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AL71-0D61
MMCF. 1971
Aerospac. Iesearch LaboratoreFs
THE DESIGN OF AN AXIAL COMPRESSOR STAGEFOR A TOTAL PRESSURE RATIO OF 3 TO I
A. 1. WEVWEPSTRGM!
RICHARD 1. HEARSEY
FLUID DYNAMcS FACILrIIES RESEARCH L-4BORATORY
PROJECT NO. 7065
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AIR -FORCE SYSTEMS COMMAND I fj C 2, --.- -Jj
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200 - J, 1971 - C0305 - 42-71-723
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UNCLASSIFIED S '1Secuuitv Classification
DOCUMENT CONTROL DATA -R &D(Security classification of title, body of abstract and Indexing annotation mu.t be entered when the overall report is classlfled) J
IO.GINATING ACTIVITY (Corporat* author) 12a. REPORT SECURITY CLASSIFICATION
Aerospace Research Laboratories (ARL/LF) UnclassifiedWright-Patterson AF Base, Ohio 45433 12b.C ROUP
3. REPORT TITLE
THE DESIGN OF AN AXIAL COMPRESSOR STAGE -FOR A TOTAL PRESSURE RATIO OF 3 TO 1
A DESCRIPTIVE NOTES (tpe ofrepo. tend Inclu i e dotes)
Scientific. Final.0 AU THORIS) (First name, middle Initial. l st n.me)
Arthur J. Wennerstrom, Richard M. Hearsey I6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS
March 1971 177 988. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMNeRSi
In-house researchb. PROJECT NO.7065-097~" 65oD E meOb. OTHER REPORT NOWS! (Any other numbers that may, be assigned
DoD Element 61 102F this rep0
d. DoD Subelement 681307 ARL 71-006110 DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited.
It. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY
TECH OTHER Fluid Dynamics Facilities Rsch LabTEHOHRARL/LF, Wright-Patterson AFB, Oh
13. ABSTRACT
Thi-s report describes in detail the aerodynamic design of a super-sonic axial compressor stage. The principal design-point characteris-tics of the stage are a corrected tip speed of 1600 ft/sec, an inlethub/tip radius ratio of 0.75, a total pressure ratio of 3.0, and anisentropic efficiency of 82%. Four features distinguish this stagefrom other reported stages. A new type of rotor airfoil is employed.The stator leading edges are swept back from both walls toward mid-passage. Unusually large and variable fillet radii blend blades withplatforms. Also, a new and precise technique was used to determineCartesian manufacturing coordinates for the airfoils, aerodynamicallydefined on streamsurfaces. The preliminary design employed a techniqueresulting in equilibrium radial distributions of loss coefficient andflow angle which are fully consistent with relative Mach numbers anddiffusion factors for each blade row and on each streamsurface accord-ing to a prescribed loss model. The detail design was accomplishedusing computing stations internal as well as external to both bladerows and attempted to optimize the axial distribution of staticpressure.
DD I NOV 1473 UNCLASSIFIEDSecurity Classification
IINrTLASSI FT EflSecurity Clausification
IW LINK A LINK B LINK C
ROLE WT ROLE WT ROLE WT
AXIAL COMPRESSOR
SUPERSONIC COMPRESSOR
GAS 'rURBI'E
TURBINE ENGINE
UNCLASSI FILD
Security Classification
i
ARL 71-0061
THE DESIGN OF AN AXIAL COMPRESSOR STAGEFOR A TOTAL PRESSURE RATIO OF 3 TO I
A. J. WENNERSTROM
R. M. HEARSEY
FLUID DYNAMICS FACILITIES RESEARCH LABORATORY
MARCH 1971
Approved for public release; distribution unlimited.
AEROSPACE RESEARCH LABORATORIES
AIR FORCE SYSTEMS COMMANDUNITED STATES AIR FORCE
WRIGHT-PATTERSON AIR FORCE BASE, OHIO
II
!V
FOREWORD
This report was prepared, by . Rict.rd M. Iarsey, VisitingResearch Associate of the Ohio State University Research Foundation,and Dr. Arthur J. Wennerstrom of the Fluid Dynamics Facilities Rersearch Laboratory, Aerospace Research Laboratories, WrIght-Patterson k
Air Force Base, Ohio.
3 The report presents results from a portion of the effort of theFluid Machinery Research Goup, supervised by Dr. Arthur J. Wennerstromand was conducted under Work Unit 09 of Project 7065, "Aerospace Simu--lation Techniques Research," under the over-all direction of Mr. timerG. Johnson.
-A
'tA,
I)
Iii
FABSTRACT
This report describes in detail the aerodynamic design of asupersonic axial-compressor stage. The principal design-point char-acteristics of the stage are a corrected tip speed of 1600 ft/sec,.an inlet hub/tip radius ratio of 0.75,,, a total pressure ratio of 3;0,and an isentropic efficiency of 82%. Four features distinguish thisstage from other reported stages. A new type of rotor airfoil is em-ployed. The stator leading -edges are swept 'back from both wallstoward mid-passage. Unusually large and variable fillet radii blend
blades with platforms. Aiso, a new and precise technique was usedto determine Cartesian manufacturing coordinates for the airfoils,.aerodynamically defined on streamsurfaces. The preliminary designemployed a technique resulting in equilibrium radial distributions ofloss coefficient and flow ahgle which are fully consistent with rela-tive Mach numbers and diffusion factors for each blade row and on eachstreamsurface according to a. prescribed loss model. The detail ,design,was accomplished using computing stations internal as well as externalto both blade rows and attempted to optimize the axial distribution ofstatic pressure.
~1
1,
iii P
A A
*TABLE OF CONTENTS
SECTION PAGE
I INTRODUCTION ...... . .... ............. III DESIGN CRITERIA.. . . . . .. ......... ...... 3
1. LOADING AND LOSS DISTRIBUTIONS 3
a. Over-all Averaged Quantities . . . . . . .. 3
b. Radial Distributions ....... ........ 3
c. Axial Distributions Within Blade Rows . 5
2. BLADE PROFILE AND SOLIDITY SELECTION ...... 7
a. Rotor Blade .. .. .. .. .. .. .. .. . '7
b. Stator Blade .. ................ .... 9
* 3.. DEVIATION ANGLES ....... ................. 10
a. Rotor Blade ..... ..................... 10
b. Stator Blade . .i......... .. . .. .. 10
4. ASPECT RATIOS, FILLET RADII, ANDSTATOR LEADING EDGE FORM . . .. ........ 11
III AERODYNAMIC CALCULATION METHOD ... .......... . 12
1. AXISYMMETRIC FLOW ANALYSIS ....... ......... 12
2 2. ITERATION PROCEDURE FOR CONSISTENT LOSSES . . . . 14
3. ALTERNATIVE FORMULATION OF MOMENTUM EQUATION . • 15
4. ANNULUS WALL ,BOUNDARY LAYER DETERMINATION . . . . 16
5. USE OF STATIC PRESSURE DISTRIBUTIONS TOOPTIMIZE IN.CIDENCE ANGLES AND ANNULUS GEOMETRY 17
6. COMPUTER PROGRAM ..... ................ ... 17
IV RESULTS FROM DESIGN CALCULATIONS .. .......... . 19
1. ITERATIVE LOSS REESTIMATION PROCEDURE ...... ... 19
V
SECTION PAGE
a. Path to a Solution . ........ . . . . 19
b. Design-Point Conditions ............ 19
2. INTRABLADE FLOW ANALYSIS.. ................ ... 35
V FINAL STAGE CONFIGURATION . ............ . . . 62
1. DESIGN-POINT SPECIFICATIONS . ........ . . . 62
2. ANNULUSGEOMETRY ..... ............ 62
3. ROTOR GEOMETRY ................ . 62
a. Number- of Blades 62
b. Blade Frn ...... ................. ... 62
c. Location of Stack Axis . . . ; .. ....... 64
d. Root Fillet. . .............. 64
4. STATOR GEOMETRY .............. . . . 123
a. Number of Blades ..... ............... 123
b. Blade Form .............. ............ 123
c. Location of Stack Axis ........ ........ 124
d. Root 'Fillet . .................. 124
e. Stator Blade Coordinates .. .......... ... 125
VI PREDICTED STAGE PERFORMANCE ........ ............ 142
1. PREDICTED PERFORMANCE USING THE ITERATIVELOSS REESTIMATION PROCEDURE ....... . . . . 142
2. PREDICTED INTRA-BLADE-ROW PERFORMANCE ......... 1112
FIGURES ....... .......................... 145
REFERENCES ..... .. ............... 169
vi
LIST OF ILLUSTRATIONS
FIGURE PAGE
1 Assumed Relationship Between Total PressureLoss Parameter and Diffusion Factor ... ........ 1115
2 Relationship Between "Im" and Stagger Angle inCarter's Rule for Rotor and Conventional Sections 145
3 Assumed Generalized Variation of Deviation
Within Blade . .. ..... .......... ....... . 1146
14 Meridional Velocity 'Distributions from
Iterative Loss ReestiMation Procedure ....... . 146
5 Annulus Geometry and Computing Stations Derivedfrom Iterative Loss Reestimation Procedure i.....147
6 Rotor and Stator Relative Mach Numbers from
I terative Loss Reestimation Procedure ... ....... 148
7 Rotor and Stator Relative Flow Angles fromIterative Loss Reestimation Procedure. .. .. ..... 1118
8 Diffusion Factors for Rotor and Stator fromIterative Loss Reestimation Procedure ....... . 149
9 Relative Total Pressure Loss Coefficientsfor Rotor and Stator from Iterative LossReestimation Procedure ...... ............. ... 150
10 Total Pressure Ratios for Rotor and Stage fromIterative Loss Reestimation Procedure . ....... .. 151
11 Isentropic Efficiencies for Rotor and Stagefrom Iterative Loss Reestimation Procedure ..... .. 152
12 Nondimensional Total Temperature Rise
from Iterative Loss Reestimation Procedure ..... 153
13 Annulus Wall Boundary Layer DisplacementThicknesses from Iterative Loss ReestimationProcedure ....... ..................... ... 1511
14 Annulus Geometry and Computing Stations forFinal Blading Analysis .... ............... ... 155
15 Meridional Velocity Distributions for Rotorfrom Final Blading Analysis and IterativeLoss Reestimation Procedure .. ............ ... 156
vii
FIGURE PAGE
16 Meridional Velocity Distribution., forStator from Final Blading-Analysis andIterative Loss Reestimation Procedure . ....... .. 157
17 Static Pressure Distribution ThroughStage from Final Blading Analysis ......... .. 158
18 Incidence Angle Distributions for Rotorand Stator from Final Blading Analysis .......... 159
19 Deviation Angle Distributions for Rotorand Stator from Final Blading Analysis ....... ... 159
20 Definition of Overall Flowpath ..... ........... 160
21 Detail Definition of Inner Wall ofFlowpath Through Compressor .... ............ ... 161
22 Detail Definition of Outer Wall of FlowpathThrough Compressor ... .................... . 162
23 Superimposed Plots of Rotor BladeStreamsurface Sections ....... ............... 163
214 Superimposed Plots of Rotor BladeCartesian (Manufacturing) Sections .......... ... 164
25 Superimposed Plots of Stator BladeStreamsurface Sections .... ............... ... 165
26 Superimposed Plots of Stator BladeCartesian (Manufacturing) Sections .......... ... 166
27 Relative Total Pressure Loss Coefficients forRotor and Stator from Iterative LossReestimation Procedure with Higher Shock Loss . . . 167
28 Static Pressure Distribution Through Stagefrom Analysis with Increased Loss Coefficients . . . 168
viii
SECTION I
INTRODUCTION
-A major goal associated with research into and development ofaircraft-related turbomachinery is reduction of the size, weight andcost of the compressor component. Reductions of size and weightwould benefit many types of equipment, but most particularly aircraftturbine engines, gas-turbine powered ground support equipment andvehicles, and other air-transportable turbocompressor systems. Suchreductions may be achieved through increases in specific performancelevels such as pressure ratio per stage and flow per unit frontalarea. Cost reductions accrue through two means. First, a reducedsize and/or number of fabricated parts leads to lower component coststo meet a particular performance objective. Second, lower componentweight allows higher payloads for associated vehicle systems. In-creases in specific performance are achieved through increases inrotational speed and aerodynamic loading levels, normally at the ex-pense of thermodynamic efficiency. This report addresses itself tothe problem of raising thermodynamic efficiency in axial compressor
*stages designed for high Mach numbers and high pressure ratios.
The design of a heavily-loaded, supersonic axial compressorstage is described. The stage target performance calls for an over-all total pressure radio of 3:1, at an isentropic efficiency (basedupon stagnation conditions) of 0.82. The rotor corrected tip speedis 1600 feet per second, with an inlet hub-to-tip radius ratio of0. 75:1. This performance level is beyond the current state-of-the-art. Accordingly, the intent is to produce a stage having the bestobtainable performance, and hence with the maximum potential fordevelopment to the objective performance level.
Axial turbomachine design is generally considered to consist offirst, the execution of an aerodynamic design procedure and, second,the determination of the geometry of blading that is compatible withthe aerodynamic design and with pertinent mechanical restraints.These two steps were followed in an integrated manner for this design.Initially, an aerodynamic design was produced which satisfied thedesign o-bjectives and criteria, calculations being made at the bladeleading and trailing edges. This calculation included the use ofselected loss models for the rotor and stator blades. Hence theresults included relative inlet and outlet flow angles and total pres-sure loss coefficients for the rotor and stator that were consistentwith the design assumptions. Subsequently, further aerodynamic cal-culations were made at locations both exterior to and within the bladerows to evaluate possible blading geometries and details of annuluswall contours within the blading.
The aerodynamic calculations were made using an axisymmetricflow analysis computed by the streamline curvature technique. Thismethod is discussed in Ref 1. (The mechanical evaluation of the de-sign was made separately from the aerodynamic design.)
1
ii
-a vi% to achieving the previously stated goals, severalnove. f~tur, were hicorporated into the design. A new rotor blade
..i employed, a key characteristic of which is that it con-tuaiz n, -lU-ontinuitles in surface curvature. This is intended tomiraii~zi tuadary iayer separation, due to abrupt velocity gradientctize- in the flow at the blade surfaces. Having designed the blade- ectluxi, on otreamsurfaces-, an accurate procedure for the determina-tiozn of Carteitn coordinates for the blade was employed to providedata convenent to the manufacturing process. A full description ofthe L'Lade a-ct'on and the method of determining manufacturing coordi-nate data iz given in Ref 2. A swept leading edge configuration wasincluded in the itator blade design. It is hoped that this will re-duce the .,ensltivity of the stator blades to incidence At elevated
I4ach numbers,_
Subsequent sections of the report describe the various aspectsand phases of the design. The criteria incorporated into the designare presented followed by details of the aerodynamic evaluationmethod. The results of the various design calculations are described,and then the final stage configuration is given. Finally, the antici-pated performance of the compressor is discussed.
2
~ 1
22
t
SECTION II
DESIGN CRITERIA
1. LOADING AND LOSS DISTRIBUTIONS
a. Over-all Averaged Quantities
The target perforinance for the stage (outlined previously)together with some leading parameters specified at the outset of thedesign process, are as follows:
Total pressure ratio 3.0:1
Isentropic efficiency (total-to-total) 0.82
Inlet hub/tip radius ratio 0.75
Rotor tip speed (corrected to SLS) 1600 ft/sec
Inlet Mach number 0.55
Exit Mach number 0.5
Exit swirl zero
An 18-inch diameter was selected for the compressor, resulting in adesign flow-rate (corrected to SLS) of 30.0 lbs/sec. (This dimensionresulted from consideration of power requirements for testing, as anupper bound, and a practical minimum size for instrumentation as alower bound. Aerodynamically, only the blockage allowance attributedto annulus wall boundary layers is significantly affected.)
b. Radial Distributions
Because maximum design-point efficiency is a principal obj'c-ti've of this stage, blade element minimum loss values have been usedfor each element, consistent with local values of diffusion and Machnumber. Losses, expressed as relative total pressure loss coeffi-cients, are assumed to be composed of two additive components; a lossdue to diffusion and a loss due to shock waves (where Mach number ishigh enough). Then, the over-all blade element loss coefficients forrotor and stator are defined.
d+ d s (1)
where i is the over-all relative total pressure loss coefficient
id is the contribution due to diffusion losses
and is the contribution due to shock losses.
3
4PI
di ffu. ijn loss component model is based upon the well-knownNiDifA <eorr,;ation pretented in Ref 3. A total pressure loss param-cter and a diffusion factor are defined by
Cod COS a2c XP ="(2a)
2aandA C c -~ IC62
D + Or r (2b)C 2C
where P is the total pressure loss parameter
is the relative outlet flow anglezr
o is the cascade solidity
o is the diffusion factor
C is the relative outlet velocity2
C is the relative inlet velocity
C 02 is the relative inlet whirl velocity
Co0 z is the relative outlet whirl velocity.
The relationship that was assumed between the total pressure lossparameter and the diffusion factor is shown in Fig 1. This is anextrarolation to higher diffusion factors of the data given in Fig 203
of Ref 3.
The shock loss component is determined from the loss across anormal shock, the strength of which is a function of the blade ele-ment relative inlet Mach number. Different blade profiles wereselected for the rotor and stator (as discussed in the followingsection) and hence two different relationships for the shock Machnumber as a function of the inlet Mach number were used.
The profile selected for the rotor blade has almost no cam-ber up.:tream of the point where the main passage shock will probablyimpinge upon the blade suction surface so that, from the viewpointof a two-dimenional cascade, the Mach number should be unchangedrelative to the inlet value. Compounded with this are effects in themeridional (axial-radial) plane. The annulus walls were assumed (attisi.; pha:t of the design) to be converged in the region of the rotorleading edge .7o that significant contraction and hence diffusion ofthe 'uperoonic relative flow would occur. The average Mach numberimmediately upstream of the shock is assumed to be given by
: ,'
Ms = 1.0 + 0.6667 (,Mr- 1.0) (3)
where M is the Mach number immediately upstream of the shock
A is the blade section relative inlet Mach number.
Then the relative total pres3ure loss coefficient component due toshock losses is given by
1- y y-! y + [2 ]1 1
+.2
Sw (4N)S[ 2ylMyi]- 1 + Y - 1 M -1
The double circular arc profile used for the stator had convex
curvature throughout the suction surface, and hence, from the view-point of a two-dimensional cascade, can be expected to expand a super-sonic inlet flow to a yet higher Mach number upstream of the mainpassage shock. Miller, Hartman and Lewis examined shock losses indouble circular arc rotors and presented (in Ref 1) a simple flow |model that correlated well with experimental data. A normal shoci i'1presumed to lie along a straight line from the leading edge of one
blade to a shock-impingement point on the adjacent blade suction sur-face. The shock-impingement point is fixed by the assumption t~hatthe shock intersects normally a blade mean-line drawn in mid-passage.The flow Mach number at the shock-impingement point is determined bya Prandtl-Meyer expansion from the value at blade inlet through theangle subtended by the suction surface upstream of the shock. byassuming the shock strength to be given by the mean of the Macn num-ber at each end of the shock, the shock loss may be determined. Forthe current design, it was assumed that the result of the two-dimensional analysis is further modified by annulus wall effects,as in the case of the rotor. The Mach number produced by the aboveanalysis is presumed to be modified according to Eq (3), the elevatedmean two-dimensional shock Mach number replacing the blade sectionrelative inlet Mach number. Equation (14) is then applied to deter-mine the relative total pressure loss coefficient component due toshocks in the stator.,
c. Axial Distributions Within Blade Rows
The averaged quantities and radial distributions discussedabove were associated with conditions spanning an entire bladc row.The detailed aerodynamic analyses (described in Section III) includecomputations made at a number of axial stations intenal to Loth
5
blade rows. For this purpose it is necessary to specify the axialdistribution of total pressure losses along each streamsurface andwithin each ,blade row. The quantity chosen to define a distributionwas the ratio of actual-to-ideal relative total pressure on a stream-surface, referred to conditions at the leading edge of the respectiveblade row. Then the (absolute) total pressure at any station may bedetermined- from
n1P nr -(idealY
where Pn is the desired total pressure
is the total pressure at blade row inlet
Tnis the ratio of total temperatures betweenI the point of interest and blade inlet
Pnris the ratio of actual to ideal relative
Pnr(ideal) total pressures at the point of interest
The value of Pnr'Pnr(ideal) at the -blade outlet was obtained from
r~ 2 - 1L1a II- 1- M12
P 2r (ideal) [~,(idea LjIrwhere
2 2P2r (ideal) _1 1 U- (7)
P1 2 a 2r
where P is the relative total pressure at blade inlet
P is the relative total pressure at the blade outlet2 r
r, ,r2 are the streamsurface radii at the correspondingtwo points
U2 is the wheel speed at the blade outlet
M is the relative Mach number at the blade inlet
a is the stagnation speed of sound relative to theblade inlet.
6t
Equations (5), (6) and (7) are equivalent to-Eqs A2, A6 and A3,respectively, of Ref 3, page 253.
Although the losses due to the passage shock occur abruptly, th-shock is not perpendicular to the meridional plane of the corr-.ressorand hence appears in mean effect as a continuous phenomenon. Art-trarily, the variation of Pnr/Pnr(ideal) was made linear between vai;ezof unity at the blade leading edge and the determined value for t"-blade trailing edge. For the rotor it was convwricnt to a itlinear with axial distance, while for the stator stra~r'u,'ace lenrtwas utilized.
2. BLADE PROFILE AND SOLIDITY SELECTION
a. Rotor Blade
The rotor blade is required to operate (at design point) atMach numbers varying from 1.22 at the hub to 1.58 at the casing. Atthese Mach number levels a prime consideration in the selection of ablade profile is the minimization of losses due to shock waves. Thirotor design is based upon the concept of achiexing essentiallyshock-free supersonic diffusion in the forward portion of the rotorpassage, this terminating with an inevitable strong shock. Then sub-sonic diffusion to the exit condition occurs.
Supersonic diffusion implies an area decrease. In this design,the area reduction is achieved by a decrease in the compressor annu-lus height. The flow angle relative to the rotor decreases by anamount sufficiently small that the associated flow area increase inthe cascade plane is relatively small. It is assumed that the super-sonic diffusion will be achieved by compression wavet, propagated fror:the suction surface of the blade upstream of the shock. The comLpres-sion waves should occur as the flow is deflected away from the suc-tion surface, toward which it will tend to move in the presence ofthe flow area reduction. (A similar hypothesis leads naturall2 tothe use of reverse or negative camber in the forward region of asupersonic blade section. A potential advantage of the design methodpursued for this stage is that the amount of positive camber require2.to achieve a specific outlet angle will cf course be less when it isnot preceded by reverse camber. A comparison of the use of "annuluscontrolled" area reduction and the 'S' profile for supersonic rotorduty is an area for future research.)
In the past, the types of profile associated with this designphilosophy have included multiple-circular-arc profiles, and pro-files consisting (on the camber line) of a straight line followed bya circular arc. For this design a new profile is employed. This iscomprised of a polynomial (quartic) camber line, with a thicknesdistribution applied about it that consists of two polynomial (cubi.curves, one ahead and one after the point of maxImum thicknesFs. Bysetting the second derivative of the camber line equal to zer, at
7
it|
the leading edge, and to one-half of its maximum value at the trailingedge, a camber line is produced that is initially straight and has a,maximum curvature forward6f the trailing edge. The second deriva--tive of the thickness distribution equation is also set equal to zeroat the leading edge-, thus maintaining a small leading edge wedge angle(assuming a conventional thickness to chord ratio), while preventinginverse curvature in the thickness distribution. At the p6int or max"imum thickness, the section thickness and firs t, and second derivativesof thickness are set equal for the two thickness equations. The re-sult is a blade section with continuous surface curvature throughout.Further details of the, profile are given in Ref 2,.
It can reasonably be assumed that the terminal shock in therotor passage will be nearly ,perpendicular to the relative flow andwill extend from the leading edge of one blade to the suctibh surfaceof the adjacent blade. (Correlations of such a flow model with ex-,perimental data were made .by Miller, Lewis and Hartmann in Ref 4 asmentioned before;) The design, philosophy outlined, previously callsfor little camber in the region of the blade between the leading edgeand shock impingement point. This p-laces a lower limit .on solidity'for the blade profile selected. The leading potation of the blade isessentially straight, whatever camber is specified being cogncentratedtoward the rear of the blade; As solidity is decreased, the pre-dicted point of shock impingement moves rearward along the blade suc-tion surface, so that there is a sol'idity below which the require-ment of little camber (in the forward re'gion}) is not met. The min-imum acceptable solidity indicated by this means is about i.7 at allradii.
I The diffusion factor loss correlation described above also pre-sents a, method of determining solidity. For a given air-angle de-sign, the variation of minimum low-speed loss coefficient with solid-ity may be obtained. Generally, a shallow minimum exists at asolidity which increases with diffusion factor. Using this ,method,"optimum" solidities of 1.3, 1.4 and 1.0 at hub, ,mid and tip respect-ively may be calculated. (These figures are consistent with thevelocity triangle data produced by the final run in the first phaseof the design. Similar figures were calculated from preliminary re-sults.) Intuitively, these figures appear to be somewhat low,, andmay represent a minimum feasible solidity for low-speed flow.
Mechanical considerations also affect the choice of rotor solid-ity distribution. The requirement of a high solidity at the tip sec-tion conflicts with the requirement to keep the ratio of the cross-sectional areas of the casing and ,hub sections down to such a valuethat unacceptable centrifugal stresses are not generated in the rotorblade.
8
'Taking into account the three factors described above,, the fol-lowing distribution of rotor blade solidity was derived.
Section Solidity
Hub 2.l172
Mean 1.937
Casing 1.861
Evidence -presented in Ref 5 indicates that no loss attributableto trailing-edge thic'kness was observed for compressor cascadeshaving trailing-edge thicknesses up to about one-third of the maxi-mum blade-elemeht thickness. Therefore, for this design, rotor trail-ing edges were simply truncated at one-third of maximum blade-elementthickness in 'order to compensate to some extent for the annulus con-vergence required between rotor and stator in order to achieve smoothwall contours.
b.. Stator Blade
The stator blade operates (at design point.) at relative inletMach numbers between 1.0 and 1.1. The double circular arc profilehas performed well at this Mach number level. It constitutes a goodcompromise between expanding the incoming flow to a yet higher Machnumber, and maintaining a sufficiently large throat width to pass thedesign flow without choking. It was therefore select-ed for the s tatordesign.
The same considerations applied to the rotor to derive solid-ities may again be used to obtain solidities for the stator. From.atwo-dimensional viewpoint, emphasis should be placed on minimizingthe expansion of the incoming supersonic flow upstream of the ter-minal shock. As the blade suction surface is a circular arc, the ex-pansion is continuously decreased as the solidity is increased-. How-
A ever, the modest inlet Mach number precludes the assumption that anextreme solidity is desirable. The diffusion factor loss coefficientcorrelation may again be used to determine optimum solidities, andindicates values varying from 1.2 at the hub to 1.9 at the casing.
The final stator solidity distribution was influenced consider-ably by the use of th6 swept leading edge, described later. However,the concepts described above guided the selection of the general
solidity level. Fihal stator solidities are as follows;
Section Solidity
Hub 2.393
Mean 1.803
Casing 2.1115
9
3. DEVIATION ANGLES
a. Rotor Blade
In order to relate blade angles to design air angles it isnecessary to have a knowledge of the flow deviation angles that willoccur. This presents a problem for the rotor design as the profiletype selected has not been previously investigated ahd hence a cor-relation of deviation with camber, outlet angle, solidity, and sofourth, is ,not available. Fortunat-ely, at the loading level forwhich the rotor is designed, a small error in deviatidn angle is notcrucial. An important result from the ,testing of the stage will bethe determination of' the actual rotor deviation angles, achieved.
A, form of Carter"s rule was used to determine rotor bladedeviation angles. Deviation is related to cascade geometry by
6 = me ; (8),
where 6 is the deviation angle
6 is the blade section camber angle
a is the cascade solidity
m is a function of the blade, section stagger angle.
Figure 2 shows the relationship that Was assumed between m and thestagger angle. (Also shown,are Carter's curves for conventional-blades having their points of maximum camber at 0.4, and 0.5 of thechord. These are -taken from Fig 160,, Ref 3.)
In ,order to perform detail design calculations on,proposed rot'orconfigurations, it is necessary to have a means of determining-meanrelative flow angles within the rotor blade. This was accomplishedby' using a generalized rela-tionship for the deviation angle (fromthe local blade camber line direction) as a function of distancealong the section meridionally- projected chord and the final devia-
tion angle. The relationship assumed i3 shown in Fig 3. The rapidincrease of deviation angle near the blade exit arises from consid-eration of the physical requirements necessary to satisfy the "Kutta"'condition at the trailing edge.
b. Stator Blade
The same requirements of knowing final and intermediate devia-tion <exist for the stator blade as for the rotor blade. However, inthis case the double circular arc profile was specified.
10
Final devlation angles -were calcUlated from Carter's -rule,which was described above in connection with the rotor blade. Inthis case the m/stagger curve for conventional blades having maximum camber -at mid-chord was used-. -Carter's rule has been widely, andsuccessfully used for double circular grc blade sections.
Within the-stator blade, the same generalized relationship forlocal deviation angle was assumed as was described above for therotor blade.
-4-. ASPECT'RATIOS, FILLET RADII,AND STATOR LEADING EDGE FORM
Some novel features ofthe design are related to attempts tominimize the detrimental effects of secondary flows within the com-pressor. Conclusions drawn from data presented in Ref 6 inspire,these attempts. A supersonic radial compressor diffuser of unusuallyhigh performance is described The diffuser is comprised of 'a seriesof uniformly distributed circular cylindric passages in a radialplane, all tangent to a 'circle in that plane. They mutually inter-sect at the inner radius ,or inlet of the diffuser, forming a series'of'sharp, elliptical leading edges. The significant features whichmay have contributed to the performance of the diffuser are believedto be the use of a circular (corner-free) passage, and the "swept"leading edge configuration.
The circular passage concept was applied to both rotor andstator. It was incorporated by choosing the number -f blades so thatthe flow passages- are approximately square when viewed normal to theflow near the blade row exits. Also large fillet radii were appliedat the rotor hub, and-the stator hub and casing.
The swept leading edge concept has been applied to the statorbiade. Swept -wing theory indicates that se'tion performance is re-lated to the normal component of the incident Mach number. HighMach- number operation of compressor-blade sections is characterizedby- reiatively large loss penalties for small variations in incidenceangle away from the optimum., The hub and the casing are regionswhere the stator design in'cidence is most likely to be violated.Accqrdingly, the stator leading edge at the hub and casing has beenswept forward to such an angle that the normal Mach number is approx-imately'0.4. A simple parabolic form connects the two extremities.
11
SECTION III
AERODYNAMIC CALCULATION METHOD
1. AXISYMMETRIC FLOW ANALYSIS
The principal means used to incorporate the design criteria intothe stage design was an axisymmetric flow analysis. The most impor--tant assumptions made are that the flow is axisymmetric, and thatthere is no transport of mass or energy across streamsurfaces in theflow. The fluid (air) is assumed to be a perfect gas. Briefly, thecalculation consists of the following elements:
(1) A number of computing stations are located in the flow
(2) The Jccations of a number of axisymrimetric streamsurfacesare estimated at each computing station
(3) The continuity, momentum, and energy equations are simul-taneously solved (iteratively) at each station in turn. The conti-nuity eqUation is satisfied in an integrated sense, that is, thespecified flow-rate at each station is maintained. The energy equa-tion is satisfied by one of essentially three means. At a stationfollowing a blade-free ,space, the enthalpy, entropy and angularmomentum are constant along streamsurfaces from the preceding station.At a station within or immediately following a blade row, there maybe specified (for each streamsurface) either the work input down-stream of a preceding station, or the flow angle relative to theblade. In both cases, the angular momentum and enthalpy change areestablished, directly or indirectly. A number of means of specifyingthe entropy rise on each streamsurface exist. For the current purpose,two alternative specifications were sufficient; an inlet dynamic headtotal pressure loss coefficient, or the ratio of actual to idealrelative total pressure. The solution to the momentum equation,which may be considered to be the principal equation, yields the var-iation of velocity, and hence all other undetermined parameters ofthe flow, along the computing station.
(1b) The estimated streamsurface pattern used to obtain thesolution described in (3) is refined to more nearly satisfy continuityon a detailed basis. That is, using the mass flux distributions de-rived ir. (3), the streamsurface location estimates are revised tomaintain a constant proportion of the total flow in each streamtube.
(5) Trie procedure is re-entered at (3) to obtain an improvedsolution to the system of equations. The new solution, differs fromthat previously determined because it is a function of the assumedstreamsurface pattern. This is repeated until the desired accuracyis achieved.
12
The momentum equation used for the above calculations is
dC2 os(y+) tan a d(r tan a) sin(y+ ) dCd 2 -os2 - -- - + +M]
d rc r d£ C di
2 co Fa H t LS )dz dS
where Cm is the meridional velocity
Z is the direction of the computing station
a is the whirl angle, defined tan a = 0C/Cm
Ce is the tangential velocity
y is the angle made by the comg.uting station with the radialdirection,, positive values indicating an increase inradius with axial distance
is the streamsurface slope angle
r. is the. radius of curvature of the streamsurface
in is the meridional streamline direction
H is the enthalpy
S is the entropy
t is the static temperature.
The continuity equation iscase
W,= ubm cos W dA (10)
where W is the flow-rate
w is the specific weight
A is flow area normal to the axis.
13
The energy equation is either
constant along stream-lines between blade-rows, (ll).
specified value -withinT = or i'mmediately following (12')
a rotor row
or'Or Un (U,/Cin + tan ar)- U(13)
T + TIgj Cl P1 )
when relative flow angle is specified. In Eq (13)',
T is total temperature
U is blade speed
'j is the acceleration due to gravity
J is Joule's equivalent
C is specific heat at constant pressurep
n indicates the location where the temperature is derived
1 indicates blade inlet
r indicates relative conditions.
Equations (5), (6) and (7) (given previously) relate total pressureto total temperature.
2. IT2ERATION PROCEDURE FOR CONSISTENT LOSSES
One of the problems faced by the designer of a compressor (orturbine) is how to specify losses in such a manner that they are com-pletely consistent with local values of Mach number and diffusionalong every streamsurface. When using a streamline-curvature calcu-lation technique, it is convenient to solve this problem iteratively.The general procedure followed was:
(1) A complete aerodynamic solution was obtained using initiallyestimated loss distributions (which could be zero loss throughout)
(2) Mach numbers and diffusion factors were calculated on eachstreamsurface for each blade row and new loss coefficients were ob-tained using Eqs (1), (2), (3) and (4)
14
(3) A new aerodynamiu solution was obtained using the loss co-efficients obtained' in step (2).
Steps (2) and (3) were repeated until the change in loss coefficientsfell within a prescribed tolerance. For these calculations, comput-ing stations within blade rows were not employed; only those corres-ponding to blade-row leading and trailing edge planes and elsewherein the compressor were used. The radial distribution of any one ofthree parameters could be defined in order to control stage perform-ance. The three options were to specify:
(1) Stage total pressure ratio at the stator trailing edge plane,
(2) Total temperature rise at the rotor trailing edge plane, or
(3) Relative flow angle at the rotor trailing edge plane.
3. ALTERNATIVE FORMULATIONOF MOMENTUM EQUATION
Some difficulty was experienced in selecting a radial distribu-tion of work (total temperature or pressure rise) that would yield asatisfactory velocity profile at the rotor exit when making the com-putations described in the previous section. An alternative formu-lation of the momentum equation was therefore derived in which the !total temperature rise is the dependent variable, and the velocity
profile is specified. The equation to be solved is formed by combin-ing Eqs (9), (13) and (5), and using the fact that for a perfect gaswe may write
dH t dS gJCpdT t g( dT_ 1 dP (-- - t Pd T : dZ OT dZ 14
Algebraic manipulation yields the following result
d2 cos( +Y) sin-= +y) dCm C +gjc (T-gjC - C 1 - + - + 2x
dZ r CM dm Jr
d [gjCPT 1 [ P1 PR/P1- .C + gRt - n - RdZ _- 1 d (PR/PIR)ideal (15)
dCjm ruC 0 1 + gJC-('T -T
15
-V
Thus the total temperature gradient is a function of the meridionalvelocity gradient,, the gradient of actual to ideal relative totalpressure (a function of the losses), and other quantities. By choosinga value of total temperature at one radius, the values at all otherradii may be calculated. The starting point value is adjusted so thattogether with the iteratively determined losses, the desired meanstage total pressure ratio is achieved. This is further described in
Ref 7,
11. ANNULUS WALL BOUNDARY LAYER DETERMINATION
A constant phenomenon in axial compressors is the build-up ofboundary layers of significant thickness upon the annulus walls. Thefollowing simple calculation was included in the computing scheme used,for the stage design.
Jansen presents a method of estimating the blockage due to annu-lus wall boundary layers in Ref 8. Boundary layer displacement thick-nesses are specified at a location upstream of the compressor, proper.-Here they will generally be negligible. Then the momentum thicknessof each boundary layer is obtained from
rt mn 0.86 + 0.006 C - C34 d 16)mn " mn f m (16)
mi
where 0 is momentum thickness. (Note that units of feet and seconds
are assumed for the dimensional quantities.)
The shape factor is obtained from
H- = 30 n-I + 1.5 (17)
n mn -1 (17
subject to the restraints 1.1 : H : 2.2 where H is the shape factor.
The displacement thickness is given by
6 =Hn n n (18)-
where 6 is displacement thickness.
The blockage due to the two boundary layers is incorporated intothe calculation by locating the outermost streamsurfaces away from theannulus walls by the amount of the displacement thickness.
16
,I
5. USE OF STATIC PRESSURE DISTRIBUTIONS 'TOOPTIMIZE INCIDENCE ANGLES 'AND ANNULUS GEOMETRY
Given the results of the iterative loss reestimation procedure,it is possible to determine feasible blade geometries by assumingincidence angle variations for rotor and stator. The calculatiohmethod employed includes the calculation of -conditions., on an axisym-metric basis, at points within the -blade rows. Hence, within thelimits of the assumptions, it is possible to determine the variationof any parameter through.the blade rows. A rational method of evalu-ating various designs was required 'to enable incidence variations andannulus configurations to be optimized.
The parameter selected for prime consideration was, the staticpressure. The basic concept employed in 'the optimization process wasthat the static pressure should rise in a smooth manner with minimumslope. This minimum was limited by the requirement that the rate ofincrease of static pressure with flow,path'length should fall smoothlyto zero at the blade trailing edge. The 'valid'ity of this approach isdebatable for the rotor blade sections, which operate transonicallywith a strong shock in the flow. However, the shock is approximatelynormal to the relative flow direction and hence, when viewed in themeridional plane and considered in mean effect, 'appears not as a dis-continuity but as a region through which conditions change in anapparently continuous manner.
An implicit result of the intra-blade analysis is a check uponthe maximum or choking flow of the blade row.
6. COMPUTER PROGRAM
A computer program to perform the calculations described abovewas created by modifying the program presented in Ref 9, which de-scribes a program for the analysis of non-axisymmetric flows in axialcompressors. The program is considerably more complicated than theaxisymmetric analysis outlined above requires, and extensive simplifi-cations were made to the deck. The principal changes made were asfollows.
(1) The system of equations solved was modified to reflect theassumption of axial symmetry. (The equations, in the modified form,were presented previously (Eqs (9), (10),. (11), (12) and (13)
(2) The loss estimation procedure described previously was pro-grammed and incorporated into an overall iteration procedure.
(3) The method of solution of the momentum equation in which thedependent variable is the total temperature gradient (Eq (15)) wasprogrammed as an alternative calculation at the rotor exit.
17
(4) One novel feature incorporated into the program is that
the station lean angle (Y)" may vary along a computing, station. This
provision was included in order to be able to locate calculating
stations along the leading edge of the stator and within the stator
biade row at constant fractions of the projected blade chord.
I
4
I
S 1I
SECTION IV
RESULTS FROM DESIGN CALCULATIONS
1 ITERATIVE LOSS REESTIMATIOI PROCEDURE
a, , Path to a Solution
As mentioned in the previous section, several different inputoptions to the calculation scheme (i.-e., computer program) were avai!-able that would determine, directly or indirectly, the rotor work dis-tribution. The criteria for selection of an option for the firstphase of the design are that the mass-averaged total presure ratio ofthe stage should be readily controllable, and that satisfactory radialdistributions of the significant parameters of Loth rotor and statorshould be easily obtained. The latter criterion is closely allied tothe rotor exit meridional velocity profile.
Specification of the distribution of either total temperaturerise across the rotor or relative outlet flow angle from the rotorsatisfies neither criteria. Specification of the distribution ofrotor (or stage) outlet total pressure gives relatively good control.For this stage design, the specification of a nondimensionalized rotoroutlet meridional velocity profile together with a masse-averaged totalpressure ratio was selected, this being thought to be the most direct jmethod of achieving the desired result. In fact, the total pressuredistribution is probably as easy to manipulate.
Having achieved a satisfactory aerodynamic result by the abovemeans, it remains to ensure that the blades implied by the foregoingcalculations are mechanically acceptable, especially in the case of'the rotor blade. The rotor relative flow angles must vary along thelength of the blade in such a manner that no severe blade twists occur.In order to achieve this for the current desigr, aerodynamic analyzeswere made for specified relative rotor outlet angle distributionswhich were produced by "smoothing" the distributions determined in thepreceding calculations. This resulted in a stage mass-averaged totalpressure ratio little different from the defined value of 3.0:1, andmechanically acceptable blade shapes.
b. Design-Point Conditions
An important result of the calculations described above wasthe over-all stage efficiency produced by the loss model discussedearlier. Actually, it was originally anticipated that a more op-timistic diffusion-loss model would be required to produce the objec-tive stage efficiency. However, this was achieved with the loss-modeldescribed, which is believed to be quite realistic as far as diffusionloss is concerned, if somewhat optimistic with respect to shock losses.Some degree of optimism may also be involved in the diffusion lossmodel inasmuch as the elevated tip loss incorporated in the NACA model
19
P
I
'v-r • ocau,,e the origin of this loss is sus-- te cntrlfugtng in the, wake region, it was
, , IIvo, loss reestimation procedure for two* :Lr ' l i.rk-astd tip loss is viewed as a radial re-
iTi ,tli n the gap between blades, it need not,rotor dezign and its omission would result
I 1riu p 'tritutton of stator conditions. Second,,," ,,1. t 'i that the stated design objectives of this
L, [ved 'after appropriate boundary-layer controlO t, II "tldld, thoe ,e modifications,, if successful, shouldS. :k. and the associated radial migration. A
,, " !i ,on.,id*Eration is that an attempt to compensate fori, Il, 1, 4J'. ' Ixumod to occur within the rotor can lead to me-
• ut ' .V1r'e [lade twists in the tip region.
'2 o .a.. f' annulus geometry and computing station loca-i- I Le fiwial computation of this phase of the design. The
"4 ,. . oV t 'mnd out lot areas were determined from the initially.t , i, l* o,jectivev. The area at the rotor outlet was de-
the ztatic pressure rise across the rotor whilei IL t,3n o satiofactory rotor diffusion levels. This resulted
,1 Vtircr s, tatic pres.:ure rise across the rotor than across,:Ot L,,,ut the mean meridional velocity rises over 100 feet per
)ni ,, r..'' tfl-o rotor and falls by a similar amount across theA- k .tlly, from stator leading edge to trailing edge the meanv. ",octy falls about 180 feet per second because it rises
r, [, t pr L-eeond in the space between rotor and stator.)
Y , .~ , h; le meridional velocity distributions at inleti ),t It tne rotor and stator. Figure 6 shows the relative Mach
,, 111t0l,ution- at inlet and wtlet to the rotor and stator.
"1-, nIt- ank' outlet flow angle distributions for the rotor" ,ol- in InFir, 7. Figure 8 shows the distribution of
futtor. op the rotor and stator and the relati!ve totalure 1 , coeffIcient distributions are shown in Fig 9. Figures
.i ,i,,w thki distributions of total pressure ratio and isen-I r 1, ei' ncy at the rotor and stage outlets. The non-dimensional
l zI t t Pt 1 , i ure ri e distribution is shown in Fig 12. The axial~triUtt; )n:, )f computed boundary layer thickness are shown in Fig 13.
'IL n, <t de.Agn phase consisted of establishing detailed blade'L:Wiv:. ,imetries consistent with the above results and the
I i.' ;,ijT.c-a. The data extracted from this first phase of the de-i- flowpath as specified by the annulus and boundary layers
i A.tI-- 1-cadin and trailing edges, and in the inlet and exit,• , ,' , !. Itributions of relative total pressure loss coefficient• 1 i I ....' "v, c, flow angle for each blade.
' L,... , r program output from the first phase of the design isi, (iA d on 1 nc Vollowing pages.
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2. INTRA-BLADE FLOW ANALYSIS
The objective of the intr -blade flow analysis was to determinedetails of blade and annulus geometries that were consistent with theresults obtained from the iterative loss re-estimation procedure, andwould also satisfy the design criteria stated earlier. The approachthat was followed consisted of analyzing conditions within the com-pressor for possible detailed blade and annulus geometries, and thenmodifying the assumed geometries until the desired results wereachieved. A somewhat lengthy trial-and-error process is implied andwas indeed necessary.
The input data to the computer program consisted of the annulusgeometry, the performance of the blading, the flow-rate, and the rota-tional speed of the machine. The annulus geometry is, of course,specified by giving the radius of the hub and of the casing at eachcomputing station. Hence this was adjusted by changing these radiiwithin the blade--rows, the values elsewhere being those established bythe results of the previous design phase. The flow boundaries usedwere the inner limits of the boundary layer displacement thicknesses,previously established. A linear variation in displacement thicknesswith length was assumed within the blade rows. The annulus geometryfinally derived and the computing stations used for the calculationsare shown in Fig 14. The performance of the blading is specified bygiving, at each computing station within or immediately following ablade row, the radial variations of the relative flow angle, the ratioof actual to ideal relative total pressure, and the blockage due tothe blades. The relative flow angle was obtained from the local cam-berline direction, the assumed deviation angle at the trailing edge,and the assumed variation of deviation angle within the blade. Theseitems were all discussed in Section II. The ratio of actual to idealrelative total pressure was obtained from the results of the iterativeloss re-estimation procedure and Eq's (6) and (7). The blockage dueto blades is the ratio of blocked to total circumference.
The computer output obtained for the analysis of the configura-tion that was finally selected is shown on the following pages. Com-patibility between the intra-blade calculations and the inter-bladecalculations performed with the iterative loss re-estimation procedureis shown by plots of the meridional velocity profile at the rotorleading and trailing edges (Fig 15), and the stator leading and trail-ing edges (Fig 16). Results from both calculations are displayed, andit is seen that differences are quite small, except at the statorleading edge. At this computing station in particular, the streamlinecharacteristics are computed to be significantly different in the twocases. This is due to details of the annulus wall contours which arenot apparent to the inter-blade calculations.
The static pressure distribution through the stage (which wasconsidered to be a key criterion) is shown in Fig 17. The establisheddesign criteria regarding the static pressure rise through the bladerows is reasonably well satisfied. The resulting incidence and devia-tion angle variations for the rouor and stator are shown in Figs 18and 19.
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SECTION V
FINAL STAGE CONFIGURATION
1. DESIGN POINT
The following figures are consistent with the data given in,Section II:
Design speed (corrected to SLS) 20371.4 rpm
Design flow (corrected to SLS) 30.0 lbs/sec
Design total pressure ratio 3.0 : 1
2. ANNULUS GEOMETRY
Figure 20 shows the flowpath including inlet bell mouth, coipres-sor proper, and exhaust that will be incorporated into the compressortest facility. Details of the inner .wall (hub) of the compressorannulus are shown in Fig 21; Fig 22 shows details of the compressorouter wall (casing). In each of these figures the origin of the axialcoordinates is the same as was used for the aerodynamic design calcu-lations; that is, the rotor leading edge.
3. ROTOR GEOMETRY
a. Number of Blades
The rotor contains 30 blades.
b. Blade Form
The rotor blade design was produced by determining profiles on15 streamsurfaces, and then stacking the sections to complete theblade definition. In order to create data convenient for the-manufac-turing process, coordinates of plane sections through the blade per-pendicular to the stack axis were interpolated (and extrapolated) bya "spline-curve" method. A brief description of the (streamsurface)airfoil sections was given in Section II of this report; Ref 2 givesa full description of the section, the stacking procedure, and themethod of interpolating (or extrapolating) the "manufacturing" sectiondata. A computer program to perform the necessary calculations wasalso presented in Ref 2. For this design, it was convenient to use aslightly modified form of this program. The program was amended sothat the entire blade construction was performed a specified number oftimes. Input data to each pass (after the first) was based on theresults of the preceding pass so that the axially-projected chord ofeach section would equal the desired value of 2.0 (inches), and so that
62
the blade leading edge, at all radii, would lie at the desired loca-tion, that is x = 0. Changes in the original input data were made toAhe stacking point location, the meridionally-projected section chordlengths, and the x-direction stacking offsets of the sections. Thusthe resulting blade exactly matched the allocated space in the aero-dynamic calculations. These iterations could have been made "by hand"using the program as published in Ref 2; the modified program enabledthe desired result to be obtained from one run. Five iterations weremade; in- fact an acceptable result for all practical purposes wasachieved after two or three iterations.
'Shown on following pages is computer program output for the rotorblade design. All dimensions are in inches. First appear sundry con-stants and a definition of the 15 streamsurfaces. The streamsurfacesare defined at eight axial locations which coincide with eight of thecomputing stations used for the aerodynamic design calculations. Theorigin for the axial locations of the stations is the same as was used,for the aerodynamic analyses. The input data printout is completedwith a table defining the geometry of each section. A detailed de-scription of the significance of each input data item is given inRef 2, but it should be noted that, in accord with the program modifi-cation described above, the stacking point location, the sectionmeridionally-projected chord lengths, and the x-direction offsets arefirst-estimates only. Next are shown details of the 15 streamsurfacesections. Only the "normalized" data has been reproduced; the equiva-lent dimensional data would be derived by scaling the non-dimensionalquantities by the meridional chord of the section (or the appropriatepowerthereof). Finally, details are shown of 11 manufacturing sec-tions through the blade. These plane sections perpendicular to thestack axis are spaced 1/4-inch apart, and extend slightly beyond theblade in both directions. The IZ coordinate is measured along thestack axis from the machine axis. The origin for the section coordi-nates is the stack axis. The "X" direction is parallel to themachine axis, and the coordinate increases in the direction of flow.The "Y" direction is perpendicular to the "X" direction, and the "Y"coordinate decreases in the direction of rotation. "XS" and "YS" de-fine the suction surface of the section, and "XP" and "YP" define thepressure surface. "XSEMI" and "YSEMI" define the leading edge radius.The trailing edge is a straight line joining the pressure and suctionsurfaces. The data reproduced shows 50 points per blade surface; formanufacturing purposes the program was run with 120 points per sur-face specified.
Figure 23 shows superimposed plots of developed streamsurfacesections 1, 3, 5 . . . 15. Figure 211 shows similar views of manu-facturing sections 1, 3, 5 . . . 11. Extrapolation of the blade toplanes beyond the hub and casing causes the larger changes in sectionalong the blade that are seen in Fig 24, relative to Fig 23.
63
4tI
c. Location of Scack Axis
The rotor stack axis is located at an axial coordinate of0.9791 inches, measured from the same origin as was used to definethe annulus geometry.
d. Root Fillet
between points 3/47inch in from the leading and trailing edgesof the blade, the root fillet is a !/4-inch radius, on both sides 6Ofthe blade. The fillet is smoothly decreased to 1/16-inch radius atthe blade edges.
64
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122i I
4. STATOR GEOMETRY
a. Number of Blades
The stator contains 49 blades.
b. Blade Form
The stator blade design was produced by the same process as wasused for the rotor design, but with two differences. First (as de-scribed in Section II of this report), the double circular arc profilewas selected for the streamsurfabe sections. Second, the sectionswere stacked at the trailing edge to complete the blade definition.
The 15 streamsurfaces on which the double circular arc profileswere designed are defined by the results of the aerodynamic analysisgiven in Section IV.2 of this report. The stator occupies stations11 through 15. Details of each section are given in the followingtable. For each section, the ratio of maximum thickness to chord is.04, and the edge radii are .005 inch.
Camber StaggerSection Angle Angle ChordNo. (degrees) (degrees) (inches)
1 (Hub) 54.39 18.70 2.349 [2 541.59 18.541 2.2410
3 54.77 18.38 2.143
4 55.03 18.26 2.060
5 55.33 18.16 1.990
6 55.59 18.o8 1.934
7 55.85 18.03 1.895
8 56.13 18.o2 1.873
9 56.39 18.05 1.869
10 56.68 18.13 1.88511 56.99 18.28 1.923
12 57.49 18.54 1.984
13 58.35 18.96 2.072
14 60.38 19.81 2.197
15 (Casing) 62.35 20.73 2.365
123
The generation of the blade geometry including intbrpoau.,A.(and extrapolation) of' "manufacturing plane" data was accomplishedusing a computer program similar to that used for the rotor blade,and output from the program is shown on following pages. The coordi-nates of 10 "manufacturing" plane sections through the blade perpen-dicular to the stack axis are given. The sections are spaced 1/8 inchapart, and extend slightly beyond the actual blade in both directions.The coordinate definitions are the same as given for the rotor bladeabove. 'XP' and 'YP' define the pressure surface of the section, and'XS-' and 'YS' define the suction surface. 'XSEMI' and 'YSEM1' definethe trailing edge radius, and 'XSEM2' and 'YSEM2' define the leadingedge radius.
Figure 25 shows superimposed plots of alternate developed stream-surface sections. Figure 26 is a similar plot of all of the manufac-turing sections.
c. Location of Stack Axis
The stator stack axis is located at an axial coordinate of4.7250 inches, measured from the same origin as was used to definethe annulus geometry.
d. Root Fillet
Between points 3/4 inch in from the leading edge and 1/2 inch
in from the trailing edge, the fillet is 1/4 inch radius on both sidesof the blade at both hub and casing. The fillet is smoothly de-creased to 1/16 inch radius at the blade edges.
124
_____4
e. Stator Blade Coordinates
CARTESiAN, COJROIVATES FOR 4ANUFACTJRING SECTIONS
SECTION .Ao . 'Z'= 7,500PO'IT 10 XP YP xS YS
1 -_2.33265 0.73382 -2o3366 0,7591 .2 -2o30979 0,75157 -2,31571 0o715643 -292860: 072012 -2 29323 0,67388
-2,26130 0,68941 -2,26942 0.633675 -2,43537 0,6593. -2z24419 0,594836 -2. 0811 0362996 -2.21740 0.557407 -2,17936 0.60110 -22 18891 09521148 -2,.14894 0257275 -Za15857 0,48601
-. 11667 ),487 -2.92624 0.4519513 -2-s0240 0,51742 -2,04177 0.41890i1 -2.04595 0,49037 -2,05500 0.38683L2 -2,007%6 0.46369 -2*0158a 0.3557)13 -196593 0,43733 -10.9 740 8 0.3255014 -1i92229 Otl,4, 4 -1,92983 0.29624,
15 -1.87637 0*3d594 -I, 83336 0,2679516 -1,82831 O.36092 -I 83 467 0,2406717 -1,77827 6.3364B3 -1,784600 02144413 -1,72642 0.31253 -1,73153 0.1,3§2919 -1667296 0 28927 -1,b7745 0,13527 .2-0 -Ii 61803 0*25670 -1,62198 0,14240al -1c561-96 024487 -1,56531 0.12071
2 -19 50481 0322384 -1,50764 0*1002323, -1.44532 0.20363 - g4491i 0,0809,324 -1.38818 0,13430 -±,39011 0.0529825 -1,12906 0#16586 -1,33061 0.04o23
26 -1269o4 0O14a37 -1.27095 090307627 -1,21011 0.13183 -1.21105 0.016552 -1,150b4 0si627 -1,15133 0.0036129 -1,0913-5 O.I0171 -is09185 -0.0080333 -1 20337 0408815 -1&03270 -0.0:85131 -0,97379 0207553 -0, 973-99 -0.02772 $
32 -091568 00-.401 -099157.3 -0.0357333 -0,d5809 0.05343 -0 E5812 -0.0425434 -0.10107 0*014391 -0, 80104 -0.0481935 -0a744b2 3.03516 -0,74456 -0.05,2713* -096S876 0.02744 -0, 6868 -0.0561037 -0633*.8 0,02064 -0. 63339 -0.0584033 -0,57875 0.01474 -0,578o5 -090596339 -0.52450 0900972 -0,52442 -0.05980i3 -0.47070 0.00555 -0,47062 -0*0589241 -0#41728 0.00223 -0,41722 -0o0570142 -0.36420 -0,00027 -0.36415 -0.0540743 -0931144 -0000195 -0*31141 -0005011
125
POJINT 4) XP ' xs Y
44 -092 996 -0,00282- -0.25894 -090451245 -0026673 -0*00290 -0il 0672 0.Oo03910
43 -0.1l5474 -0200219 -0*15473 -0.0320747 -0.0 1,Z 4 -016C0069 -0,10296 -0.024304 3' -0.o0 5 138 0*00160 -0*0513.3 -6.01490
0 o.i-Nr 13- XSEMI YSEMI XSEM2 YSEM2
-0.0052-7 0.00432 -2635719 0.804802 -3.00448 0.00431 -2*35735 0.80532
3 -0*00370 0900417 -2.3 5744 0.305924 -0.00295 ')*0039'- -2935745 0.606585 -0.00226 0.00355 -;2o35739 0.80728
6 -0.00163 3.0030? -29357-25 0.808027 -0,00108, 0900250 -2a 35704 0. 808763 -0.00063 0.00185 -2.35676- 0.80949
1 -09000"79 Oi00114 -2a35642 028103.910 -0.00007 0s,00038 -2,35604 0081085ii1 0*00004 -0.00040 -2*35561 00.81145-12 0.00002 -0000113 -2.35515 0*8119713 -0.00013 -0.00197 -2e35467 0.,8124614 -0,00039 -0,00271 -,2s,35418 0.8127315 -0.00C77 -0.00340 -2o35370 0's8 12 9 5
10 -0.00125 -0.00403 -2.3'5323 0 8 1*30a617 -0100183 -0-,00457 -2,35280 0'68130518 -0.00248 -0060501 -2&35240 0.81293I? -0S0C319 -0.00535 -2935206 0,8126923 -0.0039-5 -0.00557 -2,35107 0.81234
SECTION NO. 2 IV= 7.625
-------------------------- ;-----------------PUINIT NJ XP' YP XS Ys
1 -2*13'299 0.70408 -2.13661 0.680472 -2.10932 0.67395 -2*11473 0.640273 -2.08602 0.64467 -2iP09193 0.60175
It -2 aO--13 8 0.61bL4 r-v06805 0.55475.3 22,0B578 0.58830 -2. 043 01 0.52917
6 -2.00909 .'O -2901668 0.494777 -1*96116 0.53449 L1998896 09461593 -1. 95186 00,0341 -1.95)72 0.429539 -. 9 210 4 0.46284 -1.92883 0,39850
13 -1.88855 0.45772 -11*89o17 0.06845L 1 -1*8542b 0.43304 -1.86162 0.33936
lz -1,818o4 0.40876 -1.82506 093111713 -i.77980 O33488 -l,78640 0.2838814 -..s73955 0036141 -1374570 0*25749
126
POINT NO XP YP XS YS
15 -io9742 0533840 -1,70308 0923Z03L 5 -oo5353 3o31587 -1. 65967 0920753i7 -1.60800 0)o29388 -1,61262 0*18400i1 -1,56098 3o27246 -1,55o50 0.±614919 -1,51264 0_2516o -1951625 0o1400123 -1A46313: 0023t52 -1.46625 0.1196021 -141260 0.21 03 -is41529 0.1002622 -1.36124 0,19338 -1,35349 00820423 -1630918 0917545 -1,31105 0.064932 -0.2565q 9.15833 -1.25811 0,0484525 -1.203bl O.*-I t202 -'%&20483 0.0341025 -1045039 0412657 -1.-15134 0*0204027 -1*0970-7 0311i99 -1, 09779 0.007b428 -1204378 3.0982) -1*04430 -0.0035929 -0299063 3.035-.9 -0.99100 -0.0138833 -0.9371-2 0.07358 -0.93795 -0*0230o31 -0*88511 0.06257 -0,89524 -0,0311332 -0.i3286 0.05245 -0.8J291 -0.0381233 -0378101 0*0431 -0s73101 -00440434 -0.72-960 0.03484 -0,72955 -060489i35 -0*67864 3.62732 -02b7957 -0,0527535 -0.62813 0002057 -0, 62304 -0,0555837 -0.57807 0.01483 -0,57798 -0.0574238 -0.52843 0.00981 -0, 52834 -0.0582739 -0.47917 0.00558 -0,47909 -0o0581640 -0*43024 0.00214 -0. 43017 -090570941 -0.38160 -0.00054 -0.39155 -0.05507f+ -0.33323 -0.00247 -0#33318 -00521043 -C,28509 -0.CC0365 -0.28506 -0 00 944 "" .23715 -0.004-18 -0.237i3 -0,0433445 -0.-8941 -0900379 -0.18939 -00375345 -0.14183 -0900276 -0.14i82 -0.0307847 -0.09441 -3,30101 -0*09t41 -0.0230748 -0.04714 0.C0147 -0#04713 -001.441
POINT NI XSEM1 YSE41 XSEM2 YSEM2
1 -0.00531 0.00427 -2,15793 0,722922 -0,00452 0.00427 -21,13813 0.723433 -0.00374 0.00414 -2,15826 0,7240o4 -0900299 0oC0389 -2215830 0.724735 -0.00229 0.00353 -2,15826 0.72545
-0,00166 0.00305 -2, 15814 09726.97 -0001ll 0.00249 -2,15794 0,726938 -0.00065 0,00184 -2, 15767 0,727679 -0.00030 0.00114 -2,15733 0.72837
10 -0,00007 0.00038 -2 15.39 , 0472903
12:
P311T i)l SM YSZ-"1 X SE%12 YSEP-2
Li O'0c004 -3*Ca0040 -2 1 =f49 0,5729631! 3003 -)319-21 5,1 Oa.730 14
13 -00 000'1 -3..01O97 -2015551 0.73057-0.G3 7 -3.00272 -2*15499 0.73039
15 -C. 00074 -2.30341 -2.,154*S 0*73110-. 19OL2 2 - .i ) 4 0 4 -2.15398 0,73120
17 -0.UcO179 -'%ou045- -2,15353 O.7311313 -34,002,t4 -J*0350-t -2,15307 Ov73104U) -0,60315 -3020538 -21l5268 0.7307923 -0.00390 -'3t).05 -2,15235 0*73043
SECTI374J* 3 ~I'= 7s750
MIl~T V71xrX- YSi -lo.95751 1,5340O9 -1595953 0.61116
2 -1092994 09:5)4l 3 -i&93307 (6572133 -1.90219 3*57526 -1,90599 0*535084 -1*87420 0.54747 -1,87853 0.499825 -1.84583 O.5206i -1,859f5 0*46619
6 -1. dl71 0*49465 -1.82226 04367 -1.754791 O.4i450 1le7gz-27 0.403303 -i.75805 0*4451-v -1.76351 0*37353
4 -1.72143 0*421r+3 -1.73304 0.3zi543io -1.o9581 0 o393 -1.dz810149 0.3"824
11 -i*66323 0.37590 -1266871 0829200"1,62925 0335393 -Is 6345w 002fa669
03 -1,5938L 3o33243 -1,59832 0.24229i ' -1355638 3o 3 12.1 -1* 56L':- 00218761
-5 -1;51950 9,29086 -TL a5 22al 0.1961216 -1.47875 0.27)82 -1.37 014317 -1.43773 ;3.25132 -1.44125 0.1535713 -lo39554 3.21239 -10 39850 0.1336819 -4.35232 0*214G5 -i*35504 0.1147520 -1.30818 o 0.34- -1,316053 0.0967921 -1,26325 3,i7929 -Is 26525 0.0798222 -1,21766 091*293 -ItZ1934 0*0638-t23 -1.17154 0,14727 _101U~92 0.0488724 -1vi2501 t 223 5 -101261.2 0*0349125 -1.078817 0411313 -1*07Q04 0.0219725 S - A.11 0910478 -1,03131 0.01004
27 -0.98404 0.09215 -0,98453 -O*000F723 -0*93b95 0*03032 -0.S3730 -0.01078
27 -0186995 0.06927 -003870i3 -0.0196833 -0$34312 3.05903 -0.84325 -0.027603i -0*79651 0.04937 -01b79656 -0.0345332 -Go75O15 00040930 -0,75016 -0.04051
128
PIAUT 'VI XP YP xs YS
33 -0470409 0*0333l '-3.70405 -DcG455334 -0.6518i3 0.02593 -3*65627 -0,049623, 06!2:3 0*01954 -0.61282 -0.0528-336 -0956777 000139:, -Gs56?6-3 -0.0550537 --D. 52-795 0400;10; -0. 52-)88 -0.0564 333 -0*4764 60.O0r9Z -0.47836 -0 *05 69 234 -3e43417 0.00148 -0&43410 -0.00565343 -v.359012 -3.00125 -0.39306 -0*05527
ft1 -e34;527 -3a10329 -0 33622 -0.0531ft;23D5 -3*00 65 -0.30254 -0005915343 -34Z5903 -3.06532 -0*25933 -0004630
0.*Z!55i -0C'533 --0021563 -0.041!5q-Do47231 --34D0366 -0. 172BO -0.035983
40 -Ow12910 -0,303333 -0.12910 -0.0295147 -3*08599 -3.00O*F132 -0*08598 -0.0221643 -3*04.95 0.,00134 -0.04295 -0&01392
PclIT 10 XSEMI~ YS=Sf XEX YSEIM2
I. --90C536 0*00422 -1.%98651 0.652692 '3.O-457 0*00423 -109asaa 0.6z53263 -0.008378 0.O0411 -1.58703 0065393ff -0.00303 .3.00336 -1.598711 006r-4635 -3.00233 3,,C0351 -im98M1 Oa6553e J6 -3*09169 0.00304 -1098704 0.65610
-%9113 0,002483 -1.96,587 06;86 -0*03657 0000184 -1.098561 0*6575-39 -0.3L%031 OaO00113 -1998626 0*65833313 -0OP00 0000038 _Z6108524 0*6589511 J2,03005 -0.00040 -1,98536 0.6595312 0.00?004 -0019-1-98483 0.6600313 -0.00009 -0.00197 -1.98426 0.6604214 -0.00034 -lot00272 -1.98366 0.6601215 -0*00071 -0.00342z -1*98306 0.66089is -0.00118 -0,600C#05 -1*93247 0*660951.7 -0.600175 -O.60461 -1,98190 0#6608913 -0200239 -0.00506 -1.98136 0*65071
-3.06310 -0.00541 -1.p9dO87 0.6604220 -0.00385 -0.00564 -1*98044 0.66002
312 9
SECT134 'Us 4 'l'= 7.875
ONT-3 XP yp x YS
I -1033152 0.58554 -1283267 0*553322 -le3S0937 0.e555 76 -1980217 0.524863 -1*76917 O.52685 la M733 0,4384--1
4 -le73785 G.49906 -1.74031 0.45394-1*10637 3.47233 -le.70905 0*42113
5 -I.67457 aek-4652 -13,67753 0.339927 -1*64268 0.42168 -1. 645*1 00350193 -1.ax033 0.34771 -lv61331 0.331839 -1.57755 p3.37458 -1.58053 0.30477
La -1.5l-4425 0.35223 -It 54719 Go.27CI92L1 -1,5;635 0.33i62 -1*513Z! 0*2542!i? -i*.4t519 0*309?2 -1a47353 092305913 -1,440t49 a.23949 -1.44303 0*20801
-_,044 3.-9 -1,40535 0.1864315 -1m,36755 0.25399 -1236987 0.,15583
- 1 3,3 01 7 0.23270 -1. 331219 0.1462317 -1.292C4 0.21506 -1. 29AM5 0.12752is -. 200331 04,19500 -1. 2549. 0*1097819- - 1.;-"A40 4 0.13172 -1.21544 000929a
22 -1.17430 ee.1-604 -11,17550 000771i
22 -1.C9354 Oo-13670 -1039448 Qw0481523 -1.05236 0.12305 -1.05354 0.03506
-! 1.01136 0OU3008 -1,01240 0.022S$-50.9970-69 00-3761 -0 7i1 0.01161
22 -0.92943 0,303bZ4 -0.92)374 0.0012427 -0.88811 0.0-7536 -0,3833 -0.0082423 -0*84678 0.0o516 -0,184692 -0&016832 3 -Oe 305-.7 005569 -0, 80556 -0.0245430 -0.76423 0.04593 -0.76427 -0.03138.11 -0* 7207 0*03i80 -0o.72305 -0&0373632 -0*68232 0.,03139 -0,63200 -0.0424933 -0*64109 0*024t5 -0364105 -00.6~7S34.G6C028 3.01659 -0.60023 -0.05024
B15 -0.55961 0*01319 -0.55955 -0.0528?3* -0,51907 9.035846 -0.51901 -0.05469
37 -9,.47867 990043i -0.47861 -0*0556938 -0.43839 0,00094 -0. 43833 -0.0558931 -0*39821 -0.00185 -0934817 -0.0552940 -0.35814 -0.00401 -0,35810 -0.05388
* -0.31814 -0.00554 -0.31811 -0.05168*2 -047621 -0400544 -0.271 -0.04867
43 -0.223834 -0.000671 -0.23832 -090448644 -0.19852 -1900*36 -0.19851 -0.04023
130
PSU , Pxs YS
45 -0.15875 -3.30540 -0.15874 -0903480-3.190 -. 0381-0611931 -0=02855
-0.0793l X}6 -0,07931 -OsOZ147
48 -303954 0*30123 -0,03954 -0.01355
POTSIT 'I3 XSE$!1 YSEIH1 XSE'I2 YSEIi2
1 0.00O540 0*0014 -1. 8b368 0*6043EI
2 -0.-00461 00319 -1,56405 0,150493
3 -000382Z 0*06407 -1. 8 431 0.605654 -0.00307i 3.00584 -1. 86448 0160537
-0.00236 0.90349 - 1,66 r5 3 0.607126 -0.00172 0.00303 -1. 8644.4 0.607897 -0.00115 003024 -1,86413 0.60866
a -0.00069 1300183 -1.86406 0.609409 -0.00032 9300113 -1. S6371 0961010
10 -3000008 0.00033 -1,36326 0.6107411 0.00005 -0.00340 -1,86274 0e6113112 000005 -0890!19 -1,86216- 0*6117913 -0.0C007 -3.00197 -1.86-153 0* 61 *'-16i1- -0000032 -3.0027-7 -1585086 0.61-24215 -0*600be -1.00343 -1.86018 0*61257is -3.00115 -3.00407 -1,85950 0.61260
17 -0000171 -0.0046 -1985884 0#6125013 -3.00235 -0.00508 -1,85821 0.61228
i) -0.00306 -0.00544 -1, 857b3 0,6119523 -0.00382 -0*03557 -18-8571/, 0.61152
SECTIC0 NO* 5 IV= 3.a03)0
PO'1T 13 XP YP XS YS
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35 -02&62?23 lo.0111 -0.66240 -00665-3
36 -0, 6 14 4 q 0. 30511 -u,.1466 -0.00590)37 -0*56391 -0.03301 -0,55697 -0.07036
38 -0,51909 -3.0042a -0&,51:)--4 -0,07C67
39 -0,,'8'164 -3,00756 -%.471177 -0906993
.0 -0,42415 -003'021 -3942425 -nel.0581041 -0,.7673 -0001191 -0.37*82 -0,05534
42) -0,32933 -1301276 -0,32945 -0,0-3147
43 -0928210 -0.01277 -0,2E215 -0.0565744 -3.390 -- 0A50,23493 -0,05061
02140 _ 1U 0 .
1401
X V, IT ~3 XP Vpxs vs
.r7 -3soDS-73 -It !OJj* 1-ca7 *i 37
Pi.T 203 xst51 y iiii yXSE492
-. aC454 j.I-v3 3 * -.113-? 1 0:0 )j34 -31 S131I '5 Ia:)77 -20 3 :;-. i 38-,1-
5 -,*!Zq3 .3, 133' - .B175 NtY
) -3A.ITO,2 03.i _32 - 20 .3s *; 4
Ui I).tXtO5 -3*3 1M4 -2. 3L1M Sa.873
i ?_ 0* 0233 _)3 131 -2030555 oad 392511 -;DzCCD,39 --a* 3 5i53 -2.&303s5 O.89906
20 -A0 00 7 -100335 -ze 36TS7 0684994
SECTION VI
PREDICTED STAZ3E PERORM.ANCE
1 7 A, Z~ !7-' 1- 1 1t ti:: lesZZ C;ttistiC zup~n for_ or-Aer t- ec'A'nate tre rc-1atle perfcr.arne of theA%-Z.t-j !Ir:-:' te-Zted. -:e :::efficient ef t .e Mach rnu~er
Zi az izreszea fr:-7- to I .D, wl,.ch ir. eq v~alerstn., a, r : r--1 z e s : .r: i.- tne rotor at the relative
-- n i In :tw- at. tr~e exande- '-icn surface~
-nt~ eeate2 .i r-tzr tir I .ffi.zlen lct-z a no", intro-z -- ~- ~ rw ere -a r *-'I tte prrogran, cpticn of speci-
~.r-- :r ~ieexit f!:,; ancles. Rctcr deviaticn ang4ez weren w _=1-
atteIeI7 fle.w ratl',e of 30. ; ltfZec
F:t--r 'tzta2 prAezzare ratio .3.342
Stagre t:zal presure rat!,:, 2.730
ESta~e ientrcpIc efficienc:y 0.772
:-eridlcnal velocisy at t e rc~or exit or. tne tpsraln roppedfro ElI f/se ~513.4 ft/zec and boundary layer blockage inl the
rotor ex-It plane rse fror: 0.0208 to D.0268 of the cross-sectionalarea. The relative total pressure loss coefficients resulting fromthis analysis are shown for the rotor and stator in Fig 27.
2. PREDICTLD IINTRA-LADE-ROW PERFORM4ANCE
The distribur-ons of loss obtained as described above and pre-sented inl Fig 27 were used for an intra-blade-row analysis in theidentical manner pr-eviously described in Section !V.2 for the originaldesign. There were two objectives to this calculation. The firstobJective was to determine the choking flow for the stage at losslevels more likely to occur in an initial test. The second objectivewias to- determine to what extent the inter-nal flow distrlbution mightchange under these circumstances.
With respect to the first ob~ective, it was determined that thest-age would not pass the design flow of 30.0 lb/sec but that it wouldPazz slightly more than 29.0 lb/sec. Thus, i reduction of flow on the
142
;.r Jtr ci'f t n - r' ,- , t - :. Ie.;A 7n an t e an t I--i ra ted.- C e., oz i 1rr-rlze tc rc at tne flrzt catclatScr z'tatcn d-cnstrear. of the
t.lutlcn at d-rzir fr: 1-41 ~ .- cz t:.e r.tzr, ratner trar, tte.z-ator, contr-ol: s~t! r i.-,cide-,no' anglez orrespon-ding totr~e rediuctd lc are Pazrmx,2rate1:;,n dezree :.!*--er than dezign.Stator incidence zern- are rrrte wl.e t ,n zre degre~e of de-slon va1uez cn every ztrerzu.face -excert t:. cSt-r Ca: inic, wtere '!-hepredicted value : r. t t ter. c v tz aa!vn .
static pre-:wire wa ecei :7 the rararetz-r for tUor'e de-zignzhouid te optimized, tte ztatia rrc--zz:re d!:tri, tAtiT = correzcnd Ingto tte higher Lo:level--~ -? an atcnof T-he de art.iIefrom~ ideal cmdlit-nZ. lfhT 10 vrezerfted In. 771g ZE, -orarrig~with Fig 17 .'~hprezent:Z t d ezln di: tritutimr., t.-e cr-zied zdition ef the ,ztatr~r ataznct t- ifcn1:affect the ztatoraxial erez.:ure j -radicrnt t-ut lt clan te exrected to auch rctOr tooperate at a ryore thrt e condtirn trnan it-, reax- efftciency oper-ating point. This wn-o.d tyr-i ally result in a Ztee~er axial pressuregradient In tte entran~ce rce-icn of tnt rstor follcwed L_., a plateauas zhown In Fi, 21. 'nti 4tep: arC- fake, to reduce rotcr 'Lossez orto Increace statCor f1w area, i~t i:-, unllx~el*:: tat t. rotor 'Ail!. tatle to eperate at it:z pol.-t of -eaik ef'fic~eric at dezign zreed. Thisconclusion I7 vredicatea urorn the azzurmticn tat mxinrumn rotor 'effi-Ciercy t i?,e y t OCCIur 'at or very near tne *throttle point at x'hichthe rotor Just tecoreZ unchoi~ed. TLh'z op eratinr conditIn 2rrezpcnd:tc the iInI~ium axial ressure crad,*fnt w1 canr. ottair,.d at athrottle point, near the m~axim~um rotor creosure ratio.
This Document Contains
Missing Page/s That Are
Unavailable In The
Original Document
-ha cj- h Ca J
BESTAVAILABLE COPY
C. 0.15-'
-
S-
". 0.10
an
0.-J
C,
. 0.05
, -
-0.00)
0.0 0.2 0.4 0.6 0.8 1.0
Diffusion Factor D
Fig 1. Assiumed Relationship Between Total PressureLoss Parameter and Diffusion Factor
0.451
0. 40 -o
0.30
0.20
0,.10 - " I I I
10 20 30 40 50 60
Stagger Angle (degrees)
Fig 2. Relationship Between "m" and Stagger Angle inCarter's Rule for Rotor and Conventional Sectionz
145
1 . 0 -'C
o
°I-3
0.5-
C 0.0 -! - - 1 I I 1
0.00 0.25 0.50 0.75 1.00
t Distance from I.e. as a Function of Axial Chord0-J
Fig 3. A-sumed Generalized Variation of Deviation Within Blade
900_,.---Stator Inlet
800 "*,Stator Outlet
" 7001
0
-- Rto r Exit
- Rotor Inlet -
6000
,S.-
500 -
6.5 7.0 7.5 8.0 8.5 9.0
Radius (inches)
FiC 4. Meridional Velocity Distributions fromIterative Loss Reestimation Procedure
146
0
oI-
0-
0
- -€ 0 GJ C
- -4),
oo
0 to
Radius (inches)
ldi?
1.6 1.0
L ~Rotor Inlet ,
z Rotor Exi t1= LOV
4J r 1,2t 0.6 "
Exit
= Stator In'se t. 0l 1.2O 0.6
6.5 7.0 7.5 8.0 8.5 9.0
Radius (inches)
Fig 6. Rotor and Stator Relative Mach Numbers fromIterative Loss Reestimation Procedure
70
Rotor Inlet60
0)0)
5-
----- Stator Inlet
40
Rotor Exit
0
U- 20CD
0 -
0 Stator Exit
| I i | I
6.5 7.0 7.5 8.0 8.5 9.0
Radius (inches)
Fig 7. Rotor and Stator Relative Flow Angles fromIterr:,'lve Loss Reestimation Procedure
I~ 118
CO
E
0
0 0
0 "- 0
V) CO x 04.)
" 0-
o ta-J
4-)
CI z ° CO '-.t'
""t- "
c*0o
COz
F--l
ous nF c
D if fu s ion Factor
1.49
cO
0O
0 a R0"
z Cd
a) )
0-
V)- CIJ
rj- I r dJ
to 000 0 Q
U _j
0J *Adx 0(a
U ) 4- 0)-o 4- d
(/) 4- :3 c
L ) U) a)
4-a)
4J HO0
1/ 50
S0 00
150
0 a) 4--
co
CID
0
4-J Coo
1511
4tA
*-" C
0 ,-i
I -r-.u') c} u o
15].0
e-
Va
C34
I A . 9
L Li
ott -oa Isnr i Efiiec
00
c C
~.. 0
c-40
yE
toz
1534
qfa
II ( C
9- xO
00
- r-
r
II •
CI 0
-3: ILI
a 0
In
Displacement Thickness (inches)
r u,
1 '-
4.) (S) - .3
4 -C L
0
4--)
C 0.
0i0
C'l'.0 eI
1551
810~
-I
U
0800-
4J750 Rotor Exit
-700 -
o 650
,-600 -"---
0S550 final blading analysis
iterative loss reestimation procedurei ~~500 - -
5006.5 7.0 7.5 8.0 8.5 9.0
Radius (inches)
Fig 15. Meridional Velocity Distributions for Rotor from FinalBlading Analysis and Iterative Loss Reestimation Procedure
4
156
900
8. 0
S8001
750 final blading analysis750 iterative loss re-
>)estimation procedure A
uO 700 -
-650-Saorei
S550
7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7
Radius (inches)
Fig 16. Meridional Velocity Distributions for Stator from Final
Blading Analysis and Iterative Loss Reestimation Procedure
157
J
5400
5200
A?
5000 /
4800 ii.
4600 -
o 4400 /
4200Cr I
4000
.- 3800 -
'I)S3600
"- 3400 (-
3200
3000 ,.-oCLC
2800 =
4-)
v260-Rotor Stator
2400
2200 /2000
1800
1600- 0 1 2 3 4 5 6
Axial Coordinate (inches)
Fig 17. Static Pressure Distribution ThroughStage from Final Blading Analysis
158
6-
5_
4
-Rotor
- 3
2U
0 i J I I I
6.5 7.0 7.5 8.0 8.5 9.0
Radius at Blade Inlet (inches)
Fig 18. Incidence Angle Distributions for Rotorand Stator from Final Blading Analysis
14
1i~3 I12 Rotor
-11~Stator
C 90
8
7
6.
7.4 7.6 7.8 8.0 8.2 8.4 8.6 8.8Radius at Blade Exit (inches)
Fig 19. Deviation Angle Distributions for Rotorand Stator from Final Blading Analysis
159
II A
ooo. -x- 7o 9
000'0 ,X ---
°- 0
00
0
0
H°H
, H
o
o 3)
16o0
0!
3
F-'- f--'r-i---t"
i N Nj CN rNq
I ) fx0IT~r o ~ t~o0 co r0 t-t O 0
I a, CI V)w~t.~ - -" - 00t'L-LO---
I OD
16 nI OID tn!ol 0 I t v 4ti c
(338J) G?4tX -- -- U80 tL -
in 0
IJ E-V0H
0
-- I 0
In-
*r4
0
16:1
4pI
C4iI T
II
COORDITSK1 a65362.0 86699
86399w12.4 8632
oC 5 .86199
12.5x x2.9 8.5836DE 3_.0_ 85760
* CORO~TES3.1 8.5712
_________ 3.2 85694
3.85700I34 857233. 85754
8 834
cc w39 85852~
4 85886
44 8595445 8.5975
4.6 8.5991747 85t999 -
-1221
4.490 - 2000--5.000 -- 4725 I
Fig 22. Detail Def'inition of Outer Wall
of Flowpath Through Compressor
162
00
LLIi
F- U
(Z:)
o Cl,
I-4-)
0LL- rH
L"-S
DIRECTION OFROTATION
163
0
0o
vi
U') csZI
LL,.
.'.
- Uo) C3
0 05T°
0w cz
LL C)4
N F00
zt
00
-J30
ILd
C)L
DIRECTION OFROTATION
164
IcI
I,
L-
Li~I I010
z 4/r=-400
Liid
4p4
I0
LL1ti
t4
2~ .1
H /22
U) *
(I)C
Oz
0
0
- 43 -
0 -
00
44
4.3 :r-0
LL
O4
4-* 00-
0 00 0a Q) 0
Relative~4 Toa Prssr Lo0Cefiin
167 wN
5400
5200
5000
4800
4600
-~4400
4200 f
0 4000
3800 J -
1.5 36001
0400.
C:13200
Ln 300012800
4J. 2800
rd 60 Rotor SttorLn 2400
2200
2000/
1800
1600-10 1 -2 3 4 5 6
Axial Coordinate (inches)
Fig 28. Static Pressure Distribution through Stagefrom Analysis with Increased Loss Coefficients
168
_ _...__I.
REFERENCES
1. Novak., R.A., "Streamline Curvature Computing Procedures for Fluid-Flow Problems". Transactions of the ASME, Series A, Paper No. 66-WA/GT-3, October 1967.
2. Hearsey, R.M. & Wennerstrom, A.J., "Axial Compressor Airfoils forSupersonic Mach Numbers". Aerospace Research Laboratories, WPAFB,Ohio, ARL TR 70-0046, March 1970.
3. Johnson, I.A., Bullock, R.O., et al, "Aerodynamic Design of Axial-Flow Compressors". National Aeronautics and Space Administration,NASA SP-36, 1965.
4. Miller, G.R., Lewis, G.W., Jr. & Hartmann, M.J., "Shock Losses inTransonic Compressor Blade Rows". Transactions of the ASME, Series A,Paper No. 60-WA-77, July 1961.
5. Moses, J.J. & Serovy, G.K., "Some Effects of Blade Trailing EdgeThickness on Performance of a Single-Stage Axial-Flow Compressor".National Advisory Committee for Aeronautics, NACA RM E51C09, 1951.
6. Kenny, D.P., "A Novel Low-Cost Diffuser for High-PerformanceCentrifugal Compressors". Transactions of the ASME, Series A, PaperNo. 68-GT-38, January 1969.
7. Hearsey, R.M., "Axial Compressor Rotor Design Through Specifica-tion of the Meridional Velocity Profile". Aerospace Research Labora-tories, Air Force Systems Command, WPAFB, Ohio, ARL TR 71-0024,February 1971.
8. Jansen, W., "The Application of End-Wall Boundary Layer Effectsin the Performance Analysis of Axial Compressors". ASME Paper No.67-WA/GT-11, presented at the Annual Winter Meeting, Ncvember 1967.
9. Novak, R.A., Hearsey, R.M., et al, "Model for Predicting Compres-sor Performance with Combined Circumferential and Radial Distortion-Computer Program". Propulsion system flow stability program (dynamic),Phase I, final technical report, Air Force Aero Propulsion Laboratory,AFAPL TR 68-142, Part VIII, December 1968.
169