NASA CR-120943AT-6133-R
ADVANCED TWO-STAGE COMPRESSORPROGRAM
DESIGN OF INLET SI/
by
Dr. C . A. BryceC. J. PaineDr. A. R. S. McCutcheonDr. R. K. TuG . L . Perrone
AIRESEARCH MANUFACTURING COMPANY OF ARIZONA
Prepared for
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
NASA Lewis Research CenterContract NAS 3-15324
P-13432
https://ntrs.nasa.gov/search.jsp?R=19730023877 2018-04-10T09:42:25+00:00Z
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1. Report No.
NASA CR-1209432. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle
ADVANCED TWO-STAGE COMPRESSOR PROGRAMDESIGN OF INLET STAGE
5. Report DateAugust 19736. Performing Organization Code
7. Author(s)
Dr. C.A. Bryce, C.J. Paine, Dr. A.R.S. McCutcheon,Dr. R.K. Tu, G.L. Perrons
8. Performing Organization Report No.
AT-6133-R
10. Work Unit No.9. Performing Organization Name and Address
AiResearch Manufacturing Company of ArizpnaPhoenix, Arizona 85010 11. Contract or Grant No.
12. Sponsoring Agency Name and Address
National Aeronautics and Space AdministrationWashington, D.C. 20546
13. Type of Report and Period Covered
Contractor Report
14. Sponsoring Agency Code
15. Supplementary Notes
Program Monitor, Robert Y. Wong, NASA-I ewis Research Center, Cleveland, Ohio
16. Abstract
This final report covers the aerodynamic design of an inlet stage for atwo-stage, 10/1 pressure ratio, 2 Ib/sec flow rate compressor. Initially aperformance comparison was conducted for an axial, mixed flow and centrifugalsecond stage. A modified mixed flow configuration with tandem rotors andtandem stators was selected for the inlet stage. The term "conical flow com-pressor" was coined to describe a particular type of mixed flow compressorconfiguration whiqh utilizes axial flow type blading and an increase in radiusto increase the work input potential. Design details of the conical flow com-pressor are described.
17. Key Words (Suggested by Author(s))
Compressor/ImpellerInlet StageTwo-Stage Compressor Program
18. Distribution Statement
Unclassified-unlimited
19. Security Oassif. (of this report)
Unclassified
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
300
22. Price*
3.00
For sale by the National Technical Information Service, Springfield, Virginia 22151
NASA-O168 fRev. 6-7n
Page Intentionally Left Blank
FOREWORD
This is the final report covering work performed under ContractNo. NAS 3-15324 during the period May 1, 1971 through April 30, 1972.
This contract was under the technical direction of Mr. R. Wong,Lewis Research Center, of the National Aeronautic and Space Adminis-tration . _ .
Mr. K. W. Benn was program manager, Mr. G. R. Metty, the projectengineer, and Mr. G. L. Perrone, principal investigator. Recognitionis given to Mr. J. R. Erwin for frequent consultations and to Mr. P.Dodge for his assistance in developing one of the computer programsrequired to analyze this design.
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TABLE OF CONTENTS
Page
ABSTRACT ..... i
FOREWORD iii
SUMMARY 1
INTRODUCTION 3
COMPRESSOR SELECTION ..... 5
Centrifugal-Centrifugal Compressor Configuration .... 5Axial-Centrifugal Compressor Configuration ..... 10Mixed-Flow Centrifugal Configuration . 19
COMPARISON OF CANDIDATE COMPRESSORS . . 35
Stage Compatibility 38Boundary Layer Control • 42Size and Weight Considerations ... 44Impeller Erosion Considerations 47
CONFIGURATION SELECTION 49
GENERAL DESIGN LOGIC 50
ROTOR AND STATOR GEOMETRY SELECTION 53
DETAILED AERODYNAMIC DESIGN . 53
General • 53Rotor 1A Design 56Rotor IB Design 73Tandem Stator Design . 90Boundary Layer Control .. ..... 115Inlet Flowpath Design . 126Transitional Duct Design ...... 128Drive Turbine Aerodynamic Design 131
Drive Turbine Aerodynamic Design Summary 131Turbine Design Point • • 140
APPENDIX A - Deviation Angle Prediction for the Conical Flow Compressor .... 32 pages
APPENDIX B - Blade Section for Rotors and Stators ..... 33 pages
APPENDIX C - Turbine Blade Sections 9 pages
APPENDIX D - Complete Radial Equilibrium Flow Solution all Blade Rows 61 pages
APPENDIX E - Mechanical Design Analysis of NASA 10/1 Advanced Compressor Rig . . 11 pages
APPENDIX F - References . . . . 1 page
APPENDIX G - Performance Parameter and Symbol Definition • 4 pages
Page v
ADVANCED-TWO-STAGE COMPRESSORPROGRAM
. DESIGN OF INLET STAGE
SUMMARY
The objective of this program was to design an inlet stage for anadvanced two-stage compressor for an overall pressure ratio of 10/1 and2.0 pounds per second mass flow. As a part of this program, an optimi-zation study was conducted for various inlet stages in combination witha centrifugal compressor second stage. Axial, mixed flow, and centri-fugal compressors were examined as inlet stages with analyses made forthe optimum pressure ratio split between stages and the optimum speedfor each combination. A form of mixed flow compressor, with a tandembladed rotor and a tandem bladed stator, was selected for detaileddesign on the basis of performance potential.
The flow path in the selected mixed flow compressor incorporatesaxial flow type blading and a substantial change in radius alongstreamlines across each blade row to increase the work input withoutexceeding the loading criteria established for axial flow blading.The change in radius renders conventional methods for finding flowdeviation largely inaccurate. An improved method for computing flowdeviation was developed which essentially coupled the axisymmetric,radial equilibrium flow solution to a finite difference, blade-to-bladesolution thereby yielding a quasi three-dimensional model of the flowthrough each blade row (secondary flows excluded). A complete descrip-tion of the design philosophy used to establish blade sections for eachblade row is presented. Predicted performance for the conical com-pressor looks favorable and, if experimentally verified, this designconcept could have a wide range of applications.
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INTRODUCTION^
In order to achieve low specific fuel consumption (SFC) andhigh specific thrust, high compressor pressure ratios and high tur-bine inlet temperature are required, while at the; same time main-taining high component efficiencies. These objectives become pro-gressively more difficult to achieve as gas turbine engines arereduced in size or power output. In the small power range (500horsepower or less), the relative size of the components make manu-facturing tolerances and minimum clearances critical factors inattaining high efficiencies.
In small engines it is desirable to employ a relatively simplecompressor with a minimum number of stages consistent with perform-ance goals and weight considerations. In this class of engine, theLewis Research Center is particularly interested in a two-stage com-pressor with an overall pressure ratio of 10/1 and 2.0 pounds persecond mass flow rate. Thus a compressor program was initiated tostudy a two-stage compressor consisting of a second-stage centrifugalcompressor which is preceded by an inlet stage operating at the sameshaft speed. The inlet stage may be an axial, centrifugal, or amixed flow design. The first objective of this program was to opti-mize these combinations of stages for various pressure ratio splitsand rotative speeds. Consideration was also given to turbine speedlimitations in an actual engine application. From this study, atwo-stage compressor was selected on the basis of performance poten-tial, stage compatibility, size, weight, volume, and resistance toforeign object damage. A second objective was to incorporate thefirst stage of the selected configuration into a research packagefor delivery to the Lewis Research Center for experimental evalua-tion. This research package was to be complete with drive turbineand research instrumentation. Funding limitations resulting mainlyfrom the need to develop analytical methods for handling a novelimpeller prevented the completion of all of these objectives.
This report will describe the work that was completed undercontract with the Lewis Research Center. Included in this reportare a description of the optimization study of the three candidateconfigurations, trade-offs made in making the final selections, thedetailed aerodynamic design of the first stage of the selected com-pressor configuration, the detailed aerodynamic design of the cross-over duct between the two stages, and the detailed aerodynamicdesign of the drive turbine for the research package. The driveturbine was designed to have the capability of driving the combinedtwo-stage configuration to a speed of 110-percent of design speed.Also included in this report are:
(a) Blade shapes, coordinate, and stacking information for (1)the first stage of the selected compressor (Appendix A)and (2) the research package drive turbine (Appendix C)
(b) A complete non-isentropic radial equilibrium flow solutionfor all blade rows (Appendix D)
(c) Mechanical design analysis of first-stage compressor bladeand disk (Appendix E)
COMPRESSOR SELECTIONThe selection of the two-stage compressor configuration for 10/1
pressure ratio and 2 Ib/sec flow rate is based on an optimizationstudy of each candidate configuration for efficiency as a function ofspeed and pressure ratio split. The configurations examined analyti-cally were (1) an axial stage followed by a centrifugal stage, (2) amixed flow stage followed by a centrifugal stage, and (3) a centrif-ugal stage, and (3) a centrifugal stage followed by a second centrif-ugal stage. The results of this study were then used with the cri-teria listed below to select the compressor configuration for thisapplication.
(a) Overall compressor efficiency
(b) Aerodynamic compatibility of the two stages
(c) Potential for boundary layer control
(d) Stage size and weight considerations
(e) Impeller erosion considerations
Centrifugal-Centrifugal Compressor Configuration
The prediction of performance of a centrifugal compressor isbased on a correlation of polytropic efficiency against specific speed.The use of a specific speed correlation originates from pump practicewhere peak adiabatic efficiency has been experimentally found to beuniquely related to this parameter. Published derivations of specificspeed correlations rely on dimensional analysis and certain intuitivearguments. .A theoretical basis for the application of specific speedas a correlating parameter for compressor performance can be derivedfrom the corresponding momentum equations in nondimensional form. Thesubject derivation indicates that dynamic similarity for solutions tothe equations of motion depends on specific speed and certain dimen-sionless geometric parameters for the rotor. In the AiResearch deriva-tion, the specific speed is based on a mean volume flow through thecompressor. This formulation uses the square root of the product ofthe compressor inlet and outlet volumetric flow rates instead of theusual specific speed definition based on the inlet volumetric flow.AiResearch experience has shown that the mean effective definition ofspecific speed best describes conditions for dynamic similarity in acentrifugal compressor.
Polytropic efficiency is used to correlate centrifugal compressorperformance since it represents the true aerodynamic efficiency exclu-sive of pressure ratio of preheat effects. An empirical correlationof experimental results from a variety of centrifugal compressor testswith inlet tip relative Mach numbers up to 1.3 has shown that poly-tropic efficiency is essentially independent of compressor pressure
AIRESEARCH MANUFACTURING COMPANY OF ARIZONAA DIVISION OF THE GARRETT CORPORATION
ratio. Therefore, obtainable performance for centrifugal compressorscan be represented by a single line on a plot of polytropic efficiencyagainst specific speed as shown on figure 1. This correlation isrestricted to compressors with throughflows (Wcorr) of 7 pounds persecond or greater, nominal clearances of 0.010 inch or less, and aReynolds number (Re) of 3 x 106 or higher. Scaling these results tolower flow rates is a separate problem and will.be discussed later inthis report. This polytropic efficiency correlation is used in thedesign point computer program to compute state and overall efficiencyfor a given overall pressure ratio, rotative speed, and -first-stagepressure ratio.
With several assumed values of first-stage pressure ratio atconstant rotating speed and overall pressure ratio, the program willcurve fit the resulting overall efficiencies and determine the optimumstage pressure ratios. Results from this program are presented onfigure 2. This figure shows overall compressor efficiency for twocentrifugal stages with an overall pressure ratio 10/1 as a functionof first-stage pressure ratio and rotating speed. Peak stage effi-ciency is indicated for each speed in figure 2 corresponding to theoptimum pressure ratio split between stages. A crossplot of the peakefficiency results against rotating speed is shown in figure 3. Thisplot is used to determine design conditions tabulated below for theoptimum centrifugal-centrifugal configuration for this application.
Note that the first stage of a two-stage compressor does notrequire diffusion to as low a Mach number as the second stage and thusthe diffusion losses are lower. Experience has indicated, however,that the turning and ducting losses associated with the interstageduct are sufficiently high to compensate for the reduced diffusion.Therefore in the above analysis, the efficiency correlations that arebased primarily on single-stage performance with diffusers are alsoassumed to apply to stages with interstage ducts.
DESIGN CONDITIONS FOR THE OPTIMUMCENTRIFUGAL-CENTRIFUGAL COMPRESSOR CONFIGURATION
First Stage Second Stage Overall
Rotor speed, rpm, 75,500 72,500 72,500
Pressure, ratio 4.75/1 2.1/1 10/1
Specific speed, N 70 64 N/As
Adiabatic efficiency, nad 0.84 0.862 0.826
Previous AiResearch test experience with a two-stage .centrif-ugal compressor at approximately 11/1 pressure ratio has demon-strated an adiabatic efficiency of 80.3 percent with a corrected
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AIRESEARCH MANUFACTURING COMPANY OF ARIZONAA DIVISION OF THE GARRETT CORPORATION
flow to the first stage of 8.0 pounds per second. Predictedperformance for this configuration from the polytropic efficiencycorrelation is 81.6 percent. The difference, .1.3 points, isattributed to the fact that in order to obtain the operatingrange required for a practical two-stage compressor, it is oftennecessary to match the two stages so that their individual peakefficiencies do not coincide at the design operating point. Thus,even though each stage may achieve the peak efficiency level indi-cated by the specific speed correlation, the overall compressorpeak efficiency may be significantly lower than the value obtainedby assuming both stages to be operating at their peaks simultane-ously.
It seems logical to assume that the 10/1 compressor wouldrequire a similar matching to insure good range and, therefore, theoverall optimum efficiency should be lowered about 1.3 points toaccount for this effect.
«5In addition to a stage matching correction, a scale must be
applied to the predicted performance to account for the lower air-flow of the present design. Predicted efficiency from the poly-tropic performance correlations is based on experimental data forcentrifugal compressors with corrected flows of 7.0 pounds per sec-ond or higher. At the 2.0 pounds per second airflow of the presentdesign, clearance problems and secondary flow effects are moresevere than for a corresponding condition in the empirical correla-tion. Experience has shown that a decrement of 2.3 points in theoverall adiabatic efficiency is necessary to account for scalingdown to the 2.0 pounds per second.airflow. Thus, the combined cor-rection for the two-stage centrifugal combination is 3.6 points(staging loss plus flow rate scaling) . This results in a predictedoverall adiabatic efficiency for the centrifugal-centrifugal con-figuration of 79 percent.
A sketch showing a meridional view of the flowpath for thecentrifugal-centrifugal configuration is presented as figure 4. Inthis design the Mach number at the entrance to the transition sec—tion between stages is 0.3. This is a reasonable level for effi-cient turning in "the 'transition duct. Flow leaves the second-stagediffuser at an average Mach number of 0.2. This value was a require-ment of the contract. .
Axial-Centrifugal Compressor Configuration
Axial compressor performance prediction requires much moreparametric definition than for centrifugal compressor performance.A computer program has been developed by AiResearch which predictsstage efficiency of an axial compressor for specified conditions ofinlet corrected flow, rotational speed, and stage pressure ratio.The program solves for conditions along the pitch line with continu-ity being satisfied on a one-dimensional basis. The rotor and
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AXIAL DISTANCE, INCHES
Figure .4. - Meridional View At Flow Path ForCentrifugal-Centrifugal Configuration.
11
AIRESEARCH MANUFACTURING COMPANY OF ARIZONAA DIVISION OF THE GARRETT CORPORATION
stator efficiencies are calculated from mean effective profile losscoefficients using pitch line flow conditions. Loss coefficientsfor both shock losses and profile losses are computed as brieflydiscussed in the following paragraph.
The shock loss in the blade tip regions is directly related toboundary layer separation along the blade which is governed by thestatic pressure rise across the shock. If the shock is strong enoughto separate the boundary layer, the losses will be greater than thatassociated with a normal shock at the inlet relative Mach number.However, if the boundary layer does not separate, the shock lossescan be lessened. A correlation of the limiting static pressure risethat the boundary layer can sustain before separating was derivedfrom shock separation data for turbulent boundary layers on a flatplate as a function of Mach number (ref. 1) ..* An average pitch lineMach number corresponding to:
1.0 + M. .M 0
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was used to calculate a normal shock loss for the entire blade.This value of loss was then multiplied by a ratio of total pressurerise across the blade to the limiting value for boundary layer separa-tion to obtain shock-related losses. The blade element profile losseswere based on a correlation of AiResearch experimental data (airflowof 20 to 30 Ib/sec) in the form of loss coefficent versus D-factor asdone, in Reference 2 .
The rotational speed is determined from the inlet conditions,the desired work input, and hub turning across the rotor. Thisspeed is continuously corrected as the work input is varied toachieve the required overall pressure ratio. After the programresults converge, the vector diagram for the rotor and stator arecalculated and a preliminary size established for the compressorstage.
The results from this computer program are plotted (figure 5)in nondimensional form for an assumed absolute inlet Mach number of0.6 and an air angle of ten degrees at the rotor hub exit station.Several different hub exit air angles were investigated (3H2
= 0-;10°, and 20°) with the results showing the same general trend withhub radius ratio and pressure ratio. The selected air angle at therotor hub exit (3H? = 10°) was found to be a good representation ofseveral existing axial compressor stages. Measured performance ofthese axial stages compare quite favorably with that calculated bythe program. It should be noted that these axial stages are largerand have design corrected flows much higher than the present design,nitial design calculations were made without any scaling
*Refer to Appendix F for list of references.
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effects on performance included. A discussion of overall scalingeffects is undertaken in the latter portion of this section. Thenondimensional results in figure 5 are converted to dimensionalresults in figure 5 are converted to dimensional results by speci-fying the stage weight flow and inlet conditions. Axial-stage per-formance at constant values of rotative speed for 2 Ib/sec flow rateis presented in figure 6 .
Overall compressor performance for an axial, first-stage fol-lowed by a centrifugal compressor second stage is obtained from thedesign point matching program. In this program, the axial-stageperformance is input as a function of first-stage pressure ratio atconstant wheel speed. The centrifugal stage performance is obtainedfrom the specific speed correlation described previously. The pro-gram computes overall performance for a 10/1 pressure ratio stageas a function of input first-stage pressure ratio values and curvefits the results to define the optimum pressure ratio split betweenstages. No matching penalty has been included. ••
A summary of the predicted overall performance for the axial-centrifugal compressor configuration is presented in figure 7. Over-all compressor efficiency is shown as a function of pressure ratioacross the axial stage for several values of rotor speed. Peakoverall compressor efficiency for each speed is indicated by thearrows in this figure. Note that overall efficiency increases withrotor speed. The increase is directly attributable to the centrif-ugal stage operating at a more favorable specific speed condition athigher rotor speeds. The optimum wheel speed for peak overall com-pressor efficiency is above 100,000 rpm. Turbine stress considera-tions for this size engine have shown the wheel speed should be lim-ited to approximately 90,000 rpm. Therefore, no attempt was made todefine an optimum efficiency above 100,000 rpm in the axial-centrifugal combination. Design point wheel speed was set at 90,000rpm for this configuration. Design conditions for this configura-tion are summarized in the following tabulation:
DESIGN CONDITIONSAXIAL-CENTRIFUGAL COMPRESSOR
First-Stage Second-Stage^ Overall
Compressor Type Axial Centrifugal
Rotor Speed, rpm 90,000 90,000 90,000
Tip Relative Mach Number 1.4 lj.192
Pressure Ratio 1.73/1 5.78/1 10/1
Specific Speed 235 54.2 N/A
n , (no scale or matching 0.866 0!.821 0.813a effects included)
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Figure 7. - Overall Efficiency vs 1st Stage Pressure RatioAxial-Centrifugal Configuration,2 Ib/sec FlowRate}10/I Overall Pressure Ratio.
2.2
16
Again, it should be- noted that scaling and stage matching effectshave not been included in the efficiencies stated above. Littledata is available to estimate the effects of scaling axial flowcompressors to low airflows. Therefore/ in scaling the axial-centrifugal configuration, the incremental effect of size on overallefficiency was assumed to be the same as that estimated for thecentrifugal-centrifugal configuration. Application of a total cor-rection of 3.6 points to the axial-centrifugal configuration indi-cates that this configuration should have an overall adiabaticefficiency of 77.7 percent at design conditions (turbine speedlimit). This assumes that the axial stage scales identically witha centrifugal stage. In the axial-centrifugal stage combination,the centrifugal stage does about five times as much work as the axialfirst-stages. Therefore a scaling effect error for the axial stagewould have a minimum effect on the overall efficiency.
.A meridional view of the flow path through the axial-centrifugalcompressor combination is presented as figure 8. Mach number in thetransition section between stages is approximately 0.43. Diffuserexit conditions for the second-stage centrifugal compressor corre-spond to an average Mach number of 0.2 as required.
17
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CENTRIFUGAL SECOND STACE
1.0 2.0
AXIAL DISTANCE, INCHES
3.0" 4.0
Figure 8. - Meridional View of Flow Path ForAxial-Centrifugal Configuration.
18
MIXED-FLOW CENTRIFUGAL CONFIGURATION
The design technique employed for a conventional mixed-flowcompressor is identical to that currently used for centrifugal com-pressor design. Based on this fact, the specific speed efficiencycorrelation for centrifugal compressors is also used to predict theefficiency level for the mixed-flow configuration. This, of course,yields the same result as the two-stage centrifugal configurationanalysis, except that the mixed-flow configuration has a longeraxial length. , '
In an attempt to improve the efficiency potential of a mixed-flow type of compressor, a new mixed-flow compressor concept wasproposed. This concept which embodies a combination of axial designtechniques with a mixed-flow type of flowpath was given the nameconical-flow compressor to distinguish it from the conventionalmixed-flow compressor.
Fundamentally, the conical-flow compressor combines axial flowcompressor blade shapes with a large radius change (analogous to thatoccurring across a mixed-flow or centrifugal compressor rotor). Axialcompressor design criteria are used to select blade loadings and lossestimates. Centrifugal compressor design criteria are used in selectingthe design relative velocity ratios across the rotor. The capabilityfor improved performance arises from the use of a large change inradius, which gives increased static pressure rise, with blade load-ings designed to axial compressor loading criteria. If blade aspectratios are kept similar to those acceptable to axial compressordesign criteria, it is felt that secondary flow losses, which com-prise a large portion of conventional mixed-flow losses, will beminimized. Frictional losses due to large blade surface areas willalso be reduced. Additional advantages may be achieved.by use of atandem blading in the conical flow rotor and/or stator.
There is no data available for this type of compressor on whichto base a performance prediction. Therefore, the approach used inmaking performance calculations on the conical-flow compressor wasto assume that the pressure rise occurring due to radius change didnot directly influence boundary layer growth. This approach hasbeen used in the calculation of boundary layer growth in centrifugalimpellers at AiResearch. Reasonable agreement has been achievedbetween losses based on loss correlations and boundary layer calcul-ations up to the point of separation. Good agreement has also beenobtained between the predicted point of boundary layer separationand experimental indication of boundary layer separation using lampblack traces on the surface of impellers. This assumption permitsuse of criteria established for axial flow blading to calculateblade losses for conical-flow compressor.
19
Various conical flow configurations were examined analytically.The performance prediction computations involved an iteration proc-ess where a meridional shape was assumed to specify a radius changeacross the blade row. From the desired pressure ratio and assumedloss coefficients, inlet and outlet velocity diagrams were calcu-lated at several radial positions. These velocity diagrams wereused to compute D-factors and shock losses (similar to procedureused for axial stages described earlier) which were converted intoloss coefficients from a loss correlation for axial flow blading(Reference 2) for the-computation of new velocity diagrams. Oncethere were no further changes in the loss coefficients between suc-cessive calculations, a satisfactory flow solution was assumed.
After a satisfactory flow solution was obtained, the hub, mean,and tip vector diagrams were examined at the blade inlet and exitstations. The variation in velocities from hub-to-tip, the airangle changes across the blade, and the relative velocity ratioacross the rotor tip sections were critically examined for consist-ency with axial flow design practice. Where a single rotor was used,the relative velocity ratio for the tip section was limited toapproximately 0.6. With two rotor blade rows, this limit wasincreased to the neighborhood of 0.65 for.each row to provide addi-tional stall margin and a small degree of conservatism to the design.Where undesired values were evident from the vector triangles, achange in meridional contours (i.e., flow width, wall shape, and/orwall curvature) was necessary and a new flow solution obtained.
A summary of the configurations examined by the method justdescribed is shown on table I. These are listed in chronologicalorder to illustrate the direction in which the study progressed.In. the first two cases investigated/ a single rotor and singlestator were employed in a conical flow configuration with a 45-degreemeanline slope at the stator exit. Based on previous computationsmade for the. axial-centrifugal arrangement, a design pressure ratioof 2.5 at wheel speeds of 65,000 and 80,000 rpm was examined.
At the lower speed, the flow solution indicated that too muchturning was needed to reach the design pressure ratio (the rotor hubexit flow was overturned to discharge the flow in the direction of .rotor rotation). The operating characteristics in an engine wouldbe undesirable with this velocity diagram because, as weight flow isreduced, the hub work decreases. Thus, engine acceleration character-istics might be undesirable. Furthermore, the compressor would bemore sensitive to inlet distortion. A high rotor speed would avoidthis situation by meeting the work requirements with less turning inthe blades. At 80,000 rpm, the required flow turning was satis-factory but the diffusion factors across the blades were greater thanthe normal range for moderate loss coefficients. Thus, the profilelosses for a single rotor would be too high to efficiently produce apressure ratio of 2.5. Consequently, a conical flow rotor with two
20
N
TABLE I.
CONICAL FLOW FIRST STAGE
TWO STAGE, 10/1 PRESSURE RATIO PERFORMANCE SUMMARY
(PR)
SINGLE BLADES
65,000
80,000
2.5 Too MuchTurningRequired
2.5 "-D" FactorsOff Curve
TANDEM ROTORS
65,000
70,000
70,000
70,000
70,000
70,000
70,000
70,000
2.5 0.9
2.0 0.9431
2.5 0.9150
3.0 0.8758
TANDEM
: 2.5 0.9308
2.96 0.8983
REALIGNED
2.5 0.9395
3.06 0.9067
0.802
0.7975
0.8123
0.8248
0.8151
0.8192
0.8289
0.8233
ROTORS AND STATORS
0.8123
0.8241
ROTORS (TANDEM
0,8123
0.8265
0.8370
0.8345
STAGES)
0.8406
0.8413
DESCRIPTION
Single Rotor/Single Stator
Single Rotor/Single Stator
Tandem Rotor/+Single Stator
Tandem Rotor/+Single Stator
Tandem Rotor/+Single Stator
Tandem Rotor/+Single Stator
Tandem Rotor/Tandem Stator
Tandem Rotor/Tandem Stator
Tandem Rotors/Tandem Stators
Tandem Rotors/Tandem Stators
*Efficiency level valid for compressors with corrected flows of8 Ib/sec or more.
21
blade rows in tandem was investigated in order to lower diffusionfactors and, thus the rotor losses.
The initial tandem rotor configuration investigated was with adesign pressure ratio of 2.5 and a design speed of 65,000 rpm. Theflow solution for the tandem rotor configuration for these condi-tions indicated that the flow overturning problem of the single rotorwas eliminated as a result of a larger radius change across the rotorwith this tandem configuration. Computed stage efficiency for thistandem rotor-single stator configuration was 90.0 percent. (Itshould be noted that these efficiency values have not been depre-ciated for size effects. A discussion of size effects on perfor-mance will be presented later.) When this configuration was matchedto a second-stage centrifugal compressor, the estimated overallefficiency for both stages was 81.5 percent at 10/1 pressure ratio.A meridional view of this tandem rotor-single stator configurationis presented in figure 9.
Another tandem rotor-single stator conical flow compressor wasexamined at a pressure ratio of 2.5 but with a wheel speed of 70,000rpm. The effects of wheel speed on component and overall efficien-cies are shown on table II.
A clear performance advantage for the higher wheel speed is evi-dent since the rotor and stator efficiencies are higher due toreduced blade loadings. It is quite possible that further increasesin rotational speed would show some performance improvement based onthe analytical model used here, which define losses in terms of anormal shock loss at the inlet relative Mach number and a blade pro-file loss. Experience has shown that, above an inlet relative Machnumber of approximately 1.3, the shock strength is often sufficientto cause boundary layer separation on the suction surface of therotor. When this happens, the losses increase rapidly and the lossmodel used here is no longer applicable. The inlet relative Machnumber for the rotor tip section at 70,000 rpm is 1.29. Therefore,design wheel speed for the remaining mixed-flow configurations ana-lyzed here was specified at 70,000 rpm in an attempt to avoid shock-separation problems at design conditions.
The effect of first-stage pressure ratios of 2.0, 2.5, and 3.0on component and overall efficiency at 70,000 rpm was investigatedand is shown on table III. These results are for one tandem rotor-single stator conical flow configuration in combination with asecond-stage centrifugal compressor. These results show first-stageefficiency decreases with increasing stage pressure ratio as mightbe expected. At the same time, the centrifugal stage performanceincreases with first-stage pressure ratio reflecting more favorablespecific speed values. The combined effect on the overall effi-ciency at 10:1 pressure ratio produces an optimum first-stage pres-sure ratio for the tandem rotor-single stator conical flow configur-ation of approximately 2.5 to 2.6.
22
co5
SkHtf frU i };!«!lT-14--4-! i»-i-f -i.,,4.-(.I-*— _1_*,,J.;-V. i-.w-:--.-.,J..,.f.. i.T..,i.;-: i.:.J i.i.r.T..i I >- -1.1-* t-i i i-1-f-.i . i, i <. .
AXIAL DISTANCE, INCHES..
Figure 9\, -r Meridional View. - Conical Flowi ' "• •:' Stage -; Tandem pot:or and Single
• • Stator»;'' \: .>"'••', ' •'•.',' •', ' ...
23
TABLE II.
EFFECT OF WHEEL SPEED ON PERFORMANCEOF CONICAL-CENTRIFUGAL COMPRESSOR
Wheel speed 65,000 rpm 70,000 rpm
Conical flow stage
(a) Pressure ratio 2.5 2.5
(b) Rotor efficiency, n d* 0.959 0.963
(c) Stage efficiency, n , * 0.90 0.915
Centrifugal stage
(a) Pressure ratio 4.0 4.0
(b) Specific speed , 41.3 44.9
(c) Stage efficiency, nad* 0.802 0.822
Combined stages
(a) Pressure ratio 10.0 10.0
(b) Overall efficiency, r\ , * 0.815 0.829aa
*Efficiency level valid for compressors with corrected flow.of 8 lb/sec or larger.
24
TABLE III.
FIRST STAGE PRESSURE RATIO COMPARISONTANDEM ROTOR> SINGLE STATOR
1. Wheel speed, rpm 70,000 70,000 70,000
2. Conical flow stage
(a) Pressure ratio 2.0 2.5 3.0
(b) Rotor efficiency, nad* 0.969 0.963 0.946
(c) Stage efficiency, n -,* 0.943 0.916 0.876clQ
3. Centrifugal stage '•
(a) Pressure ratio 5.0 4.0 3.33
(b) Specific speed, Ns 42.4 44.9 47.6
(c) Stage efficiency, nad* 0.798 0.812 0.825
4. Combined stages
(a) Pressure ratio 10.0 10.0 10.0
(b) Overall efficiency * 0.819 0.829 0.823
. *Efficiency level valid for compressors with equivalent flowsof 8 Ib/sec or more.
25
At this point in the investigation, it became evident that theblade loadings for the single-stator' configurations were quite largeand that there could be an overall performance improvement associ-ated with tandem stators. A conical flow compressor configurationwas then laid out which included a tandem rotor and a tandem stator.The effect of tandem stators on the first-stage component efficien-cies is listed as follows:
COMPARISON OF TANDEM AND SINGLE STAGE STATOR
Number of stators Single Two
Wheel speed, rpm 70,000 70,000
Conical flow stage:
(a) Pressure ratio 3.0:1 2.96:1
(b) Rotor efficiency, nad* 0.946 0.944
(c) Stage efficiency, nad* 0.876 0.898
*Efficiency levels valid for compressors with equivalentflows of 8 Ib/sec or more.
The comparison indicates that the tandem stator configurationis 2.2 points better in stage efficiency than the single statordesign at a stage pressure ratio of 3/1* This difference is equiv-alent to a gain of 1.2 points of overall efficiency for the combinedtwo-stage performance as shown on table III. A similar comparisoncan be made for a 2.5:1 pressure ratio first stage by referring tothe results on table III. This indicates the first-stage performancefor tandem stators is 1.6 points higher than a single stator with theoverall two-stage efficiency gain of approximately 0.8 point. Therelative comparison of component efficiencies between the differentfirst-stage pressure ratio cases appears reasonable considering thefact that stator loadings are much higher for the 3/1 pressure ratiostage. Therefore, there is more to be gained by the use of a tandemstator configuration for the higher first-stage pressure ratio design.
Preliminary stress calculations made for the initial rotor bladeconfiguration, shown in figure 10 by dashed line, indicated thatorientation of the blade approximately normal to the flow directioncould cause blade stress problems because of the overhung blade con-figuration. As a result, a blade stacking arrangement where theblade edges are placed more nearly in a radial direction, as shownby the solid line in figure 10 was examined for efficiency andstress. This arrangement was found to be satisfactory from a stressstandpoint and also produces a backward swept blade configuration
26
REVISEDCONFIGURATION
0
1.0 2.0
Axial Length, Inches
Figure 10. - Meridional View of Conical - Flow Stage.
3.0
27
with respect to the streamline flow path over the blades.Investigators of swept blades for axial compressors have indicatedfavorable effects of transonic compressors (References 3 to 7). Theadvantages of swept wings on high-speed aircraft are well understoodat this time. The aerodynamic performance of a swept wing has beenrelated to the component of relative velocity normal to the leadingedge. Using this loss model, lower losses would be predicted forthe backswept blade configuration. In the preliminary design cal-culations for the revised stacking arrangement, no attempt was madeto include any benefit of leading edge sweep on the predicted per-formance results.
Performance for the different blade stackings is shown on tableIV. This comparison indicates a slight performance advantage forthe revised stacking arrangement despite the fact that blade sweepeffects were not taken into consideration. Investigation of thedetailed flow calculations indicated the revised stacking arrangementhad a higher radius change between rotor inlet and exit stations thanfor the initial design. This, in effect, reduced the loadings foreach rotor blade with a greater portion of the static pressure ratiogenerated by centrifugal forces. .
The effects of first-stage pressure ratio on overall.stage effi-ciency for tandem-rotor/single-stator configurations as previouslydiscussed show that optimum first-stage pressure ratio was approxi-mately 2.5:1. With the tandem-rotor/tandem-stator configurationsthe optimum first-stage pressure ratio shifts toward a value in theneighborhood of 3/1 (Table V). However, the difference in overallperformance between the 2.5/1 and 3/1 cases is essentially insignif-icant in light of the approximate nature of the design calculationsperformed here. The true optimum condition appears to be withinthis range of design pressure ratios for the first stage. Thereforethe 3/1 design was selected as the best configuration for a mixed-flow first stage based on the premise that the higher pressure ratiovalue would permit a better demonstration of the performance poten-tial of the tandem-rotor/tandem-stator configuration.
A design overall efficiency of 84.1 percent was predicted forthe selected conical flow compressor configuration. To be consistentwith the performance estimates of the other candidate compressors,an efficiency decrement of 3.6 points was assumed for scaling andmatching effects resulting in an adjusted efficiency of 0.805.
A meridional view of the two stage 10/1 pressure ratio conical-centrifugal compressor configuration is presented in figure 11. Thisshows the tandem-rotor/tandem-stator conical flow first-stage fol-lowed by a transition duct leading to the centrifugal compressorsecond stage... Average Mach number for the transition section isapproximately 0.32 and the design Mach number for the second-stagediffuser exit is 0.2. Total stage length is approximately four
28
TABLE IV.
CONICAL-CENTRIFUGAL COMPRESSOR WITHINITIAL AND REVISED- ROTOR BLADE STACKING
(SEE Figure 10)
1. Blade stacking Initial Revised
2. Wheel speed, rpm 70,000 70,000
3. Conical flow stage
(a) Pressure ratio 2.96 3.06
(b) Rotor efficiency, n d* 0.944 0.955
(c) Overall efficiency, n * 0.898 0.907clCl
4. Centrifugal stage
(a) Pressure ratio 3.38 3.27
(b) Specific speed, N 47.5 48.1s
(c) Stage efficiency, n d* 0.824 0.827
5. Overall compressor
(a) Pressure ratio 10.0 10.0
(b) Overall efficiency, n&d* 0.834 0.841
*Efficiency level valid for compressors with equivalent flowsof 8 Ib/sec or more.
29
TABLE V.
DESIGN PARAMETERS AND PERFORMANCE RESULTS
TANDEM CONICAL FLOW COMPRESSOR
_ Mean Hub
ROTOR 1A (20 BLADES, AR =s 1.028)
.SOLIDITY 1.25 1.5 2.33
TOTAL PRESSURE RATIO 1.82 1.78 1.75
EFFICIENCY, nad* 0.874 0.971 0.987
DIFFUSION FACTOR 0.443 0.418 0.399
ROTOR IB (40 BLADES, AR = 0.84)
SOLIDITY 1.57 1.68 1.79
TOTAL PRESSURE RATIO 3.27 3.19 3.32
EFFICIENCY, nad * 0.883 0.977 0.988
DIFFUSION FACTOR 0.441 0.362 0.333
STATOR 1A (53 BLADES, AR = 0.584)
SOLIDITY 1.73 1.75 1.76
TOTAL PRESSURE RATIO 3.1 3.1 3.1
EFFICIENCY, nad * 0.837 0.948 0.922
DIFFUSION FACTOR 0.535 0.502 0.525
STATOR 2A (53 BLADES, AR = 0.495)
SOLIDITY 1.5 1.57 1.69
TOTAL PRESSURE RATIO 3.06 3.07 3.04
EFFICIENCY, nad * 0.827 0.939 0.905
DIFFUSION FACTOR 0.523 0.483 0.502
*Efficiency level valid for compressors with corrected flows of8 Ib/sec or more.
30
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31
inches with the maximum diameter of the mixed flow first stage beingless than seven inches. Preliminary design vector triangles for thetandem-rotor/tandem-stator configuration are presented in figures 12and 13. Additional design parameters and performance informationalong the tip/ mean, and hub streamlines are presented on table V.
32
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34
COMPARISON OF CANDIDATE COMPRESSORS
In order to facilitate a comparison of the different candidateconfigurations, selected speeds, work splits, stage characteristics,and overall efficiency are tabulated on table VI.
The predicted overall efficiency of 0.790 for the centrifugal-centrifugal configuration is the most reliable because of recentAiResearch experience with a similar 11/1 pressure ratio compressorwith eight pounds-per-second weight flow. The dominating factor inthe overall efficiency is the rotating speed which was set at 72,500rpm in order to pl%:ce both stages as close to their optimum specificspeed as possible.
The predicted overall efficiency of 0.777 for the axial-centrifugal configuration is less reliable than the centrifugal-centrifugal configuration due to a lack of scaling effect data onaxial compressors. As discussed, this performance adjustment, of3.6 efficiency points, used for the centrifugal-centrifugal config-uration was also applied to this configuration. The predominatingfactor in the low overall efficiency of the axial-centrifugal com-pressor is the low specific speed of the second stage. It was indi-cated that operation at a higher rotative speed would improve thesecond-stage specific speed and, therefore, the overall compressorefficiency. Increasing the rotative speed was ruled out because thecalculated turbine blade stress in an engine application would beexcessive above 90,000 rpm.
The predicted efficiency for the conical-centrifugal configura-tion is the least reliable because of the complete lack of experi-mental data on the conical flow type compressor. However, the con-cept is believed to have an excellent chance for success because,based on axial flow design criteria, the design is conservative.The tip inlet relative Mach number was limited to 1.3 and the dif-fusion factor at the tip was limited to 0.44 for the rotors and 0.54for the stator.
The overall efficiency for the conical-centrifugal configurationadjusted for scaling effects and matching is 1.5 points higher thanthe centrifugal-centrifugal configuration and 2.8 points higher thanthe axial-centrifugal configuration. The higher performance shownfor the conical-centrifugal configuration is primarily a result ofthe high efficiency predicted for the conical flow first stage. Thisstage operates at a pressure ratio of 3.06/1 with a calculatedadiabatic efficiency of 90.7 percent.
If this concept is successful, a less conservative first-stagedesign could give greatly improved second-stage specific speed and,
35
TABLE VI..
PREDICTED OVERALL PERFORMANCE COMPARISON
1. Wheel speed, rpm
2. First stage
(a) Pressure ratio
(b) Specific speed
(c) Adiabatic efficiency*
3. Second stage
(a) Pressure ratio
(b) Specific speed
(c) Adiabatic efficiency*
4. Overall compressor
(a) Pressure ratio
(b) Adiabatic efficiency*
(c) Scaled performance,
Cent-Cent Axial-Cent Conical-Cent
72,500 90,000
centrifugal axial
4.75/1 1.73/1
70 235
0.84 0.866
centrifugal centrifugal
2.11/1 5.78/1
64 54
0.862 0.821
70,000
conical
3.06/1
95
0.907
centrifugal
3.27/1
48
0.827
10/1
0.826
0.790
10/1
0.813
0.777
10/1
0.841
0.805
*Efficiency level valid for compressors with corrected flowsof 8 Ib/sec or larger.
36
therefore, greater gains in overall compressor efficiency thanpredicted herein. It is believed that the relative level of effi-ciency computed for large compressors is valid for the scaled com-pressors. Thus, only the magnitude of the difference between thecentrifugal-centrifugal compressor and the other two configurationsis subject to question. The use of a constant correction factormaintains the relative levels of efficiency and gives an indicationof the levels of efficiency expected. A check was made to see howmuch error would be required in the conical flow stage efficiencyprediction to make the overall conical-centrifugal performance equiv-alent to the two-stage centrifugal combination. The required valuewas 3.2 efficiency points. This means that the conical-compressorloss factors would have to be more than 30 percent in error, whichis unlikely.
Before making a final selection of candidate compressors, sev-eral additional considerations were explored. These are discussedin the following sections.
37
STAGE COMPATIBILITY
Aerodynamic compatability between the two stages is concernedwith: . i
!• " , . - ' . ' . i • '
(a) Design of the interstage duct for an efficient transitionbetween stages
(b) The off-design operation with regard to inlet guide vanerequirements
(c) The influence of compressor configuration on engine mech-anical problems
With a two-stage centrifugal compressor combination, the transi-tion duct makes a 180-degree turn followed by a 90-degree turn.While this would seem to be a rather tortuous flow path, AiResearchexperience with similar transition sections has demonstrated verygood performance with proper design. Recommended design practice inthis case is to accelerate the flow through each turn; this practiceresults in very little distortion at the inlet to the second stage.By setting the Mach number at the diffuser exit from the first stagereasonably lower than the impeller inlet Mach number of the secondstage, the necessary acceleration can be designed into the turns.The final meridional shape is analytically evaluated using the radialequilibrium flow program to ensure a favorable velocity distributiondownstream of the transition duct.
The transition section for the conical-centrifugal stage com-bination is quite similar to that shown for the centrifugal stagesbut may require somewhat less overall turning, since the flow hasan axial component at the impeller exit. This should make thedesign and performance of the transition duct for the conical-centrifugal stages more favorable than the corresponding centrifugalstage combination design. Again, the flow accelerates through eachbend in the transition duct, and the velocity distribution to thesecond-stage is evaluated analytically. The first-stage exit andsecond-stage inlet Mach numbers can be adjusted to accomplish thedesired acceleration. Therefore, the design and performance of thetransition section for the conical-centrifugal stage combinationwould seem to present few, if any, problems based on AiResearchexperience with staged centrifugal compressors.
! •
A cursory look at the transition section between an axial stagefollowed by a centrifugal stage would seem to indicate few reasonsfor concern to the designer. The interstage flow requires littleturning and the duct lengths are quite short. For high pressure
38
ratio, low. hub/tip ratio designs, the absolute Mach number at therotor hub discharge can be an the order of 1.0. This value mustthen be diffused to approximately M =V0.45 which requires a largeamount of diffusion. This situation requires special design con-sideration to prevent deteriorated flow conditions at the centrifugalstage inlet.
Careful attention to design details can minimize or eliminatemany pitfalls in the transition region design. As a first step, theaxial stage should be designed to deliver as low a discharge Machnumber as feasible while still maintaining high stage efficiency.Secondly, the inlet hub and tip diameters of the centrifugal stageare matched closely to the corresponding diameters on the axialstage are minimize any necessary turning of the flow. Then, poten-tial flow and boundary layer analyses are made on the design meri-dional shape to assure that there are no flow separation problemsand that the velocity distribution to the centrifugal stage inletmeets.design requirements. •
In summary, transition section design and performance for theconical-centrifugal stages and the combined centrifugal stages" arenormally quite satisfactory with sufficient attention to currentdesign techniques. Transition section design for an axial-centrifugal stage combination requires careful attention be given tothe rate of diffusion between stages. Here, again/ a reasonabledesign with good performance characteristics is obtainable withastute design practice.. In this light, the transition sectiondesign and performance do not seem to favor any one of the differ-ent two-stage configurations.
Stage compatability with respect to off-design operation of twocentrifugal stages in series is normally not a problem. AiResearchexperience has shown that two centrifugal stages in series willmatch quite satisfactorily over a wide range of operating conditionswithout requiring guide vanes. An example of two-stage centrifugalcompressor operating characteristics and performance is presentedas figure 14. This stage combination has good design and off-designoperation as is readily apparent from the experimental data shown onthis figure.
The off-design operation of an axial first stage followed by acentrifugal second stage results in certain matching problems thatnormally require inlet guide vanes for the axial stage. At designspeed, where the stages are usually matched, the range of the com-bined stages is often greater than demonstrated by the axial stagealone. This seems to be due to the centrifugal stage actually sta-bilizing flow through the axial stage when the first stage is sup-,posedly in surge. However, low speed and start-up operation of thecombined stages results in a mismatch between the stages. The axialstage wants to pass more flow than the centrifugal stage will accept,
39
Figure 14. - Example Two-Stage Centrifugal Compressor Map.
40
tending to choke the back stage and stall the first stage.Therefore, inlet guide vanes are needed to limit the flow throughthe axial stage during low speed and/or start-up operation. Thiscomplicates somewhat the construction and operation of an axial-centrifugal stage combination and may result in this combinationbeing unacceptable for certain applications.
In the conical-centrifugal stage combination, the off-designoperating characteristics are expected to fall somewhere betweenthe axial-centrifugal and centrifugal-centrifugal conditions. Lowspeed and start-up operation may be a problem since the tandemrotors and stators of the conical compressor are basically axialblade shapes. However, there is a significant radius change acrosseach rotor section of the conical compressor which yields somestatic pressure rise during low speed operation. This would helpthe second stage to pass more flow and it is quite possible thatthe conical-centrifugal stage combination could start without vari-able inlet guide vanes. If this is the case, then off-design opera-tion of the conical-centrifugal combination would be as good-as twocentrifugal stages in series and much better than an axial-centrifugal combination.
From a mechanical standpoint, a design goal of the program isto have a resonant-free operational speed range and a sufficientmargin between the operating speed range and the criticals to ensurereasonable bearing life. The axial-centrifugal stage combinationfollowed by a drive turbine can possibly be designed to meet thisgoal, despite its much wider operating speed range. Design speedfor the axial-centrifugal combination is limited at 90,000 rpm sothat it is desirable to set the first bending mode of the shaft.critical above ~120,000. For this compressor to work, it must bestraddled between the two bearings and the bearing span minimizedto increase the first bending mode critical to help meet the design.goal. " . . . ; • '
Overhanging the inlet impeller of the centrifugal-centrifugal'compressor results in an unacceptable condition and, thus, straddlemounting the compressor stages is required. The only problem withthe straddle-mounted bearing arrangement in the vertical shaftorientation specified by NASA is that it is difficult to get oil toand from the outboard bearing. It is obvious that the conical-centrifugal compressor exhibits a similar mechanical characteristicto the centrifugal-centrifugal stage. However, straddle-mountingthe compressor stages is an acceptable solution and the final designof the conical-centrifugal1stage is calculated to operate below thecritical resonant frequency for bending.
41
Boundary Layer Control
The application of boundary layer control techniques to axialcompressors has received considerable attention during recent years.Research has been conducted in the areas of:
(a) Casing treatments over rotor tips
(b) Slotted and tandem blading
(c) Boundary layer suction along the blade surface
(d) Wall suction
The effect of boundary layer control techniques on overall compres^-sor performance is of primary interest in this program. A portionof the above research was conducted for the purpose of extendingthe stall margin and reducing noise. However, in most cases, theeffect on compressor performance has been measured and presented aspart of the test results. Therefore, it appears that there is suf-ficient data available, both in-house and in the literature, toselect a reasonably effective boundary layer control technique foran axial stage should this type compressor be selected for the finalconfiguration.
While there is considerable information available concerningboundary layer control with axial compressors, there is almostnothing available concerning this subject in centrifugal,compres-sors .
The conical flow compressor is sufficiently different from con-ventional compressor design to warrant a somewhat closer examinationof the boundary layer techniques. Obviously, this examination willhave to draw extensively on related experience in axial compressorswith consideration given to the larger radius change associated withthe conical design.
In a recently completed program for NASA (Contract No. NAS3-14306), two forms of boundary layer control are built into the cen-trifugal compressor configuration. First, the centrifugal impelleris made up of separate inducer and impeller sections in tandem. Assuch, the configuration can be adjusted to discharge the inducer flowfrom the inducer pressure surface to energize the suction surfaceboundary layer on the downstream impeller. The second boundarylayer control mechanism incorporated in this design is wall suctionon the impeller shroud at two meridional locations and suction onboth walls in the diffuser between stages of a cascade diffuser.These can be employed singly or in any desired combination. Both
42
concepts of boundary layer control look quite feasible forapplication to centrifugal compressor stages. However, experimentalevaluation of the effectiveness of these techniques has not beenestablished at this time.
In recent years, boundary layer removal from the junction ofthe convex stator surfaces and the convex inner wall of compressorand turbine casings has been found to be economically feasible(Reference 13 and unpublished American and British industrial data).Withdrawal of one percent or less of the flow through narrow slotshas been found to improve performance.
The rotor and stator of the conical-flow first-stage compressorhave been examined to determine the most logical location for bound-ary layer control slots. The junctions of the convex blade surfacesand the disks (or platforms) of rotors 1A and IB are logical candi-dates for boundary layer removal, but these zones experience arelief due to the presence of the blade, the wall slope, and rota-tional effects. For a given level of diffusion, the rotor blade-disk junctions appear to be less critical than stator-casing inter-sections.
Spanwise boundary layer flow along the conical-flow rotorblades will be proportionately stronger than along axial blades dueto the sweep of the blades adding to the normal outward forces onaxial-blade boundary layers. If this outward flow is sufficient tointerfere with proper performance of the outboard region of tandemrotor IB, fences attached to rotor 1A blades near mid-span shouldbe considered. Such fences would discharge the excess boundarylayer, near mid-passage. Energy addition to this wake-fluid wouldbe rapid from the surrounding free-stream. The flow into the tip-section of rotor IB should remain strong, since shock losses willbe low due to the use of only moderate Mach numbers relative to theblades. Tip clearances can be held to low values through the useof soft, abradable inserts in the shroud, so tip clearance flowscould be kept small.
The stator blades will not experience relief due to rotation,but will inhibit spanwise flow of low energy fluid if swept. Toprevent separation and the generation of excessive quantities oflow energy fluid, small narrow slots at the critical convex-blade/convex-wall chord length, located toward the rear, and sized toremove about 0.5 percent of the flow at design speed.
43
SIZE AND WEIGHT CONSIDERATIONS
In a volume and/or weight limited system, the axial-centrifugalstage combination would seem to offer a potential advantage over theother stage combinations under consideration. Obviously this is aresult of the small stage diameter and relative stage length associ-ated with the axial inlet stage. .
An overall summary of the pertinent stage dimensions and a rela-tive stage weight comparison is presented on Table VII. This tab-ulation includes the maximum diameter and length of each stage andboth stages together for the three compressor combinations consid-ered herein. Diameters for the centrifugal stages have beenadjusted to account for the design as it would appear in an actualengine configuration. In an engine, the diffuser for the centrif-ugal stage would normally be divided between two stages. The ini-tial diffuser would be oriented radially and diffuse to an inter-mediate Mach number (M 0.35). Then the flow is turned to an axialorientation where further diffusion takes place. It was felt that amore valid size comparison could be made by.comparing>each config-uration as it would appear in an actual engine installation. Alsoincluded on table VII is a relative weight comparison for the com-bined- compressor stages above (not a complete engine), where.theweights are normalized to the weight of the two centrifugal stagesin series. These weights are estimated from existing1hardwarewhere applicable with considerable scaling involved. Because of theapproximate nature of the weight estimates it was felt that thisinformation could best be presented on a relative basis. Additionalsize and weight of inlet guide vanes, actuator and control, normallyrequired for off-design operation and starting of an axial-centrifugal combination, have not been included in this comparison.
The size comparisons show the axial-centrifugal stage combina-tion will fit in a smaller diameter and have a shorter stage lengththan the other combinations. As a result, the axial-centrifugalstage combination also weighs less than the other designs. On arelative weight basis, the axial-centrifugal stage combinationweighs about 18 percent less than the two-stage centrifugal combina-tion. These weights are representative of the impellers, stators,housings, bearings, shaft, and transition section for'both compres-sor stages. The effect of the compressor configuration on theremaining engine component weights has been neglected.
The conical-centrifugal can be fit into a smaller diameter thanthe two-stage centrifugal combination because of the \kidth of thetransition section on the latter configuration. Stage length forthe conical-centrifugal stages is greater than for the other twocases. However, the stage weight for the conical-centrifugal
44
TABLE VII.
ENGINE SIZE AND WEIGHT COMPARISON
1. First Stage
Max Diameter, in.
Stage Length, in.
2. Second Stage
Max Diameter, in.
Stage Length, in.
3. Both Stages
Max Diameter, in.
Combined Length, in.
4. Relative Weights
Two Stages
Axial
3.7
2.4
Centrifugal
7.0
1.1
<1J Axial-Centrifugal
7.0
3.5
(4)0.82
Centrifugal
9.0
2.8
Centrifugal
6.4
1.0
(2)^'Centrifugal-Centrifugal
9.0
3.8
1.0
Conical
6.94
2.7
Centrifugal
7.2
1.2
^Conical-Centrifugal
7.2
4.2
0.91
NOTE:(1)
(2)
(3)
Reference flowpath (see Figure 8)
Reference flowpath (see Figure 4)
Reference flowpath (see Figure 11)
^ Does not include inlet guide vanes nor actuator/control
45
combination. Thus it appears that the conical-centrifugalcombination would compare quite favorably with two centrifugalstages in series for a volume and/or weight limited system. Butthe axial-centrifugal stage combination still offers the most sizeand weight advantages of the combinations investigated.
46
IMPELLER EROSION CONSIDERATIONS
Foreign object damage (FOD) and performance degradation effectsdue to large amounts of sand, dust, and other foreign substances aresignificant factors that must be considered in the design of enginesfor aircraft installations. Various engine test programs and a USAFstudy (NASA Technical Report No. 54, Factors That Affect OperationalReliability of Turbojet Engines) conclude that centrifugal-type com-pressors afford inherently better protection from FOD and minimalperformance degradation when compared with axial-type compressors.
A comparison of power decay due to erosion is tabulated belowfor several engines that utilize axial compressors as compared toAiResearch T76 and TPE331 engines that employ centrifugal compres-sors :
Engine
T76(Centrifugal)
TPE331(Centrifugal)
T64(Axial)
T63(Axial)
OperatingPeriod
1600 hr
1000 hr
400landings
10 hr
50 hr
PowerDecay
Percent
1.35
5
14
5
10
Remarks
Data from. 0V-10A operationViet Nam(eightengines)
Turbo-PorterSTOL roughfield oper-ation
CHS 3 PatuxentRiver tests
T-63-A-5AQualifica-tion Test(0.0015 gm/cu ft)
LOH TestData - Ft.Benning , Ga .
Source
Third QuarterlyProgress Report,AiResearch Docu-ment PE-8088-R2
"Turboprop Oper-ation in STOLAircraft" SAEPaper 680228
"Problems andSolutions forSand Environ-ment Operation"ASME Paper68GT37
"T63 Sand andDust Toler-ance " SAEPaper 670334
This illustrates dramatically the severe effect erosion can have onaxial compressor performance.
47
Blade configurations of the tandem rotors for the conical flowcompressor are similar to an axial rotor configuration. However,the inlet flow intersects the leading edge of the conical flowblades at a relatively steep angle producing a swept effect acrossthe blade rows. Sweeping the leading edge of an erosion specimen45 degrees or more has been shown to dramatically reduce the rate oferosion. Apparantly the effect of sweep is to convert the direct .impact of the hard particles to glancing blows. The acceleration-of the glancing particles, and the normal force developed due tothe collision is greatly reduced. For a given foreign particleconcentration, the number of impacts per unit leading-edge-lengthis reduced. In the case of transonic Mach numbers, the shock wavepreceding the swept leading edge produces a static pressure gradientwhich helps divert the particles, causing some to,miss the airfoiland to .increase the "glancing" angle. All of these factors tend toreduce the amount of erosion caused by hail, rain, sand, and dust.
Conventional transonic and supersonic compressors require verysmall radius, essentially sharp, leading edge to minimize thestrength and the extent of the detached bow waves and the aerody-namic losses associated with strong shock waves. Sharp edges aresubject to rapid erosion damage. The use of swept blades reducesthe Mach number normal to the.leading edge to subsonic values.Subsonic-type airfoils having larger leading edge radii can beemployed without suffering excessive losses. One method of explain-ing this behavior is to consider that the weak three-dimensionalshock which precedes the blade leading edge generates a pressuregradient which "forewarns" the air particles that a blade isapproaching and causes them to divert automatically. Thus, largerleading edge radii and thicker leading edge regions to support theimpact zone against local fracture are available. Therefore, it isquite possible that the conical flow compressor may show consider-able resistance to erosion and low FOB.
48
CONFIGURATION SELECTION
The axial-centrifugal stage combination appears to offer theleast potential advantages for this application. Examination ofthe two-stage performance results showed this combination is theleast efficient of those considered. The low efficiency isdirectly attributable to the second-stage centrifugal compressorwhich operates at a low design specific speed. There could also bestage compatibility problems associated with the axial-centrifugalstage combination. First, diffusion is required between the stage,in the transition duct, and at off-design operation, a definiteneed for variable inlet guide vanes in front of the axial stage forstart-up and low speed operation is indicated. Engine size andweight considerations would favor the axial-centrifugal combinationin a volume and/or weight limited system. However, for the appli-cation considered, the axial-centrifugal compressor is least fav-orable based on performance potential, susceptability to foreignobject damage, and potential stage compatibility problems.
The centrifugal-centrifugal stage combination clearly showedhigher design performance than the axial-centrifugal stage combina-tion but somewhat less performance potential than the conical-centrifugal stage combination. In the stage compatibility compari-son, the centrifugal-centrifugal stage combination and conical-centrifugal stage combination were essentially identical. In avolume limited system where compressor diameter is a concern, theconical-centrifugal stage combination may also have a slight weightadvantage over the centrifugal-centrifugal stage combination. Froman erosion and foreign object damage standpoint, the conical com-pressor is probably better than a typical axial but inferior to acentrifugal.
With all criteria considered, the conical-centrifugal wasselected to meet the objective of this contract primarily becauseof its improved performance potential. Therefore, the mixed flowor conical flow compressor was subjected to the detailed designanalysis discussed in the subsequent sections of this report.
49
GENERAL DESIGN LOGIC
The logic used in the calculation of blade shapes for theconical compressor is diagramatically presented in Figure 15. Thevarious calculation procedures encompassed by the logic are dis-cussed in the following paragraphs. Details of the various programinput requirements .and selection of blade element airfoil sectionswill be given in ensuing sections.
The air inlet and exit vector triangles were calculated in theoptimization study using the non-isentropic, radial equilibriumprogram. This calculation has been referred to as the across-the- .blade solution, where calculations were made just outside of theleading 'and trailing edges of each blade (and vane) row. Thedetailed blade shape design uses the same program with calculationsmade inside of each blade row. This is referred to as the through-the-blade calculation. Each rotor blade was designed separately,i.e., the aerodynamic calculations were made with only one rotorblade in the flow field. This was done for expendiency. However,the stator vanes were analyzed aerodynamically in tandem. When allblade shapes were finalized, a through-the-blade solution was madewith all blades in place. This was done to evaluate the aerody-namic interaction between blade rows.
A second aerodynamic calculation program, referred to as ablade-to-blade calculation (also. Katsanis), was used for the two-fold purpose of calculating inviscid flow deviation at the bladeexit, where applicable, and the rate of change in angular momentum.along each axisymmetric stream surface through a blade. Both resultsare used (except as noted) in the through-the-blade calculation.Details of this calculation procedure are contained in Appendix D.
Both the through-the-blade analysis and the blade-to-blade ana-lysis require a definition of the blade geometry. This informationis obtained,from a blade stacking program. The function of thiscalculation procedure is to take the specified aerodynamic bladeelement along each stream surface of a given blade and generatestacked blade properties for both aerodynamic programs. Details ofthis calculation procedure are contained in Appendix B.
From the across-the-blade calculation, initial setting of eachblade element leading edge is made, based on incidence angle cri-teria. The blade element deviation angle is estimated from Carter'srule. A specification of the aerodynamic blade element shape canthen be wade for input to the blade stacking program. A through-the-blade calculation is now made with initial assumptions of theloss, aerodynamic blockage, and energy distributions.
50
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The thermodynamic properties along each axisymmetric streamsurface from the through-the-blade calculation are used to calculatea stream-surface height distribution from inlet to exit of the bladerow. This distribution of stream-surface height, along wi.th thedefinition of blade suction and pressure surfaces bounding thestream surface, are input to the blade-to-blade calculation. Theinviscid deviation calculated by the blade-to-blade program addedto an estimated viscous deviation (see Appendix A) is now comparedto the across-the-blade vector triangle (for each streamline). Theblade element camber is then changed by the amount of the differ-ence. Also, the energy addition distribution is adjusted, whereapplicable, according to this calculation.
A revised blade shape is then calculated with the blade stack-ing program. The through-the-blade analysis is then rerun with thenew blade shape and energy distribution. This iterative loop iscontinued until the through-the-blade vector triangles agree rea-sonable well with the across-the-blade solution. The blade is thenchecked for choke flow margin and a stress analysis performed.
The final individual rotor blade designs and the tandem statordesign were then analyzed in a full through-the-blade calculation.In this way, blade interactions attributable to streamline slopeand curvatures effects were established. Ideally, blade designsshould then be adjusted if significant difference exist between theinlet and exit vector diagrams from the individual designs comparedto the complete solution.
52
ROTOR AND STATOR GEOMETRY SELECTION
The performance of each rotor blade row and stator vane row isstrongly dependent upon the selection of aspect ratio and solidity.The blade element aspect ratio, defined as
AR = mean blade height/mean chord
requires rotor blade and stator vane chords to be quite small if theaspect ratio is to be within the limit of current experience. Forrotors and stators, a lower limit for aspect ratio is 1.25. Aminimum chord length value acceptable to stress and manufacturingcriteria is approximately 0.5 inch. For rotors, chord length may beadjusted upwards for stress reasons, depending upon the aspect ratioselected.
As the flow path height is contracted through each blade row tomaintain acceptable meridional velocity ratios and D-factors, theaspect ratio is no longer under control of the designer. Hence, theaspect ratio of rotor IB and stators 1A and IB was considerably lessthan desired. For this reason, blade element losses used in theanalysis tend to be optimistic and must: be verified by an experi-mental test program.
Rotor 1A tip solidity was selected to be consistent with currentAiResearch design experience for transonic rotor blading. Rotor IBrequired twice the number of blades 1A to account for radius increaseand a decreased chord length. Stator solidities were selected togive acceptable blade loadings while being maintained within currentdesign experience.
Selection of the type of airfoil section to be used along eachaxisymmetric stream surface of a given blade was determined by theinlet relative Mach number. These section types were subject tomodification if the resultant blade loading was not satisfactory.In rotors 1A and IB, a combination of multiple circular arc (MCA)and double circular arc (DCA) sections were used. Double circulararcs were used throughout both stator vane designs. A general MCAsection with pertinent parameters required for definition is shownin Figure 17. Upper and lower surfaces and meanline are made up ofarcs which have tangency at the point of maximurh thickness. The DCAsection is a specific form of the MCA section in which the maximumcamber rise and maximum thickness occur at 50 percent of the chordlength and the camber is distributed uniformly along the entire mean-line. Parameters required for specification of a section are totalcamber ($), maximum thickness, location of maximum thickness, amountof front (or supersonic) camber, and leading edge meanline direction.
53
DETAILED AERODYNAMIC DESIGN
The section will cover in detail the aerodynamic design of theinlet stage of the conical-centrifugal compressor, the interstage ductbetween the conical flow inlet stage and the centrifugal second stage,and the drive turbine for the proposed research package.
; General
As seen in the discussion of the design logic, three computerprograms were required to .design each blade. To carry out a through-the-blade, non-isentropic radial equilibrium calculation, an initialestimate of the blade geometry was required for stacking the blade.For this design, six streamlines were used in each blade design ana-lysis.
Experience at AiResearch and elsewhere (Reference 14 ) indicatesthat for supersonic relative Mach numbers, the leading edge suctionsurface should be made parallel with the inlet relative air angle (0°incidence). As the Mach number decreases below 1.0, the suction sur-face incidence (i) was decreased to -2.0 degrees. At the blade trail-ing edge, deviation (6) was initially estimated using Carter's rule.'The total amount of blade element camber along the streamline can thenbe calculated from
«•= (3xr - B2') -i + 6
Ensuing iterations used the value calculated by the blade-to-bladeplus a viscous correction, where applicable.
With the airfoil shape, position of each surface (r, Z) andstack axis specified, a blade shape can be calculated. For all bladesin this design, the blade leading and trailing edges were held fixedin the meridional view with sections stacked on their respective cen-ter of mass in the circumferential direction only (Appendix B). Thiscalculation provided input of blade geometry for the through-the-bladeanalysis and blade-to-blade analysis.
Additional information needed in the through-the-blade calcula-tion are the rate of change in the angular momentum, distribution ofthe loss, and distribution of the aerodynamic blockage along eachstreamline. For blade rows operating with supersonic relative inletMach numbers, the angular momentum change was approximated for alliterations by a sinusoidal function of axial length given by:
r V - r, V , : ,.1 ul = sinA
r2Vu2 - rl Vul
54
The value of A was varied from 2.0 to 1.50 based on previous designexperience. The initial estimate of angular momentum distributionfor streamlines with subsonic inlet relative Mach numbers was linear.In subsequent iterations, the distribution resulting from the blade-to-blade solution was used. The loss and aerodynamic blockage weredistributed linearly with axial distance for all blade rows. The lossvalues were held constant on the basis that the final through-the-blade calculation would give the same diffusion factors as the across-the-blade solution.
55
Rotor 1A Design
The final rotor 1A design parameters, are as follows:
Corrected flow, Ib/sec 2.0
Tip diffusion factor . 0.443
Tip relative velocity ratio 0.7068
Inlet hub/tip ratio 0.45
Tip relative Mach number 1.26
Aspect ratio 1.028
Tip solidity 1.34
Number of blades 20
Figure 16 shows a meridional view of the final blade shape.Radial equilibrium calculation station lines are shown along withstraight line approximations of the six streamlines on which eachairfoil section was specified for stacking the blade. Details ofthe final airfoil sections specified along each of the conicalstream surfaces are contained in table VIII. Figure 17 provides aschematic representation of symbols used to describe the airfoilsection.
Selection of the airfoil sections used along each axisymmetricstream surface of rotor 1A was initially based on the inlet relativeMach number shown in figure 18. The multiple circular arc (MCA) typewas used for all streamlines except the hub. Here an MCA meanlinewith an arbitrary thickness distribution was used to adjust the load-ing as discussed at the end of this design section (figure 19).
A comparison of the resulting and design minimum loss incidenceangles are presented in figure 20. The two angles are not the samedue to changes which occurred in the meridional velocity distributionat the rotor leading edge during the design iteration. The differ-ence from design intent was deemed acceptable on the basis of thelower relative Mach number at which the maximum difference occurred,i.e., the low loss incidence range is somewhat wider for that Machnumber level. Also shown are the incidence angles based on the com-plete through-the-blade solution.
56
RADIAL EQUILIBRIUMCALCULATION STATIONS
STREAM FUNCTION,
1.0
0 0.2 0.4AXIAL LENGTH, IN.
0.6
Figure 16.- Meridional Flow Path for Conical FlowCompressor, Rotor 1A.
57
MlREL
TABLE VIII.
BLADE SETTING FOR ROTOR 1A
(Air) BI(Blade)
Shroud0.90.750.50.25Hub
1.2561.2141.1531.0350.8650.585
59.9559.8059.2158.1358.1054.82
57.7256.9355.8354.57 -53.7749.79
2 .222.873.383.564.335.03
1:LSS~3lMC
2.653.073.704.725.848.08
LE
0.0070.00750.00810.00950.01160.0178
6 2 (Air) 2 (Blade) TE
Shroud0.90.750.50.25Hub
55.7855.4453.9750.6644.3128.95 ;
50.5450.15 .49.1144.8935.2514.76
5.245.294.865.779 . 0614.19
0.00810.00820.00860.00980.01100.0140
0.03950.04230.04700.05500.06300.0850
a/CT
Shroud0.90.750.50.25Hub
0.8520.8540.8470.8390.8600.825
7.186.786.72
. 9 .6818.5235.03
0.730.680.610.530.500.45
0.150 . 2 40.370 .480.500.55
,342,383,438,562,841
2.265
58
TOTALCAMBER.
X
s.s.CAMBER
SPACING (*
32 (BLADE)
MAXIMUM THICKNESS
MAXIMUMCAMBERRISE LOCATION(a)
Figure 17. - Multiple-circular-arc airfoil description.
59
W
0
1.4
1.2
1.0
0.8
> 0.6HEH
0.4
0.2
0
ROTOR 1A
ROTOR IB
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.4 2.6
RADIUS, INCHES
Figure 18. Inlet Relative Mach Number For; . - • • Rotors' 1A and IB.
60
1.0
0.8
rte
0.6
w 0.4
u
EH
0.2
0 0.2 0.4 0.6 0.8
FRACTIONAL CHORD LENGTH, L/CT
Figure 19. Final Thickness Distribution ForRotor 1A Hub Section.
1.0
61
THROUGH-THE-BLADE (DESIGN)
Q THROUGH-THE-BLADE (COMPLETE)
DESIGN INTENT
TIP 0.8 0.6 0.4
STREAM FUNCTION
HUB
Figure 20.- Design Incidence Angles for Rotor 1A.
62
Final design deviation angle is shown in figure 21. These valueswere calculated to satisfy the angular momentum addition criteria fromthe across-the-blade analysis. As seen from the comparison of inletand exit relative air angle distributions (figure 21), a differenceexists between the across-the-blade analysis exit angle and those fromthe final through-the-blade design. The difference arises from intro-ducing the blade into the flow field solution. Also included is thedeviation calculated from the complete through-the-blade flow solution.The difference was insignificant implying virtually no blade interac-tion based on the analytical model.
The aerodynamic and blade blockage distributions used in.thethrough-the-blade analysis along shroud, 50-percent flow and hubstreamlines are shown in figures 22 and 23. Aerodynamic blockagealong each streamline was distributed linearly with meridional dis-tance, while the radial distribution (at each station calculation_lihe)_was_held_cons±ant.._____ .
The distribution of angular momentum normalized to a referencevelocity for the through-the-blade analysis is shown for all stream-lines in figures 24 and 25. The hub and 25-percent streamline dis-tributions were taken from the blade-to-blade Katsanis solution whilethe remaining streamlines used the sinusoidal distribution discussedpreviously on Page 54 because of their supersonic velocities.
A comparison of calculated diffusion factors at the rotor bladetrailing edge for the preliminary across-the-blade solution and thedesign through-the-blade solution are shown .in figure 26. Agreementis good except at the hub streamline.. This difference was notaccounted for due to the approximate nature of the estimated loss.
Only one blade loading is presented for Rotor 1A. This loadingcorresponds to the hub streamline and is shown on figure 27. Theblade surface velocities were obtained from the blade-to-blade pro-gram. The resultant loading for the hub section streamline, whileconsidered satisfactory for design purposes, has some undesirablefeatures that could not be corrected in the time available for thisdesign. One problem area associated with this loading is that themean velocity initially accelerates and then diffuses quite rapidlytoward the blade exit. It would be desirable to minimize the velo-city peak. However, an adjustment of this condition may have anadverse influence on the total flow field, requiring considerableredesign to achieve the desired overall design intent.
The final step in the aerodynamic design of Rotor 1A involved athroat area check for each streamline to insure that the rotor willpass the design flow. This calculation is approximate in that meanflow properties and a constant height are employed to calculate flow
63
14
CDWQ
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o
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12
THROUGH-THE-BLADE (DESIGN)
D THROUGH-THE-BLADE (COMPLETE)
TIP 0.6 0.4STREAM FUNCTION
Figure 21.- Deviation Angle Agreement for Rotor 1A.
64
1.00TIP STREAMLINE
TOTAL BLOCKAGE
50% STREAMLINE
^__ TOTALBLOCKAGE
-0.2 0 0.2 0.4 0.6
MERIDIONAL DISTANCE, IN.
Figure 22.- Blockage Distribution for Rotor 1ATip and 50% Streamline.
65
HUB STREAMLINE
IAPL,
oH
1.0
0.96
0.92
0.88
0.84
0.80
0.76
0.72-0.2 0 0.2 0.4 0.6
MERIDIONAL DISTANCE, IN.
0.8
Figure 23.- Blockage Distribution for Rotor 1A Hub Streamline.
66
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TIP
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•<•>THROUGH-THE-BLADE (DESIGN)
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STREAM FUNCTION
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Figure 26.- Diffusion Factors for Rotor 1A.
69
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600
500
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SUCTIONSURFACE
PRESSURE SURFACE
0 0.1 : 0.2 0.3 0.4 0.5 0.6 0.7
MERIDIONAL DISTANCE, IN.
Figure 27.- Final Blade Loading for Rotor 1A Hub Streamline.
70
areas at a particular meridional streamline location. The passagewidth is obtained geometrically. Obviously, this does not accountfor secondary flows and/or warped stream surface thicknesses thatare known to exist in the real case. In essence, the throat areacheck made here uses one-dimensional flow properties with areachange to calculate the minimum passage area along a particularstreamline.
Results of the throat area check for all the streamlines inRotor 1A are presented on figure 28. These are shown as the flowarea divided by the critical area for qhoked flow versus meridionaldistance along each streamline. Note th,at the first four stream-lines indicate a choke margin of 2 pe'rcent or greater and that thethroat location moves from the middle of the blade to near the lead-ing edge going from the blade tip to the 50»-percent streamline.
71
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72
ROTOR IB DESIGN
The final rotor IB design parameters are as follows:
Corrected flow, Ib/sec 1.225
Tip diffusion factor 0.493
Tip relative velocity ratio 0.655
Inlet hub/tip ratio 0.746
Tip relative Mach number 0.981
Aspect ratio 0.84
Tip solidity 1.57
Number of blades 40
The final meridional shape is shown in figure 29. Also includedare the through-the-blade calculation stations and final streamlinepositions. Details of the final airfoil sections specified alongeach of these axisymmetric stream surfaces are contained in table IX.
The rotor IB inlet relative Mach number, distribution is shown infigure 18. For this range of Mach numbers, the double circular arcmeanline was selected for initial through-the-blade analysis. Thisselection was subsequently changed to the more general multiple cir-cular arc to adjust blade loadings and to shift flow streamlines.The flow streamline shift was required to match, as closely as pos-sible, the across-the-blade inlet and exit vector diagrams.
A comparison of design intent incidence angle and the resultingthrough-the-blade values are shown in figure 30. The two values donot agree perfectly, again due to the change (from the across-the-blade calculation) through-the-blade solution. However, the differ-ences were judged acceptable based on the calculated loadings fromthe blade-to-blade program and the wider loss versus incidence char-acteristic associated with the lower Mach number level.
73
2.6
2.5
2.4
2.3
S 2.2
DHQ
2.1
2.0
1.9
1.8
1.70.3 0.4 0.5 0.6 0.7
ARBITRARY AXIAL LENGTHFigure 29.- Meridional Flow Path of Rotor IB.
0.8 0.9
74
MlREL
TABLE IX.
BLADE SETTING FOR ROTOR IB
PI(Air) Pi(Blade) i plss-plMC "LE
Shroud0.90.750.50.25Hub
.*
Shroud0.90.750.50.25Hub
0.9810.9650.9550.8880.7840.624
82 (Air)
57.2353.8150.1245.4137.7427.61
55.54.54.52.50.47.
025438678985
53.0452.0651.0049.6447.0043.92
62(Blade)
49.48.46.40.30.15.
897458096578
7535711
1.2.3.3.3.4.
6
.34
.07
.54
.32
.09
.83
984838038912
000000
3.082.002.603.835.344.17
TE
.0066
.0075
.0086
.011
.0132
.0144
0.00600.00640.00700.00800.00900.0116
t /Cmmax' T
0.0350.03920.04620.05860.070.0866
Shroud0.90.750.50.25Hub
0.572 „0.5680.5660.5600.56250.6027
3.153.324.429.5516.3528.14
a/Cn
0.5830.5700.5540.4830.4660.465
0.250.3450 .4270.6250.740.81
1,1,
487, 4 9
1.53259707
1.973
75
OTHROUGH-THE-BLADE (DESIGN)
QTHROUGH-THE-BLADE (COMPLETE)
wQ
0)-d
CO.
W
WO3WQHUaH
TIP 0.6 0.4
STREAM FUNCTION
HUB
Figure 30.- Design Incidence for Rotor IB.
76
The final design deviation angles are shown in figure 31. Thesevalues were calculated to give the correct angular momentum changeacross the second rotor blade. As seen from figure 32, the exitrelative air angles from the across-the-blade solution do not agreewith those from the final through-the-blade design. The trends areidentical to those of the rotor 1A design. Also included are thecomplete through-the-blade values. Agreement is very good whichassures the correct energy condition.
Final aerodynamic and blade blockage distributions are shown forthe shroud, 50-percent flow, and hub streamlines in figures 33 and 34,The aerodynamic blockage was distributed linearly with streamlinemeridional distance and held constant across each calculation stationline.
For rotor IB, since all inlet relative velocities were subsonic,distribution of angular momentum from the blade-to-blade program wasused for all streamlines. The final design distributions for theshroud, 50-percent flow, and hub streamlines are shown in figures 35,36, and 37.
A comparison of across-the-blade diffusion factor distributionat rotor IB exit to the final design solutions is shown in figure 38.Small differences exist across the entire blade. However, these dif-ferences were not felt to be significant enought to change the orig-inal loss values.
77
OTHROUGH-THE-BLADE (COMPLETE)
wQ
TJ
ca
CO.
W
sH
20
15
10
TIP 0.8 0.6 0.4
STREAM FUNCTION
0.2 HUB
Figure 31.- Rotor IB Final Design Deviation Angle.
78
wQ
ca
*,
W
a
TIP
£ ACROSS BLADE ANALYSIS0 THROUGH-THE-BLADE (DESIGN)
g THROUGH-THE-BLADE (COMPLETE)(ALL BLADE ROWS)
INLETAIRANGLES
0.8 0.6 0.4
STREAM FUNCTION
HUB
Figure 32.- Comparison of Rotor IB Relative Air Angles
79
BL
OC
KA
GE
FA
CT
OR
Aeff
/Ag
eo
DO
OM
t •
•-J
00
VD
O \
^ - -"
SHRC
'
••/"" ^^
\-AERC(TOT
UD»
0
+BLADEAL)
0.5 0.6 0.7 0.8 0.9 1.0 1.1
u o< (U
o
rPQ
1.0
0.9
0.8
0.750% STREAMLINE
0.5 0.6 ... 0.7 ,0.8 0.9
MERIDIONAL DISTANCE, IN.
1.0 1.1
Figure 33.- Rotor IB Blade Blockage Distribution.
80
HUB STREAMLINE
0.7 0.8 0.9 . 1.0 1.1 1.2
MERIDIONAL DISTANCE, IN.
1.3 1.4
Figure 34.- Rotor IB Blade Blockage Distribution.
81
WHERE Ufc REF = 610 FT/SEC,
CK
4.0
1.6
3.2
2.8
2.4
2.0
1.6
NOTE: ANGULAR MOMENTUM DISTRIBUTIONCALCULATED BY KATSANIS.
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
MERIDIONAL DISTANCE, IN.
Figure 35.- Rotor IB Tip Streamline EnergyDistribution.
82
V7HERE U REF = 610 FT/SEC
3.6
3.4
fn
-3 Q2.8
2.4
2.0
1.6
NOTE: ANGULAR MOMENTUM DISTRIBUTIONCALCULATED BY KATSANIS.
0.05 0.1 0.15 0.2 0.25 0.3 0.35 9.4
MERIDIONAL DISTANCE, IN.x1*
Figure 36.- Rotor IB Fifty-Percent Streamline Energy Distribution.
83
owCO
oi-Tvo
W
flO•H•P3.Q•HH-PCO
•HQ
Q)CW
0)c
•HiHerd0)M-PCO
ffi
O-P0
co
0)
84
A ACROSS BLADE ANALYSISOTHROUGH-THE-BLADE (DESIGN)Q THROUGH-THE-BLADE (COMPLETE)
TIP 0.6 0.4
STREAM FUNCTION
HUB
Figure 38. - Comparison of Rotor IB ExitDiffusion Factor Distribution.
85
The final loadings from the blade-to-blade program for the shroud,50-percent flow, and hub streamlines are shown in figures 39, 40, and41. All distributions are uniform in their deceleration rate.
Throat area checks were made for each of the streamlines to pre-clude the possibility of rotor IB choking at the design condition.The minimum area ratio occurred for streamlines 1 through 4 at 1.04 ofthe minimum value. Streamlines 5 and 6 were had considerably moremargin.
A final comparison is the distribution of inlet and exit relativeair angles (Figure 32) as calculated by the initial across-the-bladeanalysis and by the two through-the-blade analysis. This result issimilar to that observed in the rotor 1A design.
86
W2
3EHW
Q
1Ken
ot
o
m•
o
on
in01
2H
-8-O EH<N CO
• 3 'Hin Q
«-H H• OS
ino
ooCM
oo
ooo
oo
oo00
oo
oo
0)
§ .M 0)fe -H
totJ^ >.C rH
•H idOJo
nl oH M
C (d•H rH
« OH EH
rl (1)o-o4J (0o Hpj CQ
I
CO
0)
Cn•H
'AJlI^o^aA aov^nns aovrra
87
Oo
Oo
ooo
oo
oooo
oo
0)fiEH
CO
(0o
0)
onPU
0)
fflIo
s-io
ffl
o• J"
a)
•HCM
AiioblaA aDV,3Hns
88
0]•H
S wo >»
d
C•H
zO H
O H
in01
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o01•
o
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§EHtoHQ
120HQH .OSHS • .
o tr>h^ O
fl) P4Ttnj a)
n mH
-H M .n> 1C O
• -rH EH
Q)CQ 'CJH rj
r->^
M «O4J Q)0 ^PJ EH
^J«
0)
CP••H
oas/j,,i 'AiiooiaA aovjnns acnng
89
TANDEM STATOR DESIGN
The final design parameters for stators 1A and IB are asfollows:
Stator 1A Stator IB
Hub inlet Mach number 0.845 0.423'
Hub solidity 1.891 1.63
Number of vanes 53 53
Aspect ratio 0.604 0.494
The meridional shape and calculation station locations are shownin figure 41a for the first row and figure 41b for the second row.Appendix B presents plots of the stacked blades and the section co-ordinators.
The distribution of inlet Mach number for both stators is shownin figure 42. For these levels of Mach number, double circular arcairfoils were used throughout both stator vane designs.
The design incidence angle for both stators, based on currentstator technology .(Reference 10), was -2.0 degrees to the suctionsurface. A comparison of the design intent to the final values isshown in figure 43 for both stators. Deviations from the designintent vary approximately :±2 degrees for stator 1A and from +0.8degrees to -2.0 degrees for stator IB. Time limitations preventedbetter matching with the design intent. However, the blade-to-bladeanalysis did not indicate excessive leading edge loadings.
The final stator deviation angles are as shown in figure 44.These values were required to achieve the correct amount of diffu-sion in each vane row. Air angles for the across-the-blade andthrough-the-blade analysis at the inlet and exit of each stator vanerow are compared in figures 45 and 46. Good agreement (within 1degree) was achieved at the inlet to each row whereas discrepanciesup to 3.0 degrees occurred at the exit of each vane row.
90
0 INTERMEDIATE THROUGH-THE-BLADE STREAMLINES(STATOR BLADE ONLY INPUT)
D FINAL THROUGH-THE-BLADE STREAMLINES(ALL BLADE ROWS INPUT)
2.41.0 1.1 1.2 1.3 1.4
AXIAL LENGTH (Z), INCHES
Figure 41a. - Meriodional Shape for Stator 1A.
90a
3.6
O INTERMEDIATE THROUGH-THE-BLADE STREAMLINES(STATOR BLADE ONLY INPUT)
Q FINAL THROUGH-THE-BLADE STREAMLINES(ALL BLADE ROWS INPUT)
CO
enE>HQ
2.91.6 1.7 1.8 1.9
AXIAL LENGTH (Z), INCHES
2.0 2.1
Figure 41b. - Meriodional Shape for Stator IB.
9 Ob
O O
H EHCO CO
DO
ro
CN•co
oCO
v CO-
CN O!3H
CO CO• D
00•o
CM
CN
VOt i
CM
in• .
CN
CN
COMO•Pn)-Pco
_W_O.1Ma)
^Ju
•P0)
CN
<uM
•rlCM
91
O STATQR 1AEJSTATOR IB
TIP 0.6 0.4
STREAM FUNCTION
0.2 HUB
Figure 43. - Design Incidence Angles For Both Stators.
92
TIP
ASTATOR 1A
OSTATOR IB
0.8 0.6 0.4
STREAM FUNCTION
0.2 HUB
Figure 44. - Design Deviation Angles For Both Stators,
93
70
A ACROSS-THE-BLADE (DESIGN)
O THROUGH-THE-BLADE (COMPLETE)
INLET
EXIT
TIP 0.6 0 .4
STREAM FUNCTION
HUB
Figure 45. - Comparison of Stator 1A RelativeAir Angles Between Initial andFinal Design: Solutions.
94
50
w§o"HQ
A ACROSS-THE-BLADE (DESIGN)
O THROUGH-THE-BLADE (COMPLETE)
INLET
'* 30
3 20
10
EXIT
TIP 0.6 0.4
STREAM FUNCTION
HUB
Figure 46. - Comparison of Stator IB RelativeAir Angles Between Initial andFinal Design Solutions.
95
Distribution of the aerodynamic and blade blockage for the tip,50-percent flow, and hub streamline for each stator vane are containedin figures 47 through 52* Aerodynamic blockage was again distributedas in the tandem rotor design.
The rate of angular momentum decreases through each of thestators as shown in figures 53 through 56. These values wereobtained from the blade-to-blade calculation. Complete deswirl ofthe air was not achieved by the second stator. However, the amountof remaining angular momentum was not considered detrimental to theperformance of a second stage.
Stator diffusion factors are compared in figures 57 and 58.Final 1A values for the design and complete through-the-blade ana-lysis are somewhat lower than the across-the-blade analysis. ForIB, however, the design and complete through-the-blade analysis arenot consistent due to streamline shifts caused by the rotor/statorblade interaction. Where the difference is largest, toward the hubin stator IB, the diffusion factor is less which is advantageous froma loss consideration.
Final stator loadings along the tip, 50-percent flow, and hubstreamlines for stators 1A and IB are shown in Figures 59 through64. The tip streamline loadings for both stators display the high-est loading near the leading edge due to the more positive incidenceangles. However, loadings are smooth and should provide acceptableperformance.
96
100TIP STREAMLINE
1.8 1.9 2.0 2.1
MERIDIONAL DISTANCE, IN.
2.2
Figure 4. - Stator 1A Blockage Distribution.
97
10050% STREAMLINE
751.8 1.9 2.0 2.0 2.1
MERIDIONAL DISTANCE, IN.
Figure 48. - Stator 1A Blockage Distribution.
98
100HUB STREAMLINE
95 AERO-O- <D
90w
w
w
8 85
80
2.3 2.4
\- BLADE + AERO
2.5 2.6 2.7
MERIDIONAL DISTANCE, IN.
2.8 2.9
Figure 49. - Stator 1A Blockage Distribution.
99
100TIP STREAMLINE
t2.4 2.6 2.7 2.8 2.9
MERIDIONAL DISTANCE, IN.
Figure 50. - Stator IB Bockage Distribution.
100
50% STREAMLINE100
2.6 2.7 2.8 2.9
MERIDIONAL DISTANCE, IN.
3.0 3.1
Figure 51. - Stator IB Blockage Distribution.
101
1.00HUB STREAMLINE
0.803.2 3.3 3.4 3.5
MERIDIONAL DISTANCE, IN.
3.6 3.7
Figure 52. - Stator IB Blockage Distribution.
102
w
in
H
§EHCO o
HCO
EHEn
i
OrHUD
II
W
H
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o•
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EHCO
CM H• Q
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rg•
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cn
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CO
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roin
(U
•HCM
103
w2H
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g
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fflDW
CMO
-rH-P
M-PCO
•HQ
UWCO
w3
™*
§EH10
0\°
inCM
u
EHto
OHQH
tr>H0CW0)C•H
0)M-P05
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*>oin
fM
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wa
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104
w13H
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CM
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uw
WJS
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tnM0)
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-H
EHfa EH
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c»O<Ti
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OHQH
i-iO-P(d-pen
w^
inm
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§EHen
PHHEH
CN•
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tn•H
105
UwCO
w3H
2E-<CO
COz>ffi
wa
E-iCO
c*PinCM
EMH
W WPS 3W H
"4
§
HCO
o\»Oin
m•
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vo•
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•* W• Uo a
COHQN. 'aoHQH
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CnM<])C!
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O4Jrfl
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I
VDm
0)
en•HEn
106
0.5
a-En-
§•HenD
0.4
W.
.0.3, TIP
O ACROSS-THE-BLADE ANALYSIS
nTHROUGH-THE-BLADE (DESIGN)
0THROUGH-THE-BLADE (COMPLETE)
0.8 0.6 0.4
STREAM FUNCTION
0.2 HUB
Figure 57. - Stator 1A Diffusion Factor•'."• " 'Distribution.
107
0.3
O ACROSS-THE-BLADE ANALYSIS
• Q THROUGH-THE-BLADE (DESIGN)
^THROUGH-THE-BLADE (COMPLETE)
TIP 0.8 0.6 0 .4
STREAM FUNCTION
0.2 HUB
Figure 58. - Stator IB Diffusion Factor Distribution.
108
O SUCTION SURFACE
D PRESSURE SURFACE
uww\HCM
><E-iH-UO.4
1100
1000
900 rn:
"80"0
g 700•" 4
2E>enw
>
600 —
500
400
0.1 0.2 0.3 0.
MERIDIONAL DISTANCE, IN.
0.5
Figure 59. - Stator 1A Loading - Tip Streamline.
109
O SUCTION SURFACE
D PRESSURE SURFACE
uwCO
OOJw
w
PiCO
H
1100
1000
900
800
700 r
600
500
400
0.1 0.2 0.3 0.4
MERIDIONAL DISTANCE, IN.
.5
Figure 60. - Stator 1A Loading - Mean (50%) Streamline
110
o SUCTION; SURFACED PRESSURE .SURFACE
1200
owCO
1000
1000
w
waCMa;DCO
w
600
500
.0 0.1 0.2 0.3 0.4
MERIDIONAL DISTANCE, IN.
Figure 61. - Stator 1A Loading - Hub Streamline.
Ill
O SUCTION SURFACE
D PRESSURE SURFACE
uwenEHfa
TY
r
BwSDen
w
700a\
cn o
<yi
o o
Ln tn o
Cn o o
•&•
Ln o
•£> o o
W ui
o
CO o o
0.1 0.2 0.3 0.4 0.5 0.6
MERIDIONAL DISTANCE, IN.
Figure 62. - Stator IB Loading - Tip Streamline.
112
O SUCTION SURFACE
D PRESSURE SURFACE
700
650
600
550 I
500
450
owenEHfa
XE-iHOO
w>wag£3enw 400
350
300
0.1 0.2 0.3 0.
MERIDIONAL DISTANCE, IN.
0.5 0.6
Figure 63. - Stator IB Loading - Mean (50%)Streamline.
113
O SUCTION SURFACE
D PRESSURE SURFACE
700
650
600
550
Ow
XEHH 500
8iWO
D
W
>
450
400
350
300
0.1 0.2 0.3 0.4
MERIDIONAL DISTANCE/IN.
0.5 0.6
Figure 64. - Stator IB Loading - Hub Streamline.
114
Boundary Layer Control
, The purppse of any boundary layer.control device is to prohibitflow separation from the confining walls. As a'result of the inher-ent diffusion for the compression process, the boundary layers withina compressor are subject to adverse pressure gradients and, there-fore, grow rapidly. Judicious design can minimize, but not elim-inate, this growth. One of the objects for using tandem rotors andstators is to start each blade row with a new boundary layer. Thispermits the mixing and re-energization of low energy fluid at sev-eral points within the stage. Another attractive technique forremoving boundary layers internal to the compressor stage is tobleed off fluid through the shroud or hub walls. Since these bound-ary layers grow continuously through the stage, a significant bene-fit should be possible. Location of bleed parts should be such thatboundary layer removal is accomplished prior to probable separationregions. The new boundary layer created by the removal of low energyfluid is then better able to withstand adverse pressure gradient conr-ditions, thereby inhibiting flow separation.
Analysis of the impeller boundary layers was accomplished aspart of the finite difference blade-to-blade program. The subrou-tine for computing boundary layer properties is based on the methodof Von Doenhoff and Tetervin (Ref. 11) as modified by Garner (Ref.12). This program uses the free-stream velocities along flow sur-faces, as predicted by the potential flow solution, to calculateboundary layer properties along streamlines. Flow separation issaid to occur at the location where the shape factor (H) is equal to2.2 <
In examining the blade row boundary layers, the hub and tipstreamlines are of primary interest since flow separation on theblade surface in these locations may influence conditions circum-ferentially across the end walls. The blade surface boundary lay-ers of interest have been plotted as curves (figures 65 through 71)with momentum thickness as a function of surface length. Resultsfor Rotor 1A are shown on figure 65. Only the hub streamline wasanalyzed here. The potential flow field for the tip section is notadequately defined from the standpoint of the actual shock struc-ture interval to the blade row to permit a valid solution of bound-ary layer conditions. The hub region of the first rotor does notindicate any regions of incipient separation. In general, the flowconditions exiting the first rotor should be sufficiently stablesuch that an external bleed system is not necessary prior to thesecond rotor.
115
10
5SUCTION SURFACE
^PRESSURE SURFACE
STABLE - NO SEPARATION—
10-4
0.2 0.3
SURFACE LENGTH, IN.
116
Figure 65. - Rotor 1A Blade Surface BoundaryLayers - Hub Streamline.
Blade surface boundary layers for Rotor IB are shown on figures66 and 67 for the tip and hub streamlines, respectively. Note that apossible separation condition is predicted along the blade suctionsurface for the tip streamline. This potential separation zoneoccurs near the trailing edge of the blade in a region which shouldhave little influence on the overall rotor performance. However,this might affect flow conditions entering the first stator row sothat it may be desirable to install a series of bleed ports in theshroud wall between the second rotor row and first stator row. Theconsideration here being that a separated zone or a region of lowenergy fluid could possibly propagate a stall condition within thestators, thereby seriously penalizing the pressure recovery in thisregion. Thus, provision will be made for the installation of bleedports on .the shroud wall between the second rotor and first statorrows to permit experimental evaluation of this potential problemarea.
Blade surface boundary layers on Stator 1A are shown on figures68 and 69 for the tip and hub streamlines, respectively. Both stream-lines- indicate the possibility of separation on the suction surfaceof the blade. This is not an unusual circumstance and is experiencedquite often with high turning stator rows in axial compressors. Infact, previous experience has shown good performance can be obtainedwith stator sections which are marginally stable with some portion ofthe blade exhibiting potential flow separation. A stator system wasdesigned and tested where the calculations indicated an even greaterseparated condition than indicated here. Stage performance was notdegraded for these stators, indicating either: (1) the separatedarea may have been localized to a small region on the blade followedby re-attached flow, or (2) the calculation may be in error such that ••separation is predicted prematurely. The instrumentation employed in :these tests was insufficient to evaluate the existence or extent offlow separation in the stator system.
Since both the hub and tip sections for the first stator indicatea possibility of separated flow, it seems advisable to include bleedports on both walls between the tandem stator rows. These should beset up to be operated either separately, or simultaneously with therotor bleed. The recommended bleed port locations for the first-stage conical compressor are shown on figure 70.
Boundary layer conditions for the hub and tip streamlines onStator IB are presented on figures 71 and 72, respectively, computedfor meanline loading. These results show a small region of possibleflow separation along the suction surface for both cases. The effectof a small separated region in this part of the blade should be mini-mal and, therefore, does not require a bleed system for boundary layerstabilization.
117
10
INCIPIENT SEPARATION
PRESSURE SURFACE?
'SUCTION SURFACE
0.2 0.3 0.4
SURFACE LENGTH, IN.
0.5 0.6
Figure 66. - Rotor IB Blade Surface BoundaryLayers - Tip Section Streamline.
118
10
PRESSURE SURFACE
SUCTION SURFACE
STABLE - NO SEPARATION
0.2 0.3 0.4
SURFACE LENGTH, IN.
0.5 0.6
Figure 67. - Rotor IB Blade Surface BoundaryLayers - Hub Streamline.
. • ly',i
119
wi01". w
{ U. H
§
INCIPIENT SEPARATION
PRESSURE SURFACE3
?SUCTION SURFACE
0.1 0.2 0.3 0.4
SURFACE LENGTH, IN.
0.5 0.6
Figure 68. - Stator 1A Blade Surface BoundaryLayers - Tip Streamline.
120
PRESSURE SURFACE
SUCTION SURFACE
100 0.1
0.3 0.4
SURFACE LENGTH, IN.
69 ' - ir l f* S«*-~ BoundaryStreamline. Layers -
121
BOUNDARY LAYERBLEED PORTS(3 PLACES)
•§ 2.0Mc
-0.5 0.5 1.0 1.5 2.0AXIAL LENGTH, IN.
2.5 3.0
Figure 70. - Recommended Location of BoundaryLayer Bleed Ports In ConicalCompressor.
122
10
53-
*CD
cnww
oH
•a
10-2
INCIPIENT SEPARATION!
PRESSURE SURFACE
SUCTION SURFACE
10-3
i
10-4
0.1 0.2 0.3 0.4
SURFACE LENGTH, IN.
0.5 0.6
Figure 71. - Stator IB Blade Surface Boundary Layers -Hub Streamline.
123
INCIPIENT SEPARATION
SUCTION SURFACE
PRESSURE SURFACE
100.2 0.3 0.4
SURFACE LENGTH, IN.
Figure 72. - Stator IB Blade Surface BoundaryLayers - Tip Streamline. |
124
The design of the transition duct is such that the initial passageis converged slightly prior to any diffusion. This should tend tostabilize the flow prior to the turning section in the transition duct.
The boundary layer bleed ports will consist of a series of 40holes, equally spaced circumferentially around the wall at each speci-fied location. The diameters of the bleed ports should be 3/32nd ofan inch, which will take a bleed flow ratio of two percent of the mainflow. For the boundary layer bleed system to show a favorable per-formance trade-off, it will be necessary to operate the bleed systemsat less than the design flow ratio (less than 2.0 percent). Optimumoperating conditions will have to be determined experimentally sincethere are too many unknowns to permit this problem to be solvedanalytically.
125
Inlet Flowpath Design
Analysis of flow conditions in the inlet duct employed an axisym-metric flow program to solve for the potential velocity field. Aboundary layer program was used to examine wall effects. Basically itis desirable to have the flow continuously accelerate throughout theentrance region to avoid excessive boundary layer buildup with thepossibility of flow separation. The analytical programs were employedto examine various duct shapes on an essentially trial and error basisto arrive finally at an acceptable entrance configuration.
The selected inlet duct configuration is shown on figure 73. Alsoincluded on this figure are several streamlines in the flow field andthe velocity distribution presented as lines of constant velocity.The upstream portion of their duct has several support struts whichpass through the flow field. The blockage of the struts has beenincluded in the potential flow calculations. This is evidenced by thehump in the velocity profile across the strut. The fact that thestruts have been placed in a relatively low velocity region tends tominimize their effects on the downstream flow field. The resultingvelocity distribution in the entrance duct looks quite satisfactoryfrom the standpoint of potential core flow calculations. Examinationsof the boundary layers along both walls also indicated a reasonablerate of boundary layer build-up with distance. A check of the result-ing displacement thickness calculations as affecting blockage indicatedthe aerodynamic blockages assumed in the potential flow calculationswere quite satisfactory. This final comparison then completed theanalytical examination of the inlet duct configuration.
126
H
wo
c/j
o0)(00)n04§o
(d Co o•H -HC -PO 3U A
•HM MO 4JIW (0
•H-P QO3 >iQ -P
•H-P O<D OrH iHC 0)H >
(U
•Id
'sniavH
127
Transition Duct Design
A cross-section of the final flowpath from the second row statorexit down to the inducer leading edge of the second stage compressoris shown in figure 74. The resultant surface velocities (for thedesign point) are presented in figure 75.
This design involved a trade-off between the area ratio distri-bution along the meanline and local wall curvatures to achieve huband shroud wall velocity distributions which minimized the possibilityof boundary- layer separation. The final design was made within geo-metric constraints of radius and axial distance fixed by the mechanicalconsiderations, and the aerodynamic constraint of a second-stage inletshroud to meanline velocity ratio consistent with current radial com-pressor design technology requirements. (The second-stage inducergeometry was obtained from a preliminary design discussed earlier inthis report•;)
A calculation of the boundary layer conditions was conducted foreach of the final hub and shroud wall velocity distributions. In eachcase, depending upon the assumed initial conditions of the boundarylayer, a region exists where the shape factor value, H, indicatesprobable separation. These regions are shown on the meridional flow-path view (figure 74). Due to the positive wall curvature in each ofthese regions, the centrifugal body force will act opposite to theadverse pressure gradient tending to hold the fluid to the wall andthe separated zone is expected to be small with rapid reattachment.
Considerable effort was expended in obtaining this situationsince some separation is inevitable because of the severity of thecurvature required to satisfy the envelope restrictions. The designis considered conservative in that the boundary layer blockage was notincluded in the flow-field solution. The inclusion of this blockagewould decrease the effective area and increase the velocity level, theincrease being greatest where the diffusion is greatest. This typesolution requires an iterative process between the boundary layer pro-gram and the radial equilibrium program. A time limitation preventedthis more detailed analysis.
The final configuration is representative of crossover ductscurrently in use on production engines at AiResearch.
128
4.2
3.8
3.4
3.0
H
, 2.6c/i!DH
2.2
1.8
1.4
1.0
STATOR TRAILING EDGE
REGION OFPOSSIBLESEPARATION
REGION OF.POSSIBLEJSEPARATION
•SECOND-STAGE: IMPELLER INDUCER-LEADING EDGE
2.0 2.4 2.8 3.2 3.6AXIAL DISTANCE, Z, IN.
Figure 74. - Transition Duct Size and Shape,
129
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Drive Turbine Aerodynamic Design
An existing radial inflow turbine design has been selected todrive the 10/1 compressor research rig. This selection is based onconsideration of power capability, mechanical integrity, and con-tractually stipulated turbine inlet conditions. Of the two candi-date drive turbines considered (radial and axial), the radial inflowdesign selected to drive the rig is superior in available power andmechanical integrity. It can also produce maximum power at lowerturbine inlet temperature and integrates well with the research rig.An aerodynamic design summary follows. The blading geometry isdefined in Appendix A.
Drive Turbine Aerodynamic Design Summary
The drive turbine for the NASA 10/1 compressor is required toproduce sufficient power to test the two-stage compressor to 110 .percent of design speed. The compressor design point used to sizethe turbine is as follows:
• Pr = 10.0 . '
W/e"/<S = 2.0 Ib/sec
nad = 0.805
N//0" = 70,000 rpm
Achievement of this design goal requires an input horsepower of 411and an overspeed power requirement of 547 horsepower based on thecubic power law. These horsepower requirements will be provided bythe following available energy source:
Maximum flow: 7 Ib/sec
Maximum T. : 1000°Rin
Maximum P. : 350 psia
Maximum P : 4 psia
From this energy source and the required overspeed of 77,000 rpm, anexamination of existing turbines was made to determine which, if any,could produce the required 547 horsepower at 77,000 rpm and notexceed the available energy source. As a result of the examination,a radial inflow turbine design was selected for use in the researchrig. The design point of the turbine is:
131
Speed, rpm: 81,800
W/6/6, Ib/sec: 0.474
P , T-T: 4.167
n, T-T: 89.7
AH/8, Btu/lb: 37.6
The performance of the selected turbine was tested in an actualsize cold air rig. The test results are given in figures 76 through82. Using the turbine performance test data, a computer model thatwould predict turbine performance at any desired operating point wascreated. Figure 78 shows the comparison between the measured per-formance and predicted performance based on the computer model. Theagreement shown in figure 78 and like agreement at other test speedsindicates that the computer model could reliably predict performanceat any operating condition. Using the computer model, a maximumpower curve for the radial turbine was generated for a range of com-pressor speeds and inlet temperatures. Figure 82 presents a carpetplot of this information and clearly shows that the required objectiveof 547 horsepower and 110-percent compressor speed can be obtainedwithout exceeding the facility limitations.
132
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Turbine Design Point
Despite the fact that the radial turbine will operate at higherthan design pressure ratios, the initial selection of design point wascritical to the proper prediction of the off-design performance. Thefollowing aerodynamic summary is based on the design point previouslygiven in the preceding section of this report.
Figure 83 presents a vector diagram of design point, figures 84through 87 are loading diagrams at the hub, mean, and shroud stream-tube for the meridional shape shown in figure 88. The loading dia-grams present the nondimensional velocity ratios for the pressure,average, and suction surfaces of the blade as a function of percentmeridional distance. The symbols.used in figures 83 and 84 through 91are defined as follows:
Z - axial distance
R - radial distance
m - meridonal distance -
t - thickness normal to bladent - thickness tangential to blade ,
g_. -.blade angleD
6_ - blade tangential angle : . ...D
V - velocity
velocity of sound
based on stagnation temperature
T1 - stagnation temperature
T" - relative stagnation temperature
The objective of utilizing loading diagrams is to produce a geo-metry that will minimize blade surface diffusion while achieving thedesired blade circulation. Since actual cold air test data indicatesthat measured efficiency is very close to design efficiency, theobjective was achieved. The geometry required to produce these load-ings and efficiency is illustrated in figures 89 through 91. In thesefigures, the streamtube axial distance (Z) , radial distance (R), normal(t ) and tangential (t ) thickness, blade beta angle (3fi). and bladethita angle (6_) are presented as a function of percent meridionaldistance.
A complete geometrical description of the turbine wheel and nozzleis given in Appendix B.
140
AIRESEARCH MANUFACTURING COMPANY OF ARIZONAA DIVISION OF THE GARRETT CORPORATION
NOZZLE EXIT R = 3.1599 IN. 19 VANES
ROTOR TIP R = 3.0679 IN.
W/a ' = 0/287' cr= 0 .3063)
7.21°
0.036
ROTOR EXIT HUB R = 1.2500 IN.
= 0.334cr
-53.63'
|3R =-55.2'
W / a » = 0.556/ cr
U / _ , = 0.454' cr
vu/a, = o' cr
Figure 83. - Radial Turbine Vector Diagram (Sheet 1 of 2).
141
AIRESEARCH MANUFACTURING COMPANY DF ARIZONAA DIVISION OF THE BARRETT CORPORATION
ROTOR EXIT MEAN LINE R = 1.75 IN,
=-62.5°
0.334- 62.25°
U / a i = 0.636/ cr
= 0cr
ROTOR EXIT TIP , R = 2.183 IN.
=-67.6°
V, /a'x/ cr0.334
-67.13°
W a- = 0.827acr
U / a 1 = 0.793/ cr
Vu/a' = °u/ cr
Figure 83. - Radial Turbine Vector Diagram (Sheet 2 of 2)
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150
APPENDIX A ,
DEVIATION ANGLE DETERMINATIONFOR
CASCADE/'AI RFO.I LS
(32 pages)
DEVIATION ANGLE PREDICTIONFOR THE
CONICAL FLOW COMPRESSOR
The traditional approach to deviation or exit flow angle predic-tion consists of using an empirical rule derived from two-dimensionalcascade data. This rule is applied to a rotor by considering flow inthe relative plane and, in cases where there are significant variationsfrom two-dimensional conditions, corrections of one form or another toaccount for differences in meridional velocity ratio, radius change,and other three-dimensional effects have been applied.
Measurements on transonic compressors have indicated deviationangles near the rotor hub are larger than predicted by conventionaldesign rules which include correction factors. In cases where thereare large radius and meridional velocity changes in the rotor hubregions, it has been found that these conventional design rules areeven more deficient. This apparently is caused by the interactingeffects of radial and circumferential equilibrium and other effectssuch as secondary flows, hub blade boundary layer interaction, sweepeffects, and numerous other flow effects.
To account for the interacting effects of radial and circumfer-ential equilibrium on the prediction of deviation angle at the conicalflow compressor, the following analysis was used. A quasi orthogonalprogram was used to obtain stream sheet characteristics at severalradial locations. For each stream sheet and exit flow angle, a finitedifference program was used to compute blade loading. Iterations werecarried out on exit flow angle until the Kutta condition was achieved(the loading diagram at the trailing edge closed). For flow in therotor, a correction was still applied to account for other flow effects.A detailed description of this method is presented in the followingsection together with comparison experimental data.
BASIC CONCEPTS
Given a particular stream surface configuration (r as a functionof Z) , the prediction of deviation angle is equivalent to prediction oftotal turning and thereby the loading. Any technique to predict thistotal loading must first correctly predict the guided channel loadingand second, correctly handle the isolated airfoil (uncovered) regionsat the leading and trailing edge.
The following analysis is offered:
For the rotating blade row:
Cp (T' - T^) = u^V^ - r^)
Energy balance yields:
mC (T'- T') = / U (P - P ) bdmp i / P s
U = wr
m (U - u) = U (Pp - P8) bdm
m2ul / (Pp " VUj \ + U/U bdm
vu = wu + u
° = - U2
The Wm can be determined from continuity, thereby yielding theexit flow angle.
W vu V u - uU/Uu Wm U2 m W m
From this equation it can be seen that the problem of predict-ing ^2 rests with predicting the loading (Pp - Ps) through the rotor.For stationary cascades, a similar relationship can be derived from thetangential momentum equation.
It should be noted that the upstream and downstream values ofvelocity represented in the above equation represent an averaged (cir-cumferential) value of the upstream and downstream conditions. Inreality the flow conditions may vary circumf erentially. Secondly,the assumption is made that no flow crosses the axisymmetric stream
surfaces. This assumption is violated in the cases of warped streamsheets, in separated flow regions where flow migrates towards the tip,and in the blade boundary layers.
FINITE-DIFFERENCE TECHNIQUE
The traditional approach to exit flow angle prediction consistsof using an empirical rule derived from cascade data. This rule isapplied to a rotor by considering flow in the relative plane and makingcorrections of one form or another to account for differences inmeridional velocity ratio, radius change, and other three-dimensionaleffects. Since these corrections have not been verified experimentally,much rests on extrapolation from similar rotor designs to produce newdesigns. The recent advent of finite difference techniques for deter-mining blade-to-blade solutions allows for the development of anapproach more readily applicable to noncascade situations. Two suchcomputer programs currently are in use at AiResearch for obtainingblade-to-blade solutions. Both programs are restricted to subsonicflows with reasonably successful transonic corrections. The first isan outgrowth of the program developed by Katsanis and McNally (Refer-ence 1)* at NASA. The second is a program developed at AiResearch tohandle interactions between blade rows and other objects in the flowpath such as downstream struts. Because the periodic boundary condi-tions used in the Katsanis-derived program simplify the input require-ments, this program was used for the deviation angle analysis.
*Refer to Page 30 of Appendix A for the noted reference,
The basic equation used by this program is the stream functionequation:
S2,i, 1 1 Sp $f sina 1 & ( b p )' «-\ »"\ *\ *k k. f\ I _ •!_ «v "\—- S 1 I* ft2 fl2 -s 2 2 p B9 59 r bp dm dm
r
The boundary conditions for its solution are shown in Figure 1.As can be seen, they are of three types. At the upstream and down-stream boundaries, the flow angle is specified and assumed constantwith fl . The straight boundaries connecting the upstream and down-streamrboundaries with the blade, utilize the condition of periodicity.On these boundaries
il; = ilr, + 1. 'upper lower
The blade boundaries have specified values of stream function sincethe flow passing between them is known.
To use this technique, the angle on the downstream boundary isspecified and velocity distributions throughout the region and on theboundaries are calculated by a finite-difference relaxation techniquedescribed in Reference 1. This blade velocity distribution may takeon one of the three shapes indicated in figure 2. All three loadingsrepresent .valid inviscid solutions for the cascade. However, therequirement of satisfying the Kutta condition for an airfoil is basedon. viscous effects and compliance with this condition must be deter-mined on separate grounds. Reference 2 describes the Kutta conditionbasically as the inability of an airfoil to maintain continuous flowaround the sharp trailing edge. Because of the requirement for astatic pressure balance across the wake, velocities on the suctionand pressure surfaces must be equal at the trailing edge. This isequivalent to stating that the stagnation point, where the dividingstreamline leaves the blade, occurs in the trailing edge region.
The basic technique is then one of iteration where a variety ofexit flow angles in the vicinity of the expected exit flow angle arespecified until the one giving equal exit suction and pressure surfacevelocities is determined. In practice this is done graphically witha final computer run to verify the results at the determined exit flowangle.
PERIODICBOUNDARIES
CONSTANTFLOWANGLE
CONSTANTFLOWANGLE
Figure 1. - Boundary conditions for solution ofthe stream function equation.
V
m
SUCTION AND PRESSURESURFACE VELOCITIES
V
m
V
(LEADING EDGE
UNDERTURNEDFLOW
TRAILINGEDGE
KUTTACONDITIONSATISFIED
TRAILINGEDGE
OVERTURNEDFLOW
I TRAILINGI EDGE
m
Figure 2. - Inviscid cascade solutions.
ACCURACY OF TECHNIQUE
The accuracy of the finite difference technique is expected tobe influenced by the following factors:
(a) Accuracy of the inviscid solution for a given input
(b) Accuracy of the satisfaction of the trailing edge •Kutta condition
(c) Accuracy of input geometries, flows, etc.
(d) The effects of viscous flows
Since integration of the solution is all that is required, theaccuracy of the overall inviscid solution is expected to be excellent.To verify this point Carter's Rule can be analyzed for the effect ofgeometry on exit deviation angle (total turning). Since this tech-nique represents a fit to experimental cascade data, the effect oferrors in cascade parameter input and the accuracy of blade loadingsolutions for the finite-difference technique should be approximated.Carter's Rule is represented in Reference 3 as follows:
a)mc
The m- factor describes the effect of setting angle and geometry.figure 3 gives the dependence of geometry (max. camber rise point)and setting angle utilized by Reference 3. For an axial low speedcascade, equation 1 can be expressed in terms of the total turningin a cascade as follows:
( mc - 1) (a 4- £2) .+ a r-.£
6 = — — — — — ^—— — — — — — — —
where the angles are described in figure 4. Differentiating equation2 the result is
For a typical value of 6 of 10 degrees and m of 0.25
. Ap = -40 Amc
10 20 30 40 50
Blade-Chord Angle, y °, deg
60
Figure 3. - Coefficients for design deviationangle rule.
8
Figure 4. - Angle definitions.
To illustrate the use of this equation, if a 1-percent chorderror is assumed in specifying input geometry' (maximum camber risepoint), the error in the turning would be 0.15 degree for the valuesof 6 and mc given above. This leads to the expectation that inac-curacies due to errors in input geometry specification should beslight.
Utilizing the finite-difference technique requires determinationof the exit flow angle for which suction and pressure surface velo-city are equal. Due to the finite-difference nature of this calcu-lation, there is an uncertainty of the point of achievement of thisequality in velocity of one-mesh spacing. The inaccuracy caused bythis uncertainty in stagnation point can be evaluated as followsfor the cascade situation. Assuming a triangular loading (pressure)distribution typical of compressor sections, as shown below, theuncertainty in turning can be evaluated from simple areas.
Normal values of 1% range from 20 to 40 making this errorinsignificant.
Real flow effects are expected to be the largest source of error.As stated earlier, this form of approximating the Kutta conditionsconsists of selecting 0 that gives equal velocities at the trailingedge. Although the calculation differs slightly in detail, it isequivalent to the well-known technique used on isolated airfoilswhere the proper circulation is selected to give a dividing streamlineat the trailing edge. Viscous effects including the effects of suc-tion surface separation will modify the resultant lift. The magni-tude of these effects is expected to be similar to those experiencedwith isolated airfoils, where useful results can be obtained formoderate cambers at nominal angles of attack.
COMPARISON WITH EXPERIMENTAL CASCADE DATA
To verify the expected accuracy of the finite-difference tech-nique, the technique was applied to cases where experimental datawas available. The obvious starting place for this comparison is withtwo-dimensional cascade data such as that contained in References 4,5, and 6. This data provides the closest experimental agreement withthe analysis technique since no three-dimensional flow effects wereincurred. In addition, a variety of blade shapes are available foranalysis. For comparison purposes data was taken from three differentclasses of blade shapes as follows:
(a) Front loaded, A.K.*± D
(b) Mid-loaded A,_, circular arc
(c) Rear loaded, A2 !„,
10
UNCERTAINTY
M
A = C/N.m
where N is the number of mesh points between blade inlet and outletm
used in the finite difference calculation
A ' (A/C) AP maxAP Cmax
. ,—/C
= 1/N6 ' m
11
Eleven cases were examined in detail. These were selected tocover a range of setting angles, inlet Mach numbers, and bladeshapes.
Comparison with Carter's Rule was made utilizing the form of therule given in Reference 3 along with the M-factor curve shown inReference 3 and figure 3. The equations are:
B26- tan-1 U U
V
_ rr,
ml
2±_.
ml tan
m
Figures 5 through 10 show a comparison of turning angles and theratio of change in momentum to that given by a reference turningangle, (6 Ref) for experimental data, Carter's Rule, and the finite-difference technique. Figure 11 shows the geometric angle used forthe reference turning and the two approaches to Carter's Rule.
Equivalent leading and trailing edge angles were selected on thebasis of the angles shown in Figure 11. For a circular-arc camberline, the true leading and trailing edge angles are equal to theequivalent leading and trailing edge angles.
An attempt was made to correlate the differences between experi-mental and calculated (finite-difference method) deviation angles.No correlation was found with D- factor or other conventional tech7niques. Stewart's calculations were also utilized and they likewisedid not come close to predicting either magnitude or signs of theobserved differences. What did seem consistent was that the front-loaded blades 63(A^K^)06 and the 65(12Aio)10 mid-loaded blade shapesprovided consistently more experimental turning than calculated. Theheavily rear-loaded blades 65 (12A2 sb^ 10 an<^ tlie thickened circular-arc blade gave consistently less turning than calculated.
Figures 12 and 13 show the effect of Mach number on turning.As can be seen, Carter's Rule does not fit this data as well as othercases examined. Figure 14 summarizes the results on turning anglefor all cases examined. The inviscid calculation has indicated arelative error of less than 5-percent error in tangential momentumchange across the cascade. Although more comprisons to cascade datawould be desirable, the basic characteristics and accuracy of thefinite-difference method of predicting deviation angle have beendemonstrated.
12
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O EXPERIMENTAL DATA NACA RM L55J05
Q FINITE DIFFERENCE CALCULATION
CARTER'S RULE USING ACTUAL TRAILINGAND LEADING EDGE ANGLES
A CARTER'S RULE USING EQUIVALENTTRAILING AND LEADING EDGE ANGLES,
63(24A4K6)06
25 30
a (ANGLE OF ATTACK), DEGREES
Figure 5. - Turning angle versus angle of attack.
13
1.1
1.0
0.-9
0.8QH
o>01 0.7
0.6
0.5
0.420
EXPERIMENTAL DATA NACA RM L55J05I I I
FINITE DIFFERENCE CALCULATION
63 (24A4K6)06
i, = 30.0i.
a = 1.0
CARTER'S RULE USING ACTUAL TRAILING ANDLEADING EDGE ANGLES j . ~
CARTER'S RULE USING EQUIVALENT TRAILINGAND LEADING EDGE ANGLES
20 25 30
a (ANGLE OF ATTACK), DEGREES -
Figure 6. - Change in tangential momentum/ideal versus angleof attack.
14
30
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ACA RM L55
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EDGE AND LEADING EDGE ANGLES ,//
/,•/'
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Bx = 30.0
a = 1.0
10 20
a (ANGLE OF ATTACK), DEGREES
Figure 7. - Turning angle versus angle of attack.
30
15
1.1
1.0
0.9
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O P-7H
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0.6
0.5
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EXPERIMENTAL DATA NACA RM L55J05
Q FINITE DIFFERENCE CALCULATION
CARTER'S RULE USING ACTUAL TRAILINGEDGE AND LEADING EDGE ANGLESi , . iCARTER'S RULE USING EQUIVALENT TRAILINGEDGE AND LEADING EDGE ANGLES
10 20
a (ANGLE OF ATTACK), DEGREES
Figure 8. - Change in tangential momentuna/ideal versusangle of attack.
30
16
40
wwa;o .«30
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20
10
O EXPERIMENTAL DATA NACA RM L53B26AI I I
Q FINITE DIFFERENCE CALCULATION
CARTER'S RULE USING ACTUAL TRAILINGAND LEADING EDGE ANGLES_| _| : 1
CARTER'S RULE USING EQUIVALENTTRAILING AND LEADING EDGE ANGLES
65 (12A1Q)10
= 30.0
10 20
a. (ANGLE OF ATTACK), DEGREES
30
Figure 9. - Turning angle versus angle of attack.
17
O
o
1.2
1.1
1.0
2 0-9
0.8
0.7
0.6
0.5
O EXPERIMENTAL DATA FROM NACA RM L53B26A
1 1 1 ~0 FINITE DIFFERENCE CALCULATION
O CARTER'S RULE USING ACTUAL TRAILING ANDLEADING EDGE ANGLES
I I I I£ CARTER'S RULE USING EQUIVALENT TRAILING
AND LEADING EDGE ANGLES
10 20
a, ANGLE OF ATTACK ; DEGREES
Figure 10. - Change in tangential momentum/ideal versusangle of attack.
30
18
MAX CAMBER RISE POINT
e Ref = o, + 52eq/2
Figure 11.
19
30
25
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0 EXPERIMENTAL DATAFROM NACA RM L55108
I IQ] FINITE DIFFERENCE
CALCULATION
CARTER'S RULE USINGACTUAL ANGLESi i rCARTER'S RULE USINGEQUIVALENT ANGLES
65 (12A2I18b)10
a = 14.0
g. = 60.0
a = 1.0
0.2 0.3 0.4 0.5 0.6
MACH NO.
0.7 0.8 0.9
Figure 12. - Turning angle versus mach number.
20
25
cow 20
Op*
w
g 15
10Q EXPERIMENTAL DATA
NACA RM L55108El FINITE DIFFERENCE CALCULATION
0 CARTER'S RULE USING ACTUAL ANGLES
CARTER'S RULE USING EQUIV. ANGLES
0.2 0.3 0.4 0.5 0.6 0.7 0.8 .0.9
MACH NO.
Figure 13. - Turning'angle versus Mach No.
21
63-(24A4K6)06Reference 6Si = 30° a = 1.0
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL •
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
INVISCID
EXPERIMENTAL
.INV.ISCID
63-(24A4K6)06Reference 60! = 30° a = 1.0
63- (24A4K6) 06Reference 6
1 = 30" a = 1.0
63-(12A4K6)06Reference 6Bj; = 30° a = 1.0
63-(12A4K6)06Reference 6B = 30° a = 1.0
65-(12Aio)10Reference 4g = 30° a = 1.0
65-(12A10 UOReference 40! = 60° a = 1.0
10C4/30C5Reference 461 = )30° a = 1.0
65-(l!2AiQ )10Reference 5gj = :45° 0 = 1.5
m =0.308
65-(12A2Reference 5B i = 60 ° a = 1.0.a. = 8.0 mi = 0-458
65-(12A2I8b)10
Reference 53 ! = ' 60° a = 1.0a = 14.™ = °-298
10 20 30 40 50
Figure 14. - Total turning 8,
22
APPLICATION^.TO THREE-DIMENSIONAL SITUATIONS
Because ;of'the,more fundamental nature of the finite-differencetechnique when compared to techniques used in the past, one wouldexpect that much of.the uncertainty in determining deviation angle inaxial and mixed flow rotors could be eliminated. This expectation isclouded by two effects not considered by the present technique. Thefirst is the effect of Mach number at conditions where the criticalMach number is exceeded. The finite-difference technique describedherein does not provide rigorous inviscid.solutions where local Machnumbers are supersonic. This restricts the direct application ofthis technique to the hub sections of many .rotors. However, by appli-cation of this technique to lower Mach numbers for a given section andcomparison with previous cascade data, the basic radius change andarea change characteristics can be determined at extrapolated to highMach numbers. There is considerable hope that the restriction in Machnumber will soon be lifted resulting in a finite-difference techniqueof reasonable computer run times and a Mach number capability throughthe entire rotor design range.
The' second and more serious deficiency from a long range stand-point is the effect of three-dimensional factors not taken intoaccount by the application of successive radial equilibrum and blade-to-blade solutions. These are as follows:
(a) Secondary flow '
(1) Cross flow in boundary layer
(2) Vorticity generation in boundary layer
(b) Blade sweep effects
(c) Stream sheet warpage and twist
(d) Effects of blade separation and the migration of low energyflow -away from blade hub
Attempts to analytically evaluate these three-dimensional effectshave met with limited success (Reference 7-10). Therefore, a decisionwas made to attempt to derive an empirical method for accounting forthese effects.
Deviation angle data from a series of fan tests of an AiResearchexperimental fan was employed in the empirical development. This data
23
is presented in figure 15 which includes a comparison of design andmeasured deviation angles as a function of exit radius for the rotor.The design conditions shown in figure 15 are really immaterial to thefollowing argument. A postulation is made that the difference betweenthe measured deviation angle and that calculated by the finite differ-ence, blade-to-blade computer program represents the viscous componentof the deviation. A comparison of the measured and blade-to-bladecalculated deviations for the experimental fan is presented in figure16. The difference between the measured and calculated deviation anglefor each streamline is shown in figure 17. Figures 16 and 17 indi-cate that most of the postulated viscous effects are in the lower halfof the blade with the largest influence at the rotor hub.
Assuming that this difference represents the viscous effects ondeviation, consideration is given to how these effects may be appliedfor other rotor configurations. Several correlating parameters wereinvestigated with the diffusion factor (D) across the blade seemingto offer the most promise. Since the diffusion factor is representiveof the losses within the blade row, the deviation correction term fora particular streamline may indeed scale directly to the ratio ofdiffusion factors.
The proposed approach for calculating deviation angles for theconical flow compressor is then to: (1) use' the finite difference,blade-to-blade program to compute the non-viscous deviation angle,(2) obtain a deviation correction term from figure 4 for the corres-ponding streamline, (3) adjust the deviation correction by the corres-ponding diffusion factor ratios, and (4) combine the non-viscous andviscous components to get total deviation angle. A sample calculationshowing this procedure is presented as table I. This tabulation showshow data from the AiResearch experimental fan was employed to predictthe deviation for a rotor designed for NASA by the General ElectricCompany. The comparison is made at the 10-percent streamline in thehub region where considerable deviation was measured. The results ofthe comprison indicate very good agreement between the predicted andmeasured deviation for G.E. Rotor IB. Obviously this result could justbe fortuitous, but time limitations and a lack of sufficiently preciseexperimental information in this area did not permit further investi-gation.
The negative portion of the deviation correction shown in figure17 will be neglected in the design of the conical compressor. Thismeans the deviation angle in the region between the 90- and 50-percentstreamlines will come from the finite-difference calculations withoutcorrection. The reasons for omitting the correction in this regionare: (1) the correction shown is small, being less than 1 degree and(2) a reasonable explanation could not be determined for applying anegative correction for viscous effects to the deviation angle pre-diction.
24
14
13 EXPERIMENTAL DATA
QSCAN 65 (PEAK n)I I
A SCAN 86 (DESIGN SPEED)
MIDSPAN DAMPER
A\'
EXPERIMENTAL
5 10 . ' 15 20
6 ~ DEVIATION ANGLE (DEGREES)
25
Figure 15. - AiResearch experimental fan, deviation versusblade radius.
25
TIP
0.8
S3o£0.6
gPI
0.2
HUB
MEASUIJ3D
CALCULATEDBLJDE-TO-BLAIJ>E
5 10 15 20DEVIATION ANGLE, DEGREES
25
Figure 16. - AiResearch experimental fan, calculated andmeasured streamline deviation.
26
TIP
0.8
00 .6EH
§0.4enI
0.2
HUB-2
NO CORRECAPPLIED 1REGION
TIONN THIS
0 + 2 + 4
~ DEVIATION CORRECTION
+6 +8
Figure 17. - AiResearch experimental fan results, deviationcorrection for each streamline.
27
TABLE I
SAMPLE CALCULATIONOF DEVIATION FOR G.E. ROTOR IB*
10% STREAMLINE (HUB REGION)
BASIS - A IRE SEARCH EXPERIMENTAL FAN RESULTS';
5 (MEASURED) = 15.85 (CALCULATED) = 10.6 degrees (BLADE-TO-BLADE RESULTS)
V6 = 5.2 degrees
"D" FACTOR (AEF) = 0.47
ROTOR IB RESULTS;
5 (CALCULATED) = 8.2 degrees (BLADE-TO-BLADE RESULTS)
"D" FACTOR (R-1B) = 0.49
DEVIATION CORRECTION FOR ROTOR IB
V5 (R-1B) = V6 (731) X D (R-1B).D (AEF)
Y5 • = 5.2 x 0.49 = 5.4 degrees0.47
PREDICTED DEVIATION = 5 (CALC) + V8 = 13.6 degrees.
MEASURED DEVIATION = 14.0 degrees.
*Seyler, D.R. and L. H. Smith Jr. Single Stage Experimental Evaluationof High Mach Number Compressor Rotor Blading. NASA CR-54581, 1967.
28
In summary, the foregoing discussion indicates that the finitedifference, blade-to-blade program predicts most of the effects ofblade loading on the air turning in compressor cascades. In theregions where the analysis indicates that the finite-difference pro-gram was lacking, an empirical correction is recommended. Thecombination analytical and empirical approach should provide a reason-ably precise prediction of deviation angles for the conical flowcompressor.
CONCLUSION
The finite-difference inviscid technique discussed herein presentsa step forward in numerical determination of deviation angles. Partic-ularly, the effects of radius change and meridional velocity ratio onthe blade geometry can be evaluated to an accuracy not previouslyobtainable. However, three-dimensional, secondary flow effects mustbe-evaluated when applying the technique to three-dimensional cases.These serve to make the finite-difference technique of primary usein removing many of the uncertainities associated with Carter's Rule.This does not remove the need for adder factors correlated to experi-mental results from existing axial compressors. However, the combinedanalytical-empirical approach for predicting deviation angle shouldinstill a much higher degree of confidence in the blade angle settingsthan experienced through the use of sonic modification of Carter'sRule. :
29
1. Katsanis, Theodore and William D. McNally, Fortran Program forCalculating Velocities and Streamlines on a Blade-to-Blade StreamSurface of a^Tandem Blade Turbomachine,NASA, TND-5044, March 1969.
2. Milne-Thomson, L.M., Theoretical Hydrodynamics, The MacMillanCompany, New York, 1960.
3. Seyler, D.R. and L.H. Smith Jr., Single Stage Experimental Eval-uation of High Mach Number Compressor Rotor Blading, NASA CR-54581, 1967.
4. Felix, A. Richard and James C. Emery, A Comparison of TypicalNational Gas Turbine Establishment and NACA Axial-Flow CompressorBlade Sections in Cascade at Low Speed, NACA RM L53B26A, 1953.
5. Dunavant, James C., James C. Emery, Howard C. Walch, and WillardR. Westphal, High Speed Cascade Tests of the NACA 6-(RA10)10 andNACA 65-(12A2K80)10 Compressor Blade Sections, NACA RML55I08, 1955.
6. Emery, James C., Low-Speed Cascade Investigation of Loaded Lead-ing Edge Compressor Blades, RM L55J05, 1956.
7. Lieblein, Seymour, and Richard H. Ackley, Secondary Flows inAnnular Cascade and Effects on Flow in Inlet Guide Vanes, NACARM L251627, 1951.
8. Hauser, Arthur G., and Howard Z. Herzig, Cross Flows in LaminarIncompressible Boundary Layers, NACA TN3651, 1956.
9. Lakshminarayana, B., Methods of Predicting the Tip ClearanceEffects in Axial Flow Turbomachinery, ASME Paper 69-WA/FE-26,1969.
10. Wheeler, A.J., and J.P. Johnston, Three-Dimensional TurbulentBoundary Layers - An Assessment of Prediction Methods,StanfordUniversity,Thermoscience Division, Report MD-30,1971.
30
APPENDIX A
NOTATION
b Axisymmetric streamtube thickness
c Chord
C Specific heat at constant pressure
i Incidence angle
m Meridional distance
m Mass flow rate
fm Geometry constant in Carter's rule
C
N Number of mesh points leading edge to trailing edge
P Pressure surface static pressure
P Suction surface static pressures
r Radius »
T' Total temperature
U Wheel speed, free stream velocity
u Boundary layer velocity
V Velocity in absolute frame
W Relative velocity
31
APPENDIX A
NOTATION (Contd)
a Streamline slope
3 Relative flow angle . .
6 Deviation angle
6, . Boundary layer thickness
i 'w Rotor rotational frequency
Wy Vorticity
to Strearnwise component of vorticitys
\l> Stream function
o Solidity
9 Total turning angle
6 Tangential coordinate in a cylindrical coordinate system
p Density
T Circulation
Subscripts
U Tangential direction
1 Inlet -: :
2 Outlet
m Meridional
32
APPENDIX B
DESCRIPTION OF BLADESECTIONS FOR ROTORS AND STATORS
(Page i)(Rotor 1A, 8 pages)(Rotor IB, 8 pages)(Stator 1A, 8 pages)(Stator IB, 9 pages)
APPENDIX B
COMPRESSOR BLADE STACKING PROGRAM
The basic calculation performed by the Blade Stacking Program isto take the specification of airfoil shapes along a set of axisym-metric stream surfaces, interpolate the input data to cylindrical sur-faces, and "stack" the blade using the cylindrical sections. Thetype of airfoil shape can be 65-series, multiple or double circulararc or arbitrary. Axisymmetric stream surfaces can be cylindrical,conical, or arbitrary.
Required input specification parameters for airfoil sections aremean camber line direction and tangential thickness. Each inputaxisymmetric stream surface must be specified by axial and radial loca-tion and slope. •
The blade stacking axis must be defined on two, mutually perpen-dicular surfaces, the r-z plane and the r-0 plane. Normal bladestacking procedure has been to calculate the center of gravity foreach cylindrical stacking section and align each section center ofgravity along a straight, radial line. However, this program canstack the blade on an arbitrarily specified axis in both planes.
For purposes of this design, the axial location of the programstacking axis for rotor 1A is taken at the leading edge center loca-tion. All other sections have the stack point axial location atabout the blade section center of gravity (C.G.). Tangential locationof the stack point for all sections is near the section C.G. location.(Refer to center of gravity coordinates, (X, S), defined on each bladesection printout).
The output from the stacking routine gives the parameters of•cylindrical blade angle, tangential (or normal) thickness and theblade lean angle for input to the through-the-blade flow field calcu-lation. It also provides the blade geometry along any axisymmetricstream surface for input to the blade-to-blade analysis program..Plane sections are also generated for blade manufacturing purposes.
AT-6133Appendix. BPage i
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AT-6133Appendix BPage ii
ADVANCED TWO-STAGE COMPRESSOR •• CONICAL FLOW KO.TOR NO. 1
.... R A D I U S ...>•
•
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.
CENTER OF GRAVITY
^CYLINDRICAL PROFILE
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LE THICKNESS"
,009466
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CHORD"
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,022959
SOLIDITY
«TRUE CHORD
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,60*959
DIRECTION OF ROTOR ROTATION
* CLOCKWISE (VIEWED
CYLINDRICAL COORDINATESC
AL
CU
LA
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DC 0 0 R 0 I N A
,31*159
,563783
,79*577
THE TRAILING EDGE)
T E S ••«•
PLANE COORDINATES
NO. 1 ?. 3 4 5 6 7 8 9
10 11 1213 14 15 16 IT1« 1<»
20 21 22 23 2* 29
x • '
••'..
;' s
'.538200
-.02179*
.509376
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.015752
.455517
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.013975
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.288973
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.180812
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.123940
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.035119
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.022301
.036588
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.075*15
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.129218
.161267
.19671*
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-.237813
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-.2370*2
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-.233509
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NO.
26 2728 29 30 31 32333* 35 36 37 39 39 *0 *1 *2 *3***5 *6 *7 *8 *9 50 51
X .019767
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-.007236
-.013*22
-.005697
-.025892
NO. 1 2 3 4 5 6 7 8 9
10
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1» 19 20 21 2223
-.02179* .. 2*
-.232327 .. 25
-.01*515
;
X .538161
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-.054S01
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-.101003
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-.162*75
-.19*55*
-.237722
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-.239*08
-.235887
-.231665
L.E.R.C.
NO.
26 272« 29 30 31 3233 3* 35 36 37 39 39 *0 *1 *? *3 ** *5 *4*7*9 4950
51
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T.E.R.C.
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-.007236
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c c
ADVANCED TWO-STAGE COMPRESSOR •• CONICAL FLOW ROTOR HO. 1
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.CYLINDRICAL PROFILE
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LE THICKNESS*
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DIRECTION OF R
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:
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.isons
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-.018132
-.040579
-.066036
-.094337
-.125350
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-.194073
-.231305
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-.271226
-.268054
-.264226
COORDINATES
NO.
26 27 28 29 30 31 32 33 34 35 36 37 39 3940 41 42 43 44 45 46 47 4849 50
X .018025
.040830
.064207
.088241
.113030
.138334
.164193
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C U L A T E 0
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.063974
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CO
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NO. 1 2 3 4 5 6 7 8 9
10 11 1213141516 17
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19 202122232425
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THE TRAILING EDGE)
T E S •**•
PLAN
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L.E.R.C. 51
T,E.R.C.
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-.040617
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NO.
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L.C.R.C. 51
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ADVANCED TWO-STAGE COMPRESSOR •• CONICAL PLOW ROTOfl NO. 1
....
RA
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NU
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PROPERTIES OF CYLINDRICAL
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T E S ••••
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.027883
.000346
-.029391
-.060645
-.093381
-.127418
-.162516
-.198312
-.234*66
-.271339
-.308077
-.310052
-.309444
-.306609
-.303207
L.E.R.C.
NO.
26 27 28 29 30 31 32 33 34 35 36 3738 39 40 41 42 43 44 45 46 47 4849 50 SI
X .017398
. 039095
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T.E.R.C.
.505595
S-.261175
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NO. 1 2 3 4 S 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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L.E.P.C.
NO.
26 27 28 29 30 31 32 33 3* 35 36 37 38 39 40 41 424344 45 46 4748 49 50 51
X .017440
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.180710
.2.0*268
.231962
.257824
.283987
.311179
.338894
•367050
.395527
.424047
.452256
.479649
.505817
.500787
.510575
.507814
.503031
-.000002
T.E.R.C.
•504450
Y •'
•.'•
•.26431*
-.222482
-.131198
-.140840
-.101815
-.06*295
-.028565
.005123
.036492
.065878
.093119
.117997
.139566
.158014
.173017
.18*181
.191030
.193h89
.189919
.181402
.178342
.176721
.168348
.168012
-.303763
.174703
I t c
ADVANCED TWO-STAGE COMPRESSOR •• CONICAL FLOW ROTOR NO. 1
....RADIUS
.
1.600000
NUM8ER
CENTER OF GRAVITY
CYLINDRICAL PROFILE
X «
.234*73
S »
.000337
OF 20
8LAOES
PROPERTIES OF CYLINDRICAL PROFILE
SPACING
»
,502655
AXIAL
CHORD"
.494174
SOLIDITY
»
,983128
LE THICKNESS*
.006578
TE THICKNESS"
.011296
TRUE CHORD
»
.788951
DIRECTION OF ROTOR ROTATION » CLOCKWISE
(VIEWED
FROM
CYLINDRICAL COORDINATESC
AL
CU
LA
TE
DC 0 0 R 0 I N A
THE TRAILING EDGE)
T E S ••*•
PLAN
E CO
ORDI
NATE
Sr h. L C c ^ \ „ 1 w r
NO.
_..•
1 2 3 4 5 6 7 9 9_.
10 11 12 13•
14*•
15..
16 17 18 19 20 21.
22
23 24 25
X .437513
.4657\3
.444055
.4323*6
.400498
.373419
.3560?8
.333296
.309952
.285922
.261868
.2377*8
.213455
.188346
.16294
.1371".1
.111070
.084614
.057819
.030613
.003218
. .000741
-.002215
-.003897
-.0033?!
S .270019
.252906
.233183
.211027
.186611
.160212
.132106
.102507
.071867
.040365
.007719
-.025884
. -.060139
-.094S19 -
-.129209
-.164Q92
-.199055
-.234009
-.268890
-.303613
-.338116
-.339798
-.339222
-.336725
-.333770
L.E.R.C.
NO.
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
X .017717
.039082
,0607qO
.082816
.105188
.127907
.150977
.174400
.1985nO
.222972
.247.410
.271902
.297021
.3227*1
.348883
,375296
.401940
".428724
.455558
..482248
.486553
.489878
.490277
.487515
-.000042
T.E.R.C.
.48488?
S-.295027
-.256485
-.218193
-.180222
-.142634
-.105495
-.068908
-.032984
. .001879
.035944
.069165
.101365
.131916
.160578
,1872«3
.211720
.233606
.252580
.268185
.280012
.280411
.277649
.273344
.270019 i
-.335943
.275016
NO. 1 2 3 4 5 6 7 8 9 10 11 12 1
3 14 15 16 1718 19 20 21 22 23 2425
X .485314
.463938
.442632
.421237
.399673
.377836
.355649
.333081
.309815
.28589Q
.261«68
.237756
,213394
.188245
.162723
.136845
.110635
.084135
.057364
.030361
.003157
.000730
-.002146
-.003789
-.003235
Y .274546
.255291
.234099
.211036
.186155
.159613
.131566
.102124
.071666
.040299
.007719
-.025910
-.060272
-.094817
-.129701
-.164770
-,199876
-.234908
-.269785
-.304424
-.338783
-.340421
-.339867
-.337445
-.334572
L.E.R.C.
NO.
26 27 28 29 30 31 32 33 34 353637383940
41 4?43444546474849 50 51
X .017755
.039074
.060736
.082751
.10S119
,127851
.150944
.174390
.198580
,22?955
.247336
.271720
,296654
.322189
.347999
,374065
.400321
-,426682
.453091
,479415
.483599
,487069
,487783
.485314
-.000039
T.E.R.C.
.482373
r-.296093
-.257640
-.219289
-.181145
-..143316
•.105921
-.069109
-.033034
.001879
.035980
.068926
.100963
•131129
.159528
.186Q97
.210637
.232985
.252924
.270134
.284301
.284958
.282375
.278057
.274546
-.336679
.279432
ADVANCED THO-STAOE COMPRESSOR ••
CONI
CAL
FLOW
ROT
OR N
O. i
RA
DI
US
1.8
00
00
0 •
CENTER OF GRAVITY
CYLINDRICAL PROFILE
X a
.236949
S •
.0003*9
••••«••.»*«•»•*««*••••
NUMBER OF 9LAOES
30
PROPERTIES OF CYLINDRICAL PROFILE
'.SPACING
«
.565*87
LE THICKNESS"
.005650
AXIAL
CHORD-
.472722
TE THICKNESS"
.010556
SOLIDITY
»
.835956
TRUE CHORD
»
.825090
DIRECTION
NO. 1 z 3
. 4 3 6 7 9 9 10 11 1? 13 14 15 16 17 19 19 20 21 22 33 24 25
X .468177
. 447505
.42664$
.405612
.384319
.362992
.3410*0
.3199*5
.2957*9
.272506
.249212
.225947
.2022">3
.177991
.153544
.1289<)9
.103919
.078972
.0537*8
.0233/3
.002797
. 00069
-.001817
-•00328H
-.0028*0
CYLINDRICAL
S .309210
.279*17
.249198
.218027
.18615*
.153720
.120792
.087428
.054190
.020*62
-.013*78
-.0*9231
-.082922
-.117390
-.152056
-.186785
-.221573
-.256*53
-.291396
-.326192
-.361*3*
-.3*290*
-.362*67
-.360379
-.357863
L.E.R.C.
OF R
OTOR
••••
C A L
COORDINATES
NO.
26 27 29 29 30 31 32 33 3* 35 36 37 38 39 40414243444546474849 50 51
X .01798*
.039009
.06022*
.081629
.103170
.12*913
.146888
.169096
.191772
.21*909
.239054
.2*1213
.28446
.308752
,333360
.358273
.3834*0
.408857
.*3**17
.4601*6
.**3769
,*67* lj8
,**9434
.468177
-.000032
T.E
.46*172
ROTATION » CLOCKWISE
CULATEO
CO
S-.319783
-.281965
-.2***19
-.207150
-.170133
-.133*05
-.097009
-.060976
-.025495
.009338
.043909
.07801*
.111589
.1*3872
.175263
.205*85
.2350*1
.263313
.290381
.31608*
.317910
.316*53
.313049
.309210
-.359*49
NO. I 2 3 4 5 6 7 8 9 10 11 12 13 1
4
IS 16 171819
20 2122232425
,R.C.
.312647
JVIE
WEO
FROM
TH
E TR
AILI
NGO
RD
IN
AT
ES ••*•
EOGEt
PLAN
E CO
ORDI
NATE
SX
Y.465509
.311047
.4*5*39
.280*00
.425077
.2*9332
.40*449
.217819
.383582
.185818
.362348
.153392
.340745
.'.20540
.318791
,087?30
.295707
.05*128
.272498
.020*73
.2*9229
.225907
.202091
.177785
.15323*
.128*5*
.103*96
.078450
.053284
.028027
.002706
.00069*
-.001740
-.003178
-.002772
.013692
,0*8?85
.082978
.117700
.152565
, 187S*5
.222635
.257990
.293301
.32fl«98
.3*4725
.36*179
.365768
.3*3731
.361261
NO.
26 27 2" 29 30 31 32 31 34 35 36 37 3* 39 4041 424344454*47
4fl
49 50
L.E.R.C.
51
X .018019
.039001
.060181
.081563
.103095
.124844
.14*838
.169071
•19176*
.21*907
.239031
.261130
.28*260
.308380
.33274*
.357329
.382135
.407039
.432046
.457189
.**Q687
.46*576
.466576
.465509
-.000033
T.E.R.C.
.461352
Y-.322522
«. 28*1*0
-.246100
-.208398
-.170996
-.133955
-.097307
-.061096
-.025516
.009385
.043848
.077827
.111231
.143339
.17*586
.20*952
.23*418
.2630*2
.290912
.317692
.31962*
.319483
.314934
.311047
-.36299*
.31*367
AOV4WCEO TWO-STAGE COMPRESSOR •• CONICAL FLOW ROTOR NO. I
RA
DI
US
2.0
00
00
0 .
NUMBER
OF 30BLADES
CENTER OF GRAVITY
CYLINDRICAL
PROFILE
X «
.235*65
S «
.000454
PROPERTIES OF CYLINDRICAL
PROFILE
SPACING
«
.629319
LE THICKNESS"
,0047<J2
AXIAL CHORD*
.451148
TE THICKNESS*
.010170
SOLIDITY
»
.718024
TRUE CHORD
a
.856056
DIRECTION
NO. I ...
* 3 A 5 6 7 .:.
9 9.__..! 3
11 12
-_
.. 13 ....
14» 1,
._.
16 .
17 19 19 20 21 22 23 24 25 ..
X .447647
.427811
.407699
«387270
.366555
.34555?
.324242
.302311 'f
.2800?!
.2577?8
.235411 :
.213119
. . .190103
.166941
.143644
..... .120211
.096710
•0732?4
.0496*9
.026044
.002347
.000699
-.0013^6
-.002615
-.002438
CYLINDRICAL
S ,323623
.289A77
.255461
.220988
.186244
.151256
.116020
.080757
.045342
.009588
-.026487
-.062856
-.099091
-.135543
-.172212
-.209104
-.246?<U .
-.233793
-.321621
-.359778
-,3982«0
-.399579
-.399331
-.397682
-.395598
L.E.R.C.
OF ROTOR ROTATION
» CLOCKWISE (VIEWED FROM THE TPAILINO EDGE)
••••
CA
LC
UL
AT
ED
COORDINATES ••••
COORDINATES
NO.
26 27 28 29 30 31 32 33 34 .
35 36 37 38 39 40 41 42 43 44 45 46 4748 49 50 51
X .018217
.038942 ..
.059737
.080602
.101462
.122368
.143420
.164612
.195947
.207985
.230039
.252097
.274158
.296577
.319618
.342961
.366601
.390533
.414761
.439276
.442544
.446349
.448463
.447647
-.000045
T.E.R.C.
.443463
S .35534'*
.315495
.276019
.236915
.198120
.159648
.121534
,083793
.046*20
,009754
,026613
,062667
,098395
.133544
.167891
.301587
.234612
.266936
.298536
.329399
.331513
.330697
.327429
.323623
-.39693*
NO. 1 2 3 4 5 6 7 8 9 10 11 12 13 1
4 15 16 17 19 19 20 21 22 23 2425
.326511
X .444915
.425695
.406089
.386109
.365759
.345035
.323939
.302166
.279979
,257726
.235419
.213053
,199949
.166683
.143267
.119714
.096146
.072635
.049129
.025660
.002259
.000703
-.001294
-.002564
-.002363
PLAN
E CO
ORDI
NATE
SY .322289
.288767
.254955
.220593
.185998
.151101
.115930
.080715
.045327
.009587
.036494
.062899
.099211
.135800
.172696
,209938
.247630
.285883
.324743
.364303
.404679
.405992
.405773
-.404176
-.402123
L.E.9.C.
NO.
26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42
4.344
45 .
46 474849 50 51
X .018251
.039934
.059694
•08Q535
.101386
.122295
.143361
.164576
.185933
.207984
.230033
.252056
.274047
.296327
.319169
.342337
.365501
.388993
.412692
.436591
.439799
.443571
.445691
.444915
-.000050
T.E.R.C.
.440749
Y ,.-
--•(-•
.•.360162;
. 31 8969
.278462
.238572
.199185
.160287
.121880
.083946
.046464
.009756
.026599
.062601
.098239
.133287
.167520
.201093
.233984
.266136
.297487
.327994
.330031
.329205
.326000
.322289
-.403402
.325141
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33
APPENDIX C
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(9 pages)
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TABLE HIBUB CONTOURCOORDINATES
Z2.10002.01091.92181.83271.7436
1.65451.56541.48501.39501.3050
1.21501.12501.03500.94500.8550
0.76500.67500.58500.52160.4862
0.45270.42110.39110.36280 . 3360
0.31060.28670.26410.24280.2228
0.20390.1862
*R1.25001.25121.25461.25991.2671
1.27621.28731.29941.32251.3489
1.37851.41161.44831.48891.5338
1.58361.6390
" 1'. 76131.75001.7793
1.80861.83791.86721.89651.9257
-T.955IT1.98432.01362.04292% 0722
2.10152.1308
-
-*
z0,16960.1S400,13940.12580.1131
0.1013-0.09040.08030.07100,0624
0.05450.04730.04Q80.03490.0296
0.02490.02060.0169C.01370.0108
0.00850.00640.00470.00310.0023
0,00150.00090,00050,00020.0001
0.0000-0,0000
SB2.16002.18932,21862,24792,2772
2.30652.33582.36502.39432.4236
2.45292.48222,51152. 54 072.5700
2,59932.62862.65792.687?2,7165
.2.74582.77502.80432.83362,8629'
2.892?2.92152.95082,98003,0093
3,03863,9000
•
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*
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O.<?&/3O.52J5
a 9305/. 0377
':H/.S-/00
/.-7&2Z
TABCE EO0V8IDB-BDC8
CONTOUR COORDINATES
R,
-5.20003.0fe?803.OO6O*?SJ<?4G*£ c?c?/ y~f Cif *5^5
^ 7S 78£.4,&£'72.63 X,
y&s>3*%t*£l?fl•2-Z2.&52.26&^<£*/~J ^)(&^? y^5^^X*£*/ S' fc* t*
2-/6S6
*
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* Foe coNsreDcTjoN
(9SQUALLY
Y \- . 303 D/A REFALL /°H3SAGS£
SUCTIONX.0142.0068
-.0045-.0996-.1501-.2478-.3733_-.5012-.6284-.7579-.8890-1.0225-1.0505-1.0785-1.1064-1.1340-1.1613-1.1882-1.2145-1.2400-1.2646-1.2880-1.3101-1.3304-1.3486-1.3645-1.3773-1.3740-1.2864
Y3.16923.16063.15973.18803.20173.22603.25273.27513.29323.30743.31843.32583.32783.33123.33633.34293.35143.36143.37343.38733.40313.42093.44063.46253.48633.51223.53983.65603.7356
PRESSUREX.0140.0135.0050
-.0365-.0797-.1237-.1708-.2191-.2714-.3266-.3864-.4522-.5289-.6060-.6989-.8041-.9267-1.0672-1.0925-1.1178-1.1431-1.1684-1.2864
Y3.16923.18063.18823.20233.21523.22903.24303.25803.27403.29193. .31173.33393.36163.39183.43073.48193.55103.65003.66993.69013.71053.72673.7356
PROJECT AUTHORIZATION For Development Only
Alternate
Rework
W. 6. No._
for Dwg No. \0/i FUG, Next Awy_
Oyrtine—
AIRC8CARCH MANUrACTURINCI COMPANY OF ARIZONAFMOBNIX. ARIZONA
APPD
CHK
OFT
TttleNOZZLE. £4DIAL PAP 216124
>OM MTSM
APPENDIX D
COMPLETE RADIAL EQUILIBRIUMFLOW SOLUTION
ALL BLADE ROWS
(61 pages)
10/1 NASA COMP.«3/30/72**THRU THE BLADE»»ALL STAGES**
ATE 04/0 5 / 7 2 T T M ^ 1 7 X 5 4 7 ^ 8 ' " -
CODE RADIUS70000~. O O O O O .W333
GAMMA SPEC HEAT1.39470 6065.37000
MAJOR ITERS FLOW TOL20 .00100
FLOW.10000 .15000
STATIONS QM(M«1)30 1.00000
SL5PT M-T-5.23000 -5.61700
SLOPE N+l22.00000 22.00000
CURVATURE M-l-.08240 -.10324
CURVATURE N+l-.25000 -.25000
STATION.03000.04000,05000,50000.06000.07000
Rotor 1A Inlet 1.00000
1*200001.4001)01*600001*80000
Rotor 1A Exit 2 *00000Rotor IB Inlet .3, Q O O O O
3*200003*400003.600003*80000
Rotor IB Exit 4, 00000
Stator lA' Inlet 5* 00 000
5*100005.200005.300005.40000
Stator 1A Exit 5.50000 .VStator IB Inlet 6> Q O O O O
6.100006 . 20 0 0 06.300006*40000
Stator IB Exit 6.50000
SPEED610.3000U
TEMP518.68800
CUR TOL.00100
.25000
DM (N+l).30000
-6.09160
22.00000
-.11402
-.26000
AVERAGE P/P1.000001.000001.000001.000001.000001.000001.000001.145421.326281.521991.700591.780181.778762.12780
2^785283.105953.241453.241463.211303.183733.152473.124633.096193.096193.090363.083353.076343.069343.06243
FLOW STRMLNS
PRESSURE DENSITY2116.22000 .076474
SENSE SW SHOK LOG89 -0.0601)0
.25000 .25000
ANGL DAMP ROT DEL*.95000 .30000
-6.58860 -6.86600
22.00000 22.00000
-.12200 -.12515
-.31200 -.31200
AVERAGE r/T1.000001.000001.000001.000001.000001.000001.000001.04028
1.132121.170011.186051*186051.248881.297931.350271.395151.412101*412101*41210U412101*412101*412101.412101.412101*412101.412101*412101*412101.41210
MAX IT
RPM69900.86
00 LOSS-O.OOOOlT
DEL LOSS-0.00000
-6.33000
-.09970
-*3iaoo
AVERAGE EFFI .00000
.00000YOWOD.00000.00000VOOWIT.00000.96102
.95688
.95597
.95509f .95364
J .95890.96042.96144.95811.95963.95963.95073.94254.93319.92480.91617.91617.91439.91225.91010.90795.90583
STATION ,03000 STATQR XI =
p - -n. 2TIP = -4.12500 AH * 1.- 0. ZH'Jb = -4.12500 LOSS =
RADIUS **"' •3.54000 3.47QOO 3.32000
SLOPE-14.32000 -16.00000 -17.00000
CURVATURE-.22220 -.19000 -.21000
LOSS COEFF-0.00000 -0.00000 -0.00000
SOLIOI rv1.00000 1.00000 1.00000
AERO BLOCKAGE.99600 .99600 ,99600
TOTAL dLOCKAGF.996IJO .99600 .99600
BLAOE ANGLE-o.ooooo -o.ooooo -o.oouoo
LEAN-0.00000 -0.00000 -0.00000
Y-o.ooooo -o.ooooo -o.ooooo
MINOR HERS = I AREA RATIO = .99938
7IUS3.5*000 3,42314 3,24461
Z-4.12500 -4.12b.)0 -4.12500
CROSS PASSAGE ,OIST P1.26000 1.14314 ,96461
SLOPE-14..32000 -15.23712 -15.97222
CURVATUWE-.22220 -.20663 -.20057
OELTA CURv/ATUWE0.00000 -.00001 -.00015
VM152.62197 156,30901 162.17091
VU20.00000 0,00000 0.00000
U2159.40000 2088,1138(1 1979.21147 1
VR-37.74911 -41.08026 -44.62479
8ETA2o.rtoooo o.uoooo o.ooooo
BETA2*0.00000 0.00000 0.00000
0.00000
30000 .1. EXP =
3.15000
-19.00000
-.23000
-0.00000
1.00000
.99600
.99600
-0.00000
- U . 0 0 0 0 0
-o.ooooo
EXP 3
2.93771
-4.12500
.65771
-1 7.39095
-.20908
-.00006
173.40452
0.00000
792.00433
-51.82892
0.00000
o.ooooo
XN = 0. BNXT = -0,.8000 BLADES = -o.
2.75000
-20.00000
-.25000
-0.00000
1.00000
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.97400
. 0977
50.63974
-2.23997
"i,T.ff65M"
EXP a 1,50000 CHOKE
1.71516
.27377
,52"58T
35.38910
.25764
.00136"
594.97936
649.69959
046,25044
344.56821
47.51727
53.25587
1.50516
.28436
""".31056
40.82717
.30264
™ VOTT419
576.57891
486.53656
918, 150~46"
376.95563
40.15877
- 4B7I1667
1.19500
51,17000
.16800
.99818
1.00000
.07774
,97400
. 772TO
28.24758
3.66601
-lfl03Dinr
a .76550
1.19500
.30000
~^ D.OOWO
51,17000.
.16800
O.OOOOTT
553.41793
203.56435
7Z8,95UOO
431.11810
20.19509
3T),3 765
20
INCIDENCE1.07353 -.17743
.92016 .88526V21058.274/1 1017.96976
TOTAL TEMP -1.13903 1.14278
TOTAL PRESS1.49916 1.52218
EFFICIENCY.87326 .88427
STATIC TEMP1.06523 1.06487
STATIC PRESS1.18316 1.18604
DENSITY1.11071 1.11379
SUCT SURF VEL1305.9958Q 1247.92872 1
PRESS SURF VEL810.55363 788.01081
DELTA T34.04829 31.71706
WORK COEF = 2*CP*0£LT/U«»2.26989 ,26637
FLOW COEF n VM/U.47091 .49264
R BAR2.00650 1.94715
D-FACTOR.111524 .18628 ~
VM2/VMI.93515 ,92002
DELP/ti.18421 .19642
TANG BLADE FORCE LB/IN1T.7T488 - ye, 734 OS
AXIAL BLADE FORCE LB/IN30.54475 28.03795
VEL HE AD" 2.42074 .39839
Q»E»*(-S/CP).98453 .98554
RVU/1.1755Q 1.20720
bWO/UM5.17283 4.58244
STRMLN OIST M.73409 V7T627 ••••/•
-1.23243
.85693
981.31889
T.T3819
1.54610
.94968
1,05608
1.18666
1.12365
177. 64426
784.99352
27.28771
~ .25157
.53244
1.85498
--.17354
.91823
.20841
~T4 . 5ZZTJF
25.58445
.38011
.99"389
1.16840
3.70900
.69790
-1.18776
.77130
880.97105
1.13188
1.53180
.97262
1.05062
1.17729
1.12056
1047.~418~50
714.52361
22.39212
.24815
.56868
1.68503
.16957
.91198
.23074
"T0.9T4T7
18.99156
.32447
,99681
1.11500
2.98142
.69357
-1.85675
•66275
754.42763
1.12596
1.51284
.98677
1.04352
1.15639
1.10816
03. 33513
605.52013
18.71122
" ,2~69Z5
.62798
1.46916
.15078
.96233
.23137
._ ...._Tr7w3l_.
11.39760
.25454
.99852
1.06500
2.44438«
~. 74259
-.95057
.52159
589.66927
l.'Rl 73"
1.49106
.98323
1.02"928
1.10025
1.06895
719.57768"
459.76085
17.69092
.40387
.75920
1.13450
-VOD819
1.22791
.03650
5Yff3TFZ9
2.33108
.16873
.998ltf
1.02924
1.81881
- 1,02616
21
•STATION 1.80000 ROTOR XI •
"p e r. zT IP *a 0, ZHUB »..
RADIUS"2.07600 2.
SLOPE30.36000 33.
CURVATURE.39500 •
LOSS COEFF.97917
SOLIDITY1.00000 1.
BLADE THICKNESS.04829 *
AERO BLOCKAGE.97200
TOTAL BLOCKAGE.90004
BLADE ANGLE57.80893 57.
LEAN-1.03805 -.
Y •••'• •-1.62450 -1,
NOR ITERS = 1
RADIUS2.07600 2.
Z.34400
CROSS PASSAGE DIST.75707
SLOPE30*36000 32.
CURVATURE.39500 *
DELTA CURVATURE0.00000 •
VM569,05498 560.
789,02618 750.
,34400•40000
01400 1
OOWO 35
36000
98124
00000 1
04956
97200
89586
40181 56
52280
60210 -1
AREA RATIO
02196 1
34801P70288
20885 33
39718
00151
62979 573
06049 712
AR * e.LOSS *
.93500
.00000 •-"•
.39000
.99235
.ooootr,05155
,97200
,88958
.47022
,31771,
,48920
a .99980
.93658
.35434
.61727
,65790
.46160
. 00160
.51394
.23189
UUUUU A3. EXP »
1.78400
39~i 00000
.37000,
.99604
1.00000
.05429
.97200
.87784
53.50556
-.54264
-1.41300
EXP s 1.
1.78181
.36582
.46208
37,22678
.41899
.00074
552.09384
603.16532
N * U. HNX1-o.oooo BLADES
1.58700 1
46.~0 0 OOtX 52
•28000
.99806
T.OOOOO 1
.05278
.97200
~V86"91tV"~
46.75384 15
1.58310 9
•a. 36000 »r
50000 CHOKE = •
1.58784 1
.38021
.26758 0
43.60244 52
.34295
.00242 " 0
534.22265 556
446.11491 196
•• 1.= 20,
.32100
•22000
•10420
.99761
.00000
.04982
.9/200
.85531-
.13302
.81008
.3T90TT-
72113
.32100
.40000
.00000
.22000
.10420
V 00 000"
.09083
,82175U1266.36000 1233.39444 ITBi;;312B2~
VR287.61842 298.81973 317.86045 334.00108
54.20039BETA2*-5BTT055!
53.22384 51.15775
56.T68r5
47.53125
r. 5 8 45 4 13 0 5~i'8 TO 0 0
368,42700 _ 439.51704
39.86433 19.49Q80
"49.069 5 30.
22
INCIDENCE.49658
.83070V2972.82367
TOTAL TEMP1.19214
TOTAL PRESS1.72744
EFFICIENCY.87076
STATIC TEMP1.10446
.34722
.80036.936.42752
1.18949
1.72675
.88224
1.10241
-. 27445
.78640
914.43562
1.17614
1.72656
.94892
1.08889
.63285
.70561
817.68944
1.16712
1.70245
.97234
1.08149
1.56243
.60321
695.99738
1.16086
1.68236
.98600
~TTOT21T
2.6684*
.51713
589,89475
1,15598
1,65490
.98229
1.04792STATIC PRESS
1.31878DENSITY
1.19405
1*31995
1,19734
1,31493
1.20758
1.30057
1.20257
1.27022
1.18478
1.16991
1.11642SUCT SURF VEL1136.09084
PRESS SURF809.55650
DELTA T27.54538
WORK COEF a.20836
FLOW COEF •.44936
H BAR2.05200
D-FACTOR.14381
VM2/VM1.97683
DELP/Q.15781
TANG BLADE15.25267
AXIAL BLADE23.00964
VEL HEAD 2.36310
TO 7 7. Tl 637 1VEL
795.13868
24,226432»CP*DELT/U»«2
,19318VM/U
.45454
1.99609
.13938
.94689
.17051FORCE L8/IN
13.19168FORCE LB/IN
20.06602
.34338
028.70432
800.16692
19.68053
.17108
.48549
1.90853
.12040
.93901
.17628
10.87085
17.88906
.33429Qs»E**(-S/CP)
.97917RVU/
1.62450ffRVU/D"M
3.14583STRMLN DIST
.83258
,9812~4
1.60210
2.67227M
,81758
,9923s
1.48920
2.07773
".803012
926.84144~
708.53743
18.28179
,18773
.50795
1.74849
.13084
.92792
.21801
9,25958
15.82280
.28192
.996 )4
1.41300
1.86961
i 8 0721
807.70420
584.29056
18.09774
.23401
.55155
1.54650
.15457
.92654
.28829
7.99653
12.83092
.21733
.99806
1.36000"
1.70276
.¥6917
696.69691
483.09260
17.76461
.33188
.69010
1.25800
.11868"
1.00483
.31195
6.36669
7.79054
.16617
.99761
1.31881
1.34754
1,1BTO~Z~
23
Rotor 1A Exit
STATION 2.00000 ROTOR XI s
* * 1. 2TIP * .43000 AR » 7.* 0. ZHUB « .50000 LOSS m.
RADIUS .2.13000 2.08300 2*00700
SLOPE32.54000 34.10000 36.20000
CURVATURE.35550 .27500 .28400
LOSS COEFF.97719 .97969 .99180
SOLIDITY1.00000 1.00000 1.00000
BLADE THICKNESS.01230 ,01242 .01269
AERO BLOCKAGE.96900 .96900 .96900
TOTAL BLOCKAGE.96811 .96808 .96803"
BLADE ANGLE56.26243 56,19262 55.43665
LEAN-5.07140 -3.45422 -1.09982
Y-1.79600 -1.74920 -1.60560
MOR ITERS » 1 AREA RATIO a 1.00052
RADIUS2.13000 2.07962 1.99985
Z.43000 .43522 .44348
CROSS PASSAGE DIST P.67961 .62896 .54877
SLOPE32.54000 34.37235 36.54114
CURVATURE.35550 ,32311 ,37959
DELTA CURVATURE0,00000 ,00081 .00157
VM533.75767 520,44278 531.17269
VU2784.95258 755.46596 730.16081
U1299.30000 1268.56680 1219.90639 1
VR287.10210 293.82584 316.26026
BEfA255.78478 55.43761 53,96508
BETA2»60.17691 60.37760 59,69481
5.91192
Soooo XN3. EXP a
1.86700
40.10000
.23900
.99577
1*00000
.01315
.96900
796T9T~
51,94140
2,06675
-1.54170
» 0. BNAT *• 1.-o.oooo BLADES •= i.
1.69200
45,50000
•19200
.99761
1,00000
.01254
.96900
~.~9T6786
40*38929
9.18285
-1.499SO
EXP = 1.50000 CHOKE
1.85675
.45829
.40491
40.38325
.39267
.00232
513.16549
626.12523
132.62029
332.47861
50.66230
53.02329
1.68272
,47632
.22994
46.03186
.30595
.00173
494.64680
482.87482
1026.45714
356.01024
44.31002
54.58017
1.45400
b3. 40000
•10670
.99706
1*00000
.01237
\ .96900
795759'
-4.48826
21.12723
~ -1746470
a ,67449
1.45400
.50000
0.00000
53.40000
.10670
0.00000
492.21442
272.26824
886.94000
395.15846
28.94915
42.8537?
24
INCIDENCE5.25179 5.27168 4
l _,
.80309 .77722V2949.23538 917.39834 902
TOTAL TEMP1.21242 1.20689 1
TOTAL PRESS1.82049 1.80754 1
EFFICIENCY.86931 .86152
STATIC TEMP1.12510 1.12200 1
STATIC PRESS1.3979Q 1.39690 1
DENSITY1.24247 1.24501 1
SUCT SURF VEL0.00000 0.00000 1804
PRESS SURF VEL0.00000 0.00000 1
DELTA T10.52123 9.02433 7
WORK COEF • 2*CP*DELT/U**2.07560 .06803
FLOW COEF a VM/U.41080 .41026
R BAP2.10300 2,05079 1
D-FACTOR.04981 .04368
VM2/VM1.9379? .92832
DELP/Q.10523 .11148
TANG BLADE FORCE LS/IN6.31613 5.23518 4
AXIAL BLADE FORCE LB/IN10.09841 9.16290 7
VEL HEAD 2.34515 .32832
Q»E»«(-S/CP).97719 ,97969
RVU/1.79600 1.74920 1
DRVU/UM1.29161 1.06866
STRMLN OIST M.93413 .92212 '•
.90401
.77015
.92814
,13990
.79552
.94862
.10694
.39086
.25649
.31950
,53678
.14094
.05821
.43542
.96821
. 03231
.92617
.11500
.17981
.89000
.32372
.99180
.60560
,80059
.91233
5.94908
.69277
809.55026
1.18235
1.78050
.97257
1.09972
1,37839
1.25339
0.00000
0.00000
7,89552^. DT466 " "
,45308
1,81928
.03634
.92949
.15240
4.25519
8.22464
.27368
.99577
1.54170
.79600
.92624
9.70528
,59376
691,26229
1.17735
1.76557
.98413
1.09151
1.35113
1.23786
0.00000
0.00000
8.55808
.09853
.48190
1.63528
.04419
.92592
.22941
4,07574
8,77219
,21154
,99761
1,49950
.73766
1.00422
IT. 19160
.48693
562.49892
1.17329
1.74073
.98009
1.07469
1.27649
1.18778
0.00000
0.00000
8,97689
.13843"
.55496
1.38750
.10TJ97 :
.88513
,45712
3,66045
10.91845
.14921
.99706
1.46514
.59052
1,35342
25
Rotor IB Inlet
STATION
-&--*- ~ r.
3,00000 ROTOR XI 0.00000
TTIPZHU8
8NXT,70000 LOSS 3. EXP
AN *- g.-0,0000 BLADES *
i •i.
2.32000 2SLOPE
^ JL ti Q A "J A "a 7w » j ™ "f f^ *f j f
CURVATURE.10760
LOSS COEFF.97791
SOLIDITY1.00000 1
BLADE THICKNESS,01168
AERO BLOCKAGE,96100
TOTAL BLOCKAGE,96023
BLADE ANGLE59,33508 58
LEAN " "~-2,46299 -1
-1.79603 -1
MOR ITERS » 1
.27700
.08914
.98049
.00000
.01225
.96100
.96018
.61771
.98986
.74922
AREA
2.21070
,08409
,99034
l.OOOUO
,01327
,96100
,96008
58.23417
-1,78518
RATIO « 1,00017
2,08780
42.26202
.09035
.99548
1.00000
.96100
58.29549
-1.98243
-1.54172
EXP »• 1
1.93780
47,34751
.00719
.99711
1*00000
.01698
,96100
58.27538
-1.58136
-1,49950
,50000 CHOKE «
1.73000
-0.00000
.99811
1.00000
.01955
.96100
58*69649
-.02982
-1,46465
.76461
RADIUS2.32000
. .70000CROSS PASSAGE
! .59000SLOPE
36.59429CURVATURE
.10760
2.27686
.70000DIST P
.54686
37,31240
.00969
2.20915
.70000
.47915"
, 39.18222
-.06598
2,08457
.70000
Y3555T
43.04870
-.11688
1,93523
.70000
.20523 "
48.18286
-,12324
1.73000
.70000
"OYTJWOD
54,44440
-0.00000DELTA CURVATURE
0.0000(TVM659,79561
VU2942.96797
-.00224
655.37553
920.24467
-. OCT272
648,12690
904,22478
-.00178
625.72504
820.44093
.00006"
575.42108
707.83470
U.07JO OO~
487.70786
538,82859u1415.20000 1388,88351 1347,57905 1271,58847 1180.48946 1055.30000
VR393.33391 397.26293 409,47944 427,13243 428.84802 396,77563
BETA255.01946 54.54245 54.36792 52,66833 50.89123 47.85091
BETA2*60.67385 60.47i76 60.94332 60.86737 61.54112 62.24107
26
INCIDENCE1.9W44 27^8T(5r5~
.98126 .96503V2~
1150.87742 1129,76428 1
TOTAL TEMP1.21343 I. 20689"
TOTAL PRESS1.82525 1.81277
EFFICIENCY.87392 .88619
STATIC TEMP1. 10780 1.10372
STATIC PRESS1.32686 1.32194
DENSITY1. 19775 1.19771
SUCT SURF VEL0.00000 0.00000
PRESS SURF VEL0.00000 0.00000
DELTA T.00184 .00123
WORK COEF s 2»CP»DELT/U»*2.00001 .00001
FLOW COEF a VM/U.46622 .47187
R BAR2.22500 2.17824
D-FACTOR-.21242 -.23148
VM2/VM11.23613 1.25927
"DEtF7Q-.09642 -.10978
TANG BLADE FORCE LB/INYOOTOT ,W069 • - • "
AX IAL BLADE FORCE LB/IN-4.24324 -3.69989
VEL HEAD 2.45922 ,44909
QsE»*(-S/CP).97791 .98049
RVU/1.79603 1.74922
ORVU/DM6.67514 6.57895
STRMLN OIST M1.26428 1.25230
3.42960
.95543
112.51559
"1 . 1F991"'
1,78622
,93947
1739191"
1.31836
1.20739
0.00000
0,00000
.00184
.00001
.48096
2.10450
-.23211
1.22018
-.10890
.wnrc-5.14662
.44306
.W034
1,60563
5,44380
1,24340
3.4^4~8i8
.88781
1031,82127
1.18235
1.77868
.97069
1.08777"
1.32483
1.21793
0.00000
0.00000
,00123
• WWQl
.49208
1.97066
- .~2T456
1.21934
-.10311
.TJW6T ~
-3.03693
.40003
,99548"
1.54172
5,44477
1.25839
4.26901
.78437
912.21675
1.17735
1.76244
.98081
1.03923
1.33881
1.22913
O.OODOD
0.00000
0.00000
0.00000
.48744
1.80897
-,3196?r
1.16330
-•03400
ovffoinw
1.13279
.33297
,99711
1.49950
3.96447
1.34156
4T.T4459
.62383
726.77039
1.TT32T
1.74697
.98720
T.TT91W — •
1.36024
1,24446
0.00000"
0.00000
-.02386
-.UI002F"
.46215
1.59200
".29191
,99084
,37408
*.,OW19
11,75259
.23008
99311
1.46475
3,91197
1.69426
27
STATION 3.20000 ROTOR XI =
p »" 1. ZTIP = ,75700- AR *a -0, ZHUB = ,76500 LOSS »
RADIUS . • ~ •-•---•••2.36200 2*31930 2,25660
SLOPE
CURVATURE.15000
LOSS COEFF.97496
SOLIDITYI. 00000 1
BLADE THICKNESS.02596
AERO BLOCKAGE,96100
TOTAL BLOCKAGE.¥9376
BLADE ANGLE59,21263 58
LEAN-.96817 -1
Y"-2T37000 "" -2
•12298
,34853
.97768
t'OWOD
.02771
.96100
.88791
,36701-. ./. - .. -
.37002
,~32"901F —
38.2TO03
,09474
.98929
.03034
.96100
.87874
57,40559
-2,15564
-2, 10850
» . 845
6.000003. EXP =
2.14210
41,82005
-.20976
,99506
TVOOOOU
,03492
,96100
56,60486
-3.59881
-27 1 WOT
63
XN a o. "BWtT-o.oooo BLADES
2,00680 1
- 1.* 40.
.82000
46,92217 53»ief&U»
-.15283 -,04800
.99688
,03812
,96100
54,75606 51
-3.25803 -2
^ A • ' r' * *» V C
.99782
.(TOO 00
.04425
•96100
.76280
,45331
•WOW""
NOR ITERS 2 AREA RATIO 1,00078 EXP » 1.50000 CHOKE *• ,79636
RADIUS2.36200 2.32053z -. • -.-.75700 .75761
CROSS PASSAGE DIST Pi .54206 /§0 659
SLOPE38.00376 37.61596
CURVATURE.15000 .22837
DELTA CURVATURE0. 00 000 -.00556
VM658.11611 669.15864
VU2828.75395 803,30054
U
^2.25643
.75856
.43648
-.04398
-.00910
659.76570
306.41302
2.14046
.76027
.32049
41.92147
-.27358
677.55026
707.21106
2*00462
.76228
.18464
47.09760
-,22420
620.42896
622,95619
1,82000
,76500
0,00000
53,25115
-,04800
OYD"0'00"0"
568.25061
426,28117
1440. 82000 1 415 .52593 1 3T6 T,VR
^BETA2 "
51.546788ETA2*
57.96454
08,43172
50.20529
56.58136
410.20956
50.71171
57,34877
452.67926
' 46.22704
54.51663 "
454.47331
45.11644
"~ ""55705312"
455,31993
36.87590
51.4T5I7
28
INCIDENCE-1.14065 -1.63380
.88485 .87691V21058.27687 1045.49751
TOTAL TEMP1.28031 1.27546
TOTAL PRESS2.18924 2.18145
EFFICIENCY.88563 .89665
STATIC TEMP1.15194 1.14473
STATIC PRESS1.50713 1.48864
DENSITY1.30834 1.30043
SUCT SURF VEL
.48323
.88015
1041.91781
1.24938
2.11426
.94634
1.12857
1.. 47599
1.30784
1256.56349 1257.72594 1210.69616PRESS SURF VEL859.99025 833.269Q9 873.13947
DELTA T35.21207 35.56850 30.85021
WORK COEF B 2*CP*DELT/U»«2.20576 .21534 .19753
FLOW COEF B VM/U.45676 .47273 ,47933
K BAR2.34100 2.29870 2.23279
D-FACTOR.TV544 .1426* .12520-
VM2/VM1.99745 1.02103 1.01796
bELP/Q.15999 .15469 .15029
TANG BLADE FORCE LB/IN21.38554 21.61404 Tg.2~4042
AXIAL BLADE FORCE LB/IN37,37248 36.61744 34,40019
VEL HfAO' 2 ~" """ ",39813 .39302 .39510
Q=E**(-S/CP).97496 .97768
RVU/2.37000 2.32900
DRVU/DM7.1560* 7.49107
STRMLN DIST M
.98929
2.10850
6.08454
* TT~O'«fc T — "J. • «3 A o o f
-1.13020
.83105
979.39871
1.24838
2.15203
.97517
1.11850
1,45966
1.30502
1150.19510
808.60232
34.24952
.24371
.51892
2,11252
.T2892
1.08282
.15264
18.87127"
31.78009
,36333
,99506"
2.10000
5.75185
2.47947
.74727
879,20789
1.23316
2.07408
.98350
1.11479
1.45 2 00
1.30249
1024.98909
733.42668
28.94412
" Y234BT
.50738
1.96992
.11626
1.07822
.16937
13.20959
24.08295
.30886
1.97130
4.90195
1 • 43480
.93493
.60355
710.36920
1.24135
2.13024
.98879
1.11562
1,46069
1.30930
862.48547
558.25293
35.32421
.34766
.51 185
1.77500
".15870"
1.16515
.24713
12Vlff578
19,93177
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.99782"
2.04054
4.69454
1.80528
29
STATION 3.40000 ROTOR XI 1.96300
" * 1. ZTIP a3 -0. ZHUB a
RADIUS2.40500 2
SLOPE38.72212 38
CURVATURE.17500
LOSS COEFF.97200
SOLIDITY1.00000 1
BLADE THICKNESS.03180
AERO BLOCKAGE.96100
TOTAL BLOCKAGE.88011
BLADE ANGLE58.46244 57
LEAN2.53867 1
Y-2.80000 -2
NOR ITERS = 1
RADIUS2.40500 2
Z.81100
V8TTOO.82800
.36030
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.01196
.97487
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.03461
.96100
.87129
.50910
.24787
.81140
... - AR » 6.LOSS a
2.29970
39,107845
-.02285
.98825
1,00000
.03828
.96100
.85916
56,31321
-.42408
-2V50030
AREA RATIO a .99966
.36248
.81246
2,29995
,81460
00000 AN s 0. B^3, EXP a
2.19290
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.07902
.99464
1.00000
.04339
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.83995
54.03466
-2.51336
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EXP a i.
2.19192
.81830
JXT « 1.-o.oooo BLADES • 40.
2.07060
4 727763
-.09458
.99666
1.00000
.04729
.96100
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50.00377
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50000 CHOKE *
2.06891
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1.90900
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1.00000
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.96100
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43.70551
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' .78809
1.90900
.82800CROSS PASSAGE DIST P
.49629SLOPE
38.72212 38CURVATURE
.17500DELTA CURVATURE
0.00000VM566.27296 607
VU2~ "756.86289 715
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678.95802
649.68724
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46.14184
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-.00366
641,73171
557.35986
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627.34216
365.72191U1 46T. 05 000 !"*« I". II 497 14-02. 9^688 T33T. 0 7¥OT
VR374.70059354.22873
BETA253.19672
BETA2*9.72680
49.64040 49.90828
"56.37774
(T3211 lT&4~.^r9(rOO
445^9305 _ ^2.72544 506.50686
43.73793 40.97511 30.24091
~"5T772(J4T
30"
INCIDENCE.78628 -1.75854
.77434 .77211V2945.25473 938,59286
TOTAL TEMP1.331 IT 1.33252 "~
TOTAL PRESS2.48547 2.52050
EFFICIENCY.88745 .89930
STATIC TEMP1.20005 1.19006
STATIC PRESS1.72296 1.69031
DENSITY1.43574 1,42036
SUCT SURF VEL1121.98774 1112,18154 1
PRESS SURF VEL768.52172 765.00417
DELTA T26.37976 29,59*41
WORK COEF a 2*CP»DELT/U**2.14869 .17286
FLOW COEF a VM/U.38599 .42177
K BAR2,38350 2.34151
D-FACTQR.15879 .16235
VM2/VM1.86045 .90833
DELP/Q.21649 .20923
TANG BLADE FORCE LB/IN16.13329 18,69729
AXIAL BLADE FORCE LB/IN36.24671 35.94245
VEL HEAD 2.32645 .32499
Q=E«»(-S/CP).97200 .97487
RVU/2.80000 2.81140
ORVU/DM6.72371 6,16753
STRMLN DIST Ml.~404Ti 1.39364
.17045
,80433
967.07704
1 ,29573
2,39571
.94852
1.16419
1.64119
1.40973
138.26550
795.88858
24,03626
.14814
.44392
2.27819
.12217
,94399
.17136
15.06031
31,18779
,34596
.9B825
2.50030
6.19900
1Y3*96?"
-1.57220
.78852
939.72204
1.29214
2.42702
.97629
1,14378
1.57730
1.37902
1091.63953
787.75455
22.69886
.15402
.50779
2.16619
.09370
1.00208
.14122
13.92480
24.66660
.33567
.99464
2.47000
5.01324
" " 1.41815
2,44375
.71493
849.98211
~"~ 1.28268
2.38182
.98484
1.13831
1.56195
1.37216
1002.55302
697.41121
25.68652
.19564
.50849
2.03676
.10455
1.03434
.16944
13,17996
23.01029
.28793
,99666
2.39000
4.92320
r.52Z90
1. 81908"
.61255
726.16162
1729566
2.47571
.98918
1.13174
1.53505
1.35636
869.87035
582.45289
28,17153
,25201
.53873
1.86450
.08351
1.10399
.1831.0
11.23414
15,04917
.22309
.99753
2,4997,5
4.24534
1.91432
31
STATION 3.60000 ROTOR XI 2.88747
ZTIP aZHUB a
.86700
.89000AR -•*LOSS
b.OOOUO ~TT BNATBLADES
IT40.-0. 3. EXP = -o.oooo
2.45000SLOPE
2.40520 2.34510 2.24370 2.13240
39.£>0742~CURVATURE
.20000LOSS COEFF
.96906SOLIDITY
1 TOO 000BLADE THICKNESS
.03097AERO BLOCKAGE
.96100TOTAL BLOCKAGE
.88366BLADE ANGLE
57.25140LEAN
7.36479Y
-3,32000
NOR ITERS
Bl
.07639
.97207
1.00000
.03396
.96100
.87462
55.83620
5.71752
-3.19400
45.25784
.28169
1.99400
53.14836
.01780 -.11920
2 AREA RATIO
2.40684
. 166 ___„
.98720 .99423 .99643 .99725
r.OWffff ' " 1 • OtfOD 0 " l . O O O O T T 1 . 0 0 0 0 0
.03838 .04447 .04788 .05525
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.-8608T - .B3974" TBZ35T .79148
54.34767 50.9H25 43.81139 32.82765
3.55145 1.27933 1.59436 1.71574
-3.00000 -2.88000-2.83000 -2.95000
a .99981 EXP « 1.50000 CHOKE • .75771
RADIUS2.45000
2.86700 .86918
CROSS PASSAGE DIST Pi .45658 .41336
SLOPE,39.50742 38.20198
CURVATURE.20000 .07274
DELTA CURVATURE0.00000
VM517.27854
VU2667.88776
U1494.50000
VR329.08142
BETA252.24222
BETAS*"59". 13 9'18
2.34379
.87236
.35024
37.67940
.20614
.00643
595.94359
648.92864
14 6 8.17118 1429.71411
324.41549 364.26616
51.46563 47.43717
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534.57425
658.66926
2.24274
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40.11559
-.19219
-.00040
627.72697
584.74504
2.13054
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44.83716
-.06571
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650 80176
489.36428
1.99400
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1368.07215 1299.6287?
404.46456 458.87674
42.96971 36.94098
50". 61539 46.67899
647.60327
313.92687
1216.34000
518.20656
25.86186
38.94733
32
INCIDENCE
.20215 »7481V
•68037 .68137V2844,77876 842.03524
TOTAL TEMP1.39268 1.37777
TOTAL PRESS2*88452 2.80752
EFFICIENCY.89027 .89814
STATIC TEMP1.24155 1.22989
STATIC PRESS1.92222 1.87967
DENSITY1.54824 1.52832
SUCT SURF VEL1012.06728 979.44960 1
PRESS SURF VEL677.49023 7{)4. 62087
DELTA T31.90110 23.47185
WORK COEF a 2»CP*OELT/U»»2.17326 .13209
FLOW COEF a VM/U.34612 .35730
k BAR2.42750 2.36<f66
D-FACTOR.17541 .15501
VM2/VM1.91348 .86305
DELP/Q.23863 .23267
TANG BLADE FORCE LS/IN18.88538 14.44547
AXIAL BLADE FORCE LB/IN38.46296 31.87692
VEL HEAD 2.26575 .26638
QsE»*<-S/CP).96906 .97207
RVU/3.32000 3.19400
DRVU/DM6.20156 5.05842
STRMLN OIST M1.4 7595 1.46564
-1.29818
.72132
881.05456
1.35483
2.79416
.95113
1.20150
1.82782
1.52129
052.17825
709.93088
30.65573
.18193
.41683
2.32187
.15683
.95686
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19.97937
36.89320
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3.00000
5.89303
1.46214
-.68550
.70857
857.88572
1.34063
2.76045
.97729
1.18049
1.76099
1.49174
1002.46777
713.30368
25,15279
.16303
.45884
2.21733
.14710
,92454
.23049
16.28372
32.86703
.28383
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2.88000
4.71978
1.49613
2.07200
.67756
814.26060
1.33473
2.73897
.98576
1.16306
1.68394
1.44785
978.18002
650.34118
26.99324
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.50076
2.09972
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1.01413
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15.55246
25.67952
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2*83000
4.99793
1.60933
3.32469
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719.68054
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2.85143
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1.63694
1.41993
855.21794
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27.61311
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1.95150
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1.0323,0
.2311,7
12.76721
19,99862
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.99725
2.94986
3.8206,1
2.01953
33
STATION 3.80000 ROTOR XI a
,* •• 1. ZTIP » .92bOO AR ••»• -0. ZHU8 a .95600 LOSS ••
RADIUS2.49600 2. 5260 2.39450
SLOPE40.39805 39.58730 39.39B1B
CURVATURE.22000 -.01659 -.00959
LOSS COEFF.96611 .96925 .98150
SOLIDITY1.00000 1.00000 1.00000
BLADE THICKNESS.02357 .02623 .02945
AERO BLOCKAGE.95300 .95300 .95300
TOTAL BLOCKAGE.89571 .88811 .87838
BLADE ANGLE55.65959 54.43986 52.19366
LEAN11.93187 10.32751 8.86219
Y
4.25158
6.0UOOU XN3. EXP »
2.29810
41.37679
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46.98038
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2.19620
45,24561
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36.48599
9.05259
-3.70000 -3. 55400 -3.37240 -J. 22000 -3.Z7350
NOR ITERS = 1 AREA RATIO » 1.00088 EXP »• 1.50000 CHOKE
RADIUS2.49600 2.45335 2.39165
Z.92500 .92817 .93276
CROSS PASSAGE DlST P.41815 .37538 .31351
SLOPE40.39805 38.67128 39.12227
CURVATURE.22000 .00146 .22293
DELTA CURVATURE0.00000 -.00069 .00206
VM475.93052 485.77793 558.24571
VU2618.31321 612.87712 598.76248
2.29561
.93990
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41.03700
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616.12253
544.69213
2.19420
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44.88034
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645.74998
428,40587
2.07900
51.93587
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18.45993
9.51482
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2.07900
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0.00000
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0.00000
685.08553
296.81333u1522.56000 1496.54275 1458.90664 14Q0.32407 1338.45924 1268.19QOO
VR308.44782 303.53914 352.24058 404.51311 455.65977 539.38250
BETA252.41363 51.59897 47.00558 41.47874 33.56123 23.42466
BETA2*59.62152 58.24943 54.12159 49.52911 43.11484 35.0960*
34
INCIDENCE1.03619 1,23387
.62093 ,62553V2780.26988 782,04767
TOTAL TEMPIi4376g 1,42035
TOTAL PRESS3.19255 3.09437
EFFICIENCY.88867 .89610
STATIC TEMP1.27167 1.25875
STATIC PRESS2.06969 2.01933
DENSITY1.62754 1.60424
SUCT SUHF VEL872.34953 892.25923
PRESS SURF VEL688.19023 671.83612
DELTA T23.31235 22.08538
WORK COEF H 2»CP»DELT/U»»;.12199 .11962
FLOW COEF a VM/U.31259 .32460
K B^R ' -2.47300 2.43009
D-FACTO*.13184 .12490
VM2/VM1.92007 .92604
OELF/Q.21196 .20462
TANG BLADE FORCE LB/IN13.73014 13.22218
AXIAL BLADE FORCE LB/IN28.24647 26.461*5
VEL HEAD 2.22828 .23114
QsE*»(-S/CP).96611 .96925
RVU/3.70000 3.55400
DRVU/DM3.35252 3.97501
STRMLN DIST M .:1.54998 1.54077
-.57047
.66193
818,62982
1.39887
3.06522
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1.23176
1.95535
1.58744
914,09841
723.16123
22.846102
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2.36772
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15.24 77
21.70808
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3,37240
3.17291
1.53920
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822.37248
1.38085
3.05976
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1.20416
1.88616
1.56637
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725,16195
20.85841
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2.26918
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23,80633
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3.22000
2.99272
1.57795
1.27974
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774.93524
1.38718
3.13621
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1.18928
1.82050
1.53076
883.86019
666.01029
27.20796
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2.16237
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26.66630
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3.27350
3,07067
1.69983
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746.61927
1.39157
3.17989
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1.70705
1.46284
838,56459
654.67396
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2.03650
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1,05788
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12.18285
16,98435
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3.31064
2.42315
2.12715
35
Rotor IB Exit,
STATION 4.00000 ROTOR XI • 5.98088
P «--0
2TTP -ZHUB a
,~980(TO1.02000 LOSS
-6<rOOUtrO3. EXP
XN~« -------- a* - 8NXT -»* -0.0000 BLADES =
-.0,1.
2.54030SLOPE
CURVATURE.24280
LOSS COEFF.96317
SOLIDITYIYODOW
BLADE THICKNESS.01078
f fERa BLOCKAGE.95300
TOTAL BLOCKAGE
BLADE ANGLE53.46013
TEA'M ........14.67896
Y
2
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2.44280
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50.15388
13.72569
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2.35350
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1.00000
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42.06407
15,32252
"3, 36928
2.25910
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1.00000
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26.71148
18.48976
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2.15900
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20.99815
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MOR ITERS 3 1 AREA RATIO » 1.00089 EXP * 1,50000 CHOKE * ,67667
RADIUS2.54080
T~.98000
CROSS PASSAGE
SLOPE40*34944
2.49839
.98444DIST P
39.71951
.24280 .43332DELTA CURVATURE
0.00000 .W43TVM "407.76993 439.03627
VU2633.55074
VU1916.33726
U1549.88800
VR264.00977
BETA257.23358
, .TAl66.01092
BETA2*63.87138
600.12438
923.89194
1524.01632
280.55734
53.81169
64.58276
60.63288
2.44013
.99055
.28267
40.92017
,38684
514.82116
616.22463
872.25395
1488.47858
337.21150
50.12311
59.45005
57.73656
2.35017
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43.15562
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551.20328
559,09199
974,51425 ~ —
1433.60624 1
377.01336
45.40706
57.77689
54.27609
2.25727
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46.06735
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596.47451
461.68960
376,93275
429.55475
37.74096
56.90722
48.12812
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337.07818
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56.66484
39.64818
36
8ETA1«71.26618
CIDENCE-63.84075
M2.59494
Ml.79198
V2753.43404
VI1002.97073
TOTAL TEMP1.45143
TOTAL PPESS3. 26688
EFFICIENCY,88159
STATIC TEMP1.29156
STATIC PRESS2.16292
DENSITY1.67466
SUCT SURF VEL690.93919
PRESS SURF VE915.9289Q
UcLTA T7.16364
WORK COEF = 2.03618
69.92173
-65.85982
.58951
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743.5738H
1022.90233
1.44756
3.27539
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1.28126
2.12811
1.66094
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65.96390
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802.97797
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1.41269
3.21566
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1.24965
2.08486
1.66836
711.70516
894.25078
7.16548»H
.03 323
65.30698
-82.25337
.63563
.83690
785.11713
1033.73122
1.39850
3.19548
.97680
1.22867
2.02232
1.64^94
0.00000
0.00000
9,15807
,05405
65.66914
87.21228
.61512
.89091
754.28054
1092.45223
1.40058
3.24193
.98594
1.21090
1.93860
1.60096
0.00000
0.00000
6.95076
.04447
67.45669
72.49670
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727.36273
1172.88620
1.41021
3.32967
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1.19151
1.83564
1.54060
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0.00000
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2.5184QD C A f* T rt (Ufr AC TOW
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.85678OELP/Q
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2.47587
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45
STATION 5.40000 STATOR XI a
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340,91783
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42,25380
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2.3627Q 2.35988
2.32239
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565,82037
1.41269
3,10303
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3 ."007 03
47
Stator 1A Exit
STATION 5.50000 STATO«
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IVflOOOO
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BETA2*47.94451"
38.73410
45, 7~30 f5
39.00737
46.231ST
36.48873
43.69192
3Q8.5H69Q
35.80023
3 3 4j 2 4 260
34.48720
48
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7.80873
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539.60258
1.41269
3.07670
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1.63525
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2.49384
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589.29346
1.40058
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2*68422
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6.53811
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626.31338
1*41021
3*10706
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1.34T8T
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3, 09324 r
49
Stator IB Inlet
STATION
"» 0. ZtlP* -0. ZHUB
RADIUS3.25800
SLOPE33.38000
CURVATURE-.28210
LOSS "COEFF"1.00000
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= 1.84000= 1.84000
3
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3.00000
35.00000
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1.00000
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36*08000
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33
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93041
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V9303T"
-42.63979
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15 EXP * 1.50000 CHOKE
3
1
35
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3.03053
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35.48099
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324.41611
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45.77997 43.88547 45.18832 43.26590 tTi'Sl'BZT 43.25781
50
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300.60582
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51
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0".-0. ZH08 1.98500
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3.01380
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soornr —
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BETA2»34.06966 34,08931 33.86282 34.00904 33.98733
3.01380
1.92500
OVOWffO"
34.28300
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0.00000
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252.70689
1838.41800
257.84574
28.90110
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52
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2.80344
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360.89980DELTA T
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3.28515 3.255730-FACTOR
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1.09019 1.06067
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1.33866 1.34430ORVU/DM
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3.11434
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12.06016
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1,28483
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2.98390
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1.04342
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1*24854
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3.47828
53
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V-20 .8606 0 - 1 9 ,~37 0~0 6
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JOO AR » 4.UUUOO *500 LOSS a 2, EXP a
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57
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"58
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Stator IB Exit
STATION
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61
APPENDIX E
MECHANICAL DESIGN ANALYSISOF NASA 10/1 ADVANCED
COMPRESSOR RIG
(11 pages)
MECHANICAL DESIGN ANALYSISOF NASA 10/1 ADVANCED
COMPRESSOR RIG
This report summarizes the mechanical design analyses completed ohthe NASA 10/1 Advanced Compressor Test Rig. .The analyses include(1) the first stage compressor blade stress and vibration and (2) thefirst-stage compressor disk stress.
First-Stage Compressor Blade Stress and Vibration Analysis
The first-stage compressor consists of two blade rows, rotor 1A androtor IB. The compressor is made of titanium (90Ti-6Al-4V) . Thematerial properties at room temperatures are as follows:
: Tensile Strength = 130,000 psi
Yield Strength = 120,000 psi
Rotor 1A has 20 blades and rotor IB has 40 blades. A finite elementprogram has been employed to analyze the aerodynamically designedblade for the centrifugal, thermal, and gas pressure stresses. Thesame program also computes the natural frequencies and mode shapesof the compressor blade.
The distributions of centrifugal stresses in the blades of rotors 1Aand IB are shown in Figures 1 and 2. The stresses are based on the100-percent operating speed (70,000 rpm). The distributions of thecombined stresses due to centrifugal force, thermal gradient and gaspressure in the blades of rotors 1A and IB are shown in Figure 3 andFigure 4. The tangential and axial forces acting on the bladesresulting from gas pressure difference are listed in Table I. Thetemperature distribution of the blade is assumed to equal the totalrelative gas temperature. The calculated blade stresses are notexcessive and they are within the acceptable level.
The inrerference diagrams drawn for the natural frequencies of theblades are shown in Figures 5 and 6. In Figure 5, a 10-percent to20-percent increase of the first bending resonant frequency due toblade variations, as observed in the salt pattern test of NASA 6/1Advanced Compressor rotor blade,would interfere with four-per-reyo-lution excitation very close to the 100-percent operating speed.Four struts are currently used upstream of this rotor in the inletduct. The interference possibility of seven and eleven struts isalso indicated. ;
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ft
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4
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ER
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A seven-strut inlet indicates the rotor 1A blade to be free ofresonance (Figure 5), whereas the rotor IB has a possible resonancecondition near 100-percent speed (Figure 6). Eleven inlet strutsapprear to be a better configuration in that the interference (reso-nance) occurs at a low speed during a start transient.
TABLE I
PRESSURE LOADS vs. RADIUS
Rotor 1A 20 Blades
Radius, in.
Tang., Ib/in.
Axial, Ib/in.
2.13
66.0*
93.84
2.083
61.8
90.57
2.008
.54.7
86.86
1.871X
46.36
77.91
1.7
36.87
64.25
1.454
25.14
41.72
Rotor IB 40 Blades
Radius, in.
Tang., Ib/in.
Axial, Ib/in.
2.541 2.503 2.447 2.360 2.264 2.159
81.34 80.28 76.7 72.75 70.3 64.84
147.9 144.3 143.3 134.1 123.3 108.4
* Loads indicated are pounds per radial inch and are totals for indi-cated blade numbers.
-tr--r"f- ..- • ' • :" r- ;. : : - : . ' • : . . : . :~n.-.-..::1::"::-:.t~;':"r
:!_:j.___..L_....;:..;
First-Stage Compressor Disk Stress Ana3.ys.is
A finite element program has been employed to analyze the centrifugaland thermal stresses of the disks. The calculated tangential, radial,and equivalent stresses of rotor 1A and rotor IB are shown in Figures7 and 8. A summary of pertinent information is listed in Table II.The stresses based on 100-percent operating speed (70,000 RPM) aresatisfactory.
TABLE II
ROTOR 1A ROTOR IB
Weight, pounds 0.56 0.55
2Polar Moment of Inertia, in-lb-sec 0.00123 0.00293
2Diametric Moment of Inertia, in-lb-sec 0.00129 0.0015
Maximum Tangential Stress at Bore, psi 38,000 66,000
Average Tangential Stress, psi 14,077 36,697
Average Burst Speed, rpm 190,100 117,800
Average Burst Margin, percent 271 168
Blade Tip Radial Growth, in. 0.003 0.005
Blade Tip Axial Growth, in. 0.005 0.008
NOTES: (1) N = 70,000 rpm(2) 5 = 0.16 Ib/in2(3) Burst Factor Assumed = 0.8
NOTE • <// MATERIAL • Tl TAfiflUM (9o Tl-bA I-4V)
. (Z). 100%
RAD/AL STRESS
EQUIVALENT STRESS
STZ£SS DISTRIBUTIONS IN
IMPELLER D/-SK - ROTOR I A
FIGURE 7
38KSI
7AHGZNTIAL STRESS
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11
APPENDIX F
REFERENCES
(1 page)
REFERENCES
1. Love, G., "Pressure Rise Associated with Shock-Induced Boundary-Layer Separation," NACA TN 3601, 1955.
2. Johnsen, I. A. and Bullock, R. 0., "Aerodynamic Design of Axial-Flow Compressors," NASA SP-36, 1965.
3. Stark, U., "Flow Investigations Around Swept Cascades at Compres-sible Subsonic Flow," Institure for Aerodynamics of the GermanResearch Laboratory for Aeronautics and Space, DFL Report No.0331, June 1966.
4. Smith, L. H. Jr. and Yeh, H., "Sweep and Dihedral Effects inAxial Flow Turbomachinery," Trans-of ASME, Journal of BasicEngineering, Series D, Volume 85, No. 3, September 1963.
5. Beatty, L. A., Savage M., and Emery, J. C., "Low-Speed CascadeTests of Two 45° Swept Compressor Blades with Constant SpanwiseLoading," NACA RM L53L07, March 1954.
6. Godwin, W. R., "Effect of Sweep on Performance of CompressorBlade Sections as Indicated by Swept-Blade Rotor, Unswept -Blade Rotor, and Cascade Tests," NACA TN 4062, July 1957.
7. Gothert, B., "High-Speed Measurements on a Swept-Back Wing(Sweepback Angle * = 35°)," NACA TM 1102, 1947.
8. Katsanis, T. and McNally, W. D., "Fortran Program for CalculatingVelocities and Streamlines on a Blade-to-Blade Stream Surface ofa Tandem Blade Turbo-machine," NASA TN D-5044, March 1969.
9. Pampreen, R. C., "Design and Test of a Cascade Radial Diffuser,"AiResearch Internal Report AD-5100-R, June 1966.
10. Keenan, M. J. and Bartok, J. A., "Experimental Evaluation ofTransonic Stators," NASA CR-72298, 1969.
11. Von Doenhoff, A. E. and Tetervin, N., "Determination of GeneralRelations for the Behavior of Turbulent Boundary Layers," NACARep. 772, 1943.
12. Garner, H. C., "The Development of Turbulent Boundary Layers,"ARC Rep. 2133, 1944.
13. K. G. Harley, J. Harris, and E. A. Burdsall, P&W Report, "HighLoading Low-Speed Fan Study," NASA CR-72895, 1972.
14. Seyler, D. R. and Smith, L. H., Jr. "Single Stage ExperimentalEvaluation of High Mach Number Compressor Rotor Blading," NASACR-54581, 1967. •
APPENDIX G
PERFORMANCE PARAMETER DEFINITIONSSYMBOL DEFINITIONS
(4 pages)
PERFORMANCE PARAMETERS
Diffusion Factor
For the rotor,
.. , r9V - r,VV2 2 U2 l ul
D = 1.0 - w=r.+ =z -1 2raV1
l
and for the stator
v2D = 1.0 - -
vl
Loss Coefficient
For the rotor,
PI I T^ ' /T n ' I -'- * - P• /m i I ot/a-1
p pTl Sl
and for the stator .
PT ' PT0) =
PT ' PSTl Sl
TL2
- SYMBOL DEFINITIONS
a Distance along chord line to point of maximum camber linerise (inches)
A Flow area (square inches)
A* Critical flow area (square inches)
AR Blade aspect ratio (mean blade height/mean chord)
C Blade chord (inches)
H Actual stage enthalpy rise (feet)
i Incidence angle (degrees), Blj-. - 3^ -, „ -.^ . /air Dxaoe
L Distance along chord line from leading edge (inches)
m Meridional length (inches)
M Mach number
N Shaft speed (rpm)
N, Number of bladesb
W Specific speed defined on Figure 1s .
P Pressure (psia)
PR Pressure r'atio
Q Volumetric flow rate (cubic feet/second)av
R,r Radius (inches)2 P UT RT
Re Reynold's number^ ~£
s Blade circumferential spacing (inches)
t ' Blade thickness (inches)
t REF Reference tip speed = 610 feet/second
U. Rotor tip speed (feet/second)
V Velocity (feet/second)
SYMBOL DEFINITIONS (Contd)
M Viscosity, Ib/ft-sec
p Density, slugs/ft3
oW Weight flow rate (pounds mass/second)
Z Axial length
B Relative air angle or blade angle (degrees)
a Specific heat ratio
6 Reduced pressure or deviation angle (degrees)
\\> Stream function
(P2/P )a-1/oi - 1
n d Adiabatic efficiency, - T~~7r — ~~I -
a -I/a In Polytropic efficiency,p
0 Reduced temperature, T/518.68
6* Boundary layer momentum thickness
CNba Solidity, — —2irr
$ Blade camber, 32 - 3,
^ Total pressure loss parameter
Subscript
1 Upstream
2 Downstream
eff Effective
geo Geometric
LE Leading edge
SS Supersonic
SYMBOL DEFINITIONS (Contd)
Subscript (Contd)
S Static condition
t Tip ; r
T Stagnation condition
TE Trailing edge
u,e Tangential component
Superscript
1 Relative condition
;~ Averaged value
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