advanced two-stage compressor program design of inlet si

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

NOTICE

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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.


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.


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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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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FIRST STAGECENTRIFUGALCOMPRESSORPR = 4.75/1

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SECOND STAGECENTRIFUGALCOMPRESSOR

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1.0 2.0

AXIAL DISTANCE, INCHES

Figure .4. - Meridional View At Flow Path ForCentrifugal-Centrifugal Configuration.

11


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

fclPavg 2

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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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

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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/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


(b) Specific speed , 41.3 44.9

(c) Stage efficiency, nad* 0.802 0.822

Combined stages


(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 '•


(b) Specific speed, Ns 42.4 44.9 47.6

(c) Stage efficiency, nad* 0.798 0.812 0.825

4. Combined stages


(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


(b) Rotor efficiency, n d* 0.944 0.955

(c) Overall efficiency, n * 0.898 0.907clCl

4. Centrifugal stage


(b) Specific speed, N 47.5 48.1s

(c) Stage efficiency, n d* 0.824 0.827

5. Overall compressor


(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


EFFICIENCY, nad * 0.883 0.977 0.988


STATOR 1A (53 BLADES, AR = 0.584)

SOLIDITY 1.73 1.75 1.76


EFFICIENCY, nad * 0.837 0.948 0.922


STATOR 2A (53 BLADES, AR = 0.495)

SOLIDITY 1.5 1.57 1.69


EFFICIENCY, nad * 0.827 0.939 0.905


*Efficiency level valid for compressors with corrected flows of8 Ib/sec or more.

30

o u a oi-l W 09

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co•rH4JrtM

0) 3

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-P Ort! O

CM m0)

^ no a.^H Sfo O

u

aen

^H -Prt CC <1)-2V13 T3•r4 (1)n xQ) -^

en•r4

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

HIH

s

to

Cm•H

o o•p -po oa; o

0) CT5 &*C -rltd raE-i (1). Q

iH -i-lnj gU -H

•H iHC (1)O HU CU

I



EHId

7

7 7 7

CO

tnti

o-P M(tf O-P 4Jw o

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0)

rH -rHnj gO -rH

-rH rH

E5 Q)O MU PU

I

(1)S-i

7 HEH

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)



^ 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

W

o

§H

H>WQ

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


0.8

Figure 23.- Blockage Distribution for Rotor 1A Hub Streamline.

66

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D = 1.0 -V'-V 2r av|

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TIP

A'ACROSS-THE-BLADE (PRELIM. DESIGN)

•<•>THROUGH-THE-BLADE (DESIGN)

THROUGH-THE-BLADE (COMPLETE)

0.8 0.6 0.4

STREAM FUNCTION

0.2 HUB

Figure 26.- Diffusion Factors for Rotor 1A.

69

ow

HU

3-

waCQ

900

800

700

600

500

400

300

SUCTIONSURFACE

PRESSURE SURFACE

0 0.1 : 0.2 0.3 0.4 0.5 0.6 0.7


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,

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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

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^ - -"

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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


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


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


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

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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

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3EHW

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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

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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


2.2

Figure 4. - Stator 1A Blockage Distribution.

97

10050% STREAMLINE

751.8 1.9 2.0 2.0 2.1



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


2.8 2.9


99

100TIP STREAMLINE

t2.4 2.6 2.7 2.8 2.9


Figure 50. - Stator IB Bockage Distribution.

100

50% STREAMLINE100

2.6 2.7 2.8 2.9


3.0 3.1

Figure 51. - Stator IB Blockage Distribution.

101

1.00HUB STREAMLINE

0.803.2 3.3 3.4 3.5


3.6 3.7

Figure 52. - Stator IB Blockage Distribution.

102

w

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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

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600 —

500

400

0.1 0.2 0.3 0.


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


.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


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

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CO o o

0.1 0.2 0.3 0.4 0.5 0.6


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.


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

§


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


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

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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 boundarylayer 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


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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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

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ACA RM L55

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EXPERIMENTAL DATA NACA RM L55J05


CARTER'S RULE USING ACTUAL TRAILINGEDGE AND LEADING EDGE ANGLESi , . iCARTER'S RULE USING EQUIVALENT TRAILINGEDGE AND LEADING EDGE ANGLES

10 20


Figure 8. - Change in tangential momentuna/ideal versusangle of attack.

30

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CARTER'S RULE USING EQUIVALENTTRAILING AND LEADING EDGE ANGLES

65 (12A1Q)10

= 30.0

10 20

a. (ANGLE OF ATTACK), DEGREES

30


17

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1.1

1.0

2 0-9

0.8

0.7

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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

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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

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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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* CLOCKWISE (VIEWED

CYLINDRICAL COORDINATESC

AL

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DC 0 0 R 0 I N A

,31*159

,563783

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DIRECTION OF ROTOR ROTATION » CLOCKWISE

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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

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.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

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.057364

.030361

.003157

.000730

-.002146

-.003789

-.003235

Y .274546

.255291

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.159613

.131566

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.071666

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-.025910

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-,199876

-.234908

-.269785

-.304424

-.338783

-.340421

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-.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


'.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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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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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*

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(9SQUALLY

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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

.99600

.99600

-0.00000

-0.00000

-o.ooooo

.80000 CHOKE

2.61665

-4.12500

,3366.':»

-16,47023

-,22670

.00010

187,53331

0*00000

1596,15566

-59.41279

0,00000

0.00000

2.28000

-18.14000

-.28540

-0.00000

1*00000

.99600

.99600

-0.00000

-o.ooooo

-0.00000

* .26613

2.28QOO

-4.12500

0.00000

-18.14000

-.28540

o.ooooo

207,89497

0,00000

1390,80000

-64.72603

0.00000

0.00000

I N C I D E N C Eo.ooooo

.13722V2152.6219?

TOTAL TEMP1.00000

TOTAL PRESS1.00000

EFFICIENCY0.00000

STATIC TEMP.99630

STATIC PRESS.98698

DENSITY.99065

DELTA T0.00000

WORK COEF s0.00000

FLOW COEF =.07068

R BAR3.54000

D-FACTOR0.00000

1.00000

0.00000TANG BLAOE F

0.00000AXIAL BLADE

0.00000VEL HEAD 2

.01302Q=E*»(-S/CP)

1.00000

0,00000DRVU/UM

-0.00000STRMLN DIST

-4.12500

0.00000

.14054

156.30901

1.00000

1.00000

0.00000

.99612

.98635

.99019

0*000002*CP»OELT/U»«

0.00000VM/U

.07486

3.42314

0.00000

1.00000

0.00000ORCE L9/IN

0.00000FORCE LB/IN

0.00000

.01365

1.00000

0.00000

-0.00000M

-4.12500

0.00000

.14584

162.17091

1.00000

1.00000

0.00000

.99582

.98b31

.98944

0.00000>2

0.00000

.08194

3,24461

0.00000

1.00000

0.00000

0.00000

0.00000

.01469

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1.14673

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11.81866

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0.00000

20.r8DOO

.80000

49.59039BETA2

0.00000BETA2*

0.00000

49/055T8

0.00000

.00096 -.00062 -.00154

563.8886^" ""490.16335" 4HJT.62704

J) ,0 0 0 Q 0_ 0.00 00 0 0. 00000

1003.04067 874.75960 699.50432

0.00000 O.OOOOQ 0.00000

0.00000

26 4."4 026 6

0.00000

366.00000

0.00000 0.00000 0.00000 0.00000

0.0 0000

0.00000

12

INCIDENCEOe00000

.58751V~2633.45865

TOTAL TEMP1, 00000

TOTAL PRESS1.00000

EFFICIENCY0.00000

STATIC TEMP.93623

STATIC PRESS.79227

DENSITY.84624

DELTA T0.00000

WORK COEF s0.00000

FLOW COEF a VM/U.57231

R BAR1.83775

D-FACTOR-.20495

VM2/VM11.20*95

DELP/U-.41540

TANG BLADE F0.00000

AXIAL BLAOE1.45106

VEL HEAD 2•Z0773

Q=E**(-S/CP)1.00000

RVU/0.00000

DRVU/pM-0.00000

STRMLN OIST.01379

0,00000

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605.67597

1. 000 00

1.00000

0.00000

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0.00000DRCE LB/1N

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1.00000

o.ooooo

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0,00000

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563.88868

- Y. 000 00

1.00000

0.00000

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0,00000c

0.00000

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1.65572

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1.17278

0.00000

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1.00000

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0.00000

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490.16335

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o.ooooo

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1,00000

0.00000

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0.00000

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401.62704

":~ I.OOWO

1.00000

0.00000

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OTOOOOO

0,00000

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l.lTOSer

-.09075

1.09075

-.18355

0,00000

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1.00000

o.ooooo

" -0,00000

»•. 05927

0,00000

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264.40266

1.00000

1.00000

0.00000

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O.OOOOO

0*00000

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1.04355

-.08773

0.00000

-.22459

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1.00000

0.00000

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13

Rotor 1A Inlet

STATION 1.00000 ROTOR XI a

p * 1. ZTIP a U. 00000,,. ., AR a 3.= 0. ZHU8 = 0.00000 ' LOSS a

RADIUS ~ ~1.91300 1.84000 ..1. -74000

SLOPE20.3T050 21,TO(TOF 2 .Z3WO~

CURVATURE.49296 .28700 ,28600

LOSS COEFF1.00000 1.00000 1.00000

SOLIDITY1.00000 1,00000 1.00000

BLADE THICKNESS.01174 .01201 .01255

AERO BLOCKAGE.98000 .98000 .98000

TOTAL BLOCKAGE,97904 ,97899 ,97887

BLADE ANGLE59.26314 58,35051 57,17567

LEAN.94632 2,23809 3,55011

Y0.00000 0.00000 0.00000

MOR ITEHS = 1 AREA RATIO s 1.00082

RADIUS1.91300 1.85028 1.75006

Z0.00000 0.00000 0.00000

CROSS PASSAGE OlST P1. '04850 .98578 .88556

SLOPE20.33000 20.24422 20,64932

CURVATURE.49296 .40247 .34868

DELTA CURVATURE0.00000 .00351 .00671

VM675.36652 656.86940 636.21722

VU21166.93000 1128.66885 1067.53566

U1166.93000 1128.66885 1067,53566

VR234.64044 227.29167 224.36034

BETA2 - •-59.93965 59.80117 59,20638

8ETA2»61.51 11 7 61. 3639 I "60 .852*0

0.00000

400003. EXP a

1.56000

ZF.5300U

.52900

1.00000

1.00000

.01432

,98000

.97857

56.57143

4.35245

0.00000

EXP a 1

1.56071

0.00000

.69621

24.97660

.44057

.00603

592.00793

952.03020

952.03020

249.97430

58.12508

60.59075

XN a o.

>

BNXT a 1,—0,0000 BLADES s i.

1,33000

35.00000

.59900

1.00000

T.OOOW

.01835

.98000

.97785

57.55473

2.60429

0.00000

.50000 CHOKE

1,31442

0.00000

.44992

31.49755

.55846

.00303

498.98170

801.79782

801.79782

260.69912i

^ 58.10479

62.04793

.86450

42.53000

.56700

1*00000

I. 00 000

.02630

.98000

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56.48617

5,91810

0. 00 000

a ,74162

.86450

0.00000

0.00000

42.53000

.56700

0.00000

371.73075

527,34500

527.34500

251.28121

54.81959

62.549159 ~

14

INCIDENCE2.22555 2.76*22

1.25633 1.21428V21348.27503 1305.89846

TOTAL TEMP1.00000 1.00000

TOTAL PRESS1.00000 1.00000

EFFICIENCY0*00000 0.00000

STATIC TEMP.92751 .93143

STATIC PRESS.76651 .77800

DENSITY.82641 .83528

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PRESS SURF VEL0.00000 0*00000

DELTA T0.00000 0.00000

3.29834

1.15293

1242.74081

1.00000

1.00000

0,00000

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.84496

0,00000•

o.oouoo

o.oouoo

3.55899

1.03531

1121.08648

1.00000

1.00000

0.00000

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0.00000

0.00000

0.00000

4.27953

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944.38471

1.00000

1.00000

0.00000

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0.00000

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645.19493

1.00000

1.00000

0.00000

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0.00000

0.00000

0.00000WORK COEF = 2*CP*DELT/U**2

0.00000 0.00000FLOW COEF a VM/U

.57875 ,58.199R BAR

1.86375 1.80016D-FACTOR

M. 128*3 -1.15610VM2/VM1

1.06616 1.08452DELfVQ

-.12401 -.16076TANG BLADE FORCE LB/IN

0.00000 0.00000AXIAL BLADE FORCE LB/IN

-4.26027 -3.95459VEL HEAD 2

.61641 .59445Q*E*<M-S/CP)

1.00000 1,00000RVU/

0.00000 0.00000DRVU/OM

1.53101 1.98077STRMLN OIST M

".45144 .42879

o.oouoo

.59597

1.69719

-1.20388

1.12827

-.25064

0.00000

-3.70427

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1.00000

0.00000

2.38156

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0.00000

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1.49737V '

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1.20778

-.42636

0.00000

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1.00000

0.00000

2.92120

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0.00000

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1.23058

-1.35140

1,24240

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0.00000

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1.00000

0.00000

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0,00000

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-1.44020

1.40593

-.94954

0.00000

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.20649

1.00000

0.00000

2.46391

,"5795 T

15

STATION 1.20000 ROTOR XI = .81762

. uoouu AR a TOTOTTOOTJ~ XN •• 0 . B T T O T0. ZHUB B .10000 LOSS a 3, EXP a -0.0000 BLADES B 20.

RADIUS1.94700 1

SLOPE23.o"oinnr 2w

CURVATURE.48400

LOTSTTOEFF.99760

SOLIDITYl.OOOTO T

BLADE THICKNESS.03884

•SERXT BLOCKAGTT.97800


BLADE ANGLE59.17886 58

LEAN.46646 1

-.17150

.87700

.00000

.41000

.99715

.TO OUT)

.04130

.97800

.V0950

.35729

.15476

.22400

1,77800

27.00000

.39000

.99848

1.00000

.04638

.97800

,896f9

57.22589

1.77076

-.27580

1.59700

32.00000

.37000

.99915

1.00000

.05614

.97800

.86857

56.37186

.16200

-.36000

1.35500

36.uOl)oO 46

.35000

.99949

1.00000 1

.07071

.97800

.81556

55.95303 48

-2.88071

«. 4IWO -

.96600

.4uoOO

•39900

,99937

•00000

.05472

.97800

•80167

.13260

.34465)

.457100 -

MOR ITERS s 2 AREA RATIO « 1.00053 EXP a 1.50000 CHOKE « .79880

RADIUS1.94700

Z.08600

CROSS PASSAGE DIST P.98110

SLOPE23.00000

CURVATURE.48400


VM679.10299 6

VU21133.93862 10

U1187.67000 11

VR265.34678 2

BETA259.08306

BETA2»61.13291

1.88408

.08690ST P.91817

4.30210

.50565

.00190

2.26624

6.76211

9.28576

0.78528

7.64050

9.99437

1.78557

,08830

.81966

25.51653

.58653

.00361

682.41207

994,97995

1089.20059

293.96380

55.55550

5*. 24423

1.60363

.09090

.63770

28.968QO

.49929

.00206

657.34676

841.27789

978.21685

318.36697

51.99708

55.64306

1.37143

.09421

.40547

33.38571

.31142

-.00194

574.68693

654.20934

836.57348

316.23456

48.70245

53.74036

.96600

.10000

0.00000

46.40000

.39900

0.00000

329.97218

304.86549

589.26000

238.95664

42.73522

53.26189

16

INCIDENCE1.97828 1.48051

1.21917 1.17261V21321.74039 1274.71717

TOTAL TEMP1.02028 1.02649

TOTAL PRESS1.06446 1.08580

EFFICIENCY.87928 .88958

STATIC TEMP.94653 .95168


DENSITY.86267 .87322

SUCT SURF VEL147^.02201 1447.33108

PRESS SURF VEL1169,45877 1102.10325

DELTA T10.52123 13.74201

.73095

1.10666

1206.51205

1.03262

1.11411

.95188

.95720

.85219

.89029

1390.36306

1022.66104

16.91985

-.81329

.97234

1067.63910

1.04258

1.15527

.97919

.97092

.89828

.92518

1258.98112

876.29708

22.08538WORK COEF » 2*CP«DELT/U*»2

.09048 .12621FLOW COEF 9 VM/U

.57179 .59364R BAP

1.93000 1.86718D-FACTOR

.039T8 .05190VM2/VM1

1.00553 1.03866D'EL"P /Q

.04063 .04649TANG BLADE FORCE LB/IN

5.27018 6.77611AXIAL BLADE FORCE LB/IN

8.12354 9.65081VEL HEAD 2

.59704 .57188Q=E*»(-S/CP)

.99760 .99715RVU/

.17150 .22400DRVU/OM

3.30292 3.61985STRMLN OIST M

.54392 .52203

.17301

.62653

1.76782

.D6744

1.07261

.06096

8.15294

11.80633

.53464

.99848

.27580

3.70066••

.49685

.27998

.67198

1.58217

.10958

1.11037

.10302

9.77808

14.62866

.45366

.99915

.36000

3.65233

.47924

-1.72876

.78509

870.77834

1.04849

1.18001

.98897

.99072

•96584

.97489

1050.77412

690.78256

25.15279

.43598

.68695

1,34293

.1 7654

1.15172

.18189

9.03406

14.88641

.33344

.99949

.41000

3.41331

.50999

5.00144

.39858

449.24894

1.05327

1.19860

.98754

1.02307

1.08150

1.05712

597.63334

300.86454

27.62936

. 96526

.55998

.91525

.53632

.88766

.65245

5.62317

12.39769

.10335

.99937

.45037

2.57688

• 722CTO

1.7

STATION 1.40000 «OTOR XI :

... JTTP s"' 7 • 17200;;~•• AR~--•—-ZHUB a .20000 LOSS ••

1.76046

IV0.

X1 f -»^ ) j "8NXT ar- 1.3. EXP a -o.oooo BLADES a 20.

RADIUS -1.98500

SLOPE2S.56000

CURVATURE.47100

LOSS COEFF.99155

SOLIDITYI.WQOTJ


AERO BLOCKA.97600

TOTAL BLOCKAGE

BLADE ANGLE59.07060

LEAN.34847

Y

1.91700

.41000

.99147

T.WOWIESS

.06013rE ~ •

.97600GE

.87855

58,30032

.25606

•». 69020

1.82500

.33.00000

.45000

.99612

1.00000

.06590

.97600

57.19764

.10707

—• 72360

1.65300

36.00000

.39000

.99793

1.00000

.07658

.97600

.83407

55,91262

-1.86332

— .75000

1.42500

42.00000

.32000

.99900

1.00000

.08744

.97600

.78537

53,52590

-3.57562

•, 76000

1.07400

49.23000

.27400

.99877

Tvtfo ow -.07592

.97600

.7b640

38.79420

-.34511

*»74T)00

MOR ITERS s 2 AREA RATIO 9 1.00097 EXP a 1.50000 CHOKE .80065

RADIUS1.98500

2.17200

CROSS PASSAGE."91143

SLOPE25.56000

CURVATURE.47100

DELTA CURVATU0.00000

VM622.95147

VU21020.16738

U1210.85000

VR268.77629

8ETA258.59021

BETA2»61.15066

1.92408

.17387DIST P

.8504~8

27,50226

.38531RE

.00219

643.54557

954.86873

1173.68647

297.17890

56.02149

59.12901

1.82947

.17678

.75583"

30.56697

.40496

.00224

665.15009

B74. 70747

1115.97723

338.25900

52.74968

B6. 78507

1.65489

.18215

33.64937

.47264

. 0~0~?83

652*40416

733.02958

1009.48T298

361.50323

48.33055

53.46582

1.43316

.18896

.35933

37.53989

.45323

.7JOZ43-

550.75036

874.23033

365.06904

42.58992

49.21866

1.07400

.20000

D. DO 000

49.25000

.27400

U.TOWO -—

450.69335

234.34766

655.14000

341.43339

27.47287

38.53960

18

INCIDENCE~Sr.T358o .74484"

1.06951 1.02913v21195.32841 1151,48825 1

TOTAL TEMP1.07339 1.08163

TOTAL PRESS1.24641 1.28020


STATIC TEMP1.00594 1.00820


DENSITY.98512 .99047

SUCT SURF VEL

-.W8BD

.98318

098.88025

1.08558

1.31842

.95078

1.00602

1.00749

1.00147

1435.74494 1395.25521 1326.97959PRESS SURF V£L954,91189 907,72129 870.78090

"DELTA T27.5*538 28.60057

WORK COEF s 2»CP*DELT/U*«2.22791 .25186

FLOW COEF a VM/U.51447 .54831

o BAR1.96600 1.90408

D-FACTOR.14834 .15525

VM2/VM1.91732 .94325

"DELP/Q.14417 .15096

TANG BLADE FORCE LQ/IN13.96201 14.45875

AXIAL BLADE FORCE LB/IN25.33687 24,52577

WL READ 2.51288 .48865

QsE*»<-.S/CP).99155 .9~9l4T~

RVU/.62050 .69020

DRVU/DM5.26826 5.05612

STRMLN OIST M.63794 .61776

27.47176

.26759

.59602

1.80752

.15184

,97470

,15863

13,69554

22*01105

.46041

.W6T2

.72360

4.44283

.59562

-2.~T54U3

.87672

981.30706

i.oaSTi

1,34044

.97459

1.00891

1.02433

1.01528

1173.23247

789.38166

23.92583

.28*51

.64628

1.62926

714925

.99248

.16899

11.09546

16.52824

.39289

799T9T

.75000

3.53191

.58390

~-y.5TJT47

.72447

813.82060

i.oB~9B9"

1.35070

,98788

1.01621

1,05472

1,03790

974.75540

652,88581

21.47190

.341TSY

.68534

1.40230

.15283

1.04256

.18395

8.36079

11,24311

.29409

.99900

,76000

2,83097

.62307

-.00879

.44981

507.98408

T,0¥763~

1 33973

.98473

~ 1.13r2Tl r -~

1.09432

1.06545

&33T6T37T

382.15439

17.82176

.50 70

.60794

1,02000

.06262

1,36587

.10285

J. 8 658"

2.69990

.12921

,199877

.74087

1.90756

.B69TB

19

STATION 1,60000 ROTOR XI a

p * 1. ZTIP =^ . 25800 AR a 8.a 0. ZHUB a .30000 LOSS a

•' : - • • ' • ; . . \ :\ -!-'•

RADIUS2.02800 1.96200 1,87500

SLOPE28.05000 30.00000 33.00000

CURVATURE.43850 ,38000 .40000

LOSS COEFF.98453 .98554 .99389

SOLIDITY1*60006 1.00000 1 .WO 00


AERO BLOCKAGE.97400 .97400 .97400

TOTAL BLOCKAGE.88431 .87680 " .8641 I

BLADE ANGLE58,76147 58,10414 56.97868

LEAN.17521 .22499 -.35545

Y-1,1 7550 -1.20720 -1.16840

MOR ITEHS * I AREA RATIO a ,99921

RADIUS2,02800 1.97022 1.88049

.25800 .26091 .26544CROSS PASSAGE DIST P

:.~83406 .77 21 .68636SLOPE

28.05000 29.32366 31.36749COR V ATI) HE - -•

.43850 .39979 .32942DELTA CURVATURE

"- ffVD 000 0 .001 CF7 " - ~, OtfOTTVM582.55347 592.07595 610.76159

VW883.50258 828.07518 768.08661

U1237.08000 1201.83595 1T4~T.OW?T T

VR273.94116 289.96491 317.91694

BETA"2" "56.60039 54.43511 51.50921

BETA2*59,80412 58,06169 55~. 82523"

2.88642

50000 XN3, EXP '

1.71300

37.0000D

.37000

.99681

l.OfiOOO"

.07406

.97400

• 8 9~97

54.73916

-1.59983

-l.ri'5(TO~

a 0. 8NXT a lf-0,0000 BLADES a 20.

1.50000

~4C.OWOO

.30000

.99852

~ 1.00000

.07946

.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


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


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


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


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


STATIC TEMP1. 10780 1.10372


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


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


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


STATIC TEMP1.15194 1.14473


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

,21754

.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


AERO BLOCKAGE.96100


BLADE ANGLE58.46244 57

LEAN2.53867 1

Y-2.80000 -2

NOR ITERS = 1

RADIUS2.40500 2

Z.81100

V8TTOO.82800

.36030

•tJ309T

.01196

.97487

.00000

.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

41TO'9»T8-

.07902

.99464

1.00000

.04339

.96100

.83995

54.03466

-2.51336

-2.^7000"

EXP a i.

2.19192

.81830

JXT « 1.-o.oooo BLADES • 40.

2.07060

4 727763

-.09458

.99666

1.00000

.04729

.96100

.8212T

50.00377

-2.20933

--. .39000"

50000 CHOKE *

2.06891

.82252

1.90900

53". &4T23

-.oaooo.99753

1.00000

.05488. _ -

.96100

T78512

43.70551

-1.72651

-2.50WO

' .78809

1.90900

.82800CROSS PASSAGE DIST P

.49629SLOPE

38.72212 38CURVATURE

.17500DELTA CURVATURE

0.00000VM566.27296 607

VU2~ "756.86289 715

.45375 "

.05880

.04437

.00~484 "~"

•81630

.20340

. 391 IB""

37.82425

«, 19296

-. OD094

£_ r *% f\ f\ rt (J OO £ C. • O w * *•'

739,82818

.283 )9

40.96159

.02532

-.00308

678.95802

649.68724

.16000

46.14184

-.08146

-.00366

641,73171

557.35986

U.OOW(T

53.84123

-.08000

o.ouooO

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


STATIC TEMP1.20005 1.19006


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


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


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

.96100 .96100 .96100 .96100

.-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


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

.9 953 53.9895T)

-.00050

534.57425

658.66926

2.24274

.87745

.24906

40.11559

-.19219

-.00040

627.72697

584.74504

2.13054

.88311

.13671

44.83716

-.06571

-.002*7

650 80176

489.36428

1.99400

.89000

o.oooao53.14836

-.11920

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


STATIC TEMP1.24155 1.22989


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


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


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

.21499

19.97937

36.89320

.29205

.98720

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

.99423

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

;i93BT

.50076

2.09972

.11722

1.01413

.19316

15.55246

25.67952

,26395

.99643

2*83000

4.99793

1.60933

3.32469

.60151

719.68054

T734893 ~

2.85143

.93937

T.752W

1.63694

1.41993

855.21794

584.1<f3l4

27.61311

.22641

.53242

1.95150

.10580

1.0323,0

.2311,7

12.76721

19,99862

.21628

.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


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

.23315

.99381

1.00000

.03385

.95300

.86364

46.98038

8.23414

••• 0. BNAT * i»-o.oooo BLADES » 40.

2.19620

45,24561

-.19928

.99621

1.00000

.03769

.95300

.84888

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

.21721

41.03700

.54400

.00090

616.12253

544.69213

2.19420

.94744

.11551

44.88034

.13125

.00109

645.74998

428,40587

2.07900

51.93587

-.18000

.99696

1.00000

•04408

.95300

.82436

18.45993

9.51482

-3,41000

» .73301

2.07900

.95600

0.00000

51.93587

-.18000

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


STATIC TEMP1.27167 1.25875


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


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

.93512

1.23176

1.95535

1.58744

914,09841

723.16123

22.846102

.13021

.38265

2.36772

.12330

.93674

.16913

15.24 77

21.70808

.25401

. 98T50

3,37240

3.17291

1.53920

. -.44542

.67253

822.37248

1.38085

3.05976

.97756

1.20416

1.88616

1.56637

919,58301

725,16195

20.85841

.12904

.43999

2.26918

" ,V9wr

.98151

.17935

T4.16IW

23,80633

.26075

.99381

3.22000

2.99272

1.57795

1.27974

,63769

774.93524

1.38718

3.13621

.98642

1.18928

1.82050

1.53076

883.86019

666.01029

27.20796

.18424

,48246

2.16237

""V V25T2

.99224

.22614

ir.46869

26.66630

.23873

.99621

3.27350

3,07067

1.69983

4.76099"

.62024

746.61927

1.39157

3.17989

.98920

" T.166?4~

1.70705

1.46284

838,56459

654.67396

; 22.13368

' ,T¥S9T

.54021

2.03650

,0376b

1,05788

.15519

12.18285

16,98435

.22785

.99 9*

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


f fERa BLOCKAGE.95300

TOTAL BLOCKAGE

BLADE ANGLE53.46013

TEA'M ........14.67896

Y

2

1

52

13

*• 3

.50020

.31647

.96646

. ootro.01188

.95300

.95228

.87353

.99358

77¥4ir<r "

2.44280

.30135

,98517

.01298

.95300

.95219

50.15388

13.72569

•3.48920

2.35350

.06521

,99339

1.00000

.01408

.95300

.95209

42.06407

15,32252

"3, 36928

2.25910

.00277

.99598

1.00000

.01408

•95300

.95205

26.71148

18.48976

"*3. 386.80

2.15900

-.25180

.99668

.01365

.95300

.95204

- 1.286 09

20.99815

••3746765

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

,99997

.19222

43.15562

.17027

- .OTT4-9T —

551.20328

559,09199

974,51425 ~ —

1433.60624 1

377.01336

45.40706

57.77689

54.27609

2.25727

1.00970

. 09BBO

46.06735

.03806

596.47451

461.68960

376,93275

429.55475

37.74096

56.90722

48.12812

2.15900

1.02000

u .uwao

50.86984

•.25180

u ,~owotr ~

644.54236

337.07818

-"979T9T182

1316.99000

499.98Q89

2T.6U834 "

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

.81096

743.5738H

1022.90233

1.44756

3.27539

.89152

1.28126

2.12811

1.66094

0.00000L

o.ooooo

14. 11010*CP»OELT/U*

.07370

65.96390

-73.85987

.64461

.81309

802.97797

101?, 85131

1.41269

3.21566

.94923

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

.59798

.96426

727.36273

1172.88620

1.41021

3.32967

.98859

1.19151

1.83564

1.54060

0*00000

0.00000

9.66864

.06762FLOW COEF = VM/U

.26310R, BAR

2.5184QD C A f* T rt (Ufr AC TOW

. 05252VM2/VM1

.85678OELP/Q

.15228

.28808

2.47587

.08543

.90378

.17919

.34587

2.41589

,03713

.92221

.19451

,38449

2.32289

.06914

,89463

.20467

.43319

2.22573

.04669

.92369

.20686

.48941

2.11900

.05617

.94082

,25528TANG BLADE FORCE L«/IN

4.24229AXIAL BLADE Fi

13.85118VEL HEAD 2

.21226VEL HEAD 1

.337933— C &A t C / /~ O \— tw1* ( " bf Lr /

.96317r- 'M I yU /

3.81677DRVU/UM

-,0b030STRMLN OIST M

1.62092

8.710483HCE LB/IN18.38775

.20895

.35Q27

.96646

3.78400

2,40705

1.61284

5. 04456

21.24493

.24308

.35166

.98517

3.48920

-.07603

1.61463

6.72546

18.35825

.23744

.36713

.99339

3.36928

,68625

1.65910

5.08468

17.02458

.22468

.40202

.99598

3.38680

-.51399

1.78846

6.72325

22.74738

•21412

.44861

.99668

3.46825

.65352

2.2296037

Stator 1A Inlet

STATION 5.00000 STATOR XI 0.00000

p a 0, ZTIP • l.'30a -0, ZHUB a 1.30

RADIUS2.82900 2.80000

SLOPE42.17000 41.00000

CURVATURE-.08767 -.13000

LOSS COEFF1*00000 1*00000

SOLIDITY1.00000 1.00000

BLADE THICKNESS.01821 .01772

AERO BLOCKAGE.94500 .94500

TOTAL BLOCKAGE.94403 ,94405

BLADE ANGLE-64.05654 -62.67773

LEAN2.17206 .02951

Y-0.00000 -0.00000

MOR ITERS s 1 AREA

RADIUS2.82900 2.79243

Z ~"" ~~- " ' "

1.30000 1.30000CROSS PASSAGE DIST P

.35600 .31943SLOPE

42.17000 42.60118CUR1/ATURE "

-.08767 -.18711DELTA CURVATURE

TT.WOO~0 -.ODI75VM

479.06562 490.77282VU2

822.98682 826.60621U~TTZ5~. 5 0 0 0 TTo'3 .38 231VR

321.61249 332.19989BETA2

59.79603 59.30151BETA2«

66.66309 66.39333

000 AR a000 LOSS »

2.73000

42.00000

-.15000

1.00000

1.00000

.01722

.94500

.94405

-61,24885

-3.30363

3.0000BT K2, EXP a

, 2 . 6 4 0 0 0

44.00000"

-.16000

1.00000

1.00000

.01665

.94500

. 944T5

-59,10606

-10.28877

- O . O O O O O -0,00000

RATIO a 1.00029 EXP * 1.

2.73898

1.30000

.26598

43.52334

-.18604

,00042

528.43361

777.08113

1670.77963

363.90594

55,78334

63.75295"

2.65199

1.30000

.17W9~

44.63871

-.18796

""."DrffOTr

543.45949

774,98706

T6T7.7TFIS

381.85318

54.95993

63.48191

fR|-iF ~-^T. BWXT » -0.•0,0000 BLADES = i.

2.56000 2.47300

^5.00000

-.18000

1,00000

r.iroinnj"

,01649

.94500

.^4403

-58.72378

-15.69511

«*0.00000{,

50000 CHOKE

2.56267

1.30000

.08967

45.63315

-.12816

-.00047

575.73768

806.17146

156T;?2BXI

411.58200

54.46696

63.46344

46.00000

-.13050

1.00000

T.ffooT)ir

.01708

.94500

,94~3TO

-60.71567

-17.14941

-F.iroroo~o

»•. .67317

2.47300

1.30000

0.00000

46.00000

-.13050

O.WOW

609.02632

855.52931

I508".S3TOTJ

438,09702

54.55402

63.58726

38

INCIDENCE3.52232 4753728

.74740 .75643~V2

952.26633 961.31982TOTAL TEMP

1.45143 1.44756TOTAL PRESS

3.26688 3.27539EFFICIENCY

.88159 .89152STATIC TEMP

1.30731 1.30068STATIC PRESS

2.25760 2.24429DENSITY

1.7269Q 1.72547SUCT SURF VEL

0.00000 0.00000PRESS SURF VEL

0.00000 0.00000DELTA T

0.00000 0.00000WORK COEF a 2»CP*DELT/U**2

0.00000 0.00000FLOW COEF = VM/U

.27761 .28812K BAR

2.6849Q 2.64541D-FACTO*

•"05055 ~" .06020VM2/VM1

1.17484 1.11784DELP/Q

.08577 .10127TANG BLADE FORCE LB/IN

-.odooo -.00000AXIAL BLADE FORCE L8/IN

29.95129 31,87609VEL HEAD 2

.30894 .31480Q*E«»(-S/CP)

.96317 ,96646"RVU/

3.81677 3.78400bRVUVOM

-7.54163 -7,12164STRMLN DIST M

"2.05157 2\0*4l6-

2,06065

,74763

939.73249

" T. 4 1269

3*21566

.94923

1.27234

2.22173

1.74618

o.ooooo0.00000

o.ooooo

o.ooooo.31628

2,58956

"— ;07ZT9-1.02644

.12104

-.(TOOOO

31,72610

.30909

~~.91BT7

3.48920

-5.92516

2.04483

2.17 32

.75790

946.54802

1 .398~5b

3.19548

.97680

1.25611

2.18647

1.74067

0.00000"" ""

0,00000

0,00000

0 . 0"0~OW~

.33594

2.50108

TW3*

.98595

,13992

-.00 (TOO

35.37090

.31576

799339

3.36928

-4.83079

ZTOBSSB '

•99235

.79687

990.64944

VTfOOSB"

3.24193

.98594

1.24460

2.13609

1.71628

0.00000

0.00000

0.00000

~ " (T. 000 00

.36830

2.40997

.09319

.96523

.15152

~ --,DOOOO~~

42.08068

.34111

,9¥5W

3.38680

-3.75732

2.20981

-1.04916

.84805

1050.16354

1.41621

3.32967

.98859'

1.23493,

2.08318i

1.68688j

0.00000

0.00000

0.00000

U. 00000

.40372

2.31600

.10465 "

.94490

.16575

,00650

55.46356

.37436

.99668

3.46840

-2.92013

2Y6503T

39

STATION 5.10000 STATOR XI a .83443

f> * 0. ZTIP « 1.36000 AR = 4.UUUOU AN »•• 1. BNAT « 0,a -0. ZHU8 a lt 365:0:0-- LOSS a 2. EXP •• -0,0000 BLADES a 53,

WADTUS2.88260

SLOPE

CURVATURE-.12135

2.84000 2.79000

42 . 0 0 OW 4^. 00 OW

-.14000 -.14000LOSS COEFT

.99691 .99695SOLIDITY

l.OODOO 1.00000BLADE THICKNESS

.04100 .03978AERO BLOCKAGE

.9*331 .94335TOTAL BLOCKAGE

.83013 .83189BLADE ANGLE-58.01493

LEAN-2.55017

Y-50.70000

NOR ITERS s

RADIUS2.88260

Z1.36000

CROSS PASSAGE.34334

SLOPE41.68900

CURVATURE, -.12135

-56.74558

-3.72303

-50.20000

1 AREA

2.84845

1.36050DIST P

.30919

42.10591

-.30510

.99744

- r;oooou.03918

.94335

.83161T

-55.49516

-4.55138

-48.08000

2.70000

44.00000

-.14000

.99830

1.00000

.03867

.94337

78294:0"

*53. 62422

-7.80551

-47.62000

RATIO a .99944 EXP a 1,

2.79748

1.36124

.25821

42.74873

-.42811

2.71297

1.36247

.17369

43.30337

-.50772

2.62000

45,00000

-.14000

.99733

.03979

.94338

.92252

-53.45886

-10.13416

-47.SOOW

50000 CHOKE s

2.62730

1.36372

.08801

44.51415

.,44498

2.53930

45*33150

-.15075

•99603

.04285

,94336

-55,59224

-9.26323

-48Y640TO

* .91667

2.53930

1.36500

0.00000

45.33150

-.15075DELTA CURVATURE

. o.oooooVM536.35408

VU2655.29714

U1758.38600

VR356.72225

50.70000BETA2*

5B~. 56586

-.00115

546.67429

660.56095

1737.55593

366.54695

50.38913

58.45025

-."00385

558.86425

629,86729

1T66.46566

379.34848

* 8. 4 1820

56.9T34T

-.00412~

586,51717

643.29447

1654.91356

402.26946

47.64330

b6. 43560

-.00383-

626.11142

690.10885

1602.65195

438.95773

47.78363

57.09914

~ 0.00000

663.59530

753.68468

r548Y97300

471.93990

48.63709

58 .24162

40

INCIDENCE-.08326 .60754

.65710 .66703V2 • "846.81169 857.43429

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.23135 3.24018


STATIC TEMP1.33746 1.33071


DENSITY1.80971 1.80854

SUCT SURF VEL1622.28594 1026.61076"

PRESS SURF VEL671.33745 688.25781

DELTA T0.00000 0.00000

WORK COEF a 2*CP«DELT/U**20.00000 0.00000

FLOW COEF = VM/U.30503 .31462

h BAP2.85580 2.82044

0-FACTOR.19150 .18675

VM2/VM11.11958 1.11391

OELP/Q.16132 .15746

TANG BLADE FORCE LB/IN-25.71603 -25.38746


VEL HEAD 2.25096 .25725

Q=E**(-S/CP).96019 .96351

RVU/3.09665 3.08455

ORVU/DM-8.70669 -8.31977

STRMLN DIST M2.13202 2.12662 : ;

-.01940

.66276

842.05823

1.41269

3.18669

.94061

1.309W

2.37555

1.82735

995 . 85888

668.25757

0.00000

0.00000

.32750

2.76823

.17436

1. 05759

.15476

-22.87246

44.01699

.25454

,98265

2.88860

-7.26621

2.12953

.34850

.69103

870.53441

1.39850

3.17635

.97088

1.27806

2.31059

1.80789• • •

1013.53923

727.52960

0.00000

0.00000

.35441

2.68248

.14136

1.07923

.12301

-19.75665

37.59349

.27256

.99ITO

2.86105

-6.67322

2. 17198 —

.43898

.74419

931.80778

1.40058

3.21151

.97666

1.26258

2.22604

1.76308

1063.74831

799.86724

0.00000

0.00000

.39067

2.59498

.10857

1.08749

.08134

-16.34520

28.90475

.30686

.TJ9333

2,97233

-b, 22702

~2.3005T

-,16576 "'

.80604

1004.19Q88

1.^1021

3.28325

.97500

1.24994

2.14373

1.71506

1123.01222

885.36953'•

0.00000

0.00000

.42841

2.50615

.08213

1.08960

.04858

-13.09659

21.06481

.34707

.99273"

3.13743

-5.80077

2.74315

STATION 5.20000 STATOR XI • 1.72583

P * -0. ZTIP »s -0. ZHUB »

RADIUS2.93108 2.

SLOPE41.11230 42.

CURVATURE-.15349

LOSS COEFF,99717

SOLIDITY1.00000 1,

BLADE THICKNESS.04564 ,

AERO BTTCTCK AGE.94178

TOTAL BLOCKAGE.81808 ,

BLADE ANGLE-52.62893 -51,

LEAN-4.98158 -5.

Y-45.50000 -44.

1.4150(71.42500

89000

OOUUO

16000

99723

OtJOW

04430

94186

82009

41668

82798

83000

AH » 4.•> .LOSS «

2.84000

43. OOUUO

-.17000

.99763

1.00000

.04332

.94183

,82065

-50.23110

-5.92520

-43.38000

UUUUU AN2. EXP «

2.76000

43,00000

-.17000

.99843

1.00000

.04309

.94186

.81783

-49.03793

-6.22135

-42.30000

«Q.oooo BLADES • 53*

2.67000

44.00000

-.18000

.99752

1.00000

.04417

.94187

.81044

-49.04520

-6.72153

-42.40000

2.59919

44.52400

-.18223

.99636

1.00000

.04715

,94187

.79774

-51.36890

-4.14150

-42.60000

\<OR ITERS = 1 AREA RATIO

2.89769

,99966 EXP * 1.50000 CHOKE » .83773

RADIUS2.93108

z1.41500 1.41601

CROSS PASSAGE DIST P.33204 .29864

SLOPE41.11230 41.40934

CURVATURE-.15349 -.13664

DELTA CURVATURE0.00000 .00072

VM506.QB948 521,06408

VU2515.00075 521,67700

U ;1787.95880 1767.59113 1737.29456 1686,75112 1636.59655 1585.50590

VR332.77268

BETA245.50000

2.84802

1.41750

.24895

41.86401

-.10039

-.00048

5H3. 08847

498.46310

2.76517

1.42000

.16605

41.96615

-.05288

-.00283

553.13392

503.82078

2.68295

1.42243

.08379

43.13245

-.12327

-.00232

585.29689

533.98048

2.59919

1.42500

0 . 00000

44.52400

-.18223

0.00000

631.06646

580.28705

BETA2»53.48427

345.17884

44.98971

53.12011

349,09103

43.61909

51.99156

369,87601

42.32873

50.77466

400.16010

42.37493

51.34340

442.50898

42.59957

52.21193

"42

INCIDENCE-.73718 -.37631

o55388 .56761V2722.04733 737.89498

TOTAL TEMP1.45143 1,44756

TOTAL PRESS3,19921 3.20853


STATIC TEMP1.36857 1.36102


DENSITY1. -09918 1.89603

SUCT SURF VEL875.69116 891.14155

PRESS SURF VEL568.403*9 584.64842

DELTA T0.00000 0.00000

WORK COEF a 2*CP*DELT/U**20.00000 0.00000

FLO* COEF • VM/U.28305 .29524

K BAR2.90684 2.87307

D-FACTOR.22441 .21450

VM2/VM1.94357 .95462

DELP/Q.22043 .20862


AXIAL 8LAOE FORCE LB/IN44.42298 43.48173

VEL HEAD 2.18756 .19573

Q=E»»(-S/CP).95748 .96084

RVU/2.4746Q 2.47813

ORVU/UM-6.9791Q -6.88229

STRMLN DIST M2.20534 2*20082

-.48717

.56231

722.55588

1.41269

3.16008

.93264

1.32971

2.55156

1.91888

864.82969

580.28207

o.ooooo

oYOoooo

,30109

2.82275

.2r394

.93598

.21700

-22Y60406

41,98918

.19256

.98032

2.32727

-6.23984

2.20515

-.61181

,58673

748.19283

1,39850

3.15872

,96541

1,30954

2.50404

1.91215

890,21071

606.17495

0.00000

0.00000

,32793

2.73907

.21437

.94308

.22344

-24.20329

45.98877

.20726

.99014

2.23385

-6.12844

2,24965

-,25534

,62338

792.28000

1.40058

3.18343

,96804

1.30082

2,45187

1,88488

937,37929

647,18072

0,00000

0.00000

.35763

2*65512

.22663

.93481

.22917

-26.58490

51.77275

.22980

.99086

2.34859

-6.33107

2.38150

«•• 71660

,67648

857.30854

1.41021

3,24123

.96258

1.29340

2.38792i

1.84624

1005,39156

709.22552

0.00000

O.WOSO

,39802

2.56924

,?24W "

.95098

.21429

-28.4171*

54.93544

.26327

.98912

2.47258

-6.58885

2.82793

43


p « ^. 2TTP aa -0, ZHU8 a

RADIUS -—•2.98275 2

SLOPE40.33100 41

CURVATURE-.19161

LOSS COEFF,99694

SOLIDITYi.ootfoo T

BLADE THICKNESS•04002

A~Epro BLOCKAGE.94012


BLADE ANGLE-46,84601 -45

LEAN-6.71432 -7

Y-^rrroooo -4<rMOR ITERS a \

RADIUS2.98275 2

7 " "" "'1.47500 1

CROSS PASSAGE DlSV3T664

SLOPE40.33100 40

CURVATURE-.19161


VM470.71372 489

VU2419.39089 420

1.47500 AH « 4.1,49500 LOSS a

.95000

.20000

.99683

.WOOD

.03915

.94016

.48986

.46853

.70000

AREA

.95044

.47704T P. 2S427

.63542

.16847

.00023

.20562

,96115

2.89000

41.00000

-.20000

.99737

1.00000

.03862

.94014

.83417

-44.19821

-7.18996

-39.50000

RATIO a 1.00055

2.90256

1.48007

40.77724

-.18299

-.00008

484.84543

402.88279

00000 XN e 1. BNXT = -0.2. EXP a -0.0000 BLADES = 53.

2.82000

42,00000

-.20000

.99819

1.00000

.03854

.94013

-43.80426

-5.15956

-37.80000

EXP a 1,

2.82243

1.48515

.15601

41,37999

-.16119

~ . OOT88

522.42112

405.97415

2.74000

4Z.UOOOU

•,20000

.99712

1.00000

.03935

.94013

-43.99808

-3.88857

-37.55000

50000 CHOKE

2.74462

1.49007

.07804

42.04346

-.14714

— .— TOiP'OT

552.31914

424,87807

2,66674

43,39600

-,22377

.99572

1.00000

.04104

.94012

•81808

-46,56846

.19175

-37,15000

a ,76556

2.66674

1,49500

OiOWOD "

43.39600

-.22377

595.25271

450.98375u1819.47750 1799,76974 1770.56380 1721.68531 1674.21813 1626.7114D

VR304.64712 318.59205 316.66228 345.34654 369.88498 408.96065

BETA241.70000 40.71196 39,72490 37.85081 37.56970 37.14879

BETA2*49.44947 48.59H2 47,65674 46.00365 46.00887 46.19693

44

INCIDENCE.05374 .09476

.48017 .49278V2630.44438 645.39169

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.16476 3.17269


STATIC TEMP1.38826 1.38136


DENSITY1.94798 1.94664

SUCT SURF VEL735.14932 753.29718

PRESS SURF VEL525.73944 537,48619

.24297

.48697

630.38848

1.41269

3.13079

.92380

1.34953

2.66358

1.97371

730.49010

530.28687"DELTA T " ~ "• ""

0,00000 0.00000 0.00000WORK COEF a 2»CP»DELT/U»*2

0.00000 0.00000FLOW COEF a VM/U

.25871 .27182"~K TOR~ -— ~ -

2.95691 2.92407D-FACTOR

.18742 .18784VM2/VMI

.93010 .93742BEUP7BT" "

.17521 .17273TANG BLADE FORCE LB/IN-16.06146 -l«.13ZbO

AXIAL BLADE FORCE LB/IN24.3468? 25.29719

VEL HEAD 2.14550 .15245

QsE»*(-S/CP).95455 ,95779

RVU/2,05072 2.03610

DRVU/DM-4,37341 -4.43345

STRMLN OIST M2.28452 2.28149

0.00000

.27384

2.87529

.18778

.92689

,18407

-16,95246

25.34783

.14923

.97774

1.91704

-4.05731

2.28816

-.11T8S

.51504

661.61835

1.39850

3.13852

.95910

1.32893

2.62071

1.97204

759.63035

563.60634

0.00000

0.00000

.30344

2.79380

.94447

.17822

-1TV6~4 T93

26.22906

.16498

,WB35~

1.87842

-3.88111

2.33639

i 2 1*43-

•54359

696.83414

1*40058

3.15118

.95808

1. 32340

2.57927

1.94897

796.16420

597.50407

0.00000

0.00000

.32990

2.71378

" .18245

.94366

.17414

-19,54492

28*51699

.18149

•98801

1.91169

-3.94372

.58297

746.80127

1.41021

3.19252

.94804

1.32T5T

2.53812

1.92053

851.9U57

641.69097

0.00000 :

•36592

2.63296

.19660 ~

.94325

.17602

-2T. 0*548"

33.02691

.20498

,98489

1.97157

-4.18526

45

STATION 5.40000 STATOR XI a

P a -0. ZTIP = 1,53500 AR • 4.s -0. ZHUB = 1.55500 LOSS »

RADIUS3,03287 3.00000 2.95000

SLOPE39.38000 40.00000 40.0tHJOO

CURVATURE-.23374 -.23000 -.23000

LOSS COEFF.99697 .99704 .99748

SOLIDITY1.00000 1.00000 1VO 0 OT) 0


AERO BLOCKAGE. .93848 .93858 .93854

TOTAL BLOCKAGE '.86620 .86677 ,86590

BLADE ANGLE-40.96506 -39.57368 -38.31786

LEAN-8.37788 -8.91084 -8.39222

Y-39.34000 -38.1500D -37.35(rOO

MOR ITERS » 1 AREA RATIO a 1.00047

RADIUS3.03287 3.00088 2,95349

z1.53500 1.53706 1.54011

CROSS PASSAGE DIST P-.31113 .27907 .2315T?

SLOPE39,38000 39.72089 39.95845

CURVATURE ~-.23374 -.23201 -.16813

DELTA CURVATURE"OVOOOTHJ -.OOD31 .OD~031T

VM437.87178 457.16175 449. 53830

w?358*90489 359.42973 343.61025

U1B50V0507Q 1&30.5339B lBTnY63U31 I

VR277.81255 292.14854 288.70797

39.34000 38.17512 37.39293BETA2«

^•~67967 45.6ZBT6 44.9T9617

3.68557

00000 *N"«- 1.2. EXP a

2.87000

4ivtrotro(r

-.23000

.99839-

iTOoxxno

,02733

.93860

.86321

-38.66671

-4.77394

-35.0^01)0-

EXP = 1.

2.87406

1.54523

. 15199

40.50369

-.21618

*,00123

491.02652

345.60601

753«"I7380

318.92038

35.13955

42 . 7894TI

8NXT a -,<),-o.oooo BLADES * 53.

2.79000

4~1 vOOOOO

-.23000

.99752

1 OOITOO^

.02799

.93863

- ."85918

"39.55225

-1,92047

-•v*4-,84W<r

50000 CHOKE

2.79825

1.55011

.07603

41.22299

-.20055

-.00280-

517.33267

360,35491

17D67932B7

340,91783

34,85964

42,80262"

2,72238

"4-2,25380 —

-,26448

.99633

tVOWOD

.02923

.93862

,.85361"

-42.38635_. _..

2.81818

*34V20WO—

•• ,70798

2.72238

1.55500

O'ilTOWO"

42,25380

-.26448

o.oooiro

559,06760

379,91410

1660,65180

375.92607

34.19803

42.554-07

"46

INCIDENCE1 .94096 1 YB051 5 ;

.42933 .44204V2566.16641 581.53813

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.13102 3.13967


STATIC TEMP1.40049 1.39381

STATIC PRESS2.75965 ?. 74675

DENSITY1.97049 1.97068

SUCT SURF VEL604.41277 629.95351

PRESS SURF VEL527.92006 533.12275

DELTA T0.00000 0.00000

WORK COEF = 2*CP*OELT/U»»20.00000 0.00000

FLOW COEF s VM/U.23668 .24974

H BAR3.00781 2.97566

D-FACTOR.14470 .T4148

VM2/VM1.93023 .93450

DELPVQ.12020 .11939

TANG BLADE FORCE L8/IN- 1 OT56 195 " IT. 02472

AXIAL BLADE FORCE L8/IN11.35957 11.90294

VEL HEATT 2.11861 .12515

QaE*#(-S/CP).95166 .95495

RVU/1.78445 1.76820

-1.48180 -1.84514STRMLN OIST M

2.3627Q 2.35988

2.32239

.43512

565,82037

1.41269

3,10303

•91538

1.36181

2.72580

2.00160

606.00545

525.63529

0,00000

0, (TOO 00

.24952

2,92803

,14429

,92718

.13317

"• 10 i .~40~531

12.34327

.12157

,97526

1.66369

-1.51614

2. "36689"

'" 1.55092

.46529

600.45863

1,39850

3.12075

.95354

1.34120

2.69188

2.00706

641.9460"6

558.97119

0.00000

0.00000

.28008

2.84825

.13291

.93991

.13744

-117038F9

14.84290

.13743

. 98t>76

1.62835

-1.52427

2T4TS61

2.07392

.48923"" '

630.46709

1.4005B

3.12362

.94950

1.33740

2.65357

1.98412

- -651,46075

579,47343

0.00000

o.ooow

.30308

2.77144

,13609

.93666

.12992

"""11.74725"

14.63525

.15048

,98556

1.65305

-1.87340

2.55351

1.47942

.52448

675.93735

1.41021

3.15133

.93562

1.33760

2.61437

1.95453

735.4502B~

616.42443

0.00000

0.00 (TOO

.33666

2.69456

.13673

.93921

.11652

-13.05149

15.02985

.17039

.98TZ7

1.69553

-2.18208

3 ."007 03

47

Stator 1A Exit

STATION 5.50000 STATO«

r s 0. ZTTP's 1.59000 AR «s -0. ZHUB s 1.62000 LOSS

XI s 5.74866

s""3.00WO "AN » 1. BNXT * Wi"EXP * -o.oooo BLADES »• 53.

RADIUS"3.07700

SLOPE38.35000

CURVATURE-.2769Q

LOSS COEFF.99725

SOLIDITY1.00000


AERO BLOCKAGE.93700


BLADE ANGLE-35.37778 -33.94082

LEAN,-10.05552 -10.35747

Y i-41.00000 -38.50000 ,-39,02000

3.04000

3B.50000

-.15000

.99704

1.00000

.01183

.93700

.90624

3.00000

39. (TOO 00

-.20000

.99759

1.00000

.01160

.93700

,90644

-32.57263

-9.82442

2.90000

39.0TOOO

-.25000

.99832

1.00000

.01150

.93700

.90567

-33.30880

-5.06253

2.82000 2.77900

MOR ITERS =

-.25000

.99730

IVflOOOO

.01150

.93700

.90476

-34.90349

-.38821

-35 .5000 0 ~ -56 . 0 0 OD 0 "

1 AREA RATIO = 1.00078 EXP = 1.50000 CHOKE

RADIUS3.07700 3.04636 3.00098

z """ ""1.59000 1.59309 1.59765

CROSS PASSAGE DIST P.29951 .26871 .22310

SLOPE38.35000 38.56134 39.11304

CURVATURE-.27690 -.22466 -.21224

DELTA CURVATURE0.00000 -.00085 ,00017

VM411^03116 434,23695 M_9v3P629

VU2 '357.30416 348.31419 339.63694

U

2.92407

1.60540

.14583"

39.26516

-.16328

.00179"

461.20854

2.85208

1.61264

.07345

40.21386

-.24100

477.95310

344.71382

40.3bOOO

-.29450

•99600

1.00000

.01136

.93700

.90470

-37.35585

4.51900

34,50600

« .67707

2.77900

1.62000

O.ODOOO

40.35000

-.29450

0.00000

516.24041

354.63262341.13623

.97000 1858.27681 1830.59704 1783."6805T T73T777~074 16"95. 190"00VR255.02998 270.68262 264.52040 291.90370

BETA241.00000

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

INCIDENCE7.30093 5.94156

.41243 .42246V2544,62177 556.67271

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.10075 3.10693


STATIC TEMP1.40429 1.39831


DENSITY1.96490 1.96611

SUCT SURF VEL539.17143 565.41498

PRESS SURF VEL550.07211 547.93044

DELTA T0.00000 0.00000

WORK COEF * 2»CP»OELT/U»»20.00000 0.00000

FLOW COEF = VM/U.21899 .23368

N BAR3.05494 3.02362

Q-FACTOR.04121 .04774

VM2/VM1,93870 .94985

DELP/Q-.00096 .00632

TANG BLADE FORCE LB/IN.72260 -1.21542

AXIAL BLADE FORCE LB/IN-3.35485 -1.841B4

VEL HEAD 2.11012 .11513

Q*E**(-S/CP).94905 .93213

RVU/1,80234 1.73949

DRW/DM.20652 -.32210

STRMLN DIST M2.43321 2.«3205

7.80873

.41426

539.60258

1.41269

3.07670

,90734

1.36641

2.73510

2.00167

537.46396

541.74119

0.00000

0,00000

.22905

2.97724

,04764

.93275

,02467

"" .30033'-1,35962

.11103

.97293

1.67089

,07747

2.44149

6.73144

.44370

573,66126

1.39850

3.10229

.94772

1,34620

2.71137

2.01409

571.66057"

575,66196

0,00000

0.00000

.25857

2.89906

.04584

.93927

.04545

.3W2~

1.66176

.12601

.9851 IT"

1.63525

.06986

2.49384

7.27017

,45592

589.29346

1.40058

3.09396

.94021

T; 34539

2*68422

1.99513

600*22227

578.36466

0*00000

0.00000

.27472

2.82517

.07238

,92388

.06520

- -1.93443

2.74449

.13243

.98290

1.61173

-.38966

2.6367)2

6.53811

.48412

626.31338

1*41021

3*10706

.92214

1.34T8T

2.64827

1.96478

646.55703

606.06974

;' 0.00000

0.00000

.30453

2.75069

.08652

.92340

.06312

-3,97202

4,01748

.14766

,97735

1.61561

-.70945

3, 09324 r

49

Stator IB Inlet

STATION

"» 0. ZtlP* -0. ZHUB

RADIUS3.25800

SLOPE33.38000

CURVATURE-.28210

LOSS "COEFF"1.00000

SOLIDITY1.00000

6.00000 STATOR

= 1.84000= 1.84000

3

3J

-1

1

.

.

.

•

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23000

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3.00000

35.00000

-.28000

1.00000

1.00000

2

a ,0,= 1.

.95400

36*08000

•»

1

I

.29350

.00000

.00000BLADE THICKNESS

.01277AERO BLOCKAGE


.93042BLADE ANGLE-42.56001

LEAN-2.51652

Y-0.00000

NOR ITERS «

RADIUS3.25800

Z1.84000

CROSS PASSAGE.30400

SLOPE33.38000

CURVATURE-.28210

-42

-2

-0

1

3

1

.

.

•

.

.

.

•

.OIST

33

-

•

•

.

01276

93100

93041

56017

66727

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AREA

22812

84000P27412

60852

29582

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93041

57532

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22926

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33810

-42

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.01273

.93100

."93039

.61664

,04335

.00000

.01270

.93100

V9303T"

-42.63979

-3*06200

-0.0 OWO

15 EXP * 1.50000 CHOKE

3

1

35

-

.10517

.84000

.15117

.12798

.31722

3.03053

1.H4QOO

.07653

35.48099

-.30995

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.01263

.93100

V93~077"~

.43921

.86163

700000 ~

51304

.95400

.84000

.00000

.08000

.29350DELTA CURVATURE

0.00000VM393.26146

VU2337.45393

tm

410

328

.

.

.

00067

33761

70200

-384

320

.

.

.

00044

81860

18873

417

321

.00045

.30214

.24025

.00018

419.55221

324.41611

0

438

333

.00000

.70681

.62886u1987.38000 1969.15193 1941.7BT17 1894.15267 1848.62277 1801.94000

VR216.36833 227.12826 216.57259 240.11774 243.52194 258.36080flETS'2™ ' '""~~' •" """"'" " "' ""~"""

40.63256 38.69655 39.76217 37.58915 37.71275 37.25234BETA2*

45.77997 43.88547 45.18832 43.26590 tTi'Sl'BZT 43.25781

50

INCIDENCE2.28982 .36330

•39180 .39824V2518.19854 525.75846 !

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.10075 3.10693


STATIC TEMP1.40875 1.40362

STATIC PRESS2.7904Q 2.78636

DENSITY1.98076 1.98512

SUCT SURF VEL0.00000 O.UUOOO

PRESS SURF VEL0.00000 0.00000

DELTA T0.00000 0.00000

WORK COEF * 2*CP»OELT/U»*20.00000 0.00000

FLOW COEF = VM/U* 19788 .20838

K BAR3.16750 3.13724

D-FACTOR.04852 .05553

VM2/VM1,95677 .94496

DELP/Q,09112 .10379

TANG BLADE FORCE LS/IN0.00000 -.00000


VEL HEAD 2.10009 .10318

QsE»*(-S/CP).94905 .95213

RVU/1.80234 1.73949

DRVU/DM-3.46478 -2.93009

STRMLN OIST M2.74186 2.73865

1.53990

.38341

300.60582

1.41269

3.07670

.90734

1.37286

2.78098

2.02568

0.00000

0.00000

0.00000

O.UOUOX)

.19818

3.09212

.07227

.91775

,13429

-.00000

11.63334

.09612

,97293

1.67089

-3,13213

2.74474

-.46897

.40608

526.62736

1.39850

3.102Z9

.94772

1,35443

2.77036

2.04541

u.Gouoo

0.00000

0.00000

O.OOOoO

. .22031

3.01462

.08199

.90480

.15090

-.00000

13.05247

.10699

.98510

1.63525

-2.52160

2.79022

-.26758

.40873

530.34882

1,40058

3.09396

,94021

1.35587

2.75890

2.03477

0.00000

0.00000

0.00000

0 . 0 0 0 0 0

.22695~ "

2.94131

.10003

.87781

,18226

-.00000

15.37957

.10830

.98290

1.61173

-2.49886

2.92504

«•» 28765

.42382

551.15504

1.41021

3.10706

.92214

r.36T93

2.74721

2.01714

0.00000

0.00000

0.00000

0.00000

,2*346"" " ~ "2,86650

,12001 —-

.84981

.21566

.00116

17.89691

.11582

.97735

1.61564

-2.57883

3.37435

51


P 8-

4

0".-0. ZH08 1.98500

AR »— ~ 4.-00t)Ot)LOSS » 2. EXP

»-— tv ----- BNXT-0.0000 BLADES

O.T53.

3.31230SLOPE-------- 31.75800CURVATURE

-.27834LOSS CUEFF ~

.99943S O L I D I T Y------- l.THTOUUBLADE THICK

.02960

.9*902TOTAL BLOCKAGE

BLADE ANGLE*33. 29322

LEAN-1.211«8

Y

i 3.27000

1 32.00000

-.27000

1 .99945

[NESSi .02965

! .92915;AGEF .85808

! -33.27384

1 -1.31286

3.23000

33. 00000

-.27000

.99952

1.00000

.02973

.92910

,85698

-33.24764

-1.47931

3.15000

33.00000

-.27000

.99957

1.00000

.02984

.92909

-33.23007

-1.73056

3.08000

-.27000

.99949

i.ooooo —

.02995

.92912

.85291

-33.28473

-1.86968

3.01380

-.28133

•99916

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.03007

.92910

-33,32775

-1.91519

-29.7800 0 --29;-

MOR ITERS

soornr —

1 AREA RATIO « ,99954 EXP * 1.50000 CHOKE B .60600

RADIUS3.31230 3.28334 3.23933 3.16352 3.08982

z "• ....... " ..... " ..... : ~" ...... "~ ..... " "~1.92500 1.92500 1.92500 1.92500 1.92500

CROSS PASSAGE OIST P.2SIQ50 .26954 ,22553 .14972 .07602

SLOPE31.75800 32.01613 32.57193 33.07773 33.50506

CURVATURE-.27834 -.33836 -.33176 -.41787 -.32499

DELTA CURV/ATURE0.00000 -.00063 -. 00082 -.00432 -.00363

VM428.72926 435.23229 414.53995 438,18863 442.45862

VU2246.53038 249.75379 234.41757 247.74486 248.73348

U2020.50300 2002.83572 1975.99211 1929.74777 1884,78778

VR225.65429 230.74193 223.17100 , 239.15309 244.24193

BETA229.90000 29.84892 29.48765 29.48311 29.34303

BETA2»34.06966 34,08931 33.86282 34.00904 33.98733

3.01380

1.92500

OVOWffO"

34.28300

-.28133

0.00000

457.75676

252.70689

1838.41800

257.84574

28.90110

33.74817

52

INCIDENCE.23767 ,23434

.37342 .37957v2 ~ :494.55637 501.80085

TOTAL TEMPN 1.45143 i.4~4756~

TOTAL PRESS3.09447 3.10087


STATIC TEMP1.41256 1.40754


"DENSITY1.99030 1.99526

SUCT SURF VEL619.12829 620.97376

PRESS SURF VEL369.98445 382*62794

-,02750

,36424

476.22996

1.41269

3.07153

.90575

1.3766T

2.80344

2.03643

"591 .560 IT

360.89980DELTA T

0.00000 0.00000 0.00000WORK COEF ~ 2*CP*DELT/U*«2

0.00000 0.00000FLOW COEF a VM/U

.21219 .21731

3.28515 3.255730-FACTOR

.I79TO ~ .IT5WVM2/VM1

1.09019 1.06067

.06772 .06877TANG BLADE FOrtCE L*/IN-T 775 0 73 6 -15. 33 16 6

AXIAL BLADE FORCE LB/IN13*71605 12.27059

VEL HEAD 2.09147 .09432

.94850 .95160RVUY

1.33866 1.34430ORVU/DM

-4.29822 -4.11463STRMLN OIST M

2.84272 2.84001

O.OITOOO

.20979

3.21129

.IZ957

1.07723

.07596

12.76375

.08728

,97247

1,24485

-3.97232

2.84657

.01225

.38761

503,37540

1.59850

3.09762

.94625

1.35823

2.79376

2.05691

604,89570

401.85509

0.00000

0.0 OWO

3.11434

.TD890

1.05005

.07050

12.06016

.09809

,9846"ff

1,28483

-3.50433

2.89332

-.125*7"

,39064

507,58051

1*40058

3*08835

.93844

2.78095

2,04537

H60 7715*59

0,00000

0700000

3,06017

.-10905

1.05460

•06582

11.64992

,09954

1*25990

-3.43930

3*02667

-.44200

522.8/859

3,09784

.91932

T.366T6

2.77351

2.02926

622.36372

423.39346

0.00000

~070001TO

2.98390

7IT939

1.04342

.07309

11.91641

.10469

.97653"

1*24854

•3.42878

3.47828

53

STATION 6.20000 SJATOR XI 0.00000

Pa 0. ZTIP a 2.025s -0, ZHU8 a 2,02?

RADIUS3.37200 3.33000

SLOPE29V92500 30.000W

CURVATURE-.27042 -.27000

LOSS COEFF.99937 .99924

SOLIDITY1.00000 1.00000

BLADE THICKNESS.03624 .03632

AERO BLOCKAGE.92686 .92660

TOTAL BLOCKAGE,84284 .84136

BLADE ANGLE-22.98716 -22.96542

LEAN-.22307 -.27711

V-20 .8606 0 - 1 9 ,~37 0~0 6

MOR ITERS a l AREA F

RADIUS3.37200 3.34336

z ' • ~ • ~ " ~ "2.02500 2.02500

CROSS PASSAGE DIST P.29256 «263¥6

SLOPE29.92500 30.00666

CURVATURE-.27042 -.24247

DELTA CURVATUREOVODOOO -,OflUF3"

VM418.24868 429.44417

VU2158.87785 152.42625

U2 656 .92 000 2639. 451 24

VR208.65011 214,76541

8ETA220.80000 19,54172

BETA2*23.66778 22.28750

JOO AR » 4.UUUOO *500 LOSS a 2, EXP a

3.29000 3.21000

~' 30.0000~0~ 30. 0"OODtT

-.27000 -.27000

.99943

1,00000

,03645

.92684

.84023

-22.95318

.99950

1.00000

.03666

.92686

.83T5T

-22.97066

-.37393 -.51419

~ ~52ff~. 45 OU 0 -20 ."5 0"0 OT)

*ATIO a 1.00082 EXP a 1.

3.30013

2*02500

.2206T

30.17291

-.25919

. . 0 OT80

405.17255

149.42925

203.64436

20.24417

23.16325

3.22554

2,02500

.14664

30.49287

-,22648

-•U0014

434.48819

162,31818

I967V5T963

20.48491

23,43903

-0,0000 BLADES » 53,

3.14000

-.27000

.99939

1,00000

.03688

.92690

-23.14303

-.58997

50000 CHOKE

3.15376

2.02500

.07426

31.01146

-.29044

•00154

435.55481

163.56271

224.40209

20*58252

T3T.66088

3.07950

-.27868

.99900

r.txoooo.03716

.92685

,83250 --

-23,43325

-..60406

» ,56170

3,07950

2.02500

, D,oo"ocro32.36080

",27868

o . trornn*449,28407

168,87337

240,47895

20.59983

3,98~8IO

54

INCIDENCE.51587 -.72943

.33698 .34383V2447.40824 455.69294

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.08762 3.09256


STATIC TEMP1.41962 1.41455


DENSITY2.01113 2.01514

SUCT SURF VEL552.29279 566.78215

PRESS SURF VEL342.52368 344.60374

DELTA T0.00000 0.00000

-Y02159

.32953

431.84939

1.41269

3.06539

.90387

1.38305

2.84411

2.05640

534.70406

328.99472

0.00000WORK COEF * 2*CP*DELT/U**2

0.00000 0.0 00 00FLOW COEF * VM/U

.20334 .21057k BAR

3.34215 3.313350-FACTOH

.18029 .18523VM2/VM1

.97555 .98670OELP/0

,15411 .14403TANG BLADE FORCE LB/IN

îq g— 05 1 5 o - 2 o .372 43AXIAL 8LADE FORCE LB/IN

13.02157 13.50688'VET. HEW 2 - - . - - .

,07533 ,07826Q*E»»<-S/CP>" ,9*791 .95&BBRVU/

,87826 ,83544

-3.41230 -3.59005STRMLN HIST M

2.959T9 2.95664

0.00000

.20127

3.26973

.T7F68

.97740

.15169

r[ 6" , ff4 9S4

12.47174

.07219

.97T9Z

.80842

-3.34453

~ "2V96360

.20572

.35635

463.81805

1.39850

3 • 0?2 18

.94453

1.36431

2.83323

2.07667

566. 23879

361.39731

0.00000

0.00000

.22082

3.19453

,15948

,99156

.12988

-17.59822

13,19989

,08375

; ,9B*zo

,85830

-3.34736

3YUT099

.24392

.35721

465.25342

1.401)58"

3.08169

.93634

1.36617

2.82243

2.06594

563.59389

366.91296

0.00000

0,00000

.22640

3.12179

.16313

.98440

.13496

- -irj6.V6104

12.87090

.08413

.98179

,84563

-3.22739

~ 37T4737

.20685

.36751

479,97333

r.4l62T

3.08686

.91595

1.37360"

2.81285

2.04780

575.00833

384.93832

0.00000

0.00000

.23917

3.04665

.15787

.98149

.12131

•16.30954

11*33118

.08877

-.97555"

.85253

-3,13175

3.59793

55

STATION 6.30000 STATOR XI a 0.00000

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RADIUS3.42750 3.39000 3.34000

SLOPE28.18870 29.00000 29.0000D

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BLADE ANGLE-13.15601 -13.16994 -13.19334

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Y-13.50000 -12.20000 -12.20000

MOR ITERS = 1 AREA RATIO = 1.00020

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Z2.12500 2.12500 2.12500

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13.50000 12.41610 12.20000BETA2*

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EXP m 1,50000 CHOKE » .53144

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2.12500

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29.36327

-.30472

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428.49523"93.54715

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210.11061

12.31532

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3.21319

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225.00055

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14*4-3013

INCIDENCE2Tff3TJ97

.31464

418.34231TOTAL TEMP

T.45V4TTOTAL PRESS

3.08050EFFICIENCY

.83053STATIC TEMP

1.42362STATIC PRESS

2.87692DENSITY

2.02085SUCT SURF VEL509.11301

PRESS SURF VEL327.57161

DELTA T0.00000

WORK COEF = 2*0.00000

FLOW COEF = VM.19456

K BAR3.39975

D-FACTOR.13104

VM2/VM1.97259

OELP/Q.09405

.97533-

.32148

426.68Q11

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3.08608

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2.87357

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515.56572

337,79451

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488,43764

316,46389

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3.32825

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1.36793

2.85482

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529.16008

348.01546

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0.00000

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3.25431

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439.46557

r.TOT5B-

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528.12211

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0.00000

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3.18347

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453.97299

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3.07605

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1 .37746

2.83093

2.05519

539.43613

368.50965

0.00000

0.00000

.23135

3.11007

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-.986491

.06598TANG BLADE FORCE LB/IN '-12.94938 -13.03610 -13,15202 -14.81712 -14,25732 * 14. 49429

AXIAL BLADE FORCE LB/IN6.00297

VEL HrAD 2.06609

Q=E«»(-S/CP>. 9 47?9

RVU/.54874

DRVU/DM-2.82062

STRMLN OIST M3.-(T735fc

5.85769

.06886

.95031

.51122

-2.75349

3.om*-

5.90540

.06291

797137

.46795

-2.66624

3T07833

6.27725

.07513

~ .9837T)

.50348

-2.81695

3Tl2fc36

5,62460

.07531

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.50017"~ " "" " '"'"'

-2*76638

3 i 26 370

5.69144

.07969

,97458

.50589

-2.67704

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57

STATION 6.40000 STATOR XI *

P * 0. ZTIP =* -0. ZHUB a

RADIUS- 3.47930 3.

£.££3UU2.22500

45000SUOPE

^6«5655o 27.00000CURVATURE

-.34373 -.LOSS COEFF

.99931 .SOLIDITY

I* 00000 1.BLADE THICKNESS

.02607 •AERO BLOCKAGE


,86393 .BLADE ANGLE

-3,58613 -3.LEAN

.69020 •Y

-6,13000 -5.

JOR ITEMS = I

RADIUS3.47930 3.

Z2.22500 2.

CROSS PASSAGE DIST.26180 •

SLOPE26.56550 26.

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VM388.19074 397.

VU2~41.69123 37.

25000

99924

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02612

92209

863 1 9

61283

72157

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AREA RAT

45121

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76860

24397

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26.88784

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.99949

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2.22500

.13883

27.02864

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411.63113

38.96125

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2.22500

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-.37492

-.00196

412.49350

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424.08728

43.80101u

2122.37300 2105.23827 2079.34369 2035.16049 T993.66219 1950.4T500VR

173.60696 179.02344 169.02796 187.06000 ^•l^?47 2°3L92_?3_8

BETA2" ' "~" "• - " ~ " 1 ' ~ " '""' ' "6.13000 5.32046 5.48131 5.40699 5.35331 5.B9677

BETA2* ^ __6.84706 5.95473 6.14089 6.06527 6.027TTJ 6.TTB26

"58

I N C I D E N C E, 3.22945 2.41868

•29328 .30040V2 .390.42311 399.20660

TOTAL TEMP1.45143 1.44756

TOTAL PRESS3.07296 3.07785


STATIC TEMP1.42721 1.42223


DENSITY2.02880 2.03324

SUCT SURF VEU454.10807 473.14639

PRESS SURF VEL326.73816 325,26680

DELTA T0,00000 0,00000

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ft BAR3.4534Q 3,42519

D-FACTOR.13238 .12737

VM2/VM1.95429 .95389

DELP/Q.09139 .08544


AXIAL BLADE FORCE LB/IN3,40931 3.24050

VEL HEAD 2,05774 .06047

Q=E**(-S/CP).94663 .94960

RVU/.23780 .20943.

DRVU/DM-1.89095 -2,19422 ;

STRMLN DIST M3.18618 , 3.18389 .

2.55757

.28576

375.46949

1.41269

3.05324

.90013

1.39028

2.88553

2,07550

439.46148

311,47750

0.00000

0.00000

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3.38257

.12698

.95015

.09716

-10.35787

3.31056

.05493

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y -1,90196

3.19122

2.36682

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413.47088

1.39850

3.08118

.94105

1.37133

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2.09636

480.24168

346,70008

0,00000

o.ooow

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3,30971

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-12.39567

4.54100

.06698

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-1.98762

3.23966

2,02908

.31726

414.30055

1.40058

3.06743

.93184

1.37330

2.86147

2.08365

472.77691

355.82418

0.00000

OYOCTOOO

,20690

3.24074

.12002

.96133

.08194

-12,38497

4.33940

.06714

.98051

,20710<

-1.74397

3,37788

•63911

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426.34323

1.41021

3*06527

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1.38132

2.84909

2.06258

491.08079

361.60566

0.00000

0.0 000

.21743

3.16907

.11944

.95685

.07406

-11.74902

3.10238

.07053'

.97361

.22960

-1.93782

3.83017

59

Stator IB Exit

STATION

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CURVATURE-.28200

LOSS COTFF.99936

SOLIDITY1TOWOD



3.51000

25.00000

-.26900

.99938

l.Ouooo>JESS

.01005

.92000ftGE

.89777

6.29478

.71747

0.00000

3.48000

£5.50000

-.27000

.99941

1.00000

.01005

.92000

.89758

.93884

-1.00000

3.40000

26.00000

-.27200

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.01005

.92000

.89707

5.71909

1.42878

-1.00000

3.33000

ib. 50000

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.92000

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2.00686

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3.25000

27.00oOO

-•29350

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1.00000

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.92000

3.92472

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LEAN '.59872

Y-3.30006

JOR ITERS » 1 AREA RATIO = 1.00006 EXP a 1,50000 CHOKE 3 .47065

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z • " • ' -2.33000 2.33000 2.33000 2.33000 2.33000

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U (, • ' '2153.30000 2136.42133 2110.81596 2066.83300 2025.77559

VR150.87740 169,17288 168.35704154.95537

BETA23.30000

t,-fAl80*24256

BETAS*3.64027

160.53134

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79.99337

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80.56356

1.10838

1.32677

79.J30919

1.47379

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78.87235

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60

3.07105

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1.42501

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BETA1*81.14153 80.93131

, JIDENCE74.24256 73.99776

M2,27561 .28312

Ml1.62355 1.62933

V2367,26449 376.61103

VI2163.45494 2167.37006

TOTAL TEMP1.45143 1.44756

TOTAL PHESS3.06596

EFFICIENCY.82646

STATIC TEMP1.42999

STATIC PRESS2.90892

DENSITY2.03422

SUCT SUKF VEL370.41478

PRESS SURF VEL164.11421 334.49046

l/^LTA T0.00000 0.00000

WORK COEF = 2*CP»DELT/U»»20.00000 0.00000

FLOW COEF a VM/iJ.17028 .17628

P BAP3.50465 3.47677

0-FACTOW.08505 .10007

VM2/VM1.9445? .94747

OELPVQ.075b3 .07329

TANG dLttOE FORCE Urt/IN-4.56362 -8,01992

AXIAL 8LA0E FO«C€ L8/IN.9S699

VEL HEAO 2.05122

VEL HEAD 1.77236

Q*E»<M-S/CP>.94602

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STRMLN DIST M3*30278

1 .09990

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-1.19365

3.30067

81.47214

74.63323

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1.62212

349.86004

!133. 58131

1.41269

3.04633

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1.39323

2.90114

2.08231

382*73456

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3,43456

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1.10046

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-.93215

3.30821

80.35495

73.59784

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i. 60297

388,59313

2094.18477

1.39850

3.07549

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2.89301

2,10477

416.69578

360.49048

0.00000

0.00000

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3.36229

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1.64145

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.98269

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3.35679

80.26176

74.17218

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1.56259

383.85428

2043.39274

1*40058

3.06115

.92985

1.37716

2.88409

2.09423

385.62224

382.08631

0.00000

0.00000

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3.29462

.09705

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.10982

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1.93936

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.10166

-.05131

3.49533

80.05957

76,52902

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1.S3156

387.9b474

2009.44951

1.41021

3.05379

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1.38629

2.87464

2.07362

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353.19203

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3.22375

.12816

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.05866

.73928

.97258

,05769

-.99084

3.94757

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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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.

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:!_: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

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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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