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N7 4- 33789
NASA CR-134662PWA-5069
TWO-STAGE LOW NOISE ADVANCED TECHNOLOGY FAN
I. AERODYNAMIC, STRUCTURAL, AND ACOUSTIC DESIGN
30 September 1974
by
H. E. Messenger, J. T. Ruschakand T. G. Sofrin
Pratt & Whitney Aircraft DivisionUnited Aircraft Corporation
Prepared for
National Aeronautics and Space Administration
NASA Lewis Research CenterContract NAS3-16811
1. Report No. I 2. Government Accession No.
NASA CR-134662 I4. Title and Subtitle
Two-Stage Low Noise Advanced Technology Fan
I. Aerodynamic, Structural, and Acoustic Design
7. Author(s)
H. E. Messenger, J. T. Ruschak and T. G. Sofrin
9. Performing Organization Name and Address
Pratt & Whitney Aircraft Division
United Aircraft Corporation
East Hartford, Connecticut 0610812. Sponsoring Agency Name and Address
National Aeronautics and Space AdministrationWashington, D. C. 20546
3. Recipient's Catalog No.
5. RePort Date
30 September 19746. Performing Organization Code
8. Performing Organization Report No.
PWA-506910. Work Unit No.
11. Contract or Grant No.
NAS3-1681113. Type of Report and Period Covered
Contractor Report14. Sponsoring Agency Code
15. Supplementary Notes
Design Report - Project Manager, W. L. Beede, Fluid System Components Division.Technical Advisor, M. F. Heidmann, V/STOL and Noise Division.NASA - Lewis Research Center_ Cleveland, Ohio 44135
16. Abstract
A two-stage fan was designed to reduce noise as much as 20 dB below current requirements.
The first-stage rotor has a design tip speed of 365.8 m/sec (1200 ft/sec) and a hub/tip ratioof 0.4. The fan was designed to deliver a pressure ratio of 1.9 with an adiabatic efficiencyof 85.3 percent at a specific inlet corrected flow of 209.2 kg/sec/m 2 (42.85 lbm/sec/ft2).
Noise reduction devices include acoustically treated casing walls, a flowpath exit acoustic
splitter, a translating centerbody sonic inlet device, widely spaced blade rows, and the
proper ratio of blades and vanes. Other features include multiple-circular-arc rotor airfoils,resettable stators, split outer casings, and capability to go to close blade-row spacing.
17. Key Words (Suggested by Author(s))
Quiet Fan
Two-Stage Fan
Aerodynamic Design
Structural Design
19. Security Classif. (of this report)
Unclassified
18. Distribution Statement
Acoustic DesignAcoustic TreatmentsSonic Inlet Unclassified - Unlimited
I nclass,fied 1 1" For sale by the NationalTechnical InformationService, Springfield, Virginia 22151
22. Price"
NASA-C-I68 (Rev. 6-71)
TABLE OF CONTENTS
SUMMARY
INTRODUCTION
AERODYNAMIC-ACOUSTIC CONSIDERATIONS
FLOWPATH AND VELOCITY VECTOR DIAGRAM DESIGN
Design IterationsLosses
Flow Blockages
Air Angles and Velocities
Flowpath Spacings
LoadingsExit Duct Aerodynamic Design
AIRFOIL DESIGN
RotorsAirfoil Series
Partspan Shrouds
Chords, Thicknesses, and Numbers of Blades
Incidence and Deviation AnglesChannel Areas
Rotor GeometryStators
Airfoil Series
Chords and Thicknesses
Incidence and Deviation AnglesChannel Areas
Stator Geometry
INLET AERODYNAMIC DESIGN
Objectives and Techniques
Sonic Inlet Geometry
Inlet Cowling and CenterbodySonic Inlet Lip Shapes
Inlet Mach Number Distribution, Boundary Layer Characteristics,
and Estimated Pressure Recoveries
Page
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iii
TABLE OF CONTENTS (Cont'd)
STRUCTURAL AND VIBRATION ANALYSIS
RotorsBlade and Disk Vibration
Rotor Blade Stresses
Rotor Blade Flutter
Partspan ShroudsDisk and Attachment Stresses
Stators
Stator VibrationStator Stresses
Stator Flutter
Interstage Seals
Sonic Inlet Support Struts
Critical Speeds and Forced ResponseBaseline Standard Inlet Cowling Configuration
Sonic Inlet Configuration
ACOUSTIC DESIGN
Sonic Inlet, Acoustic Considerations
Flowpath and Blade Geometry
Rig Spectra Predictions
Treatment Attenuation TargetsAcoustic Treatment Selection
Inlet
Interstage and Aft Fan Duct
Predicted Attenuation - Interstage and Aft Treatment
Competing Noise Sources
APPENDIXES
A. Symbols and Definitions
B. Aerodynamic SummariesC. Airfoil Geometry on Design Conical Surfaces
D. Airfoil Coordinates on Manufacturing Surfaces
E. Two-Ring Acoustic Inlet Aerodynamic and Acoustic Design
REFERENCES
DISTRIBUTION LIST
Page
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Figure
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LIST OF FIGURES
Title
Rotor and Stator Total Loss Spanwise Profiles
Rotor Adiabatic Efficiency Spanwise Profiles
Rotor Inlet and Exit Relative Air Angles Spanwise Profiles
Rotor Meridional Velocity Spanwise Profiles
Stator Meridional Velocity Spanwise Profiles
Inlet and Exit Mach Number Spanwise Profiles for Rotors
Inlet and Exit Mach Number Spanwise Profiles for Stators
Fan Flowpaths
Schematic of the Quiet Two-Stage Fan
Rotor Diffusion Factor Spanwise Profiles
Stator Diffusion Factor Spanwise Profiles
Total Pressure Ratio Spanwise Profiles
Stator Inlet and Exit Absolute Air Angle Spanwise Profiles
Fan Exit Duct and Acoustic Splitter Flowpath
Multiple-Circular-Arc Airfoil Definitions
Rotor Airfoil Thickness Spanwise Profiles
Rotor Chordwise Location of Airfoil Maximum Thickness
Spanwise Profiles
Rotor Chord Spanwise Profiles
Rotor Inlet and Exit Metal Angle Spanwise Profiles
Rotor Incidence Angle Spanwise Profiles
Page
26
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Figure
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LIST OF FIGURES (Cont'd)
Title
Rotor Deviation Angle Spanwise Profiles
Minimum Rotor Channel Area Ratio Spanwise Profiles
Rotor Front Camber Angle and Chord-Camber Parameter
Spanwise Profiles
Rotor Channel Area Ratios Versus Axial Distance
Meridional View and Polar Representation of Blade Mean-Camber-Line
Airfoil Coordinate Definition for Manufacturing Sections
Stator Chord Spanwise Profiles
Stator Chordwise Location of Maximum Thickness Spanwise
Profiles
Stator Airfoil Thickness Spanwise Profiles
Stator Incidence Angles Spanwise Profiles
Stator Deviation Angles Spanwise Profiles
Stator Inlet and Exit Metal Angles Spanwise Profiles
Ratios of Channel-Throat-Area to Captured-Area Versus Spanfor Stators
Stator 1 Front Camber Angle and Chord-Camber Parameter
Spanwise Profiles
Stator 1 Channel Area Ratios Versus Axial Distance
Baseline Standard and Sonic Geometries
Baseline Standard Inlet Outer Wall Mach Number and Shape FactorDistributions
Sonic Inlet Throat Mach Number Spanwise Profile - Approach
Configuration
vi
Page
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44/45
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Figu re
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LIST OF FIGURES (Cont'd)
Title
Mach Number Distributions Along Inlet Walls - Approach Configuration
Mach Number Distributions Along Inlet Walls - Cruise Configuration
Mach Number Distributions Along Inlet Walls - Takeoff Configuration
Boundary Layer Shape Factor Distributions Along Inlet Walls - Cruise
Configuration
Boundary Layer Shape Factor Distributions Along Inlet Walls -
Approach Configuration
Boundary Layer Shape Factor Distributions Along lnlet Walls-
Takeoff Con figuration
Rotor 1 Campbell Diagram
Rotor 2 Campbell Diagram
Rotor 1 Tip Mode Campbell Diagram
Rotor 2 Tip Mode Campbell Diagram
Rotor 1 Goodman Diagram
Rotor 2 Goodman Diagram
Schematic of Rotor Partspan Shrouds
Stator 1 Campbell Diagram
Stator 2 Campbell Diagram
Rotor Sideplate Seal Resonance
Stator Seal Resonance
Sonic Inlet Support Struts, Campbell Diagram
Spring-Mass Model for Critical Speed Analysis - Standard Inlet
Spring-Mass Model for Critical Speed Analysis - Sonic Inlet
Critical Speed Mode Shapes
vii
Page
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Figure
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LIST OF FIGURES (Cont'd)
Title
Schematic of Sonic Inlet Configuration
Effect of Rotor- Stator Spacing on Blade-Passing Frequency NoiseLevel
Fan Aft One-Third Octave Spectra - Untreated
Fan Aft Noise Attenuation Targets
Inlet Estimated Attenuation Due to Wall Treatment - Approach
Summary of Acoustic Treatment
Treatment Attenuation - Fan Discharge Ducts
Tuning Curves
Analytically Predicted Attenuation of Aft Fan Noise at Takeoff
Predicted Jet and Treated Fan Noise Levels - Approach
Predicted Jet and Treated Fan Noise Levels - Takeoff
Two-Ring Acoustic Inlet Design Schematic
Two-Ring Acoustic Inlet Predicted Attenuation
Page
77
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158
159
°.o
Vlll
Table
I
II
Ili
IV
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIV
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
LIST OF TABLES
Title
General Aerodynamic Design Parameters
Design Performance
Flow Blockages (% of Annulus Area) at Blade Edge Axial Location
Predicted Blade Aerodynamic Diffusion Factors at Stall
Flow Blockages Assumed for Exit Duct Design
Rotor Blading Parameters
Stator Blading Parameters
Baseline and Sonic Inlet Total Pressure Recoveries
Summary of Rotor Steady Stresses - 105% Design Speed
Rotor First Coupled Mode Flutter Parameters
Partspan Shroud Parameters
Rotor Disk and Attachment Stresses - 105% Design Speed
Analytically Predicted Fan Aft PNL at 45.7 Meter (105 Foot) Radius
Identification of Aerodynamic Summary Table Headings
Identification of Spans and Diameters for Blade Element Data
Aerodynamic Summary - Rotor 1
Aerodynamic Summary - Stator 1
Aerodynamic Summary - Rotor 2
Aerodynamic Summary - Stator 2
Airfoil Geometry on Design Conical Surfaces - Rotor 1
Airfoil Geometry on Design Conical Surfaces - Stator 1
Airfoil Geometry on Design Conical Surfaces - Rotor 2
Page
3
4
5
7
7
9
II
14
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17
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25
95
96
97/98
991100
1011102
103/104
105
106
107
ix
Table
XXIII
XXlV
XXV
XXVI
XXVII
XXVIII
LIST OF TABLES (Cont'd)
Title
Airfoil Geometry on Design Conical Surfaces - Stator 2
Airfoil Coordinates on Manufacturing Surfaces - Rotor 1
Airfoil Coordinates on Manufacturing Surfaces - Stator 1
Airfoil Coordinates on Manufacturing Surfaces - Rotor 2
Airfoil Coordinates on Manufacturing Surfaces - Stator 2
Two-Ring Acoustic Inlet Treatment Parameters
Page
]O8
109/123
124/133
134/147
148/156
157
X
TWO-STAGE, LOW NOISE ADVANCED TECHNOLOGY FAN
I. AERODYNAMIC, STRUCTURAL, AND ACOUSTIC DESIGN
H. E. Messenger, J. T. Ruschak and T. G. Sofrin
SUMMARY
Advanced, long-range, commercial transport aircraft will require a major reduction in enginenoise without compromising requirements for high efficiency and adequate stall margin.
To achieve a reduction of noise 20 dB below current requirements and to attain efficiency
levels, stall margin, flow, and pressure ratio typical of an advanced fan, a two-stage, low tip-speed fan was selected as optimum for the flight Mach number range of 0.85 to 0.90.
Design features to reduce noise include use of low tip speeds and moderate blade aerodynamic
loadings, proper relationship of the number of blades and vanes, axial spacings between blade
rows of two aerodynamic chord lengths, acoustically treated casing walls, a towpath exit
acoustic splitter, and a translating centerbody sonic-inlet device.
The aerodynamic design was governed by the approximate parameters specified in the con-
tract and applicable test data. Successful NASA-sponsored research fans tested by P&WA TM
were used to establish criteria for good efficiency and stall margin. Important fan design
parameters include a pressure ratio of 1.90 with a fan adiabatic efficiency of 85.3 percent,
a first-stage rotor tip speed o f365.8 m/sec (1200 ft/sec), and a specific flow at the first-stage rotor inlet of 209 kg/sec/m 2 (42.85 lbm/sec/ft2). Other features of the design include
a fan flowpath with a constant outer diameter of 0.836 m (32.90 in.), constant diameter
hub sections between blades and vanes to facilitate use of axial spacers for alternate test
configurations, multiple-circular-arc rotor airfoils, stators with resettable stagger anglecapability, and split outer casings to accommodate on-stand configuration changes.
Structural and vibration analyses included calculation of blade-disk frequencies and their
resonances with rig excitations, blade and vane steady-state stresses and flutter parameters,rig critical speeds, and rotor forced response to unbalance. Predicted stresses due to centri-
fugal, gas bending, and untwist forces are well within the capabilities of the materials selected.
To avoid resonances and flutter, first-stage and second-stage rotor blades have a partspan
shroud at 66.5 and 60 percent span from the hub, respectively. All blades and vanes werepredicted to be free of flutter.
INTRODUCTION
A fan research program is being conducted by P&WA for NASA-Lewis Research Center un-
der Contract NAS3-16811. The objective of the program is to develop fan technology for
application in turbofan engines for an advanced, long-range commercial transport with a
cruise Mach number of 0.85 to 0.9. These future engines will be required to meet stringent
noise reduction goals with minimum performance penalties. To achieve these goals, fans in-
cluded in such engines must, during their design phase, incorporate features both to minimize
the generation of noise and to obtain the maximum suppression of the noise generated.
An earlierNASA-Lewisstudyhadbeenconductedfor Advanced-Technology-Transport(ATT)applicationto determinetheoptimumfanconfigurationandperformanceparametersfor acruiseMachnumberof 0.85to 0.9andthestringentnoisereductiongoalof 20dBbelowcurrentrequirements(FAR 36). Thestudyshowedthat theoptimumconfigurationwasalowtip-speed,two-stagefanwith a low hub/tip ratio [ref. 1]. Theoptimumpressureratiowas1.9andthetip speedwas365.8m/sec(1200ft/sec). Undercurrentprogram,ContractNAS3-16811,thisoptimumfanis to bedesigned,constructed,andtested.
Severalfeaturesthat havethepotentialfor minimizingnoisewereincorporatedin this two-stagefan. Thesefeaturesincludesubstantialaxialspacingbetweenbladesandvanes,properrelationshipof thenumberof bladesandvanes,extensiveuseof acoustictreatmentin casingwallsandin aflowpathexit acousticsplitter,andasonicinlet deviceusingatranslatingcenterbody.
Aerodynamicconditionsfor thefanarewithin therangeof dataobtainedon two earlier,successfulNASA-Lewissponsoredresearchfanstestedby P&WA: 1)a304.8m/sec(1000ft/sec)tip-speed,low-noise,single-stagefan [ref. 2] and2) atwo-stage,442.0m/see(1450ft/sec)tip-speedfan [ref. 3]. Theinformationobtainedfrom thesetwopreviousprogramsprovideasolidfoundationfor performancepredictionsandfor selectionof bladeandvanesectionsfor thecurrentdesign.
Thisreportpresentsdetailsof theaerodynamic,structural,andacousticdesignof thecurrenttwo-stagefan. Specialterms,abbreviations,andsymbolsusedin thisreportarede-finedin AppendixA.
AERODYNAMIC-ACOUSTIC CONSI DERATIONS
Both general design parameters and detailed elements of the fan design were significantly
affected by the need to incorporate low noise features. A low tip-speed of 365.8 m/see
(1200 ft/sec) and moderate blade loadings were selected for low noise. As a result, two
stages were required to obtain the design pressure ratio. A rather high fan-flow/unit-annulus-area of 209.2 kg/sec/m 2 (42.85 lbm/sec/ft 2) was chosen consistent with low enginefrontal area and minimum diffusion from sonic inlet throat to fan inlet. The numbers of
blades and vanes were chosen to restrict propagation of interaction tone noise at blade-
passing frequency and yet maintain the desired solidities. These aerodynamic-acoustic
considerations imposed a blade number relationship of s = 2r + 6, where s is the number of
stator vanes in a given stage and r the number of upstream rotor blades. To reduce blade-passing tone noise, axial spacings between blade and vane rows were set such that at all
spanwise positions the leading edge of each blade row is a minimum of two aerodynamic
chords downstream of the trailing edge of the upstream blade. Constant diameter casing
wall sections are provided between blade rows to permit tests with alternate spacings and tofacilitate incorporation of wall acoustic treatments. Fan exit ducting was designed to in-
clude a removable acoustically treated flow splitter as well as wall treatments. A two-ring,
acoustic inlet was initially selected to aid in suppression of forward radiated noise; however,
this eftbrt was discontinued in favor of a translating centerbody sonic inlet device. Acoustic
treatments were also included in the inlet casing walls.
2
FLOWPATH AND VELOCITY VECTOR DIAGRAM DESIGN
General aerodynamic design parameters (Table I) for the two-stage low noise fan were
chosen to conform with contract requirements, to provide similarity with advanced-techno-
logy NASA fan-stages of proven high performance, and to permit the use of existing hardware
and test facilities. Because this fan is for application in an engine with a rather high bypass
ratio, representative aerodynamic and acoustic data can be obtained without splitting the ductand core flow at the fan exit.
TABLE I
GENERAL AERODYNAMIC DESIGN PARAMETERS
Overall Total Pressure Ratio
Overall Adiabatic Efficiency (%)
Parameters at Inlet to First Rotor:
Tip Diameter - meters (inches)
Tip Speed- m/sec (ft/sec)
Hub/Tip Ratio
Specific Flow- kg/sec/m 2
(lbm/sec/ft 2)
Corrected Flow - kg/sec
(lbm/sec)
Corrected Speed (rpm)
CONTRACT WORK
STATEMENT
1.8-2.0
0.762 (30) (min.)
335.3-396.2 (1100-1300)
0.4 (approx)
DESIGN
1.90
85.3
0.836 (32.90)
365.8 (1200)
0.4
209.2 (42.85)
96.39 (212.5)
8367
DESIGN ITERATIONS
The flowpath and velocity vectors used to design the rotor and stator blade elements of the
fan were determined from a series of iterations. The iterations were started using a reasonable
flowpath shape and general design parameters consistent with requirements for a high bypass
ratio turbofan engine, together with estimated efficiency profiles and flow blockages.
Velocity vectors and flow conditions were then calculated by a computation system that
provides an axisymmetric, compressible flow solution of continuity, energy, and radial
equilibrium equations, with curvature, enthalpy, and entropy gradient terms included in the
equilibrium equation [Appendix A of ref. 4]. To control velocities and loadings and to
maximize predicted stall margin, a series of streamline analysis program runs was used to
adjust flowpath shape, blade solidities, and spanwise total pressure slopes. Losses were
reestimated using correlations of loss versus Mach number and loading for each significant
aerodynamicchange.Stallmarginwasestimatedby usingtheflowfieldcalculationto pre-dict bladeloadingincreasesasthefanisback-pressuredandbyusingloadinglimits es-tablishedfromtestdataascriteriafor stall. Thefinal setof designvelocityvectors,to-getherwith assumedsoliditiesandnumbersof blades,wasthenusedin thedesignof rotorandstatorbladeelements.Stressandvibrationanalyseswereperformedconcurrentlywiththeaerodynamicdesignt? insurethattheaerodynamicdesignwouldbecompatiblewithmechanicaldesigncriteria. In subsequentflowpathandvelocityvectoriterations,calcula-tion stationswererevisedto conformto actualleadingandtrailingedgelocationsof eachbladeandvanerow andto retaindesiredaxialspacingsbetweenbladerows.Performanceparametersat thedesignpointaresummarizedin TableI1.
TABLE II
DESIGN PERFORMANCE
Blade Row
PRESSURE RATIOLocal Cumulative
(per blade row)
ADIABATIC EFFICIENCYLocal Cumulative
(per blade row)
Rotor 1 1.485 1.485 89.5% 89.5%
Stator 1 0.984 1.461 85.6%
Rotor 2 1.317 1.924 90.9% 87.3%
Stator 2 0.987 1.898 85.3%
Stage
First 1.461 85.6%
Second 1.298 86.1%
LOSSES
Design values of rotor loss (Figure 1, lower set of curves) were estimated using a correlationof total loss versus inlet relative Mach number and loading based on fan rotor test data. No
additional losses were added in the partspan shroud regions. Design stator losses (Figure 1,
upper set of curves) were based on data correlated as loss parameter versus diffusion factor
and percent spa_. A comparison of the final estimated values of rotor and stator designlosses with data T from tests of the 304.8 m/sec (1000 ft/sec) single-stage _a'ef. 5] and the
442.0 m/sec (1450 ft/sec) two-stage [ref. 3] NASA fans is also shown in Figure 1. The corre-
sponding spin, wise profiles of rotor adiabatic efficiency are given in Figure 2.
FLOW BLOCKAGES
Flow blockages were included in the aerodynamic design to account for boundary layer
growth on casing walls and to account for the presence of a partspan shroud on each rotor.
Blockages due to casing boundary layers at the fan inlet were calculated from analytical
predictions of displacement thicknesses. Wall boundary layer growth through the blade rows
was estimated from test data from the 442.0 m/sec (1450 ft/sec) fan which achieved itsdesign flow rate [ref. 3]. In addition, to account for the presence of the retor partspan
Unless otherwise indicated, all data shown in comparisons are for test points at design speed on all
operating line pas_ing through the design point of the referenced fan.
shrouds, a blockage equal to the percent of annulus area occupied by each shroud wasapplied at the exit of the rotors, and approximately one-fourth of this amount was used atthe inlet of each rotor. In calculating the design velocity vectors and flow conditions, thetotal blockages listed in Table III were applied equally to all stream tubes at each of theindicated axial locations.
TABLE III
FLOW BLOCKAGES (% OF ANNULUS AREA)AT BLADE EDGE AXIAL LOCATIONS
LOCATION TOTAL BLOCKAGE
RI L.E. 2.6
PAT. E. 4.9
$I L.E. 3.1
S1 T.E. 3_3
R2 L.E. 3.7
R2 T.E. 6.1
$2 L.E. 4.3
$2 T.E. 4.6
AIR ANGLES AND VELOCITIES
The fan was designed with a constant tip diameter to, allow all the flowpath convergence tobe taken at the root of the flowpath, which tends to minimize critical root-loadings and thelarge past-axial turnings inherent in a low speed, low hub/tip ratio fan rotor. As shown inspanwise profiles of flow angle (Figure 3), the first-stage rotor is designed to turn the flowapproximately 30 degrees past axial at the rsot, about 10 degrees less than the rotor designvalue of the 304.8 m/sec (1000 ft/sec) fan [ref. 6].
Fan exit flow (aft fan-duct) is axial, as specified by contract, and the annulus area is set toprovide an average exit Mach number of about 0.40, a practical value for effective noisetreatment and for low losses from struts and ducting downstream of the fan. Flowpathconvergence and curvature of the inner casing walls between the inlet spinner and fan exitwere used to control velocity profiles and blade aerodynamic loadings (diffusion factors).Resulting profiles of meridional velocity and Mach number at leading and trailing edges ofblade rows are shown in Figures 4 through 7.
FLOWPATH SPACINGS
Two flowpath configurations are shown in Figure 8. The lower configuration is the basictest configuration, and the upper configuration is an alternate configuration with more
closelyspacedbladerows. Toreducenoiseassociatedwith blade-vanewakeinteractions,theaxialspacingsbetweenadjacentbladerowsof thebasicflowpath(wideblade-spacing,lowerconfiguration)weresetsuchthat atall spanwisepositionstheleadingedgeof eachbladerow isaminimumof two aerodynamicchordsdownstreamof thetrailingedgeof theupstreambladerow. Constantradiushubsectionswerespecifiedbetweenbladerowstofacilitatetheuseof spacersfor increasingor decreasingaxiallengthsbetweenbladerowsforalternatetestconfigurations.Thealternateconfiguration,theupperconfigurationinFigure8, hasaxialspacingsbetweensuccessivebladerowsof 1, 1,and2aerodynamicchordsandanoveralllengthapproximately0.17m (6.5in.) lessthanthatof thebasiccon-figuration. Streamlineanalysiscalculati?nsindicatethatvelocityvectorsfor thetwo con-figurationsaresubstantiallythesameand,hence,no significantdifferencesin aerodynamicperformancearepredicted.
A schematicshowingthemechanicallayoutof therig ispresentedin Figure9.
LOADINGS
Spanwise profiles of design diffusion factors for the current fan are compared in Figures10 and 11 with the diffusion factors that had been obtained from tests of the two previousresearch fans. The Figures show that the average loadings of the current fan are lower thanthose of the 304.8 m/sec (1000 ft/sec) single-stage fan [ref. 5] and the 442.0 m/sec (1450ft/sec) two-stage fan [ref. 3] at test points where each was operating with a practical stallmargin and high efficiency. Considerable effort was devoted to balancing the design loadingsamong blade rows to achieve maximum predicted stall margin. Parameters which werevaried in these attempts include hub casing contours, average total pressure ratios and span-wise total pressure slopes of each rotor, and first-stage stator exit air angles. Stall marginwas estimated by using the flowfield calculation to predict blade loading increases as thefan is back-pressured and using loading limits established from test data as criteria for surge.The fan stall margin obtained with this method, which in previous applications has givengood agreement with test values, is about 18 percent. The predicted fan stall was set by thesecond-stage stator hub which reached diffusion factor levels of 0.65, considered the loadinglimit for statars.
The resulting higher loadings and design pressure ratios of the first-stage relative to second-
stage, as shown in Figures 10, 11 and 12, reflect a provision for an anticipated, more rapidincrease of second-stage blade loadings with an increase in fan back-pressure. Radial profiles
of total pressure were sloped negatively (i.e., higher pressure near the hub than near the tip)
to obtain high velocities on the hub wall to reduce critical loadings. Also, as part of the at-
tempt to achieve a desirable loading balance, flow angles were set at 7.5 degrees at the exit
of the first-stage stator (Figure 13).
The predicted loadings for the four blade-rows at the estimated stall point are presented inTable IV below.
6
TABLE IV
PREDICTED BLADE AERODYNAMIC DIFFUSION FACTORS AT STALL
HUB MEAN TIP
(5% Flow) (50% Flow) (90% Flow)
Rotor 1 0.55 0.55 0.51
Stator 1 0.62 0.46 0.45
Rotor 2 0.61 0.47 0.42
Stator 2 0.65 0.47 0.50
Tabulations of aerodynamic parameters at rotor and stator leading and trailing edges are pro-
vided in Appendix B (Tables XVI to XIX).
EXIT DUCT AERODYNAMIC DESIGN
The exit ducting and acoustic splitter contours for the fan were selected: 1) to provide con-
ical casing surfaces convenient for incorporation of acoustic treatment, 2) to control Mach
numbers for low losses and low noise, and 3) to allow use of existing rig hardware. Blockages
were included in the flowfield calculation in order to account for boundary layer growth
along the four flow-surfaces of the exit duct, and annulus areas were gradually increased along
the duct to compensate for boundary layer growth to hold a Mach number of about 0.4
throughout the duct at the design point. The boundary layer parameters were estimated
from limited test-data on flow over a perforated plate which is qualitatively similar to the ac-
oustic treatments of the present design. Annulus blockages were set somewhat higher than
are probably required, which should provide ability to operate at lower than design back
pressure without choking of the flow in aft portions of the duct. Exit duct blockage values
are listed in Table V. Use of these parameters and of an existing inner support structure re-
sulted in the nearly parallel sloped duct casing walls and splitter contours as shown in Figure14.
TABLE V
FLOW BLOCKAGES ASSUMED FOR EXIT DUCT DESIGN (% OF ANNULUS AREA)
AXIAL LOCATION FROM ROTOR 1
ROOT L.E. REFERENCE PLANE
(Meter) (inch)
TOTALBLOCKAGE
(%)
1.0363 40.8
1.0668 42.01.3208 52.0
1.5748 62.0
1.8288 72.0
2.0930 82.4
2.3368 92.0
5.6
6.0
7.3
8.9
10.5
12.212.2
7
Splitter geometry was determined from acoustic treatment dimensions, which set splitterthickness at 0.0157 m (0.62 in.), and from the previously discussed Mach number consid-
erations. The splitter nose was designed as an ellipse with a ratio of semi-major to semi-minor
axis of 2.5: 1, and the splitter trailing edge was clesigned as a boattail with a 15-degree in-
cluded angle. In order to reduce the splitter incidence angle, and hence to eliminate under-
sirable flow separations at the fan aerodynamic design point, the splitter nose was inclined
at an angle of 3 degrees with respect to the rig centerline as compared to a 7-degree angle
for the major portion of the splitter. The splitter is supported by two sets of five struts which
are circumferentially aligned with five exit duct support struts (Figure 14). These struts arecontoured as 400 series airfoils.
AIRFOIL DESIGN
ROTORS
Airfoil Series
Rotor blades for both stages of the fan were designed using multiple-circular-arc (MCA)
airfoils generated on conical surfaces which approximate streamsurfaces of revolution. Asshown in Figure 15, each MCA airfoil section is defined by specifying a value of total chord,
front chord, tot',d camber, front camber, maximum thickness and its chordwise location, and
leading and trailing edge radii. Blades of this airfoil series have been used successfully in
several applications, providing much useful test data for design of airfoils in the transonic
and high subsonic Mach number regimes. Such data have been applied to the present design.
Partspan Shrouds
Both rotors have a partspan shroud to provide mechanical stability. These shrouds are lo-
cated at 66.5 and 60 percent span from the hub of rotor 1 and rotor 2, respectively, with
relative spanwise positions chosen such that the second-stage rotor shroud lies approximately
in line with the expected wakes from the first-stage rotor shroud, thus minimizing total loss
and other aerodynamic penalties normally associated with the shrouds.
Chords, Thicknesses, and Numbers of Blades
A summary of rotor blading parameters is given in Table VI. Chords, solidities, and numbers
of blades were chosen to be consistent with acceptable aerodynamic loadings, moderate axial
lengths, structural requirements, low noise,:and previous experience. In particular, to restrict
propagation of blade-vane interaction noise, the numbers of blades and vanes were selected
according to the relation s = 2r + 6, where s is the number of stator vanes in a given stage
and r the number of upstream rotor blades. The number of rotor 1 blades was determinedaccording to the relation s = 2r + 6, where s is the number of stator vanes in a given stage
and r the number of upstream rotor blades. The number of rotor 1 blades was determined
flutter-free operation and by maximum solidity limits which were set by channel flow area
requirements. The number of rotor 2 blades was selected to provide a 5:4 ratio for the num-ber-of-rotor-2 blades to the the number-of-rotor-1 blades to give desirable fan noise character-
istics (see the Acoustic Design Section).
TABLE VI
ROTOR BLADING PARAMETERS
R1 R2
Number of Airfoils 28 35
Airfoil Series
Aspect Ratio (1)
Aspect Ratio (2)
Taper Ratio (3)
MCA
2.75
2.19
1.232
MCA
2.54
2.21
1.028
Hub Chord- meter (inch)
Tip Chord- meter (inch)
Tip Solidity
0.0897 (3.530)
0.1105 (4.350)
1.18
0.0859 (3.382)
0.0883 (3.476)
1.18
Hub Solidity 2.28 2.14
(1)(2)(3)
Average length/axially projected hub chord
Average length/chord at tip
Tip chord/hub chord
Rotor maximum-thickness to chord ratios, t/c, (Figure 16) were selected to provide mech-
anical stability while maintaining minimum airflow blockage. The chordwise locations of
maximum thickness for both rotors (Figure 17) were set to give the blades the minimum
possible leading edge wedge angles without creating cusp-shapes in the front portion of the
blades. Rotor total chords and front chords are shown in Figure 18.
Incidence and Deviation Angles
Rotor leading and trailing edge metal angles (Figure 19) were determined from application
of incidence and deviation criteria to the design velocity vectors. For rotor airfoil sections
whose inlet relative Mach number exceeded 1.0, incidence angles (iss a,) were set at a locationhalfway between the leading edge and the poiat from which a Mach wave emanates that meets
the leading edge of the following blade. A nominal design value of issa, of 1.5 degrees was
chosen to account for development of the suction surface boundary layer, blockage at the
blade leading edge, and bow wave losses. Actual values of incidence for rotors of the subject
design (Figure 20) varied between approximately 1.0 and 2.4 degrees, the variation resulting
from a selection of geometry to fulfill channel area requirements and to provide smooth
blades. For subsonic sections, incidences were chosen at the leading edge at values consistent
with minimum loss data from previous tests and with smooth distributions of blade geometry.
9
Rotor deviation angles were calculated using P&WA's cascade method modified by correction
factors based on applicable rotor test data. Figure 21 shows the predicted deviations and
comparisons with deviation angles calculated using Carter's Rule.
Channel Areas
To provide sufficient fan flow capacity while allowing the rotors to operate near minimum
loss, the minimum critical area ratio (A/A*) rain. in channels between adjacent blades forboth rotors (Figure 22) was set at approximately 1.03 over most of the span. Desired channel
areas were obtained by varying the chordwise distribution of airfoil camber. Near the location
of each shroud, front camber was increased to provide higher values of (A/A*) rain." In cal-
culating A* through the blade channels, losses were distributed in the following manner: no
loss was applied ahead of the assumed normal shock at the blade passage entrance, a normalshock loss was applied at the blade passage entrance, and the remaining loss was distributed
linearly through the rest of the channel.
The resulting profiles of front camber angle and chord-camber parameter are shown in
Figure 23. Distributions of flow area ratio through the blade channels of both rotors areshown in Figure 24 for several spanwise locations. The distinctive shape of the A/A* distribu-tion at the root of rotor 1 is typical of a rotor root with past-axial turning [ref. 6].
Rotor Geometry
Rotor geometry on design conical surfaces is summarized in Appendix C (Tables XX andXXII); for each airfoil section, two values of total and front camber are tabulated. Figure 25
gives a polar representation of a blade mean-camber-line and the two definitions used tocalculate these values of camber. For manufacturing purposes, the airfoil sections were re-
defined on planes normal to the stacking line, a radial line through the center of gravity ofthe root conical section. Rotor blade coordinates for these redefined sections are tabulated
in Appendix D (Tables XXIV and XXVI), and Figure 26 gives the airfoil coordinate definitionsused in these tabulations.
STATORS
Airfoil Series
MCA airfoils were also used in design of the first-stage stator vanes since this series of airfoils
offers greater control of channel area than more conventional airfoil series and the potentialfor lower stator losses at the rather high stator root inlet Mach numbers of the present design.The second-stage stators were designed as 65/CA vanes (circular arc meanline with 65 series
thickness distribution) since these vanes will operate with inlet Mach numbers less than 0.65,
a regime where 65/CA airfoils have low losses.
Chords and Thicknesses
A summary of stator blading parameters is given in Table VII. To restrict propagation ofblade-vane interaction noise, the numbers of vanes were selected according to the relation
10
s = 2r + 6 as discussed under Rotors. Stator chords and the locations of maximum thickness
for both stators are shown in Figures 27 and 28. To provide low stator losses, maximum
thickness-to-chord ratios were set at minimum values consistent with structural requirements.
These thickness ratios (Figure 29) are somewhat higher than those for stators tested in pre-
vious NASA fans because of the higher aspect ratios of the present design. Any loss penalties
should be small, however, since most of the thicker airfoils will operate with rather low inletMach numbers.
TABLE VII
STATOR BLADING PARAMETERS
Sl S2
Number of Airfoils 62 76
Airfoil Series MCA 65/CA
Aspect Ratio (1) 5.03 3.89
Aspect Ratio (2) _ 3.81 3.73
Taper Ratio (3) 1.099 0.9709
Hub Chord- meter (inch) 0.0513 (2.020) 0.0489 (I .930)
Tip Chord- meter (inch) 0.0564 (2.220) 0.0475(1.8707)
Tip Solidity 1.33 1.38
Hub Solidity 2.50 2.46
(1) Average length/axially projected hub chord
(2) Average length/chord at tip(3) Tip-chord/hub chord
Incidence and Deviation Angles
Selection of design incidence angles and calculation of deviation angles for both stators
(Figures 30 and 31) were based on P&WA's cascade system and minimum loss data from
previous tests. The resulting metal angles are shown in Figure 32.
Channel Areas
Minimum values of channel area ratio (A/A*)min" near the stator 1 hub were set a few per-cent above the A/A* for the corresponding stator inlet Mach number (Figure 33) according
to a correlation of capture-area/throat-area ratio at minimum loss as a function of stator inlet
Mach number [ref. 7]. The outer half of the blade has a front camber selected to give nearly
11
double-circular-arc (DCA) airfoils for this low Mach number portion of the vane. The re-
sulting profiles of front camber and chord-camber parameter are shown-in Figure 34, andthe channel distributions of A/A* for stator 1 are given in Figure 35. Channel area ratio was
not a critical parameter in the design of stator 2 airfoils since the inlet Mach numbers are
sufficiently low (0.50 - 0.65) that choking problems should not be encountered with the vanes
selected by means of the P&WA correlation of cascade data.
Stator Geometry
Stator geometry on design conical surfaces is summarized in Appendix C (Tables XXI and
XXIII). For manufacturing purposes, the airfoil sections were defined on planes normal to a
radial (stacking) line. The resulting blade coordinates are presented in Appendix D (Tables
XXV and XXVII).
INLET AERODYNAMIC DESIGN
OBJECTIVES AND TECHNIQUES
The purpose of the inlet aerodynamic designs is to provide inlet configurations that meet the
program acoustical requirements while providing a minimum length in order to approach
practical requirements of aircraft installation. Two inlet configurations were chosen for the
program: a baseline standard inlet cowling configuration and a translating plug, choked (sonic)inlet configuration. Contours of these two configurations are shown in Figure 36.
The principal reason a translating centerbody, sonic inlet was chosen is because it provides a
means of controlling flow area to achieve throat Mach numbers that give the desired noise
suppression for a range of fan operating conditions. Furthermore, this configuration requiresa minimum inlet length without excessive boundary layer growth or separation. Originally
a two-ring, acoustic inlet had been selected; however, that design was discarded when the
sonic inlet configuration was decided upon. A summary of the limited work done on the
two-ring inlet is provided in Appendix E.
An inlet fabricated previously for another program is to be used as the baseline standard
inlet cowling. This inlet provides a one-dimensional throat Mach number of 0.68 and has an
inlet-length to fan-t, ip-diamete, r ratio (L/D) of 1.03 and an overall contraction ratio (Ahighlite/Athroat ) of 1.65 -- 'highlight is defined as the farthest forward point on the inlet cowling(Figure 36). The aerodynamic contours of the sonic inlet were designed using a transonic
axisymmetric flow analysis and a modified Reshotko-Tucker mass-momentum integral bound-
ary layer solution. The inlet contours for both the baseline and sonic inlet configurations
were selected to minimize the velocity overspeed along the surface downstream of the throat
which should result in the best diffuser performance with the least distortion at the fan face.
It should be noted that the inlet flow for the aircraft approach condition used in the aero-
dynamic design of the sonic inlet was assumed to be 80 percent of design flow, which is
believed to be the lowest practical flow for a sonic inlet design within present constraints.
12
Any lowerflow assumptionwouldnecessitatelengtheningtheinlet beyondpracticalmech-anicalandflightenginelimits. The80percentdesignflow conditionis theoreticallypossiblewith avariable,fan-ductnozzle,permittingfanoperationat ahigherspeed(approximately80percentdesignspeed)andalowerpressureratio (1.19)at thedesiredthrustconditionforaircraftapproach.
Thegeometriesof the fixedouterinletcowlingandtheinnertranslatingcenterbodyareshownin Figure36in thefully extended,intermediate,andfully retractedpositions.Thesepositionsarespecifiedastheapproachpositionat 80percentdesignflow, thetakeoffposi-tion at 92.6percentdesignflow,andthecruisepositionat 100percentdesignflow. Theone-dimensionalthroatMachnumbersassociatedwith thesepositionsarerespectively0.9,0.9,and0.71.
SONIC INLET GEOMETRY
Inlet Cowling and Centerbody
Since the fan aerodynamic design was essentially complete when the sonic inlet aerodynamic
design was initiated, the inlet design had to be compromised to retain the fan root flow angleassociated with the conventional spinner. This resulted in an overall inlet length of about
1.2 meters (47.5 inches) for an inlet-length to fan-tip-diameter ratio (L/D) approximately
1.45, which is somewhat larger than 1.0, the maximum ratio judged practical for a flightapplication. An L/D ratio of 1.0 would have been possible had it not been necessary to dif-
fuse the inlet flow to a rather high area in order to retain the fan root platform contour.
A 0.0032 meter (0.25 inch) truncation, or step, was added at the trailing edge of the center-
body to improve boundary layer characteristics in the region where the centerbody meets
the fan spinner (Figure 36). The maximum centerbody radius was set at 0.19 meter (7.39
inches) at the throat of the inlet. The minimum cowling radius was set at 0.37 meter (14.55
inches) at an axial station 1.02 meters (40.0 inches) upstream of the first-stage rotor hubleading edge (reference plane).
Sonic Inlet Lip Shape
Since the sonic inlet is to be tested at static conditions only, an attempt was made to re-produce, as nearly as possible, the accelerations on the inlet surface which would be encoun-
tered at aircraft approach flight conditions. This was done by generating a 2.5:1 elliptical
shape from the throat to approximately the inlet highlite station and then blending this con-
tour to a circular arc by making them tangent and continuing the circular arc to complete
the inlet contour. The overall contraction ratio (A highlite /A throat ) of this configuration isequal to 1.45.
INLET MACH NUMBER DISTRIBUTIONS, BOUNDARY LAYER CHARACTERISTICS,AND ESTIMATED PRESSURES RECOVERIES
The outer wall Mach number and the boundary layer shape factor distributions were calcu-
lated for the baseline standard inlet configuration, and the results are shown in Figure 37
for the 100 percent speed, cruise flight condition. The shape factors are well under theseparation limit of 2.2 to 2.5.
13
For the sonic inlet configuration, attempts were made to obtain a uniform Mach number
profile at the inlet throat to meet acoustic criteria. As shown in Figure 38, the desired flat
profile was achieved for the approach configuration at the throat, an axial distance of 1.016
meters (40 inches) upstream of the rotor 1 hub leading edge.
Mach number and shape factor distributions along the sonic inlet walls for the approach, cruise,
and takeoff positions are shown in Figures 39 through 44. The Mach numbers along both
inner and outer walls for the approach configuration (Figure 39) are quite similar, showing
a peak Mach number of approximately 0.92 near the throat of the inlet, while peak Mach
numbers for the cruise configuration (Figure 40) are 0.77 and 0.83 for the inner and outer
walls, respectively. At takeoff (Figure 41), the inner wall Mach number reaches a peak of
0.98 near the inlet throat while the outer wall value is 0.81 at this location.
The shape factors for the wall boundary layers shown in Figure 42 for the cruise configura-
tion indicate a stable boundary layer on the outer wall, but the inner wall boundary layer
deteriorates rapidly as the flow approaches the centerbody truncation. This deterioration
could lead to locally separated flow in this region - separation is indicated when shape factor
reaches values of 2.2 to 2.5. This would, however, be followed by a reacceleration and re-
attachment of the flow on the spinner surface. A similar deterioration of shape factor in the
area of centerbody and plug shaft truncation for the approach configuration is indicated in
Figure 43 and an improvement in the boundary layer can be noted as the constant area por-
tion of the inlet duct is reached; additional improvement will occur as the flow accelerates
around the spinner. The takeoff configuration shown in Figure 44 has shape factor distribu-
tions similar to the cruise condition with the inner wall approaching a critically high value
(2.17) near the intersection of the centerbody spinner. As in the cruise condition, the flow
is expected to reattach on the spinner if any local separation occurs.
Baseline and sonic inlet total pressure recoveries were estimated from the analytical boundary
layer solution and are presented in Table VIII.
TABLE VIII
BASELINE AND SONIC INLET TOTAL PRESSURE RECOVERIES
FLOW CONDITION
INLET CONFIGURATION (%W_'/$) (Throat Mach No.) TOTAL PRESSURE RECOVERY
Baseline, Cruise 100 0.68 0.993
Sonic, T/O 92.0 0.90 0.975
Sonic, Cruise 100 0.71 0.987
Sonic, Approach 80 0.70 0.970
STRUCTURAL AND VIBRATION ANALYSIS
Design of the fan blading included structural and vibration analyses to determine configurations
that satisfy mechanical design requirements. The analyses included calculation of: blade-disk
frequencies and their resonances with rig excitations, steady-state stresses, blade-vane flutter
parameters, rig critical speeds, and full rotor system response due to imbalance at the rotor 1
location.
14
The material for rotor 1 blades is AMS 4973F (titanium alloy) and for rotor 2 blades is
AMS 4928 (titanium alloy). The material for the stator vanes is AMS 5613 (stainless steel),
and the material for the disks, hubs, spacers, and seals is AMS 5616 (stainless steel).
ROTORS
Blade and Disk Vibration
A partspan shroud is required for each rotor to avoid first bending resonances with first and
second order rig-frequencies in the operating range. The airfoil geometry and shroud loca-
tion were chosen to provide the best compromise between high speed margin with a 3E re-sonance (3E = 3 excitations per rotor revolution) and the speed at which a 4E resonance
would occur. The shroud location selected for rotor 1 (i.e., 66.5 percent span from the hub)gives this rotor a predicted 5.6 percent 1st coupled mode (bending and torsion) 3E resonance
frequency margin at 105 percent of design speed and positions the 1st coupled mode 4E
resonance at 75 percent design speed (Figure 45). For rotor 1, no 2nd coupled mode or 3rd
coupled mode critical resonances exist in the operating range.
During sonic inlet testing, the five support struts for the translating centerbody will createa 5E, 1st mode resonance on rotor 1 at 4800 rpm (Figure 45). This resonance is not consi-
dered a problem because the inlet struts are 0.254 meter (10 inches) forward of rotor 1 lead-
ing edge and the resonance occurs low in the speed range where the excitation energy is low.
The second-stage rotor, with a shroud location at 60 percent span from the hub, has a 1st
coupled mode 3E resonance frequency margin of 5.4 percent and a 1st coupled mode 4E
resonance at 72 percent design speed (Figure 46). For rotor 2, no 2nd coupled mode or 3rd
coupled mode critical resonances exist in the operating range. The 5.6 and 5.4 percent mar-
gins on 1st coupled mode 3E resonance are adequate, based on previous test results that have
shown good correlation with design predictions. Moreover, increasing these margins on 3E
resonance would position the 1st coupled mode 4E resonance at higher speeds in the operat-
ing range. Due to these limiting 3E margins, the operational speed of the fan will be held to105 percent corrected design speed during the test program.
Rotor blade tip chordwise bending modes are of great concern with the thin tip sections ot
modern fan blades. Excitations from inlet struts and stator vanes upstream and downstream
of the rotor can interact with the natural frequency of these tip chordwise modes to produce
high dynamic stresses. Figures 47 and 48 show that the tip chordwise bending mode reson-
ances will not occur in the critical portion of the speed range (70 - 105 percent of designspeed).
Rotor Blade Stresses
Stresses due to centrifugal forces, air loads, and untwist forces were calculated for 105 per-cent of design speed, and the results are shown in Table IX. The allowable stresses for the
blade material based on 338.6°K (150°F)metal temperature for rotor 1 and 421.9°K (300°F)
15
metaltemperaturefor rotor 2arealsoshownin thistable. Themaximumcombinedstressesof 3.24x 108N/m2 (47,000lbf/in.2) for rotor 1and2.03x 108N/m2 (29,500lbf/in.2) forrotor 2 arecomparableto stresslevelspresentin experimentalandproductionbladesandarewellbelowtheallowablestresses.
Gasbendingstresseswith centrifugalrestorationswerecalculatedat 105percentof designspeed.Airfoil stresseswereminimizedfor thecombinationof loadandnoloadconditions.Theselectedaxialandtangentialtilt of 0.00107meter(0.042inch)resultsin amaximumstressof 4.1 x 107N/m2 (6,000lbf/in.2) for rotor 1and2.8x 107N/m2 (4,000lbf/in.2)for rotor 2.
TABLE IX
SUMMARY OF ROTOR STEADY STRESSES
105% of Design Speed - N/m 2 x 10-7 (Ibf/in. 2 x 10"3)
ROTOR1 ROTOR 2
P/A 20.0 (29) 14.5 (21)
Centrifugal Untwist 8.3 (12) 3.1 (4.5)Gas Bending 4.1 (6) 2.8 (4)Combined 32.4 (47) 20.3 (29.5)Allowable 60.7 (88) 53.1 (77)
Modified Goodman diagrams (Figures 49 and 50) indicate that at the maximum steady stresspoints the maximum allowable vibratory stresses for rotors 1 and 2 are 10.67 x 107 (15,500
lbf/in. 2) and 12.72 and 107 N/m 2 (18,500 lbf/in.2), respectively. During testing, a vibratorystress limit of 6.89 x 107 N/m 2 (10,000 lbf]in. 2) will be imposed. Since no low order reson-
ances are expected in the high speed operating range, the actual vibratory stress levels thatwill be encountered during testing should be less than the 6.89 x 107 N/m 2 (10,000 lbf/in. 2)
limit set as part of the test procedures.
Rotor Blade Flutter
Flutter is a self-excited, self-sustaining vibration which occurs in either a torsional or bendingmode or a combination of both. To prevent rotor blade flutter, a partspan shroud is required
for each rotor of the two-stage fan. Values of flutter parameters for the shrouded blades
were calculated at 105 percent of design speed, the operating speed considered most critical
in regard to flutter, and these values were compared with correlated test data from previousprograms. The calculated values of reduced-velocity parameters (2 V' i/cco b) and torsional-
twist-to-bending-deflection ratio (q_ c/d) for the 1st coupled mode flutter are summarized
in Table X and lie within the range of P&WA experience where flutter problems have not
been encountered. Values of reduced-velocity parameter (2 V' 1/ c co t) for torsional flutter,calculated at 105 percent speed (0.95 for rotor 1 and 1.2 for rotor 2) are also well within
the range where flutter has not been experienced. The torsional frequency, oat , is based on
the entire blade.
16
ROTOR
1
2
Partspan Shrouds
TABLE X
ROTOR FIRST COUPLED MODE FLUTTER PARAMETERS
REDUCED VELOCITY PARAMETER
(2 Vtl/C cob)
TORSIONAL TWIST/
BENDING DEFLECTION
(_ c/d)
2.75 0.16
3.05 0.14
The partspan shrouds were sized and positioned to satisfy aerodynamic and structural re-
quirements, including the 3E margin requirement. Shroud design parameters and stresses
are summarized in Table XI, and a sketch of the shrouds is shown in Figure 51. Bearin_
stresses for the shroud are 3.55 x 107 N/m 2 (5,150 lbf/in. 2) for rotor 1 and 3.45 x 10TN/m 2
(5,000 lbf/in. 2) for rotor 2, which are below values tested successfully on P&WA research rigs,
e.g. 5.86 x 107 N/m 2 (8500 lbf/in.2). The shrouds were designed to fit together sufficiently
tight to provide adequate damping of vibrations without "shingling".
The Z* ratios, a measure of the relative stiffnesses of the shroud and adjacent airfoil as de-
fined in Appendix A, are within the realm of successful experience.
Spanwise Location
(% Span From Hub)
Contact Angle - deg.
Z* Ratio
Bearing Stress
- N/m 2 x 107 ( lbf/in. 2 )
Bending Stress- N/m 2 x 10-7 ( lbf/in. 2 )
Thickness -
meter (inch)
TABLE Xl
PARTSPAN SHROUD PARAMETERS
( 105% Speed)
ROTOR 1
66.5
55.0
1.30
3.55 (5,1513)
4O.O (58,000)
o.oo5 (0.20)
ROTOR 2
60.0
70.0
1.49
3.45 (5,000)
29.1 (42,246)
0.0046 (0.18)
17
Disk and Attachment Stresses
Conventional dovetail attachments were selected for the blades of both rotors. The calcu-
lated and allowable disk and attachment stresses for critical locations are listed in Table XII.
All calculated values fall below the maximum allowed. In addition, the dynamic stress ratio
(airfoil root stress divided by attachment stress) is above the minimum recommended value
of 2.0, indicating that the attachment can withstand vibratory stresses greater than those theairfoil can tolerate.
TABLE Xll
ROTOR DISK AND ATTACHMENT STRESSES
(105% Design Speed)
LOCATION TYPE OF STRESS
CA LCU LATE D ST R ESS/A L LOWAB L E ST RESS
N/m2x 10 -7 (Ibf/in.2 x 10"3)ROTOR 1 ROTOR 2
Blade Attachment Combined 27.6/53.1 (40]77)
Bearing 26.2/59.3 (38/86)Disk Tangential (avg.) 26.2/66.2 (38/96)
Radial (max.) 15.9/53.8 (23/78)
Front Seal Hoop 22.1/96.5 (32/140)
Bending 4.1/96.5 (6/140)
Rear Seal Hoop 22.1/96.5 (32/140)
Bending 8.3/96.5 (12/140)
17.2/59.3 (25]86)
20.0/66.2 (29/96)
42.7/58.6 (62/85)
11.0/47.6 (16/69)
37.1/95.2 (53.8/138)
13.8/95.2 (20/138)37.1/95.2 (53.8/138)
10.3/95.2 (15/138)
STATORS
Stator Vibration
Stator frequencies were calculated from a coupled bending-torsion analysis which included
a model with the following end conditions:
• bending motion - moment restraint at airfoil hub and tip
torsional motion - free at tip and restraint at spindle/actuation-arm junction
(includes torsional flexibility of actuator arm).
As shown in Figures 52 and 53, the first two bending and torsion modes for stators 1 and 2
will not be excited by blade-passing orders in the operating range. Adequate margin on the
first bending mode 3E resonance exists throughout the operating range and, based on past
experience, higher order excitations should not result in vibrational problems.
Stator Stresses
Stator vane bending stresses due to air loads were calculated at 105 percent design speed.
The maximum bending stress for stator 1 was calculated as 3.03 x 108 N/m 2 (44,000 lbf/in. 2)
18
and for stator 2 as 2.99 x 108 N/m 2 (53,500 lbf/in.2).which are considerably lower than the
allowable stresses of 58.6 x 107 N/m 2 (85,000 lbf/in. 2) and 52.4 x 107 N/m 2 (76,000 lbf/in.2)
for stators 1 and 2, respectively. Stress allowables are based on vane material properties which
are a function of metal temperatures. Vane metal temperatures used to determine allowable
stresses for stator 1 and stator 2 are 65.56°C (150°F) and 148.89°C (300°F), respectively.Since no critical resonances are predicted in the operating range, vibratory stress levels are
expected to be low. A maximum vibratory stress level of +6.89 x 107 N/m 2 (-+10,000 lbf/in. 2)will be imposed during test operation.
Stator Flutter
Flutter parameters were calculated for both stators and compared with correlated test data.
Values of the dimensionless reduced-velocity parameter for bending flutter (2V/CCOb) cal-culated for stators 1 and 2 were 2.1 and 1.4, respectively, which are within the successful
(no flutter) area determined through experience. A similar conclusion was indicated by
the values of reduced-velocity parameter (2V/coot) for torsional flutter, which were com-puted as 2.05 and 1.87 for stators 1 and 2, respectively.
INTERSTAGE SEALS
The resonances were checked for the interstage rotor sideplate and stator seals (Figure 9)because of the long, cantilevered, stator inner-shrouds required for acoustic considerations.
Frequencies of the seals were obtained from shell revolution structural analysis programs.
The hoop stiffness effects of the stator inner shroud honeycomb construction were included
in the vibration analysis. Resonances for all rotor and stator seals are above the 25 percent
frequency margin requirement at 105 percent of design speed, as shown in Figures 54 and55.
SONIC INLET SUPPORT STRUTS
Frequencies were calculated for the fan inlet strut using fixed-end conditions. The resultingfrequencies are shown in Figure 56. The blade passing frequency for rotor 1 does not excite
the fundamental bending and torsion modes. There are no low order resonances (1E and
2E) in the operating range. Static load (one-G) plus the maximum aerodynamic load on thecenterbody causes a maximum stress of 2.95 x 107 N/m 2 (4280 Ibf/in. 2) on the inlet struts
at the inner and outer diameter fillet welds. This is well below the allowable stress of 54.5 x
107 N/m 2 (79,000 lbf/in. 2) for the AMS 5613 material used. The dimensionless, reduced-
velocity parameter (2V/C_b) for bending flutter was calculated to be 1.25, within the suc-cessful (no flutter) area determined through experience. The torsional flutter, reduced-
velocity parameter (2V/coot) was calculated to be 0.6, also in the stable area.
CRITICAL SPEEDS AND FORCED RESPONSE
A rotor-frame critical-speed analysis was performed to determine the vibrational characteristics
of the fan, with and without the sonic inlet configuration. The analysis was based on models
which included all significant structural members of the rig and used the spring-mass system
shown in Figure 57 for the baseline standard engine inlet cowling and Figure 58 for the sonicinlet.
19
BaselineStandardInlet CowlingConfiguration
Two critical speeds occur within the rig operating range at 4811 rpm and 8764 rpm for the
standard inlet cowling configuration. Two other critical speeds occur at 10,729 rpm and
15,777 rpm, which are above the expected maximuin operating speed (8785 rpm). Themode shapes of the 4811 rpm, 8764 rpm and 10,729 rpm speeds are shown in Figure 59.
The mode at 8764 rpm has only 1.6 percent of the total of the rotor strain energy and, hence,
is of little concern. The modes at 4811 rpm and 10,729 rpm have significant motion of the
fan rotors and have more than 25 percent of the total strain energy in the rotating compon-
ents. To determine whether a bearing damper is needed to reduce the vibratory amplitudes
of these modes, a forced response analysis was performed on the system with and without a
front bearing damper for these two critical speeds. This analysis was similar to the critical-
speed analysis except that an unbalance was simulated and the resultant vibratory deflections
calculated. Deflections were calculated at the first-stage roto_ plane and at the flexible dia-phragm behind the second bearing for an unbalance of 72 x 10 '_- kg-m (one oz-in.).
A damper was chosen for the front bearing due to the relatively high 7.6 x 10-4m (0.030
in.) deflection at the rotor for a 72 x 10-5 kg-m (one oz-in.) unbalance at the lowest criticalspeed without a damper. The damper would reduce this sensitivity to 0.13 x 10-4 m (0.0005in.)
per 72 x l0 -5 kg-m (one oz-in.). The rotor assembly will be balanced to better than 36 x 10-5
kg-m (0.05 oz-in.) unbalance but may reach 17 x l0 "5 kg-m (0.25 oz-in.) during testing. This
will give a maximum deflection of 0.030 x 10 .4 m (0.00012 in.) at the rotor at 4811 rpmand 0.46 x 10-4 m (0.0018 in.) at 10,729 rpm, well within the tip clearance tolerance. Vibra-
tion accelerometers and amplitude pickups will be used to monitor rig and drive system vibra-
tion during testing.
Sonic Inlet Configuration
The addition of the sonic inlet did not change the critical-speed predictions of the standard
inlet fan although it did create two additional natural frequencies at 2215 rpm and 8909
rpm, both out of the normal operating range. The mode at 8909 rpm, although close to the105 percent speed line, should not present a problem since only a rather small fraction of
the rotor strain energy is involved.
An analysis was made to determine the amount of radial "closure" at the sonic inlet throat
in its fully extended position due to static (one - G) stress and dynamic deflections at all cri-
tical speeds. A schematic is presented in Figure 60 defining radial closure and showing the
relative locations of the centerbody and bearing supports. The static (one - G) radial closureat the throat is 2.3 x 10-4 m (0.009 in.). The maximum total inlet throat dynamic closure
in the operating range due to a 0.51 x 10 -4 m (0.002 in.) deflection at each bearing suppo_rz_is4 104 0010m d namlc foratotalof48x 10 m2.3x10- m (0.009 in.) static plus 2.5 x " ( . " .) y " ,
(0.019 in.) occurring at 8685 rpm. This total deflection is judged to be acceptable, and theprobability of any resulting wall-separation or inlet total pressure distortion should be mini-
real. The effect of structural damping, not included in this analysis, will reduce the dynamicdeflections further.
20
ACOUSTIC DESIGN
Known concepts of low noise turbofans were incorporated in the design of this two-stagefan. A low tip-speed and moderate design aerodynamic loadings were chosen to minimize
generated noise. The number of blades and vanes were chosen to "cutoff" blade-passingtones, and an axial blade spacing of two chords was selected to minimize blade interaction
noise. However, to meet the extremely low levels implied by FAR 36 minus 20 PNdB, thebasically quiet fan must also incorporate extensive noise suppression in the inlet and exhaust
duct. The noise spectra of the basic fan design were estimated, and the desired noise attenua-
tions identified. Acoustic treatment was selected using both analytical and empirical models,and a final prediction of noise reduction was made. A sonic suppression device was selected
to attenuate inlet radiated noise in lieu of inlet acoustic splitters (Appendix E). An aft acous-
tic splitter was incorporated to provide the required suppression of aft radiated noise.
SONIC IN LET, ACOUSTIC CONSIDERATIONS
An inlet operating with a completely choked throat does not transmit sound upstream. Ina rig or engine, the exact variation of attenuation as throat Mach number increases toward
1.0 is a function of the details of the inlet design. Extensive information on this subject is
available in the literature and from a variety of tests performed at Pratt & Whitney Aircraft.At full choke, the amount of attenuation that can be measured is not a function of design
but depends on flanking path and background noise levels. The sonic inlet for this rig was
designed for a Mach number of 0.9 with the capability of running at full choke or less. In
order to allow operation at part-choke conditions for reduced distortion generation, a
limited amount of acoustic treatment was incorporated in the sonic inlet design so that full-choke noise attenuation characteristics could be approximated. Selection and design of the
sonic inlet for this rig were based on aerodynamic, structural and engine compatibility con-siderations that are described in the Inlet Aerodynamic Design section of this report. The
only acoustic design criterion used was that the flow disturbances produced by the sonic
inlet hardware be minimized so that aft-radiated fan interaction noise could be kept as lowas possible.
A translating centerbody was selected as the most practical compromise among acoustic,
aerodynamic, and mechanical design criteria. The centerbody will be tested in three axial-
positions representing the ATT engine (STF 433 engine) [ref. 1 ] conditions of cruise (design),takeoff, and approach with the latter two positions having capability of sonic inlet Machnumbers.
FLOWPATH AND BLADE GEOMETRY
To reduce the interaction tone noise at blade-passing frequency, the numbers of fan blades
and vanes were chosen using the Tyler-Sofrin criterion [ref. 8] which specifies that if the
number of stator vanes (s) is greater than twice the number of rotor blades (r), interaction
noise generated at subsonic tip-speeds willdecay within the inlet and exit ducts of a fan.
The numbers actually selected (see Tables VI and VII) satisfy the relationship s = 2r + 6
for all adjacent blade row combinations except stator -1/rotor -2 which, due to mechanical
and aerodynamic constraints limiting the number of stator 1 vanes, satisfies the relationships=2r-8.
2l
Axial spacingsbetweenbladerowswereselectedto reducearesidualblade-passingtonenoiseassociatedwith blade/vanewakeinteractions.Asshownin Figure61, thisnoisecom-ponentdecreasesrapidlyasspacingis increasedup to two or threechordlengthsrelativetotheupstreambladerow. After two or threechordsspacing,furtherreductionsin noisecan-notbeobtainedwithoutsevereweightandlengthpenalties.Thevaluesselectedfor thecon-figurationto betestedin thecurrentprogramaretwo aerodynamictip chordlengths;how-ever,the capabilityfor alternatecloserspacingisprovidedin themechanicaldesignof therig.
An additionalnoisecontrolfeaturewasincorporatedin thefandesignfor psychoacousticpurposes.A ratioof blades35/28(=5/4) in thetwostageswaschosento avoid,asfar aspossible,dissonantchordsusuallypresentin multistagemachines.Thisratio iscalleda"major third" inmusicaltheoryand,by westernstandards,isconsidered"consonant".Psychoacoustictests,usingoscillatorsandabroadbandnoisegenerator,wererun at P&WAto simulateanumberof twin rotorbuilds. Rotor frequencyratiosselectedaccordingto mu-sicalprincipleswasfoundto producelessannoyingspectrathanthoseselectedrandomly,but thisadvantageheldonly at lowfrequencies,roughlybelow1000Hz. At higherfrequen-ciestypicalof flightoperations(approachandtakeoff),theadvantageof harmoniustonestendedto disappear.However,theharmonicratioconceptwasretainedin thesubjecttwo-stagefansinceit coulddonoharmandshouldprovidealessannoyingspectrumat speedscorrespondingto someairportgroundoperatingconditions,suchastaxiingandidling.
RIG SPECTRA PREDICTIONS
As in the case of the full scale ATT engine (STF 433), noise spectra for the two-stage rig
were predicted using one-third octave band data for an existing two-stage fan engine, the
JT3D. This procedure may appear to have a disadvantage in that the differences in the ratio
of the number-of-rotor-2-blades/number-of-rotor-l-blades, 35/32 in the JT3D and 35/28 in
the present rig, prevent accurate spectral simulation. However, the 35/28 = 1.25 ratio issufficiently close to 1.26 (_/'ff) to insure that both rotor tones are in neighboring third
octave bands, so that for purposes of PNdB calculations and for selecting sound absorbing
liner parameters the predicted spectral shapes should be satisfactory.
To predict the rig spectrum at a particular condition (e.g., approach), tlm blade linear tipspeed was found for the approach RPM. At this tip speed, fan data from the JT3D engine
were selected. To convert these spectral data to the higher rig blade-passage frequencies,the one-third octave JT3D spectra were shifted to the right by the required number of third
octaves.
Next, corrections for changes in size, blade-vane spacing, and pressure ratio were applied,as noted below. A correction of 2 dB was added to each frequency band to allow for the
estimated increase in aft radiated noise associated with use of the sonic inlet. This amount
was obtained from a set of choked inlet tests run on a JT8D engine in the late 1960's and
represents both the backscattering at the sonic throat of forward propagating sound and ad-
ditional noise generation caused by blade interaction with inlet flow velocity disturbances
produced by the sonic inlet hardware.
22
Thecorrectionsmentionedabovewereasfollows:
• Blade-vanespacing, dB= 10log(projectedchordratio)= -3.5 dB
• Fansizecorrection, dB= 20log(diameterratio)= -3.9 dB
• Fanpressureratio, dB= 20log(pressurerise)= +3.8dB
Thespacingcorrectionwasappliedin thethirdoctavescontainingblade-passagetones;othercorrectionswereappliedacrossthe spectrum.Thesecorrectionswerebasedon resultsof anFAA fundedfannoiseresearchprogram(ContractNo.DOT-FA69WA-2045)andextensivedocumentationof P&WAenginenoisecharacteristics.Theywereincorporatedinto acom-puterprogramthat predictsthespectralcharacteristicsof studyengines.
Theresultingpredictedrigsourcesound-pressure-level(SPL)spectraat a45.7m (150ft)radiusfor theangleof maximumperceived-noise-level(PNL)aft of therigarepresentedinFigure62.
TREATMENT ATTENUATION TARGETS
To determine the appropriate acoustic treatment, the dominant annoying frequency range
first had to be identified. For the inlet, this is described under Acoustic Treatment Selection.
For aft noise, the dominant annoying frequency range was determined from source noise
spectra transformed into subjective "NOY" values. These spectra were simply truncateduntil a required integrated value of target attenuation was established for the aft noise. Since
the full-scale engine study [ref. 1 ] predicted a level just at FAR 36, and the goal of this con-tract is to achieve levels of FAR 36 minus 20 PNdB, a target attenuation of 20 PNdB was
set as the treatment goal. Figure 63 shows the resulting aft attenuation spectrum at approachand takeoff with a peak attenuation near 3500 Hz.
ACOUSTIC TREATMENT SELECTION
Inlet
To provide improved attenuation of forward-radiated noise during operation with the sonic
inlet not at full choke, a limited amount of treatment was applied to the walls of the sonic
inlet. The inlet treatment was designed to be mainly effective in absorbing the upstream trav-
eling waves (i.e., treatment was tuned to attenuate waves propagating forward from within the
fan). The forward attenuation spectrum expected from the inlet treatment is shown in Fig-ure 64 and represents a preceived noise level of 3 PNdB.
The inlet treatment was restricted to axial locations where the wall Mach number does not
exceed 0.7 at any of the operating points. Flow separation at the wall could occur because
of surface roughness in a region of flow diffusion if the treatment had been extended to re-
gions of higher Mach number. With the translating centerbody in the forward (approach)
position, the lengths of treatment exposed are approximately 0.482 m (19 in.) on the inner
wall and 0.599 m (22 in.) on the outer wall to provide a treatment length to passage height
23
ratioof about1.6. Retractionof thecenterbodycoversthetreatmenton theinnerwallandreducestheratioby aboutone-half.Backingdepthis0.635cm(0.25in.)anddesignfacingsheetpercentopenareaissixpercentbothfor theinnerandouterwall treatments.Thesevalueswerechosen,in accordancewith methodsdescribedin thenextsection,to tunetheinlet treatmentto thecenterof the inlet attenuationtargetspectrum.
InterstageandAft FanDuct
Thetreatmentin the interstageregionwasselectedto attenuatethelowestblade-passing-frequency(28Eat approach);thelongaft duct treatments,includingtreatmenton theinnerandouterwallsandonbothsidesof thesinglesplitter,weretunedfor thecenterof thetarget,about3200Hz(Figure63). Onthebasisof empiricaldata,includingcurvesof tuningversusbackingdepthandPNLreductionversustreatment-lengthto duct-heightratio, thissinglesplitterconfigurationwasfoundto besuperiorto theno-splitterandtwo-splitterdesigns.By selectionofdeeperbackingdepthsfor theductwall treatmentandmoreshallowdepthsfor thesplitter,arelativelythin, 0.016m= (0.62in.) splitterwaspossibleandaminimumblockageachievable.At thesametime,theattenuationspectrum,comparedto aspectrumfor thesplitterandwalltreatmenttunedto thesamefrequency,couldbebroadenedto covertheattenuationtarget. Thefacingsheetvaluesshownin Figure65werechosenfor anopti-mumcombinationof bandwidthandpeakattenuationratherthan for peakattenuationalone.
Preliminaryestimatesof requiredtreatmentareaweremadeby referenceto guidelinecurvesof PNdBreductionasafunctionof treatment-lengthto passage-heightratio (L/H) suchasshownin Figure66. Thisfigurecontainsdatafromvarioustests,includingseveralNASAfundedprograms,for fanductswith L/H ratiosup to 23. It hasbeenobservedinaxialtraversetestsatP&WAthat theflatteningof thesecurvesat highervaluesof L/H isnot dueto afailureof longtreatmentsto attenuatefannoisebut ratherto the limitingeffectofflankingpathnoiseandthepresenceof othernoisesources,suchasjet noise,on theoverallobservedattenuationspectrum.For thecurrentprogram,NASAQuietTwo-StageFanRig,anaxial lengthof about1.016m (40 in.) availablefor treatmentandapassageheightof0.178m (7 in.)wouldresultin L/H ratiosof about5.8with nosplitter,12with onesplitter,and20with twosplitters.Thecross-sectionalblockageof thesplittersreducesthe passageheight,andthishasbeentakeninto account.Thesingle-splitterconfigurationwastakenasastartingpointfor thedesignonthebasisof Figure66andvariousotherconsiderationsdis-cussedabove.
Tuningcurves,suchasshownin Figure67, that relatetreatmentbackingdepthto frequencyof peakattenuationwereusedfor initial selectionof backingdepths.Generally,the initialvalueof facingsheetinstalled-resistanceis takento beequalto thevalueof thedimension-lessfrequencyparameterin Figure67at thedesignpoint. A successionof iterationswasthenperformedin whichattenuationspectrawerecalculatedby meansof ananalyticalsolu-tion of thewaveequationfor theprincipalmodein theduct [ref. 9] for incrementedvaluesof backingdepthsandfacingsheetresistancesuntil anoptimumcoverageof theattenuationtargetwasfound.
24
PREDICTED ATTENUATIONS - INTERSTAGE AND AFT TREATMENT
On the basis of the procedures previously described, the attenuations shown in Figure 68 were
obtained. PNL numbers for takeoff and approach at 45.7 m (150 ft) radius and maximumPNL are summarized in Table XIII.
TABLE XIII
ANALYTICALLY PREDICTED FAN AFT PNL AT 45.7 METER(150 FOOT) RADIUS
DESIGN PNL PNL PNLCONDITION SPEED UNTREATED TREATED ATTENUATION
Approach 70% 112.3 dB 92.6 dB 19.7 dB
Takeoff 94% 125.0 dB 104.2 dB 20.8 dB
The results of the analytical design system indicate a reduction of approximately 20 PNdBin aft noise.
COMPETING NOISE SOURCES
In tests it is often difficult to realize large predicted values of duct attenuation. Fan jet mix-
hag noise and additional noise generated by the rig fan air scrubbing the test rig afterbody
tend to obscure measurements of treated fan noise levels in the farfield. However, empirical
estimates of jet mixing noise have determined that at low speeds (e.g., approach) the majority
of fan noise attenuation should be measureable at the farfield microphones (Figure 69).Use of narrow band spectral analysis, which increases the ratio of tone to broadband noise,
will facilitate detection of fan noise attenuation. Further signal detection will be provided
by operating at the widest possible nozzle condition, which reduces the jet nozzle velocityand consequently the jet noise. At higher speeds, the high levels of jet noise will at least
partially mask the effect of the treatment (Figure 70).
25
% DESIGN
SYMBOL SPEED VANE M 2 ROOT M 2 TIP
100 $1 0.85 0.61
100 $2 0.66 0.51
(_ 85 S1 (REF 3) 0.82 0.59
(_ 85 S2 (REF 3) 0.77 0.53
13 [] 100 S (REF 5) 0.88 0;68
.2
o_ ui Lr _ u0 10 20 30 40 50 60 70 80 90 100
¢n HUB TIP
13
¢/3O
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% DESIGNt tiP
SYMBOL SPEED BLADE m/sec ft/sec M 1
100 R1 365.8 1200 1.31
100 R 2 329.8 1082 1.08
(_ 85 RI(REF 3) 376.1 1234 1.22
(_ 85 R2 (REF 3) 305.4 1002 1.10
95 R1 (REF 3) 419.4 1376 1.12
[] 100 R (REF 5) 304.8 1001 1.40
.3
.2[
.1(_ (}
0 10
ROTO R
Q
20 30 40 50 60 70 80 90 100
PERCENT SPAN AT TRAILING EDGE TIPHUB
Figure 1 Rotor (lower) and Stator (upper) Total Loss Spanwise Profiles
26
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(1N301::13ci) Or& 'AO3NIOI-I-13 311VSVlQV i:lOIOH
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ROTOR EXIT (DESIGN), REF. 6
Eg TEST DATA, REF. 5
FLAGGED SYMBOLS ARE EXIT AIR ANGLES
i
30 40 50 60 70 80 90
PERCENT SPAN
, -'- "'1
i i
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Figure 3 Rotor Inlet and Exit Relative Air Angles Spanwise Profiles
28
>>-
(JoU..j i11uJ ¢/_>_
Z
o_5-m
I,LI
230
220
210
2O0
190
180
170
160
150
140
IJ..Io_
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700
. I" ROTOR 1 INLETI
_j_[Yo" o n [] r] ooon660 J f []
620
"_"0 ;'_'_' 0 [] or 7T°R 2 IN_ ET
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ROTOR 2EXIT "" "-_
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EXIT VELOCITIES) _-
46o I I I I I0 10 20 30 40 50 60 70 80 90 100
HUB PERCENT SPAN TIP
Figure 4 Rotor Meridional Velocity Spanwise Profiles
220
210
2O0
>=190
6UOua-- _ 180
>2_1 w,_ F- 170
g_5-
160iii=£
150
140
130
--720 E_O g rL] __ _oo _' c½ _ o o
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-- 620 fSTATOR 1 INLET
°oo580ILl -" Cf STATOR I EXIT I _ "-"
I _ " STATOR 2 INLET-540 ] / [ -.. -_ ./
STATOR 2 EXIT _ _ _ _"520 l/"
=o[480
4400
HUB
l_l REF. 5
(FLAGGED SYMBOLS ARE
EXIT VELOCITIES)
I l10 20 30 40 50 60 70 80 90
PERC ENT SPAN
100
TIP
Figure 5 Stator Meridional Velocity Spanwise Profiles
29
1.30
1.20 --
I I I I[] REF 5
O REF 3 (85% DESIGN SPEED)__,
(FLAGGED SYMBOLS ARE
/
,.,o EX'TMAOHNUMBERS'I /ROTOR I INLET / --] _j,,
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= ,o,o XTl..ir-.
" . Cf + (f.5o_"O" + Cf
O 10 20 30 40 50 60 70 80 90 100
HUB PERCENT SPAN TIP
Figure 6 Inlet and Exit Mach Number Spanwise Profiles for Rotors
,9O
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10 20 30
[] REF. 5 ]
(FLAGGED SYMBOLS ARE IEXIT MACH NUMBERS) I
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_-ch- -_.ok 4 -_cf J _ _ _,
STATOR 1 EXIT ........ _ ----[]_.[_J"
STATOR 2 EXIT --_ _-- _--b
40 50 60 70 80 90
PERCENT SPAN
lu0
TIP
Figure 7 Inlet and Exit Mach Number Spanwise Profiles for Stators
3O
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PERCENT SPAN AT TRAILING EDGE
9O 100
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Figure 10 Rotor Diffusion Factor Spanwise Profiles
a
n-oi--
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.2G0 10 20 30 40 50 60 70 80 90
HUB PERCENT SPAN AT TRAILING EDGE
#,/(
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Figure 11 Stator Diffusion Factor Spanwise Profiles
33
ill/ZI
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2.0
1.8
1.6
1.4
1.2
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f-------
m_ m
.... ROTOR 1.......
STAGE 1
ROTOR 2
1.0
0 10 20 30 40 50 60 70 80 90 100
HUBPERCENT SPAN AT TRAILING EDGE TIP
Figure 12 Total Pressure Ratio Spanwise Profiles
62
60 [
m 58
(-9 56wa
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STATOR 2 EXIT AIR ANGLE = 0°
STATOR 1 INLET
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36 _ STATOR 2_ i_'/"
INLET /_ /
320 10 20 30 40 50 60 70 80 90 100
HUB TIP
PERCENT SPAN AT LEADING EDGE
Figure 13 Stator Inlet and Exit Absolute Air Angle Spanwise Profiles
34
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35
TANGENTIAL DIRECTION
CONSTANT ANGULAR MOMENTUM
STREAMLINE AT MID-GAP
"OTAL CAMBE R, (_
AXIAL
DIRECTION
CAMBER
• MAXIMUM
THICKNESS, t
FRON
CHORD. c t
TRANSITION
POINT
DISTANCE TO LOCATION
MAXIMUM THICKNESS
CHORD, c
ROTATION
DIRECTION
Figure 15 Multiple-Circular-Arc Airfoil Definitions
36
R2Z
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<f-,, _ R1
z_ 1 I IIIII III I I I I I I I I I II I<
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/
ROTOR 2 •
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0
HUB
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Figure 16
3O 40 50 60 7O 80
PERCENT SPAN AT LEADING EDGE
Rotor Airfoil Thickness Spanwise Profiles
90 100
TIP
LU 70
(J 60<1--.:;z /
Ore
w
1-
5Oo o.,.I
HUB
Figure 17
If
ROTOR 1
_ o_ _' _'m_' _w' _
10 20 30 40
I
ROTOR 2
I50 60 70
I
PERCENT SPAN AT LEADING EDGE
I
80
f
90 O0
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Rotor Chordwise Location of Airfoil Maximum Thickness Spanwise Profiles
37
3.0
dr,r'
I-- "'
zOrt-M.
.07
.06 m
.05- "r"
.03
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2 'J'_
ROTOR
.%
\ROTOR 2
1.0
r,r'O A"r(.3 r_
I.-
.11 -
.10 --
.09
.08 "=
4.4
4.2
_,_
3.8
Z
= /3.6 /
3.4 ....
3.20 10
HUB
20 30 40 50 60
m_ mm
ROTOR 2
170 80 90
PERCENT SPAN AT LEADING EDGE
lOO
TIP
Figure 18 Rotor Chord Spanwise Profiles
38
60
qo..
.=1
Z
I--.
I.LI
5O
40
30
2O
I0
0
-10
-20
-3O
-40
J
//
/f
//
//
/
/
ROTOR
/
/
//I'/ /
' //
2
J I
F
1 t
-50
.,1
Z
w e_
I,-w'_.1Z
60
50
40
I30
20
0 10
HUB
Figure 19
J
I
ROTOR 2
/v ROTOR 1
20 30 40 50 60 70 80
PERCENT SPAN AT LEADING EDGE
Rotor Inlet and Exit Metal Angle Spanwise Profiles
9O 100
TIP
39
2
_ Z _ 0
-- 0 -4--
-6
()0 _ 0
i
0 0 °
tM, >1.0
M',>,.o _1
ROTOR 1
ROTOR 2
Z ,,-I-n:
_z_ w
0 10 20 30 40 50 60 70
HUB PERCENT SPAN AT LEADING EDGE
d)
" io.80 90 100
TIP
Figure 20 Rotor Incidence Angle Spanwise Profiles
40
i11i11n,"(9iii
v
LU..I
n."
f.,On,.-l.t.I
l=
o
Io
// n b (_ (]
2/D O O _ 3 D O _:)ROTOR 2
-2
[]
E
O R1 (REF 3)
(_ R2 (REF3)
[] R (REF 5)
-4
I.LIIaan,"f3U,.I13
o
{,,,Q
--IcOz
z0P
W0
18 /
0
1_ O (
• ()
y "\\\c.) O "_D O [] |
12 OR 1
6
ROTOR 2 O 00
40 10 20 30 40 50 60 70 80 90 100
HUB TIPPERCENT SPAN AT LEADING EDGE
Rotor Deviation Angle Spanwise ProfilesFigure 2141
o_ []
_,,',._,,= ,.0_ _o o _,o_' oO ,,_
O R1 (REF 3)O..a
,,_ (_ R2 (REF 3)_ .95[
] r"-I R (REF 5)"2
° 1 I.90
0 10 20 30 40 50 60 70 80 90
HuBPERCENT SPAN AT LEADING EDGE
10o
TIP
Figure 22 Minimum Rotor Channel Area Ratio Spanwise Profiles
42
iiiLLIn,-r3iiic't
1.5..J
Z
IJJoo
l-Zon-
,lb.
15
10
5,."
0
-5
m
\
ROTOR 1
--10
v "E
EwI-w
a.
w111
O
o
U
1.5
DCA CAMBER DISTRIBUTION
1.0 _
_OTOR 1
! "FRONT CAMBER = O ROTOR 2-- --
--.5 %""%
\'t
--1.0
-1.50 10 20 30 40 50 60 70
HUB PERCENT SPAN AT LEADING EDGE
8O 9O
• /
100
TIP
Figure 23 Rotor Front Camber Angle and Chord-Camber Parameter Spanwise Profiles
43
ROTOR 1
m -,-,-_- ROTOR 2
<-iii
.J({(J
F-
(J
O
<Illt_
.J<
F-(J
II
O
O
1.3
1.2
1.1
1.0
1.3
1.2
1.1
1.0
1.2
1.1
1.00
I
0% SPAN (HUB)
(SPANS TABULATED
ARE AT LEADING
EDGES OF BLADES_Ip
i I
S I
1.3
1.2 /
1.0
27.3%SPAN
//
/
dJ
//
SPAN
1.3
1.2
1.1
1.0
38.4%p
7
!
48'6%P/SPT_
1.2
1.1
SPAN_
1.01.0 2.0 3.0 0 1.0 2.0
INCHES
I I I I I I I I•02 .04 .06 .08 0 .02 .04 .06
METERS
AXIAL DISTANCE FROM BLADE LEADING EDGE, Z-ZLE
3.0
I.08
44
Figure 24 Rotor Channel Area Ratios Versus Axial Distance
=k
<
<{
<-iii
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<{
mp.
(J
0I-
<
n-
I-0
IJ..
0
0
}--
n-
1.2
1,3 n
1,2 m
1.1
1.0
1.1
1.0
,9
O
t0
62.7% /
_ '_5%SPAN
I I
ROTOR 1
m _ _ ROTOR 2
1.2
67.2% / /
sPAN_j_ ,o
,.,,.,_ 69.3%SPAN
I I
71.6%
PA____73.5
SPAN
I I
1.3 m
1.2--
1.1--
1.0
75.8% /
sP%,.4'_ '_7.6%
I I sPAN
_92.2% SPAN 1.1
B 92.9% 1.0SPAN
lOO%./ /SPA",'_V//X- o
_(J 100_ (TIP)
SPAN
I I I .9 I I1.0 2.0 3.0 INCHES 0 1.0 2.0
I I I l i I I.02 .04 .06 .08 METERS 0 .02 .04 .06
AXIAL DISTANCE FROM BLADE LEADING EDGE, Z-ZLE
I3.0
I.08
Figure 24 (Cont'd) Rotor Channel Area Ratios Versus Axial Distance
45
LOCUS OF TRAILING EDGES
LOCUS OF POINTS WITH
RADIUS r, POLAR RADIUS R
AND AXIAL LOCATION Z
LOCUS OF LEADING EDGES
APEX OF CONICAL
DESIGN SURFACE
ETE
BLADE MEAN
CAMBER LINE
ON UNWRAPPED
CONICAL SURFACE
POLAR RADIUS R
R LE
MERIDIONAL VIEW
OF BLADE SECTION
Figure 25 Mefidional View and Polar Representation of Blade Mean-Camber-Line
Q
AIRFOIL SECTION ON PLANE
NORMAL TO RADIAL STACKING LINE
Figure 26 Airfoil Coordinate Definition for Manufacturing Sections
46
6e¢0
z0
n..w
z
0
,_1
I-0I--
.O6
.O5
.04
.03
.02 --
c/}UJ.I.(,3Z
2.4
2.2
1.8
1.6
1.4 _,
1.2
1.0
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.60 10
HUB
__I
C
STATOR
C
STATOR 2
II
cf
STATOR 1
JI v
20 30 40 50 60 70 80 90
PERCENT SPAN
//
100
TIP
Figure 27 Stator Chord Spanwise Profiles
47
52,
50(/)
uJZ
48
t_ 46
UJ
_ 44I,I,.o_Z0-- 42I.--
0
40----
STATOR 1 /
/
STATOR 2J
-- __f
3E0
HUB
Figure 28
10 20 30 40 50 60 70 80 90
PERCENT SPAN AT LEADING EDGE
100
TIP
Stator Chordwise Location of Maximum Thickness Spanwise Profiles
.10
O-r
o_o')iiiZv
m
I--
X<
.09
.0_
.07 F
.06
Jf
.05
J
STATOR 2
fJ
f /STATOR 1
.040
HUB
10 2O 30 40 50 60 70
PERCENT SPAN AT LEADING EDGE
80 90 100
TIP
Figure 29 Stator Airfoil Thickness Spanwise Profiles
48
10
i,iiii¢f
iii
¢3
iii/
Z
uJ
F
c_.m
O STATOR 1 /
-15
-20
10
$1 (REF 3)
--10 (_ S2 (REF 3) / _
[7 S (REF 5) STATOR 2 / _
-200 10 20 30 40 50 60 70 80 90
HUB
PERCENT SPAN AT LEADING EDGE
100
TIP
Figure 30 Stator Incidence Angle Spanwise Profiles
49
w 4i,u
,,,o_J
= J (1_ 3(!I [iiiI-- J STATOR 2 []
" C rl-: [3
C C%
I-4 0%
-6
()
18_
16
O Sl (REF 3)
14( [] [] (_ $2 (REF 3)
i! _ _,._ -- STATOR 2
(;[_-_ _ _ !_"_'
[
C'_,] [ _"_ ]"_ • STATOR 1
6 C
O
4 (_)"0 10 20 30 40 50 60 70
HUB
PERCENT SPAN AT LEADING EDGE
80 90 100
TIP
Figure 31 Stator Deviation Angle Spanwise Profiles
50
A
ILlU.Ir¢
U.Ir_v
,,IOZ
,.I
I-iii
I-
Xu,I
10
-10.
5 ....
/ _ W......-- _ "_
/
0 / 4_m 'mm" _ _mm,
/ _ s_o_
-15
-20,
I/ STATOR 1
I
2
60,
ELI
,e_ 50.
'"- % "x .-/_ _ , m _mm m mmmm,mm li _, i m imm Immmmmm #
I"- 40.
"' /w
Z"J 35. /
-- STATOR 1 /
300 10 20 30 40 50 60 70 80 90 100
HUB TIP
PERCENT SPAN AT LEADING EDGE
Figure 32 Stator Inlet and Exit Metal Angle Spanwise Profiles
51
1.08
1.06
1.04
I
O $1 (REF 3)
I_ $2 (REF3)
[] S (REF 5)
1.02 0 L..]
"_" STATOR 1 / ) C 0 /
D @.9( @
•94 0 10 20 30 40 50 60 70 80 90 100
HUB TIPPERCENT SPAN AT LEADING EDGE
Figure 33 Ratios of Channel-Throat-Area to Captured-Area Versus Span for Stators
52
3O
iii
ill
n-
iii
r_v
U.
iii
tn
Z0
l.i=
25
20
15
10
5
J
fI
J
STATO R 1
/
la,I. -_-,_
C
• _ (_,
W
W
<0.
e_w
e_
o
1.4
1.2
1.0
.8
.6
/
.2
DCA CAMBER
DISTRI BUTION
/
/
ff
_J
STATOR 1
NO FRONT CAMBER
/0 10 20 30 40 50 60 70 80 90 100
HUB PERCENT SPAN AT LEADING EDGE TIP
Figure 34 Stator 1 Front Camber Angle and Chord-Camber Parameter Spanwise Profiles
53
({
<-L&Jn-
.J({O
(J
0
e_
0
0
0
F-
ew
1.4
1.3
1.2
1.1
1.0
0 % SPAN (HUB)
(SPANS TABULATED
ARE AT LEADING
EDGES OF VANES)
1.4
39.5% SPAN
1.3 /1.2
1.4
15.8% SPAN
1.3 /1.2
1.1 j
1.0
1.4
1.3
1.2
1.1 1.1
1.4 1.4
1.3
I84.5% SPAN
/1.2
59.1% SPAN
/
1.3
1.2
I100% SPAN (TIP)
i//
1.1 1.10 1.0 2.0 3.0 0 1.0 2.0
INCHES
L I i I I I I I I0 .02 .04 .06 .08 0 .02 .04 .06
METERS
3.0
I.08
AXIAL DISTANCE FROM VANE LEADING EDGE, Z - ZLE
Figure 35 Stator 1 Channel Area Ratios Versus Axial Distance
54
F--iii.JZ
(3
_:-J
zo<(J
w DZO
w ._1(,_ _J,_w
,.JJ
_J
AI'--
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ROTOR 1 ROOT
LEADING EDGE
LOCATI ON
/
.435 30 25 20 15 10 5 0
AXIAL DISTANCE'vlNCHES
I I I I I8 6 4 2 0
METERS
AXIAL DISTANCE
Figure 37 Baseline Standard Inlet Outer Wall Mach Number and Shape Factor Distributions
56
.95
.9C
n,"u,J
.85:::)Z
'I"tJ"_ .80=E,--I
....I
.75
rr
.700 10 20 30 40 50 60 70 80 90 100
HUB TIPPERCENT SPAN
Figure 38 Sonic Inlet Throat Mach Number Spanwise Profile - Approach Configuration
=;
I,LI
IIl
z
-v-
.-I
J
1.0
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.7
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I
CORRECTED FLOW = 77.11 KG/SEC (170 LBM/SEC)
'ouz . /WALL
t-,,..._,NNERWALL
-5O
LOCATIONOF MINIMUM FLOW AREA
I-4O -30
(INCHES)
ROTOR 1 ROOT--
LEADING EDGE
LOCATION
1-20 -10 0
I-1.4
I I I I I I I-1.2 -1.0 -.6 -.4 - .2 .1 0
(METERS)
AXIAL DISTANCE
Figure 39 Mach Number Distributions Along Inlet Walls - Approach Configuration
57
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ZLM
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g.
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NOTE: TOTAL S
IN LET SUPPORT STRUTS
FOR CENTERBODY
n
50% SPEEDm
m
1ST COUPLED
MODEm
0 1 2 3
3RD COUPLED
MODE
105% 12E
DESIGN SPEED
SPEED 10E
2ND COUPLED
MODE
OPERATING RANGE
4 5 6 7 8
ROTATIONAL SPEED, RPM X 10 .3
8E
6E
5E
4E
3E
6% FREQUENCY
MARGIN
9 10 11
I12
Figure 45 Rotor 1 Campbell Diagram
63
N-I-v
Z
0
1.8
1.6
1.4
1.2
1.0
.8
.6
.4
.2
0 1 2
50%
SPEE
3RD COUPLED
MODE
2ND COUPLED
MODE
DESIGN iSPEED
/
__ _ _05% SPEED 4E
1ST COUPLED
MODE
5.4% FREQUENCY
MARGIN
OPERATING RANGE _-_
II I I l3 4 5 6 7 8 9 10 11 12
ROTATIONAL SPEED RPM X 10 .3
Figure 46 Rotor 2 Campbell Diagram
64
N"I-v
>-
Z
0u,I
ii
1062E (STATOR 1)
_/ _ SPEED
1 2 a
DESIGN
SPEED
_OPERATING RANGE_
I I I I4 5 6 7 8
2ND MODE
#F, 105% SPEED
1ST MODE
I I I9 10 11 12
ROTATIONAL SPEED, RPM Xl0 "3
Figure 47 Rotor 1 Tip Mode Campbell Diagram
65
10 76E
(STATOR 2)
62E (STATOR 1)
N"r
>-Z
0Ill /
4 --
3
2-- 50%
I I I I0 1 2 3 4
DESIGN
SPEED 105%
OPERATING RANGE _._,..
I I I I I I
5 6 7 8 9 10
I
11
ROTATIONAL SPEED, RPM X 10 .3
2ND
MODE
1ST
MODE
12
r_,=- ....
66
50
AMS 4973F TITANIUM
3 _ AT 338.6°K (150°F)
40 SMOOTH
_ % 3o
__.:" _2o _
STEADY
STRESS
o _ _0 20 40 60 80 100 120
LBF/IN 2X 10 -3
I I I I I I I I I I0 1 2 3 4 5 6 7 8 9
N/M 2 X 10 -8
STEADY STRESS
14o
Figure 49 Rotor 1 Goodman Diagram
5O
3
40
_ . '_ 30
i i2o10
MAX. STEADY
STRESS I
t I0 1
\
20 4L, 60 80 100
LBF/IN.2X 10 -3
I I I I I I2 3 4 5 6 7
N/M 2 X 10 .8
AMS 4928 TITANIUMo o
AT ,421.9 K(300 F)
120 140
I I8 9
STEADY STRESS
Figure 50 Rotor 2 Goodman Diagram
67
0.0051 METERS (.20 IN.)
35 °
.033M --1
F 11.3 iN.)
a) R-1
0.0046 METERS (.18 IN.)
B-B
L.E.
b) R-2
68
Figure 51 Schematic of Rotor Partspan Shrouds
N"I"v
>-
Zw
0.i
u.
2.0
35E(ROTOR 2)
RANGE
__.I.__L__3 4 5 6 7
ROTATIONAL SPEED, RPM X 10 -3
10
Figure 52 Stator 1 Campbell Diagram
69
N
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>-
z
0U.I
I,L
3.0I
2.5
2ND BENDING
2.02ND TORSION
1.5
(ROTOR
//
50% SPEED
/
1.0
2)
il
DESIGN
SPEED
105% SPEED --
1ST BEN_G
/ lS_TORS,ON/_5 4E'_i_ I I
• _ _ ,._
0 2 4 6 8 10
ROTATIONAL SPEED, RPM X 10 .3
Figure 53 Stator 2 Campbell Diagram
70
8000
7000
6000
O ROTOR
r-] ROTOR
_ ROTOR
N
"r 5000
)-
4000
_ 3000
lOOO _ _
0 1
].1 REAR SIDEPLATE _f
2 FRONT SlDEPLATE
2 REAR SlDEPLATE
I I25% FREQUENCY MARGIN
@ 105% SPEED
I I I2 3 4 8 9 10 11 12
NODAL DIAMETER
Figure 54 Rotor S_deplate Seal Resonance
10,000
9000
8000
7000
6000
5O00
4O00
200
1000
O STATOR 1
STATOR 2
,..I jr
2 3 4 5 6 7 8 9 10 11 12
_*_25% FREQUENCY
MAHGIN @ 105% --SPEED
NODAL DIAMETERS
Figure 55 Stator Sideplate Seal Resonance
71
N"r
>-ZuJ
Ot_
M.
3000
2500
2OOO
1500
1000 ""
500
NO. OF: ROTOR" 1 BLADE'S /
28E
50% SPEED
DESIGN
SPEED
105% SPEED
2ND TORSION
/
2ND BENDING
1ST TORSION
/
/
!
1ST BENDING j
3 4 5 6 7
ROTATIONAL SPEED, RPM X 10-3
i
i
_..,_
I
8 9 10
Figure 56 Sonic Inlet Support Struts, Campbell Diagram
72
¢,,1(
n"
01'-
0rr
tr
0I--
0
rr
88
Z
G ou. xu.
0
z_ _
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73
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0
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d_Z_
/rr
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74
FAN jFLEXIBLE FRONTINLET & DIAPHRAGM
CAS S /SEARING T
_-/ SUPPORT j DRIVE SHAF
'_r"" NO. 2 SEARING --
NO t FAN SHAFT
ROTOR 2
NATURAL FREQUENCY = 48112 RPM
I I
AXIAL DISTANCE
INLET & FAN
CASE J ROTOR2 BEARING
- J" .j_uPPORT
X" "PAN /\\j.\ S. FT / "N,.
NATURAL FREQUENCY = 8764 RPM SHAFT _. _
AXIAL DISTANCE
Figure 59 Critical Speed Mode Shapes
?5
O
ROTOR 2
FAN SHAFT BEARING
_ SUPPORT
/
/_ FAN CASES FLEXIBLE
FAN CASES _RArLOp_TRAGM
ROTOR 1
I I I
NATURAL FREQUENCY = 10,729 RPM
AXIAL DISTANCE
Figure 59 (Cont'd) Critical Speed Mode Shapes
76
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0
0
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78
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Figure 67 Tuning Curves
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APPENDIX A
A
A/A*
a
a f
C
C
D
E
G
H
I
1D
i
K
APPENDIX A
SYMBOLS AND DEFINTIONS
area - meters 2 (feet z)
ratio of actual-area to critical-area (where local Mach number is 1.0)
distance along chord from leading edge of airfoil to point of maximum
elevation of airfoil above chord line - meters (inches)
a point on the suction surface of a blade halfway between the leading edge
and the point from which a Mach wave emanates that meets the leading edge
of the following blade
structural damping coefficient - N/m-sec (lbf/in.-sec)
Chord (aerodynamic on flow surface) - meters (inches)
diffusion factor,
for rotor
for stator
r2 V02 - r 1V01t P
= 1-Vz/V 1 +(r I + r2) V'o
r2 Vo2-r3 V03= 1-V3/V 2 +
(r2 + r3) V 2 o
displacement in the direction normal to the minimum moment of inertia
axis - meters (inches)
epse, the angle between rays drawn to a conical design surface, one ray to
the leading edge of an airfoil section, the second to some other point on theairfoil - degrees;
excitations per rotor revolution
gravitational force
boundary layer shape factorpassage height
moment of inertia about minor axis - meters 4 (inches 4 )
inner diameter of casing - meters (inches)
incidence angle, inlet air angle minus blade metal angle - degrees
blockage factor;
linear spring constant - N/m (lbf/in.)
89
L
L.E.
M
MCA
N
OD
P
P
PNL
RLE
RPM
RTE
r
R
r, O, z
S
S
SPL
T
T° E.
U
90
SYMBOLS AND DEFINITIONS (Cont'd)
length of inlet - meters (inches)
length of acoustic treatment
leading edge of blade row
Mach number
multiple-circular-arc
rotor speed (rpm)
outer diameter of casing - meters (inches)
static pressure - N/m 2 (lbf/in. 2)
total or stagnation pressure - N/m 2 (lbf/in. 2)
perceived noise level (dB)
leading edge airfoil radius - meters (inches)
revolutions per minute
trailing edge airfoil radius - meters (inches)
radius measured from rig centerline - meters (inches);
number of rotor blades
rotor
cylindrical coordinate system, with z axis as rig centerline
stator
blade spacing - meters (inches);
number of stator vanes
sound pressure level (dB)
total temperature - °K (°R);
torsional spring constant - m-N/rad (in. - lbf/deg)
trailing edge of airfoil
blade maximum thickness - meters (inches)throat
rotor speed - m/sec (ft/sec)
APPENDIX A
PRATT& WHITNEY AIRCRAFT APPENDIX A
V
W
Z'ratio
z
A_
3'
6 °
0
p
O
_E
SYMBOLS AND DEFINITIONS (Cont'd)
air velocity - m/sec (ft/sec)
weight flow - kg/sec (lbm/sec)
(I/C)shroud cross-section /(l /C ) airfoil cross-section above shroud
axial distance - meters (inches)
absolute air angle [cot "1 (V m/V 0)] - degrees
vibratory twist deflection - degrees
relative air angle [cot-1 (V m/V_)] - degrees
metal angle, on conical surface, between tangent to mean camber line and
meridional direction at leading and trailing edge - degrees
air turning angle - degrees
blade chord angle, angle between a chord line and axial direction (measured
in a plane parallel to z-axis) - degrees;ratio of specific heats for air
ratio of total pressure to standard pressure of 1.01 x 105 N/m 2 (2116 lbf/ft 2)
deviation angle, exit air angle minus tangent to blade mean camber line at
trailing edge - degrees
angle between tangent to streamline projected on meridional plane and axialdirection - degrees
efficiency (percent)
ratio of total temperature to standard temperature of 518.7°R
mass density - kg/m 3 (lbm/ft 3)
solidity, ratio of aerodynamic chord to gap between blades
blade camber angle, difference between blade angles at leading and trailing
edges on conical surface, 13'*1 -/3'* 2 for rotors and/3* 2 -/3* 3 for stators -degrees
blade camber angle on plane of "unwrapped" conical surface fl'*l -/3"2 -E_ for rotors and/3*2 -/3*3 "ETE for stators - degrees
amplitude of torsional vibration (radians)91
APPENDIX A
COb
COt
Subscripts
ad
f
Ef
in
LE
m
P
SS
st
t
TE
Z
0
0
SYMBOLS AND DEFINTIONS (Cont'd)
total pressure loss coefficient,
_.X.__
t
- P2
t
P1 "Pl
P2 - P3(stators)
P2 - P2
bending vibrational frequency (Hz)
torsional vibrational frequency (rad/sec)
adiabatic
front
refers to front camber definitions which include epse angle E
inlet
leading edge
meridional (velocity); mean camber line (angle)
profile (loss); polytropic (efficiency)
suction surface
stage
transition, throat
trailing edge
axial component
tangential component
plenum chamber
(rotors)
92
APPENDIX A
1
2
3
Superscripts
t
SYMBOLS AND DEFINITIONS
station into rotor
station out of rotor or into stator
station out of stator
(Cont'd)
relative to rotor
blade metal (angle); critical, at Mach number unity (area)
93
APPENDIX B
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APPENDIX E
APPENDIX E
TWO-RING ACOUSTIC INLET AERODYNAMIC AND ACOUSTIC DESIGN
An acoustic inlet design was studied in addition to the translating center-body finally cho-
seri. A schematic of this additional design, a two-ring configuration, is shown in Figure 71.
Mach number distributions are included on the O.D. wall and splitter surfaces. Although
the inlet flow is not choked, the blockage of the rings was estimated to be about 3 percent
of the area. Boundary layer shape factors on all surfaces were well below the separationcriterion of 2.2 to 2.5.
For acoustic purposes, the rings, the extended centerbody, and the inner and outer walls
were all treated with various combinations of honeycomb and facing sheet. These acoustic
treatment parameters are listed in Table XXVIII. An effective-treatment-length to passage-
height of about six was achieved for the two outer passages and about four for the inner
passage. Treatment was tuned to the predicted inlet fan noise spectrum to maximize the
PNL reduction at approach. The inlet attenuation target and predicted treatment attenua-
tion are shown in Figure 72. The attenuation target represents a PNL reduction of 15PNdB at the peak inlet noise angle.
TABLE XXVlll
TWO-RING ACOUSTIC INLET TREATMENT PARAMETERS
TREATMENT BACKING
LENGTH DEPTH
METERS (INCHES) METERS (INCHES)FACING SHEET
% OPEN AREA
HONEYCOMB
CELL SIZE
METERS (INCHES)
Outer Wall 0.61 (24) o.o13 (0.5) 12 0.0095 (3/8)
Outer Ring 0.43 (17) 0.006/0.006 (0.25/0.25) 12/9 0.0095 (3/8)
Inner Ring 0.38 (15) 0.006/0.006 (0.25/0.25) 9/6 0.0095 (3/8)
Centerbody 0.30 (12) o.o13 (0.5) 0.0095 (3/8)
157
APPENDIX E
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IIIII
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Figure 72 Two-Ring Acoustic Inlet Predicted Attenuation
159
REFERENCES
. Brines, G. L.: "Studies for Determining the Optimum Propulsion System Characteris-
tics for Use in a Long Range Transport Aircraft," NASA CR-120950, PWA-4449, July1972
2, Keenan, M. J. and Burdsall, E. A.: "High-Loading Low-Speed Fan Study - V Final
Report," NASA CR-121148, PWA-4517, April 1973
, Rugged, R. S. and Benser, W. A.: "Performance of a Highly Loaded Two-Stage Axial
Flow Fan," NASA Technical Note (to be published)
4. Messenger, H. E. and Kennedy, E. E.: "Two-Stage Fan - I Aerodynamic and Mech-
anical Design," NASA CR-120859, PWA-4148, January 1972
o Harley, K. G.; Odegard, P.A.; and Burdsall, E. A.: "High-Loading Low-Speed Fan Study -
IV Data and Performance with Redesign Stator and Including a Rotor Tip Casing Treat-
ment," NASA CR-120866, PWA-4326, July 1972
6. Monsarrat, N. T., Keenan, M. J.; and Tramm, P. C.: "High-Loading Low-Speed FanStudy - I Design," NASA CR-72536, PWA-3535, July 1969
7. Keenan, M. H. and Bartok, J. A: "Experimental Evaluation of Transonic Stators -
Final Report," NASA CR-72298, PWA-3470, 1969
8. Tyler, J. M. and Sofrin, T.G.: "Axial Flow Compressor Noise Studies," SAE Trans.Vol. 70, pp. 309 - 322, 1962
9. Rice, E.J.: "Performance of Suppressors for a Full Scale Fan for Turbofan Engines,"
NASA TMX-52941, 1971
161
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