AD-R14l 796 AERODYNRMIC DESIGN AND PERFORMRINCE OF A TIJO-STRGE 1/3

A XIAL-FLOW COMPRESSOR (..(IJ) IOWA STATE UNIV AMESENGINEERING RESEARCH INST M D HATHAWAY ET AL. DEC 83

7UNCLASSIFIED I S-ERI-AME -4R FOSRT 4-417 F/G 2/ NL

EMENEEEEEEEohEEEEEEEmhEEmhhhEmhEEEEEEEEEEEEshEmhEEEEEEEmhEEEmhEmhEEohEEmhhhhmhhI

- -. . .. . .T'__77777777'37

4..

-. Lo

% A' 111 .

11. P

11111L25 is 3

NAOA BUEA1111NDRI 1f

V%

-gt,-, _f._

£FOS-TR. 84-041 7

M. D. HATHAWAYT. H. OKIISHIDECEMBER 1983

.., 3

AERODYNAMIC DESIGN AND PERFORMANCEOF A TWO-STAGE, AXIAL-FLOWCOMPRESSOR (BASELINE)

A

A'

84 05 30 055

Tc. p OFvo fo publicGE release;O

8M 05JW 133040 055itibto nlmtd

..4 ~f.. _'4-,-'., ,: :'. ,:..., .'''''..'..- .- , -. :, .- ,. . .

...................... ....... ........

~Qualified requestors may obtain additional copies from the~Defense Documentation Center; all others should apply.. to the National Technical Information Service.

CONDITIONS OF REPRODUCTION

or in part by or for the United Stae Govrnment Is permitte.

6 -

"I

I.

C..

4 f r - -

ENGINEERINGRESEARCHENGINEERINGRESEARCHENGINEERINGRESEARCHENGINEERINGRESEARCHENGINEERINGRESEARCH

% N

TECHNICAL REPORT

AERODYNAMIC DESIGN AND PERFORMANCEOF A TWO-STAGE, AXIAL-FLOW

COMPRESSOR (BASELINE)N ~'rRFC~ ~r 1'C1 (KJS.C)

CI- * ov7 nd Mchael D. HathawayI).-12. Theodore H. Oklilhi

'~apprO~December 1983

u.ATTKSW J.K" raiu~vs~c.,TeGbfliOl Inf 0mt~ni~O

DEPARTMENT OF MECHANICAL ENGINEERINGISU-R-As-41 ENGINEERING RESEARCH INSTITUTEERI Projeocts 1394,1490, 1645 IOWA STATE UNIVERSITY, AMES

.1,7.

UnclassifiedSECURITY CL ASSIFICATION OF

THIS PAGL (1Wh.. flCI. t.v.rd)

REPORT DOCUMENTATION PAGE i0.-kI( ~COMNPLETINC. PORM

I.RLJM 2GV ACCESSION NO. 3 RECIPIE NT'S CATALOG PJLJL41JER

i*. TITL Sat~bll)5 TYPE OF REPORT A PERIOD COVERED

Technical Report-Aerodynamic Design and Performance of aTwo-Stage, Axial-Flow Compressor (Baseline)1Ocoe 1980Nvmbr92

6. PERFORMING ORO. REPORT NUMBER

___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ TCRL-247. A UT HO0R(m) S. CONTRACT OR GRANT NUMBER(a)

Michael D. Hathaway F92-3K02

Theodore H. Okiishi F92-3K02

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKrurbomachinery Components Research Laboratory AREA A WORK UNIT NUMBERS

Engineering Research Institute/Department of (91IIOL FMechanical Engineering 307I Ac

Iowa State University, Ames, Iowa 50011 ~c?,i-1I. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE I

Air Force Office of Scientific Research December 1983Directorate of Aerospace Sciences (AFOSR/NA) 13 NUMBER OF PAGES

Boiling Air Force Base, Washington, D.C. 190 pages14. MONITORING AGENCY NAME &ADDRESS(iI different from, Controlling Office) 15. SECURITY CLASS. (of this report)

Unclassified15a. DECLASSIFICATION/DOWNGRADING

SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

Approved for Public Release; Distribution Unlimited

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, If different fromt Report)

I1. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on revess side It nece.ssary and Identify by block number)

aixial-flow turbomachineryaxial-flow compressor

V ~'multistage axial-flow compressor

20 ABSTRACT (Continue on reverse side If necessary and Identify by block number)

A two-stage, baseline configuration, low-speed, axial-flow research

co~mpressor was designed, built and tested at design flow. The design,

fabrication and data acquisition and reduction details are described.

Time-averaged, spatially detailed and overall flow and aerodynamic

* performance data for design flow operation of the compressor are presented

and discussed.

DD JA 7 1473 EDITION OF I NOV 6S IS OBSOLETE _______ HSPG

7.4

Unclassified iv*lECURITy CLA. IFICATION OF THIS PAGE(Wihten Dera £FeAved)

-S|.deq

C...,-!_.

'.1

.4...

I.

.4"-

.

i

[" '- -

U n c l a s s i fie d

'T1.

SECURITY

CLASSIFICATION

OF THIS

PA E(117

D-1.n~rd)"

%-1

"A..

4. v

TABLE OF CONTENTS

Page* I

SYMBOLS AND NOTATION ix

LIST OF FIGURES xiii

LIST OF TABLES xvii-I

1. INTRODUCTION 1

2. RESEARCH COMPRESSOR FACILITY 3

2.1. Axial-Flow Research Compressor 3

2.1.1. Aerodynamic Design 3

2.1.2. Mechanical Design 9

2.1.3. Blade Fabrication and Installation 13

2.2. Probe and Stationary Blade Row Actuators 20

2.3. Pressure and Temperature Sensing Instrumentation 21

2.4. Computer Control System 22

2.5. Calibration Equipment 23

3. EXPERIMENTAL PROCEDURE AND DATA REDUCTION 27

3.1. Calibration 29

3.1.1. Cobra Probe Yaw-Angle Calibration in Free-

Stream Portion of Flow 31

" 3.1.2. Cobra Probe Calibration in Wake Portion of

Flow 31

3.1.3. Spanwise Calibration of the Cobra Probe 33

-. 3.1.4. Scanivalve Pressure Transducer Calibration 33 53.2. Data Aquisition 37

• 3.2.1. Overall Performance Map 37

3.2.2. Time-Averaged Measurements 39 .

°'f . . . . .. . - . - . . - . . . - . o

> .. .. . :..::..: ...... . . ... : . . .. .:. . . . ; .. : :: ' : .A.. :- :- . -A.2 :.: . : - . ..• '.- 'S - ,V t . . -. . . -. . ".•-". . . . ,.tt-'.%q'".",,", ,, ,,,, ", . - ," .- ,."-" . ."""". """ . - "". . """ .' "". . "" "-.""b

___ __ ___._ _.___ __ ___ __-___-__"__ _ ."_ __. ___• • . •. ° •.,- • .-

vi

3.3. Data Reduction 42

3.3.1. Flow-Field Parameters 43

3.3.2. Performance Parameters 45

4. PRESENTATION AND DISCUSSION OF DATA 47

4.1. Error Analysis 47

4.2. Overall Performance Map 51

4.3. Spatially Detailed Time-Averaged MeasurementResults 57

4.4. Comparisons of Circumferential-Mean Data with

Design Code Predictions 86

5. SUMMARY AND CONCLUSIONS 111

6. RECOMMENDATIONS FOR FURTHER RESEARCH 113

7. REFERENCES 115

8. ACKNOWLEDGEMENTS 117

9. APPENDIX A: CORRELATIONS USED IN NASA DESIGN CODE 119

9.1. Blade Loss 119

9.2. Incidence and Deviation Angle 121

10. APPENDIX B: NASA DESIGN CODE RESULTS 123

11. APPENDIX C: COMPUTER PROGRAMS AND DATA STORAGE 155

12. APPENDIX D: PARAMETER EQUATIONS 157

12.1. General Parameters 157

12.1.1. Basic Fluid Properties 157

12.1.2. Blade-Element Location 159

12.2. Flow-Field Parameters 159

12.2.1. Point and Circumferential-Average BladeElement Quantities 159

12.2.2. Global Parameters 163 %lei

--I

4" . . f- .- ,.- .'. ...... • ,. . • " . .-. .....- . *..- - ." .% . .-..-.. . ,.....~ . .. . -'. -.-. , ...

vii

12.2.3. Performance Parameters (based on cobra

probe measurements) 1646

12.2.4. Performance Parameters Used in GeneratingPerformance Map 166

13. APPENDIX E: TABULATION OF EXPERIMENTALLY DETERMINEDDATA 169

1.,.4.°

.-•o

7122

4'.

4-g

A-,' C i ', - C -'

.JN.:t . .

• " .f'.r ,. + + • . + - . - - + • ° + . . • - . .. . o . . .. - - + -+ ,.. , . • • - . . +- - *

"i, +- "+.+ '.•' Itl

'-•" " "o .- ° """. °" "". ++ .' " o.o"

".-• -- +.. ° " +"°" ." .. " .°".k " " " ' -" ' +m

° - - "- L-" -"

.

• • + • -. +. . + . -. - -. . . . . + •. -.- - -. . m • . . • ii ii • . +. . . . • . . ° . . . m -4

| ,, , ,,, -,.,, i "- +,- + + " * ' ,-: _ _ , o ++ " - - In 1J 4 '. : +

SYMBOLS AND NOTATION

2A compressor flow passage annulus area, m

c blade chord length, m

FCC comparison of integrated and venturi flow coefficients 0(Eq. 12.34), percent

g local acceleration of gravity, m/s2

2Sc gravitational constant, 1.0 kgm/Ns

H total head with respect to barometric pressure (Eq. 12.5or 12.48), Nm/kg

h static head with respect to barometric pressure, Nm/kg

h barometric pressure, m of Hg* hg

h annulus outer-surface end-wall static head with respect toww4 barometric pressure (Eq. 12.9 or 12.10), Nm/kg

i incidence angle (Fig. 12.1; Eqs. 12.25 or 12.27), deg

P barometric pressure (Eq. 12.1), N/m2atm

P t total pressure with respect to barometric pressure, m ofwater

P annulus outer-surface static wall pressure with respect to 'w barometric pressure, m of water

PHH percent passage height from hub (Eq. 12.4), percent

Qa integrated volume flow 5ate at probe-traversing measurementstations (Eq. 12.32), m /s

V 3Q venturi volume flow rate (Eq. 12.30), m Is

V

R gas constant, Nm/kg*K

r radius from compressor axis, m

RPM rotor rotational speed, rpm

S circumferential space between blades, blade pitch,m or deg

T compressor drive motor torque, Nm

-. .-

p.,-

4 .,

t temperature, *K

tbaro barometer ambient temperature, OK

t blade section maximum thickness, mmax

U rotor blade velocity (Eq. 12.14), m/s

V absolute velocity (Fig. 12.1; Eq. 12.12 or 12.13), m/s

""VI relative velocity (Eqs. 12.21 or 12.22), m/s

V tangential component of absolute fluid velocity (Fig. 12.1;Eqs. 12.17 or 12.18), m/s

Vt tangential component of relative fluid velocity (Eqs. 12.19or 12.20), m/s

V axial component of fluid velocity (Fig. 12.1; Eqs. 12.15 or12.16 and 12.47), m/s

Y circumferential traversing position, deg

absolute flow angle with respect to axial directiony (Fig. 12.1; Eqs. 12.7 or 12.8), deg

relative flow angle with respect to axial directiony .(Eqs. 12.23 or 12.24), deg

.20 specific weight of water manometer fluid (Eq. 12.3), N/m

2 3YHg specific weight of mercury, N/m

Pvent differential pressure across venturi, m of water

6 deviation angle (Fig. 12.1; Eqs. 12.26 or 12.28), deg

lrl hydraulic efficiency (Eqs. 12.42, 12.43, and 12.44)

K blade angle, angle between tangent to blade camber line andaxial direction (Fig. 12.1), deg

p density of air (Eq. 12.2), kg/m3

a blade row solidity

. flow coefficient (Eq. 12.29)

integrated flow coefficient at probe-traversing measurementa stations (Eq. 12.33)

v venturi flow coefficient (eq. 12.31)

- . .

%,. 5(' ' .' . .' ' " . ",- . . . . - . . - . . . . . . • .. . . . , , . . . . - , . .

xi

1P head-rise coefficient (Eqs. 12.36 through 12.41 and 12.49,12.50)

W total-head losss coefficient (Eqs. 12.45 and 12.46)

Additional General Subscripts

h annulus inner surface, hub

i ideal

me mechanical

overall overall compressor

pm torque meter based performance parameters

R rotor

. S stator

stage stage

t annulus outer surface, tip

1 blade-row inlet

2 blade-row outlet

'-4 IR first rotor

2R second rotor

iS first stator

2S second stator

Superscripts

relative to rotor

- average; blade-to-blade circumferential average value O

l mass-averaged in the radial direction

cross-section average

.F %

." .

'

xiii

LIST OF FIGURES0

Page

Figure 2.1 Schematic of baseline compressor showingoriginal and redesigned components. 4

Figure 2.2 Representative rotor blade sections at threespanwise locations. 6

Figure 2.3 Representative stator blade sections at threespanwise locations. 7

Figure 2.4 Meridional-plane view of redesigned section ofbaseline compressor with each ring assemblyidentified. 10

Figure 2.5 Schematic diagram showing axial location ofprobe measurement stations relative to adjacentblade rows (dimensions in mm). 12

Figure 2.6 Radial and circumferential interlock design ofouter ring assembly. 14

Figure 2.7 Probe access hole configuration. 15

Figure 2.8 Schematic of blade fabrication showinglaminates sandwiching trunnion spline. 17

Figure 2.9 Representative eyelash drawing. 18

Figure 2.10 Schematic diagram of data acquisition system. 24

Figure 3.1 Baseline compressor overall performance curveand operating point. 28

Figure 3.2 Logic diagram of data acquisition system. 30

Figure 3.3 Cobra probe yaw-angle total-head calibrationcurve in free stream portion of flow for flowcoefficient = 0.587 at 2400 rpm. 32

Figure 3.4 Cobra probe total-head calibration curve in wake

portion of flow for flow coefficient = 0.587at 2400 rpm. 34

Figure 3.5 Cobra and Kiel probe comparison behind first rotorand first stator for flow coefficient = 0.587at 2400 rpm (Y/SS 0.0). 35

xiv

Figure 3.6 Blade cascade showing circumferentialmeasurement window. 41

Figure 4.1 Predicted and measured overall performance data. 52

Figure 4.2 Blade-to-blade distribution of time-averagedtotal head for flow behind the first and secondstage rotors (# = 0.587 at 2400 rpm). 58

Figure 4.3 Blade-to-blade distribution of time-averagedtotal head for flow behind the first and secondstage stators (# = 0.587 at 2400 rpm). 61

Figure 4.4 Spanwise distribution of circumferential-meandata for flow behind the first and second stagerotors (# = 0.587 at 2400 rpm). 67

- Figure 4.5 Spanwise distribution of circumferential-mean

data for flow behind the first and second stagestators (# = 0.587 at 2400 rpm). 70

Figure 4.6 Contour map of the distribution of total headbehind each blade row (0 = 0.587 at 2400 rpm).Data enhancement employed. 74

Figure 4.7 Locations of actual data points used inconstructing the contour map behind the firststator. 78

Figure 4.8 Contour map of the distribution of total headbehind the first stator (0 0.587 at 2400 rpm).No data enhancement. 79

Figure 4.9 Comparisons of measured circumferential-meanincidence and deviation angles for both stages( = 0.587 at 2400 rpm). 83

Figure 4.10 Comparisons of measured and predicted velocitytriangles behind the first rotor (0 = 0.587 at2400 rpm). 87

Figure 4.11 Comparisons of measured and predicted velocitytriangles ahead of the second rotor (0 = 0.587at 2400 rpm). 88

Figure 4.12 Comparisons of measured and predicted velocitytriangles behind the second rotor (0 = 0.587 at2400 rpm). 89

Figure 4.13 Comparisons of the measured and predictedspanwise distributions of circumferential-meanaxial velocity (4 0.587 at 2400 rpm). 91

.p.4,. . . .%,," .,,. -..

xv

Figure 4.14 Comparisons of the measured and predictedspanwise distributions of circumferential-meandata for the first and second stage rotors

= 0.587 at 2400 rpm). 94

Figure 4.15 Comparisons of the measured and predictedspanwise distributions of circumferential-meandata for the first and second stage stators

= 0.587 at 2400 rpm). 97

Figure 4.16 Spanwise distributions of design code rotorblade angles. 101

Figure 4.17 Spanwise distributions of design code statorblade angles. 104

Figure 4.18 Comparisons of measured and predicted spanwisedistributions of blade loss for each blade row

= 0.587 at 2400 rpm). 105

Figure 9.1 Blade loss correlation curves used in NASAdesign code. 120

Figure 10.1 Typical rotor and stator blade sections usingmanufacturing coordinates. 154

Figure 12.1 Sketch showing nomenclature and sign conventions(all positive except as noted) for slow-responseinstrument parameters. 158

'--4

5-%

"S

sed5,-

-7....

xvii

LIST OF TABLES

Page

Table 4.1 Uncertainty estimates of measurement parameters. 48

Table 4.2 Flow coefficient comparison between venturi andintegrated measurement station flow coefficients. 51

-. - Table 4.3 Rotor, stator, stage, and overall performance

parameters. 85

Table 10.1 Design code input parameters. 124

Table 10.2 Design code predictions of aerodynamic parameters. 132

Table 10.3 Design code stage and overall performancepredictions. 143

Table 10.4 Rotor blade manufacturing coordinates generatedby NASA design code. 144

Table 10.5 Stator blade manufacturing coordinates generatedby NASA design code. 149

- Table 13.1 Point-by-point distributions of circumferentialsurvey data. 171

Table 13.2 Circumferentially-averaged flow-field parameters. 190

%

'. %P

O

PIBLN

.°

1. INTRODUCTION

A significant portion of the inefficiency of axial-flow turbo-

machines is associated with viscous and turbulent flow phenomena in

the boundary layers which develop on blade surfaces and on annulus hub

and casing walls. For example, large secondary flow losses can

accompany the complex, three-dimensional flow patterns of annulus-wall

boundary layers passing through blade rows. This behavior affects

both local work transfer and the management of the flow in subsequent

blade rows. It can be appreciated, therefore, why there has been

considerable interest in the possibility of reducing axial-flow turbo-

machine stationary-blade-row secondary and end-wall flow losses by

incorporation of unusual blade configurations (e.g., Mitchell and

Soileau [I; Wisler [2]; Senoo, Taylor, Batra, and Hink [31).

In order to initiate a local program of research to provide a

_. clearer understanding of the potential for better controlling the

secondary and end-wall flows in axial-flow turbomachines, a suitable

baseline research compressor was required. The existing three-stage,

axial-flow compressor [4] of the Iowa State University Turbomachinery

Components Research Laboratory was evaluated for possible service in 9

this capacity. It was decided that the best course of action would

involve the design and fabrication of new blades which would be more

representative of conventional compressors. However, much of the

rest of the existing compressor rig such as drive system, inlet flow

. path, and flow-rate control and measurement duct could be used with

the new blades to form the baseline compressor. The design of the new O

--°' . . *"

4- - . 4. - 4 4 . 4 . o.-..

2

baseline blades was accomplished with the aid of a NASA computer code

[51 and included the following considerations:

1. Higher blade-chord Reynolds numbers than were previously

attainable with the three-stage compressor blading.

2. A better blade material which would be more durable than

that already available.

3. Conventional blade-section shapes.

4. A favorable ratio of number of rotor blades to number of

stator blades.

5. Elimination of inlet guide vanes.

In order to use as much of the existing compressor rig as possible

while also achieving a significantly higher blade-chord Reynolds number,

a two-stage configuration without inlet guide vanes was selected.

Fiberglass blades were fabricated and fitted into specially made flow-

path rings to form the baseline compressor.

This report is intended to document in detail important aspects

of the design, fabrication, and aerodynamic testing of the baseline

compressor configuration. Subsequent reports will deal with specific

stator blade modifications for possibly improved control of end-wall

and secondary flows as well as related tests and comparisons of data.

O

4~o.

. ... . .. - . . .,_

~.° 3

2. RESEARCH COMPRESSOR FACILITY

The axial-flow research compressor and data acquisition system of

the Iowa State University Engineering Research Institute/Mechanical

Engineering Department Turbomachinery Components Research Laboratory

were used to accomplish the research described in this report. The

compressor, instrumentation, data acquisition system, and calibration

equipment are described in this section.

2.1. Axial-Flow Research Compressor

Aerodynamic considerations mentioned earlier led to the design

of a new two-stage, baseline, axial-flow research compressor configur-

ation. An existing three-stage axial-flow compressor [4] was modifiediP

to form the baseline compressor. Much of the existing compressor such

.- as the drive system, inlet flow-path, and flow-rate control and

measurement duct were incorporated into the current system. A schematic

of the baseline compressor rig which indicates the extent of the re-

designed section is shown in Figure 2.1.

2.1.1. Aerodynamic Design

Aerodynamic design of the two-stage baseline compressor was

accomplished with the aid of an axial-flow compressor design code [5]

developed at NASA Lewis Research Center. The aerodynamic portion of

the code assumes steady, axisymmetric flow and uses a streamline

curvature method for the iterative solution--between blade rows--of

the property, continuity, and momentum equations with empirical

subsonic flow viscous loss correlations provided by the user (see

?1b

9:! I

A... . . . . .. b

.. . . . .. . . . . . . . . . . . . . . . . . .

- , -. , " _ ,- ? * ,I * " * " , -, . . . . .,.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . "

L ~CD

4~Ch

I-. 00 bi

- x ) 0)

LLlJ V) 2

U)O

La4i 1

0 ca

W UG)

o6 1

Co4.'i

I- . 40

P ~ 0.

/,-., , ,- o°:. ,. -. . . - .i o . .. . . •. . . . . . .-. ... °. :. .. . . . -. -•- . ".

5

Appendix A). Coupled with the aerodynamic solution iterations, is a

blade design procedure which constructs blade elements on specified

conical surfaces and then stacks them on a user defined axis (see

Reference [51). These blade elements are positioned in the flow with

incidence and deviation angle correlations selected by the user (see

Appendix A). After aerodynamic and blade design solution convergence

has been achieved, blade fabrication information consisting of coor-

dinates for several blade sections--formed by the intersection of

planes perpendicular to the radial direction and the blade at differ-

ent radii--are provided by the code. Blade sections between elements

are obtained by interpolation. Examples of such blade sections at

three spanwise locations are shown in Figure 2.2, for the baseline

rotor blade, and Figure 2.3, for the baseline stator blade.

. The baseline compressor was designed to have high reaction stages

typical of transonic compressor configurations. Further, a uniform

spanwise distribution of total pressure was prescribed for each rotor

exit. The stators were designed to discharge fluid axially and inlet

guide vanes were not used.

J. ~The coordinates of the annular flow path for the existing4S

compressor were retained in the baseline compressor to allow use of the

existing inlet and exit flow sections. A rotor speed of 2400 rpm was

selected as it was considered to be the maximum safe level obtainable

with the existing equipment. A mass flow-rate of 5.25 lb/s (2.29 Kg/s)

was established from preliminary design trials with a simple radial

equilibrium based computer code [61 developed by Detroit Diesel Allison

for NASA. An overall compressor pressure ratio of 1.0125 was obtained

%

o% %. . . . .. . . . . . . . . . . . . .. -. .. '... . -55 5.* '

. -.. . - .. . " •--." •" "•". .. ". . "-". .°".". "- -". .""" . " .''""-..'''.V .'''-. " - "',-* '.-.-.-"" . .-S-- . . " -

6*

4r.• -

3.00- 1.20

2.00,- 0.80 - TIP MID-SPAN

1.00 0.40 HUB

""' 0.00 0.00-

...- 0 -0.40 .4 BLADE TION

.4 W.-... -2. 0.00

2.00 -0.80 -

'in-

-2.00 -0.80

-1.20 II

-0.80 -0.40 0.0O0 0. 40 0.80in.

L I I I-2.0O0 -1.0O0 0.00 1.00 2.0

AXIAL DISTANCE, cm

Figure 2.2 Representative rotor blade sections at three spanwiselocations.

%S

- - . . .. . .- -. . . .". . . -.. . .. . - . . . . . . .. . ... . .[' t,, *,,, ,,*°' " . 4 . , .. .4 ' . , . -. " . -. . . o , . . . . . . -. 4 . . - . . . 4 . " . . . " , .. .

cu1

C> C

C)a

CD o

CJ

o 0oC 0C) C

o4

C - 9

o: C

C C. Cu

C C-J -

W:'3NVCI IVI..39N1

8

with the codes--with the rotor tip diffusion factor limit specification

of 0.4 being the only aerodynamic limit reached during the design I-".

process. Circular arc blade-elements were selected as they were con-

sidered suitable for the low Mach number service involved. For the

baseline configuration, blade chord and leading and trailing edge radii O

were held constant across the span. The blade maximum thickness to

chord ratio was varied linearly from 0.1 at the blade root to 0.06 at

the other extremity. In order to maximize the blade chord Reynolds

-[. number, the rotor chord length was made as large as possible while

- .[ still allowing two stages to fit within the predetermined flow path.

The selected rotor chord length, 2.39 in (6.07 cm), coupled with a

reasonable value of rotor tip solidity (1.0) yielded 21 rotor blades.

At design point, the blade chord Reynolds number was on the order of

51.8 X 10 . To achieve a reasonable ratio of number of rotor blades to

number of stator blades, the acoustics-related guidelines of Reference

[71 were used which set the number of stator blades at 30. A stator

chord length equal in value to the rotor chord length resulted in a

reasonable stator solidity (1.4 at the tip) and was thus adopted. The

aspect ratio of each blade row was 1.0. A radial stacking axis through

the center of gravity of each blade element was considered appropriate 6

'S for the baseline rotor and stator blades. Additional blade parameters .

.and blade fabrication coordinates are given in Appendix B. Annulus-wall

blockage factors (see Appendix B) were estimated, keeping in mind that

specifying smaller than anticipated blockage is conservative. If

blockage is higher than specified, the flow in the mid-span region will

S be accelerated and loading will be relieved. On the other hand, if

N "V

%

% IN''S

-Si [[-[ [.[ : -[ . [ [???>.. ? - : .-- "- [.-.--[7[k" [-<[[[. : [<J.* .'-': '.'.'-(V -" '--i2"" ". "- -"" " -'-'- ' * ' "•' -"-"-'- ,"- -i -'-''.--.''..-.-.....--.

I,

9

blockage is less than specified, the flow in the mid-span region willlId. tend to be accelerated less and loading will increase. Tabulated

velocity diagram output from the NASA aerodynamic design code are

provided in Appendix B.

2.1.2. Mechanical Design

Except for the blades, all machining and fabrication of the base-

line compressor was performed in the Iowa State University Engineering

Research Institute Machine Shop. The geometry of the baseline compres-

sor as well as improvements in the original compressor mechanical

design are described in this section.

A meridional-plane view of the redesigned portion of the compressor

rig is shown in Figure 2.4. The basic components of the baseline com-

pressor consist of eleven independent rings which facilitate disassembly

and reassembly of the compressor flow-path. The five inner rings

4;-' (M201 to MH203) which make up the hub flow path are mounted on the

original rotor drum and are held in place by friction. Four indepen-

dent circumferentially and radially interlocking rings (MHil01 to MH104)

-make up the outer casing of the baseline compressor. The two stator

blade row supporting rings (MH105) are mounted in circular tracks in

the outer casing, formed by rings (M]1101 to MH104), to permit independ-

ent circumferential positioning of each stator blade row about the com-

pressor axis of rotation. The stator blade rows can, thus, be moved

circumferentially during tests by means of a circumferential motion

k' actuator which is mechanically linked to each stator blade row mounting

ring (M1l05) through slots provided in the outer casing rings. Cylin-

drical trunnion holes were used in each stator and rotor support ring

..

. --. .

.- e ." s ' %. . , , . , '. , . . . ." ' -'- - .. ". . . ". ". ". S S , - -. .. - - - .

10

ULLI>-

-- 4

cnn

-4 -

00

0r-4

rmI-

Coo

C14i

C,.

Cd0cli C:0u 4i1

* -4CD

L-4-

(MI05, MH201) to facilitate blade attachment and to simplify readjust-

ment of blade setting angles. For the present study, both rotor blade

row rings (MH201) were positioned circumferentially during assembly

so that the blade stacking axes for each rotor row were in line axially.

Since no discernible difference in compressor aerodynamic noise level

was noticed for different relative circumferential positions of the

stator rows with respect to each other it was decided that, for this

study, the stator blade rows would also be aligned so that their

stacking axes were in line axially. Probe traversing stations were

arranged in line axially and positioned upstream of the first rotor

V blade row, downstream of the second stator blade row, and between all

other blade rows. The axial location of each probe measurement station

.. relative to adjacent blade rows is shown in Figure 2.5. Static pressure-

tap holes, spaced 90 degrees apart circumferentially, were also provided

at each probe hole axial location.

Several improvements to the original compressor were achieved

during the redesign effort and are described herein. Binding and

sticking during circumferential rotation of the stator rows was

avoided in the baseline compressor with the aid of teflon pads. The

teflon pads were placed around the full circumferential extent of

both vertical edges of each stator blade row supporting ring (MH105).

Ten equally spaced teflon pads were also attached to the outer cylin-

drical surface of each stator blade row supporting ring. The teflon

pads eliminated metal-to-metal contact on all sliding surfaces which

-at.' ,resulted in smooth operation of the stator blade row support rings

during circumferential positioning. Some of the binding problems

. . ... e

-. 12

~0 4!0I-

C) c)C/)Cd0

No I CDr

*~A 41~~'

- N N

Li- c~-

C,))

a'..,- v

0r UJ)d

a 00

4 * u

b-4 C)NON N O

V~a . N N cc,

% 4

9.4 13

experienced in an earlier build were attributed to poor radial and

ilcircumferential positioning of the outer annulus rings. This problem

was eliminated by matching the outer annulus rings so that each ring

interlocked both radially and circumferentially with adjacent rings

(see Figure 2.6). Reference marks were provided at each coupling

point to insure proper circumferential positioning of both stator and

rotor blade rows.

Anticipated tests of blade-fillet geometry effects on stator

performance required that at least one of the stator blade rows be

provided with a stationary flow path at the stator tip. Since the

rotor drum surface is the annulus hub, it was necessary to extend an

aluminum skirt upstream from the outlet duct hub contour in order to

provide a stationary hub surface for the second stage stator. Both

*.. the rotor drum and outlet duct hub contour were provided with a

circumferential recess to allow for adequate running clearance between

the rotor drum and the aluminum skirt, and to insure sufficient con-

tinuity of the hub contour. The circumferential recess in the down-

stream rotor ring (MH203) is shown in Figure 2.4.

The probe access holes were designed to facilitate mounting and

dismounting of the probe actuator assembly. A keyway configuration

(see Figure 2.7) was chosen since it provided minimal intrusion into

the flow path and yet permitted insertion of all anticipated probe

configurations.

2.1.3. Blade Fabrication and Installation

Fabrication of the blades for the baseline compressor was per-

formed at Dayton Scale Model Company, Dayton, Ohio. Several materials

°~. -. .° . ° o o ° o o ° . °°..... .- .. .. o . . ,% .° . - -. - -.- -.- - . ° -• - - ,- - - . °

14

MH101MH10

MH101MH10

Figure~~~_ 2. ailadcrufrnilitrokdsg fotrrn

assemb y. '7

15

(0. 1875 in)

(0120 n

SIZ

10 TIMES SIZE

Figure 2.7. Probe access hole configuration.

16

such as aluminum, plastic, and fiberglass were considered for possible

use in the construction of the blades. Molded blades constructed with

a fiberglass reinforced epoxy resin material were selected as being

most appropriate for this application.

Rotor and stator blade section coordinates at eleven different

radii (see Appendix B) were generated from the design code for use in

construction of a master rotor blade and master stator blade. These

coordinates were also used to produce ten times size drawings of each

blade section, on mylar, for use in checking the shape of the master

and actual blades. The master blades, constructed of aluminum, were

used to manufacture molds for both the rotor and stator blades. The

fiberglass reinforced epoxy resin material, in sheet form, was cut to

the general shape of the blade and stacked in layers in the mold

bottom, sandwiching a spine which protruded from the trunnion base for

the blades (see Figure 2.8). Each fiberglass layer was stacked so that

the glass fibers of adjacent layers were perpendicular. The mold top

was then put in place and the entire mold assembly was placed in a

press which slowly applied pressure while also heating the fiberglass

to an appropriate temperature to insure complete filling of the mold

and bonding of the fiberglass laminates. Upon cooling, each blade was

removed from the mold and the leading and trailing edge radii were

checked under a microscope and dressed if necessary. Ten times size

"eyelash" profiles (see Figure 2.9) of each blade section, correspond-

ing to the blade sections of the mylar drawings, were produced at each

,. step of the manufacturing process. These eyelash drawings of the

master blades and a few representative finished blades were compared

% .. . . .

." .°•"

S. . . . . . . . . .. ".

-. -

_ _ c

4

ca4

~.. '-

\ N

-1 C-1

Li~4 18* 4. ~

I.

I

'-4

'.4-. *p 0

- 0

: *

~~.4~~.

4$ 4--4

4$..-*4$ .4-

C- CA0'-4

0S ~*.

0%~.4'..\ *'4 4

'4 C.,I4..

01.4 .4.

4.

p.4

4im' 4'

4.

44~4.4

-A 'I

4... p

II

... * *4 *4.. 4 4 - ... *.- 44*

19

to the mylar drawings to insure precision control. The maximum devia-

tion from the mylar drawings was less than 0.005 inches (0.127 mm)

along the entire blade surface. The trunnion base for the blades was

a machined cylindrical plug with an extended flat spine on one end to

which the fiberglass blades could be formed around, and a threaded

stud on the other end for attachment to the blade mounting ring (see

Figure 2.8). This simple trunnion design allowed for easy adjustment

of blade setting angles and facilitated blade attachment to the

mounting rings. The length of the trunnion base was made slightly

less than the depth of the corresponding holes in the blade mounting

rings to prevent any intrusion into the flow. After all stator and

J% rotor blades were attached to their respective blade mounting rings,

specially made gauges were used to insure correct adjustment of blade

setting angles. The blade setting angles were checked at the blade

root and mid-span and found to be within 0.25 degrees of the design

setting angles for all blades. The stator blade mounting rings and

the rotor drum assembly, with rotor blade mounting rings installed,

were placed on a lathe and a high speed grinding tool was used to

grind the blade tips to an appropriate radius. The grinding insured

that the blades would conform to the curvature of the end-walls with a

mean clearance of 0.034 inches (0.864 mm) (1.4% span) for each blade

row. Silicon rubber glue was then used to fill in the gap between the

rotor root section and rotor hub in order to provide a smooth transi-

tion between the blade and the rotor drum surface. A caulking com-

pound, Mortite (Mortell Company, Kankakee, Illinois), was used to seal

the gap between the stator blade root and stator blade mounting ring.

(-°

.. .

-. . , .

:7 • -17 7 7 . -V. " "7

20

No attempt was made to provide a particular fillet radius, however,

the fillet was made as small as was practical. The entire rotor drum

% ,assembly was dynamically balanced for smooth operation up to 3600 rpm.

2.2. Probe and Stationary Blade Row Actuators

A circumferential motion actuator [41 was used to control circum-

ferential positioning of the stator blade rows during testing. The

actuator was connected to each stator blade row mounting ring through

- .:*an adjustable hand-screw link. Each blade row mounting ring could

then be moved independently or simultaneously. The circumferential

. .- position of each stator blade row was determined from calibrated scales,

marked in degrees, which were attached to the outer casing. The scales

were marked such that positive circumferential angles were in the

direction of rotor rotation. The zero degree circumferential position

was set with the aid of reference scribe marks on the stator blade

mounting rings and outer annulus rings such that the probe was posi-

tioned circumferentially in the flow midway between two stator stacking

axes. The circumferential positions of the actuator were determined by

monitoring the voltage from a linear potentiometer. The potentiometer

was calibrated to indicate the circumferential position of the

actuator through a linear least-squares fit. The circumferential

position of each stator blade row was ascertained by recording the

circumferential position of the actuator in degrees as determined from

.% of each blade row when the circumferential position of the actuator was

. .......

,~~~~~~~~~~~~~~~~~~.',.,..,-,-.-...... . .-..- -...--....... ...................... -........ ,..... .,....;; :,; .,, : .. '. '. '. '- -.--' - " " '. '. .-' . ..." " . .- .- . - . .*- . . . .. . .' .. . .. .

21

at zero. The actuator system could be used to determine the circum-

ferential position of the stator blade rows to within ±0.05 degrees

(Y/S5 = 0.004).

A probe actuator (L. C. Smith Company model BBS-3180) was used for

probe yaw-angle and immersion positioning. Mechanical digital counters

as well as linear potentiometers were used to determine the probe yaw-

angle and immersion positions which were calibrated to indicate the

extent of their respective motions using a linear least-squares fit.

The probe actuator could be used to set the probe yaw-angle and immer-

sion to within ±0.05 degrees and ±0.1 mm, respectively. A probe

actuator control indicator (L. C. Smith Company model DI-3R) and probe

actuator switchbox (L. C. Smith Company model DI-3R-SB4) were used to '-.

control the probe actuator.

2.3. Pressure and Temperature Sensing Instrumentation

A scanivalve pressure-port selector actuator system (Scanivalve M

Company model 48D3-1) including a strain-gauge pressure transducer

(Scanivalve Company model PDCR22), a signal conditioner (Endevco model

4470), and an amplified bridge circuit conditioner (Endevco model

4476.2A) were used to obtain all quantitative pressure measurements.

4' A scanivalve actuator control box (Scanivalve Company model CTLR2/S2-S6)

6 was used to control and monitor selection of up to 48 separate pressure

ports. Transducer voltage was correlated with pressures from four

separate reference columns using a linear least-squares fit. A pre-

* cision micromanometer (Meriam model 34FB2) was used as a standard for -

,../ , ... . , .,. .,.., , # .,, . , :::,: .. :. .... . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .y.. . . . . ...... . .'.. . . . ..' .-

~ *%*A * 4. AX * . ..A ~ ~ .. %

, . .. , .•.*, . F, - , .S. . . - - - - , So .

22

calibration of all pressure measurements. All pressure probes, static

pressure taps, etc., were connected to the pressure-port scanivalve. A

cobra probe (United Sensor type CA-120-24-F-18-CD)--capable of measur-

ing flow angle and total pressure--was considered to be most suitable

for use in the baseline compressor and was relied on for all slow-

response (time-averaged) measurement tests. A Kiel probe (United

Sensor type KBC-24-L-22-W) was used as a standard of calibration for

all total-pressure measurements. A depth micrometer was used to insure

correct radial positioning of the probe in the actuator. The probe

yaw-angle was set by placing the probe actuator assembly in a uniform

nozzle flow and insuring that the side-port pressures balanced when

the actuator yaw-angle counter read zero. Annulus-wall static-pressure

taps were provided at all probe axial measurement locations. Static-

pressure taps were also located at the inlet and throat of the venturi.

Copper-constantan thermocouples were used to measure room air tempera-

ture, compressor inlet temperature, and venturi throat temperature.

Precision mercury-in-glass thermometers were used to calibrate all

thermocouples. A mercury-in-glass barometer (Princo Instruments, Inc.V.

model B-222) was used to measure atmospheric pressure.

2.4. Computer Control System

A desk top computer (Commodore PET model 2001-32) and digital

voltmeter (Hewlett Packard model 3455A) were used in conjunction with

a multiple channel voltage scanner (Hewlett Packard model 3495A) to

provide automatic control of the data acquisition process. A schematic:"a

V...

,-

.'.

,,,,. "..,,. -.--.

23I. -1

of the data acquisition system is shown in Figure 2.10. The computer

controlled data acquisition system was used to control probe and

circumferential motion actuators, to control the scanivalve pressure-

port selection actuator, and to allow automatic reading of individual

thermocouple voltages and all pressures. The data acquisition system

also allowed for on-line calibration of the pressure transducer used -

for all pressure measurements. A tape cassette and printer were inter-

faced with the computer to record on tape and paper all pertinent data.

The computer was also interfaced with a central disk-storage unit (UNIX)where all pertinent data and computer programs were also stored.

Because of limited printing and plotting capabilities of the desk top

computer, the Iowa State University Computation Center computing system

-' (National Semiconductor AS6) was utilized for data reduction, tabula-

tion, and plotting.

2.5. Calibration Equipment

An air nozzle, described in detail in Reference [4], provided a

uniform nozzle exit velocity suitable for checking probe yaw-angle and

total-pressure calibrations. A pressure reference system [8] was used

to enable on-line calibration of the scanivalve pressure transducer

used for all quantitative pressure measurements. The pressure reference

system consisted of four columns of water, balance scales, and glass P

tubes inserted to an arbitrary depth in each column. The glass tubes

were connected with tygon tubing to the scanning valve. The pressures,

in volts, from each column were read individually and correlated, using P

.... .. .44.4*,,.,* 4 .. . . .. ,,

.4o .. .. . . . • - .*4 o.. . - ..S [ [ ,.-i " " "" " - . . " ' " - •. . - - • . -. -- - - .,

24

PRESSURE

I TO BE READ

SYSTEM

PCONTTOLLER

FMPLTFER

POSITIONER J

COILTTE

TE14PERATURES ATNE SSTM

Fiur 2.1 BcE diagra ofLAG daaCcqANtonsstE.R

CIRCL04RENTIA

MOTION

25

a linear least-squares fit, with the true column pressures. A pre-

cision micromanometer was used in conjunction with the balance scales

to calibrate, using a linear least-squares fit, the pressure of each

column with its corresponding weight. Correlation coefficients of

0.99999 or better could be achieved consistently.

% I

.~2 .

°4'

-4'j:':-

- U . . .. . . . . . . . . . . . . U - L - -

27

3. EXPERIMENTAL PROCEDURE AND DATA REDUCTIONmpU.-.

.- - The objective of the experimental procedure included: 1) gener-

ating an accurate overall performance map in order to establish the

operating characteristics of the baseline compressor over a large

operating range, and 2) obtaining spatially detailed time-averaged

measurements of total pressure and flow angle between adjacent blade

rows, at one flow rate (design condition), in order to determine

pertinent velocity triangle information for comparison with the values

associated with the compressor design code.

The time-averaged measurements were obtained at several span

locations between blade rows, using appropriate probes, with the

,''U. compressor operating at the same design point used in the compressor

design code; i.e. 2400 rpm, with a flow coefficient of 0.587 as shown

*. - in Figure 3.1. The rotor speed was maintained to within ±1 rpm. The

.... flow coefficient was calculated from equilibrium venturi flow meter

data and ambient conditions. Adjustments of the flow to maintain the

reference flow coefficient value were made by moving the throttle plate

at the exit of the diffuser section. Using this procedure, it was

possible to maintain the flow coefficient to within ±0.0005 of the

reference value.

A data acquisition program was written for the PET computer to

control the step-by-step procedures of the experimental tests. Data

were either entered into the computer by the operator or read by the

computer through an interface from the digital voltmeter. The data

acquisition program consisted of seven major parts as shown in the

i - . ,- .- ,.-,.,-,,.-.,, .,.~~~~~....,....:....,....../...-....,.... ........- ,,.........-,........._..........,.....,......,......,-......,.....

-W -. S

28

0.5-

> 0.4/

zS

0.3-

U

0.10.3

0.

0. 0. 0.2 0. 240.RP

VENUR FLO OPRTNCOFITNT.J..

Fi.31Bsln0opesr vrl efrac uv

an peain oit

0.17

.-. ... ,-

9029

logic diagram of Figure 3.2. These parts were:

1. Set flow coefficient and measure test conditions.

2. Input probe survey position parameters.

3. Position probe radially and in your plane. ""

4. Determine circumferential survey parameters with oscilloscope

wake trace.

5. Yaw-null cobra probe in free-stream portion of flow.

6. Measure cobra probe pressures and shroud end-wall static

pressures.

7. Print out data and store data on magnetic disk.'0

In addition, data reduction programs were written for the mainframe

computer (National Semiconducter AS6) to accept data and preliminary

results recorded on disk, and to perform the calculations required to

obtain final results. All data and computer programs stored on tape

(cassette or reel) are listed in Appendix C.

3.1. Calibration

A micromanometer and a mercury-in-glass thermometer were used

respectively as standards for pressure and temperature calibration.

Calibrations of all electronic components used in this experimental

investigation were performed at the Iowa State University Engineering

Research Institute Electronic Shop. Before each test, approximately

one hour of running time was allowed for the electronic instiimeutation

to warm up and for the laboratory and compressor fluid temperatures to

reach equilibrium values.

14 7

30

Ln

w -

---- a.1 = -

V) V) 3c Lnioi<WmwLi.

Lu w i Ln/ l

- DW ; L )a:<L

=-) j - (0

coS< LL- D Ln 4

a'.LL 0a'Q -aLL i

co~CD M V)

= aJ.ce LJ V) CL == LL

9.LL L-C

'a,.) W LA .i LjC

ae= 'a= cF = - : 4=D LJ =D m W LLJ 3 < U g .

7 9 c co ) v) :D I cn :) V--a o (D V) V) LU LnCL C d.1< 0 i -j LJ cc L- L&

< = Li LLJix 4-

C- LC W I

CL'

LLJ1

2c C) 3

31

All time-averaged measurements of total pressure and flow yaw- jangle were obtained using the cobra probe. Extensive total-pressure

and yaw-angle measurement calibrations with the cobra probe in a uni-

form nozzle exit flow have already been documented in Reference [4].

This section will, therefore, deal only with verifying cobra probe

measurements in the compressor. Kiel probe data were used to validate

the cobra probe measurements. The Kiel probe provides accurate total-

pressure information for probe yaw-angles within ±45.0 degrees of the

true flow angle, see Figure 3.3.

3.1.1. Cobra Probe Yaw-Angle Calibration in Free-Stream Portion of Flow

Since total-pressure measurements using the cobra probe are

sensitive to flow angle, it is necessary to determine how accurately the

probe yaw-angle must be set in order to achieve accurate total-pressure

measurements. A comparison of cobra probe and Kiel probe total-pressure

measurements from -45.0 degrees to +45.0 degrees of probe yaw-angle is

shown in Figure 3.3. The test was made behind the first stator,

station 3, 50% span, Y/S. = 0.0 (free-stream) operating at the design

point flow conditions. The results indicate that the cobra probe will

give fairly accurate total-pressure measurements, ±2.0 Nm/Kg, (±0.45%),

if the probe yaw-angle is set within ±5.0 degrees of the true flow angle.

3.1.2. Cobra Probe Calibration in Wake Portion of Flow

Using the cobra probe to measure total pressures can be very

inaccurate if the probe yaw-angle is set too far from the true flow

angle (see Figure 3.3). This can be a significant problem in regions

of high total-pressure gradients, such as in stator wakes, where the

cobra probe cannot be used to accurately determine the true flow angle.

%J % I[loll

0~i 32

5.00

CD CD4.00- Q) CD

~3.0O C CN'

o FIRST STATOR EXIT50% SPAN FROM HUB C

x

~2.00 0 COBRA PROBEAKIEL PROBECDD

V.~ 1.00 C) o

O.OIt

-48.0 -36.0 -24.0 -12.0 0.0 12.0 24.0 36.0PROBE YAW ANGLE, DEGREES

Figure 3.3 Cobra probe yaw-angle total-head calibrationcurve in free stream portion of flow for

a.-.,flow coefficient 0.587 at 2400 rpm.

/*'

' ' ' * -.- - - . 77 -77P-7771- -rr r .7 i

In order to circumvent this problem, the cobra probe yaw-angle in the

wake region is set to the integrated-average free-stream flow angle

measured by the cobra probe. A comparison of the cobra probe and Kiel

probe measurements--with the Kiel probe set at the integrated-average

.- free-stream flow angle--is shown in Figure 3.4. This comparison test

was made behind the second stator, station 5, 50% span, operating at

the design point flow conditions. The results show very good agreement

in the free-stream regions, +5.0 Nm/Kg (±0.6%). The wake region data

also show good agreement in total-pressure levels, but some slight

shifting of the wake position is evident.

-'.. 3.1.3. Spanwise Calibration of the Cobra Probe

A spanwise comparison of cobra probe and Kiel probe total-head

measurements are shown in Figure 3.5 for flows behind the first rotor

and first stator. The results show fairly good agreement between the

cobra probe and Kiel probe measurements, less than 10.0 Nm/Kg (1.7%)

difference, except near the end-walls where the difference was as much

as 17 Nm/Kg (4.5%). The larger error near the end-walls was suspected

to be due to wall effects. Total-head measurements behind the first

rotor were generally better than behind the first stator.

3.1.4. Scanivalve Pressure Transducer Calibration

On line pres. ure-transducer calibration was accomplished using a

pressure reference system consisting of water columns and triple-beam

r balances. The pressure reference system is described in detail in

Reference 18]. The system provides four reference pressures against

I-.' which the pressure transducer can be calibrated. The pressure trans-

ducer is calibrated every time the flow coefficient is to be readjusted

%, .

Z . . . . . . . . . . .

34

10.00

SECOND STATOR EXIT50% SPAN FROM HUB

* - 0~9.00

8.00 - 0. COBRA PROBE

,L' KIEL PROBE

CS

~7.00

6.001III0.00 0.20 0.40 0.60 0.80 1.00

FRACTION OF STATOR BLADE PITCH, Y/Ss

* . Figure 3.1& Cobra probe total-head calibration curve in wake portion offlow for flow coefficient -0.587 at 2400 rpm.

lip

-,- , 79. 1 . - T, " . W-

35

6.00FIRST ROTOR EXIT

0 COBRA PROBEZ KIEL PROBE

5.00 -

N

4.00[

5.00FIRST STATOR EXIT

.Co-r

4.00

3.00 I I t I0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

Figure 3.5 Cobra and Kiel probe comparison behind first rotor and firststator for flow coefficient - 0.587 at 2400 rpm (Y/S S = 0.0).

00

.%.%

.S..

-p...

.' . . .. . - . , - . . - . . . : . , _ . ,,. . . . . . . . . . . . . . . . . . . . . , . . . . . . . . . . . . • . . . . . - . . . . . . . . -

36

. prior to taking any total-pressure measurement. Periodic on-line

recalibration of the pressure transducer helps reduce thermal drift

and other transient errors inherent in strain-gauge transducers of

this type. Tests have shown that the reference pressures can be deter-

mined with resolution better than 0.003 inches (0.076 mm) of water.

All pressure reference columns are calibrated using the precision micro-

manometer. Calibration of the pressure reference system is performed

once every three months or more often as needed.

An additional water column is used to provide a back pressure to

the scanivalve transducer in order to insure that the pressure trans-

ducer is always displaced from zero. This eliminates errors from

having the transducer pressure fluctuate around zero. On-line cali-

bration of the pressure transducer consists of a linear least-squares

correlation of transducer output voltage versus the known reference

column pressures. The reference column pressures are determined from>.

%" linear least-squares correlation equations entered into the computer

which have been previously determined from a calibration of column

pressure versus column weight. Therefore, it is only necessary to

weigh each column prior to testing in order to determine the reference

column pressures. During on-line calibration, each column pressure

and transducer voltage recorded is referenced to one of the columns,

the same column each time. Again, this is done in order to reduce

_. errors due to thermal drift as well as other transient errors between

successive readings. In addition, it helps insure that the linear

correlation goes through zero, as it should. As mentioned earlier,

this procedure consistently provided a linear correlation coefficient

-:,.-

, .- _ ', -' . -. . - .... . . . . .. ...... . ., •* * . , ..-.. . -. . .. .... '.. --. V. .

37

of transducer voltage versus column pressure of 0.99999 or better. The

calibration is repeated if this correlation criterion is not met.

,, 3.2. Data Aquisition

The data acquisition procedure consisted of obtaining two types of

information: overall performance data, and spatially detailed time-

averaged measurements of total pressure and flow angle between adjacent

blade rows. The details of obtaining both types of measurements are

described below.

3.2.1. Overall Performance Map

The overall performance map parameters are based on compressor

drive motor torque meter measurements (to establish the compressor

ideal head rise), static-head measurements at the compressor exit (to

estimate the actual head rise), and venturi flow rate measurements (to

determine the compressor flow coefficient). The above procedure was

used to quickly and accurately establish a performance map for the

baseline compressor. The method for establishing the compressor exit

total head relies on the stator exit swirl being zero and, therefore,

the static head at that station being a constant across the span. The

venturi-measured flow rate was used to determine the average axial

velocity at the compressor exit which, since the swirl is zero, is also

the fluid velocity. Using the measured circumferentially-averaged

static head and the computed average fluid velocity at the compressor

exit, the compressor exit total head was determined. The actual head

rise delivered to the working fluid could then be determined by

b • • .S

38

referencing the compressor exit total head to the total head at the

compressor inlet (atmospheric conditions, zero velocity).

The measurements involved in establishing the performance map were

obtained as follows. With the compressor operating at 2400 rpm, the_I.

diffuser exit throttle plate was adjusted to provide incremental con-

trol of the compressor flow rate. At each flow rate, venturi flow

meter measurements, torque meter measurements, and compressor exit

static-head measurements were recorded along with other pertinent

data related to the operating and ambient conditions. The torque meter

measurements were obtained with the compressor drive motor floating on

air bearings while various weights were added to the torque arm in

order to balance the drive motor torque. A calibrated meter employing

an incremental load transducer consisting of a solid-state gauge bridge

on a cantilevered beam was used to resolve torque arm loads to within

±0.0125 Kg. The meter was calibrated to read from 0.0 Kg to 1.0 Kg full

scale. Meter fluctuations due to motor vibrations and minute torque

fluctuations reduced torque measurement accuracy to within ±0.25 Kg.

Static-head measurements at the compressor exit were obtained from four

equally spaced (circumferentially) outer annulus-wall static pressure

taps. The measurements were made while decreasing the flow rate from

maximum flow rate unti1 stall occurred and then repeating the measure-

ments from stall to the maximum flow rate. The stall limit was

accurately established by adjusting the flow rate until a slight

disturbance at the diffuser exit would instigate a full span stall,

which was audibly detectable. Once the stall flow rate was determined,

measurements were made just before and after stall.

4.k"'.'"-

'p-

39

3.2.2. Time-Averaged Measurements

Time-averaged total pressure and flow angle data variation in the

radial, axial, and circumferential directions of the compressor flow

field were obtained with the cobra probe set at five passage height

locations of 10%, 30%, 50%, 70%, and 90% of span from the hub--ahead of

and behind each of the rotating and stationary blade rows--at several

circumferential positions over one stator pitch. In addition, outer

annulus-wall four-hole-averaged static-pressure measurements were made

at each axial measurement location. The steps followed to obtain these

data are described below.

Prior to testing, several preliminary setups were accomplished.

The cobra probe was mounted in the probe actuator and the probe yaw-

angle zero was set by balancing the side-tube pressures with the probeIp.

immersed in the calibration nozzle jet. The probe radial positioning

was set using a depth micrometer. The probe actuator mechanical

counters were set to read zero yaw-angle for compressor axial flow and

5.6 inches (14.22 cm) for contact with the hub surface. Thus, the

.. counters would indicate true probe angular and radial positions. All

calibrations were performed through the data acquisition system with

sthe PET computer controlling the calibration procedures. Before each

test, the scanivalve pressure reference system columns were refilled

with water to predetermined levels and each column was reweighed. The

reference column ice bath was checked and reiced if necessary.

The following miscellaneous data were recorded by the computer for

-. each test to insure the attainment of intended measurement conditions.

a7t,

- V...- ° ° o Q . °. 4j°S. ° :8 $\ "2.'° . '° .-. . .- . .. - . . . <.* - .. . .. . . . • °

40

1. Probe axial measurement station number, (see Figure 2.5)

2. Compressor rpm

3. Static pressure difference across venturi throat, N/m2

4. Barometer ambient temperature, degrees Kelvin

25. Barometric pressure, N/m

6. Temperature at compressor inlet, degrees Kelvin.2' m2 K i

7. Static pressure at venturi throat, N/n

8. Temperature at venturi throat, degrees Kelvin

9. Date

10. Time

The circumferential surveys were made by moving the stators

circumferentially past a stationary probe located at one of the probe

axial measurement stations at the proper depth of immersion. Figure 3.6

- shows, to scale, the axial position and extent of each circumferential

measurement window as well as the circumferential survey coordinate

" direction. A qualitative trace of total pressure versus circumferential

position with the probe set at the approximate average flow angle was

recorded on an X-Y storage oscilloscope screen from the electrical

signals of the strain-gauge pressure transducer and the circumferential

motion potentiometer. The trace was used in selecting the spacing of

circumferential measurement points and in determining the extent and

position of the wake and free-stream regions. For each survey,

measurements were made over one stator blade pitch. The circumferen-

e , tial measurement positions in the wake and free-stream regions were

% determined by the computer, based on the number of free-stream circum-

ferential measurement positions desired and the circumferential measure-

%J ,

"-.-

"'" ." "" g " " "

41

MEASUREMENTx x STATION 1

FIRSTROTOR

MEASUREMENT

STATION 2

.- FIRSTSTATOR

MEASUREMENT

STATION 3

SECOND

-,. MEASUREMENT" - STATION 4

SECONDSTATOR

MEASUREMENT

i0.0 0 STATION 5

Y/SS

Figure 3.6. Blade cascade showing cicumferential measurement window.

........... .... ,... .. . . . .. . . .

. S. -. ,...

"S*

42

ment increment desired in the wake region. Flow angle measurements

were made by balancing the cobra probe side-tube pressures through a

computer controlled algorithm or by manual over-ride with the aid of a

) N U-tube manometer. Flow angle measurements were made at every flow

* .field measurement point behind a rotor blade row and at free-stream

.. measurement positions only behind stator blade rows. The circum-

. ferentially-integrated-average free-stream flow angle was thenI DI-

determined with the computer acquisition program and this flow angle

was used when making total-pressure measurements in the corresponding

--.'. stator wake regions of each circumferential survey. The probe yaw-

angle, circumferential position, and total pressure were recorded at

each circumferential measurement point. After the last measurement

at each circumferential survey was taken, the miscellaneous data,

-" flow-field data, and measured circumferentially-averaged static head

were printed out and stored on magnetic disk for reduction at a later

time.

.. 3.3. Data Reduction.? ,-'

Preliminary reduction of the time-averaged data was performed

during data acquisition and consisted of determining primary flow-field

values of total head, static head, and absolute flow angle. These

primary values were then read into the data reduction program where -

other flow-field parameters such as absolute velocity, relative

velocity, incidence angle, deviation angle, etc., were calculated along

with their circumferentially-averaged values. Finally, overall rotor, "

.'., -' . 5 . . . . . .-

*,.. .. .. .- h . . .

43

stator, and stage performance parameters such as ideal head-rise (Euler

* . turbine equation based values), actual head-rise, efficiencies, and

losses were determined. The flow was assumed incompressible for all

*" - calculations as the velocities involved Mach number levels less than

0.2. Integrated values were computed using a spline-fit integration

[9]. A complete list of all quantities and equations used in reducing

the data is presented in Appendix D.

3.3.1. Flow-Field Parameters

The total head was determined at each flow field measurement point

from the cobra probe measured total pressure. Circumferentially-

averaged values of total head and absolute flow angle were determined

for each radial position at every axial measurement station. All

circumferential averages except for flow angle averages behind stator

" blade rows were determined by integrating over one stator blade pitch.

The circumferentially-averaged absolute flow angles behind stator blade

rows were obtained by integrating over the free-stream portion only.-p'... The static head was assumed to be circumferentially constant, and the

V radial distribution of static head was determined at each radial posi-

tion for every axial measurement station by solving the radial equi-

librium equation in the following form:

2-dh 2 sin (H-h)dr r (see Reference [4]) 3.1

using the Runge-Kutta numerical technique [10]. The circumferential-

averaged outer annulus-wall static he3d was used as an initial value,

and the solution was obtained by marching radially toward the hub at

%-N.

A%. ..

.- - . r C

, - 44

increments of 5% of passage height. The circumferentially-averaged

-. values of total head and absolute flow angle required at each step of

the Runge-Kutta solution were obtained by a second-order Lagrange inter-

polation of their measured radial distributions.

From the radial distributions of total head, absolute flow angle,

and static head; the circumferentially-averaged absolute velocity was

determined at each radial position for every axial measurement station.

With the circumferentially-averaged absolute velocity and the flow angle

determined, the following circumferentially-averaged variables were

calculated at each radial position for every axial measurement station.

* 1. Axial velocity, m/s, Eq. 12.16

2. Absolute tangential velocity, m/s, Eq. 12.18

3. Relative tangential velocity, m/s, Eq. 12.20

4. Relative velocity, m/s, Eq. 12.22

5. Relative flow angle, degrees, Eq. 12.24

6. Blade incidence angle, degrees, Eq. 12.25 and Eq. 12.27

7. Blade deviation angle, degrees, Eq. 12.26 and Eq. 12.28

8. Flow coefficient, Eq. 12.29

In addition, for each axial measurement station, an annulus cross-

section integrated flow coefficient was calculated for comparison with

the flow coefficient determined from venturi flow meter data. In

determining the annulus cross-section flow rate and corresponding flow

coefficient, the axial velocities at the hub and shroud end-wall

surfaces were assumed equal to zero.

9._,... ..........1,.,., .. _... .... ... . . . .. ... . .

-45

3.3.2. Performance Parameters

The actual and ideal (Euler turbine equation based) head-rise

coefficients and their ratio (hydraulic efficiency) were determined at

each of the five radial positions for both rotor rows, stages, and for

the overall compressor. Total-head loss coefficients were also deter-

mined for each rotor and stator blade row. In addition, radially

mass-averaged values of each of the above quantities were determined

for both rotor rows, stages, and for the overall compressor (see

Appendix E). The above parameters were calculated from spatially

detailed time-averaged measurements and circumferentially-averaged

• . values of the previous section.

Performance map parameters and mechanical efficiency were calcu-

"- lated from motor torque-meter measurements and the overall head-rise

ft ,across the compressor. The overall head-rise for the performance map

was determined from the measured venturi flow rate and the circumferen-

tially-averaged static head at the outer annulus-wall of the last axial

measurement station.

ft.'.%

" . -

0,o.

0' f,

U-L

47

4. PRESENTATION AND DISCUSSION OF DATA

The results of the torque meter related performance measurements

and the slow-response (time-averaged) data are presented and discussed

in this section. Comparisons between these measured results and cor-

responding calculated values associated with the design code are also

presented and discussed. The design code results are tabulated in 3Appendix B. The experimentally determined data are tabulated in .

Appendix E. In gra,hing the results, all data variation curves--except

for the performance curves--were drawn with interpolated curves through

the actual data points. Smooth curves were drawn through the per- C

formance map data using a least-squares fit. All measured data points

are graphed with a symbol marking the actual data point. The design

code results are represented with continuous curves.

4.1. Error Analysis

Measurement errors associated with the primary measurement quan-

tities and flow-field parameters are presented in Table 4.1. Repre-

sentative values of each primary measurement quantity and flow-field

parameter are presented, along with their estimated uncertainty and Ipercentage of error. The uncertainties of the flow-field parameters

were determined using the procedures of Kline and McClintock [11I based

on the estimated uncertainties associated with the primary measurement

quantities. The estimates of the uncertainties of the primary measure-

ment quantities were based on the repeatability of the measurements,| -04

and comparisons with the Kiel probe in the case of total pressure

,"7

S ' .°• " ' .• " . " . " . -• -. .. . . °

,' '.' ...... ... .... .- .. . . . . .. .. . . . . .. . • . .. .. . . . -.. .. .. .. . . ..~ .. . ...

48

Table 4.1. Uncertainty estimates of measurement parameters.

Typical Estimated UncertaintyFlow Parameters Symbol Values (20-to-1 odds)

Primary measurements

Temperature t 299 deg. K 0.25 deg. K (0.08%)

Transducer pressure Pt 52.0 mm Hg 1.2 mm Hg (2.2%)tS

Absolute flow angle B 20.0 deg. 1.0 deg. (5.0%)y

Barometric pressure P 735 mm Hg 0.03 mm Hg (0.003%)atm

Torque T 4.0 Kg 0.03 Kg (0.6%)

Flow field parameters

Absolute velocity V 30.0 m/s 0.3 m/s (1.1%)

Axial velocity V 28.0 m/s 0.4 m/s (1.3%)Z

Absolute tangentialvelocity V 10.3 m/s 0.5 m/s (4.9%)

y

Relative flow angle B' 50.0 deg. 0.6 deg. (1.1%)y

Performance parameters 5

Actual head-risecoefficient k 0.17 0.004 (2.3%)

Ideal head-risecoefficient %P . 0.19 0.02 (8.7%)1

Hydraulic efficiency 0.88 0.07 (8.0%)

Rotor total-head losscoefficient wR 0.05 0.03 (60.0%)

Stator total-head losscoefficient w 0.06 0.02 (33.0%)

Ideal work coefficient W. 0.4 0.005 (1.3%)1. Opm .

Mechanical efficiency lme 0.75 0.01 (1.8%) S

...

49

measurements. The uncertainty levels given in Table 4.1 are generally

* - consistent with the random scatter observed in the results. It should

*-" be noted that the uncertainty levels tend to be higher near the end-

walls (see Figure 3.5).

Of the primary measurement quantities, absolute flow angle

measurements have the most uncertainty, primarily because of the total-

pressure gradients affecting the cobra probe yaw-angle measurements.

Behind the stator blade rows, ascertaining the circumferential extent

of the free-stream--particularly near the end-walls--was difficult.

Comparisons of total-head measurements obtained using a cobra probe

and Kiel probe were presented in section 3.1. These comparisons

show that even with the uncertainties of determining the absolute flow

angle, the cobra probe gives a fairly accurate measure of the totalIS

head. Performance parameters based on the Euler turbine equation ideal

head-rise, however, are highly dependent on the accuracy of the absolute

flow angle measurements (see Table 4.1). It would be reasonable to

*" conclude, therefore, that very little confidence can be afforded the

Euler turbine equation based performance parameters. The effect of

torque measurement accuracy on the torque based performance parameters

is also given in Table 4.1. The torque based efficiencies are more

reliable than the Euler turbine equation based efficiencies, but only

as an indicator of relative measure. The torque based efficiencies

e.." were very repeatable, but were highly dependent on the mechanical

characteristics of the compressor and drive motor which affected the

absolute measure of the efficiencies. Since the torque meter based

efficiencies were affected by bearing friction and other mechanical

Z.I

".' -"' "-" ,, . . . ."""""''- -' """- --- """""" - -.:- - .""""'"- - - -""""""- - .: '''.."' . .-.. . . . .. . ..I' ""

' ,. 50 -.,

losses, they are not reliable as an absolute measure of efficiency.

However, with precautions they are a reasonable indicator of relative

measure of efficiency.

All time-averaged measurements were obtained with the throttle

plate adjusted so that the venturi flow coefficient was within ± 0.0005

of the desired flow coefficient of 0.587. An integrated average flow

coefficient based on the spanwise distribution of circumferential-mean

axial velocity--as determined from cobra probe measurements--served

as a check between venturi based and cobra probe based flow coeffi-

cients. Comparisons of the integrated flow coefficients and venturi

flow coefficient for each axial measurement station are given in

Table 4.2. The integrated flow coefficient was obtained by two dif-

ferent approaches; 1) using the extrapolated circumferential-mean

axial velocity at the end-walls, and 2) by considering the circum-

ferential-mean axial velocity to be zero at the end-walls. A spline-

fit integration routine [9] was used to perform the integration. Even

2 with only five spanwise measurement locations, the integrated-average

flow coefficients--based on zero axial velocity at the end-walls--

compared very favorably with the venturi based flow coefficients. The

integrated flow coefficients--based on extrapolated circumferential-

mean axial velocity at the end-walls--were consistently higher than the

venturi based flow coefficients.

"2"

-%

're.4.t

. -i Q , ' ",~r.. •* .. "W .q.- * • . V .. ". '° -" ° . . .. .

51

Table 4.2. Flow coefficient comparison between venturi and integratedmeasurement station flow coefficients.

V extrapolated to endwall V = 0.0 at endwallz z

Flow FlowCoefficient CoefficientComparison Comparison

Station Percent Station Percent

1 6.0 1 1.0

2 4.4 2 -0.2

3 2.5 3 -1.9

4 3.4 4 -1.0

5 o.8 5 -2.9

4.2. Overall Performance Map

The results of the torque meter related performance tests are

- presented in Figure 4.1. Overall compressor head-rise coefficient,

work coefficient, and efficiency variations with flow coefficient are

plotted. The curves were obtained by recording venturi flow rate,

compressor exit (station 5) shroud static pressure, and drive motor

.... torque. The venturi flow rate was used to determine the average axial

velocity at the exit of the compressor. Since swirl was virtually non-

* .~ existent at the compressor exit, the static pressure was presumed

constant across the span; thus making it possible to determine repre-'• . .

sentative total pressures and subsequent head-rise coefficient at the

compressor exit. The torque meter measurements were used to determine

'.' .. .. o. • % , ... . ., . -. '• '°'. ' . V. ." .' . . . '.. •..,.. . . ...... -.- . .. • .... . .. *.' • -" ... . .

'" ---,---.-.',. .-. - .. '°- -'-'--..--'.-''- - ,''-. " " < ,. , ". -- "" .-"-".3 . •.' .- ,- - *. .' .. -.-. -

".' .-"52

0.80

.-- , 0.70

I- 0.60

0.50-

0.402400 RPM

+ TORQUE METER RELATED TESTS

4. .** E

Q DETAILED MEASUREMENTS0.30 * PREDICTED

0.20 --0.20 0.30 0.40 0.50 0.60 0.70

,DA VENTURI FLOW COEFFICIENT

(a) WORK COEFFICIENT

a.Figure 4.1 Predicted and measured overall performance data.

...... ......... ............ ..... .. l

* . - p * S . . - 6-

53

40.6

0.50

LU

.40.0

0.30

S0.40

240 RPM

0.0

0.0 0.0 04 .5 .0 07

0o 0 DETILE MESUEMENTISEOFIIN

0.10r 4. PREDICTED.

.4%

54

1.00

2400 RPM

+ TORQUE METER RELATED TESTS0.90',0 DETAILED MEASUREMENTS0.90 K PREDICTED

0.80

.70

,l",(.)

U-

*~* 0.70

.a_

0.60 "

0.50

0.401III0.20 0.30 0.40 0.50 0.60 0.70

VENTURI FLOW COEFFICIENT(c) EFFICIENCY

rFigure 4.1 concluded.

I,

,,,)

;L•'.

the work coefficient from Equation 13.50. Also noted in Figure 4.1

are the design point overall head-rise coefficient and hydraulic

efficiency as determined from the detailed time-averaged measurements

and Euler turbine equation based ideal head-rise, as well as the design

point overall hydraulic efficiency and head-rise coefficient predicted

from the design code. Both measured efficiencies corresponding to the

design point flow coefficient are significantly lower than the pre-

dicted efficiency. The reason for this discrepancy will be explored

further in a later section (4.4. Comparisons of Circumferential-Mean

Data with Design Code Predictions).

As mentioned in the previous section, the Euler turbine equation-

based performance parameters are highly dependent on the accuracy of

the absolute flow angle measurements and are, therefore, unreliable

measures of compressor performance. Although the relative character-

istics of the performance curves depicting work coefficient and

efficiency variations with flow coefficient proved to very repeatable,

the absolute values of each curve were sensitive to the mechanical

characteristics of the compressor, such as bearing friction. These

mechanical effects appeared as shifts in the absolute magnitudes of

the torque measurements which tended to move the level of the work

coefficient and efficiency curves, but did not significantly affect

the relative aspects of each curve. The head-rise coefficient curve

was consistently repeatable and compared favorably with the design

point overall head-rise coefficient determined from the detailed time-

averaged measurements, thus lending credence to the procedure used in

determining the head rise versus flow coefficient performance curve.

°. %

- :,. . . . .:... . . % .. .'-....... ? .:. .... ......... .. .

10156

Because of the effects of bearing friction on torque measurements, the

performance curves could not be used for absolute predictions of the

compressor performance. Thus, no means were available for comparing

the design program efficiency predictions.

To obtain an accurate performance map which could be used for

absolute as well as relative measures of efficiency, the compressor

should be run without blading to measure the tare torque; thus obtain--Ib •

ing corrections for bearing friction and other mechanical effects.

Without regreasing the bearings and with the blades reinstalled, a new

performance map could be generated from which the tare torque is sub-

tracted. This procedure was not attempted because of insufficient

time.

The curve of compresscr efficiency variations with flow coeffi-

cient shows an uncharacteristic flat portion where the efficiency is

essentially constant over a range of flow coefficient values. The flat

portion of the efficiency curve may be due to the fact that blade

losses were constant over a range of incidence angles. However, there

may also be some over-riding effect that is causing slight improvements

in efficiency to be "washed out." For example, Wisler [2] shows a con-

.. siderable Reynolds number effect on compressor efficiency for a low-"

speed four-stage axial-flow compressor. Wisler's results show a

-P... flattening of the efficiency curves as the Reynolds number is decreased.

The Reynolds number range examined by Wisler was 1.0 X 105 to 4.0 x 105.

The Reynolds number for the baseline compressor is about 1.8 X 105.

Further discussion of the constancy of compressor efficiency over a

range of flow rates may be found in Reference 12.

,'

57

4.3. Spatially Detailed Time-Averaged Measurement Results

• "Detailed time-averaged aerodynamic data were obtained in the

baseline compressor at numerous circumferential positions for 10%, 30%,

50%, 70%, and 90% span locations--measured from the hub, ahead of and .

behind each blade row. The axial measurement locations and circum-

ferential survey windows relative to each blade row are shown in

Figure 3.6 for one spanwise location. Figure 3.6 should be referred .

to when analyzing the figures in this section. All total-head measure-

ments presented in this report are referenced to atmospheric conditions.

Graphs of the blade-to-blade distribution of total head for all spanwise

-. '. locations at each axial measurement station are illustrated. Figure 4.2

is for flows behind the first- and second-stage rotors, and Figure 4.3

is for flows behind the first- and second-stage stators. The data for p

flow behind the second rotor (Figure 4.2) indicate a peculiar pattern

involving two regions of lower total head. This unexpected trend is

explained in Reference 12. The detailed time-averaged measurement data

.: were used to obtain circumferential-mean values of total head, flow

angle, and absolute velocity. The spanwise distributions of these

circumferential-mean quantities are shown in Figure 4.4, for ti ws

behind the first- and second-stage rotors, and in Figure 4.5, for flows

behind the first- and second-stage stators. The graphs of the spanwise

distributions of circumferential-mean total head and axial velocity "

behind each blade row (Figure 4.4 and 4.5) show significantly lower

total head and axial velocities at the 90% from hub measurement loca-

tion indicating higher losses near the shroud end-wall there. Evidence P

A-.

. . . . . . . . .. . . . . . . . . . . . . . . . . .

58

5.00

FIRST ROTOR EXIT

4.0

SECOND ROTOR EXIT -

8.0

FIRST ROTOR EXIT V

4. 50

SECOND ROTOR EXIT

.8.5

0.00 0.20 0.40 0.60 0.80 1.00 1.10 .FRACTION OF STATOR PITCH I(b 70% SPAN FROM HUB

Figure 4.2 Blade-to-blade distribution of time-average total head for '

flow behind the first and second stage rotors (4=0.587~s at 2400 rpm).

4 -%

__7.

* 4 59

5.50FIRST ROTOR EXIT

4.50Q

SECOND ROTOR EXIT

.77.50 IIp0 (c) 50% SPAN FROM HUB

00

8.50

SECOND ROTOR EXIT

7.50 10.00 0.20 0.40 0.60 0.80 1.00 1.10

FRACTION OF STATOR PITCH(d) 30% SPAN FROM HUB

Figure 4.2 continued.

p..

60

5.50

FIRST ROTOR

0 .0(

x

01

SECOND ROTOR EXIT

7.00 III0.00 0.20 0.40 0.60 0.80 1.00 1.10

FRACTION OF STATOR PITCH(e) 10% SPAN FROM HUB

Figure 4.2 concluded.

9LA

:W -. 6 -. a* I -. . . . . . .

61

.5.4.50

4.50(p

%S~. E

.2.50

0.5

01.50

-0.50

0.00 0.20 0.40 0.60 0.80 1.00 1.10FRACTION OF STATOR PITCH

(a) 90% SPAN FROM HUB

Figure 4.3 Blade-to-blade distribution of time-average total head forflow behind the first and second stage stators (~=0.587at 2400 rpm).

62

9.00

8.00

CJ7.00'

6.0

4 .000.0 02 .006008 .0 11

FRACSECON STTF EXIT PTC

(a) 90% SPAN FROM HUB

Figure 4.3 continued.

63

3.00

~3.0

2.00

0 FIRST STATOR EXIT

C1.00 III

8.0

7.00

6.00 SECOND STATOR EXIT

up0.00 0.20 Q.40 0.60 0.80 1.00 1.20

FRACTION OF STATOR PITCH

(b) 70% SPAN FROM HUB

Figure 4.3 continued.

643

3.00

*-2.00

Cj FIRST STATOR EXIT

9.5

* 8.5

7.50

6.50

SECOND STATOR EXIT

a... 5.50 I0.00 0.20 0.40 0.60 0.80 1.00 1.10

FRACTION OF STATOR PITCH

()50% SPAR FROM HUB

Figure 4.3 continued.

a.

W. 2

65

5.00

p.003.00

E2.00 FIRST STATOR EXIT

x0 .5

*8.5

.50

5.50,

Fiue . cnine

lot.5

66

5.00

4.00-

)U

3.00

A= 2.00.14

0,p. FIRST STATOR EXIT

- x

.. 1.0o I I I I

- .0

7.00-

SECOND STATOR EXIT

6.00I0.00 0.20 0.40 0.60 0.80 1.00 1.10

FRACTION OF STATOR PITCH(e) 10% SPAN FROM HUB

Figure 4.3 concluded.

J .) ,.:, ...:-+ ,. ..:..-,'.,'..:z , ,-. ; :/-;-;-:.-.. .-- -:.- .-'.-.... .'.-.' .'.: ..........---.:--...--:.. :..,:-..:.-:.. ..,>->. -.:.,i

I J .",' L J" -.'.,"..-.''. ' ..'' -" , ."w :w: ' . .'. :,'"" '% % -, " . ''- ,-,-,'.-'"' . . , ", "",:,". " "S

S5.0

E5O FIRST ROTOR EXIT

44 x 4.001

9.50 SECOND ROTOR EXIT

Vi8.50 -'

-I

LL7.501 1 1 1 1 I

~, 0.00 20.0 40.0 60.0 80.0 100.0PERCENT SPAN FROM HUB

(a) TOTAL HEAD

Figure 4.4 Spat'.wise distribution of circumferential-mean data for flow SP behind the first and second stage rotors (~=0.587 at 2400

rpm).

68

26.0

26.00 FIRST ROTOR EXIT Icz

Ls

S22.00

1800

261.00 III

SECOND ROTOR EXIT

~- 22.00

z

(b BOLT LO NL

Fiue4. otiud

117 W.2..

69

32.00

I-

30.00

C 28.001 II

S33.00

SECOND ROTOR EXIT

.- 3.0

293.00

29.00 1

0.00 20.0 40.0 60.0 80.0 100.0PERCENT SPAN FROM HUB

* (C) AXIAL VELOCITY

Figure 4.4 concluded. I

* . 70

4.50

FIRST STATOR EXITj

'3.50

SECOND STATOR EXIT

S8.00Jj

U.

7.001II0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

(a) TOTAL HEAD

- Figure 4.5 Spanwise distribu~tion of circumferential-mean data for flowbehind the first and second stage stators (~=0.587 at2400 rpm).

. ...* . .'V%

71

4.00

LULU

.~..M 0.00

LU

39

S-4.00 FIRST STATOR EXIT

U,

S4.00

S0.00 .

LU

-4.00 SECOND STATOR EXIT

0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

.4 1 (b) ABSOLUTE FLOW ANGLE

Figure 4.5 continued.

4%

72

34.00

FIRST STATOR EXIT

32.00

30.00

280 -S

26.0

32.00

27! 3.001

PERSECON STATN EXITHUW XA VLCT

Fiue4. ocldd

73'a--

of hub end-wall effects appears behind the second rotor and stator as

seen by the appreciable decrease in total head and axial velocity levels

there.

Circumferential-radial plane contour maps of total-head variation

at each axial measurement location are presented in Figure 4.6.

Figure 4.7 shows the locations of the actual data points used in con-

structing the contour map for station 3. The single-stator pitch data

actually acquired were repeated over two stator blade pitches in order

to afford better visualization of the flow pattern. The abscissa and

ordinate correspond to fraction of blade pitch, Y/Ss, and percent span

location measured from the hub, PHH. The actual data were taken

between Y/SS = 0.0 to Y/SS = 1.0. In order to provide a smoother repre-

sentation of the flow pattern, a data enhancement option provided by

the contour plotting program was utilized. The data enhancement option

was only employed in the radial direction since there were an adequate

number of points available in the circumferential direction. For each

contour map, an additional five enhanced data points between each pair

of actual data points in the radial direction were requested. For the

contour map of station 3, there were five circumferential survey line I

segments consisting of an equal number of data points--for this case

51--therefore, the total number of enhanced data points was ((5-1)*5*51)

= 1020. The data of station 3 without enhancement are shown in

Figure 4.8 for comparison with enhanced data contours of Figure 4.6(b).

The contours with enhanced data are a slightly smoother representationII of the flow field. Trends, however, are not significantly altered by

iN the enhancement process.

a-- "i* . - . . a

74

(a) FIRST ROTOR EXIT STATION 2TIP

go% 90%

co 70

.2 o%

.30% 30U-

10% HB 1p

-0.50 0.-

000 0.00

FRACTION OF STATOR PITCH

KEY-ftCURVE CURVE

LAB EL VALUE1 O.415O00E 03 Nm/kg2 0.430000E 03 Nm/kg3 0.445000E 03 Nm/kg4 0.460000E 03 Nm/kg

ft5 0.475000E 03 Nm/kg

Figure 4.6 Contour map of the distribution of total head behind eachblade row ()=0.587 at 2400 rpm). Data enhancementemployed.

ITIP

/5 -U

gok 0

cO 1 ak 7j(b)o FIS50AOREITSATOw

0 S

U-U

T T - -. T

-0...50 0.00 0.50

FRACTION OF STATOR PITCH

KEY

CURVE CURVE4...LABEL VALUE

1 0.150000E 03 Nm/kg2 0.200000E 03 Nm/kg3 0.250000E 03 Nm/kg4 0.300000E 03 Nm/kg

I..5 0.350000E 03 Nm/kg6 0.380000E 03 Nm/kgA7 0.410000E 03 mk8 0.430000E 03 Nm/kg9 0O.450000E 03 Nm/kg10 0.470000E 03 Nm/kg

* -. Figure 4.6 continued.

J... 76

()SECOND ROTOR EXIT STATION 4TIP

co -7 0% -70

ejS

50% 50%

U.7.00

FRCINOU-AO IC

-KEY

4 0.80000E0.00/k

CUV CURVOOE 0 mk

10 0.930000E 03 Nm/kg

2 iur 4.600 03 ng ed.

77

(d) SECOND STATOR EXIT STATION-5- TIP

7---

90k.0

co I 70S

0.0

0-50 -0-5

00 7.

0S

FRACTION OF STATOR PITCH

KEY

CURVE CURVELABEL VALUE1 0.550000E 03 Nm/kg2 0.600000E 03 Nm/kg3 0.650000E 03 Nm/kg4 O.700000E 03 Nm/kg "5 0.750000E 03 Nm/kg6 0.800000E 03 Nm/kg

v7 0.830000E 03 Nm/kg8 0.860000E 0 Nm/kg

49 0.880000E 03 Nm/kg 410 0.900000E 03 Nm/kg l

Figure 4.6 concluded.

78

0FIRST STATOR EXIT STATION 3

TIP

90% 9ox

03 0

mmm~~ m m mmm .m m mU-1

5-. 30% 3,

p5-4

-0 5 0 .0 0 0 .5 0 7 0'.5 FRACTION OF STATOR PITCH

NOTE: SINGLE PITCH DATA ACTUALLY ACQUIRED REPEATED OVER TWO

STATOR BLADE PITCHES FOR VISUALIZATION ENHANCMENT

Figure 4.7 Locations of actual data paints used in constructing the

contour map behind the first stator.

U,- 79

FIRST STATOR EXIT STATION 3

TIP

00

050 0.050 p-1.0 7.-

FRACTION OF STATOR PITCH

KEY

CURVE CURVELAB3EL VALUE1 0.150000E 03 Nm/kg2 0.200000E 03 Nm/kg3 0.250000E 03 Nm/kg4 0.300000E 03 Nm/kg5 0.350000E 03 Nm/kg6 0.380000E 03 Nm/kg7 0.410000E 03 Nm/kg*8 0.430000E 03 Nm/kg9 0.450000E 03 Nm/kg 0

'N10 0.470000E 03 Nm/kg

Figure 4.8 Contour map of the distribution of total head behind thefirst stator (4=0.587 at 2400 rpm). No data enhancement.

A,

80

The contour map of total-head variation behind the first rotor,

Figure 4.6(a), indicates a fairly uniform total pressure level distri-

bution with some evidence of an end-wall loss region (lower total head) -

from about 70% span to the shroud end-wall. The majority of the span

from about 10% to 70% span is at about the same total head level,

except at about 30% span where there is a core of slightly higher

total-head fluid.

The contour map for flow behind the first stator, Figure 4.6(b),

shows very well defined stator blade wakes involving steep gradients in

total head and the lower total-head values. Again, the shroud end-wall

region from about 70% span to the shroud end-wall consists of lower

,6 total head fluid associated with end-wall related losses. The highest

total head--as for the first rotor exit flow--occurs at about 30% span.

%The second rotor exit contour map, Figure 4.6(c), involves a very

nonuniform total head variation in contrast to the fairly uniform total

head distribution found behind the first rotor. Zierke and Okiishi

[3] discussed the large influence of rotor/stator wake interaction on

rotor exit total-head distribution when stator wakes are chopped and

transported through a downstream rotor blade row. Evident from the

contour map of flow behind the second rotor, in Figure 4.6(c), are two

regions of lower total-head fluid (as mentioned earlier in discussing

Figure 4.2) along the span. Several possible explanations for the

occurrence of these two regions of lower total-head fluid were investi-

gated. The wakes of upstream struts used to support the inlet bell

housing were eliminated as a possible cause of this trend since they

remained stationary relative to the probe during any circumferential

[j~%J

81

survey and, thus, would not show up as a circumferential variation of/IS-. total pressure. Only those compressor components which moved relative

S.. to the probe were considered further. Potential flow effects upstream

from the second stator leading edge were considered next, although they

seemed an unlikely cause; no evidence of this kind of effect was ob-

served behind the first rotor. Subsequent tests with the first stage

stators held stationary during a circumferential survey demonstrated

that as the second stage stators only were traversed circumferentially

relative to the probe, the first rotor exit flow total-head remained

essentially constant with no evidence of either region of low total-

head fluid appearing. Similar tests, with the second stator held

stationary while the first stator was circumferentially traversed

relative to the probe, resulted in both regions of low total-head

fluid appearing. Both regions of low total-head are, thus, quite

clearly related to the first stator blade row. This unusual observa-

tion has been studied further. Heated first stator wake fluid was

tracked through the first rotor row and a logical explanation of the

appearance of the two regions of lower total-head fluid behind the

first rotor may be found in Reference 12.

The second stator exit contour map, Figure 4.6(a), shows the same

end-wall loss region near the shroud end-wall region--from about 70%

span to the shroud end-wall--and the same core of high total-head fluid

at about 30% span as found in the other contour maps. The unusual wake

contours were studied further (Reference 12). Adjustment of the contour

plotting procedure resulted in more conventional wake contour lines.

4-St- . . . . ... .-. "'

. . .. . . . . . . . . . . . . . .

82

The core of high total-head fluid at about 30% span, apparent at

all stations, suggests that there was no significant radial migration

' of fluid. This is to be partly expected because the hub and shroud

end-walls are parallel. Further, the rotor and stator boundary layer]I

flows were probably not substantially separated from the blade sur-

faces and, thus, as was demonstrated by Dring, Joslyn, and Hardin 114],

little radial migration of blade surface flow should have been antici-

pated. Hub end-wall loss regions could only be detected in the second-

stage contour maps. The difference between the extent of hub and shroud

loss regions indicates that the shroud losses are higher as discussed

further in the next section (4.4. Comparisons of Circumferential-Mean

., .Data with Design Code Predictions).

Comparisons of the spanwise distributions of the measured rotor

and stator incidence and deviation angles for both stages are shown in

Figure 4.9. Analysis of this figure indicates that the rotor deviation

angles are about the same for both stages; whereas, the first rotor is

*....operating with greater negative incidence. The first-stage stator is

also operating with slightly more negative incidence and its deviation

angles are considerably greater than for the second-stage stator.

Although the stator exit circumferential-mean absolute flow angles are

difficult to determine accurately, the difference in stator deviation

angles are much larger than the estimated uncertainty of the absolute

flow angle measurements (see Table 4.1). The negative incidence angles

experienced by both stages resulted in the compressor not operating at

optimum efficiency--a consequence already seen in the overall perform-

* - ance map results (see Figure 4.1). Table 4.3 shows head-rise coeffi-

V.

-'#;-;~~~~~....................... ............. :-...'.. -. ..-..- .: .:.... "... ,- '..:... -..... : -.-.-....

83

4.00ROTOR

0.00 *0

4.0

4.000 FIRST STAGE STATOR

SSECOND STAGE

-0.00

-4. 000.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

(a) INCIDENCE ANGLE

2" Figure 4.9 Comparisons of measured circumferential-mean incidence and4.4.deviation angles for both stages (4=0.587 at 2400 rpm).

4.o

z -

ii A* 11-6 -1.L ill- ~ 4.......- . . . .. . .

AD-R14i 796 AERODYNAMIC DESIGN AND PERFORMANCE OF R TNO-STGE21

I ARXIAL-FLOW COMPRESSOR (.. (U) IONA STATE UNIV AMES

U R ENGINEERING RESEARCH INST M D HATHAWAY ET AL. DEC 93

p NCLASSIFIED ISU-ERI-RES-8478 AFOSR-TR-84-47 F/G 2/5 NL

~~~r~~ .s ~ ... .~ . . .-- . .

,j+.

Ll .6

' °~

14-0 11112 .0

1111 ----

.91.8

'I4

IIIJL25 .4 1.6

,U"

MICROCOPY RESOLUTION TEST CHARPT--

S-.. --

%%

-2

4..

,C.",

* * *. Ci

iF 1 r , g + v ' .,o .. , ° ., ° ., .• .. I =°

484

8.0

.4.0 84

*~4%~%

8.00

STATOR

8.00 0 IS-TG

4.' 4.001

Fiur .9 cocudd

-. ... -. . -7ii

85

Table 4.3. Rotor, stator, stage, and overall performance parameters.

First Stage

R stage WR us ~ R ~stage

10.0 0.179 0.167 -0.016 0.055 1.042 0.96930.0 0.183 0.171 -0.014 0.054 1.040 0.97150.0 0.178 0.165 0.018 0.060 0.949 0.87870.0 0.176 0.160 0.035 0.075 0.893 0.81190.0 0.170 0.133 0.078 0.0193 0.769 0.599

Mass*Averaged 0.178 0.160 0.025 0.083 0.926 0.833

Second Stage

PH R 1Pstage WR WS FIR ristage0

10.0 0.156 0.141 0.120 0.070 0.728 0.658

30.0 0.172 0.158 0.067 0.063 0.830 0.76050.0 0.173 0.163 0.049 0.044 0.864 0.81570.0 0.176 0.163 0.049 0.059 0.858 0.79690.0 0.194 0.168 0.048 0.136 0.870 0.752

MassAveraged 0.175 0.159 0.063 0.071 0.833 0.760

Ove ral1l"

'1 overall 1 overall

10.0 0.307 0.796

30.0 0.329 0.85750.0 0.328 0.846 .70.0 0.323 0.80390.0 0.300 0.676

MassAveraged 0.319 0.795

86

cient, blade losses, and hydraulic efficiencies for both stages and for

the overall compressor. The performance parameters are based on the

Euler turbine equation ideal-head rise and are subject to large errors

(see Table 4.1). Even considering these large errors, the first stage

is apparently operating more efficiently than the second stage.

4.4. Comparisons of Circumferential-Mean Data withDesign Code Predictions S

Comparisons of the velocity triangles for the circumferential-mean

measurements and the design code calculated results are presented in

Figure 4.10 (for flow behind the first rotor), Figure 4.11 (for flow

ahead of the second rotor), and Figure 4.12 (flow behind the second

rotor). Inspection of these velocity triangles shows very good agree-

ment between the measured and predicted rotor exit relative flow

angles, except near the end-walls. This indicates apparent success of

the rotor deviation angle prediction option. Also apparent, is the

higher axial velocity level of the measured data and the poor agreement

between measured and predicted absolute flow angles for almost all

cases shown. It is suggested that the differences in measured and

predicted absolute flow angles behind the rotors are primarily due to

the differences in predicted and measured axial velocity levels. Since

the axial velocity levels can be related to the end-wall blockage esti-

mates, this observation indicates that poor blockage estimates were

used in the design process. From the calibration tests in section

3.1, the cobra probe was found to be able to accurately measure the

total pressure as long as the probe was yawed to within ±5.0 degrees

.. v

87

I- 00

C))

La5, ccCL.

-- N D

w 6-1 CIA m, m, Mam

CD ! .v . * ". : z44

/00/L

w0)

S.4:%

44

too

I- 4-p

0l 0! 0l 11 p

LN A,04 I -,

88

A.A

J~ A A/ / i

/ I *- ~ 00

$4.CD 41 r

f (/ ) u4c*41 8 0 0 4

I- I-. 10 0 0 r U~ r. r -~ N IA

0IAU ~ ID~0 0 0~~ ~ -. >

Qa Q 0 U . . 0 u i-

w0 w OO a,.- =0 0 Q 141.11

4) 0

4--a' I 4-4

40

/ / 0

a.. aa Lac- I- I-oow w

-a.-. 0 0 m~ m. a, cc 01 - v :r c

04 acooc 0 OD0

%c' -O. ~ ~ 00~CJ ICI

89

ClI

PI 00

a ua 00kn r4' 00

U, v- 5 %r--%

01-0

I~ 4.

v,.. m LU 000 c ra ce -(I) m co

oj "! "! -wa -wLa2 ;

f" cmm-

* .~ ~ O ~ ~ L~O O v. OIQjmn - In -- ,- - 0

%a %

90

of the true absolute flow angle. The estimated uncertainty in the p

absolute flow angle measurement for 20-to-i odds is ±1.0 degrees (see

Table 4.1). Static head measurements were found to be constant across

the span as expected, and were estimated to be accurate to within p

±5.0 Nm/Kg for 20-to-i odds (see Table 4.1). Since absolute velocity

is a function of the difference between the total and static head, it

is estimated that the uncertainty in absolute velocity should be no

more than ±0.34 m/s for 20-to-i odds (see Table 4.1). Given these

observations, if the rotor exit absolute flow angle was truly in error

by a significant amount, this error should also be evidenced as an

error in the rotor exit relative flow angles. Since this is not the

case, the large differences in measured and predicted rotor exit

absolute flow angles must be predominantly due to the axial velocity

discrepancies. Inspection of Figure 4.10--first rotor exit at 90%

span--shows good agreement between the measured and predicted axial

velocities and, as expected, also shows good agreement between the

measured and predicted absolute and relative flow angles. On the other

hand, discrepancies between measured and predicted relative flow angles

at the inlet of the second rotor were due to errors in measured absolute

flow angles as well as differences in axial velocity levels. As men-

tioned in section 4.1, the difficulty in ascertaining the circum-

• ferential extent of the free-stream and wake regions behind the stator

blade rows adversely affects the precision of those circumferential-

mean absolute flow angles determined from the measured data.

Figure 4.13 shows a comparison between measured and predicted

circumferential-mean axial velocities ahead of and behind each blade

oI

'p 1 W

91

34.0oo

,y .- STATION 1

30.00

0 MEASURED"- PREDICTED

- 26.001

.34.00 .?-."STATION 2

30.00

-F

":'-:" 26.001 1. 34.00

u. STATION 3|--J

30.00

26.00 I I I I I0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB-,,-

-4

Figure 4.13 Comparisons of the measured and predicted spanwisedistributions of circumferential-mean axial velocity

= 0.587 at 2400 rpm).

5?..

--" " '-'- " ... .. ...- " '" " " ". ' : :.. . . . .: .::"::.:.: i::::".i :. ?q : ',' 'd * ." .. -4- -.- "."" .........."" " " " "

W. K ..T.

92

34.00STATION 4

S30.00

< 26.00,

34.00STATION 5

S30.00- 00MEASURED

' -PREDICTED

26.00 II0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

Figure 4.13 concluded.

93

row. The measured axial velocities are higher than the predicted

axial velocities except near the shroud end-wall. As shown in the

contour maps of the previous section (see Figure 4.6), there was a

.' loss region (lower total-head fluid) near the shroud end-wall. The

lower total-head fluid corresponded to lower axial velocities. In

order to achieve the design point flow coefficient, the actual midspan

axial velocities would have to be larger to compensate for the lower

axial velocities near the shroud end-wall, thus explaining the higher

measured midspan axial velocities. Subsequent tests using tuft probes

showed that the flow was separating at the shroud lip of the compres-

sor inlet bell housing. This behavior contributed to a larger shroud

*- end-wall boundary layer than might be expected normally. Subsequent

tests with a new inlet have all but eliminated flow separation at the

=- 2 inlet of the compressor.

, - Spanwise distributions of the circumferential-mean values of total

head, incidence angles, and deviation angles are shown for the first-

and second-stage rotors in Figure 4.14, and for the first- and second-

stage stators in Figure 4.15. The comparisons of the measured and

predicted spanwise distributions of circumferential-mean total head

behind both rotor and stator rows (Figure 4.14 (a) and 4.15 (a)) show

-VI significantly lower measured total-head levels than predicted by the

design code, and less measured energy addition per stage as well as

less overall energy addition than predicted by the design code. As

mentioned earlier in connection with the velocity triangle plots

(Figures 4.10, 4.11, and 4.12), the measured axial velocities were

generally higher than predicted by the design code (also see Figure

% .:

*" "-.." " " - . " " % ' ,' ' ' - ' . . . . " . . " . ". " " " " "

#2..",,, r " " ,, :. ' . ' . , .... ". ", . . : i; .:. Y ."': ,. . :",:.;

6.00 FIRS" ROTOR EXIT

5.00

* IEC

c~4.00

0

3.001 1 1 1' 10.50 __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

wjSECOND ROTOR EXIT

9.50

0 MEASURED- PREDICTED

8.50

7.501*0.0 20.0 40.0 60.0 80.0 100.0

N PERCENT SPAN FROM HUB

(a) TOTAL HEAD

__Figure 4.14 Comparisons of the measured and predicted spanwisedistributions of circumferential-mean data for the

first and second stage rotors (4=0.587 at 2400 rpm).

J*. ...

4.00 FIRST ROTOR INLET

LUJ

LUJ

0.00

LUJ

LU

-4.00

4.00 0 MEASURED SEODROTOR INLET

S0.00LU

-40

-.00.00 20.0 40.0 60.0 FR M H B80.0 100.0

PERCENT SPAN FO U

(b) INCIDENCE ANGLE

Figure 4.1.4 continued-

96

8.00FIRST ROTOR EXIT

LaJ

0.0

8.00

4 .00

-

r I-L

0.0010.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

(c DEVIATION ANGLE

* ~.Figure 4.14 concluded.

97

5.50FIRST STATOR EXIT

4.50

............................

3.50

2.50 III

~11.00SECOND STATOR EXIT

z10.00

S.9 . 0 0

.0

.,4 .00 1

oa MEASUREDAFigure~~~~~~~~~ 41CoprsnoftemaueanprdcdPREDITE

v ditiuin fcrufreta-endt o h

0.0s 20.0 40.0 n 60.0e 80.0or 0.0 t20 p)

98j

4.00FIRS STTOR NLE

UU

4.00 FIS TTO NE

LU

Ua

SEON STTO-LE

L. 0.00

U

-4.00,0.00~SEON 2TAT0 INLET.8.010.

PERCET SPN FRM HU(b-NCDNE NL

Fiue41-cniud

99

8.00 FIRST STATOR EXIT

UD

.4.00

0OMEASURED-- PREDICTED

0.00 III

8 .00

U.'

IL

SECOND STATOR EXIT

0.00 II0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

(C) DEVIATION ANGLE

Figure 4.15 concluded.

d4,

100

4.13). The higher measured axial velocities resulted in less measured

flow turning than was predicted. With less measured flow, turning the

measured energy addition would be less than predicted, as is shown in

Figure 4.14 (a) and Figure 4.15 (a). The measured circumferential-mean

.- total head is consistently lowest at the shroud which again shows

effects due to the higher shroud end-wall losses as a result of the

-" " flow separation at the shroud lip of the inlet bell housing. The

measured total head behind the second rotor and stator is also low

near the hub which is due to hub end-wall effects beginning to appear

there.

*..' As found from inspection of the velocity triangles, the first-stage

rotor measured and predicted deviation angles (Figure 4.14 (c)) compared

favorably. Flow behind the second rotor exit shows slightly poorer

agreement between the measured and predicted deviation angles. The

poorer agreement between the measured and predicted deviation angles

for the second-stage rotor is due to the fact that the second-stage

.. blade angles for the actual compressor and design code are different

(see Figure 4.16). For economic reasons, both stages of the actual

compressor were designed based on the first-stage blading of the

design code. The actual second-stage rotor exit blade angles are

greater than the design code blade angles, and since the measured and

predicted relative flow angles were about the same this resulted in

smaller deviation angles than predicted by the design code. Figures

4.16 and 4.14 (c) show that the design code blade exit angles for the

first rotor are greater than those for the second rotor, and that the

design code deviation angles are slightly greater for the second rotor

-Ri

.. ...

"" -". .. . - .- . . . .- - . - - . '- - -- " " -' .- "' "' '- " " '- ' " " - " ".i i i". ?.i'-. > - ".'" .' .

- - . . . . . . .v VW- .- - -

.5.. 101

ROTOR

66.00-

62.00-

_j 58.00

U.'

J*IJ-. SECOND STAGE

Note: First-stage blade angles50.00used for both stages of

baseline compressor.

0.00 20.0 40.0 60.0 80.0 100.0-~PERCENT SPAN FROM HUB

Figure 4.1.6 Spanwise distributions of design code rotor blade angles.

.

.5

102

50.00ROTOR

* 46.00p

S42.00

LL;

S38.00-Lii

-FIRST STAGE--SECOND STAGE

Note: First-stage blade angles:1.0 used for both stages of

baseline compressor.

.1 ~ ~ ~ 2.00 -0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM HUB

Figure 4.16 concluded

_P P -_ 7

{ .:0

103

than for the first rotor. The actual blade exit angles for the first

and second rotors were the same, and the actual deviation angles for

the first and second rotors were about the same. The good agreement

between measured and predicted deviation angles indicates that the

deviation angle prediction correlation used in the design code (see

Appendix A) is quite good. Measured incidence angles (Figure 4.14 (b))

were lower than desired for both rotors. However, these incidence

angle differences did not result in appreciable deviation angle differ-

ences. Measured stator incidence angles (Figure 4.15 (b)) show poor

agreement with predicted stator incidence angles. Comparisons of the

measured and predicted stator deviation angles (Figure 4.15 (c)) also

show poor agreement. The reason for the poor agreement between

measured and predicted stator deviation angles in contrast to the good

agreement between measured and predicted rotor deviation angles is

partially due to the greater uncertainty in absolute flow angle measure-

ments behind a stator blade row (see Table 4.1). However, not all of

the difference between the measured and predicted stator deviation angles

can be accounted for by the measurement uncertainty. No satisfactory

explanation has been found for the additional differences in measured

and predicted stator deviation angles, except to blame the deviation

angle prediction method used. A comparison of the stator blade angles

for both stages is shown in Figure 4.17.

The spanwise distributions of the measured and predicted blade

loss coefficients for each blade row are shown in Figure 4.18. The

difficulty in accurately predicting blade losses is evidenced by the

large discrepancies between the measured and predicted blade losses.

*, S

104

34.00STATOR

U 30.00- FIRST STAGEILU SECOND STAGE

LUj

0 Note: First-stage blade angles fW used for both stages of

baseline compressor.-z 26.00--/.

LI.'220

lop

0.00

STATOR

U,

, -4.00'V 0

0.0 20. 40060080010.

PERCENT SPAN FROM HUB

Figure 4.17 Spanwise distributions of design code stator blade angles.

105

0.20FIRST STAGE

0.16-

0.12

U-

LI.

'~0.08

0.0

-VJ

-0.0

PERCENT ERROR BANDHU

.,

% -00 60.00. 004.08. 0.

106

0.24SECOND STAGE

0.20

V. 0.16

0 MEASURED- PREDICTED

IERROR BANDB0.12

cc

0.0

0.08

0.04

0.0 0.20 0.40 0.60 0.80 100.0PERCENT SPAN FROM HUB

(a) ROTOR LOSS

Figure 4.18 Continued.

ho

107

0.24

0.20

FIRST STAG3E

0.16

LAA.

0.1

0.08 -

0.0

0.00

0 MEASURED- PREDICTED

ERROR BAND

-0.04,III0.00 20.0 40.0 60.0 80.0 100.0

PERCENT SPAN FROM4 HUB(b) STATOR LOSS

Figure 4.18 Continued.

%.%

.4-rz ~

'IL

108

0.0SECOND STAGE

0.16

'.LA.

0.12

0.08

J(J

- PREDICTE

*ERROR BAND

(b) STTO LOS

Figur 0.00onlued

$A

109

Although the uncertainties in the measured loss coefficients are quite

large, the design code blade loss predictions are generally lower than

the measured losses. Thus, it seems the blade loss correlation used in

-. the design code (see Appendix A) is inadequate. With the lower pre-

* - dicted losses and higher predicted overall energy addition, the pre-

dicted overall efficiency would be expected to be much higher than the

measured overall efficiency, as is shown in Figure 4.1 (c).

.

5. SUMMARY AND CONCLUSIONS

A two-stage baseline research compressor has been designed which

has resulted in:

1. Higher blade-chord Reynolds numbers than were previously

attainable with three-stage compressor blading.

2. A better blade material which would be more durable than

that already available.

3. Conventional blade-section shapes.

4. A favorable ratio of number of rotor blades to number of

stator blades.

5. Elimination of inlet guide vanes.

This baseline compressor can provide a suitable means for evaluat-

ing specific stator blade modifications for possible improved control

of end-wall and secondary flows. The data acquisition system and

computer programs developed during this research program are expected

to aid in the acquisition and reduction of associated time-averaged

measurements.

Some limitations of the design code used to design the baseline

compressor have been observed. The blade loss prediction correla-

tions (see Appendix A) were shown to be inadequate. The deviation

angle correlation (see Appendix A) proved to be quite accurate for

predicting rotor but not stator blade deviation angles.

A curious pattern of total head distribution was observed down-

stream of the second rotor. The relationship between the observed

distribution of rotor exit total head and the interaction between

*; .--. . * ~ * - *. . . U ... -

. . .. . . . . . . .

112

upstream stator wakes and the rotor has been studied further and is

discussed in another report (Reference 12).

Z%,

6;.

113

6. RECOMMENDATIONS FOR FURTHER RESEARCH

The next phase of research included tests of a specific stator

blade geometry designed for improved control of end-wall and secondary

flows (see Reference 12). A stator blade geometry, designed for

improved control of end-wall and secondary flows, was selected and

p ~tested in conjunction with the baseline compressor described in this

report.

Relative to the compressor design code used to design the baseline

compressor, it is clear that improvements in stator blade deviation

angle and rotor and stator blade loss prediction correlations are

required. These correlation methods were developed in the 1950s from

two-dimensional cascade tests of fairly conventional blade sections

(i.e., parabolic, circular arc, double circular, etc.). Periodically

unsteady effects due to blade wake chopping, transport, and interaction

.. should also be investigated further to help explain the unusual total-

head distribution behind the second rotor of the research compressor.

LS-

A,'.

4.-'.

r.-. .;-; **. . .. . . .. . . . . . .

?. ",, ,..

115

7. REFERENCES

1. Mitchell, W. S., and Soileau, J. F. "Turbine Exit Guide Vane

Program." AFAPL-TR-77-75, November 1977. .•

2. Wisler, D. C. "Core Compressor Exit Stage Study, Volume lI-Data

and Performance Report for the Baseline Configurations." NACA

CR-159498, November 1980.

3. Senoo, Y., Taylor, E. S., Batra, S. K., and Hink, E. "Control of 61

Wall Boundary Layer in an Axial Compressor." Gas Turbine

Laboratory Report No. 59, Massachusetts Institute of Technology,

June 1960.

4. Schmidt, D. P., and Okiishi, T. H. "Multistage Axial-Flow Turbo-

machinery Wake Production, Transport, and Interaction." ISU-ERI- . .

Ames-77130, TCRL-7, November 1976.

5. Crouse, J. E., and Gorrell, W. T. "Computer Program for Aerodynamic

and Blading Design of Multistage Axial-Flow Compressors." NASA

Technical Paper 1946, 1981.

6. Bryans, A. C., and Miller, M. L. "Computer Program for Design of

% Multistage Axial-Flow Compressors." NASA CR-54530, 1967.

7. Sofrin, T. G. "Aircraft Turbomachinery Noise, Fan Noise." Notes -O

from the Course in the Fluid Dynamics of Turbomachinery, Iowa

State University, Ames, Iowa, 1973.

8. Morgan, B. D. "A Water Column Balance Pressure Reference System."

Unpublished Report, Department of Mechanical Engineering, Iowa

State University, Ames, Iowa 1979.

4 9. Greville, T. N. E. Theory and Applications of Spline Functions.

New York: Academic Press, 1967.

.-

° .PREVIOUS PAGE...""" --ll IS BLANK.i,

- .[ -r. r * * .

116

10. Wylie, C. R. Advanced Engineering Mathematics. New York:

McGraw-Hill Book Company, Inc., 1975.

11. Kline, S. J., and McClintock, F. A. "Describing Uncertainties in

Single Sample Experiments." Mechanical Engineering, 75 (1953),

3-8.

-~.12. Tweedt, D. L., and Okiishi, T. H. "Stator Blade Row Geometry

Modification Influence on Two-Stage Axial-Flow Compressor Aero-

dynamic Performance." ISU-ERI-Ames-84179, TCRL-25, December 1983.

13. Zierke, W. C., and Okiishi, T. H. "Measurement and Analysis of?. .-

4

the Periodic Variation of Total Pressure in an Axial-Flow

Compressor Stage." ISU-ERI-Ames-81121, TCRL-18, November 1980.

14. Dring, D. P., Joslyn, H. D., and Hardin, L. W. "An Investigation

of Axial Compressor Rotor Aerodynamics." Transactions of the ASME,

Journal of Engineering for Power 104, No. I (January, 1982):

- .. 84-96.

15. Johnson, I. A., and Bullock, R. 0., eds. "Aerodynamic Design of

Axial-Flow Compressors." U.S. NASA SP-36, 1965.

Ae.

• ° %"A

St 117

8. ACKNOWLEDGMENTS

We would like to express our appreciation to our colleagues of the

Iowa State University Engineering Research Institute/Mechanical

Engineering Department Turbomachinery Components Research Laboratory

for their assistance and encouragement, in particular, Daniel L. Tweedt

for his help in obtaining and reducing data and George K. Serovy for

his helpful comments. We are also grateful to Leon Girard and Kurt

Ante for their dispatch of related machining, and to the staff of the

Iowa State University Engineering Research Institute/Office of Edi-

torial Services/Technical Illustration for their patience and expertise ,

in editing the text and in helping to prepare the many figures and

. tables in this report. Finally, we acknowledge the support of the Air

Force Office of Scientific Research (James D. Wilson - Contract Monitor)

throughout.

I-o

..

:'.,i'- D

-. .. . . . .

119

" 9. APPENDIX A: USER-DEFINED CORRELATIONS USED IN NASA DESIGN CODE

Advanced compressor design codes frequently require the user to

input various empirical correlations of blade profile losses and

incidence and deviation angles, and annulus-wall blockage factors. The

various user-defined correlations required as input to the NASA design

code are presented in this section. The actual tabular input to the

design code is given in Appendix B. The variables used in the correla-

tion parameters are defined in the symbols and notation section.

9.1. Blade Loss

The blade loss correlations used are illustrated in Figure 9.1.

The loss curves are typical of annular cascade tests of double-circular-mSarc blades as used in the baseline compressor. The correlating param-

eters are:

Loss aramter cosp ,SLoss parameter 2 approximate measure of blade wake

momentum thickness to chord ratio.

where 0 c/s

v2 (rVy) - (rV)D-factor 1- - +

V1 o(r 1 + r2)v 1

* Percent span from hub

The trends shown are similar to those indicated in Figure 203 of

Reference 115].

15 BLANK

, .. • ......" ." .. " ..-... ," ,;.." ..-. ," . . . ..,....,.... ..... .... .... . .. .. ,,-.' . " . .,. ' '.... . 4 .

w!~ ~ -_z~- 7,7

120

K:-2.00 pROTOR BLADE LOSSHI STREAML INES

100% SPAN

1.50 -FROM HUB

90%

1.00

80%

0.50000

0.001

0.50'STATOR BLADE LOSS ALL STREAMLINES

0.00.0.20 0.30 0.40 0.50 0.60 0.70

DIFFUSION FACTOR

Figure 9.1 Blade loss correlation curves used inNASA design code.

121

**,-'..

'9.2. Incidence and Deviation Angle

The design code provided several options for the incidence and

- :-:deviation angle correlations. A two-dimensional incidence angle cor-4..

relation was considered suitable for the baseline compressor design.

Carter's rule was selected for the deviation angle correlation. Both

correlations are described below.

The incidence angle correlation is described in Chapter VI of

~... Reference 15 in the form of:

i =i +nO0

where n is obtained from Figure 138 of Reference 15 as a function of

C" and K1

0= blade camber angle

1= (K) (K) (i incidence angle for zero cambersh 1 t 10

where (io) is obtained from Figure 137 of Reference 1510

(Ki) 0.7 for double circular arc bladessh

(K) is obtained from Figure 142 of Reference 15 as a

function of t /c• ,i-.,max

The deviation angle correlation (Carter's rule) described in

Chapter VII of Reference 15 is

mc mO

where m is obtained from Figure 160 of Reference 15 for circular arci c

blades.

'7-. . . . . . . . .- '

• . ,. ,.. -, -. -. -. . , .- . . . . .. ,, ., _ .. . . .• .,- .- .- ,,- . - - -. - - - - - - ,. ,, , , - . ,. ' , %

0:4 123

10. APPENDIX B: NASA DESIGN CODE RESULTS

The output from the NASA design code is presented in the following

tables. Table 10.1 lists all input parameters and user-defined corre-

lations, in tabular form, required for the design code analysis.

Table 10.2 lists the aerodynamic output (e.g., velocity triangle in-

formation, blade element performance, etc.) for 11 streamlines at each

axial computation station. The NASA design code gives the streamline

radial positions as a percentage of the blade span measured from the

shroud end-wall, whereas, the convention used for all data figures in

this report is percent span measured from the hub end-wall. Table 10.3 p

lists the stage and overall mass-averaged aerodynamic performance param-

eters. Table 10.4 and Table 10.5 list the manufacturing coordinates at

17 spanwise locations for the rotor blade and stator blade, respectively.

Only the first stage stator and rotor blade manufacturing coordinates

generated from the NASA design code are given as they were used for

both stages of the baseline compressor. Figure 10.1 shows representa-

tive rotor and stator blade sections and associated manufacturing

coordinate nomenclature.

• • IS BLANK "'

124

0 coooo

a0 wi wP) 0 421-40

.4 IL .

N .4J

a u I w 02I4p.~a. n IAI m-.

.0 31 a0%0 a x.4 (A .4 a.

I. 0. aL W10 U IU ar 7 *

4~~~ 00lhft Z 0* . . -4 - u r. u

U, I- I

N~ a-h 4ai 0.t 2

1110 ai 0. hiat IA 0 J O0 - W

0. W0. orIJ0

C4n a- v-04 U -i .4-.

0 J~

4 ~ ~ I 0 M- .4 z -. 0022224

W 0. 0-(9 .U 2k IL 2 ~

4a Jhek a.t I- a

* L 0 J 00+

o U42 0 a-

L 0 -4 .022024..4

0 U, I

000

. ... . . . . . .0

..Z-

% 125

(X 00000000000 Ir 00000000000-C :NUm000o000 000000O00~0

0 oo0o0ooo000 000000000001.- 00000000000 I- 00000000000o 00000000000 U 00000000000

W. I.Vi; 00000000 1 00000000000 1 0000000ooo

!,uM t 0000000 00

m 00000000000 m 00000000000

.0 00 00 0 0.0O00~U) . . . . U

1% 000

JW 0 000000000 0 00000000000000000000000000000000

:0, 000 0u) 00000000000 u 00000000000

w = 0O0O~~ 00 000000 00

U) U 00 0000000 .) U 0 00 0 0

oL .) .... 0000000. 00000000000

0 C N 4f= ! Nl1~I A = = =00F.j ~ oll * - - - - - - - -

* 00000000000 * 00000000000o 0 .......... .U)

VIVI- OoZOOO to 00000000000 U) 0000000

ft~~w -P60000 - a

iC ......... 00000000000 s-0 0000000000

Q 0000000 0ggggg I- 00000000000

C) IL

44Idi-i U) 00000000000 j) 00000000000

0 UU

0 000000 0 000000

V)I* a -q ceV) 06 00000000000 a 00000000000

t .. . . . . . . L . . .4A k 00000000V) 000coono V 00000000000

a uJ

C, --o a

AZ ;;.jzz

CL.

~0 00000000000:-:N 0 00000000000:

F.% P. W.W

126

WjinJo 00 in

c- I. I Ix0i Ui 0

U. U. I

m 0 0 0 0 0 10

w 0 0A0I 0I

I.- x

I.In

0 J0 i

4 Z4 0 cJ 0 -em em L U

* 20 20 202ft~- 020 20

0V 0 0 0

2 4 0 40

I- 2U 2 U U2

- 0L4. 4 (L 4x I

o) 00002W 2W C ) to2W 0 011

a- u I) 40 0n 413 0n 4 0r 4 x 4 n 0 0 4 0 51

a ! !! rY * Ir * Ir * -C -

-0 X- 0 0

c -C

- 0) 0 00I

o 2 2 ' 2

*: a a z a !! a!2

. 4. . . . . . . .

127

Li I om~4 V 0

Cr Cr i 4 0

J 4i oco.J- 0 -Z 0m 0 0g o1-: -

ni N tu0 0 C.CCC ) 40 0 ~0

w w 2 z

0 v

j 10 0 004~~i 2Cwto0

if If a ' 04VLi40 0000

Cc' m 0 .0 ttLI x 0 0

W-0 00

0 0mC. 1z .Ic U. v z

Q 0 . 0 U)

0 ) t it 91f

0 C 0 - 04x6 , .0 00 j- 0 - I

0 0 U) L A

in' 0 ;1 0

0 1C Cr Cr )

*~' ** J 0 0 02 ~ -I

0. I 0 - 00. .0

0 0 0' 01 0 -

ICC 0) ft Of 00 m-U)o I- 0 I- 0 0.r .

V) <t I- 70 00

n.'~~ ~ 0 O. . - U)C7 Cr Cr 1- V

U) 0 40O 0. WI

c. -W Z

C) uli -

2 r >- 0 .. 4

-~ ~~~~ Cr-C . )0m

0 U) 4 C 7 0 000000 01* j to 4 - 00 *. -Z

-4v~ (z 40 *xL1- o 1-) Cr 0 0

ft 4 ) Cr 4C w0 V)r 0-C uW C I

W) 20 0(101 0 4

U)U 40 U)-m

0 0 0

.4L

128

n

w CD

0 ) 0 U

J J P.I. 4 - 00

0 0 I

x. 000an anr a

0 0 ZU. a. 7

v a- 010w

0 00-

zz0v

0 0 C 1z

0 cc

l J J a. (I 0) 00A 0 2I 0 04

i IJ 0zJ00 0

w IL u 10

'~~~~ w 0 - a l74~ - 0

o le 10 y K1- a 0.4 .. u 000 .*

4 0 0 0 0- a 0a- j j. 0- IL 'C Z a

1-4 0 a M1 -

zt 2 '. 0Do 4 z 111 101 0(D $-- a

IL I I- I. a- 000-0 .*..

-, a- 0 U-U J J - 0. 4 0 00 2

In - 0J 010

-l m -l vmIl Il0. V) U 0.00 00 1 - a 0- h 4

- i a 0 - 0 0 go l

L- Ia- a - n 0 a -0 0 ;000 0;: a-4

o 8 0 000 0Ma F 2 - 40L.c

a J00 4- 0

0 an ' O P2 w 0 -0re - if a- so 0) 0

7 x an ; uj w 0 0 2 Ia4 000

-ri 0 w

J0 0

0.00 w -1

0- w0 21300 -

t- an-

0 83

44 ~ . - a-.

129

0 uI- w

W i 0 J4: 0

V) 0 .90 0- 00 0 40 0 4

0 0 0 40i zjJ w

x 000 U- 4

-o 0 vJ

IL 2, w cc xLa 4 Q It

*~ ~ 0j .JV l 00 .

-z N M g 220 0

0 00

Ix

2~ I- I~ )- 0 x . .

0 av 0 V 0 000 0 - 0.- L 0oco0~~~~ 2 o 0 I L

- L 000 t- N z K 0 Zo - iiiJ 0 Ua -. 2

0 co a N 10 t!

Li 0L,1 z JZ C

N l ) -0 J

w MD wN- - 9 J -a

00 0 j 4 0 J .

a, v Z - 0 u t-

0Z 4L NW -W Li N0 O 0 J 40 4 00

IL. 4 ;; 42. N J-0 -. O 0 300

00

M J 2i 0j 42 W

*w -z a

W 04 Uu2 a

*14 u00 0

-J0 4 -J 00 00 *' 0 0

(Z. ( 4S.0 IL 0 W

.- 100 0 0 U -Z (

a a 404 -Ca w0 -

- Li DM5010N N 224V0.

0130

0z

IJ JU~0L

U) 00a0 0U.

-C C, c W >0 L

0 I2{a Lu

0 0 co cc

to 09 -C III 0004 4 W w 00 1a o o*L

-I 0 N - 0001-0 WI 00 T m .~ .

- . 1- a T xW

ICl vp n *0 Ow uJ w LI7I - I 4 j J D In* 4 -z 1 Z 2Z20 U) z 2044 ILI 0 0 - 0 D

0 4 01 a : -C x-I CL 0 - 1

i0 0 UP C t- Inz 4 U I

20 0J Ikl w 0 0> LI 0 k9 :' D J. QZ 4c 4 l'- - 0 0..- ~a 0. LI LI X 4c 0000.. Z 0 4 Z vDI z 0 o 0 80 10 a U. 0 4 $- 4 I4.

C4 7 4 0 J00 n U) alJ zI w 0.

0 - N N) -W) In II4 - 4Ilk t- InI . n

o. J) I? J 1- v 4 I I. toUA. 4 40 I.1 0

Z~ b.4

2~L a 0p. p

0 11 LZ 0 LI 0 z-0 - IC, Zn I'll q ~ 0 1-0L A 000.In 0 I 00. 1J- Z; 4 v

*w W 4~ Ix 0 0 1- 4 * C

Z 0 0w 0 4; a 0 0 -.;X 10.4 0* I14v% 41) 0

4' 0. InO0 LI -* V

121

0~~ U, 0 200 a

00 cc-

*1 40 $- 00 Uto -z 0

LIV 0z j v 22131-5 4 10

1- 1-:1

131

72 0

I'- I-

4U 4

IJ

in

u v

A -C

U. U.

9 Oo 0 4N 00

0r 0

0 0

0 0

-j j

24 244t ........ n

J 0 0 z 0. 0- 0- -Np--N

o olIn nOnN4nPI,'

a z CL z~QOnO0 2 ; 0.4O.O~~N0N

0 -c 0

x I- W2 I ---

3 6

0

z z.0 - - -P0 eJ)-I n- 0 - 6

jIw 0 J~l a w 0N4.O *n

42In 427 0U

% %

13 2

'0I

v 11000 4"44 -41 * molceyeowi

W0. 0 V, 0 V, oo44u

9W. .0 C C O .-- . AIo1 O

0oo000000:O0 00000000000j

DW J04CO0000500 01W"n- C 'a-C

, 44 0004000'OZZ I 44- 00000C0OO0

2 0

4 & . ot-w -~ 4 N ON Mo i

042u 00000000000 $- I-u . 0000000000

I I

-9 A

o C00000000000 1 400000000000

44 4

OW'. C0044N.O1-r- mW'. 0 H4-,"0m0.0.z4. 4c >s. ** A 1141I~N c.Iq 2 >I-. In 411U44*fqf

0 . 0 .5

. 000000000 0- 00000024W00 00000000004 4' 00000000000

0. - 0

II. T1U 4N0.4 U1 0 M 0N44004

0 WI, ~ ~ (IV4u.,1r 0) W CON N00P141'

... . ... IVOGN.06N S W ....... 0....

% >L 0,0 01g* I . 1 0I n( f(

0- -' a-- i lw

0 ~~~~~~~~~~~ * W0WoVI)~4Q W40.OSN0.F

11 11 1 oi C00N4I10 114. . .W ' o i l9 4 0 I

219 *44444 Nr~mrIVNAJ-

oz4 IIo

K. 00 -

z i. ..

I- W

-------- -0 - I - -

J 0. UOo f0VIf5Af S S)WffftSolol

<w- 000o

00000000 0 00000

;w- *ZO oc 0000000 j .0 000000

50 50I...'Az z-41 s- l 4

I. m4e-0u Sj oo ooo

w wo - w ow

P. 'D Q13o"n w ~ W O W4mu %M.M ! w " . 1 U

10 2.( z.S

.10 ....0~ E (n 0l j L 0')0- I

(0 01% c v) m c c Z * c.Z wwl oUM~o M ooa0-

.s ew F w cc0 .v Q v = N

v) 110 %N04lI-'i.cO X> f -N 5oo' V n w z 0 ew

tUI44 4E

C..,'n~

0 -

80 -.. ... I4. InP. 11.

C14 5 ft.-- I

2 -M= - .

aca.5.

.. . . . . . . . .9 .%

134

0Ow., 0 E0f 0,00

- ~ 00 O41w OOOOl O0+.O .000 0 0

-Q ~ ~ Cz -020 1-O000000 - 0000000000

4LUo NNNNNNN.N .Jo10- - 4a 2.

21-4 00000000000 +ZVZWOOa 00000000000 *UOU 10,10

0200000000000 +2 V.. .

g-~~ OW~~0'C W2... .. +;P-O 00000000000A - - - - -- --- --

0~WWOISO4 .10 OOOOOOOOO +X*22 WoW-N2000*m1 0 000440 00 00 0 00V . . . . O. . + ow o,.,

110- 00000000000 + *2 1

0 0044044 IN 00000000000 +Z4

2 1W .. . . f0 4> u.

022a 444E,00444. 41V . . . +000 00000000000IL- -------- X2'. 00000000000 +*J4

+

W OM o.m 0 m~l+0~o 0

2 u On z' ooooooooo' o NC 4DY040 + I 0i

-. 4.0 000I00.40. -0 0019" N9000J2

w 0 11 00000000000000000:~ 0 0 0 0 0 0 0 ; ; 0 0 0 0 o 0 0 0 0 0 0 0 0 0

00000000000 + -

0000000 - 00000 z; !04 21 -2 V1-

0400.1-0Aa 0 *OW mIt4Mt wc

-o .1mo41-o g.0 +020 00r.0).-u W ......... +4 N-CU- 000000000

W .. W \OCI0 0000009Ilfl# M c.J. +-- +-.

.. J 4>1 0000000000O ,0.0- 0-0f4:0J.40

I z * *20W0 ON0. 4W VO oC.+0o0CI+44 +4 0 N0-g..

p 00000000000 +0-

0I *12JJ i1- IIZ*.iiii-

Wo ~ 0.0 .. My0

C1N..fq0

2 2>1- Is00In0u--- ------ + W.ILI

*2 NO WWWWWWOMC0OI. - .j. -24 4 0 a,00a,+1

0 Vm o..000+0"4400 WV1 MMN-0gfl..In) ..m Aw uMc'jooo *>W j0r0000#0444 m

'.1 - *' 4.0. . . . . .. +0.. . .W W 0004000000 W' -O004I1 W

0 - 1.,. +KWW; O CDNO ~

I,) +*W'. %4:. -1-Q0ii112

Ir+ '0 No 01- 041E.rJ Wm 01W1 ;0

w U0G1,* 00 COM) 04 1- 04) - " In0In In 0-In to.

I.- 420 -000000000000 4,

c- 0 1 -- 2- -C2 -O 4--I -N

SC.

j -w .. . . . . . . . . . . . . . 2. .. .

4 d

4/. 135

#W r.

w CYN TO0 -to wI-0r-0W.20JM . . 44.

Z- J8O0~N t 4' ; Nr00NC.J#0I'

-00 ~-4~04zoo~ 0~00000f000VO 440o 0'0000000004

.0 44 44 M*)N0*O - jZV-000000 *00 00000000000

0W 1001ON 400 000020000000

v.00000000000 *vq*04 MM

* ~ ~ ~ ~ ~ ~ ~ P1 :000,;0;;a00 00. 000000

4 VC0 04444 4 4. ..... .2 -9-*CJo wa 40-. N..1. 00000000000 Z2 n r P If,*4 ONO,

1.,. .. .. ...- i *Nom4-C 40 0#n 0

~~0 000. **** **E

0 -.Q.044.'40)44A;. 59 0 9 0 9 Q* 9zz44zzzoo0 W.1 4 0 0 4 -4 .

a an w- c1 tJ4' >.J 4-~,

I.-0 00000000000 0 000009-V 00000000000 0

i2i. . 4. 00J49-NO0440 0 00000000000

x 4e4444 0000000000000

a 40.0 NN9 00044W 40 .i U- 9 0 WOnDC D DC

* 0000000 0 I0 -

0w 9 0..00 F 40D,0 WO 0 000 . 4444444444j')

2 4v 0 00 00 0

4Z 40 4'O.4t-

4 00 0000000 1

... 1uw 0444m J; f-0 =

4t um 040.0.0 0 400444004

4~ . 00000=0000. ;w 0-mo= :-N - -9-40444

4 U -opM-4i 0=0.4

4 $.>I WOMM444 W g gz2-0o zuZ A

Z L a4 U1.9.4440 - ......444

o- V-9 0,4444444444 W #00000000 40 rw040IL 0 44....o0000 0DODD

2 4-

10. ..4 4 4 4 4-0yrIn"0t

ci 0.4 446OO04444P) 44 R 4400(Z 7,4 P. 04' 9-0449-40 40=2= 2=.1

C II OX hnM.CL -- V 4 N. N4444NN4NN4MN4N4

IL -j-0 0 0M N 0 9 .. 046,,D0 W4W 04440)4444 *

~~~~~>w M o4 N40444 a 0..4.4.4 0..44444to 0 j~ MT0i .. ',

644!4O440040'. 4404a.4 00)f, O 0- 00000000000

0 4IL 4 W4v4 -----------

0O *P 4044- 40 4.j M11fO 04 ON44444Z4404440.99-0 *0... ...- 00000000000404Z1z1 44.. QN!Qm w 04 .0000=;Oo9-

Vpi~- r4 41 ..... .. 00 . . .U 4-6-p. -9-44444JV 4o

I.?. 0 0.0. N00to0 2 W44904-

429- all

* .~.136

iO 0 00 00000 00 00

I" We~0fW W14 U I

4 *..o 00000

I-li **** %9 .444444 4...

W W.

-- ~I-f 0000000000134

74

at 1* 4m- 00000 0 4 '0 + *5-nO*

I- W1i

I- - 4004 2. OOO::4: 00000000000 p

L W v .2

4 3 n20 = = 1 t.. I..P~4 I- 000000 *W4 4404-0W WOW ... J~n ftt 00000000000 .nA oIp-O-4

* *I- 00 0000000 4 .In

J mjU .OOOou 10-4 00*0000 uoI goo !-. ~ ~ O% 000 00 44 No' o oo oo oo :Q- 11 11

W 0001100.0 49 Z8 0 0

2 ~ ~ ~ ~ ~ 42 -4440.MAO .. 0 000000

*. CY 0 NN.W 11wQmc YPP NP 1n SOOOoOOOOO +W 0 4 ONID 0 400000

I-9 XW 41111-1-440 4 00 0;(.CKU +V). 000000000.......

4 - N O O M 20u 0444I111-1-44p. + Z, 014411-5- 4040440,P.4.0

-Z 000N M I-f j 410I1.P$40 44x 00000000000 4,900-U ..... 5-r

. 1% 00000000000 : -14.. .0 0O\o +020 ::t 4Wvoc

41 +2 1;3 XC. 00000000000 +

9 4>1- 40444 *0000000000-!V0- -- ---- *440 040 .:14 - 4. 14440.

0 WUOWc2-W ONQON 4

W Id + W0 4.40..414

.0W

J +ZW 4. .1 n44

60 00000000000J 4+444 0 c 00000coo

* O.P..2oop0 *44.44 p- 2= 22=4101. 0 24 (Y NN Z.4444@

M 000000;;50 +.444W 4 W

Cu ft.Lu fn ft ot cu P.i F U.= ,

.- d 42 i i . .. --

-Z;4: .

I WV O ;I.o N oAm'_ 01 2;V)O0

'4MOOVM

0 10 0 coo

~~~J 0 ;%.' ~ V - V -. . * . * * .

V.. -7 ' -

137

24 -E.-.*1f0.Z.C- 1 .1 117 n.~

* U~ 00000000000-

~1 I-I-.11**'t M02404 960446040

In - 00O00000.

*~~i W ,*000000

0 %J. 4 4 00"'00", COO 00000

I~ 00000000 000000.

4 > 00-00 00410

cc -TV 0000000-0-0000OW V. 00000707000 40 0000000 400

In lis I I 00044444 -. .m 0t00o0 +j 0000000 40 i 0.

4WN 00000040

J .- kis 4r.. .. . i440 ON

4 4l!-- O 00000000000 01- 0040000..

-1 zg0000000 0 I 00000000000..Ww W0* -44444

JJV- 00000000000

I. -u I I I I0W-9- U. ONMOOM-000

S. .. . It tWOc 00000000000

* - W~w ........ U 1!0-l~10 0 4I; 10 Z00000.00 1 009I0

:000000 0000 000000

0 .4-1. 00000000000

- w 00WI0.00000 6-. I0

-C OIM O 00OO W N

w 4 44 009999999 9 10

a 8l4. W 9om = = =z C0N1-.4040

I a. 0 4 0 1 9 17 KU . .. . . . n-in 999I.00 91,0000 111 00000000000 JJC)000 9 00-. 0

0)0 P0 00 . 2 22

w j4 w 0 00000000 00 Wos .4- 9000-.4!.

"" * * -9 .Ofl0 4-0 --- --- 02 WW% coo 4*Q.;;%999900000 x 1...-.

I". ivl. 99999900000 000009 4 O Z0004

.4 L- - 0 JI

.i'.W~~~~I. 000000..... .. g.InM O 24. .. . 4 000000 00000 *'. ooo-W! o~

0 .4 0 0 00 000 6. io i :

.... 1 400.00000 04 44009

4 -Cv 0 G% 9990 000 4Q 00000001 00000

IL L

-Cc 4m0 00000000000

~1- 9999900000*0000000004 n I 0.4 - -X O

.00

-:777. 1. T. r

138

0* '0 000000000004!0 owwome.ozw j

.~ OJ0 -1. 21- 00000000000 +..z 0oO~oo

Zi- 00000000000 +21J200000000000N 30 .. 00 00.0000000000 u4.. 104~ 000000 +M-0 0000000000 4200

+ 4.

'000000000000 +24 ozw1-P'.. 54444444444 1.0 00000000000 +VUIL 0Pl~VIIH~

0i 4f 1.--- ----- 0 0000000000 4+u. NNNVVrfl4

X, ooo ooo;. .'z.. e. oln +0, o.oot%00000000000 NNNNN1.m

l 1d 00000000000 4424 0-00I0-00!=.0_ O OaOOOO +X0 N 0 P 00

I-I..)* ooo ooooo o 1(2 00000 000.. +20II2 -2m% QOOOOOooOO +U-C +I

40. NNO0000..000 a *M *#---M

0a.1 N f1040)coo

I.- oooo00 00 0 xX oop- oNw ,oo vW 04 - 0 0 0 0 0 0

oW .1 7nm +-1 0000000000000000

.0 00000000000 DvJ4' v C, Cy w Cy Cy

o~N * 4M4Mn r n 41,

cooa AX 000 00 U4L1-;00000

V W) 041 NOW 400100 P.. 0 )E..

Z In (00000000000 O4 004 (I 411.

4 4W fMN..1-+001 4020 N 00N4.404O0 1 0 100,. 444 NZ44

2 C - *0 U40+

w +t *4NOnf1o 44I NO nv)N2 - 4 010.40A.0401 +44. 441

4 0 * 00000000000 2 4

Z00000 4111% Oooooo 4 000000m*MN 40w mn 00-

0 ~ 044001N 4.10,

M N2 IFi. 0. . .~ 0 oo N4 1. 01--44001m4* ,104IL #0. m -Y 0 -

9 v - N 4 P Nr. IN+. Nmw oin W 092 0 .NP I'J.O.-

.1 0 9 mN 4 1 4:PNI'JI'J W V ;F01044001-4 W mo 4.w0:;.. I-N414...oO

01 .II\ 40.400-000 W 0 0014 00004Q4 C

xZ oz-.I-I oIlo

14 a -'4 ~ Isi~m Igli

- t. .. ~-~ I

139

-j 0Vi. -----------0~ WO 000~00oooa

0Nlt.4OO~. W 0U ~ ~ ~ 94 VJ+4EUN0W 0LJ 00000(0I00w0

v + .Co 00000C000000

oulw V-10 00000000000

01 101 NNP 0000000 C 0000000000aJJ 00000000000

* ~0000000004Wr-.4oq 8 0, q

II- Vt W 00U Itn w in 0 *

0 10W 0100NO NA <0

0 j 0 WW~~QIMgCfW0I T.I. n 00 .O . . . .0cc We.. 00D0D 0000 4& 00000000000 4.

t-IJ * 0 0 0 0 0 0 0 0 0 0 0 0 V

I. - V 0000000.I0 A-O 000000I- ~ ~ 00 0 Ql. 0 ININ 0 0 0 0 0

-v\ 000000000000IItog if

OW-. tONNO.W...eVego O OOOO00ooeo

00 VM . 48 .I e-PM..0 00000000 0WI-000 000000

Ow 4w 0000OO

* ~ ~ ~ i S i i i t 1 t To N. 1 -01011V 4.. O- V qt 'II0

NNNNN WI -eo oo o. Il.U . 44%

vt .9 00 0 0 0 0

.4..,0VOO 44 eOoox 00000,00000ow 0.0 0.0 .- .1.1 . . . . . .

4-9~ ~ ~ O#OOO1-1001 4Im 0 00 0 0

* VI~ V OOVO'..00N - JaIw FI0-ul#0.

4.~~~ - ~ *II % iii ii Vt01Vt010.N-.ID M0' 00 0 t110 ' ZZ . 1-01....1~~Lm .~. .0 0 . .11 .i..

'A !i .0 "0 - 4 1-- 00NO"1

0 -z Z jglo 4u

'A XoL NNNNNNm-x..

9. ,W .... n eJOIWZ9

.9 0 W% Om~e1-j

at 1,I- 00000000000 - - - - --: c mre0enm

CL -U NNNNNNNNJII. -

0 Vt w 411.. . . . *V......0 T- .uiTN71MQ W4~~mNP...~ ~ ~ ~ ~~0000 oorooo z1. 11 o1tt-o X. 00000

.y J4 ---------- -4W

C4 --- --- --

............. . . . 00000000000

24044 0,0 -0100 4P. 0 0O 00 m00 00 !4 %

. .. .. . . .. VIZI 0,0 - VI.

1.0 -NVON00

1%

4. 5.

140

ow. 01 ~100 0 I W11 0 00.1-M 10

U. * NN~flN..010N0W0u I cmN ON N 0 40 Wi*Z 000 00 0

41110 0010101010101

410 4N104 n0J" we0 NNo-emflMl.-+Z

O~; 0.1f4 0000000-1

13+)e Z .401040 00o

Ii -Q. -0000000000 +- z 44444

+ vW1 -coNON O InN4 401 ,.P+.- M .4 0 10 Q 4

CK 41= + U

N~~~+0 0000000000000u.-10001 1-01 +U I

z I. +0 4

NK I i4N4440001N0 0 +H1.10 0140MW0.-..0"No N>z 000000000- I-Z; ;0900 0mN-M 0 *+ ) 0000100100

I- -1. 00000000000 ).We 00000000000 +1 l.1 ....W N 1 41.. +4000 00000000000

a +

w OW .. .. W4 00000000000 V2Z - 1110-41-00001

w wow w a Z 00000000000 UZ 0NN

!~~04- 00000000000Q000 Xo

iL.W . . . .0 1a.~~~~~~~~~d N ..0ONiio.O -0 OOoOOOO 4z~1.I14I01.- 04- IWNNNNN 01l114 8.N 00000000000 4000, O '10000...0i

0 D- 00000000000 4 ~101-40N0'400+ N0'.000000000 *..

- I 1-O 00000000000 #_01

C- 000000 z 00000000000 +OZ id, 000011

7~ 0 : : 0 0 0 0 0 +-0 0 0 0 0 0 N - . .0 W , 0 . O O O f O 4 O 1 . 0 0 0 0 0 0 0 0 0 0 0 + O 2 : NQ4W 0 0

za4 000 0000000000+

COW NWI0 400'0001- 424

a- 000 0.110140 +4 0 vofN0000000I - 0 2001000mr10100 404- - -

I N N. LI 0 1 N01 fn11VmOID x X? .00000 00a 41-0A .1 ... . ... 42

W. zli N lp.i~... it..2' 00000000000 +Ww 4W% 9=0-MV000c0 40W

M ) 4444 44 400+K; :,DNa O

J 3l 0 .1 .0Z 00 00000000000 + .0 ! 00001000

w1 . ...01..M NNNO'.-0 is 22-.22

In 0w- 4;, -zz N00010 00000000000 IN0a c.40. . . . . .1111.

- wM

w

~ N o 01oom~-m 0 Z.. IONOONN

N~(CC I-Y4 NOI0N N N

N-At 0*; u 00 J a 00 W %ft M wv

J00N10I WAb 00400* NO; *M~#0

-r4 I- .~ - ej ooow

c-li - -. 20 0000

o J*~~~~IZ 00- 00000 ---0ooe~N .J

WO04O-OOON" W&00Kcomom '. . . . . . ... 0M4090N0

N-01In.i~ i W N .,0 ~ zU0. 0 6 N % a. M

1-0 ..-fl4O N00 at 1-0 ..- m0oO000000 0 ~ N4,1-00

.* I

a.-8

................................W-~Nm...........

141 ~

A. 00:0N

NY 4wo 0===001-W N

V* NNN~N~#1 UOZ 0fIF)4 lN0)§.0. *9000

07 m m mmm000I- - ... N 777

* ~ ~ ~ ~ ~ Mt P-NNI))N MowN'00.

at .- L ... 0 01

I -ucqm O7mm W7*777 000000 000 U 0NNON

~~~~~ I -0. 'D0 ~ 0O 0 0

WO7

= Z00 00 000000

I- 10Z 000000000 ZOO OWN m-70.0.Nmo4 W7 0 ... M 0000000000 0 N

I- 72 4 0000000 00 00Z 00000000000N 90*00000000000 ....... +407 000,000000000 - 11111011 I Ow 00000000000 %i.1 00000000000

U. -0 X Z NNONO0 -1 WX-v. . .Z40Q.N 00000000000

I G ZNw=ONVI-0'IJ z Oxw O 0.-WNM' 0. 0'000I'70 f- V,J- 040 000000 0N 0W-0JO000 -0

42 O0O0uw a 0 ~ 0- - -=00=0 4' *0.000 0 U*..A ... .. o 1.10 )-O9I700

11.1. 00000000000 17W . .

N J 00 - .o1 00000000000

N4. 0000000 * Q0oON040ON +* ~U. 00-4--00 I

7 4 cW 0 ' ' 0 1V I..ii.......lW.- 0'44.0knc1c470

in -0 NO ,00C ) 1: 00000000000 9- 4774 0

:000 000 00V - 77 77 4 7 ZO I l ll l

040000 000000 W*W 07NO*44 0 40

VY .9-C 0004070 .0 1000 000 7.l s 4 4 v00*0,00'7700P I-.... ... I-WW. . . .

.w 0C0000 7000000 N- -- - -NZ 0-N407000M

4 4uI 00000000000 .w.. w

---------- 0 j0a ME- 00&0P 007 o p1-00 00000000000

01- 0000 ~47 0000000000

uW OR 000000 N 00000000000 iI." 000000

W I. 0OOOOO

ZW 'D 00N00490 o .00007-700ovjot .0 - 00 *Z 7=22-277-

I- N.. .. .0 .N.. ... ........0 WW N -- -- W 00000000000 W9-7 00000000000

%L-

V. 770700 NmNN000000000 W!Z 0..7000-007W - w w 020000000000 Ox.. M0- 00000W

!J & ;00000 .. JN. . ..14 4 - - - 0000000000 077 a 00000000000

4 4 -4 -- !O

:0om~ W~.077777 0 0001ol ja, *vAIO0770700l~. 0 00009 .J -90 00

o ~ ~ ~ j .000'00Q0 W 00 0000 a- 0.77..

N == ~N4V.000 0 000400000000 M

-4 NN. 0 747 -NmM0 W&. 0.7...O0N0700 0 W *Z 007-.0700004

* Zo04700P.77I0 g.. 0 70Q070 00 Z-4 070,-II

149 47 a 000000000000 4K- W W

1-0 000I70 1-8 .. 00407IN0'0

Oz I- O

dl.

142

lo - QN .N,,1

0U~Ifl00 0 0 0 0 0 010 aa0

04Z -000000000 I..04 -00000000.00 :.0 -000.0000000

* oz;;;0u~000000 D4~ -. ozzzzuv) * S-oC40ooIf

01 00 ;Uz~co40- M 0 000000 I O0 *.. O. 10 -0 100D0 1. 10D00

40 444440444 _ 0 ...... 040 .0.. 440402 cat0 z oat. z 1-0 !9 - ----- - ,- ---- -- 4 1- - -- - - -

z 0 0.o0-00(mv 0000000000- K.*000000000000 4>! 000000000000 2oo 00000 42000000

- W 00000000- !4 00000000000 C> :4 0000000000

--uJ 00000000000 I-U 0000000Iu: 00000000000v V)

o;0ONOOOgON A 14i 0-0000000;14OooooJoo 00000000000 440 OO0OOO0oO

- 4.0 00000000 - 4.1 OUUO0000 .. 4.1 00000000000u-0 It Ili-0 I I tll t-v0 III ii fiI

* 0 .

2 w oAw- - ow

1- .000000000000 1- .000000000000 1.- .20 00000000000

0~~~r 004 0~0 40 0 0 :0

u 0090000000 0 x 0,00009-4V4 00 000900g 0O I 00041-0 0 OOOOO

2 0 000000Z 050000000 000 Z 0 00000000000

.R: 000000 JE 00000000.1 000000000004 44r U 0moomo M400-41,,.000004-0040

I- 04 0 0.1 ' 0 .0. 0 4Z mvnII 0;4 V.0 O W i~~ii IW V!1 .

-- - -- -0 0 IL - -- - 2

1- 0*4Uoozooooo I- 0. 00000000000 w- 0*wo 00000000000

4 IL 4 IL 4 IL

ii 4~ tl0. O! W 1 .111

--------- ------- ------------ ----W -- -- -- -Jp

0 0M0000040000 U 04=.00"0004(W iii _204

SU-- -- - --------- ----.. .

0 .J0.000000000000 .,10000000000000 .100 00oo 0oo0o0o44 .0000000000000 4m *0000000000000 J4 *0000000.. 82040000000c 90000000000000

4U.'00000000004U4000 044

z .0444044410 x *444N0-e0P0

N 004NO 0 2 9 4..04 to) 0 to 4444)000 091..1-1-4400

4- 'A002' I. -- x z 1- -x

NI.. .

.4-....................

143

Uh .4 0* 0- 4W 4

In a7

hi 3c "MN 3£ C,

.4 NhI. c

0. 31 z .9 3 Mo.

0 4LI- '

4Z N

N) Y OO V) N ~ hi 0 0 r 04

LL ! oco olmo0-CL 0 NN 0000 vocom)l. I O

la. 4l. a U

hi 0 x 4 00ILL 04

In 00- Q1 N hi1 I0 V M I ON CY

0 00

in40, 1(-. 04 V4 w

m. u* Ji LL 3,0,0 *** NS O

w i~ N(iN Ui 040004

%1 O hiLL 40 0

0.) N CD

O W9 000C0 , 4. Q 40

od ~~ Ou. z u. wO P)-u Ix .5 T 24W *

A 4h 00000. J. Z0) IL NCO414

z n i 411 00O ~ 0 h 0.z 40 0151 * n z . c .40 0 0.

0

>) hiln 0 4h. C40 ;W 0 .00

0 hi 4 0901 **. 'n-0hi C, o 00 0 000

U) u V) I- c 4 o4, n M. T

-4. a hi4 ONNO0w ON CO 4 NI

hi 0 WY NOi ~0 Z0i ~

4 4 40 MN 4 4 0 04)0

4 w 4 hi 00 7 hN 00

I N 00 0 hi

SU 1-00 (SIN 4 NI. . .C

N si 0 OD 0o 0 014411

00 In In a - A;UI

0 w 4 0000 44. m 550

w- a 0 0 0000 OL UO

0200

ic z ) 5 ) )1 1 10 3U N-.4 73W 0)0))0)Z

h W 40 0

144

Z*M fj"Do fl MwNmO4W4-m m:0

ZIZOOCO 000

0 -U00 o *:00O000000O0000o0o0000o000

00

X!Wiwv -. - 00 0o00000000000I*omco ~ )Q *NO~r 2 000000000000000000000000C.J

ID *.0000l000.000000000000000000

! z W-CONII0 0000W~ Z 0000O000O0000000 ------ Nmwm

0 J *'(JNOJ

wL MIfl 000 L 0 0 0 0 00M(CC~N

0- - IOZN~

~hc 0000 0 ~00u -. x %..

4 W 0 .00000000000000000000000

zC Zl N4LIOU -

U) 00 J* o 0000 0 040

z ao0 *N 00000000000oooooooo 00o

0--D~.Q Z 000000000000000000000000100

0J-0ZI.. 0q 4000000000000000000000004 1I- O. 4.1 " CD 0IIO(JIN (Y20O000C00000000000000!00~w'AI V X* . . . . . . . . . . .

I- V) -00 .00000000000-------NNN

CI a U) ZooOO0fr

c01 - ** .

o U 4 .0000 V, - OM O4. .41 h )Nmc nkoN

v-I 0 - -n............... i..

14 9-1 . .900 00(N0.QIr-~40

v0 0 W" OOOOoooo ooooooooty

zz

... 0040000000000000000000000000

LI LI 4000000000000000 -NN4NN

44

................................................................ *. @4 -

145

W I - . - - .0 U I n o l N O O 0I 0 : N - 0 04w I-"0%000o0 -4 NN.

0n a :9zZ0O000000000O00O0000000000

1-e .00 s ~ t 1OO OOI'llOOOO O...-OOO(

I.Z 20000 OMOO0o0OOOO0oOOOOOOOOO00000*WOo-Oi%.. M ... i.. %O2 enI-U-Ooo * -000000o0oo000000oo0000o000

I., W-.Ow- z 0000000000000000000000000@Q1

i 2C.. *N0 40- 000000000000000000000045

-W en ;0~f4* Wu .00000000000 ------ NNNNNN~N U)

an 04 4

C z .342 - W . Z 0 0 0 0 00 0 0 0 0 0 0 0 0

-0000

C), 0 -000000000000000000000000000

I-IL ,..-.WOOO NOOOOO= OOOOOOn OOOOOOOOOOVJI

U. Wj -ZooCo Lu. .oo ooo0 oo :.)M.W(,0 0M -'Mo L)oC -

0 -000000000e0ccno

Z

40000000Z00000000envo Li.. N 0000 0 L00000000000O~0 2~~m 040

4- Zj 0 1 -.. n . . . . . . . .U. WO ...0W 000000000000----------000000

0 4~J-... U)~4 4*4* 4O.(I W4z0O--..PP.tlP.0

0 * -.. IJ .. 0 m- = - -O- .-O

J 0U . . . . .... .4i

eno 0 -0000000000----- 0NP000

e0nI- ~f- --

4 OIW00000.00..000000enO* ~ ~ x 000 cc00 Lu 00O4 N N t )Q O.

Z! - - 4 z- - 5 l 5 4 ~ N - 0 0 - 4

II. 20 ? zZZ O- - --0000000 0 0400 00040i

4 us. 00oo0000000o00000000000000

I ZO 000 0000000000000000000.0

W 000O000000000000000 ------ NNN

-4z 0 .a1o -mJ-. ) b. 10 20 9Wx r-o a-eoOOo~~ooo~~q

).I Lu0 0000 00000 - - - -

0!0

4 V M ! -,? 0~: 4............> ... I.,~ 4.

4 146

11 nfl In

U, ; (M 0 0n4fn r

In 0-0001,- *

In 0 '.000000000000000000000000000

l--Qr 0X!*= ZZ* ZJ1 ;0000000000001

004-.,- U-000 -0N OPIMOP)ON000g-nn.0 NN *NOOOOOO.OOOOOOOO

ucrzzoooo JZo0ooo00,00000000ooorIomg!§* U NmOO-.o.. -

0 I

NL ;4000000000M0000~- 1-0000* Z00WEO0OQ~..MI

00 0 00000000000-----(JNNNNN a0

0 0 W p4

I ,U- *0. 00

-- a 0t-.Oo 000 Z O Nn0000 cU 0 a zz -rz 0 00

0.000000000000000000000000000

u 0 *00.00 0 0O

.1 0 -- . tZ00000 00000000000o000004

4~~ -4= 02 .. 000000000000000000000U MP IIInIlI~IIIII

4 . *I .0000 0 -0f0000000000 ---------- 00040

zow in *iom

I- 0- *I f- f- 0 Q0 W! -Z0000 1- ;00n I

flU woo~ -0000Nt-j 0 .n . ..........................4 jO a .- 000000000000000000000000000

- W o-NW U.)x - w -4444 04 .j *Oo a 0

oftZN0000000000 000000 coo00ON

-000000000000000000O00O00000

oZ-)4 z oooooooooooo-

.. ~ P * ihi4r-'I. z NOOOOO0000000000000000000Qm0~ ka~ In n a44 Z000000 00W40.aW4n0..aNWcoo

N U-00 r-O20 .. 000O... ao,

hi .00000000000--IJNNI1%n

0 -awZoOM

.9 M - .a. I

M0 ozOO U, J000MO

n*U - . ................0 o - .f-o 0 .-0000o0o0o0o000ooo000o00oo00

h40 omm (K0

h-jz=a- 00 Ia- C, 0 ao"I10900 on a ~0C~O-0~-.I~WQ I0*

z IW. .NOoOOOOOOO0O00OO00OOOOQOOONY

LZ 1z000000000000000000000000000)41~ ~ -00zo 000000000000000000000000

zZ .00000000020000000OOILI00

Wi hi-.00000000000------- NNCJNN.0I

4 W W.a

jI Z

ad0

P '

ala'%

'A-!L l

AA

NO. 147 11, 1 10-4

.. nZ- .I0 c w CL ,4 0 - oo 000000 000-ECO0-..lA. io.Ee I-.I *.0OEQ-O0-. nM .... to4

ol ..V0000 --.

in 0 .000000000000000000000000000

04 4 N0V

0 A t*nM'W ;: *~I~op in

9K 2. 7. - 0-- .400

a001 l 1000 ZZ o NNeNNNNNN in00004

00 0 -O.;4OoOOOojooOOzzOOOOOOoOz-fOD *ONOO 0iI-m *n)EoN0 0W I-. .0000 co C0-NN N N .0000.NNNNoNN 004x ZZOCOC inQ.C N00O00000 0oO0 00000 000000 00ON

.0 - ** *.2000000000000000000000000000

- z

0-0i '.C0. - 000C0000020000000002000-. 4. ~ ~ ~ ~ U CK -J *InE r I 3_ZOO2i0-00fio0WO.FM

W 4 Z.... V *W. in "000o in -00000000000 ----- NNNNNN0 - i

zo 0!00o- W N D-.o0

U I--Z - . . .Wi -In.Im-l i0j..0oi.winn-0 u;; -. 0000 NoVO "100,O'EN0-IAO40j3 W0 4i *N004O00.NNN...0O N~o* 0164M

4Wo 0 -. 000000000000000000000000000- v -0"0Ot0 Ix

.4 4 I .. .0OG 04 J *j 0040 0. .00.NiiP44~n0

U .-. It 0. o4 0 000000000000000 a0000Z.2Z0000000000000 0000000009

-0000000)OO000000000000000000

0 UI-ZW ***I *0000000 ... 000.0000=4W W., xN. 2 000000000000020000000000000

in -00000000000 ------ NNNNNN

W Z.n *wol-inizoooI4 00-0000 W

IL 20 WZZeO O ! NNNNNN OU

o I~ -0000000000.000000vo i#440o m ooooooooooeoo

o ~ ~ -*N0000000000000000000000000

z 000z

0-g.3- * 00000000000000000000000..0.** * o40000niU' 0 4000000000000000000000000#0

* -d i W *'00000000000------- NNNNNN

.1 006i% % ~t~

148

-. Z a-.

'Jxzz0*woo.

(o * ,0

,x XJo

00

o z..z-o -

0 ~v 4

W ZI--

41 0

O- W _4D

z o

o !U, a- z - - -- o 4, ,

I- U~ . . :V.

"4 -Cv z Q

m 00mm 4m N oo co

-OZIOI-I -00..coocoooooo

C) #oooo-ZW ooccoQ.w WW4O0'ooooooooooo~mc

- A U,,

w IaVoocco------NNN

* II

1%

U, I.. %W ZU ;:!c

149

I-- -IL . 04" .- In 01' I Iy n nN9 DN0V0 n I nN(.

Ifl 1-0f0 -...

* .. * 11~1-4 N D0 8ooOoO~ooe~o~oe

um z 0 0o ZZ00000CO000000000 0000 000wo-.. *W b* -....... .. MO....c!. 1

z 01U-0000 8 -Oooo000000oo000000000000o00

0 0 z

oS *Wffz 00000000000000000000000000J *ID NOV 0 PICO000:Z000000:00000000f0

01 .0 WD 'a 00000 0 C.C04N(4JC cowo -J . N *n1140 yntno- (C.YIP

0 44

W *Z X_ It 0 No 11

0 U-. ; .. 00 V0- 40--4Q-o 4O W "O4 04"ZX00--!C'4N N NNNrN=l2.-0O

*.v 016 . . .. n . ...

0U 11FV4W 000000000000000000000000000in0 .00,10 0

I~.- Z-- * 1040-O O-*11141 N-- V

J ZNOOOOOOOOOOOOOOO

$3* j 000000000000000000000000000

~0 z1 2 POOOOOOOOOOOOOOOOCOOOOOOQN;

~~~4=1 0 0wa'i~ - 4 00000000000000000000000to 1111 ;-

TtILA :00W -0000000000 -------- NNN

4.1 a ("~ t

WW 711 209!.~

.0 0-A O 411 10 .Nv, 111N o0 d ,vv ov'mm4 N Ow- f-wnt

" ..... 0n -.U -.....00 -c w 11) 0 -0000O00OO0oo0oOOOOOOoOOOoo

av uo -on.

J. 0. 0 PIZ- 0rJ) C0 "1 0 N.. oi "N.O O Q.-0E 4 O

v --- q40 -.. N* .OOoooo oooooe0o o0 oo0o

2 .- 00 00000000000000

=1 ,302=4 z - OCOOOOOOOOOOOOCOOCOOO:4o! - ft0000000000000000000000

oi vw 9 w.000000000-----df'EE4JNN0

ine% f O!

.5 150

zS

u u31 c F o C' 01 *. 0 -M Q Em0 !V0 r--

tf -0 0 . . . . 2.-. 0O 0---=

in' a 000000000000000000000000000

ZZZOf'404Q- 0

* O0~~~~~~*ZOONO U 0 040 JfO~t4O~)~lOWO-m .0000 40. . . 0 % 0

Z (4ZZV0000 1Z000000000000000000000000000

j ,i-~0o *M n000000000000o000000000000000

0 4S000 . N00000000000

00000000000000

W40p-C00 U .

as -u. . . V) . 000000 00. = (14(

04 14

bi . .....0~0 .U. .. .. .

W 0000 _ro o--- N N N'J C N " = 000nU OO -5 . ..ONM*4000 4PI O

0-OOOOOO'00000000000000000000%z z~ej-

vi ZI N P04- .. ,444 gf0..-f0W .... 004 z 00000000000000)

I * 0W0 0000-0N4400Ilf 0If44)000NI .5, .4 . 000.0OOO 0o00000C00000000000 V 00o MIWO -JO"0

0. w :00 000o00000000.; -------- NNNNNN

z

V . z. .

u0 U! 0004 o- mOOq(Qo~ Ooo o v0oo00yONSoONOM(A4 *1f44 0z -2! N0 NN00O O O0000

.4 I-ba a1 CU 0 - 00000000000000000000600000

o 9 o- t

z ScU --1---. - Q. = NMO0*4 v44MAG O

4 StO 0 000000000040000O0000000000

!U 00 *N0 0 .b 000004qE#*4E0b10000J0 vf- ZL IZ 0 0000000000000000000000000

5- 000O 0 0000000000000 -- -- -- 4Nee,

ZO 0OztiJ.NO0

Afl IL ..~W40 01.

! .. .. 0.4 '..00 2t 4N N 4 N ~ 4 .4.....0 Z -to 4 3 40000000000000004.F-0l~.I0 0000

UL O ZIvoo aNN(NN~ 0Cy O 44E z =*Ut V- .a.a.a..

S t - - - v MOO .Divioo rym m O OOOOOOOOCz. wne . NOoooooooooo- - - - -NNNmmm CON

z0 0 0s.ION 40a.0000tt

Mi.

II..-00 0

OO ;#N z -~*~f ) 5~~~5

151

z @1mO

z1 * in$ ID22W p*! -- OO-4 ON .~. .p Sp ZZ0 -OllNgaNfti WCO0e

I. NN a ~ *m.m~m .. oooooeooooo onoOo

U0EE 00(%, 0

(4z nW~ 0- .e0000000000800000000000j

Z WSU0000* 2 1400000000000 00000000000Clow

-1a40609 P - . a t~t.T0I W .. 00000000000 ------ NCNNNN

04 * t:10II a I O 1

cf WO§ 6=.00 Wa2L . z--- 10,0 0

v ILI...aa2 . . .W *N?.MIOP*lI. P. . . .

a, 0 D Q O Q 0 Z Z Z O C OOOCa JOWN I % C J N E .I O O O

U,0 *OMON~ 0c*0000 0 ,0,g0

US0 NZ-- 0 ON5

4X 0 :-.1 .z00000000000 00 000 0000 c00 000a -0000000000E0000O0

z %19 z NFVOWv

U..00 0I..00U OOOOOO - -

- 0000 00. 000003t" -e ; In JOOw1, 0

4L W) 000 W 000000000000----------000000-0 *1P

V) -Po lopa* n00 *Ci 0N1IVI66 1)E1.0

j, -- 4 . to 4 N0 N

0 : i~z .. .. .. . 2 .. . .. .p~ o o a o o o oe Inw; 00006~ 000000000000000000000

00

a,~~ US .00000000 -. VJ

11) 0 N 0091- ID 0

.. 0 00 U 6N000000 C.V00 OP1000 100 900 F1

I- £0 ZZZOO IIDNNWNIISNNWNNN -ooo0. 0 0 4;t000o0000900000o000000000W

to I ..p)O - 0f~a Q.U .6 4P. PoIn

a, tI z Ob W.. c 0 !00 "CI :m

at*e8 -o -000000000000000000000000000

US.000000000000-00000000000

0~ 00~a00.00.wo

.1,00In0p:I*~#1 -O .r

v.- *.* . * . . * *

152

z 0* IOQW)* 0ZZO, Q. 0

-l 'X~

z (fI-).00 -000000000000000000000000000lz

c~ -0000-.- Om 2.0401OAZOO00e0-000oOON~

.w Eoo... . .. . . .. . .

04 4

o .. ,00 ZZZ00O 00000 --------- NNN000

4 0 'y 440

0 I- 0000 X NNAA N p244 . . .- .* . . .zo o o o o ~ ~~ o ~ o o o o

w0 *MM 0 oooo~oO0ooo~o

z 0 QON 7 00000O 0O0 O000W-0000 moooo0 moo 0040M oooo on

~~~~~WN I 00 W .00000 00 0 NCUNNNC'J- In

x -0 0

0 ..- 0 0 - 0000000000000

.6 v04*ON ZIO 900000000000000 000000.000

4 -1 0 .00 000000000000000000000000 0I- OU 0WN0 N

%~~ -M M

0 :000 w 00000000O000 ---------- NNNNN

70 0

.4. I NWO W

i wnA -*'A; mIII'lA

j 0- .~ .

44 4o, *0W

U. -077000000N000000000000 00000 o ;0 1

.4. W - 01 01 *9 z~VNUM z 0 0000000000000

. I -w~ .. . U 0N0UQ000.0.0000If00mg

0 Ow 0oNoOOOO00eOOO OOu*w :4 zg. 9 0 ---- ---- 0N N

O~.0*0

A M4- Z0 -0000 N M in00 I0 IIAJI. 0000000000eJNMeg

0. WO c

C 0 4 141

*1Z- 00 .

20v;jO*o z ~ ~ . *.%**%*.***.*.*.*. .- -

V_'.7 7477

153

UIL -OW

in 1--Q

On

U ZZO0t I.w 0.

Z P ziw

N

a

00ni -t

v i C

ft Z.XN-Q

0 -4UIL u

- 01

0 wa

x -C

I.-

4 .4 0

I -qv

oL zo 0'nc.

a Uo -,,0

-z aU'

9 x 4.1* 4 0J 0 000'0

w - N OS- 0 00:00

-J *

ID

J*~ % N .Z-4 %i .V

* * -. . -. -. - k . ~ - - - - - - -

. . . . . . . . . . . . . . . . .. . . . . . . ..U

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

N.Dcl (5

0 LOcoo

tAA

LLe -J 0

UIZ

LU a

cci

o c

CDl

LL4J

ic

ccCCDC/) CD

U L0 ClC U DC

L ~ tf!

CDJ ..

WO W:)U'

155

11. APPENDIX C: COMPUTER PROGRAMS AND DATA STORAGE

The computer programs used during this research program are listed

in this section. These programs as well as all experimental data and

reduced data results are stored on magnetic tapes (cassette or reel)

and are indexed according to tape and file numbers as specified below.

Actuator position correlation program: Linear least-squarescorrelation between actuator potentiometer voltage readout andactuator motion for probe and circumferential positioningactuators; cassette 1, file 1

Slow-response data acquisition program: Acquisition of time-averaged total-head and flow angle survey data; cassette 2, file 1

Compressor overall performance acquisition program: Acquisitionof compressor torque meter based performance data; cassette 2,file 2

Time-averaged data reduction program A: Reduction of time-averaged data to obtain point flow-field parameters andcircumferentially-averaged flow-field parameters (a plottingoption is available); tape DSMDH, file 16

Time-averaged data reduction program B: Reduction of time-averaged data to obtain rotor, stator, stage, and overallperformance parameters; cassette 3, file 1

Contour map generation program: Generates contour maps of pointflow-field parameters over two stator pitches behind any bladerow; tape DSMDH, file 15

Data uncertainty: From estimates of primary measurementuncertainties calculates, using the procedure of Kline andMcClintock [11], the uncertainty estimates for all flow-fieldand performance parameters; cassette 3, file 2

Time-averaged data, station 1: Storage of circumferential surveydata at 10%, 30%, 50%, 70%, and 90% span locations including probedata, outer annulus-wall static-head data, and test conditionparameters; tape COMP, file 1

Time-averaged data, station 2: Storage of circumferential surveydata at 10%, 30%, 50%, 70%, and 90% span locations including probedata, outer annulus-wall static-head data, and test conditionparameters; tape COMP, file 2

* ""p. --..- -. .- - - -. -,' . . ..- '.' - .'.'.- -.€ -.- -' -. '- -. " . ' --- - -.,. - . -'-'- - -' '- -. . -..i. ' .'. .. .

156

Time-averaged data, station 3: Storage of circumferential survey

data at 10%, 30%, 50f, 70%, and 90% span locations including probe 6data, outer annulus-wall static-head data, and test conditionparameters; tape COMP, file 3

Time-averaged data, station 4: Storage of circumferential surveydata at 10%, 30%, 50%, 70%, and 90% span locations including probedata, outer annulus-wall static-head data, and test conditionparameters; tape COMP, file 4

Time-averaged data, station 5: Storage of circumferential surveydata at 10%, 30%, 50%, 70%, and 90% span locations including probedata, outer annulus-wall static-head data, and test condition

parameters; tape COMP, file 5

Reduced time-averaged data, station 1: Storage of results of datareduction program A; tape COMP, file 6

Reduced time-averaged data, station 2: Storage of results of datareduction program A; tape COMP, file 7

Reduced time-averaged data, station 3: Storage of results of datareduction program A; tape COMP, file 8

Reduced time-averaged data, station 4: Storage of results of datareduction program A; tape COMP, file 9

Reduced time-averaged data, station 5: Storage of results of datareduction program A; tape COMP, file 10

10

4-.

I,

157

12. APPENDIX D: PARAMETER EQUATIONS

The equations used in calculating the time-averaged and performance

parameters are presented in this section. The symbols used in the equa-

tions are defined in the symbols and notation section and the sign

conventions are shown in Figure 12.1. Circumferentially or radially

.-

averaged parameters were obtained using a spline-fit integration scheme--,

12.1. General Parameters

12.1.1. Basic Fluid Properties

'.9°

2Barometric pressure, N/n

Patn = hg@t (1.0-0.00018 (tiaro-273.15)) Yhg@273o' eba ro

12.1

*3. Density of air, kg/n

.4.

Patmp Rt 12.2R t

3Specific weight of water, N/in 3

"H20 = I (996.86224 + 0.1768124 t - 459.67)- 2.64966 x 10 -

12.3

.-IO• "" '" " "' " " " "° " " " "" "" " • " % ". " " % '% %$ % " ",'% "% - " " " %" " "" " ' "'"~ "" '*' " "* " '" ,€ " • " " "' ""

* N..158

Y911N K V'

YVV

K V

y Vi

-I...

STATOR

US/K

VV~

V SY

2

v2

Figure 12.1 Sketch showing nomenclature and sign conventions(al p os itivye except as noted) for si ow-response

% instrtlment parometers.

W--~~~~ 7.y ---.

159

12.1.2. Blade-Element location

Percent passage height from hub:

PHH r-0.14224 x 100 12.40.06096

12.2. Flow-Field Parameters

12.2.1. Point and Circumferential-Average Blade Element Quantities "

Total head, Nm/kg:

P tyH 0H = 2 12.5

p

and

SIH dY 12.6SJS " S

0

Absolute flow angle behind rotors (see Figure 12.1 for sign

convention), degrees:

ScfPy P dY 12.7

S 0

Absolute flow angle behind stators (see Figure 12.1 for sign

convention), degrees:

py acoss PdY'" Y~freestream ro s y.-

L. freestream""'

-

160

Annulus outer surface endwall static head, Nm/kg:

P YjqwHO

2h = 12.9w p

-

- and

S..-

S.S

hS f P dY 12.10

- I - 0

.4,.

Static head (radial equilibrium equation), Nm/kg:

"'. d 2 sin y(-h)dh _ _ _ _ 12.11

dr r

Absolute fluid velocity, m/s:

V = ' 2 g (H-h) 12.12cp

and

-. Ja.

S1 0 V dY 12.13=Ss

Blade velocity, m/s:-'

rnRPHU= 30.0 12.14-30.

~.- .. '

..... .

161

Axial component of absolute fluid velocity, m/s:

V Vcos~ 12.15z y

and

V =Vcos 12.16z y

Tangential component of absolute fluid velocity (see Figure 12.1

* . for sign convention), m/s:

V Vsin~ 12.17y y

and

V =Vsin p12.18y y

Tangential component of relative fluid velocity (see Figure 12.1

., for sign convention), m/s:

V =U-V 12.194.y y

and

V =U- 12.20y y

-4Relative fluid velocity, m/s:

V = (V ')2 +(V )2 12.21y z

I .,

162

and

V VV' 2 - 2 12.22y

• Relative tangential flow angle (see Figure 12.1 for sign convention),

degrees:

I,.- 9(V13 tan 1 12.23

.J I

and

5. V

I-..,

Incidence angle for rotors (see Figure 12.1 for sign convention),

degrees:

1y -K 12.25R y,1,R 1,R

"J S

Deviation angle for rotors (see Figure 12.1 for sign convention),

- degrees:

6R y,2,R - K2 ,R 12.26

,~ .o

5%o o

-' ' •

_.-_%°

%° , °

S: O

.-'oV , .. o . - o .o ' . • . - ., - .. . - , - -. * ' . . . . - . . ° ' . . - o ,- ' o % . . - . ' - - . ' .

Al" ""' ."-"."-"-; . ... _-,' '., ,, .,-,-". -"- .''-""'-'-'''' '.-.." '. ,,' "-" '. "",""' .. I ' ,- - . ,", .,;".

163

Incidence angle for stators (see Figure 12.1 for sign convention),

degrees:

s- K 12. 27

lS y,l,S KS

" . Deviation angle for stators (see Figure 12.1 for sign convention),

:!!'i.!idegrees:",

S6S = Py,2,S K K2,S 12.28

Flow coefficient:

Z 12.29

4,..

12.2.2. Global Parameters3 14m3/s :

Venturi volume flow rate, m /s:

2gy AP"."-" vent

Qv 0.05229 2 12.30

:.**-*.'.

Venturi flow coefficient:

Q r= At 12.31

q . .. . . .

.. Ut

1 ..W.. -..T. 7W . r rW.. .. C

164

Integrated volume flow rate at probe axial measurement locations,

3m /S:

Q = 2n t r12.32a frh

LIntegrated flow coefficient at probe axial measurement stations:

aat

Integrated and venturi flow-coefficient comparison, percent:

a -,

FCC a vX 100 12.34 N2-v

General radial mass-average parameter equation (let be any

g eneral parameter):

] VZ r drh

h 12.35

frt V z,2 rr d

rh

12.2.3. Performance Parameters (based on cobra probe measurements)

Actual total-head rise coefficient for rotor:

4# HR 12.36'A R 2

t

%*

165

Actual total-head rise coefficient for stage:

g (H -H )c 2,S 1,R 12.37stage 2

Ut

Actual total-head rise coefficient for overall compressor:

g (H 2 2 Hl )- 2,2 12.38

1Poverall U2 L223

t

Ideal total-head rise coefficient for rotor:

U(V - V )-vT y,2,R y1,R123

i,R2

Ideal total-head rise coefficient for stage:

U(V - Vy I'S y1PR

i=tg 2 yp12.40

Ideal total-head rise coefficient for overall compressor:

4f +P ='P 12.41i,overall 1,1R i,2R

Hydraulic efficiency for rotor:

rl 12.42

Hydraulic efficiency for stage:

%P

stage124

*...... .. *. . ...... *.** 1.43 r

.........................

.5 ***'

166

Hydraulic efficiency for overall compressor:

~overall W 1 veal 24i ,overall

Total-head loss coefficient for rotor:

UR 2 W 12.45

(VlR

Total-head loss coefficient for stator:

WS -2g (H 2, Is 12.46c (V 2)

i's

12.2.4. Performance Parameters Used in Generating Performance Map

Cross-section average absolute velocity at the exit of the second

' ~ stator assuming zero swirl, m/s:

Qv

*V 12.47z,2,2S,pm A

Cross-section average total-head at the exit of the second

stator assuming constant circumferentially average static-head,

Nm/kg:

H =h+V1242,2S,pm w,2,2S,pm 2,2S,pm124

4ZI b

.4.7-7%

167

Actual head-rise coefficient for overall compressor:

2,2Spm124overall,pm 2

U t

Ide.'-l work coefficient:

4 - TYCRPI 12.50IPM 3OpQ U2

V t

Mechanical efficiency:

"overall ,pm 1.5ne % .~~ 25

*44

IM

Ito

Zee.

169

13. APPENDIX E: TABULATION OF EXPERIMENTALLY DETERMINED DATA

The time-averaged data obtained ahead of and behind each blade row

are tabulated in this section. All data were obtained at the design

point flow condition predicted by the design code (i.e., 2400 rpm at a

flow coefficient of 0.587). The measured point-by-point distributions

of various flow-field parameters are listed in Table 13.1. The corre-

sponding circumferentially-averaged flow-field parameters are listed

in Table 13.2. The axial locations of the measurement locations with

respect to the blade rows are depicted in Figure 2.5, for a radial

(spanwise) view, and Figure 3.6, for the circumferential survey window.

Total head and static head were measured with respect to atmospheric

pressure. The sign conventions for flow angles, incidence angles, and

deviation angles are shown in Figure 12.1. A complete listing of

mathematical symbols is given in the SYMBOLS AND NOTATION section. The

definitions of the Fortran variables used in the computer output

listings of Tables 13.1 and 13.2 are:

o BETA R = Relative flow angle, yy

o BETA Y = Absolute flow angle, fy.y

o FC = Flow coefficient, *.

o HS = Static head with respect to atmospheric pressure, h,

Nm/kg.

o IT = Total head with respect to atmospheric pressure, H,

- -. Nm/kg.

o PHIH = Percent passage height from hub, PHH.

o V = Absolute velocity, V, m/s.

%[" IS BLANK

%

",' -.....,- .',..,..'.• ''"",. .'.. .",. , ... , ,'.' .' . '... •" ,".',, , .. , + .v "0 ' , "" ,. " ' "-" . . +" " ," "

7-w~~s~ -W.~* 777:777"7- -.

• .':-.' -

1701

Uo VR = Relative velocity, V, m/s.

o VY = Tangential component of absolute fluid velocity, V, m/s.

o VZ = Axial component of fluid velocity, V, m/s.

o VYR = Tangential component of relative fluid velocity, V , m/s.

0 Y/SS = Circumferential spacing, Y/Ss "

,%

!..

-1"2.1

l .. ," "

4".

,-,

.'' " ,e_ A'.J. *.4.. '. ' ,-" - ... -. *. - A. . -- -..*. - . _ . . ... . . . . . -.-.- ,.-¢ -,* * A . . -. . r. . - - . .: : , . . '

171 5

am am 4404000onf - t r- N aoe

0W 0 a 0 0a a0 10". *0 OI~ 0W 6 , o00.a06o00.21.7o~o 000a40a >~O~ )1 NNNN~l~N4NNN

z wwwwwwwwwo X 000000000- MMMMMOO444404 00000000 000000I

WO O~~S4D0QQ0G O 000-000-. WaPF00

'.45

N) a ~ ON--p NnNOMMf- 0 rNNNNN-"a0t

MM000000Co P. 00000000r-00 0 )-. 0000000000I4 000000 z eeOCO 00000 0000

u If of I

4-4 5%No Ooccooa~oo No 000000000 N No 00000000000 >-% *...esooso -\* *.. .. 4\S.

o NNNNaN No NoN G4444- .4

Aj I-4-4

Ill 0 OC.000000O 4" I 0000000O000 V) W 0000000000

I NNNNNNNJN z NNN44444 4444444444n

o cc -b-N p~nn0a I-N % oo 4mn OfE0 45 u-w0~la. j IIE *.Xe.S #I *... II 6 6..geg.Z.

2 44.4. 1 2 1 Isol4 I 2 I off

410)

o ~ * ~* -.=61000000n

-40- N04 0E I..~ ID ofV0tO4. *D o 6 aa a * *s es*s

ID ~ ~ ~ ~ ~ ~ W -.IV0.Cl -~ t~ -n # I 4IsQ.

1-4 00000000 N0 00- M *0000w0000

* S % 5* ~ ** . . - -- - *-. - .* - ..- .. 5D(d* .5 . - . S* .. , ~ ..

4e.~~S7 t4- 5*55

* % % -Is

172

0-4 0-Orr ot

~oo~~tnJ Jor-Qo a

I 00000000000000O

or- cornrmo

W- a

0C1 0000000000 0C1 0000000000

cio i l

P4( 004' flQ co 40 cc, cc- qOV)

z z

W A10=9011-9 I M21.1 s e e s*~.4 . . 0Q C a 0

MMMMMM ZN~A~l I~ Pon-.~

* 000.0000 * -000O"w-

30.

I"4 W 00 0 00 0 WiO 0 0 0 0 0

OD ID-r.- e too of~rS)0

"O',S))O00-NeI 4A M )S00 cc" %JE

000 00 00 3 0 00 00

-e V

or ..

4,-, "furr Af- !r

L4

173

MIO 6 O Ina f ::r 0 D t fnIn N01 D 0%0 n 4 0 I QDCY2

*N(~NfJ~~l * N D EE 00 1 A f) I O O O 1

0 0000 000 Iwao4- 7 >X 0 D ~40EJN~ N OD OD OD OD C

MN4 a 0 0 n4 nU a rr-o-0% a(Yc 0 10P,0 0 0aeu P- 01 1 nin too 0 MNoFv~~t In aV*U 4 D4 0 D, i n P o f~- r--. P.P.*12' i'XE~r 44 -. G 40O 4 4 432

wXON 0ny %O*F-tr--? CC fn-o--o wO-O cr =..e..e..)M0 l M 0O 0f)0 0 0 W-O~.t dDU)f 0 * ' 0o QE#n#41 4

N(JtC4iCI0lJCCJ4 0 -- ----- p., -IT-, I- -I -

MonIn4v)&0-I-r-D0 O-&~o ONOP0~00

0% ~rJ~~4n 0 0 I NNANNN~NJN 0~ I CU-h--0--)-D 0---D

0L 010ef YF 0 0COMFI~ I 4nf -. WN O O MO00tv o r

P4 4A N N V) -1 N U) r0N0

cm Al INnO nI O fm Nn ru0I40 Nn Nn cyc0NG0zNN NN NNG.-- O --

mnmnmm *Enmmmmmmmmmt44*q.

z z zr.

OD 000 in0000in 0 0000000 A r -' o o t-000- ~ ~ ~ ~ ~ ~ ~ ~ ' 0- ;004~f~t 000N Or-N4I)0- nN NE O t l-

4A U -1 * ' 10 * . . .0 .* U In *... *4** It) It)*** 0* 1 00 V k ba P N

w0000000000 v. 0000000000 v 0000000000I. N t- Ot 0 f-M r 1- r-ON..#tee -

WO -- -- -- - wo0000000000 IU0 0000000000I4 r NN('Jt'Jt'N 0o nN'NNNNNNNN a) t4JCNNNNNNN

@2n

(n 0='004o (A 0=0r~n0= W 0=4U'0Ok-N

1-4 000000000- 000000000-00000

%,

* -. 174

N0 m* ~ ~ ~ ~ ~ 0 in tooQ~ ~ 0i~JOO

ina 0 ~lt0 In -W.0 00Uo (,.DSOP4

I uI

- ---I --

00 N.# #E4t 0 06 MSom o-

0 00000~E0000 0 0000w 000000 0000000000r-rr--v

*Z . #~ ..**...*..* . a ... a.6*a.*.. 10 00000 -- -. - - -- - - - -

-H

wo ,.N I0~5 a w oooonn

W 10 W) 04 4rN )N 0Ir W O -MAr040-

0 0.n&P000 1% #f~-.p.- o0G -~ 0 30-

ItI fEIfPU n a) .l O 6 0 .%~ %. . . *4 * * a**

.1~~~~ ~ ~ .a

." .. , r. .. .%..

.4 175

!00:NZON aoom 0k4 4D N ue O! 1060OON

0 Z CY N p.ofmmm mmmmmm mmmmmmm~x

x

13 00000000000lI00 O0000000O000000

w coo 00000 c-in 0Om-o0000o0o00000

*- 0 w"? PU) 0m0*one M 00 O-n 0 .m.#.ONr04a. 4 MMN r4404 :

.4 1

U . InOONI01r D- 44,in mN 0nN..00 0U)(%jOD,. O .4mm:

% wo~~i Inf F)NNCNM QOCY NNN CyNNANN (onMr

.m mi"Nti In Mo nin NNf 4 NN mm act Cmi mm mm i0

176

f~ ~ ~ a0 . 0.no ~ PO N~ .,oN0 9 ~ ctQ

(Z N 001-ONNNW JNN

moo Mn Oni n

3.0 'a...fI. v~ 00 1-tN 0 m m we mo ----- - -

omowwwww

C0LO Ei # ft ~ U O

:e 0: :w4) M mfo;c: ~t o

2..

* 0. p~0w .. O NMO~ O0~ MMQeMMN

* woO.o~en -~in-QNP

\j Wel

V S * *.* e ** e e *O.. *@ * *P- 46 NN M N NN%~.N N N N N~

177

~~40 K * V )V)I P 4P

r). b)I n n I

or~ #eE ~fV...m)e

N IA

on z

rr

4 V4

Ai93 ). *s.0 . 0 0 0 "00 0 0 0 a - M OP*

NO , f -f f, I f.. t4m aanoafea f- f. fc.'J-m-

f, ON 0000000 000000000O0000000

178j

0MMIfl00r-0.~)' =0000'1,A190 O

or (AtO O 0, i O-

inI f nk ni ni f )0jr) if i inSW~- in if) iu n nin ) i i

0IU .%~ m-Piaoo M~ni nm)of )ko0U 011 4 -0M 1 n n W) nI oV W 1,1)

If) f) ) W)W) n t if)W) n 00 10v I) 9)in ) I in n I) M

o 0o *Ovi *nJPOOOM "

'0 NZ**..**********

o 0000000000000

Ift NA -MO0EC #. 0OI)i

Vz

%0

.-.

L.-6-.

179

coo. -o-~-MON Wn1

II..

Wo * OG 0 Q0 G Q e 000 0 0 Q 0

onn z

0

o om .f Q 4 E ~4N

I c I .0.bQoe-oo0.0.00o00O.00000000000"

NN~Jn mVI J~fJN %

180

NNN CUM lNN NN NCJflN(NNNNN NNNNN 4~NNflJ

r-Oopt4NMD700000OOON4MMO

OcmK * -om-.7 ~ ~ O S0 S

.4mm

h.~~~~~ 4r-W **** mrMi go**** * * * * * ** * **

WO o ~ ~ ~ ,

n ----- - - -- - - ---- - - - ----- - - -

* ~ *~O~ .00-000000#

000 0 MPc- o- 04O MO oof NmtN :r-

Id on )NO 4~Io%~r DGD~t0Q JOOA -00N . N o0 O o f%4O 04 4f d fin' An 4r Ion N IS IN e~ Q O 10 P r4O P m

xx e , . ,

Og4 %zf MNf

*D4 CDr -- rf -PI44 DWWO OD0I 00 D0 O 00.VD

Ff-r f- r-, r r- *-Pr,-P- l-O ~k 4 m -O* -Oa P P O Sf

181

'r IImOo 0O OMONJlWeOMe

Oin er-Ior-r 0- M-N--o Ofon f-

~~MM00 .roo.OnQ oNonnJVr-I- NE*r "I -ooo 'oZ--nN~ri~N~sOn

4W~~~~~~ 00an- ~ n ~ r r.~I O r

-, " r 0% ..... .*** *****.z 0A a 0 NNNNNNNNN on N m n n NnCjty a

Wo -- - "C- -- -- -------

ID

(U ..er-er-ON o -o Nmewo ?t-em- 00

182

~zp ---- - ------ --- N NN - -------- --

f r-C 0NW~( 010N N n0Ia 00eMAOO-*~ r.N 0;;uI -in W~~fI O O O;;4D N i Md m Ez;0P n

* ~ ~ ~ w .4 .a.*... . *.. *......***

0 e 4e '

9) --------------

IDOO ~O 0 0O00DOOMM00000

4.1

I-

*E0N m4 0 ~ 000-eo- -Ogoz hOOOOOOOOOOOOO0OOO).0G

%.N) 0- N 0 m N ~ tr w V%~.. * . * * ** **.*

17-

183

0 10 4r 4 In0

ltii 0 0 00In I N0I m MlN no 0i

orI N40 01-0'0 ad 0 no'.D.

z 44

in w

w Coo VM4-s e 4eer-r-r- 00r- o-0 Ml-r-e 0EEeEEee#teE~E N **# f m*0o 0 o *n~ p

movNto-.ov#w~ -4000-poWMNr000010 .44eOam..IgroomNon- eO#- f-

o ~~~~- w~~ 0~0O O 0 )K.0 05 0040% * @ , * @ 4 O* 4 S * * * 4 * *

o 1 ------ N-----

184

N r- 0N 0N 00 f wNr- r-;

WOUJ N J-0000o---fneJN (J-0J~u'

M r r.

o ~~~~~ -------- - --------- - -t - - -- - -

OI

0 0 0.WQ 0 0 00000 0 a0 00 00 00 0Ch0 0 0NNNNNJNNNNNNfw

.Q0o0 n 4r 0a4 -l l e-v.P0.n eO#*OO.

Moo -4On En

000--- ~ e-O 0 ~ m o

0r -

v RD-R141 796 AERODYNAMIC DESIGN AND PERFORMANCE OF A TW-STRGE 31ARXIRL-FLON COMPRESSOR (..(U) IOW4A STATE UNIV AMESENGINEERING RESEARCH INST M D HATHAWAY ET RL. DEC 83

UNCLASSIFIED ISU-ERI-MES-8417B AFOSR-TR-84-@4i7 F/G 21/5 NL

EEIhEEI7

4, - -. F - - -- -I - -w

" "I

1-.122

Q6.

L60 111112.1.84

11111L2 LA ~ 2

•-( MICROCOPY RESOLUTION TEST CHARTNATIONAL 1UREAU OF STANDAR IS-1963 A

-". '.

--. %-,..- "- , " 1. - * -- "

%11 111.

185 1'

f-:0 vtto0omCz ,0 r 0_ 0C o

2.-r -f .9.. .t -r f .NP .1. l .f.fP f -f t .f .1Mmm m.4mmMMMMi MMm m m m ni o

or n wof Zv~ Zt *.....&eon,...e v cooNinoneeety 4e

4*0 on .~eown)r n-94er-m or- n or e -reOakON- iO

I

a z aoeoaoccocoaeeooo COC0a0aOOO000

2.%

0

4l 03n En 0Z%

bw 0-o 0 m SC 9Q0J)0SV#f0 0E0

.4A.

186

M o. . ..

. --- -------- - ........--- 0

InO -. %Jo ~ m o~. .4..

cr OfklJ*0 On .. 0 ogf%1t-emoah0o O~~EU OL InhC

ft.- LA 00 ..... e O .a V 0.

I wo FM.e ~J0O- - j u

ft ; 404D*Y 0000 -i nlOfM-0NN 0

0

* *"Z O 4O O O O O O O O O O O O .O

A 0-o~.. vaN ..11,re

. NW % %v-.~~o o~ #.n.-e-%~I,,. **** ***************

4' ~ ~ ~ ~ ~ ~ ~ . -. . ... ~ . . * . .

.94' 187

4..qef4p E~p#*.4&dE4 ee on *.w qq~* .0o~r4 rr4If4.4 0PV W4 0#rW rt~o-.4r f4.0V.

a.4fc n0 - 4i e~e r40 a 4co14 0I

W N0ofN0 0 QWS awO~tr aOM)EI r- O4

g0! ~t Ie~moneJmosro9-.*4A k cok 0O q rlf~-f4 n qc f ~ 40 j-I" f

eqqeE).*c.MpkE9 0 inV) e4O- tEWq-000 00EElw

-'Is

In a .*.*...*.... *.* * *...

z

0.~~-m- aS-S Q e O fS 04e -Mofochm

ecamewe90 09 0w

2-4.4 0

30-

K .eOK O ~ 'JS N .M9 9 9 90 0 0 099R90 0 0

. . .. . ..

188

aw ow Nrf-e r-.E3)UUUU f-1- -0of-mgOU)U - ot

.~ ~ = CP--cNPr-QawFm 00 "Mc O wer. N1-4r r NOU)&#O 1 Qf -r-ome MAJO~r

a A,

le N~ln M 0 M-! r t nin .00e ynm flSPSASQ.4 . a IFOwI-*% ********s**,****0**0*01*.*********** Colx Z

z ~ ~ N ~ W oweer P 0"0041000 0000afeov V) 0

u zOkCCC 00nw

ey ,y onnAn4r4 i 4n o o01 .Xr

Op*hS~)~E * ~)P UP-

189

V~I.

0&40ONO wo~owoo t-*"ON

*o 0.% oeScoOcoee O. -4--coee* 0 0000 *0ew

If

% Noh P

in 0

-MO COOO-WM04O oe

K 0

ID

0 0MU C 0 *O~.ossmi~ne~s~eN

1 *00MUO N= ":MON: Me0r400 O- 0 M O"O"N N

WO NI~a~fia

190

0,N 4 N t0 9 10 r- N 0 N-rvly N 94 fm v in M j~ NJ N~- f u orn N ; F v oey e-II 00.4 U 0.U. . .00 U. .000 U. 1.0 0

ca000 000 00000 00000 00000

00.000 Vineel NNOWOE ID0so.opdof 4n -N PW 0-.- In t- o O forr- t n Ng~.3.., 1 * ... 30- \ *.. 1 .1 01%,a .,. I. 8.**QI

'0 0 CN 0Ok 21X rG; 111 ZSop 40 s..n0 zi rnP-r- r-

N o )I40 4r 0 MY Fn o

& 0 00 0 C4*. M .000 ca.C 2y1,NoP 00 M0 PC-

Z ar-. a *omn- #D a.o.. 0 ,0 Z 0(1ai NO O of 0 f

0 000 o V4gp o 00000 on pw a n 0 I0

*~ ~ -N 0, a l~W 0.*5 N.S0 drnNO

00000 . N tu 0 000l 0 rnN 1 0000-00~ In to ID In 0 #ow4 nSI nI f o o It In ini

oN~n O P.-e 0- 0 on P 00 NWIOO

b. 10AINN 3 I NWl .lot K,0 -N -t f 0 'aN- r. N-4-Sl ) yI ~D n 00

M 0I m.-o-o z N-- 3p-orns4

30% n~~a 1 -rn r % 1. .1 o4!4.nr Mlio-u~~~~~ *rnp @ N 6-(;;o *0NS 05 0* *0 N

zN- S ga INN 0 II

;2; ;4)Q 4MMm e-

0~ 110,-o 0.t mOw t0 O

0 rnrnrnr 0* rn-a a 0 OO 0 000o@. 4 00000-

22 *- j Z.r) N-oa 2 t-r--r-r 2 -Mow

OU %3 o, or- -a. 0, We- 0--Ow is co.o

ow2 o r- o rn0 . 0 -2 * e - 0 .

X% 6 . t-rO A

- 00000 N x oo 00000 00000*Cc 0 00000x 00 2 411 z~o x ocoo x 00000 2 00000

3 3 0400 Z .... 22 ... . z .. 43

-not0 a a C, a-a

4

I4~** %..-%

-. %%

td * YIN

ilk.

~~14

p

1,