Am)-series blades_____________________________ _-
`C-Series circular-arc blades ______________________________ __
`Double-circular-arc blades_______________________________ -_
`I Other blades ___________________________________________ _-
`Effect of blade maximum thickness _______________________ _-
`Effect of inlet Mach number_____________________________ _.
`Summary__________________________________________________ __
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`X
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`CONTENTS
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`CHAPTER
`VI. EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES-Con.
`
`PAGE
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`LOSS ANALYSIS___ _ _ _ _ _ _ _ _ _ _ _ __ ___ _ _ ___ _ _ __ _ _ _ _ _ _ _ _ _ _ - - - - _- - - - -
`Preliminary Analysis ______ __ ____________ __ _____ _ ____ __ ___- - _--
`201
`Data Correlations- - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - _ - - - - -
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`Velocity dif€usion based on local velocities_-- _ _ _ _ _ _ - - _ _ _ - - - - -
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`Velocity diffusion based on over-all velocities- _ _ _ __ _-___
`202
`Effect of blade maximum thickness- _ _ _ _ _ - _ _ _ _ _ _ __ - _ _ _ _ - - - - -
`--- --
`203
`Effect of Reynolds number and turbulence _________ _____---
`204
`Effect of inlet Mach number . . . . . . . . . . . . . . . . . . . . . __ ___-__
`--
`--
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`$ummary _____ - - _ _ - __ __ - - - -- - - - - - - - - - __ - - ______ ____ -- __ -- __ --
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`DEVIATION-ANGLE ANALYSIS- _ - . . . . . . . . . . . . . . . . . . . . . . . . -----
`Preliminary Analysis ________________ _____________________----
`209
`-
`- _ _ ____ ______ ________ __ _____-- ---
`Data Correlations- _ ___-_____
`209
`
`Form of correlation ________ _____ __ ______ ______ __ ____ _____ -
`210
`NACA 6&(&0)-~&8 blades- __ __ _ ______ _ __ ____ ___ ___ _ - --- -
`210
`C-Series circular-arc blades- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ___ _ _ _ - _ _ _ _ - -- - -
`211
`Double-circular-arc blades- _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ - _ - _ _ - - _ _ _ _ - - - - -
`211
`Comparison of rules- _ _ - _ _________ _ _ ______ ____ __ ____ _---- -
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`Effect of blade maximum thickness- ____ ____ __________ _---- -
`Effect of Reyonlds number- _ _ ___ __ __ ___________ ____ _ _- ----
`216
`Effect of inlet Mach number _____ __ ___ _____ ____ _______ -- ---
`216
`Variation with incidence angle- - _ _ _ ______ - _ _______ ___ _ - ----
`Summary- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -
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`CONCLUDING REMARKS___ ________ _ _ _ ___________ _ __ ___ __- -_- -
`221
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`INTRODUCTION- _ - _ _ _ _ _ - _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -
`VII. BLADE-ELEMENT FLOW IN ANNULAR CASCADES _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -
`227
`SYMBOLS- _ _- _ - _ _ _ __ _ _ _ __ _ _ _ - _ - _ _ _ _ - __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ - - - - -
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`PRELIMINARY CONSIDERATIONS- - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - _ _ _ _ -
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`Factors Affecting Blade-Element Performance__ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ - _ _
`Blade-ElementConcept-______________________________________
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`Total-pressure loss ___________ ____ _ ___ ___________ __ ________
`Incidence a n g l e _ _ - - _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
`229
`Deviation angle- _________ - __ _ __________________ ______ ____
`230
`Correlation Approach- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - _ - _ -
`231
`Experimental Data Sources ______ _ _________________ ________ ____
`231
`INCIDENCE-ANGLE ANALYSIS- _ _ __ _ _ _ _ _ _ _ _ _ -_ _ _ _ _ _ _ _ _ __ _ _ _ _ _ -
`233
`Method of Correlation- - _ ______ __ ____________ _ __ ______ ____ _ ___
`234
`NACA 6&(A&3eries blades- _ _ __ - _ _ _ __ _ _ - _ _ __ _ _ _ __ _ - - _ _ - -
`234
`Double-circular-arc blade___ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ - - - _ - _ - - -
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`Su,~mmary Remarks _________________________-_____--_____-___-
`TOTAL-PRESSURELOSS ANALYSIS- - _ _ _ _ _ ___- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -
`
`238
`239
`Correlation of Data _ _ _ _ r _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ -
`239
`DEVIATION-ANGLE ANALYSIS- _ - _ _ _ _ _ _ _ - _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _
`239
`summary Remarks _ _ _ _ r _ _ _ c _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ - - - - -
`Method of Correlation- - ___ _____ ___ ___ __________ __________ ____
`239
`NACA 6&(Alo))-series blades- _ _ __ _ _ _ __ _ _ _ - _ _ _ _ _ _ _ _ _ _ __ _ _ _ _
`241
`Double-circular-arc blades- _ _ _ _ _ _ _ _ _ _ _ _ _ _ - __ _ _ _ _ _ _ _ __ _ _ _ - _ -
`242
`243
`Summary Remarks ________________________________________-__
`244
`APPLICATION TO DESIGN ______________________-_-____________
`Design Procedure ___________________ ____________ _______ ______ -
`245
`245
`Summary Remarks ______________________________________-----
`252
`CIENCY-_ - - - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ - _ - _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ -
`FOR BLADE-ELEMENT EFFI-
`APPENDIX-EQUATIONS
`253
`VIII. DESIGN VELOCITY DISTRIBUTION IN MERIDIONAL PLANE- _ _ _ _ _ _
`255
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`INTRODUCTION _______________________________________________ 255
`SYMBOL8 ______________________________-________-_____-_______-
`256
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`VIII. DESIGN VELOCITY DISTRIBUTION IN MERIDIONAL PLANE—Con.
`STATEMENT OF DESIGN PROBLEM............... _ .' .... - .7». _ __
`Specification of Compressor Performance and Configuration Require-
`ments................................................... - -
`Flow and Geometry Conditions To Be Determined .......... __~-_..
`GENERAL EQUATIONS’..................... -L;-;-,----;_ ..... -;
`Basic Assumptionsr______________ _; ......................... -_
`Simplified Flow Equations.......... - ; ________________ _ _ _____ .. _
`SOLUTIONS OF EQUILIBRIUM EQUATIONS.................. -__
`Simple-Radial-Equilibrium Equation Neglecting Entropy Gradients-
`Simple-Radial-Equilibrium Equation Considering Radial Gradients
`of Entropy .............................................. --
`Radial-Equilibrium Equation Considering Radial Accelerations--,_-
`CONSIDERATION OF WALL BOUNDARY-LAYER EFFECTS- -_ _
`Correction for Weight-Flow Blockage Factor................... __
`Correction Factor for Stagnation-Temperature Rise............. _-
`Correction Factor for Stagnation Pressure ..................... __
`Work—Done—Factor System .................................. _ _
`SELECTION OF DESIGN VARIABLES......................... _-
`Velocity Diagrams.......................................... -_
`Compressor-Inlet Conditions_________________________________ __
`Variation of Design Parameters through Compressor____________ __
`Axial velocity__________________________________________ __
`Diffusion factor________________________________________ _-
`Efficiency _____________________________________________ --
`Bounda.ry—layer characteristics _____ ---. ___________________ __
`Physical Aspects __________________ _ _,. ______________________ _ _
`OE-Design Performance_____________ -_. _____________________ ._
`APPLICATION OF EQUATIONS_______________________________ __
`Design Equations _________________________________________ _;._
`General Determination of Axial Velocity Distribution___________ __
`Method I__________________________________________________ __
`I'nlet guide vanes_______________________________________ __
`Rotor_________________________________________________ _ _
`Stator_________________________________________________ _ _
`Method II_______________________ ...- ________________________ __
`Method III________________________________________________ _ _
`Remarks _________________ _ ._ _______________________________ - _
`NUMERICAL EXAMPLE______________________________________ _-
`CONCLUDING REMARKS____________________________________ __
`
`IX. CHART PROCEDURES FOR DESIGN VELOCITY DISTRIBUTION.-___
`INTRODUCTION_____________________________________________ -_
`SYMBOLS____________________________________________________ --
`
`DESIGN EQUATIONS_________________________________________ - -
`FORMULATION OF CHARTS____________________________ __» ____ -_
`Radial Equilibrium _________________________________________ --
`Continuity_________________________________________________ - _
`Energy Addition and Efficiency............................... --
`Vector Relations, ........................................... --
`Diffusion Factor____________________________________________ - ..
`EXAMPLE____________________________________________________ _-
`COMPARISON OF CHART AND CALCULATED VALUES_______ _-
`
`X. PREDICTION OF OFF-DESIGN PERFORMANCE OF MULTISTAGE
`COMPRESSORS................................................. --
`INTRODUCTION..................... -; ....................... --
`SYMBOLS.................................................... - -
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`X i i
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`CHAPTER
`X. PREDICT10
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`_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ c _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
`
`INTRODUCTION _______________________________________________
`311
`Off-Design Operation- _ ______________________-__________--____
`311
`Inlet-stage s t a l l _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ - _ - _ _ _ _ _ _ - _ - _ _ _
`311
`Stall-limit or surge line _____________________-______________
`312
`Stall Phenomena
`312
`SYMBOLS _____________________________________-__---_____-_____
`312
`ROTATING S T A L L _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ - _ _ - _ _ - - _ _ _ _ _ _ _ _ _ _ _ _
`313
`Experimental Detection of Rotating Stall _____ ___ _____ _ _ __ _ _ ___ - _
`Mechanism of SWI Propagation _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 313
`313
`Characteristics of experimentally observed stall patterns_-___.._ 314
`Single-stage and multistage stall data summary ______________
`315
`Classification of Stall _________________________--_-_______------
`315
`Progressive or abrupt stall _________________________________
`316
`Partial- or total-span stall _________________________________
`317
`General Observations on Rotating-Stall Phenomena _____ _ _ _ _ _ - - - - -
`Steady or intermittent stall ________________________________
`317
`317
`Stall-propagation rates- _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
`Hysteresis effect _________________________________________- 317
`318
`Flow and pressure fluctuations _____________________________
`318
`M u l t i s t ~ i n g e f f e c t _ _ _ _ _ _ - _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ - -
`319
`Variation in stall patterns _________________________________
`319
`Effect of inlet temperature _________________________________
`Blade Vibration Incurred during Rotating Stall- _________________
`320
`Single-stage compressors _______________ ___ ___________ ____ __
`320
`Multistage compressors ___________ ___________ ______________
`320
`Methods of alleviating blade vibration- . . . . . . . . . . . . . . . . . . . . .
`320
`321
`Theories of Rotating Stall _______________________________-_____ 321
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`CONTENTS
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`cnarrmz
`XI. COMPRESSOR STALL AND BLADE VIBRATION—Continued
`STALL FLUTTER............................................. -- ‘
`Distinction between Stall and Classical Flutter................. --
`Mechanism of Stall Flutter .................................. --
`Brief literature survey .................. -—.----.--'.‘....... --
`Experimental evidence ..................... -.—--..... -.«..—.-..-
`CONCLUSIONS___________________ - -'.......................... - -
`Aerodynamic Aspect........................................ --
`Vibration Aspect ........................................... --
`
`XII. COMPRESSOR SURGE............................................. --
`INTRODUCTION............................................. - -
`SYMBOLS____________________________________________________ -_
`STEADY-STATE COMPRESSOR CHARACTERISTIC........... --
`EXPERIMENTAL INVESTIGATIONS OF SURGE.............. --
`Surge Due to Abrupt Stall................................... --
`10-Stage subsonic axial-flow research compressor............ --
`16-Stage subsonic axial—flow compressor ................... --
`Surge in jet engines..................................... --
`Surge Due to Progressive Stall_______________________________ _-
`THEORETICAL INVESTIGATIONS OF SURGE................ --
`Surge Due to Abrupt Stall___________________________________ -_
`Surge Due to Progressive Stall ............................... --
`Comparison of Compressor Surge with Other Oscillatory Phenomena-
`SUMMARY OF RESULTS _____________________________________ ..
`
`XIII. COMPRESSOR OPERATION WITH ONE OR MORE BLADE ROWS
`STALLED_______________________ -; ______________________________ __
`INTRODUCTION_____________________________________________ _ _
`GENERAL CONSIDERATIONS________________________________ -_
`Single-Stage Stall Characteristics _____________________________ _-
`Stage Interactions__________________________________________ __
`Radial maldistribution of flow____________________________ __
`Unsteady