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AERODYNA IC DESIGN OFAXIAL-FLOW COMPRESSORSREVISEDPrepared- bN members of the staffof Lewis Research Center, Cleveland, Ohio.Edited bg h m . ~. Jo- and ROBERT.BULLOCK.hispublication supersedesdecassifiedNACA Memorandum E56B03, E56BOa, and E56BO3b, 1956

S&i@ d ecbnuul InformationDivision 1 9 6 5NATIONAL AERONAUTICS AND SPACE ADMINISTRATIONwarbington, D.C.

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C O N T E N T SCHAPTER

I. OBJECTIVES AND SCOPE________________________________________ - - -IRVING. JOHNSENND ROBERT. BULLOCKROBERT. BULLOCKND ERNST. PRASSEROBERT. BULLOCKN D IRVING. JOHNSENWILLIAMH. ROUDEBUSHWILLIAMH. ROUDEBUSEN D SEYMOURIEBLEIN

SEYMOURIEBLEINWILLIAMH. ROBBINS,ROBEFJT. JACKSON, AN D SEYMOURIEBLEINCHARLES . GIAMATI,R.,A N D HAROLD. FINGERARTHUR. MEDEIROSND BETTY ANEOOD

II. COMPRESSOR DESIGN REQUIREMENTS _ _ _ _ _ _ _ _ - - - _ _ - - - _ _ _ - - --III. COMPBESSOR DESIGN SYSTEM _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _IV. POTENTIAL FLOW IN TWO-DIMENSIONAL CASCADES:- _ _ - - - - - - -- - _V. VISCOUS FLOW I N TWO-DIMENSIONAL CASCADES_ _ _ _ _ _ - _ - _ _ _ - _ _ _ - -

VI. EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES-----------VII. BLADE-ELEMENT FLOW IN ANNULAR CASCADES--- -- - -- --- - - - - ---- -

VIII. DESIGN VELOCITY DISTRIBUTION IN MERIDIONAL PLANE_----_- --IX. CHART PROCEDURES FOR DESIGN VELOCITY DISTRIBUTION---_ -- -

' "T J53 -

101 J151 Ir'183 J227 I /

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J255 JIf. PREDICTION OF OFF-DESIGN PERFORMANCE OF MULTISTAGEC O M P R E S S O R S _ _ _ _ _ _ _ - _ _ _ - - - - - - - _ -- - _ - _ _ _ _ _ -_ - _ - - - -_ _ - - - - -- _ _97 J4 /

i /

WILLIAM . ROBBINSND JAMES. DUGAN,R.ROBERTW. GRAHAMND ELEANOPOSTILOW UENTERTMERLEC. HUPPERT

XI. COMPRESSOR STALL AND BLADE VIBRATION _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 311XII. COMPRESSOR SURGE_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - _ - - -31

XIII. COMPRESSOR OPERATION WITH ONE OR MORE BLADE ROWSSTALLED_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ _ - - _ _ - - _ - _41

WILLIAMA. B~ NS ER64'IV. THREE-DIMENSIONAL COMPRESSOR FLOW THEORY AND REALFLOW EFFECTS_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - _ -65

HOWAED.HEEZIG ND ARTHUR . HANSEN JV. SECONDARY FLOWS AND THREE-DIMENSIONAL BOUNDARY-LAYER EFFECTS_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - _ -85ARTHURG. HANSEN N D HOWARD.HERZIG

XVI. EFFECTS OF DESIGN AND MEASUREMENT ERRORS ON COMPRES-SOR PERFORMANCE_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

XVII. COMPRESSOR AND TURBINE MATCHING_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ._ _ _ _ _ _ _ _ _ _ _REFERENCES _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _

ROBEET . JACKSONN D PEGGY. YOHNEIIJAMES. DUBAN,E. 469

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CHAPTER IO B J E C T I V E S A N D SCOPE

By IRVING. JOHNSENnd ROBERT . ULLOCK -This$rst chapter of a report on the aerodynamic a design system, and stimulated by the urgent need

design of a x id $ m compressors presents the general for improving gas-turbine engines, research onobjectives and scope o the Over-aU report. The basic axial-flow compressors has been accelerated bothproblem of compressor M g n is outlined, and the /Gn thi s country and abroad. The results of thisapproach generally taken to accomplish its solution I esearch have been presented in numerous publi-these reportg presents only a fragmentary bit ofinformation which taken by itself may appear tothe report are summ.arized.

is pointed out. l7w &een succeeding cations. In the majority of instances, each ofINTRODUCTION

Currently, the principal type of compressorbeing used in aircraft gas-turbine powerplants isthe axial-flow compressor. Although some of theearly turbojet engines incorporated the centrifugalcompressor, the recent trend, particularly for high-speed and long-range applications, has been to theaxial-flow type. This dominance is a result ofthe ability of the axial-flow compressor to satisfythe basic requirements of the aircraft gas turbine.These basic requirements of compressors foraircraft gas-turbine application are well-known.In general, they include high efficiency, high air-flow capacity per unit frontal area, and highpressure ratio per stage. Because of the demandfor rapid engine acceleration and for operationover a wide range of flight conditions, this highlevel of aerodynamic performance must be main-tained over a wide range of speeds and flows.Physically, the compressor should have a minimumlength and weight. The mechanical design shouldbe simple, so as to reduce manufacturing time andcost. The resulting structure should be mechani-cally rugged and reliable.It is the function of the compressor designsystem to provide compressors that will meetthese requirements (in any given aircraft engineapplication). This design system should be accu-rate in order to minimize costly and time-consum-ing development. However, it should also be asstraightforward and simple as possible, consistentwith completeness and accuracy.In an effort to provide the basic data for such

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have inconsequential value. Taken altogetherand properly correlated, however, thi s informationrepresents significant advances in that science offluid mechanics which is pertinent to axial-flowcompressors. It was the opinion of the NACASubcommittee on Compressors and Turbines andothers in the field that it would be appropriate toassimilate and correlate this information, and topresent the results in a single report. Such acompilation should be of value to both neophytesand experienced designers of axial-flow compres-sors. Realizing the necessity and importance ofa publication of thi s type, the NACA Lewislaboratory began reviewing and digesting existingdata. This report represents the current statusof this effort.This chapter outlines the general objectives andthe scope of the design report and indicates thechapters in which each specific phase of compressordesign information isdiscussed. The general com-pressor design problem and the approach usuallytaken to accomplish its solution are indicated.The various aspects of compressor design to betreated in the over-aU compendium ar e outlined,as well 85 the specific sequence in which they willbe presented.Because axial-flow compressors are most ex-tensively used in the field of aircraft propulsion,and because this field requires the highest degreeof excellence in comprwsor design and perform-ance, the attention in this over-all report hasbeen focused primarily on the problems pertinentto the axial-flow compressor of turbojet or turbo-

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2 AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORSprop engines. The results, presented, however,should be applicable to any class of axial-flowcompressors.

DESCRIPTION OF AXIAL-FLOW COMPRESSORThe basic function of a compressor is to utilizeshaft work to increase the total or stagnationpressure of the air. A schematic drawing of an

axial-flow compressor as installed in a turbojetengine is shown in figure 1. In he general config-uration, the first row of blades (inlet guide vanes)imparts a rotation to the air to establish a pecifiedvelocity distribution ahead of the first rotor. Therotation of the air is then changed in the first rotor,and energy is thereby added in accordance withEulers turbine equation. This energy is mani-fested as increases in total temperature and totalpressure of air leaving the rotor. Usually ac-companying these increases are increases in staticpressure and in absolute velocity of the air. Apart, or all, of the rotation is then removed inthe following stator, thus converting velocityhead to static pressure. This stator also setsup the distribution of airflow for the subsequentrotor. The air passes successively through rotorsand stators in this manner to increase the totalpressure of the air to the degree required in thegas-turbine engine cycle. As the air is com-pressed, the density of the air is increased andr---- ln let guide vaneII r-- RotorI I1 I ,--StatorI 1

the annular flow area is reduced to correspond tothe decreasing volume. This change in area maybe accomplished by means of varying tip or hubdiameter or both.In this compression process certain losses areincurred that result in an increase in the entropyof the air. Thus, in passing through a compressor,the velocity, the pressure, the temperature, thedensity, the entropy, and the radius of a givenparticle of air are changed across each of the bladerows. The compressor design system must pro-vide an adequate description of this flow process.

HISTORICAL BACKGROUNDThe basic concepts of multistage axial-flow-compressor operation have been known for ap-proximately 100 years, being presented to theFrench Academie des Sciences in 1853 by Tour-

naire (ref. 1). One of the earliest experimentalaxial-flow compressors (1884) was obtained byC. A. Parsons by running a multistage reaction-type turbine in reverse (ref. 2). Efficiencies forthis type of unit were very low, primarily becausethe blading was not designed for the condition ofa pressure rise in the direction of flow. Beginningat the turn of the century, a number of axial-flowcompressors were built, in some cases with theblade design based on propeller theory. However,the efficiency of these units was still low (50 to 60

RQURE.-Axial-%ow compressor in turbojet engine.


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OBJECTNES AND SCOPE 5to satisfy the design-point velocity diagrams andto obtain high efficiency. Basicahy, this selectionrequires knowledge of loss and turning character-istics of compressor blade elements. With thecompressor geometry establfshed, the h a l step isthe estimation of the performance characteristicsof the compressor over a range of speeds and flows.In view of the importance of offdesign operation,this procedure may be iterated so as to properlycompromise design-point operation and the rangerequirements of the engine.A more complete discussion of the compressordesign system adopted for this over-all report isgiven in chapter 111. The generalities of theconcepts involved have been given merely toclarify the general approach to the problem.

OBJECTIVES OF DESIGN REPORTThe desire to provide a sound compressor designsystem has formed the basis for most research onaxial-flow compressors. As a result, in this coun-try and abroad, design concepts and design tech-niques have been established that Wiw providehigh-performance compressors. In general, thesevarious design systems, although they may differin the manner of handling details, utilize the samebasic approach to the problem. This over-allreport is therefore dedicated to summapizing andconsolidating this existing design information.Thiseffort may be considered to have three generalobjectives:

(1) To provide a single source of compressordesign information, within which the major(representative) contributions in the litera-ture are summarized(2) To correlate and generalize compressordesign data that are presently availableon ly in many different forms and in widelyscattered reports

(3) To indicate the most essential avenuesfor future research, since, in a summariza-tion of this type, the missing elements(and their importance to the design system)become readily apparent

In this compressor report, an effort is made topresent the data in a fundamental form. Toillustrate the use of these data, a representativedesign procedure is utilized. However, since thedesign information is reduced to basic concepts,it can be fitted into any detailed design procedure

SCOPE OF DESIGN REPORTBecause of the complexity of the compressor de-sign problem,'even the simplest design systemnecessarily includes many dift'erent phases. Inorder to summarize existing compressor infor-mation as clearly and logicdy as possible, thisover-all compendium is'dividedinto chapters, eachconcerning a separate aspect of compressor de-

sign. The degree of completeness of these chap-ters varies greatly. In some cases, rather com-plete information is available and specific da ta aregiven that can be fitted into detailed compressordesign procedures. In other cases, the informa-tion isnot yet usable in design. The chapters maygive only a qualitative picture of the problem, orthey may merely indicate the direction of futureresearch. Those aspects of the compressor prob-lem which are considered pertinent are included,however, regardless of the present applicability ofthe information.The following discussion provides an over-allperspective of the material covered in this compres-sor design compendium. Each chapter is sum-marized briefly, and the relation of each to theover-all report is indicated.In order to provide proper emphasis in the de-sign summarization, it is desirable to establish andevaluate the essential characteristics of compres-sors. Chapter I1 accomplishes this objective byfirst evaluating engine requirements with respectto airplane performance. These required enginecharacteristica are then used to identify essentialrequirements of the compressor. Characteristicsof the compressor that are directly related to en-gine performance, such as compressor pressureratio, efficiency, airflow capacity, diameter, length,and weight, are discussed. Other considerationsin compressor design, including offdesign require-ments and the relation of the compressor to theinlet diffuser, combustor, turbine, and jet nozzle,are discussed. Compressor design objectives,based on these considerations, are summarized;these objectives indicate the direction in whichcompressor designs should proceed.Chapter I11provides a general description of thecompressor design system that has been adoptedfor this report on the aerodynamic design of axial-flow compressors. The basic thermodynamicequations are given, and the simplifications com-monly introduced to permit the solution of theseequations are summarized. Representative ex-


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6 AERODYNAMIC DESIGN OFperimental data are presented to justify thesesimplifications. This chapter thus provides avalid simplified model of the flow, which is the realbasis of a design system. The elements of theresulting design system are then individually sum-marized ; asic equations and techniques are given.Finally, the limitations ofpointed out, and promisingresearch are indicated.The literature on plane potentid flow in cascadesis next reviewed (ch. IV). Many of the methodsare evaluated within the bounds of limited avail-able information on actual use. Some of themethods that have beeh used successfully arepresented in detail to illustrate the mathematicaltechniques and to indicate the nature of theactual computation. The potential-flow theoriesdiscussed include both the design and analysisproblems and consider both high-solidity andlow-solidity applications. Compressibility is con-sidered, but effects of viscosity are ignored.

A necessary adjunct to this subject of two-dimensional potential flow is the considerationof two-dimensional viscous effects, presented inchapter V. In this chapter, the problem ofboundary-layer growth in the calculation oftwodimensional flow about compressor bladeprofiles is reviewed. A qualitative picture ofboundary-layer behavior under various conditionsof pressure gradient, Reynolds number, andturbulence normally encountered in two-dimensional blade-element flow is presented.Some typical methods for computing the growthand separation of laminar and turbulent boundarylayers are presented. Analyses for determiningthe total-pressure loss and the defect in circulationare discussed.

Because of recognized limitations of theoreticalcalculations such as those presented in chaptersIV and V, experimental blade-element data aregenerally required by the designer. The availableexperimental data obtained in twodimensionalcascade are surveyed and evaluated in chapterVI. These data (for conventional compressorblade sections) are presented in terms of sign%-cant parametere and are correlated at a referenceincidence angle in the region of minimum loss.Variations of reference incidence angle, total-pressure loss, and deviation angle with cascadegeometry, inlet Mach number, and Reynoldsnumber are investigated. From the analysis and

AXIAL-FLOW COMPRESSORSthe correlations of the available data, ru les andrelations are evolved for the prediction of blade-profile performance. These relations are devel-oped in simplified form readily applicable tocompressor design proceduresBecause of modifying effects (wall boundarylayers, three-dimensional flows, etc.), blade-element characteristica in an annular cascadecan be expected to differ from those obtainedin two-dimensional cascades. Chapter VI1 at-tempts to correlate and summarize availableblade-element data as obtained from experimentaltests in three-dimensional annular cascades (pri-marily rotors and stators of single-stage compres-sors). Data correlations at minimum loss areobtained for blade elements at various radialpositions along the blade span. The correlationsare compared with those obtained from two-dimensional cascades (ch. VI). Design rules andprocedures are recommended, and sample calcula-tion procedures are included to illustrate theiruse.As discussed in the preceding paragraphs,chapters IV to VI1 deal with the two-dimensionalblade-element aspect of design. The designproblem in the meridional or hub-to-tip plane isintroduced and summarized in chapter VIII.This meridional-plane solution presumes theexistence of the required blade-element data tosatisfy the velocity diagrams that are established.The general flow equations are presented, togetherwith the simplifying assumptions used to deter-mine the design velocity distribution and flow-passage configuration. Techniques for accountingfor effects of viscosity (particularly for wallboundary layers) are described. The applicationof these design techniques is clarified by a samplestage design calculation.Since procedures for determining the designvelocity distribution and flow-passage configura-tions in the meridional plane are usually iterative,it is desirable to have approximate techniquesavailable to expedite this process of stage design.The equations for radial equilibrium, continuity,energy addition, efficiency, and diffusion factor,as well as vector relations, are presented in chartform in chapter IX. An example of the applica-tion of the chart technique to stage design isincluded.In addition to the design-point problem, thecompressor designer is vitally concerned with


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OBJEemvES AND SCOPE 7the prediction of compressor performance over arange of flow conditions and speeds. Three tach-niques for estimating compressor off-design per-formance are presented in chapter X. The fmtmethod establishes the blade-row and over-allperformance by meanselement characteristics.lizes generalized stages age-by-s tage calculawhich is based oncharacteristics of existing compressors, may beused to estimate the complete performance mapof a new compressor if the compressor design con-ditions are specified. The advantages and limita-tions of each of these three offdesign analysistechniques are discussed.Chapter XI is the first of a group of threeconcerning the unsteady compressor operationthat arises when compressor blade elements stall.The field of compressor stall (rotating stall, indi-vidual blade stall, and stall flutter) is reviewed.The phenomenon of rotating stall is particularlyemphasized. Rotating-stall theories proposed inthe literature are reviewed. Experimental dataobtained in both single-stage and multistage com-pressors are presented. The effects of this stalledoperation on both aerodynamic performance andthe associated problem of resonant blade vibra-tions are considered. Methods that might beused to alleviate the adverse blade vibrations dueto rotating stall are discussed.Another unsteady-flow phenomenon resultingfrom the stalling of compressor blade elements iscompressor surge. It may be distinguished fromthe condition of rotating stall in that the net flowthrough the compressor and the compressortorque become time-unsteady. Some theoreticalaspects of compressor surge are reviewed inchapter XII. A distinction is made betweensurge due to abrupt stall and surge due to pro-gressive stall. Experimental observations of surgein compressor test facilities and in jet engines aresummarized.The blade-element approach to the predictionof off-design performance (as presented in ch. X)is essentially limited to the unstalled range ofoperation. Because of the complexity of the flowphenomenon when elements stall, no quantitativedata are available to permit a precise and accuratesynthesis of over-all cornpressor performance inthis range. A prerequisite to the complete

solution of this off-design problem, however, is aqualitative understvolved. An anproblem in high-pressflow compressors is pThe principalefficiency, multipcteristics at intermeintermediate-speed surge or stall-limit character-istics. The effects of compromising stage match-ing to favor part-speed operation are studied.Variable-geometry methods for improving part-speed performance are discussed.The design approach adopted for this series ofreports is based essentially on twodimensionalconcepts, assuming axial symmetry and blade-element flow. With the continuing trend towardincreasing requirements in compressors, however,a condition may be reached where this simplifiedapproach may no longer be adequate. Therefore,chapter XIV is devoted to a summarization ofthose existing design methods and theories thatextend beyond the simplified-radial-equilibriumaxisymmetric design approach. Design proce-dures that attempt to remove the bwodimensionaliz-ing restrictions are presented. Various phasesof three-dimensional flow behavior that assumeimportance in design * are discussed, includingradial flows, the over-all aspects of secondaryflows, and time-unsteady effects.As pointed out in chapter XIV, secondaryflows represent one of the most critical aspects ofthe three-dimensional design problems. In viewof the growing importance of this subject, exist-ing literature on secondary flows and three-dimensional boundary-layer behavior is summa-rized in chapter XV . The material is discussedfrom two aspects: (1) the principal results ob-tained from experimental studies, and (2) thetheoretical treatment of the problem. The ex-perimental phase is directed at providing aqualitative insight into the origin and nature ofthe observed secondary-flow phenomena. Thetheoretical results include a summary and evalu-ation of both the nonviscous dnd the boundary-layer approaches.

Errors in blade-element design can seriouslyaffect over-all compressor performance, since theseerrors not only cause deviations from desiredblade-row performance, but also alter the inletconditions to the next blade row. The effects of


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8 AERODYNAMIC DESIGN OF AXIAL-FLOW COM P RES S ORSerrors in the three basic blade-element designparameters (turning angle, total-pressure loss, andlocal specEc mass flow) on compressor perform-ance are analyzed in chapter XVI. The resultsare presented in the form of formulas and charts.These charts may be used to indicate those designtypes for which the design control problem is mostcritical and to estimate the limits in performancethat can be anticipated for design data of a givenaccuracy. Typical design cases are considered,and signiscant trends are discussed. A secondphase of this chapter concerns accuracy of experi-mental measurements. Proper interpretation andanalysis of experimental data require that meas-urements be precise. This chapter presents asystematic evaluation of the effect of measure-ment errors on the measured compressor perform-ance. These results,which are also presented inchart form, can be used to estimate the requiredaccuracy of instrumentation.

One of the most important aspects of gas-turbine engine design, particularly for applicationswhere high power output and wide operatingrange are required, is th at of compressor and tur-bine matching. The existing literature on com-pressor and turbine matching techniques, whichcan be used to compromise properly the aero-dynamic design of the compressor and turbine toachieve the best over-all engine, is summarizedin chapter XVII. Both single-spool and two-spool engines are considered. For equilibriumoperation, the basic matching technique, whichinvolves the superposition of compressor andturbine maps, is presented, as well as a simplified

and more approximate method. In addition, asimple technique for establishing an engineoperating line on a compressor map is reviewed.An available technique for matching duringtransient operation is also discussed. The use ofthis method permits engine acceleration charac-teristics and acceleration time to be approximatedfor either single-spool or two-spool engines.CONCLUDING REMARKS

The subsequent chapters in this report s u m -marize available information on the aerodynamicdesign of axial-flow compressors. It is recog-nized that many techniques have been proposedfor describing the flow in an axial-flow compressorand for accounting for the complex flow phenomenathat are encountered. Obviously, considerationof all of these techniques is impossible. However,the available literature in t.he field is reviewedextensively, and the material presented is con-sidered to be representative and pertinent. Ingeneral, the attempt is made to present the in-formation in its most basic form, so that it maybe fitted into any generalized design system.

Because of the many diBcult and involvedproblems associated with compressor design, veryfew of these underlying problems are treated withfinality. In some cases, the problem is onlypartly defined. Nevertheless, many successfuldesigns (by present standards, a t least) have beenmade with the use of this information. The voidsin the information clearly indicate the researchproblems for the future.


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CHAPTER VIE X P E R I M E N T A L F LO W I N T W O - D I M E N S I O N A L C A S C A D E S

t By SEYMOUBIEBLDIN \Available e x p e r i m d two-dimensional-cascadedata for conventional cornpressor blade sections arecorrelated. The two-dimensional cascade and some

of the principal aerodynamic factors involved i n itsoperation are first briefly described. Then the dataare analyzed b y examining the variation of cascadeperformance at a reference incidence angle in theregion of minimum loss. Variations of referenceincidence angle, total-pressure loss, and deviutionangle with cascade geometry, inlet Mach number,and Reynolds number are investigated.From the anulysis and the correlations of theavailable datu, rules and relations are evolved for theprediction of the magnitude of the reference totat-pressure loss and the reference deviation and inci-

the correlation of isolated data was very difEcult.Some efforts were made, however, to correlatelimited experimental data for use in compressordesign (e.g., ref. 187). The British, in particular,through the efforts primarily of Carter and Howell,appear to have made effective use of their earlycascade investigations (refs. 31 (pt. I) and 188to 190).In recent years, the introduction of effectivetunnel-wall boundary-layer removal for the estab-lishment of true two-dimensional flow gave asubstantial impetus to cascade analysis. I nparticular, the porous-wall technique of boundary-layer removal developed by the NACA (ref. 191)was a notable contribution. The use of effectivedence angles for conventional 6 W e proJles. These/\ tunnel boundary-layer control has resulted in morerelations are developed in simplged forms readily ' consistent systematic test data (refs. 39, 54 , 123,and 192 (pt. 11))and in more significant two-pplicable to compressor design procedures. @NTRODUCTION

Because of the complexity and three-dimensionalcharacter of the flow in multistage axial-flowcompressors, various simplified approaches havebeen adopted in the quest for accurate blade-design data. The prevailing approach has beento treat the flow across individual 'compressorblade sections as a two-dimensional flow. Theuse of twodimensionally derived flow characteris-tics in compressor design has generdy been satis-factory for conservative units (ch. 111).In view of the limitations involved in thetheoretical calculation of the flow about two-dimensional blade sections (chs. IV and V),experimental investigations of two-dimensionalcascades of blade sections were adopted as theprincipal source of bladedesign data. Earlyexperimental cascade results (e.g., refs. 184 to186), however, were marked by a sensitivity toindividual tunnel design and operation. Thiswaslargely a result of the failure to obtain true two-dimensional flow. Under these circumstances,

dimension2 comparisons between Georeticd andexperimental performance (refs. 98, 167 (pt. I),and 193). With the availability of a considerableamount of consistent data, it has become feasibleto investigate the existence of general relationsamong the various cascade flow parameters.Such relations curtail the amount of futureexperimental data needed and also result in moreeffective use of the da ta currently available.Since the primary function of cascade informa-tion is to aid in the design of compressors, thepresent W t e r expresses the existing cascade da tain terms of parameters applicable to compressordesign. Such expression not o n l y facilitates thedesign of moderate compressors but also makespossible a rapid comparison of cascade data withdata obtained from advanced 'high-speed com-pressor configurations. Since the bulk of theavailable cascade data has been obtained at lowspeed (Mach numbers of the order of O.l), thequestion of applicability to such high-speed unitsis very significant. It is necessary to determinewhich flow parameters c an or cannot be applied,

183

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EXPERLMENTAL FLOW IN TWO-DIMENSIONAL CASCADES 185

FIGUBE23.-Layout of conventional low-speed cascade tunnel (ref. 168).shtUze01210

A

blade shapeblade maximum thicknessupper surfaceaxial directiontangential directionfree streamstation a t cascade inletstation at cascade exit (measuring station)10 percent thick

PRELIMINARY CONSIDERATIONSDESCRIPTION OF CASCADE

schematic diagram of a low-speed two-dimensional-cascade tunnel is shown infigure 123to illustrate the general tunnel layout. Theprincipal components of the conventional tunnelare a blower, a diffuser section, a large settlingchamber with honeycomb and screens to removeany swirl and to ensure a uniform velocity d i s -tribution, a contracting section to accelerate theflow, the cascade test section, and some form ofoutlet-air guidance. The test section containsa row or cascade of blades set in a mounting devicethat can be altered to obtain a range of air inletangles (angle p1 in figs. 123 and 124). Variationsin blade angle of attack are obtained either byrotating the blades on their individual mountingaxes (i.e., by varying the blade-chord angle -yo)while maintaining a fixed air angle or by keepingthe blade-chord angle fixed and varying the airinlet angle by rotating the entire cascade. Outletflow measurements are obtained from a traverse

II MeasuringI plane

I ine

FIGURE24.-Nomenclature fo r cascade blade.of suction through slots or porous-wall surfaces.Examples of different tunnel designs or detailedinformation concerning design, construction, andoperation of the two-dimensional-cascade tunnelcan be obtained from references 39, 122, 168, 191,and 194. ignating cascade '

layer control in the cascade is provided by mea& related mean lines (refs. 39 and 123), the circular-


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186 AERODyNABdIC DESIGN OFarc mean line (ref. 31,pt. I), and the parabolic-arcmean line (ref. 192, pt. 11). Two popular basicthickness distributions are the NACA 65-seriesthickness distribution (ref. 39) and the BritishC.4 thickness distribution (ref. 31, pt. I). Ahigh-speed profile has also been obtained from theconstruction of arc upper and lowersurface (ref. 40); is referred to as thedouble-circular-arc blade.

PEBFOBMANCE PARAMETEBBThe performance of cascade blade sections hasgenerally been presented as plots of the variationof air-turning angle, lift coefficient, and flow lossesagainst blade angle of attack (or incidence angle)for a given cascade solidity and blade orientation.Blade orientation is expressed in terms of eitherfixed air inlet angle or fixed blade-chord angle.Flow losses have been expressed in terms of 60-efficients of the drag force and the defects inoutlet total pressure or momentum. A recent in-

vestigation (ref. 156) demonstrates the significanceof presenting cascade losses in terms of the thick-ness and form characteristics of the blade wakes.In this analysis, the cascade loss parametersconsidered are the wake momentum-thicknessratio O*/c (ref. 156) and the total-pressure-losscoefficient Wl, defined as the ratio of the averageloss in total pressure across the blade to the inletdynamic head. Cascade losses are considered interms of Ul since this parameter can be conven-iently used for the determination of compressorblade-row efficiency and entropy gradients. The

parameter e*/c represents the basic wake develop-ment of the blade profile and as such constitutesa significant parameter for correlation purposes.Values of e*/c were computed from the cascadeloss data according to methods similar to thosepresented in reference 156. The diffusion factorD of reference 9 was used as a measure of theblade loading in the region of minimum loss.In the present analysis, it was necessary to usea uniform nomenclature and consistent correlationtechnique for the various blade shapes considered.It was believed that this could best be accom-plished by considering the approach characteris-

tics in terms of air incidence angle i,the acteristics in terms of the camberangle 9, and the air-turning characteristics interms of the deviation angle 13 (fig. 124). As in-

AXIAL-FLOW COMPRESSORSdicated in figure 124, these angles are based onthe tangents to the blade mean camber line at theleading and trailing edges. The use of the devia-tion angle, rather the turning angle, as ameasure of the air direction has the advan-tage, for coyelation purposes, of a generally smallvariation with incidence angle. Air-turning angleis related to theangles by

Ag=p+i--s (57)Incidence angle is considered positive when ittends to increase the air-turning angle, and devia-tion angle is considered positive when it tends todecrease the air-turning angle (fig. 124).The use of incidence and deviation angles re-quires a unique and reasonable definition of theblade mean-line angle at the leading and trailingedges, which may not be possible for some bladeshapes. The principal difiiculty in this respect isin the 65-(Alo)-seriesblades (ref. 39), whose mean-line slope is theoretically infinite at the leadingand trailing edges. However, it is still possible torender these sections usable in the analysk byarbitrarily establishing an equivalent circulai -arcmean camber line. As shown in figure 125, theequivalent circular-arc mean line is obtained bydrawing a circular arc through the leading- andtrailing-edge points and the point of maximumcamber at the midchord position. Equivalentincidence, deviation, and camber angles can thenbe established from the equivalent circular-arcmean line as indicated in the figure. The rela-tion between equivalent camber angle and isolated-airfoil lift coefficient of the NACA 65-(Alo)-seriesmean line is shown in figure 126.

A typical plot of the cascade performance pa-rameters used in the analysis is shown in figure127 for a conventional blade section at fixedsolidity and air inlet angle.DATA SELECTION

In selecting data sources for use in the cascadeperformance correlations, it is necessary to con-sider the degree of twodimensionality obtainedin the tunnel and the magnitude of the testReynolds number and turbulence level.Two-dimensionality.-As indicated previously,test results for a given cascade geometry obtainedfrom diferent tunnels may vary because of a fail-


15/82

EXPERI MENTAL FLOW IN T/Point o f/ maximum

I camber65-(Ala) -series

FIGURE 25.-Equivalent circular-arc mean line forNACA 65-(Alo)-seriesblades.ure to achieve true two-dimensional flow acrossthe cascade. Distortions of the true two-dimen-sional flow are caused by the tunnel-wall bound-ary-layer growth and by nonuniform inlet andoutlet flow distributions (refs. 191 and 168). Inmodern cascade practice, good flow twodimen-sionality is obtained by the use of wall-boundary-layer control or large tunnel size in conjunctionwith a large number of blades, or both. Ex-amples of cascade tunnels with good twodimen-sionality are given by references 39 and 194.The lack of good two-dimensionality in cascadetesting affects primarily the air-turning angles andblade surface pressure distributions. Therefore,deviation-angle data were rejected when the two-dimensionality of the tunnel appeared questionable(usually the older and smaller tunnels). Practi-cally all the cascadelossdata were usable, however,since variations in the measured loss obtained froma given cascade geometry in different tunnels willgenerally be consistent with the measured diffusionlevels (unless the blade span is less than about 1or 2 inches and there is no extensive boundary-layer removal).Reynolds number and turbulence.-For thesame conditions of two-dimensionality and test-section Mach number, test results obtained fromcascades of the same geometry may vary becauseof large differences in the magnitude of thebladechord Reynolds number and thefree-stream turbulence. Examples of the effectof Reynolds number and turbulence on thelosses obtained from a given blade section at

WO-DIMENSIONAL CASCADES 187fixed incidence angle are presented in figure 128.S i a r pronounced effects are observed on thedeviation angb. AB discussed in chapter V, theloss variation with Reynolds number is associatedprimarily with a local or completthe laminar boundary layer on theThe data used in the correlation are restricted tovalues of blade-chord Reynolds number from about2.OX1O6 to 2.5X1OS in order to minimize theeffects of different Reynolds numbers. Free-stream turbulence level was not generally deter-mined in the various cascade tunnels.In some cases (refs. 39 and 195, e.g.), in tunnelswith low turbulence levels, marked local laminar-separation effects were observed in the range ofReynolds number selected for the correlation.Illustrative plots of the variation of total-pressure-loss coefficient with angle of attack for a cascadewith local laminar separation are shown in figure129. In such inbtances, it was necessary to esti-mate the probable variation of loss (and deviationangle) in the absence of the local separation(as indicated in the figure) and use valuesobtained from the faired curves for the correlactions.The specific sources of data used in the analysisare indicated by the references listed for the vari-ous performance correlations. Details of the tun-nel construction and operation and other pertinentinformation are given in the individual references.

Ina correlation of two-dimensional-cascade datathat is intended ultimately for use in compressorblade-element design, the variations of perform-ance parameters should be established over a widerange of incidence angles. Experience shows (fig.130) that the variation of loss with incidence anglefor a given blade section changes markedly as theinlet Mach number is increased. Consequently,correlated low-speed blade performance at highand low incidence angles is not applicable at highMach numbers. The low-speed-cascade perform-ance is therefore considered at some referencepoint on the general loss-against-incidence-anglecurve that exhibits the least variation in locationand in magnitude of performance parameters asMach number is increased.

The reference location herein is selected as thepoint of minimum loss on the curve of total-

APPROACH


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188 AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS


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EXPERI MENTAL FLOW IN ~ O - D l A I E N d l f o N A L CASCADES 18914

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Q12 -8 -4 0 4 8 12 16Incidence angle, i , egFIGURE27.-Illustration of basic performance parametersfor cascade analysis. Data obtained from conventionalblade geometry in low-speed two-dimensional tunnel.

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(a) NACA 65-(12) 10 blade. Inlet-air angle, 45O; solidity,1.5 (ref.39) :(b) Lighthill blade, 50 percent laminar flow. Inlet-airangle, 45.5'; solidity, 1.0 (ref. 167, pt. I).

FIGURE28.-Effect of blade-chord Reynolds number andfree-stream turbulence on minimum-loss coefficient ofcascade blade section in two-dimensional tunnel.

(a) NACA 65-810 blade. Inlet-air angle, 30'.(b) NACA 65-(12)lO blade. Inlet-air angle, 45O.

FIGUBE29.-Loss characteristics of cascade blade withlocal laminar separation. Solidity, 1.5; blade-chordReynolds number, 2.45X 106 (ref. 39).

pressure loss against incidence angle. For con-ventional low-speed-cascade sections, the regionof low-loss operation is generally flat, and it isdifEcult to establish precisely the value of incidenceangle that corresponds to the minimw loss. Forpractical purposes, therefore, since the curves ofloss coefficient against incidence angle are gener-ally symmetrical, the reference minimum-loss loca-tion was established at the middle of the low-lossrange of operation. SpecZcally,as shown in figure131, the reference location is selected as the inci-dence angle at the midpoint of the range, whererange is defined as the change in incidence anglecorresponding to a rise in loss coefficient equal tothe minimum value. Thus, for conventional cas-cade sections, the midrange reference location isconsidered coincident with the point of minimumloss. In addition to meeting the abovementionedrequirement of small variation with inlet Machnumber, the reference minimum-loss incidence


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' 190 AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS

Incidence angle, i, deg(a) C.4 Circular-arc blade. Camber angle, 25'; maximum- (c) Double-circular-arc blade. Camber angle, 25'; maxi-thickness ratio, 0.10; solidity, 1.333; blade-chord angle, mum-thickness ratio, 0.105; solidity, 1.333; blade-chord42.5' (ref. 40). (b) C.4 Parabolic-ard blade. Camber angle, 42.5' (ref- 40). (d) Sharp-nose blade. Camberangle, 25' ; maximum-thickness ratio, 0.10; solidity, angle, 27.5'; maximum-thickness ratio, 0.08; solidity,1.333; blade-chord angle, 37.6' (ref. 40). 1.15; blade-chord angle, 30' (ref. 205).

FIGWRB30.-Effect of inlet Mach number on loss characteristics of cascade blade sections.angle (as compared with the optimum or nominalincidence settings of ref. 196or the design incidencesetting of ref. 39) requires the use of only the lossvariation and also permits the use of tke diffusionfactor (applicable in region of minimum loss) asa measure of the blade loading.

At this point, it should be kept in mind thatthe reference minimum-loss incidence angle isnot necessarily to be considered as a recommendeddesign point for 'aompressor application. Theselection of the be& incidence angle for a par-ticular blade element in a multistage-compressordesign is a function iof many considerations, suchas the location of the blade row, the design Machnumber, and the type and application of the design.In general, there is no one universal definitionof design or best incidence angle. The cascade

incidence ongle, I ,degF'IGURE 131.-Definition of reference minimum-loss iaci-dence angle.reference location is established primarily forpurposes of analysis.Of the many blade shapes currently in usein compressor design practice (i.e., NACA 65-series, C-series circular arc, parabolic arc, double


19/82

EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES 191circular arc), data sufficient to permit a reasonablycomplete and significant correlation have beenpublished only for the 65-(Alo)-series blades ofreference 39. Therefore, a basic correlation ofthe 65-(Al0)-series data had to be establishedfirst and the results used as a guide or foundationfor determining the corresponding performancetrends for the other blade shapes for which o n l ylimited data exist.Since the ultimate objective of cascade testsis to provide information for designing com-pressors, it isdesirable, of come, that the structureof the data correlations represent the compressorsituation as closely as possible. Actually, ablade element in a compressor represents a bladesection of fixed geometry (Le., fixed prosle form,solidity, and chord angle) with varying inlet-airangle. In two-dimensional-cascade practice, how-ever, variations in incidence angle have beenobtained by varying either the inlet-air angle orthe blade-chord angle. The available systematicdata for the NACA 65-(A,,)-series blades (ref. 39)have been obtained under conditions of fixedinlet-air angle and varying blade-chord angle.Since these data form the foundation of theanalysis, it was necessary to establish the cascadeperformance correlations on the basis of fixedinlet-air angle. Examination of limited unpub-lished low-speed data indicate that, as illustratedin figure 132, the loss curve for constant air inletangle generally falls somewhat to the right ofthe constant-chord-angle curve for fixed valuesof Dl and yo in the low-loss region of the curve.Values of minimum-loss incidence angle for fixed81 operation are indicated to be of the order of loor 2 greater than for fixed yo operation. Anapproximate allowance for this difference is made

0Incidence angle, I,degFIGURE32.-Qualitative comparison of cascade rangecharacteristics at constant blade-chord angle and con-stant inlet-air angle (for same value of & in region ofminimum loss).

in the use of reference-incidence-angle data fromthese two methods.With the definition of reference incidence angle,performance parameters, and analytical approachestablished, the procedure is first to dehow the value of the reference minincidence angle varies with cascade geometry andflow conditions for the available blade profiles.Then the variation of the performance parametersis determined a t the reference location (as ndicatedin fig. 127) as geometry and flow are changed.Thus, the various factors involved can be ap-praised, and correlation curves and charts canbe established for the available data. Theanalysis and correlation of cascade reference-pointcharacteristics are presented in the followingsections.

INCIDENCE-ANGLE ANALYSISPBELIMINAEY ANALYSIS

In an effort to obtain a general empirical rulefor the location of the reference minimum-lossincidence angle, it is first necessary to examine theprincipal influencing factors.

It is generally recognized that the low-lossregion of incidence angle is identified with theabsence of large velocity peaks (and subsequentdecelerations) on either blade surface. For infi-nitely thin sections, steep velocity gradients areavoided when the front stagnation point is locatedat the leading edge. This condition has fre-quently been referred to as the condition ofimpact-free entry. Weinig (ref. 80) used thecriterion of stagnation-point location to establishthe variation of impact-free-entry incidence anglefor infinitely thin circular-arc sections frompotential-flow theory. Results deduced from ref-erence 80 are presented in figure 133(a). Theminimum-loss incidence angle is negative forinfinitely thin blades and decreases linearly withcamber for fixed solidity and blade-chord angle.While there is no definite corresponding i-incdence-angle theory for thick-nose blades withrounded leading edges, some equivalent resultshave been obtained based on the criterion tha t thelocation of the stagnation point in the leading-edge region of a thick blade is the controllingfactor in the determination of the surface velocitydistributions. Carter, in reference 190, showedsemitheoreticdy on this basis that optimumincidence angle (angle at maximum lift-drag ratio)


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AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS

I I I I I 120 40 60Comber angle,(a) Impact-free-entry incidence angle for infinitely thin C-series profiles according to semitheoretical develop-bladesaccordingto potential theory of Weinig (ref. 80). menta of Carter et a2. (refs. 190 and 196). Outleeair(b) Optimum incidence angle for 10-percent-thick angle, 20.FIQURE33.-Variation of reference incidence angle for circular-air-mean-fine blades obtainedfrom theoretical or semi-theoretical investigations.

fo r a conventional 10-percent-thick circular-arc A preliminary examination of experimentalblade decreases with increasing camber angle. cascade data showed that the minimum-lossThe results of reference 190 were followed by incidence angles of uncambered sections @ = O )generalized plots of optimum incidence angle in of conventional thicknesses were not zero, asreference 196, which showed, as in figure 133(a), indicated by theory for infinitely thin blades (fig.that optimum incidence angle for a 10-percent- 133(a)), but always positive in value. Thethick C-series blade varies with camber angle, appearance of positive values of incidence anglesolidity, and blade orientation. (In these ref- for thick blades is attributed to the existence oferences, blade orientation was expressed in terms velocity distributions at zero incidence angle thatof air outlet angle rather than blade-chord angle,) are not symmtrical on he two surfaces. TypicalThe plot for an outlet- ngle of 20 is shown in plots illustrating the high velocities generallyfigure 133(b). Apparently, the greater the blade observed in the inlet region of the lower (pressure)circulation, the lower in magnitude the urn- surface of thick uncambered blades at zero inci-

e to dence angle are shown in fime 134. Apparently,tion of an increase in incidence angle from the zero valueminimUm-loss incidence angle for conventional is necessary in order t o reduce the lower-surfacecity to a more equitable distribution thatby thin-airfoil theory. in a minimum of the over-all loss. This


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EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES 193zero-camber thickness effect will appear only forblade-chord angles between Oo and goo) since, asindicated by the highly simplified one-dimensionalmodel of the blade passage flow in figure 135, hevelocity distributions at these limit angles aresymmetrical.

The effect of blade thickness blockage onimpact-free-entry incidence angle(uncambered) blades of constant chordwise thick-ness in incompressible twodimensional flow isinvestigated in reference 34. The results ofreference 34 are plotted in terms of the parametersused in this analysis in figure 136. It is reasonableto expect that similar trends of variations ofzero-camber reference. minimum-loss incidenceangle will be obtained for compressor bladeprofiles.

On the basis of the preceding analysis, therefore,it is expected tha t, for low-speed-cascade flow,reference minimum-loss incidence angle will gen-erally be positive at zero camber and decrease withincreasing camber, depending on solidity andblade-chord angle. The available theory alsoindicates that the variation of reference incidenceangle might be essentially linear. If so, thevariations could be expressed in terms of slope

FIGURE134.-Illustration of velocity distribution for angle with camber at fixed solidity and chorduncambered blade of conventional thickness at zeroincidence angle. Data for 65-(0)lO blade of reference39.

Percent chord(a) Inlet-air angle, 60'; solidity, 1.5.(b) Inlet-air angle, 30'; solidity, 1.0.

-


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194 AERODYNAMIC DESIGN OF AXUL-FLOW COMPRESSORS

FIGURE 36.-Theoretical variation of impact-free-entryincidence angle for constant-thickness uncamberedsections according to developments of reference 34.and intercept values, where the intercept valuerepresents the magnitude of the incidence anglefor the uncambered section (function of bladethickness, solidity, and blade-chord angle). Ref-erence minimum-loss incidence angle may alsovary with inlet Mach number and possibly withReynolds number.

D A T A CORRELATIONSForm of correlation.-Although preliminarytheory indicates that blade-chord angle is thesignificant blade orientation parameter, it was

necessary to establish the data correlations interms of inlet-air angle, as mentioned previously.The observed cascade data were found to berepresented satisfactorily by a linear variationof reference incidence angle with camber anglefor fixed solidity and inlet-air angle. The varia-tion of reference minimum-loss incidence anglecan then be described in equation form as

i=i,+ncp (261)where io is the incidence angle for zero camber,and n is the slope of the incidence-angle variationwith camber (i-io)/(p.Since the existence of a finite blade thicknessis apparently the cause of the positive values ofio, it is reasonable to assume that both themagnitude of the maximum thickness and thethickness distribution contribute to the effect.Therefore, since the 10-percent-thick 65-series

blades of reference 39 are to be used as the basisfor a generalized corrblade sylapes, it is proreference incidenceformzo=

where (io)1oepresents the vacamber incidence angle for the65-series thickness distribution, (K1)epresentsany correction necessary for maximum bladethicknesses other than 10 percent, andrepresents any correction necessary for a bladeshape with a thickness distribution different fromthat of the 65-series blades. (For a 10-percent-thick 65-series blade, (K J = 1 and (K i )sn=)The problem, therefore, is reduced to finding thevalues of n and io (through eq. (262)) as functionsof the pertinent variables involved for the variousblade profiles considered.

NACA 65- (A1,)-series blades.-From the exten-sive low-speed-cascade da ta for the 65-(Alo)-seriesblades (ref. 39), when expressed in terms ofequivalent incidence and camber angles(figs. 125 and 126), plots of io and n can bededuced that adequately represent the minimum-loss-incidence-angle variations of the data. Thededuced values of io and n as functions of solidityand inlet-air angle are given for these blades infigures 137 and 138. The subscript 10 in figure137 indicates that the io values are for 10-percentmaximum-thickness ratio. Values of intercept ioand slope n were obtained by fitting a straight lineto each data plot of reference incidence angleagainst camber angle for a fixed solidity and airinlet angle. The straight l i e s were selected sothat both a satisfactory representation of thevariation of the data points and a consistentvariation of the resulting n and io values wereobtained.

The deduced rule values and the observeddata points compared in -re 139 indicate theeffectiveness of the deduced representation. Inseveral configurations, particularly for low cam-bers, the range of equivalent incidence anglecovered in the tests was insuf5cient to permitan accurate determination of a minimum-lossvalue. Some of the scatter of the data may bedue to the effects of local laminar separation inge characteristics of the sections.


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WWuc..-eWN

EXPERIMENTAL FLOW IN TWO-DlMENSIONAL CASCADES 195

Inlet-air angle, p, , de gFIGURE37.-Reference minimum-loss incidence angle for zero camber deduced from low-speed-cascade data of 10-per-cent-thick NACA 65-(A13-series blades (ref. 39).

Although the cascade data in reference 39include values of inlet-air angle from 30" to 70"and values of solidity from 0.5 to 1.5, the deducedvariations in figures 137 and 138 are extrapolatedto cover wider ranges of fll and u. The extrapo-lation of io to zero at &=O is obvious. Accord-ing to theory {fig. 133), the value of the slopeterm does not vanish at &=O . In figure 138,therefore, an arbitrary fairing of the curves downto nonzero values of n was adopted as indicated.Actually, it is not particularly critical to deter-mine the exact value of the slope term at @,=Onecessary to locate the reference incidence angleprecisely, since, for such cases (inlet guide vanes

and turbine nozzles), a wide low-loss range ofoperation is usually obtained. The solidityextrapolations were attempted because of theuniform variations of the data with solidity.However, caution should be exercised in anyfurther extrapolation of the deduced variations.C-Series circular-arc blades.-The variousthickness distributions used in combination withthe circular-arc mean line have been designatedC.l, C.2, C.3, and so forth (refs. 196 to 198). Ingeneral, the various C-series thickness distribu-tions are fairly similar, having their maximumthickness located at between 30 and 40 percentof the chord length. The 65-series and two of


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196 AERODYNAMIC DESIGN OF AXIAL-F'LOW COMPRESSORS

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Inlet -air angle, p , ,degFIGURE 38.-Reference minimum-loss-incidence-angle slope factor deduced from low-speed-cascade data for NACA65-(A1&series blades as equivalent circular arcs.the more popular 6-series thickness distributions((2.1 and (2.4) are compared on an exaggeratedscale in figure 140. (The 65-series profile shownis usually thickened near the trailing edge inactual blade construction.)In view of the somewhat greater 'thicknessblockage in the forward portions of the C-seriesblades (fig. 140), it may be tha t the minimum-lossincidence angles for zero camber for the C-seriesblades are somewhat greater than those for the 65-series profiles; that is, (KJ&l. In the absence ofany definitive cascade data, the value of (Kf)shorthe C-series profiles was arbitrarily taken to be1.1. Observed minimum-loss incidence anglesfor an uncambered 10-percent-thick C.4 profile(obtained from ref. 192, pt. I) are compared infigure 141 with values predicted from the deducedvalues for the 65-series blade (fig. 137 andeq. (262)) with an assumed value of (KJab=1.l.(For 10-percent thickness, (Kf)=1 )In view of the similarity between the 65-(A1,)-

series mean line and a true circular arc (fig. 125),the applicability of the slope values in figure 138to the circular-arc mean line was investigated.For the recent cadcade data obtained from tunnelshaving good boundary-layer control (refs. 167,(pt. I) and 199), a check calculation for the 10-percent-thick C.4 circular-arc blades using figures137 and 138 with (Kf)8b=l.l evealed goodresults. For the three configurations in reference199 tested at constant /31(p=30"), the agreementbetween observed and predicted minimum-lossincidence angles was within lo . For the oneconfiguration in reference 167 (pt. I) tested atconstant y0((p=31"), the predicted value ofminimum-loss incidence angle was 1.7' greaterthan the observed value. However, in view of thegeneral 1' to 2' difference between fixed B1 andfixed 7' operation (fig. 132), such a discrepancyis to be expected. On the basis of these limiteddata, it appears that the low-speed minimum-lossincidence angles for the C-series circular-arc


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EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES 197

FIGURE39.--Comparison of data values and deduced rule values of reference minimum-loss incidence angle for 65-(A10) 10blades as equivalent circular arc (ref. 39).

blade can be obtained from the io and n values ofthe 65-series blade with UG)8h=l.l.Double-circular-arc blades.-The double-circu-lar-arc blade is composed of circular-arc upperand lower surfaces. The arc for each surfaceis drawn between the point of maximum thick-ness at midchord and the tangent to the circlesof the leading- and trailing-edge radii. Thechordwise thickness distribution for the double-circular-arc profile with 1-percent leading- andtrailing-edge radius is shown in figure 140. Lackof cascade data again prevents an accuratedetermination of a reference-incidencegle rulefor the double circular arc. Since the double-circular-arc blade is thinner than the 65-seriesblade in the inlet region, the zero-camber in-

cidence angles for the double-circular-arc bladeshould be somewhat different from those of the65-series section, with perhaps (KJsnS. Itcan also be assumed, as before, that the slope-term values of figure 138 are valid for the double-circular-arc blade. From an examination of theavailable cascade data for the double-circular-arcblade (9=25O, u=1.333, ref. 40; and (p=4Oo, u=1.064, ref. 197), it appears that the use of figures137 and 138 with a value of (Kt),h=0.7 in equa-tions (261) and (262) results in a satisfactorycomparison between predicted and observed valuesof reference incidence angle.Other blades.-Similar procedures can be ap-plied to establish reference-incidence-angle cor-relations for other blade shapes. Cascade data


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198 A B R O D WA MI C DESIGN OF AXIAL-FLOW COMPRESSORS

Percent chordFIGURE400.-Comparison of basic thickness distributions for conventional compressor blade sections.

? 6.$-0

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z 2CW-0uc.-- 0 IO 20 30 40 50 60inlet-air angle, PI, deg

FIQURE41.-Zero-camber minimum-loss incidence angleangle for 10-percent-thick C.4 profile. Solidity, 1.0(ref. 192, pt. I) .are also available for the C-series parabolic-arcblades (refs. 40, 192, 200, and 201) and theNACA 65-(AI)-series blade (ref. 123); but, inview of the limited use of these forms in currentpractice, no attempt was made at this time todeduce corresponding incidenceangle rules forthese blades.Effect of blade maximum thickness.-As indi-cated previously, some correction (expressedhere in terms of (KJt,eq. (262)) of the basevalues of (io)lobtained from the 10-percent-thick 66series blades in figure 137 should existfor other values of blade maximum-thicknessratio. According to the theory of the zero-camber effect, (&)# should be zero for zerothickness and increase as maximum blade thick-ness is increased, with a value of 1O for a thicknessratio of 0.10. Although the very limited low-

speed data obtained from blades of variablethickness ratio (refs. 202 and 203) are not com-pletely definitive, it was possible to establish apreliminary thickness-correction factor for ref-erence zero-camber incidence angle as indicatedin figure 142 for use in conjunction with equation(262).Effect of inlet Mach number.--The previouscorrelations of reference minimum-loss incidenceangle have all been based on low-speed-cascadedata. It appears from limited highapeed data,however, that minimum-loss incidence angle willvary with increasing inlet Mach number forcertain blade shapes.The variations of minimum-loss incidence anglewith inlet Mach number are plotted for severalblade shapes in figures 143 and 144. The extensionof the test data points to lower values of inlet Machnumber could not generally be made because ofreduced Reynolds numbers or insufficient pointsto establish the reference location at the lowerMach numbers. In some instances, however, itwas possible to obtain low-apeed values of inci-dence angle from other sources.The blades of Sgure 143 show essentially novariation of minimum-loss incidence angle withinlet Mach number, a t least - p o a Mach number

of about 0.8. The blades ol: figure 144, however,evidence a marked ncrease in incidence angle withMach number. The difference in th8 variation ofminimum-loss incidence angle with Mach numberin figures 143 and 144 is associated with the


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EXPERIMFXNTAL FLOW lX TWO-DIMENSIONAL CASCADES 199

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Ma x i mu m- th i c k n e s s r a t i o , t / cFIGURE 42.-Deduced blade maximum-thickness correction for zero-camber reference minimum-loss incidence angle(es. (262)).different way the general pattern of the loss varia-tion chmges with increasing Mach number for thetwo types of blades. For the thick-nose blades,coefficient increases with Math number at bothmht a j n the 8-8 point of minimum loss. Forthe sharp-nose blade, as illustrated by figures

130 (c )and (d ) , he increase in lossoccursprimarilyon the low-incidencewgle side; md a positiveshifting of the ~ u m - l o s sncidence angleas illustrated in 130 (d and fi), he loss res,&. Data for other thickmnose sectionsinthe high and low ncidence angles, hus tending to reference201 Show the h1OSS to O C C W at bothends of the curve, but plots of reference incidenceangle against Mach number could not validly be


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200 AERODYNAMIC DESIGN O F

.CI,aJ I I I I I I I I l I l l l

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-4.I .2 .3 .4 .5 .6 .7 .ain le t Mach n u m b e r , M I(a) C.4 Circular-arc blade. Camber angle, 254; solidity1.333; blade-chord angle, 42.5' (ref. 40).(b) (2.4 Parabolic-arc blade. Camber angle, 25'; solidity,

1.333; blade-chord angle, 37.5'; maximum camber at40-percent chord (ref. 40).(c) C.7 Parabolic-arc blade. Camber angle, 40'; solidity,1.0; blade-chord angle, 24.6O; maximum camber at45-percent chord (ref. 216).FIGURE 43.-Variation of reference minimum-loss inci-dence angle with inlet Mach number for thick-nosesections. Maximum-thickness ratio, 0.10.made for these blades because of evidence of stronglocal laminar-separation effects.Since the most obvious difference between theblades in figures 143 and 144 is the constructionof the leading-edge region, the data suggest thatblades with thick-nose inlet regions tend to show,for the range of inlet Mach number covered,essentially no Mach number effect on minimum-loss incidence angle, while blades wth sharp lead-ing edges will have a significant Mach numbereffect. The available data, however, are toolimited to confirm this observation conclusively atthis time. Furthermore, for the blades that doshow a Mach number effect, the magnitude ofthe variation of reference incidence angle withMach number is not currently predictable.

SUMMARYThe analysis of blade-section reference mini-mum-loss incidence angle shows that the variationof the reference incidence angle with cascadegeometry a t low speed can be established satis-factorily in terms of an intercept value ioand a

AXLAL-FLOW COMPRESSORS

$ 8W0cw 4E0C- 0

I I I I I A 1 - 4 1 l I I I

Inlet Mach number, MI(a) Double-circular-arc blade. Camber angle, 25";man-mum-thickness ratio, 0.105; solidity, 1.333; blade-chordangle, 42.5' (ref. 40). Camber angle, 27.5';

maximum-thickness ratio, 0.08; solidity, 1.15; blade-chord angle, 30'; maximum thickness and camber at50-percent chord.

(b) Blade section of reference 205.

FIGURE 44.-Variation of reference minimum-loss inci-dence angle with inlet Mach number for sharp-nosesections.slope value n as given by equation (261). De-duced values of i, and n were obtained as a functionof B1 and u from the data for the 10-percent-thick65-(Alo)-seriesblades of reference 39 as equivalentcircular-arc sections (figs. 137 and 138). It wasthen shown that, as a first approach, the deducedvalues of (io)lond n in figures 137 and 138 couldalso be used to predict the reference incidenceangles of the C-series and double-circular-arcblades by means of a correction to the (io>lovalues of figure 137 (eq. (262)).The procedure involved in estimating the low-speed reference minimum-loss incidence angle ofa blade section is as follows: From known valuesof B1 and u, (io)lond n are selected from figures137 and 138. The value of (&), for the blademaximum-thickness ratio is obtained from figure142, and the appropriate value of (KJShs selectedfor the type of thickness distribution. For NACA65-series blades, (Kt)sh=l.O; and it is proposedthat (KJshe taken as 1.1for the C-series circular-arc blade and as 0.7 for the double-circular-arcblade. The value of io is then computed fromequation (262); and finally i is determined from


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EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCAFES 201the blade camber angle accordingtoequation (261).It should be noted that the values of (&),agiven for the circular-arc blades are rather tenuousvalues obtained from very limited data. The useof the proposed values is not critical for goodaccuracy; the values were included primarily forcompleteness as a reflection of the anticipateddifferences in the blade thickness blockage effects.Further experimental data will be necessary toestablish the significance of such a correction.Also, a marked increase in reference minimum-lossincidence angle with Mach number is to be ex-pected for sharp-nose blade sections. The magni-tude of the Mach number correction for theseblades is currently unpredictable.

LOSS ANALYSISWith the location of the low-speed referenceminimum-loss incidence angle established forseveral conventional blade sections, the magnitudeof the losses occurring at this reference position(fig. 127) will now be investigated. Accordingly,the nature of the loss phenomena and the variousfactors Muencing the magnitude of the loss overa range of blade c6nfigurations and flow conditionsare first analyzed. The available experimentalloss data are then examined to establish funda-mental loss correlations in terms indicated bythe analysis.

PRELIMINABY ANALYSISTwo-dimensional-cascade losses arise primarily

from the growth of boundary layer on the suctionand pressure surfaces of the blades. These sur-face boundary layers come together at the bladetrailing edge, where they combine to form theblade wake, as shown in figure 145. As a resultof the formation of the surface boundary layers,a local defect in total pressure is created, and acertain mass-averaged loss in total pressure isdetermined in the wake of the section. The lossin total pressure is measured in terms of the total-pressure-loss coefficient; defined generally as theratio of the mass-averaged loss in total pressureA P across the blade row from inlet to outlet sta-tions to some reference free-stream dynamic pres-sure (Po-j$relt or

Velocity variation V2 l /across blade spacing-,,

FIGURE 145.4chematic representation of development ofsurface boundary layers and wake in flow about cascadeblade sections.For incompressible f low, Po-po is equal to theconventional free-stream dynamic pressure poV72.The total-pressure-loss coefficient is usually deter-mined from consideration of the total-pressurevariation across a blade spacing s (fig. 145).A theoretical analysis of incompressible two-dimensional-cascade losses in reference 156 showsthat the total-pressure-loss coefficient at the cas-cade-outlet, measuring station (where the staticpressure is essentially uniform across the bladespacing) is given by

where is the loss coefficient based on inletdynamic head, O*/c is the ratio of wake momentumthickness to blade-chord length, u is cascadesolidity, b2 is the air outlet angle, and H2 is thewake form factor (displacement thickness dividedby momentum thickness). The wake character-istics in equation (264) are expressed in terms of


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202 AERODYNAMIC DESIGN OF AXIATJ-FLOW COMPRESSORSconventional thickness in a plane normal to thewake (i.e., normal to the outlet flow) at the meas-uring station. Definitions of wake characteristicsand variations in velocity and pressure assumedby the analysis are given in reference 156. Theanalysis further indicates that the collection ofterms within the braces is essentially secondary(sinceH2s generally 5 bout 1.2 at the measuringstation), with a magnitude of nearly 1 for conven-tional unstalled configurations. The principaldeterminants of the loss in total pressure at thecascade measuring station are, therefore, the cas-cade geometry factors of solidity, air outlet andair inlet angles, and the aerodynamic factor ofwake momentum-thickness ratio.Since the wake is formed from a coalescing ofthe pressure- and suction-surface boundary layers,the wake momentum thickness naturally dependson the development of the blade surface boundarylayers and also on the magnitude of the bladetrailing-edge thickness. The results of references156, 202, and 204 indicate, however, that thecontribution of conventional blade trailing-edgethickness to the total loss is not generally largefor compressor sections; the preliminary factorin the wake development is the blade surfaceboundary-layer growth. In general, it is known(ch. V, e.g.) that the boundary-layer growth onthe surfaces of the blade is a function primarilyof the following factors: (1) the surface velocitygradients (in both subsonic and supersonic flow),(2) the blade-chord Reynolds number, and (3)the free-stream turbulence level.Experience has shown that blade surface velocitydistributions that result in large amounts of diffu-sion in velocity tend to produce relatively thickblade boundry layers. The magnitude of thevelocity diffusion in low-speed flow generally de-pends on the geometry of the blade section andits incidence angle. As Mach number is increased,however, compressibility exerts a further influenceon the velocity diffusion of a given cascadegeometry and orientation. If local supersonicvelocities develop at high inlet Mach numbers,the velocity difFusion is altered by the formationof shock waves and the interaction of these shockwaves with the blade surface boundary layers.The losses associated with local supersonic flowin a cascade are generally greater than for subsonicflow in the same cascade. The increases in lossare frequently referred to as shock losses.

Caseade-inlet Mach number also influences themagnitude of the subsonic diffusion for a fixedcascade. This Mach number effect is the con-ventional effect of compressibility on the bladevelocity distributions in subsonic flow. Com-pressibility causes the maximum local velocity onthe blade surface to increase at a faster rate thanthe inlet and outlet velocities. Accordingly, themagnitude of the surface diffusion from maximumvelocity to outlet velocity becomes greater asinlet Mach number is increased. A furthersecondary influence of Mach number on losses isobtained because of an increase in losses associatedwith the eventual mixing of the wake with thesurrounding free-stream flow (ref. 37).On the basis of the foregoing considerations,therefore, it is expected that the principal factorsupon which to base empirical cascade-wake-thickness correlations should be velocity diffusion,inlet Mach number, blade-chord Reynolds number,and, if possible, turbulence level.

D A T A CORBELATIONSVelocity diffusion based on local velocities.-Recently, several investigations have been re-ported on the establishment of simplified diffu-sion parameters and the correlation of cascadelosses in terms of these parameters (refs. 9,38, and

156). The general hypothesis of these diffusioncorrelations states that the wake thickness, andconsequently the magnitude of the loss in totalpressure, is proportional to the diffusion invelocity on the suction surface of the blade inthe region of the minimum loss. This hypothesisis based on the consideration that the boundarylayer on the suction surface of conventionalcompressor blade sections contributes the majorshare of the wake in these regions, and thereforethe suction-surface velocity distribution becomesthe governing factor in the determination of theloss. It was further established in these correla-tions that, for conventional velocity distributions,the diffusion in velocity can be expressed signifi-cantly as a parameter involving the differencebetween some function of the measured maximumsuction-surface velocity V,,, and the outletvelocity Vz.Reference 38 presents an analysis of blade-loading limits for the 65-(Alo)10 blade section interms of drag coefficient and a diffusion parametergiven for incompressible flow by (va,,,-V:)/vz,,,.


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EXPERIMENTAL F'LOW DN TWO-DIMENSIONAL CASCADES 203Results of an unpublished analysis of cascadelosses in terms of the momentum thickness of theblade wake (as suggested in ref. 156) indicatethat a local diffus ammeter in the form givenpreviously or insatisfactorily correlate expedata.' The term 'local diffusion parameter" isused to indicate that a knowledge of the maximumlocal surface velocity is required. The correla-tion obtained be tween calculated wake momen-tum-thickness ratio O*/c and local diffusionfactor given by

(265)mU2-vV-l O C =obtained for the NACA 65-(Al,)-series cascadesections of reference 39 at reference incidenceangle is shown in figure 146. Values of wakemomentum-thickness ratio for these data werecomputed from the reported wake coefficientvalues according to methods similar to thosediscussed in reference 156. Unfortunately, bladesurface velocity-distribution data are not availablefor the determination of the diffusion factor forother conventional blade shapes.

Local diffusion facto;,FIQUBE46.-Variation of computed wake momentum-thickness ratio with local diffusion factor at referenceincidence angle for low-speed-cascade data of NACA65-(A,0) 10 blades (ref. 39).

The correlation of figure 146 indicates thegeneral validity of the basic diffusion hypothesis.At high values of diffusion (greater than about0.5), a separation of the suction-surface boundarylayer is suggested by the rapid rise in the momen-tum thickness. The indicated nonzero value ofmomentum thickness at zero diffusion represents

aA later analysis of cascade totfd-pressure losses is given in Andy& ofCompressorBlade Caseadesby sepplourLiebein. NACA RM E67A28.1957.Expe-mtal Low-SpeedIAXS a d ta l l CharaoteristieOf W0-D

the basic friction loss (surface shear stress) of theflow and also, to a smaller extent, the effect ofthe finite trailing-e thickness. The correla-tion of figure 146 indicates that wakemomentum-thickness ratio at reference incidenceangle can be estimated from the computed localdiffusion factor for a wide range of solidities,cambers, and inlet-air angles. The loss relationsof equation (264) and reference 156 can then beused to compute the resulting loss in the totalpressure.

Velocity diffusion based on over-all velocities,-In order to include the cases of blade shapes forwhich velocity-distribution data are not available,a diffusion parameter has been established inreference 9 that does not require a specific knowl-edge of the peak local suction-surface velocity.Although originally derived for use in compressordesign and analysis, the diffusion factor of refer-ence9 can also be applied in the analysis of cascadelosses. The diffusion factor of reference 9 at-tempts, through several simplifying approxima-tions, to express the local diffusion on the bladesuction surface in terms of over-all (inlet or outlet)velocities or angles, quantities that are readilydetermined. The basis for the development ofthe over-all diffusion factor is presented in detailin reference 9 and is indicated briefly in figure 147.The diffasion factor is given by

which, for incompressible two-dimensional-cascadeflow, becomes

As in the case of the local diffusion factor, thediffusion factor of equation (266) is restricted tothe region of minimum loss.Cascade total-pressure losses at reference mini-mum-loss incidence angle are presented in refer-ence 9 as a function of diffusion factor for theblades of reference 39. In a further unpublishedanalysis, a composite plot of the variation ofcomputed wake momentum-thickness ratio withD at reference minimum-loss incidence angle wasobtained from the available systematic cascadedata (refs. 39 and 192) as shown in figure 148.'Blade maximum thickness was 10 percent in all


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204 AERODYNAMIC DESIGN OF

Pressuresurface

--V0W->

FIQURE47.-Basis of development of diffusion factorfor cascade flow from reference 9. D=v"'az-v2= maz- vs;,,, =V,+f ('9);hus, equations (54)and (266).

VasVl

cases. A separation of the suction-surfaceboundary layer at high blade loading is indicated

AXIAL-FLOW COMPRESSORSv) .06InWe32.04s PETa3c -e 0.02r:W L

0 .I .2 3 .4 .5 .6 .7 .8Diffusion factor,DFIQUBE148.-Variation of computed wake momentum-thickness ratio with overall diffusion factor at referenceincidence angle for low-speed systematic cascade dataof references 39 and 192. Blade maximum-thicknessratio, 0.10; Reynolds number, = 2 . 5 X 1W.by the increased rise in the wake momentumthickness for values of diffusion factor greaterthan about 0.6.For situations in which the determination ofa wake momentum-thickness ratio cannot be made,a significant loss analysis may be obtained if asimplified total-pressure-loss parameter is usedthat closely approximates the wake thickness.Since the terms within the braces of equation(264) are generally secondary factors, a loss pa-rameter of the form Ul2 syhould con-stitute a more fundamental expression of the basicIoss across a blade element than the loss coefficientalone. The effectiveness of this substitute lossparameter in correlating two-dimensional-cascadelosses is illustrated in figure 149(a) for all the datafor the NACA 65-(A,,)-series blades of reference39. (Total-pressure-loss coefficients were com-puted for the data from relations given in ref. 9.)A generalized correlation can also be obtained interms of ;J 1 ~ B Z ,u aa shown in figure 149@), butits effectiveness as a separation indicator does notappear to be as good. Such generalized lossparameters are most effective if the wake formdoes not vary appreciably among the variousdata considered.Effect of blade maximum thickness.-Since anincrease in blade maximum-thickness ratio in-creases the magnitude of the surface velocities(and therefore the diffusion), higher values ofwake momentum-thickness ratio would be expectedfor thicker blades. From an analysis of limitedavailable data on varying blade maximum-thickness ratio (refs. 202 and 203), it appears thatthe effect of blade thickness on wake momentum-thickness ratio is not large for conventional


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EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES 205cascade configurations. For example, for an in-crease in blade maximum-thickness ratio from0.05 to 0.10, an increase in O*/c of about 0.003 atD of about 0.55 and an increase of about 0.002 atD of about 0.35 are indicated. The greater in-

O*/c at the higher diffusion level isrstandable, since the rate of change of O*/cDIocncreases with increasing diffusion (see146).If blade surface velocity dBtributions can be

will auto-cally be included in the evaluation of thelting local diffusion factor. When an over-(54) is used,he corresponding loss prediction. However, inof the small observed effect and the scatterf the original P / c against D correlation of figure

148, it is believed that a thickness correction isr, the analysis does indicate that, for highit may be ad-

he reference condition.Thus, the plots of figures 146, 148, and 149ha t, when diffusion factor and wakeen um - hickness ratio (or to al-pressure-lossparameter) are used as the basic blade-loadingand loss parameters, respectively, a generalizedcorrelation of two-dimensional-cascade loss datas obtained. Although several assumptions andestrictions are involved in the use and calculationof these parameters, the basic diffusion approachconstitutes a useful tool in cascade loss analysis.In particular, the diffusion analysis should beinvestigated over the complete range of incidenceangle in an effort to determine generalized off-design loss information. .Effect of Reynolds number and turbulence,-The effect of blade-chord Reynolds number andturbulence level on the measured losses of cascadesections is discussed in the section on Data Selec-tion, in chapter V, and in references 39, 167(pt. I), and 183. In all cases, the da ta reveal anincreasing trend of loss coefficient with decreasingReynolds number and turbulence. Examples oithe variation of the total-pressure-loss coefficientwith incidence angle for conventional com-pressor blade sections at two different valuesof Reynolds number are illustrated in Sgure

.04

.020

D i f f u s i o n factor, D(a) BasedonGI-(z2(b) Baaed on Z1.

FIGURE 49.-Variation of loss parameter with diEusionfactor at reference minimum-loss incidence anglecomputed from low-speed-cascade data of NACA65-(A,0)10 crrscade blades (ref. 39).150. Loss variations with Reynolds numberover a range of incidence angles for a given bladeshape are shown in figure 151. A composite plotof the variation of total-pressure-loss coefficient

.I5

.IOcc .05ca30;EW

.- I I I I I ( a ) I-:: 0' 8 16 24 32 40Angle of attack, a ,deg

Incidence angle,i, eg

(a) 65-Series blade 6&(12) 10. Solidity, 1.5; inlet-airangle, 45O (ref. 39).(b) Circular-arc blade lOC4/25C50. Solidity, 1.333; blade-chord angle, 42.5' (ref. 40).FIGUFUG50.-Effect of Reynolds number on variation ofloss with incidence angle.


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206 AERODYNAMIC DESIGN OF AXIAL-FLOW COMPRESSORS

FIGURE 51.- Variation of total-pressure-loss coefficientwith blade-chord Reynolds number for parabolic-arcblade 10C4/40 P40. Inlet-air angle, 28" to 40";solidity, 1.333 (ref. 183).

at minimum loss with blade-chord Reynoldsnumber for a large number of blade shapes isshown in figure 152. Identification data for thevarious blades included in the Sgure are given inthe references. For the blades whose loss data arereported in terms of drag coefficient, conversion tototal-pressure-loss coefficient was accomplishedaccording to the cascade relations presented inreference 9. The effect of change in tunnelturbulence level through the introduction ofscreens is indicated for some of the blades.It is apparent from the curves in figure 152 thatit iscurrently impossible to establish any one valueof limiting Reynolds number that will hold for allblade shapes. (The term limiting Reynoldsnumber refers to the value of Reynolds number atwhich a large rise in loss is obtained.) On thebasis of the available cascade data presented infigure 152, however, it appears that serious troublein the minium-loss region may be encounteredat Reynolds numbers below about 2.5X105.Carter in reference 19 0 places the limiting blade-ber based on outlet velocityat 1.5 to 2.0X105. Considering that outletReynolds number is less than inlet Reynoldsnumber for decelerating cascades, this quoted

value is in effective agreement with the value oflimiting Reynolds number deduced herein.The desirability of conducting cascade investi-gations in the essentially flat range of the curve ofloss coefficient ag nolds number in orderto enhance the corr of da ta from varioustunnels, aswell asfrom the configurationsof a given tunnel, is indicate cade operationin the flat range of Reynolds number may alsoyield a more significant comparison betweenobserved and theoretically computed loss. Reyn-olds number and turbulence level should alwaysbe defined in cascade investigations. Furthermore,the development of some effective Reynoldsnumber (ch. V) that attempfs to combine theeffects of both blade-chord Reynolds number andturbulence should be considered for use as theindependent variable.

Effect of inlet Mach number.-In the previouscorrelations, attention was centered on the variousfactors affecting the loss of cascade blades for

Blode-chord Reynolds number, Re,FIGURE 52.-Composite plot of loss coefficient againsterin region of minimum lo s ~blade sectionsat low speed.


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EXPERIMENTAL FLOW IN TWO-DIMENSIONAL CASCADES 207essentially incompressible or low Mach numberflow. Tests of cascade sections at higher Machnumber levels hav

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