287
D-A126 456 PREIMINAY MEASUREMENTS AND CODE CLCULATIOS OF FLOM 1/3 THROUGH A CASCADE OF DCA BLADING AT A SOLIDITY OF 167 (U) NAVAL POSTGRADUATE SCHOOL MONTEREY CA W D MOLLOY IUNCLASSIFIED JUN 82 F.'G 21/5 N

THROUGH A CASCADE MEASUREMENTS OF DCA BLADING · PDF fileof DCA Blading at a Solidity of 1 .67 S. PeRPOR~eiGa ORG. REPORT ... avoid the aero-mechanical problems encountered. . S DD

Embed Size (px)

Citation preview

D-A126 456 PREIMINAY MEASUREMENTS AND CODE CLCULATIOS

OF FLOM 1/3THROUGH A CASCADE OF DCA BLADING AT A SOLIDITY OF 167(U) NAVAL POSTGRADUATE SCHOOL MONTEREY CA W D MOLLOY

IUNCLASSIFIED JUN 82 F.'G 21/5 N

__ 1111 .0 1 .5111 1 5.0 is' 1j2

l 1 3 62 11 2 . S M111 La _ _j .i I ', 1.8

,1u -0 1112.0

1 1.8

11L25m 1.-4 I 111--4 un.

MICROCOPY RESOLUTION TEST CHART

MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS-1963-A

NATIONAL BUREAU OF STANDAROS-1963-A

II".- .I....

"

-A nfl

111114 __

1111 1. ,___°0 ,__,

- -11111=.-- I~ ll

MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS-1963-A

_ II_11111 ___. ..... IIII111I,.o MO 1 20111 * * - l__AO= 112.0

I_1_ 112.2__ __.o 1I 11 .2 11111 .24 U1l11 .

MICROCOPY RESOLUTION TEST CHARTMIOOP SLUI TETCAT•

t "

NATIONAL BUREAU OF STANARS 1963-A NATIONAL BUREAU OF TANDARD -963A

/-1

+111 111U

' + : ,+ _+ -_+

.." U

NAVAL POSTGRADUATE SCHOOLMonterey, California

*

' ""

THESISPRELIMINARY MEASUREMENTS AND CODE

CALCULATIONS OF FLOW THROUGH A CASCADEOF DCA BLADING AT A SOLIDITY OF 1.67

by

* William D. Molloy Jr.

LAJ June 1982

C Thesis Advisor: Rayrond P. ShreeveA4o

I

Approved for public release; distribution unlimited

0

* 82 -• m • • '

u UNCLASS IFIEDsacumTv cLAssoiFcAriams ow Tias P~aa wn m e n a

REPOR DOCMENTATION PAGE BEFORECMLE!N ORMu* *UPORT NUMuUR 2 6Vt AcceSS16~ S. MCCIP1iIT'S CATALOG "UN61.R

4. TT. (and SuS16116j S. TYPE OF REPORT 6 PERIOD COVERED0

Preliminary measurements and Code Master's ThesisCalculations of Flow through a Cascade June 1982of DCA Blading at a Solidity of 1 .67 S. PeRPOR~eiGa ORG. REPORT NuNSeRf

7.- AUTN0RW.) S.CONTRACT OR GRANT MSRg

LV William D. Molloy Jr.

6. 0PRPORMING 0OGNIZATION NAME ANO ADDRESS As REGAN CMCT WORK ~ cT T

Naval Postgraduate SchoolMonterey, California 93940

1 1. CONTROLLING oppicE NAME Also &Goats$ 1. REPORT DATE

Naval Postgraduate SchoolJue1815. flumOeRkOF PAGES

Monterey, California 9394028

_1-4.WMONITORING* AGENCY WAVE 6 A0006680! d1#110000 ta CPRII#M O 010) It. SECURITY CLASS. (oftht be tenj

* Unclassified

IS. ECLASSIPrICATION/loowNGrmAOINGSC4EOu Le

T. OISTt@IUTIONf STA~tMENT (of 1614 ARP00f)

' Approved for public release; distribution unlimited

17. 0,STRIGUTION STATIEMENT fat Mie 4691#01 MR100lm MOOG&"* . H9000O lbein twi RWfe)

14. SUPPLEMENTARY MOTIES

it. KEY VoRaS (ConflU.0 o reverse side El01noodo an IlptifF 1W Wook Rle)

Cascade QQ4e ()L*:()

DCA Blades

* QSOU-ICA RACT (Cmut00we en ,.,w; olde of 0....ep and Mientor? 6 boo"0g 00 0)

An experimen/tal program to obtain uniform inlet flow tothe test bladinj in a large cascade facility designed to useinlet turning vines, and to measure t1~e conventional bladeelement perforn~nce, is described. A tempts to reduce non-uniformities (X1% in velocity) using screens were unsuccess-ful and so abandoned. Preliminary"Dda blade elementperformance data were obtained without screens at one

DO~ 1473 Eot-Tiof, ,09NO 66 is OBOLETs UNCLASSIFIEDSIR010-04-601SECURITY CLAWFIICATION OF THIS PAGE (Nhe ain 0Eawe

S UNCLASSIFIED

incidence angle before aero-mechanical problems with the in-let guide vane assembly curtailed testing. The blade surfacepressure distribution at the one test condition compared veryfavorably with the distribution predicted using the NASAcomputer code QSONIC. Recommendations were made that wouldavoid the aero-mechanical problems encountered. .

S

DD Forya 1473 2 UNCLASSIFIED1 i .,

O12A460 CgV 6M IAINOPvlsP4fO w FOPe

Approved for public release; distribution unlimited

Preliminary Measurements and CodeCalculations of Plow through a Cascadeof DCA Blading at a Solidity of 1.67

by

William D. Molloy Jr.Lieutenant Commander, United States NavyB.S., United States Naval Academy, 1974

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLJune 1982

w

Author: L

Approved by: r/Ue(7,c / c-"Thesis Advisor

Chairm".n, o Aeronautics

lip - Dean of Science and Engineering

3

ABSTRACT

An experimental program to obtain uniform inlet flow to

the test blading in a large cascade facility designed to use4

inlet turning vanes, and to measure the conventional blade

element performance, is described. Attempts to reduce non-

uniformities (±1% in velocity) using screens were unsuccess-

ful and so abandoned. Preliminary DCA blade element

performance data were obtained without screens at one in-

cidence angle before aero-mechanical problems with the inlet

guide vane assembly curtailed testing. The blade surface

pressure distribution at the one test condition compared

very favorably with the distribution predicted using the

NASA computer code QSONIC. Recommendations were made that

would avoid the aero-mechanical problems encountered.

4

U

U

b4

!.

TABLE OF CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . 15

II. FACILITY DESCRIPTION AND MEASUREMENT APPROACH . 20

A. SUBSONIC CASCADE WIND TUNNEL ............. 20

B. INSTRUMENTATION . . . .. .. .. .. .. .. 22

C. REFERENCE MEAS UREENT ETS... .. ....... 23

D. TEST B.ADING . . . . . . . . . . . . . . ... 23

E. DATA ACQUISITION, REDUCTION AND ANALYSIS ... 24

III. EXPERIMENTAL PROGRAM AND RESULTS . . . . . . . . . 25

A. PROGRAM OF TESTS . . . . . . .. .. .. .. .. 25

B. TEST PROCEDURES ........ .. .. .. .. 25

1. Cascade Adjustments.................25

2. Measurements. . .. .. .. .. ... .. 27

C. VERIFICATION OF INLET GUIDE VANE (IGV)AS SEMVBLY . .. .. ... .. .. ... .. .. 27

D. TESTING WITH WIRE GAUZE SCREENS...........28

E. PRELIMINARY TESTING OF DCA BLADES .......... 30

IV. DISCUSSION OF EXPERIMENTAL RESULTS . . . . . . . . 31

A. EFFECT OF INLET GUIDE VANE (IGV) MODIFICATION 31

B. EFFECT OF WIRE GAUZE SCREENS ........... 32

C. PRELIMINARY TESTING OF DCA BLADES .......... 34

1. Inlet Uniformity.................34

2. Two-Dimensionality .. .. .. .. .. .... 34

3. Periodicity.....................36

5

- - - - - -

4. Blade Performance .... ........ . 36

5. Aero-Mechanical Problems Encountered . . . 37

V. COMPUTATIONAL PROGRAM . ... ......... . 40

A. DESCRIPTION OF QSONIC ............. 40

B. APPLICATION TO THE TEST CASCADE . . . . . . . 42

C. COMPARISON OF CODE CALCULATIONS AND MEASUREDDATA . . . . . . . . . . .......... . . 43

VI. CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . 44

APPENDIX A: MODIFICATION TO THE INLET GUIDE VANESECTION OF THE SUBSONIC CASCADE WINDTUNNEL . . . . . . . . . .. 119

APPENDIX B: SELECTION AND INSTALLATION OF SCREENMATERIAL . . . . . . . . . . . . . . . . 126

APPENDIX C: CASCADE PERFORMANCE PARAMETERS (by F. S.Cina; reproduced with minor changes fromRef. 7) . . . . ................. 130

* APPENDIX D: INSTRUCTIONS FOR PREPARING INPUT ANDOPERATING QSONIC USING A RECTILINEARCASCADE CONFIGURATION. . . . ....... 132

D.1. BACKGROUND INFORMATION . ....... 132

D.2. INPUT DESCRIPTION ... .......... 134

D.3. PREPARING INPUT FILES . . . . .... 146

D.4. PROGRAM OUTPUT . . . . . . . .... 150

D.5. RUNNING THE PROGRAM .. ......... . 151

D.6. QSONIC UPDATE ............. 153

APPENDIX E: QSONIC PROGRAM LISTING ... .......... 169

LIST OF REFERENCES ....... ................... 278

INITIAL DISTRIBUTION LIST ..... ............... 280

6

LIST OF TABLES

I. MEASUREMENT UNCERTAINTY .......... . . . 47

II. CASCADE CONFIGURATION FOR DCA BLADE TESTS . ... 48

III. SUMMARY OF MEASUREMENTS WITHOUT SCREENS . . ... 49

IV. SUMMARY OF MEASUREMENTS WITH SCREENS ( = 350) 50

V. PROBE DATA, UPPER PLANE AT MIDSPAN (i = 5.30) 51

VI. PROBE DATA, LOWER PLANE AT MIDSPAN (i = 5.30) . 52

VII. CENTER BLADE DATA (i = 5 .3 O ) .......... 53

VIII. ADJACENT BLADES DATA (i = 5.301 . . ......... 54

IX. BLADE PERFORMANCE DATA .. .......... . 55

D.1. INPUT DATA FOR MESH GENERATION RUN OF OSONIC 154

D.2. TEST BLADE COORDINATES . . . .......... 155

D.3. INPUT DATA FOR FLOW SOLUTION RUN OF QSONIC . . . 156

D.4. DATA FILE FOR QUASI-3D SOLUTION . . . . . . ... 157

D.5. SAMPLE OUTPUT FROM MESH GENERATION RUN ....... 158

D.6. SAMPLE OUTPUT FROM FLOW SOLUTION RUN . . . ... 161

7

LIST OF FIGURES

1. Subsonic Cascade Facility .... ............. . 56

2. Plenum Chamber as Modified by Bartocci . . . . .. 57

3. Plenum Chamber as Modified by Moebius ....... ... 58

4. Lower PlaneSurvey Probe...... ............. 59

5. Upper PlaneSurvey Probe...... ............. 59

6. Blade Edge Detail . . ............... 60

7. Photograph of Instrumented Blade . ......... . 61

8. Instrumented Blade ..... ................ . 62

9. Instrumented Blade Tap Locations . ......... . 63

10. Data Acquisition System .............. 64

S 11. Probe Survey Data at Itidspan of Lower Plane, EndWalls at 350, Points 1 to 50, (PPLENUM - Pt)/Qref 65

12. Probe Survey Data at Midspan of Lower Plane, EndWalls at 350, Points 51 to 100, (PPLENUM - Pt)/Qref 66

13. Probe Survey Data at Midspan of Upper Plane, EndWalls at 350, Points 1 to 50, (PPLENUM - Pt)/Qref " 67

14. Probe Survey Data at Midspan of Upper Plane, EndWalls at 350, Points 51 to 100, (PPLENUM - Pt} /Qref 68

15. Probe Survey Data at Midspan of Lower Plane, EndWalls at 300, Points 1 to 50, (P - Pt re 69

16. Probe Survey Data at M4idspan of Lower Plane, EndWalls at 30° , Points 51 to 100, (PPLENUM - Pt)/Qref 70

17. Probe Survey Data at Midspan of Upper Plane, EndWalls at 300, Points 1 to 50, (PPLENUM - Pt )/Qref 71

18. Probe Survey Data at Midspan of Upper Plane, EndWalls at 300, Points 51 to 100, (PPLENUM - t)/Qref 72

8

I

19. Probe Survey Data at Midspan of Lower Plane, EndWalls at 500, Points 1 to 50, (PPLENUM - Pt)/Qref 73

20. Probe Survey Data at Midspan of Lower Plane, EndWalls at 500, Points 51 to 100, (PPLENUM - P t)/Qref 74

21. Probe Survey Data at Midspan of Upper Plane, EndWalls at 500, (PPLENUM - Pt)/Qref............... 75

22. Probe Survey Data at Midspan at Lower Plane, End

Walls at 500, Two Runs, Points 1 to 50,(PPLENUM - P t)/Qref ............................. 76

23. Probe Survey Data at Midspan at Lower Plane, EndWalls at 500, Two Runs, Points 51 to 100,

8(P PLENUM - Pt ) / Qr e f .. . . . . . . . 77

24. Probe Survey Data at Midspan at Lower Plane, EndWalls at 300, Two Runs, Points 1 to 50,(PPLENUM - Pt. / Qr e f ................ 78

25. Repetitive Samples with Fixed Probe Position (10"Left of CTR Midspan, End Walls 300, Lower Plane,(PPLENUM - PAMB ) / Qref ) 79

26. Repetitive Samples with Fixed Probe Position, 10"7Left of CTR, Midspan, End Walls at 300, Lower

Plane (P - AMB ) / Qref ........... 80

27. Repetitive Samples with Fixed Probe Position, 10"Left of CTR, Midspan, End Walls at 300, LowerPlane (PPLENUM - Pt)/Qref ............. 81

28. Repetitive Samples with Fixed Probe Position (onCenterline at Midspan, End Walls at 300, LowerPlane (PPLENUM - PAMB ) / Qr e f ) . . . . . . . . . . . 82

29. Repetitive Samples with Fixed Probe Position (onCenterline at Midspan, End Walls at 300, LowerPlane (Pt - PAMB)/Q r e f ) 83

30. Repetitive Samples with Fixed Probe Position (onCenterline at Midspan, End Walls at 300, LowerPlane (PPLENUM - P.t. / Qr e f ) .............. ... 84

31. Repetitive Samples with Fixed Probe Position (10"Right of CTR Midspan, End Walls at 300, LowerPae(PPLENUM - PAMB ) / Qref) ........... 8Plane(PLNM- /ref).............. .. 85

32. Repetitive Samples with Fixed Probe Position (10"Right of CTR Midspan, End Walls at 300, LowerPlane (Pt - P AMB)/Q r e f ) .............. 86

9

U

33. Repetitive Samples with Fixed Probe Position (10"Right of CTR Midspan, End Walls at 300, LowerPlane (PPLENUM - Pt..Q ref ............... ... 87

34. Probe Survey Data at Midspan, Lower Plane, 16 Mesh

Screen, Walls at 350, Points 1 to 50,(PPLENUM - Pt)/Qref ................ 88

35. Probe Survey Data at Midspan, Lower Plane, 16 MeshScreen, Walls at 350, Points 51 to 100,(P.PLENUM - re f .. ....... ....... 89

36. Probe Survey Data at Midspan, Upper Plane, 16 MeshScreen, Walls at 350, Points 1 to 50,(PPLENUM - Pt)/Qref............... 90

37. Probe Survey Data at Midspan, Upper Plane, 16 MeScreen, Walls at 350, Points 51 to 100,

..PLENUM -..t)/Qref............... 91

38. Probe Survey Data Span Traverse, Lower Plane, 16uMesh Screen, Walls at 350, 10" Left of CTR,

(PPLENUM - Pt)/Qref *.. *'*** ********* 92

39. Probe Survey Data Span Traverse, Lower Plane, 16Mesh Screen, Walls at 350, Center of Test Section,(PPLENUM - Pt)/Qref ................ 93

40. Plane Survey Data Span Traverse, Lower Plane, 16Mesh Screen, Walls at 350, Center of Test Section,(PPLENUM - Pt)/Qref ................ 94

41. Probe Survey Data at Midspan, Lower Plane, 16 Meshand 2 Mesh, Walls at 350, Points 1 to 50,(PPL M - Pt)/Qef ................ 95

42. Probe Survey Data at Midspan, Lower Plane, 16 Meshand 2 Mesh, Walls at 350, Points 51 to 100,(P.PLENUM - Pt /Q re f ................ 96

43. Probe Survey Data at Midspan, Lower Plane, 4 MeshScreen, Walls at 350, Points 1 to 50,(P.. .- Pt)/Q. ................ 97

44. Probe Survey Data at Midspan, Lower Plane, 4 MeshScreen, Walls at 350, Points 51 to 100,(PPLENUM - Pt)/Qref ............................. 98

45. Probe Survey Data at Midspan, Lower Plane, 5 MeshScreen, Walls at 350, Points 1 to 50,(P.PLENUM - P.t)/Qref 99

10

U .. . . . .

46. Probe Survey Data at Midspan, Lower Plane, 5 MeshScreen, Walls at 350, Points 51 to 100,(P PLENUM . . ....... .. 100

47. Wall Static Pressure Distribution ........... 101

48. Probe Survey Data at Upstream Midspan (i = 5.3,P PLENUM - P lULower Plane). ............ 102

49. Blade Surface Pressure Distribution on ThreeCenterinost Blades (i = 5.3) ............. 103

50. Probe Survey Data at Midspan (i = 5.3,(PPLENUM - Pt)/Qref Upper Plane).... ............ 104

51. Probe Survey Data at Midspan (i = 5.3, (X/), UpperPlane) .................... . 105

52. Probe Survey Data at Midspan (i = 5s3, sPwl) el,Upper Plane) ............... ......... 106

53. Probe Survey Data at Midspan (i = 5.3, Outlet Angle,Upper Plane) ........................ 107

54. Spanwise Probe Data Surveyed 1 in. from Suction Sideof Centermost Blade (i -5.3, (PPEU - PtA1Upper Plane) ........ .................... . 108

55. Spanwise Probe Data Surveyed 1 in. from Suction Sideof Centermost Blade (i 5.3, X/Y, Upper Plane).. 109

56. Spanwise Probe Data Surveyed 1 in. from PressureSide of Centermost Blade Ci = 5.3, (PN NM- P t '

Upper Plane) ........ .................... 110

57. Spanwise Probe Data Surveyed 1 in. from PressureSide of Centermost Blade Ci = 5.3, X, Upper Plane) 11).

58. Resultant Blade Force Vectors by Momentum Balance5 ------s Pand from Surface Pressure Integration

)i = 5.3.... .................... 112

59. Measured Blade Surface Pressure Distribution (i =53, Pressure Side, + = Suction Side) .............. 113

60. Measured Blade Surface Velocity Distribution (i =5.3, * = Pressure Side, + = Suction Side) . .... 114

61. 2D Code Blade Surface Mach Number Distribution(i = 5.3) .......... ..................... 115

11

62. 3D Code Blade Surface Mach Number Distribution(i = 5.3) . .. .. .. .. .. .. ... .. .... 116

r63. Measured Blade Surface Mach Number Distribution(i - 5.3)......................117

64. Blade Surface Mach Number Distribution (i=5.3) 118

A.l. Inlet Guide Vane Assembly .. .. .. .. .. .... 121

A.2. Cascade Wind Tunnel Sub-Assemblies ........... 122

A.3. View of th IGV Adjustment Mechanism. ........ 123

A.4. Side View of the IGV Assembly.............124

A.5. View of the Subsonic Cascade Wind Tunnel (NorthWall Removed)............ . .. .. .... 125

3.1. Screen Installation. .......... ... .. 129

D.l. Blade Coordinates .......... .. ... .. 167

D.2. Blade Coordinates Translated and Rotated.......167

D.3. Mesh Points on Blade Surface, Horizontal Chord . 168

D.4. Mesh POints on Blade Surface, Chord at Stagger

Angle ........ . .......... . . .. .. 168

12

LIST OV SYMBOLS

AVDR Axial velocity-density ratio

CPl Coefficient of pressure at the inlet

CP2 Coefficient of pressure at the outlet

CPSTATIC Coefficient of static pressure rise

C Blade chord (inches)

D Diffusion factor

i Incidence angle (degrees)

P Pressure (in. H2 0)

Q Dynamic pressure (in. H2 0)

T Temperature (0R)

V7 X Non dimensional velocity

8 Air ahgle, measured in the cascade midspan planewith respect to the axial direction (degrees)

y Stagger angle

K~a Solidity (C/S)

Loss coefficient

Subscripts

amb Ambient

P Pressure

PLENUM Plenum (supply)

s Static

wl North wall, lower plane

13

ACKNOWLEDGMZNT

I would like to express my sincere thanks and apprecia-

tion to Dr. R. P. Shreeve, Director, Turbopropulsion Labora-

tory, for his guidance during the project. His affable

nature and professional expertise made this study a most

enjoyable learning experience.

A special note of thanks to Jim Hammer, Al McGuire, John

Morris and Kelly Harris. Without their prompt and efficient

help, this study would not have been possible.

Lq.

14

U

I. INTRODUCTION

The need for lightweight, fuel efficient gas turbines

that are capable of developing large amounts of thrust or

power has motivated a continuing drive to obtain more ac-

curate predictions of the flow through turbomachinery.

Cascade testing of blade rows has, in the past, been a logi-

cal and relatively inexpensive way to learn more about the

phenomena involved in the flow through compressor and tur-

9 bine stages. It is required more today in order to verify

two dimensional and near-two dimensional analysis codes for

flow through cascades. Such testing also provides two-

dimensional blade element performance data which, in the

absence of reliable analytical predictions, are required in

the design of compressors and turbine stages. Reference 1

describes how cascade measurements are obtained using a cas-

cade wind tunnel and then used in the design process.

Before subsonic cascade wind tunnel data can be accepted

* as being valid, the flow conditions must meet three require-

ments. These criteria are discussed in detail in Refs. 1, 2

and 3. First, any disturbance in the airflow should be

caused by the test blades; that is, the inlet flow to the

test section must be acceptably uniform.

Secondly, the measured flow characteristics should,

ideally, be independent of spanwise position along the test

15

blades. The flow, ideally, should be two dimensional.

Duval [Ref. 3] demonstrated that excellent flow conditions

could be achieved in the Naval Postgraduate School Turbo-

propulsion Laboratory (NPS/TPL) Subsonic Cascade Wind Tunnel

using test blades with an aspect ratio of approximately two.

The absence of suction along the walls results however, in

some degree of streamline contraction which is measured in

terms of an Axial Velocity Density Ratio (AVDR).

The third requirement which must be satisfied is the

periodicity of the inlet flow to the test section and of the

outlet flow. Within one chord length of the leading edges

of the test blades an upstream perturbation occurs as the

streamlines adjust to negotiate the blade passages. Since

the rectilinear cascade is simulating an infinite cascade of

blades, the flow characteristics should be the same at cor-

responding axial and blade-to-blade positions within each

blade passage. This same condition should be true at any

measurement plane downstream of the test blading.

As described by Rose and Guttormsen [Ref. 41 several

* unique features were incorporated into the design of the

NPS/TPL Cascade to ensure a two-dimensional and periodic

flow at the test blading. Initial evaluations of the fa-

* cility were conducted and reported in Refs. 3, 4, 5 and 6.

Work by Moebius [Ref. 6] involved modifications to the tun-

nel plenum chamber which established satisfactory uniform

16

U

flow at the exit of the belimouth contraction into the test

section.

In order to maintain an aspect ratio close to 2.0 at a

solidity of 1.67 Cina [Ref. 7), following the work of Duval

[Ref. 3], used a cascade configuration of 20 blades with 3

inch spacing. Cina conducted a program of tests of OCA

blading at five (5) different air incidence angles. With

this cascade configuration, Cina found that the inlet flow

to the test section was uniform in direction and of uniform

static pressure, but with an imposed variation in velocity

* and stagnation pressure resulting from the wakes of inlet

guide vanes. Although excellent periodicity was found over

pairs of test blades, departure from strictly periodic con-

ditions were detected from one blade passage to another.

Cina explained this condition as being the result of the

inlet guide vane wakes being separated at two inch intervals

and entering a test section configured with a three inch

blade spacing. Because of these flow conditions, Cina con-

sidered his results to be preliminary.

* As a result of these findings the Cascade Wind Tunnel

was modified so that inlet guide vanes were provided at one

inch intervals. The object of the study reported herein

was to obtain blade performance data on Cina's cascade with

good periodic and uniform flow conditions. A necessary

condition was to obtain agreement in the results for blade

forces evaluated from surface pressures and from a momentum

17

* balance. A second objective was to compare measured blade

surface Mach numbers with the results of code calculations.

At the outset, it was first necessary to carry out an

extensive testing program to verify the new inlet guide vane

section and the effect the new spacing had on flow uni-

formity and periodicity. It was found that the uniformity

of dynamic pressure was improved with the inlet guide vanes

spaced at one inch intervals. Attempts were made to further

improve the flow by the use of (various) wire screens placed

downstream of the inlet guide vanes. These methods proved

unsuccessful for the range of parameters tested and in fact

aggravated the situation.

Cina's testing of the Double Circular Arc blading was

pi repeated without screens and with the Cascade Wind Tunnel

configured with the modified inlet guide vane arrangement.

Limited measurements were obtained before aero-mechanical

problems with the new IGV arrangement, at the higher tunnel

speeds, were encountered.

The overall purpose of the testing program initiated by

Cina was to obtain data with which to verify design optimi-

zation computer codes developed by NASA. Towards this goal

a fast, reliable computer analysis code (QSONIC) for cal-

culating the flow field about a cascade of arbitrary 2-D

airfoils was obtained from NASA. The code was adapted and

modified to run on the Naval Postgraduate School's IBM

370/3033 computer.

18

The program QSONIC was developed by NASA to overcome the

Mach number limitations of the earlier program TSONIC (Ref.

81. QSONIC is described in Ref. 9. Procedures for using

the program QSONIC at the Naval Postgraduate School's com-

puter facility are given in Appendix D. The procedures are

documented for the case of the DCA blading in the NPS/TPL

cascade wind tunnel. A program listing is included to docu-

ment changes made to the code in order to adapt to the oper-

ating system of the NPS computer.

Preliminary results show that experimental measurements

and code predictions are in very good agreement.

19

II. FACILITY DESCRIPTION ATD MAS'URMET APPROPCH

A. SUBSONIC CASCADE WIND TUNNEL

The Naval Postgraduate School's Rectilinear Cascade

Facility is shown in Fig. 1. A description of the facility

as it was originally configured is given in Ref. 4. The

test facility is an open cycle wind tunnel, designed for

the purpose of testing cascades of axial-flow turbomachinery

compressor or turbine blades. The unique design of the test

section ensures that the airflow paths from the inlet guide

vanes to all of the blades of the cascade test section are

of equal length. This particular design was intended to

eliminate the problems found in other cascade wind tunnels

caused by having wall boundary layers ot different thick-

nesses entering the cascade at different points.

As a result of the work reported in Ref. 1, two fine

mesh screens were installed at the bellmouth entrance to

improve flow stability. A follow-on study into the cascade

performance was conducted by Bartocci and is reported in

Ref. 5. As a result of Bartocci's findings, plenum turning

vanes were installed to direct plenum inlet air towards the

bellmouth entrance and to decrease the total pressure fluc-

tuations present at the bellmouth entrance. Figure 2 shows

the configuration of the plenum chamber as modified by Bar-

tocci. Reference 6 describes work by Moebius that resulted

20

U

U

in further modification to the plenum chamber in which the

original contraction was changed to two two-dimensional con-

tractions in series. After this modification, acceptably

small variations in velocity and flow angle were measured

at the inlet guide vane station. Figure 3 shows the in-

ternal arrangement of the plenum chamber as modified by

\ Moebius and as it was configured for the work presented

here.

Using the plenum configuration shown in Fig. 3, Duval

[Re4J3] found that the wakes from the inlet guide vanes

were not mixed out at the lower measuring plane of the test

section but gave a well defined periodic variation in the

impact pressure. The peak-to-peak variation was ±4% of

dynamic pressure over two-inch periodic intervals. This

condition was undesirable, but was tolerated while looking

only to establish the values of parameters required to

li achieve two-dimensionality and periodicity. Since the

inlet flow conditions were not uniform, mass averages were

used to calculate properties at the inlet plane from probe

* measurements.

In order to achieve a solidity of 1.67 and aspect ratio

of about 2, a blade spacing of 3 inches was required for the

tes'a carried out by Cina (Ref. 7]. The tests showed unac-

ceptable departures from blade-to-blade periodicity under

conditions of high blade loading and the installation of

q additional guide vanes was recommended. The modification

21

to the inlet guide vane section of the tunnel resulting from

Cina's findings is described in detail in Appendix A.

In the present work, several tests were completed with

the tunnel further modified by the introduction of wire

screens between the inlet guide vanes and the lower plane of

the test section. Appendix B describes the screen material

and the criteria used to select the particular screens used

in this study.

B. INSTRUMENTATION

The instrumentation used in the present study is that

*whicA is described in detail in Ref. 7. Twenty static pres-

sure taps were located on the north and south side walls.

The taps on the south wall were connected to a water mano-

meter board so that the uniformity of the static pressure

distribution of the inlet and outlet could be monitored

visually. Additionally, one upstream tap on each wall and

one downstream tap on each wall (near the centerline) were

also connected to the Scanivalve so that these static pres-

sures were recorded.

Figure 4 shows the probe that was used for the upstream

survey (at the lower plane). The probe was a United Sensor

Corporation DA 125 probe, serial number A847-1, calibrated

earlier at various Mach numbers and yaw angles in a cali-

bration facility. The United Sensor Corporation DC-125-24-

F-22-CD probe, serial number A981-2 (Fig. 5), which was used

22

at the upper plane was similarly calibrated. The charac-

teristics of the probes were approximated analytically to

facilitate automatic data reduction procedures. The cali-

bration and application procedures were those given by Duval

[Ref. 3]. Appendix B of Ref. 3 describes both the upstream

and downstream probes in detail. The mounting and traversing

mechanisms are described in Ref. 7.

C. REFERENCE MEASUREMENTS

Plenum chamber (supply) pressure and temperatures, and

atmospheric pressure were recorded on each data scan.

S Plenum pressure was also displayed on a water manometer

board. The total temperature in the test cascade was as-

sumed to be the same as the plenum chamber temperature.

D. TEST BLADING

The double circular arc test blading modeled the midspan

IN I section of the stator of the compressor stage reported in

Ref. 10. Coordinates describing the profile of the blading

are listed in Table D-2. The leading edge and trailing edge

* are shown in detail in Fig. 6. A photograph of the center-

most blade is shown in Fig. 7.

The three blades centrally located in the cascade were

* constructed with surface pressure taps along the midspan

section as shown in Fig. 8. The centermost blade had 19

ports on each of the pressure and suction surfaces and one

tap at the leading edge. The two blades adjacent to the

23

center blade had 3 surface pressure taps located on each of

the pressure and suction surfaces. The surface pressure tap

locations for the centermost blade are given in Fig. 9.

E. DATA ACQUISITION, REDUCTION AND ANALYSIS

Data were recorded, reduced, and plotted using the modi-

fied Hewlett Packard HP-3052A Data Acquisition System shown

in Fig. 10. Reference 11 describes the system in detail.

The system incorporated a HP-9845A desktop computer as a

controller, with all components connected on the HP-98034A

HP-IB Interface Bus. A NPS/TPL HG-78K Scanivalve Controller

IU with two 48 port Scanivalves allowed the programmed acqui-

sition of probe and blade surface pressure measurements.

The software used in the present study for acquisition,

reduction and plotting of data were developed from software

originally created by Duval and Cina. The programs are

listed and described separately in Ref. 12.

The uncertainties in the measurements are listed in

Table 1.

2

K.

U

24

III. EXPERIMENTAL PROGRAM 'AD RESULTS

A. PROG2RAM OF TESTS

The test program was in three phases. First, in order

to verify the new inlet guide vane assembly, tests were con-

ducted with no blading in the test section and with the

upper and lower endwalls set parallel at 350 (design condi-

tion), 300 and 500 with respect to axial.

Secondly, tests were made of the effect of wire gauze

screen materials in reducing non-uniformities in the flow

entering the test section. Appendix B describes the type

of screens used and how they were installed.

1(,J The last phase of the test program was a continuation

of the work initiated by Cina. Table II lists the cascade

configuration tested. One test was completed successfully

before aero-mechanical problems were encountered and testing

was halted until the causes were analyzed.

B. TEST PROCEDURES

1. Cascade Adjustments

In the first and second phases of testing, the same

procedures were used to realign the cascade for each new

configuration. The lower and upper end walls were set to

the desired flow angle and the inlet guide vanes were set

so that their trailing edges were approximately aligned with

25

the end walls. The flow was started, and the desired inlet

dynamic pressure was set. All tests were run at an average

dimensionless inlet velocity (X) of about .13, corresponding

to an inlet flow dynamic pressure of 18 inches water. Be-

fore recording data, the water manometer board was checked

to ensure that the distributions of wall static pressures

at the inlet plane and outlet plane were acceptably uniform.

If required, the inlet guide vanes were adjusted to obtain

uniform static pressure to within ±0.5 inches of water.

In the third phase of testing, initially the pro-

cedures used by Cina IRef. 7] were followed, namely: the

lower end walls were set to the desired inlet air angle and

the upper end walls were set approximately to the expected

exit air angle. The inlet guide vanes were set very approxi-

mately and the cascade was turned on and set to an inlet dy-

namic pressure of 18 inches water. The upper end walls and

the inlet guide vanes were adjusted in turn to obtain wall

r static pressure distributions upstream and downstream which

were acceptably uniform. Using this procedure however it

* was found on occasion that the inlet air angle sensed by the

probe at the lower plane at mid-span could be 2 or 3 degrees

different from the setting of the end walls.

The following procedures was subsequently adopted.

The lower end walls were set to the desired inlet air angle.

The upper end walls were adjusted to be "wide open", to form

9 a diverging passage in which, when the cascade was turned

26

on (to an inlet dynamic pressure of 18 inches water), the

flow was completely separated. The inlet guide vanes were

adjusted to obtain the required inlet air angle on the chan-

nel center line over the center 24 inches in the blade-to-

blade direction. The upper end walls were then moved

individually towards the vertical until the lower plane

static pressure distribution was uniform and the upper plane

static pressure distribution was acceptably uniform at a

value close to atmospheric pressure. No readjustment of the

inlet guide vanes was made.

2. Measurements

Probe surveys were carried out in the blade-to-blade

direction at midspan at the upper and lower planes. In the

W) first and second phases of testing, data were taken over

approximately 2h inches of the test section at intervals of

0.25 inches. Also, in order to test the repeatability of

measurements, repetitive samples were taken with the probe

held fixed at midspan at the lower plane at the center, 10

inches to the right and 10 inches to the left of center.

During the third phase of testing, data were taken

using the procedures established by Cina in Ref. 7.

C. VERIFICATION OF INLET GUIDE VANE (IGV) ASSEMBLY

The results of the first phase are presented (as shown

in Table III) in Figs. 11 to 32. The results are arranged

into groups. The first group (Figs. 11 to 14) are

27

I"

measurements of tunnel conditions with the end walls set at

35 degrees. Plots of conditions at the lower plane are fol-

lowed by plots of conditions at the upper plane.

Results for a wall angle of 30 degrees are given next

(Fig. 15 to Fig. 18), followed by results for a wall angle

of 50 degrees (Fig. 19 to Fig. 21). Data were taken over 24

inches at the lower plane, and also at the upper plane at

300 At 500, at the upper plane, only the center 12 inches

were surveyed.

The degree of repeatability of conditions in the wind

tunnel from test to test (with no change in wall setting) is

demonstrated by the results plotted in Figs. 22, 23 and 24.

The last group of plots, Figs. 25 to 33, shows the de-

gree of repeatability in the probe data from scan to scan.

Data for these plots were obtained by holding the probe sta-

tionary at midspan in three specific blade-to-blade loca-

tions in turn and taking 50 repetitive scans of the channels

normally recorded for survey profile data. The time inter-

val. for each scan was approximately 20 seconds.

D. TESTITIG WITH WIRE GAUZE SCREEN7S

The selection and installation of the wire gauze screens

is described in Appendix B.

The measurements obtained with the various screen con-

figurations are given (as shown in Table IV) in Fias. 34 to

45. The results are arranged in four groups.

28

iI

The first group of plots (Fig. 34 to 40) give data ob-

tained with the 16 mesh .0105 inch diameter wire screen in-

stalled. Over a blade-to-blade distance from -1.0 to 7.0

inches (Fig. 35) a peak-to-peak variation in velocity of

about 1 percent was noted. This is slightly greater than

the less than 1 percent (0.9 percent) variation noted over

the same survey region without a screen installed (Fig. 12).

The results shown plotted in Figs. 41 and 42 were ob-

tained with two screens installed. One screen (16 mesh,

.0105 inch diameter) was installed as discussed in Appendix

B, while the second screen (2 mesh, .0400 inch diameter) was

attached across the duct at the leading edges of the inlet

guide vanes.

Wje The fourth group of plots (Figs. 43 to 46) show the re-

sults for two different single screens. Probe survey data

for these screens was taken only at the lower plane. The

results shown plotted in Figs. 43 and 44 are data obtained

with a 4 mesh, .041 inch diameter wire screen installed.

The variation in velocity in the blade-to-blade direction

was as much as ±1.1 percent, ?eak-to-peak. The results

shown in Figs. 45 and 46 are for a 5 mesh, .041 inch diameter

wire screen. The variation in flow velocity was approxi-

mately ±1.5 percent, peak-to-peak.

29

E. PRELIMINARY TESTING OF DCA BLADES

The results contained in Tables V to IX and Figs. 47 to

60 are arranged in the following manner.

The results shown plotted in Figs. 47 to 60 are divided

into two separate groups. The first group (Figs. 47 to 57)

contain results which exhibit the quality of the wind tunnel

flow conditions. The second group (Figs. 58 to 60) shows

the blade forces (and surface pressures) from survey data.

In the first group of figures, results are presented first

to examine the inlet flow uniformity (Figs. 47 and 48);

* second, to examine the outlet flow periodicity (Figs. 49 to

53); and, finally, to examine outlet flow two dimensionality

(Figs. 54 to 57).

All points are shown connected with straight lines.

30

IV. DISCUSSION OF EXPERIMENTAL RESULTS

A. EFFECT OF INLET GUIDE VANE (IGV) MODIFICATION

The probe survey data shown in Figs. 11 and 12 were

taken at the lower plane, with the end walls set at 35 de-

grees. A turning angle of 35 degrees corresponded to the

"design point" of the inlet guide vanes, when the airflow

from the plenum chamber was at zero angle of incidence to

the leading edge of the IGV's. These two figures show that

the inlet plane total pressure at midspan in the blade-to-

blade direction had a peak-to-peak periodic variation of

about ±2 percent and therefore about a ±1 percent peak-to-

wig peak variation in the velocity. Corresponding data from

probe surveys at the upper plane (Figs. 13 and 14) show that

periodic variations in total pressure were reduced to about

25% of the value at the lower plane by the mixing of the in-

let guide vane wakes.

It can be seen in Figs. 15 to 21 that at "off-design"

conditions for the IGV's (endwalls at 300 and 500) there is

a greater periodic variation in total pressure at the lower

plane in the blade-to-blade direction than at the design

point conditions. In Fig. 15 and Fig. 16, it can be seen

that the periodic variations in total pressure are more pro-

nounced with the flow from the plenum at a negative incidence

angle to the IGV's (endwalls at 300). Except for the first

31

8 data points in Fig. 15, there is a well defined period of

about 1 inch of travel.

Figures 19 and 20 show the probe surveys conducted with

endwalls at 50 degrees. At this off design condition the

periodic variation in total pressure was considerably

greater than the design point and the individual wakes from

the inlet guide vanes were much less well defined.

:The repeatability of the survey was examined at wall

angles of both 500 and 300. Figs. 22 to 24 show that the

non-uniformities in the flow conditions were repeated to

* (generally) better than 0.5 percent of total pressure. The

question was then, to what accuracy could the individual data

points be repeated in successive samples. This was examined

V Vil at several probe positions and the results given in Figs. 25

to 33 explain the departures in Figs. 22 to 24.

B. EFFECT OF WIRE GAUZE SCREENS

All testing with screens was conducted with the end walls

and inlet quide vanes set to yield a flow angle of 35 de-

a grees. The data obtained with screens installed were there-

fore compared with the data obtained without screens, shown

in Figs. 11-14. The effect of the pressure drop across the

screen on the pressure coefficient plotted in Figs. 34-35

should be noted. With the first screen installed the drop

in total pressure from plenum to the probe in the lower plane

q was about 10 inches of water (plenum pressure minus total

32

- ----

pressure measured by the probe at the lower plane). With-

out the screen (at design conditions), the pressure drop

from the plenum to the probe at the lower plane was approxi-

mately 2.0 inches of water. Since Q ref was defined as the

difference between plenum pressure and lower wall static

pressure, the value of Qre f with the first screen installed

was about 28 inches water and without the screen installed,

about 20 inches water. In comparing the peak-to-peak varia-

tion in P1 seen in Fig. 11 with that obtained with the first

screen installed in Fig. 34, the difference in the values of

0re must be considered. Examinations showed that the peak-

to-peak variation in velocity remained at approximately 1%

when the screen was installed.

V:igures 38 to 40 are plots of data obtained during a

spanwise traverse of the probe at the lower plane. These

figures 3how that the pressure drop through the screen and

turning vanes was nearly uniform over approximately 8.0

inches of the 10.0 inch span of the tunnel.

In an attempt to generate upstream disturbances that

might trigger early boundary layer transition on the IGV's

and increase the rate of mixing of the wakes, a second screen

was attached to the leading edge of the IGV's. The results

in Figs. 41 and 42 showed that this was not the case and in

fact the second screen increased the magnitude of the non-

uniformities at the lower survey plane. Measurements made

with a single 4 mesh (Figs. 43 and 44) and a single 5 mesh

33

screen (Figs. 45 and 46) of similar blockage showed that

neither screen influenced the flow in a particularly favora-

ble manner. The 4 mesh screen caused the peak-to-peak

variation in velocity to be about ±1.1 percent, while the

5 mesh screen caused the variation to be about ±1.5 per-

cent. This compared unfavorably with the variation ob-

tained without any screen installed which was less than ±1

percent.

It was therefore decided to proceed with measurements

of the test cascade without using screens.

1

C. PRELIMINARY TESTING OF DCA BLADES

1. Inlet Uniformity

The probe survey at the lower plane in Fig. 48 shows

that the inlet plane total pressure at midspan varied in the

blade to blade direction less than 0.5 inches of water, with

no well-defined spatial period. This was an improvement in

the inlet conditions found by Cina [Ref. 7: Fig. 16]. That

the spatial period was not well defined agreed with the

findings presented earlier in this report. The wall static

pressure distribution (Fig. 47) showed small variations

(less than 0.5 ins. water peak-to-peak at the lower plane,

q.4 ins. water peak-to-peak at the upper plane).

2. Two-Dimensionality

The data in Figs. 54 to 57 show that, at the down-

stream plane, an area of (spanwise) nearly uniform conditions

34

existed near the centerline of the cascade. Reference 2

points out that at higher loadings it is difficult to estab-

lish a substantial spanwise area of uniform flow in the

region near the suction side of the blade. This difficulty

is evident in the data shown in Figs. 54 and 55 which show

that only about 20% of the spanwise distance is acceptably

uniform. It is noted that Cina also found reduced areas of

uniform flow at this incidence angle; however, 30-40% of the

spanwise distance was found to be acceptably uniform in his

case. The difference could be the result of the reduced

spacing of the IGV's and its effect on the side wall boundary

layers.

Figure 58 shows results for inlet and outlet flow

angles and blade force vectors derived in two ways as shown

in Appendix B of Ref. 7. These two methods are first the

applications of momentum conservation to probe survey data

and second, the integration of surface pressures measured

over the blade area. Reference 2 points out that for truly

two dimensional flow the blade forces derived from the two

methods should be the same. As shown in Fig. 58 the magni-

tudes and the directions of the two vectors representing the

blade forces are in reasonable agreement. It is noted how-

ever that at this particular incidence angle Cina (Ref. 7]

measured blade forces that were in total agreement in direc-

tion but disagreed slightly in magnitude. The values of the

35

force magnitudes were about 1.5% lower than those measured

by Cina.

3. Periodicity

As can be seen in Figs. 50 and 51 the total pressure

and velocity qualitatively repeated fairly well over three

central blade passages. Acceptably small quantitative dif-

ferences are noted. There was also a small but measurable

difference in the surface pressures on adjacent blades, as

is evidenced in Fig. 49.

4. Blade Performance

* Figures 59 and 60 are plots of the pressure and

velocity distributions respectively over the centermost

blade. These results compare favorably to those obtained

T vile by Cina for an incidence angle of 5.30

Table IX contains the blade performance parameters

deduced from the probe survey data listed together with the

data obtained for corresponding test parameters in Ref. 7.

While differences in two sets of data are evident, the dif-

ferences are not large. It is noted that the value of the

loss coefficient was only 10% lower than was measured by

Cina, but the AVDR was less than 2% different from unity

rather than the 6.5% measured by Cina. Further measurements

need to be made, particularly in the light of the following

discussion, before stronger conclusions can be drawn.

36

5. Aero-Mechanical Problems Encountered

Fifteen cascade tests were made while evaluating the

new inlet guide vane assembly and testing the wire screens.

All runs were made without test blades installed, with a

plenum total pressure of about 20 inches of water and with

the upper and lower end walls parallel. No difficulties

were encountered in establishing the desired flow conditions

or in using the inlet guide vanes to arrive at a satisfactory

distribution of wall static pressures.

The first time the Cascade Wind Tunnel was set up

with test blades installed to take data at an air inlet angle

of 39.2 a, the tunnel operated normally and the test was com-

pleted. (The data from this test were subsequently found to

wy be highly suspect and are not reported here.) During the

next test, with an inlet air angle of 42.4, the start-up

appeared normal and previously established procedures were

used to arrive at a satisfactorily uniform wall static pres-

sure distribution. Tunnel operation appeared to be normal

while taking data, but on shutdown a very noticeable high

q frequency vibration was encountered. Examination of the in-

let guide vanes revealed that about 40% of the 60 blades

were damaged. Damage included chips missing from the trail-

ing edges, blades bent, cracks at the weld where the blade

is joined to its support and indications that the suction

side near the leading edge of one blade had been vibrating

37

against the pressure side near the leading edge of an ad-

jacent blade.

After the inlet guide vanes had been repaired and

reinstalled extreme care was used at the beginning of the

next test to adjust the inlet guide vanes, wth two indi-

viduals monitoring the movement of the adjustment mechanism.

(IGV adjustment mechanism is described in detail in Appendix

A.) A lack of stiffness in the mechanism was suspected as

having been a contributing factor to the failure.

one successful test was completed at an inlet flow

*angle of 42.4 0 and these data were discussed above.

with the next cascade configuration set, at an air

inlet angle of 45.90 , when the IGV's were adjusted after

U) w starting up, high frequency vibrations were again experi-

enced. The wind tunnel was shut down and no further testing

was attempted at plenum total pressures as high as 20 inches

of water gauge.

The difficulty encountered with the IGV's is not

fully understood, however the lack of stiffness present in

* the actuation of the two separate rows of vanes is suspected

of having allowed the problem to occur. Certainly, the pos-

sibility of an aerodynamic~ flutter condition being present

* (due to the misadjustment perhaps) can not be ignored. It

was noticed after the initial failure that the lead screw

which adjusts the IGV's could be turned but the blades

mounted from only one side would be caused to rotate. This

38

could lead to the trailing edge of one blade contacting the

trailing edge of an adjacent blade and effectively closing

the blade passages.

Also, the holes in which the cylindirical shanks of

the IGV's were held were found not to be uniformly machined.

As much as 0.1 inches of movement at the tip of some vanes

was possible while others could barely move. (The most

seriously damaged blades were found in or adjacent to :Zhe

larger holes.)

The tendency for the mechanism to "hang-up" on one

side would be greater as the vanes became more highly loaded.

It is noted that the IGV problem was encountered first when

going to increased incidence angles with the compressor test

V cascade installed. In setting a constant plenum t otal pres-

sure of 20 inches of water gauge, the static pressure in-

crease across the test blades to a constant atmospheric

pressure at the downstream side implies that a progressively

increasing dynamic pressure was being generated out of the

turning vanes. This can be seen in Table IX, where for

the test at $1 42.4 was 25 inches of water.

39

V. COMPUTATIONAL PROGRAM

A. DESCRIPTION OF QSONIC

LThe computational code, QSONIC, was developed by the

staff at the NASA Lewis Research Center.1 This code is able

to calculate the blade-to-blade flow conditions in turbo-

machinery blade rows assuming inviscid flow but including

streamtube convergence and radius change in the throughflow

direction. QSONIC is flexible enough to allow the input of

the appropriate boundary conditions to calculate the flow

through the test blading in the Subsonic Cascade Wind Tun-

nel. The program uses a fully conservative solution of the

'- *" full potential equation combined with the finite volume

method on a body-fitted mesh. QSONIC uses an artificial

density imposed in the transonic region, if such a region

exists, to ensure stability and the capture of shock waves.

The analysis used by QSONIC is a combination of transonic

analysis methods to calculate the flow conditions in the vi-

cinity of a cascade of airfoils. A conservative form of the

full potential equation is discretized at every point of a

body fitted periodic mesh and a mass balance is calculated

through the finite volume surrounding the point. The volume

iThe help and advice received from Charles Farrell atI ASA Lewis R.C. in the process of adapting QSOtIC to theNPS computer is gratefully acknowledged.

40

is corrected three dimensionally for any change in stream-

tube thickness along a streamtube, if a quasi-3D solution is

desired. Either elliptic or hyperbolic non-linear partial

differential equations are used, depending on the local Mach

number.

The analysis used in developing QSONIC made the following

assumptions:

1) The airflow is inviscid and adiabatic.

2) The airflow relative to the test blades is steady.

3) Air is a perfect gas with constant specific heat.

4) The airflow is isentropic and any discontinuities suchas shocks are so weak that they may be approximated asisentropic jumps.

5) There is no velocity component normal to thestreamsurface.

6) The airflow relative to a fixed reference frame (i.e.absolute velocity) is completely irrotational.

Assumption 4 requires that the peak local relative Mach num-

ber on a blade surface be 1.4 or less. The Mach numbers

measured in test blades in the Subsonic Cascade Wind Tunnel

would be well within this limit. However, this limitation

would probably preclude the use of QSONIC for analysis of

the flow field in the NPS transonic cascade wind tunnel.

There are some combinations of blading geometry and flow

conditions which cause unsatisfactory results to be gener-

ated. For example, because of assumptions 1 and 6, sharp

leading edges at high incidence angles (more that a few

degrees) cause large velocity peaks in the blade surface as

41

the flow tries to turn from the stagnation point to the

suction surface.

Reference 9 gives a detailed description of QSONIC and

the solution method used including the governing equations.

Appendix D describes the operating procedures to use QSONIC

on the Naval Postgraduate School's IBM 370/3033 computer.

Appendix D also describes the input and output required as

applicable to the Subsonic Cascade Wind Tunnel.

B. APPLICATION TO THE TEST CASCADE

Appendix D describes in detail the generation of the

input required for OSONIC when applied to test blading in

the Subsonic Cascade Wind Tunnel facility. In the present

work one comparison olf code calculations and measured data

U). was made before testing was stopped. The comparison was

for an inlet flow angle (B81) of 42.40

Tables D.1 and D.3 show the input data generated. Table

DA6 shows the flow solution output by QSONIC. The flow cal-

culated on the blade surface, using a 15 by 97 mesh, was

examined. Figure 61 is a plot of the calculated Mach number

along the blade surface using two dimensional inputs. Fig-

ure 62 is a plot of computed Mach number incorporating quasi-

three dimensional effects. The method of incorporating

quasi-three dimensional effects is explained in Appendix D.

42

C. COMIPARISON OF CODE CALCULATIONS AND MEASURED DATA

Table VII lists the data measured in the cascade wind

tunnel. Cp,1, C p2 and Xvel are defined in Appendix C. The

surface Mach number distribution measured on the center blade

is shown plotted in Fig. 63.3:

For comparison, the computed two dimensional, computed

quasi-three dimensional, and the Mach number measured in the

cascade wind tunnel are plotted together in Fig. 64.

Excellent agreement between all three cases is seen.

As would be expected, the greatest difference between mea-

sured and calculated data is near the leading edge in the

suction side and at the trailing edge of the blade.

43

VI. CONCLUSIONS AND COMENDATIOIS

Based on the results of the first part of the present

study, to evaluate the effects of the altered inlet guide

vane spacing on flow uniformity and periodicity, the follow-

ing conclusions were drawn:

1. With the inlet guide vanes operating at design, thepeak-to-peak variation in velocity was about ±1%, andthere was a well defined spatial period of about 1inch.

2. Operating the cascade wind tunnel in a configurationthat requires the inlet guide vanes to be set to otherthan zero incidence resulted in peak-to-peak varia-tions in velocity greater than ±1% and a spatial periodthat was less well defined.

The second part of the study, to evaluate the use of

wire gauze screens to further reduce the non-uniformities in

the flow field, led to the following conclusions:

1. A 16 mesh screen with a blockage factor of .69 had aslightly aggravating effect in the variation in velo-city. The peak-to-peak variation in velocity with thescreen installed was slightly greater than with noscreen installed. This occurred at the expense of apressure drop of about 10" of water across the screen.

2. The use of screens with similar blockage but withlarger mesh and larger diameter wires resulted inlarger peak-to-peak variations in the velocity at thelower plane.

The overall objective of the present study was to mea-

sure the performance of the DCA test blading. Because of

aero-mechanical problems encountered with the inlet turning

vanes the performance of the blades was obtained at one

44

V

incidence angle only. The following was concluded from the

limited test program:

1. As a result of the reduced inlet guide vane spacingthe variations in velocity and total pressure at theinlet plane were much less than those reported by Cina.

2. Good periodicity was found from one blade passage toanother.

3. An acceptable region of spanwise uniformity (20-40% ofblade span) was found at the downstream plane at theone test condition reported. However, this was lessthan was previously reported for the same incidenceangle.

4. The blade forces derived from the integration of sur-face pressure measurements and probe survey data werein close agreement in both magnitude and direction.

5. The Mach number measured by surface pressure taps overthe surface of the blade and Mach number calculatedusing the program QSONIC were in excellent agreementqualitatively and reasonable agreement quantitatively.

6. The specific reasons for the aero-mechanical problemsW). experienced with the inlet turning vanes have not been

identified completely.

Based on these conclusions and other observations, the fol-

lowing recommendations are made:

1. Use of the present inlet guide vane assembly and ad-justment mechanism for testing at inlet dynamic pres-sures higher than about 15 inches of water is unsafe.There are three possible solutions to this problem.

a) Operate only within the dynamic pressure range of10-15 inches of water.

b) Modify the new inlet guide vane assembly so thatthe vanes are supported at both ends on their axes

q of rotation. (Supporting the IGV's from both endswould prevent flapping vibrations of the (present-ly) cantilevered vanes. Such vibrations, when thevanes are supported alternately from opposite endsand the gaps are small compared to the chord,might lead to a potentially destructive fluttermode at particular flow velocities.]

45

c) Replace the entire inlet turning vane section withone of entirely new design.

2. The procedure should b'R adopted immediately of adjust-ing the vanes and walls of the cascade at lower valuesof the dynamic pressure before increasing the blowerspeed to the desired operating condition.

3. More time needs to be spent to examine the flow field'Is produced between the guide vanes and the test blades,

and to establish the effects of the movement of thetail boards. The uniqueness of the flow field when thewall static pressure uniformity is used as a criterionof good inlet flow, needs to be examined by conductingrepetitive tests at nominally similar test parameters.only when the adjustment of the flow in the facilityand the quality of the flow itself is fully understoodshould the measured blade performance data be acceptedas final.

4. The upper el.ectrical yaw adjustment mechanism shouldbe replaced with a manual system to greatly decreasethe time required to achieve probe pressure (angle)balancing.

5. Develop the computer code necessary to take advantageps of the plotting data created by QSObNIC.

6. Modify the data acquisition and reduction software forthe HP 9845 so that real time plots of blade perfor-mance parameters can be displayed.

46

TABLE I. MEASUREMENT UNCERTAINTY

Item Description Method Uncertainty

x Blade-to-Blade dimension Position -. 01 in.x - 0 in. West end Potentiometerx - 60 in. East end

z Spanwise dimension Position t.01 in.z - 0 in. North wall Potentiometerz - 10 in. South wall on probe mount

01 Inlet flow yaw angle Angle Potenti- ±.2 deg.ometer on probemount (handadj ustment)

a2 Outlet flow yaw angle Angle Potenti- ±.5 deg.ometer on probemount (motordriven adjustment)

Pplen Plenum total pressure Static tap in ±.01 in. H20plenum chamber gauge

V= 0

Ps Ctatic pressure at the Calibrated pneu- ±.l in. H20test plane matic probe gauge

Pvt Static pressure at Static tap on ±.O1 in. R20x - 0 in., y - -16.25 in., North wall gaugez - 0 in.

P ATM Atmospheric pressure Absolute Strain ±.3 in. H20Gauge Transducer

P Pressure Scanivalve ±.Ol in. H20Transducer gauge

47

w

TABLE II. CASCADE CONFIGURATION FOR DCA BLADE TESTS

Constant Parameters

Number of Blades 20

Spacing (Pitch) 3 inches

Chord 5.01 inches

Solidity 1.67

Thickness 7.0 percent of chord

Camber Angle 45.72 degrees

Stagger Angle 14.72 degrees

Variable Parameters

42.4 degrees

u i 5.3 degrees

48

U

TABLE III. SUMMARY OF MEASUREMENTS WITHOUT SCREENS

01 Survey Plane Survey Direction Fig. os. Purpose

35 Lower B-B 11 & 12(24 inches)

Upper B-B 13 & 14(24 inches)

30 Lower B-B 15 & 16(24 inches) Flow Field

DeterminationUpper B-B 17 & 18

(24 inches)

50 Lower B-B 19 & 20(24 inches)

Upper B-B 21(12 inches)

50 Lower B-B 22 & 23(24 inches)

SurveyRepeatability

30 Lower B-B 24(24 inches)

30 Lower Fixed Probe 25-27(iO" L. of 1

Point

(on () 28-30 Repeatability

(10" R. of t) 31-33

49

U

TABLE IV. SUMMARY OF MEASUREMIENTS WITH SCREENS

350)

SurveyScreen Survey Plane Direction Fig. Nos.

1. 16 mesh Lower B-B 34 & 35.0105 wire

Upper B-B 36 & 37

Upper Spanwise 38-40

2. 16 mesh Lower B-B 41 & 42.0105 wire

+ 2 meshahead of IGV's

3. 4 mesh Lower B-B 43 & 44.041 wire

4. 5 mesh Lower B-B 45 & 46.041 wire

50

U!

TABLE V. PROBE DATA, UPPER PLANE AT MIDSPAN (i = 5.3*)

BLrilIE TO BLHEDE rTR .-EI E IRIIEPtN

UPF'EfR PLFHE

Po ,iV,1 Lo, i,', Beta 0 1lb ar F' I . ,Cl,, I, ,'b , " s:w

I -7.31 -1.59 .5686 .2614 .0920 .64752 -6.84 -. 84 .5532 .2669 .1041 63:911: -6.37 -. 3 .4276 .2561 . 236 . 5634 -5.37 -2.56 .5096 .2707 .1380 .614'?5 -5.67 -2.56 .5622 .263a .995 P42-6 -5.48 -2. 56 .5780 .2 534 .01'902 65.37 -5.23 -1.79 .5739 .2573 .09168 -5.34 -1.79 .5747 .2626 .0927 64839 -4.80 -1.78 .5697 .2579 .0952 .64801 -4.60 -1.78 .5705 .2588 .0901 .649511 -4.41 -1.78 .5687 .2575 .0955 .47:12 -4.16 -1.36 .5650 .2591 .0994 .645113 -3.96 -1.35 .5629 .2636 .0987 .644314 -3.73 -1.36 .5462 .2682 .1123 .6.33315 -3.58 -1.36 .4863 .2684 .1739 .597816 -3.39 -1.35 .4349 .2611 .2269 .567717 -3.19 -1.88 .4239 .2571 .2456 .55971 -:3.00 -3.16 .4886 .2738 .1668 .598919 -2.80 -2.41 .5467 .2744 .1108 .6:3182) -2.60 -2.19 .5717 .2636 .0962 .646121 -2.40 -1.92 .5751 .2608 .0951 .648222 -2.20 -1.92 .5773 .2597 .0926 .649823 -2.01 -1.92 .5814 .2599 .3926 .650?24 -1.81 -1.92 .581i .2612 .0951 .649325 -1.61 -1.48 .5765 .2606 .3901 .650226 -1.42 -1.47 5755 .2644 .3912 .648327 -1.22 -1.48 .5748 .2626 .0947 .647628 -1.02 -1.46 .5679 .2661 .1004 .643029 -.83 -1.47 .5378 .2726 .1217 .626730 -. 64 -1.46 .4.704 .2693 .1954 .586231 -.44 -1.47 .4140 .2553 .2698 .549732 -.25 -1.47 .4295 .2658 .2442 .559433 .5 -:3.00 .5011 .2740 .1616 .6040.34 .15 -:32 .5562 .2718 .140 .637135 .36 -1.74 .5776 .2672 .0879 .648836 .55 -1.71 .5795 .2636 .0865 .650937 .75 -1.83 .5880 .2591 .0872 .6541:38 .95.. -1.38 .5915 .2613 .0833 .6554:39 1.15, -1.83 .5902 .2591 .0844 .655540 1.35 -1.83 .59e3 .2587 .083:3 .656141 1.85 -1..3 5810 .2681 .092'42 .35 -1.8:3 .4490 .2598 .2202 5494.3 2.5 -1.84 .4421 .2670 227h3 56bI44 :3.34 -2.01 .5722 .2600 .0990 646545 3.35 -2.01 .576.3 .2597 0'972 E4E

51

TABLE VI. PROBE DATA, LOWER PLANE AT MIDSPAN (i = 5.3')

"kTfr FROI FILE LBRED2:T14BLADE TO BLADE TPR'YERSE MIDSPRN

LOWER PLANE

LUPo. r t Lo.: 1r) Bet. -a Q'. 1 b ar P .s I bar P,... Ii at.:r Xbir'

1 -4.00 -42.43 .953:3 -. 1372 .0932 .8457-3.50 -42.42 .9603 -. 1444 .0967 ..3474

3 -3.00 -42.42 .9567 -. 1427 .0996 .:4544 -2.50 -42.44 .9614 -. 1519 .1031 .84805 -2.00 -42.43 .9741 -. 1469 .0871 .:95246 -1.50 -42.43 .9767 -. 1493 .0875 .85327 -1.80 -42.43 .9722 -. 1481 .0889 .85228 -.50 -42.4:3 .9743 -. 1564 .0921 .85469 0.00 -42.43 .9799 -. 1567 .0935 .8540

10 .50 -42.42 .9849 -. 1592 .0854 .8585I 11 1.00 -42.43 .9814 -. 1604 .0858 .3593

12 1.50 -42-43 .9871 -. 1628 .0779 .863513 2.8 -42.43 .9787 -. 1615 .0890 .858214 2.58 -42.43 .9742 -. 1632 .0971 .855615 3.00 -42.41 .9731 -. 1650 .1059 .852616 3.50 -42.42 .980? -. 1663 .0924 .858917 4.00 -42.44 .9736 -. 1651 .0968 .8567

52

TABLE VII. CENTER BLADE DATE (i = 5.30)

• -,C '," C 41I Mp2ach W.E,)

PRESSURE SIDE CENTEP BLADE

.O07 .0054 .6655 .4573 .1785 .0796

.0160 .0019 .6417 .4140 .1849 .0824

.0319 .0866 .5240 .1999 .21:36 .13951

.0479 .0112 .5287 .2083 .2126 .0946

.0658 .0215 .4871 .1327 .2219 .098

.12 13 .0303 .4818 .123p .2231 .099.3

.1956 .0452 .4700 .101? .2257 .1004

.2695 .0576 .4757 .1120 .2244 .0999

.3433 .0663 .4764 .1133 .2243 .0998

.4192 .0716 .4892 .1366 .2215 .0986

.4930 .0736 .4871 .1327 .2219 .0988

.5669 .0727 .4771 .1146 .2241 .0997

.6407 .0678 .4956 .1482 .2201 .0979

.7146 .0601 .4889 .1359 .2216 .0986

.7884 .0487 .4949 .1469 .2202 .0988

.8283 .0411 .4672 .0965 .2263 .1007

.863 .0327 .4537 .0719 .2292 .1020

.9082 .02:38 .4245 .0189 .2354 .1047

.9431 .0123 .3815 .0594 .2443 .1086

.9880 .0006 .2778 -.2482 .2646 .1175

SUCTION SITE CENTER BLADE

.0 16 .0227 -1.3641 -3.2355 .4973 .2171

.1319 .0310 -.7756 -2.1647 .4249 .1667

.0479 .0389 -.4980 -1.6597 .387S .1709

.0858 .0563 -.354-1 -1.3979 .3675 .1622

.1218 .0718 -.3431 -1.3778 .3659 .1615

.1956 .0970 -.2923 -1.2853 .3585 .1583

.2695 .1170 -125r0 -1.2084 .3522 .1556

* .3433 .1309 -.2038 -1.124J .3453 .1526

.4192 .1399 -.15 0 -1.0338 .3377 .1493

.4930 .1432 -. 854 -.9090 .:3278 .1447

.5669 .1412 -.0584 -.8599 .32;7 .1423

.6407 .1339 .0102 -.7351 .3116 .1:380

.7146 .1209 .0631 , -.638? .2028 .1342

.7:84 .1021 .1456 -.4887 .2886 .1280

.8283 .0895 .1911 -.4059 .2805 .1245

.8683 .0755 .z3a6 -.3303 .2730 .1212

9 32 .0593 .2636 - 2748 .2673 .I167

.3481 .0407 .2842 -. 2365 .2624 .1170

.3968 .0206 .2948 -.2171 .2613 .1161

53

TABLE VIII. ADJACENT BLADES DATA (i = 5.30)

p C Mach

PRE ES.URE SIDE LEFT BLADE

.1218 .0.30:3 .4014 -.02931 .249: .1068

.4192 .0716 .4619 .0668 .2275 .I012

.328:3 .0411 .4491 .0635 .2302 .1024

SUCTION SIDE LEFT BLADE

.1218 .0710 -.3438 -1.3791 .3668 .1615

.4192 .148 -. 1505 -1.8273 .3371 .1491

.8283 .0895 .1975 -.:,943 .2794 .1240

* PRESSURE SIDE RIGHT BLADE

.1218 .0363 .4648 .0907 .2270 .1818

.4192 .0716 .4658 .8939 .2266 .1008

.2893 .8411 .4597 .8829 .2279 .1814

:UCTION SIDE RIGHT BLADE

.1218 .0718 -.3285 -1.351:3 .3638 .1686

.4192 .1400 -. 1519 -1.8299 .3374 .1492

. 283 .0895 .1911 -.4059 .2805 .1245

54

TABLE IX. BLADE PERFOPWCE DATA

Present Results From Ref. 7

81 42.42 42.42

i 5.3 5.3

82 1.85 0.4

10.44 9.0

D 0.455 0.46

" 0.037 0.041

Cos 2 0.020 0.023

2a cos B2

C2 (xlO 2 ) 1.09 1.242

AVDR 1.015 1.065

CPSTATIC 0.413 0.351

CxM -1.385 -1.380

CyM -0.669 -0.566

CxB -1.330 -1.476

CyB -0.572 -0.645

Q1 (in. H20) 25 22

.14 .12

q

UU

I-i

j'aJ

Io w .

_____ WJ

win

ml %2 -

FF1 U. cor1,

W5

a1 . .*1..

Ii; I .4

i~i *.14

W)I

Sr

.3 ~ RI-4.. r ,

i114A

57 4-

944

.14 W 480

U .9.4

.9.

-~4 - -4vJW 0

/ 0d

58W

Fig. 4. Lower Plane Survey Probe

- .~~~ . ~ ~ mm *(-......

Fig. 5. Upper Plane Survey Probe

59

5Im

UU

0

60

U

Fig. 7. Photograph of Instrumented Blade

61

1!!

U 5.00

I

MVSSUf* WA LOCArIONI; -- __ _ _ _

Fig. 8. Instrumented Blade

6

62

I q ........

-r

NW _ _ _ _ _ _ON__ _0

*41

m

i

0;

N I 0

24

In1-

q 1. , I

o

63

UX

>>

4.)

00 .-

zU)

0r

z

64-

FCINlT . 1 T::D 50. L," ER PLANE 35 OE,

r

~ I-

6I

.:._-..A.

gW

oi 1** 7-. rJq . N." -, , ,

-IJ • I I AI II

INCHES

6

Fig. 11. Probe survey Data at Midspan of Lower PlaneEnd Walls at 350, Points 1 to 50(P PLENUM Pt)/Qref

65

P fplI r ri u m '-; I 'r

P'.'It-Ti. 51 Ti. 100~ LC'JER PLAIiE -35 DF

V.

I NCHE S

Fig. 12. Probe Survey Data at Midspan of Lower PlaneEnd walls at 350, Points 51 to 100

V ~PLEN4UM - ~t'ref

66

V

P p Iti rn'r~IF Ire#

P,,-,T I T) 50 UPPER PLINE 35 OE,:2

MCH-

i.

, , I I Ii ,

, I I £fl

ENCFIES

Fig. 13. Probe Survey Data at Midspan of Upper Plane

End Walls at 350, Points 1 to 50(PPLENUM - t ) / Qr e f

67

P (p I anum)-PI.'Cr fP.It5T.1 1 T,- 100 UPPER PLArE 35 DEG

UA

iL

1 .3 I I. I I l I Ii

I NCHES

Fig. 14. Probe Survey Data at Midspan of Upper PlaneEnd Walls at 350, Points 51 to 100(PPLENUM - Pt ) /Q ref

I6

: 68

Pi a !i !r -P I

F',ti, l>5 1 T,_, 5 L,::,tEI PLHPIPE 3 0 DE,.-3

F

U

.%2

g7

Ed W a

(P V LNU <JP t )/Q ref~t A

i ,, 6 9 I I I

SNC HE S

Fig. 15. Probe Survey Data at Midspan of Lower PlaneEnd Walls at 30, Points 1 to 50(PPLENUM - Pt ) / Qref

V

69

KP 17F I . n ,. r, -P 1 ',.r a iF'ck.1ITS 51 TO 1-3 L,*IER PLANE 30 DEG

F

Wyet

FA

Lm

I _ i Ijt I I I I I

I NCHE'.

Fig. 16. Probe Survey Data at Midspan of Lower PlaneEnd Walls at 300, Points 51 to 100(PPLENUM - t ) / Qref

70

U

F ,. 1 en en, -P /LCr I +

.. 1 TO 51-3 UPPER PLANE 30 OEG

II '

I

I N C HE'-

Fig. 17. Probe Survey Data at Midspan of Upper PlaneEnd Walls at 300, Points 1 to 50(PPLENUM - t ref

71

U

P" I .ni.,mi-PI 1PO[INTS 51 TO 10 UPPER FLAIE 30 DEG

.2

II

p. I p I , I - I

I~h pJ I*2

[ riC HE

Fig. 18. Probe Survey Data at Midspan of Upper PlaneEnd Walls at 300, Points 51 to 100(PPLENUM - Pt ) /Q ref

72

q

P PI r- rn) -P1 I 'j~P0'1TST I TO 50j L:4JER PLANJE 50 DE,.;

I

P,:I:,INTWllsS, 500 Pont 1k to)~al L~l 50 ,

7.73

I A

a I

r I', C HE S

Fig. 19. Probe Survey Data at Midspan of Lower PlaneEnd Walls at 500, Points 1 to 50(PPLENUM - Pt ) / Qref

73

q m -bT

m -" I I "I

S

P pl .ium )-P1."Qrof

P0,NTS 51 TO 100 LOWEP PLAIIE 51 DEG

2

IV*.

SN 2 HEE

Fig. 20. Prol 2 Survey Data at Midspan of Lower PlaneEnd Walls at 500, Points 51 to 100(PPLENUM - Pt ) / Q ref

74

i

PPl ,num)-P/Qref50 POINTS UPPER PLANE 50 DEt

iF

.2

Fig.. Prb SuvyDt"a isa f pe ln

• / I

- L

II

I NCHES

Fig. 21. Probe Survey Data at Midspani of Upper Plane

End Walls at 500(PPLENUM - Pt ) /Q ref

75

U

P(Plrpnum'-Pl "rsfP')INTS I TO 50 LOWER FLANE 50 DEC,it FIRS&T RUN + SEC'-ND RUN

Ur

'A",

'I

U ]j L ,I ,, I iI iI I I

- I II

In 7

[NCHES3

Fig. 22. Probe Survey Data at Midspan at Lower PlaneEnd Walls at 500, Two Runs, Points 1 to 50

• (PPLENUM - Pt ) /Q ref

76

w

P(Pltnum)-Pl/OrefPOINTS 51 TO iW LOWER OLANE 50 DEG* FIRST RUN + SECOND PUN

.2

tY' t

N 4. 4. ' 'i

I NCHES-

Fig. 23. Probe Survey Data at Midspan at Lower PlaneEnd Walls at 500, Two Runs, Points 51 to 100(PPLENUM Pt )/Q ref

77

ip ( p I mn urn) -P!I ./,Ore 9 .

.* FIRS3T RUN+ SECOND RUN

.2

It

roI I

F

I NCHES'

Fig. 24. Probe Survey Data at Midspan at Lower PlaneEnd Walls at 300, Two Runs, Points 1 to 50(PPLENUM - Pt ) / Q ref

78

iq

10 INCHES LEFT OF CTR :30 BEG LOW ER

TIN w 7- it - ,A

IL

I I * I I I I & I I I I I | I I I I I I I | I I I J I I 1 I I I I ! t J I 1 1 I A 1 1

UTIM1E ( INTER-'V"FLS5.'

Fig. 25. Repetitive Samples with Fixed Probe Position(10" Left of CTR Midspan, End Walls 30*,Lower Plane (P PLENUM- PAMB)/Qref )

79

P -P ab i,"Qr.4

10i INCHE5 LEFT OF CTR 30 DEG LOWER

a..

L

w,.} t - , .

U I

*1 i I I i i , I I I I I i I I i I I i ...A..J i ...-.. J----.....A --.J....L--L....L...L. L....L .

- -- - rj ,u ., eXj !ij A~ *' .,r1i~r -

TINE INTEPVRL'S,

Fig. 26. Repetitive Samples with Fixed Probe Position(10" Left of CTR Midspan, End Walls at 300,Lower Plane (Pt - P VIBllQref )

80

.22PCpA erID a-P1, c Cr610 INCHES LEFT IF C i 3 T DEG L L'WE

(10 Lef of" "T "is n Wlsat30

FE

• 4

C3' ,i £ I I * i i , I II £ I * 2 I , I I 4 . I . J i . -_..._..,._J*\ C C' 4 -- ra ," ,, c,"4 #.] U C.l ,"p , ", -" ,," - "- -

TY tlE "IrITER ',;ALE.)

Fig. 27. Repetitive Samples with Fixed Probe Position(10" Left of CTR M1idspan, End Walls at 30,[" Lower Plane (PLENUM - t)/ref

81

S

P(pl snumI-P( &rwt /r.4'

CENTER 30 DEG LOER

2

!"70

cu ,r , ",LU I I I , i l l 1 1 1 1 1 1 i U l i i C I i l l (n1

T[E'E I' r[ rER,",,ALS

Fig. 28. Repetitive Samples with Fixed Probe Position(on Centerline at Midspan, End Walls at 30 0,Lower Plane (P PLENUM - 2AMB)/Qref)

82

I

FL[-Pi imb )"2 reo+"

CENTER :30 DEG LOWER

'F

' L, I I I I * I 1 1 'LJ I A I I ! _£ J-L J- J ..--.

J .' -I f" " , i -r -r if

TEME (INTER"/AL,-

Fig. 29. Repetitive Samples with Fixed Probe Position(on Centerline at Midspan, End Walls at 300,Lower Plane (Pt - PAMB)/Qref )

83

4I

Pf p I onIm)-P I/Qr .fCENTER 30 DEG LOWER

r

.2II

I L 1--1- 1 1" l1 1I 1 t I I I I I I I I I I Ii LL L J ALL . .J .

- -a -a - -4. C ' ' Q m r "

TIME (INTEr.ALSi

Fig. 30. Repetitive Samples with Fixed Probe Position(on Centerline at Midspan, End Walls at 300,Lower Plane (PPLENUM Pt' /Qref )

84

U.

r

P(p] a nurn)-P( :mb)/QroiI0 INCHES RT OF CTR 31 D.EG Lc:wEF

2 -

IIS!

V.'t

U [1 I 1 I I t I 1 I I I I i J I I I I _ I | j jj

T r hE 1 NTEF",iALS

Fig. 31. Repetitive Samples with Fixed Probe Position2(10" Right of CTR Midspan, End Walls at 30,

Lower Plane (pPLENUM - PAMBI/Qref )

85

Um

U

PI -Pki mbI/0r..10 INCHES RT OF CTR 30 DEG LOWER

2r

-t tr

i_ A i #i i £ II u1IlII I pI u lam mu ii a a a 1 i I, a

TrNE C INTER.iALS.

Fig. 32. Repetitive Samples with Fixed Probe Position(10" Right of CTiR Midspan, End Walls at 300,Lower Plane (Pt - PAkBI/Qref )

86

P(Pienum)-P1GIrOF ,

0 IINCHES RT OF CT, 30 DEG LO.JER

Lower*~* Plan (P PLENUM - .49.ref

I-7

3 I I I I I I I I I I I I I

i t~ a U . ~ * ~ a U~i*• - -rr;.j 1' t w r t t

TIE(IIE.RS

UI

Fi.3.RpttveSmlswt ixdPoePsto(1"Rgto T ispn n al t30Loe ln 2 LEU- 1 rf

U•

87A

Ui

P pl enuml-P1 /Ore4PIOINTS 1 T70 50 LOW4ER PLANE 35 DEG TEMP 9CREDW

*~*h

.4

q2

Fig. 34. Probe survey Data. at Midspan, Lower Plane16 Mesh Screen, Walls at 351, Poin~ts 1 to 50

(P "PLENUM - P tlo ref

88

R -'p I niur '-P IQre+POiINTS 51 TO 10 LOWER PLANE 35 DEG TEO1P 5.. EErN

k ..k .. " . " , 4 ,'... .

rI

-5

*

I N C HE 3

Fig. 35. Probe Survey Data at Midspan, Lower Plane16 Mesh Screen, Walls at 35', Points 51 to 100

(PLENUM pt )/Qref

89

Ut

F ip 1 enum) -Pl ."OrefPOCtINTS 1 TO 51 UPPER PLANE 35 OEG TEMP 9(CPEE.j

Fi

//

INHE

.4 I-

II

Fig. 36. Probe Survey Data at Midspan, Upper Plane16 mesh Screen, Walls at 350, Points 1 to 50(PPLENUM - p t)/Qref

90

Pt plestum)-Pi /Ore;PO)INTS 51 TO 100 UPPER PLANE .35 DEG TEMP SCPEEN

11-ICHES

Fig. 37. Probe Survey Data at Midspan, Upper Plane16 Mesh Screen, Walls at 350, Points 51 to 100

(PPLENUM - Pt)/Qref

91

si

4

P(P I anum)-PI /Or;e#10 in. LEFT OF CIR SP1IN TRRVERSE35,DEG UPPER PLANE TEMP SCREEN 4

i4

* '4

.404 \r A.

In I

I N C HE S3

Fig. 38. Probe Survey Data Span Traverse, Lower Plane16 Mesh Screen, Walls at 350 10" Left of CTR(PPLENUM - Pt ) /Q r e f

92

P(pI numl-P1/'re'

CTR SPFtI" TRAVERSE35. DEG UPPER PLFINE TEMP SCREEN

IV 0

.4 L

t

SINCHE

I 39 Pb S

.c- ( P L E .P t' '

9 NCHE'

Fig. 39. Probe Survey Data Span Traverse,, Lower :Plane16 Mesh Screen, Walls at 350, Center of TestSection (P LNM-P t)/Q re

93

P(Plinum)-P,".Qro

10 in. RT OF CTR SPAN TRAVERSE

35 ?EG UPPER PLANE TENP SCREEN.7

' I?

, I

.6 I

Fig., 40. Prb Sre Dt Sa raes, " Lower Pln16 Mes .Sc-een-, Walsa-3 Cnero Ts

5 .94

41 i .. . • I I..,_. -- . . . . c . . .

i ti,: H E

Fig. 40. Probe Survey Data Span Traverse, Lower Plane16 Mesh Screen, Walls at 350, Center of Test

• Section (PPLN -P t)/Qr e

94

U

P'pl .num)-P1 /Qref35 DEG LOWER PLANE 2 SCOEENSPOINTS 1 TO SO

rAA

16 /~ Mehad2Meh al t 5,it I to 50

I

--

( iPLENUM - /r

95

OD-Ai2P 456 PRELIMINRY IERSUREMENTS ND CODE CLCULTIONS OF FLOW 2/3

THROUGH A CASCADE OF DCA BLADING AT A SOLIDITY OF 167(U) NAVAL POSTGRADUATE SCHOOL MONTEREY CA W D MOLLOY

IUNCLASSIFIED JUN 82 F/G 21/5 L

,I

iii1 .2

H4'0

S 11111LA IU125L2 LA

MICROCOPY RESOLUTION TEST CHART

MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS-1963-A

NATIONAL BUREAU OF STANDARDS- 1963-A

lulI. -1111 L4.0 1220

II INl 1.8

MICROCOPY RESOLUTION TEST CHART r-NATIONAL BUREAU OF STANDARDS-1963-A

122.1 20

11116.

IIII .I1 '11.. =I1 ,., 1111 IIII-4 1

MICROCOPY RESOLUTION TEST CHART MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS-1963-A NATIONAL BUREAU OF STANDAROS-1963-A

-- - '~-~-~--------- --- _

39 LIEG LOWER PLANE 2 SCREENS.POINTS 51 TO 100

'

AI

.4

IF

[NC HE 3

Fig. 42. Probe Survey Data at Midspan, Lower Plane16 Mesh and 2 Mesh, Walls at 350, Points 51 to 100

PPLENUM - )Qe

96

U

Pip I inurn,)-Pl IQre

PT 1 TO 50 LOWER PLAfE 35 DEG

4 MESH .041 WIRE SCREEN

.5

V"

.4

4 ' -& . .,..,.=

II.o • . . I I I , ...I ,.

INCHES

Fig. 43. Probe Survey Data at Midspan, Lower Plane4 Mesh Screen, Walls at 350, Points 1 to 50

(PPLENUM - Pt ) /Q ref

97

UA

P( p1 .num)-PI/ OrePT 51 TO 10 LOWER PLF"E 35 DEG

4 MESH .041 HIRE SCREEN

.4

Il

Fg . P Suve D a -Lo.

4 Mesh Screen, Walls at 350 , Points 51 to 100(P PLENUM - P t)/Q re f

98

.i. . m liiii il I Ira I 1 - '

I,,

P p | enum i-P /OrefPT 1 To 50 LOWER PLANE 35 DEG5 MESH .041 WIRE SCREEN

oi 7

T , I LL.... '

1 UCHE_;

Fig. 45. Probe Survey Data at Midspan, Lower Plane5 Mesh Screen, Walls at 350, Points 1 to 50

(PLENUM -Pt ) / Qr e f

99

P(p lenum.-P1/orfPT 51 TO 100 LOWER PLANE 35 DE".5 MESH .041 WIRE SCREEN

.4

q• , iI I ,II i I . i I

[ NCHESI

Fig. 46. Probe Survey Data at Midspan, Lower Plane5 Mesh Screen, Walls at 350, Points 51 to 100(PPLENUM - Pt)/Q ref

100

I

Plenum

Ambient

Upper Lower

Fig. 47. Wall Static Pressure Distribution

101

L Pp 1 en ',-Pt .-, I b ar"

LOWER FLIt.JE rIDSPAN -5.3

.1 I-

U!

.14 L

.13

(i "= 53(PPEU /l , wer .. Plne

0 i I

INCHES

Fig. 48. Probe Survey Data at Upstream Midspani

4i = 5.3 (PLENUM - Pt/1 Lower Plane)

102

.- -,- p I . -." ." ."

(-p1 C..THR.EE ,-ENTEPr-Ii:'.,T BLADES OVERLAYED,. i=5 .* -.

It

++1 +

4 - -,0,

"1"-

,q,

" Symbols :BLADE LEFT CENTER RIGHTPressure Side 1 *rSuction Side L + R

Fig. 49. Blade Surface Pressure Distribution on• Three Centermost Blades (i = 5.3)

103

(Pp 1 *num-Pt )/Q1 bar

UPPER PLANE MIDSPJ (i-5.3)(TPMEE PASSAGES OVERLAYED)

.175

i /0.075

ii / ,,,I.

Fig 50 Pr buv y D t t fi s a

.o" ' I f . %,," -,--- -"f

INHE

(i = 5.3, (P PLENUm - P t ) Q I , Upper Plane)

104

• - i" " I I'- -I - i I II -I -"

.

U

X b rUPPER PLANE MIDSPAN (i-5.:3)(THREE PASSAGES OVERLAYED).-

As|I I" "

.52h

.947

INCHESFig 51. Prob SuvyDt a is

(i =\ 5.,(/,) UprPae

105...-

q -

I NCHE S

Fig. 51. Probe Survey Data at Midspan(i = 5.3, (X/X)', Upper Plane)

105

0!

UPPER PLANE MIDSPMN 0~-5.:3)(JHPEE PASSAGES OVERLAYEl)

.45

.4

.25.

NC HES

Fig. 52. Probe Survey Data at Midspan

(i = 5.3, (Ps- P wi lf Upper Plane)

106

q s P ,]1" a

01

OUTLET RNGLEUPPER PLANE MIDSPfN , -5 o3)

I-

ICE

I!I

BV 4

II II

[N FCHE 3

Fig. 53. Probe Survey Data at Midspan(i = 5.3, Outlet Angle, Upper Plane)

107

V'.

I k . Pp Io i-P't I"' ba r

1 0 in FROM SUCTION SIDE

CENTERMOST BLADE (i-5.3.,

r

.4 i/

I-

.3L

Fig.54. Spanwise ,. S ed 1 in. from

(i =5.3 (PPLENM -Pt)QlpUpper Plane)

T / "10'

4' r

in FROM SUCTION SIDE

CENTERMOST BLADE (i =5 :3)

,iw

.7 .

t N CHE S

I

I€

Fig. 55. Spanwise Probe Data Surveyed 1 in. fromSuction Side of Centermost Slade(i - 5.3, X/X, Upper Plane)

109

I . . . I q/ " I

S.

kPp Ion-Pt j-'QI lkr1.0 in FROM PRESSURE SIDE

CE.Q4TERMOST BLADE (0-5.3)

II .4

.3

SL

., N

I..

NCHES

Fig. 56. Spanwise Probe Data Surveyed 1 in. fromPressure Side of Centermost Blade(i - 5.3, (PPLENUM - P't)/Q' Upper Plane)

110

wi

1.0 in FROM PRESSURE SIDECEITERMOST BLADE (i -5.3)

F{

rn - 4

... A

INCHES

Fig. 57. Spanwise Probe Data Surveyed 1 in. fromPressure Side of Centermost Blade(i - 5.3, X/i, Upper Plane)

%0101 i

Fig. 58. Resultant Blade Force Vectors by Momentumq Balance (-- -- -) and from Surface Pressure

Integration - ) i = 5.3

112

C1 1 ,. >% c1X .i=5. 3.CENTERrV:'5T BLADE

.7

3 '-9----...---j -_

#3

Fig. 59. Measured Blade Surface Pressure Distribution(- = 53, * = Pressure Side,

+ = Suction Side)

113

VC.

-IENTERMIOST BLADE469 ,

.25

.175

.125

.'5

X.

Fig. 60. Measured Blade Surface Velocity Distribution(, = 5 - * -Pressure side,

+ -Suction Side)

114

"5

U

0.6

SCD - 2D

0

0 801

0.4

00

00000 000000000

(_)

°°000o

0000000 00000000 0 00 0

0.2 0

1

0o

0.0 I I II,m0.0 0.2 0.LI 0.6 0.8 1.0

X/C

Fig. 61. 2D Code Blade Surface Mach Number Distribution(i = 5.3)

115

0.6

°+ - 3D

+

0.4 +++

+ + + + + + + + + + + + + + +4

++ +

U +

++

lu ~+ t+-+

' ~0.2 -

0.0

0 .0 I I I I , I I

0.0 0.2 0.4 0.6 0.8 1.0

X/C

Fig. 62. 3D Code Blade Surface Mach Number Distribution(i = 5.3)

116

0.6

*- MEASURED

0.4

CCS

NEA

NINE

0.2

0 .0 - II I I I I I

0.0 0.2 0.4 0.6 0.8 1.0

X/C

Fig. 63. Measured Blade Surface Mach Number Distribution(i = 5.3)

117

q

0.6

(D - 2D OS01IC

4k + - 3D QSONIC

X - MEASURED

0.41

(-d)

0.2 d

U ~~0.0 I I

0.0 0.2 0.'4 0.6 0.8 1.0

X/C

qFig. 64. Blade Surface Mach Number Distribution

(i = 5.3)

118

APPENDIX A

MODIFICATIO11 TO THE INLET GUIDE VANE SECTION

OF THE SUBSONIC CASCADE WIND TUNNEL

As discussed in Section I, Cina discovered during his

test program that while the inlet flow to the test section

was uniform in direction and uniform in wall static pres-

sure, it contained a variation in velocity and stagnation

pressure resulting from the wakes of the IGV's. Because the

inlet guide vanes were spaced at intervals of two inches and

the test cascade blades spaced at three inches, departures

from strictly periodic conditions were detected from one

Wo 9, test blade passage to another.

To alleviate this problem, the inlet guide vane arrange-

ment was modified so that the guide vanes were placed at 1

inch intervals. In'order to preserve the option of reverting

to a two inch IGV arrangement and because it was not possi-

ble to machine the south wall to hold additional blades, a

separate structure was placed between the bell mouth contrac-

tion and the walls of the cascade. By mounting the IGV's

in a separate unit which remained fixed once installed,

hardware adjustments between tests associated with a change

of end wall angle were greatly simplified.

The new inlet guide vane assembly was constructed using

two lengths of 10 inch steel channel as shown in Fig. A.l.

119

one set of guide vanes was mounted on the south side of the

unit at 2 inch spacings. A second set of vanes was mounted

at 2 inch spacings on the north side of the unit. When the

unit was assembled the guide vanes mounted from alternate

sides meshed, resulting in an inlet guide vane spacing of

1 inch. The unit was provided with a single hand crank at

the east end so that the vanes would be adjusted in unison.

once installed the complete structure could be left in place

when the cascade north wall was removed to adjust air inlet

angle. The one inch vane spacing ensured that periodicity

at the test section would result for any test blade spacing

which was a multiple of 1 inch. Equally important, the

wakes remaining at the inlet to the test cascade would be

WJ greatly reduced as a result of closer spacing.

Figure A.1 shows the details of the inlet guide vane

unit, while Fig. A.2 shows the assembly in relation to the

bellmouth contraction and the side walls. Figure A.3 shows

the mechanism to adjust the inlet guide vanes. Figure A.4

shows a view of the IGV assembly from the north side. A

view of the Cascade Wind Tunnel partially assembled (north

side wall off) is shown in Fig. A.5.

120

'4J

(D

44

U 121

as 4

4) 4J

tot

0 c'0

4)T

olo

7-

o22

o I

od

• -,'0

,1 I %

* ~ "12I

1

'U

4J4)

.4

U 123

1241

i 'i

413

rr

125-

APPENDIX B

SELECTION AND INSTALLATIOIN OF SCREEN MATERIAL

Pankhurst and Holder [Ref. 17] show that the turbulence

of an airstream can be increased by placing a coarse mesh

across the flow upstream of the test section. One of the

most effective methods which is used for the reduction of

turbulence and non-uniformities also consists of placing a

mesh screen across the tunnel. Screens used for this pur-

pose are of a finer mesh and are placed at a greater dis-

tance from the test section, and normally in the low-speed

region upstream of the contraction in a conventional sub-

Wj sonic wind tunnel. By using such a screen the large scale

eddies are removed at the expense of the introduction of a

greater number of smaller eddies which decay rapidly.

llcEligot [Ref. 16] investigated the possibilities of

reducing non-uniformities in the test section of the sub-

sonic cascade wind tunnel. His investigation and recoin-

q mendations were completed while the inlet guide vanes were

still at 2 inch spacings. £cEligot concluded that some

modification was necessary to achieve one percent uniformity

q for the mean velocity at the test cascade inlet plane and

suggested several options. one of the options suggested was

placing the turning vanes (inlet guide vanes) at a closer

q pitch. As explained in Appendix A, the pitch of the inlet

126

guide vanes was reduced from 2 inches to 1 inch. This new

inlet guide vane arrangement did result in a one percent

uniformity for the mean velocity at the test cascade inlet

plane.

The other approach suggested was the use of wire gauze

screens. lMcEligot showed that the velocity distribution ap-

peared to be largely dependent on a pressure drop coefficient

K, defined by the equation

K Pl - P

where p1 and P2 are the pressures upstream and downstream of

the screen respectively. This pressure drop coefficient de-

wy' pends mainly on the blockage coefficient B defined by the

equation

8=(1 - dX)

where d is the diameter of wire used in the screen and X~ is

the distance between the wires. This blockage coefficient

is commnonly referred to as "percent open area" in catalogues

of industrial wire cloth and woven wire screens.

For the velocities and flow angles used in the cascade

q wind tunnel, IMcEligot recommended using a wire gauze screen

with a resistance coefficient, K, of 2.2 and a blockage

coefficient, $, of 0.47. However, since the new inlet guide

vane arrangement resulted in a one percent uniformity for

127

L

the mean velocity and the pressure drop across a screen with

a blockage coefficient of 0.47 was expected to be higher

than could be tolerated for the desired test conditions,

screens with a slightly higher blockage coefficient (higher

percent of open area) were selected to be tested.

The screens tested were of the following configurations:

MESH WIRE DIAMETER (inches) BLOCKAGE COEFFICIENT

4 .0410 .6989

5 .0410 .6320

16 .0105 .6922

Until the effectiveness of wire gauze screen in reducing

non-uniformities in this facility was proven, a temporary

Ive installation of the screen material was considered adequate

for testing purposes. The test screen was installed in the

cascade wind tunnel by placing it between the inlet guide

vane assembly and the north and south end walls. This ar-

rangement placed the screen 7.25 inches downstream of the

inlet guide vanes and 19.3 inches upstream of the lower test

plane. Figure B.1 shows the installation of the wire gauze

screen.

1 29

*1p

L0

'".

w U i-i' n

129

910

U

APPENDIX C

CASCADE PERFORMANCE PARAVMERS

(by F. S. Cina; reproduced with minor changes from Ref. 7)

The performance of a cascade is specified in terms of

the deviation angle (6) and the loss coefficient (7) for

given inlet conditions. In Ref. 1 the loss coefficient is

shown to correlate in terms of the Diffusion Factor (D). In

the present work, the performance parameters were calculated

using the following expressions:I

1. Loss Coefficient (7)

CPt 1 ?pt2

CPt 1 CP1

where the mass averaged pressure coefficients in Eq. (1) are

defined in Appendix C of Ref. 7. It is shown in Appendix

C of Ref. 7 that the effect of time dependent supply con-

ditions are removed and the effect of AVDR is included in

the use of Eq. (1).

2. Diffusion Factor (D)

D2 + WuD 1 2aW 1 3

130

3. Pressure Rise

Cpstatic 1 (3)

4. Blade Surface Pressure Coefficients

PS - P

C - 1 (4)

C = P 2 (5)

5. Dimensionless Velocity

Vt

where V is the local velocity, V t = /T is the "limiting"t p t

velocity and Tt is the stagnation temperature.

1

131

APPENDIX D

INSTRUCTIONS FOR PREPARING INPUT AND OPERATING

QSONIC USING A RECTILINEAR CASCADE CONFIGURATION

D.1 BACKGROUND INFORMATION

QSONIC has the capability to calculate an axial, mixed

or radial flow field and the test cascade can be rotating or

stationary. The geometry of the streamsurface can be a 2D

planar cascade or axisymmetric with varying channel thick-

u ness and radial position. The capabilities of QSONIC, be-

yond those of previous cascade analysis methods (such as

described in Ref. 8) include the ability to calculate

We through weak shocks with a peak relative Mach number less

than 1.4, and completely around both leading and trailing

edge regions of a blade profile. The blade shapes in the

leading and trailing edge regions are not restricted to

circular arcs. Detailed instructions for preparing input

for a configuration other than an axial flow, stationary and

rectilinear cascade may be found in Ref. 9. What follows

are instructions for preparing the input applicable to the

Rectilinear Cascade facility and running QSONIC on the Naval

Postgraduate School's.computer and associated operating sys-

tem. It is assumed that the reader has a working knowledge

of the NPS computer operating system and is familiar with

Refs. 13 and 14.

132

OSONIC operates in two parts. The first part gener-

ates a body (blade) centered mesh (geometry generation).

The second part actually solves for the flow conditions at

points in the mesh (flow solution). The data necessary to

generate a mesh consists of a two-dimensional description of

the blade shape. This is in the form of pairs of (X,Y)

points on the surface, together with parameters that de-

scribe the cascade layout, such as chord and stagger angle.

Additionally, parameters describing the density of mesh

lines complete the input for the geometry generation.

For flow field calculations, the upstream flow condi-

tions, convergence criteria and a schedule of meshes to be

used should be input. If quasi-three dimensional effects

are to be considered, a data file containing a description

of the streamchannel's radial thickness and position as a

function of distance along the stream surface is needed.

For the case described herein, this was input by assuming a

linear reduction in streamchannel thickness using a factor

of 1/AVDR. This gave excellent results. (The output of

another NASA code, Meridl [Ref. 15], can be used to input

data to QSONIC for compressor flow field calculations. This

program has recently become operational on the NPS computer.)

The output of QSONIC consists of listings which con-

tain an echo print of the input data, generated mesh coordi-

nates on the blade surface, progress reports on the flow

convergence and a list of the final velocities, pressures

133

and densities on the blade surface for each grid that was

included in the schedule of solution meshes.

D.2 INPUT DESCRIPTION

The input for QSONIC falls into the following

categories:

Logical and case control parameters (NAMELIST PARAMS)

Bulk data input:

For geometry generation runs (NAMELIST INSTUFF)

For flow solution runs:

Mesh point storage files

Streamchannel data file (for quasi-3D)

The following is a description of the logical and case

control parameters for the Rectilinear Cascade. Except for

TITLE, the format for all these variables is in namelist

form. The namelist is PARAMS. This information is taken

from Ref. 9 and adapted to the Cascade Wind Tunnel. Name-

list variables can be entered in any order. If a default

value is listed, it is not necessary to enter that particu-

* lar variable. If the default value is listed as none, then

a value for that parameter must be input.

The following parameters apply to both the mesh gen-

• eration and the flow solution runs, but the values need not

be the same.

134

U

Variable DefaultName Tye Value Description

TITLE Alphameric None This is a one-line name forthe case being run. TITLEmust appear on the first lineof the data file that will bereferred to as NAMELIST DATA.

NOFLOW Logical False NOFLOW = .TRUE. if a run isto stop after generating amesh, such as the mesh genera-tion run.

NOFLOW = .FALSE. for the flowsolution run.

MS Integer None MS is an array (max. dimension10) of values (mcx. value =25) for the number of gridlines in the mesh that willenclose the blade. 25 is asatisfactory number for bladesof solidity near unity. Assolidity increases the maxi-mum value in MS should de-crease.

NOZES Integer None NOZES is an array (max.dimension 10) of values (max.value = 49) for the number ofgrid lines in the mesh ra-diating from the blade on onesurface. If a value of NOZESis greater than zero, a meshwith that many lines will bedeveloped and stored in thefile MESHGEN DATA. If thevalue is negative, QSONICassumes that this MESH al-ready exists in the fileMESHGEN DATA and will be readin. For Geometry Generationruns NOZES > 0 and for flowsolution runs NOZES < 0. Forelectrostatic analog gridgenerator, NOZES must be odd.

135

U

BETAl Real None BETAl is the flow angle at theupstream boundary, in degrees.BETA1 is measured from the aero-dynamic chordline to the direc-tion of flowl clockwise isnegative. This can be obtainedfrom the output of the cascadetunnel data reduction program'CX4431'. It is listed as "in-let air angle." Because of adifference in definition, itis necessary to use the usualinlet air angle minus the stag-ger angle for BETA1.

Example: The output of CX4431lists an inlet air angle of42.4290. The cascade is con-figured with a stagger angle of14.270.

42.4290- 14.27

28.16 = BETAl

- V)S BETA2 Real None BETA2 is the flow angle at thedownstream boundary in degrees.It is measured from the aerc.dynamic chordline to directionof flow. Clockwise is negative.This can be obtained from theoutput of the cascade tunneldata reduction program 'CX4431'.It is listed as outlet airangle. Because of a differencein definition, it is necessaryto use the outlet air angle

* minus the stagger angle forBETA2.

GAMMA Real 1.4 This is the ratio of specificheats. For the Subsonic Cas-cade Wind Tunnel the defaultvalue works well.

TOLS Real None This is an array of dimension10 of tolerances correspondingto MS and NOZES. Each gridsolution will proceed until itsTOLS value is satisfied.

136

U

MESH1 Integer 1 This is an index in thearrays 14S and NOZES of thefirst mesh to be generatedand/or used for the flow so-lution. For geometry genera-tion runs, MESH1 selects oneof the grids to be stored,provided NOZES(MESH) > 0.

MESHN Integer None This is an index in thearrays MS and NOZES of lastgrid to be calculated forgeometry generation runs orused for the flow solution.For geometry generation runs,MESHN = MESH1. Subsequentflow solution runs then solvethe case for all grids listedin MS and NOZES between indexMESH1 and MESHN. For flowsolution MESH1 normallypoints to the coarsest mesh.

To insure eqnal spacing ofgrid lines over the entiremesh,

NOZES(I) - 1 Integer,K (I - RMIT1 Itgr

where MESH1 I I - MESHN andK = 2, 3, 4, . . . (K = 2 ifgrid lines are doubled be-tween successive grids).

LAMDAO Real None Stagger angle of the bladerow in degrees measured fromthe throughflow direction tothe blade chord line. (Clock-wise is negative.)

CHORD Real None True chord of the blade, inthe same units as the bladecoordinates.

S Real None Blade spacing in the sameunits as the bladecoordinates.

137

The following parameters are required only f or the

geometry generation run. OSONIC gives the user a choice of

two grid (mesh) generators. The Electrostatic Analog grid

generator is applicable to any blade shape and any value of

stagger or turning. The interpolation scheme grid genera-

tor works for most blades except those with sharp leading

edges where the edge radius is less than .5% of chord. The

1 14 interpolation scheme allows the user to concentrate grid

lines in areas of high interest around the blade. With the

Electrostatic Analog grid generator no concentration of grid

1 lines is available. For the cascade configuration used in

this study, the interpolation scheme provided gross errors

in the flow solutions, so the Electrostatic Analog grid

I Wye generator was used with good results.

Name Tye Default Description

NED Integer None Total number of body definitionLe coordinates that are input. These

are the X,Y points that describethe profile of the blade, with thefirst point repeated as the lastpoint.

KN Integer None KN is used to indicate which gridgenerator is to be used. KN = 0will call the electrostatic analoggrid generator. For interpolationscheme, KN = number of body pointson upper surface from the minimum

q to maximum X points, inclusive.

NED and KN are required for eit'., grid generator. If

the electrostatic analog grid generator is used, no other

138

parameters are used. If this grid generator is used the

value from NOZES that is used must be odd.

The following parameters are used only if the Interpo-

lation Scheme is used to generate the mesh.

Name Type Default Description

RLE Real None RLE is the leading edge radiusof the blade, with units thesame as the coordinates de-fining the blade profile.

RTE Real None RTE is the trailing edge radiusof blade.

THETL Real 0 THETL is the camber angle of6 the leading edge in degrees.

It is measured from the aero-dynamic chord to the line tan-gent to the mean camber line atthe leading edge; clockwise ispositive.

THETT Real 0 THETT is the camber angle atthe trailing edge in degrees.It is measured from the chordline to the mean camber line atthe trailing edge. Clockwiseis positive.

CAMPER Integer 6 For blades whose chordline liesoutside the blade profile, suchas the DCA blading discussed inthis report, extra grid linessurrounding the blade areneeded to interpolate the bladeposition. The truncated valueof MS( )/CAMPER is added toMS( ). The maximum allowedvalue of MS( ) + MS( )/CAMPERis 30 grid lines. These arethe grid lines that enclose theblade profile.

STABAC Real 0.999 STABAC is used only for testcases where no blade shape isto be input. Default value isusually adequate.

139

U

I

CHOP Real 0.99 If leading edge or trailingedge radius is less than 2% ofchord consult Ref. 9 forclarification. Normally,0.9 < CHOP < 1.0.

SMOOTH Logical False For automatic addition of moreblade definition points in theregion of the leading and trail-ing edges set SMOOTH. = .TRUE.This should be done for allblades except cusps and wedges.

LEONLY Logical False LEONLY = .TRUE. for smoothingabout the leading edge only;this is used if the trailingedge is a cusp or a wedge.SMOOTH must also be .TRUE.

SLPl Real 1 These parameters control theSLP2 Real 2 concentration of grid lines, ifSLP3 Real 1 desired. The default valuesSLP4 Real 1 worked well for the DCA blades

reported herein. For con-trolling the amount and loca-tion of the concentration

Wye consult Ref. 9.

The following logical and case control parameters are

required only for flow solution runs.

Name Type Default Description

MINF Real None This is the Mach number at theupstream boundary. This can bedetermined from the non-dimensional velocity X outputfrom the cascade tunnel datareduction program 'Redd 5' andthe relationship,

y- M2 X which yields1 - X

I - X2

140

TOLS(I) is the tolerance forMS(I) and NOZES(I). There arethree forms of input permitted.

A) -1.0 < TOLS(I) < 0.0: Cal-culations of the flow solu-tion will proceed until therelative circulation error

NCALC-XCT < ITOLS(I)ICEXACT

TOLS values between -103

and -106 are typicalvalues for grids. Thismethod of input is appro-priate only for lifting(non-symmetric blades)cases.

B) 0.0 < TOLS(I) < 1.0: Cal-culations of the flow solu-tion will proceed until theaverage relative change in

yyw potential is less than theabsolute value of TOLS(I).

< TOLS(I)AVE

Typical values should be-3 -5

between 10 and 10

C) 1.0 < TOLS(I): Calcula-tions proceed until thenumber of iterations equalsTOLS (I).

Regardless of TOLS input, thesolution for each grid willstop after 300 iterations ifthe TOLS criteria has not yetbeen made. All three formswere used for the cascade con-figuration reported hereinwith no discernible differencesin results.

141

U

OVEREL Real 1.5 The default values of theseUNDERL Real 1.0 parameters are adequate forSUPREL Real 1.0 flow conditions in the subsonicNOWREL Integer 20 cascade wind tunnel.NOTYET Integer 2TEGARD Real 2.0DA14P Real 1.0CII Real 0.2

IT Integer 10 Number of iterations betweenintermediate printouts of re-siduals and Mach number. Theinformation controlled by thisparameter is of limited valuein comparing with measureddata, so a value greater than10 reduces the amount of com-puter printout. For the studyreported herein 40 was used.

ALLOUT Logical .FALSE. To list the flow quantities atall grid points in the lastmesh set ALLOUT = .TRUE.. Un-less a very coarse grid isused, the output resulting fromALLOUT = .TRUE. would be ex-

P)o tremely voluminous and oflimited value. Until the cas-cade is configured so it ispossible to take data frombetween the blades, ALLOUTshould be .FALSE..

QUASI3 Loqical .FALSE. QUASI3 = .TRUE. to activatestreamchannel thickness and/orradius variations. The cascadewind tunnel has no radiusvariations, but to simulate 3-Deffects the streamchannelthickness is reduced at theexit boundary by a factor ofI/AVDR. This data is placed ina file used by QSONIC if a

* quasi 3-D solution is desired.

NSTRM Integer 1 This is the position of desiredstreamsurface data on thestreamchannel file used ifQUASI3 = .TRUE.. Currently the

• default value of 1 identifiesthe proper streamsurface data

142

in the streamchannel file. Ifthe output from the NASA code'Meridl' is used for thestreamchannel data, then byusing different values ofNSTRM, different streamsurfacedata may be used.

RIN? Real 1.0 This is the spanwise radiusat the upstream boundary di-vided by aerodynamic chord.Radius effects are activatedif RINF # 1.0. The currentversion of QSONIC allows thefollowing cases.

QUASI RINF Results

1) .FALSE. 1.0 Planar 2D flow

* 2) .TRUE. # 1.0 Thickness onfile; radiuson file.

3) .TRUE. 1.0 Thickness onfile; con-

rye stant radius.

Only 1) and 3) apply to thecascade wind tunnel.

WAKE Real 0.0 These parameters apply only ifMINF2 Real 10.0 the test cascade is rotatingOMEGA Real 0.0 and/or the downstream Mach isVAXIAL Real 999.0 near ..0.FLOCO Real 999.0

S At this point all of the logical and case control para-

meters necessary to use QSONIC for the flow conditions pos-

sible in the subsonic cascade wind tunnel have been discussed.

The following is a description of the Bulk Data input for

the geometry generation run and the flow solution run.

143

.

The format for all variables in the bulk data for mesh

generation (geometry) is namelist form. The namelist is

INSTUFF.

Name T Default Description

H2 Complex None This is a table of points de-fining the blade profile. Thereal part = X, and imaginarypart = Y coordinate. The tablebegins at the point of maximum Xvalue at the trailing ;dge andproceeds clockwise bacA aroundto the first point, which is re-peated. The blade must be at thestagger angle and the origin atthe point of minimum X. ForElectrostatic Analog grids, thestagger angle must be positive(leading edge low, trailinq edgehigh). The maximum number ofpoints in H2 is 99 for the inter-polation scheme or 63 for theElectrostatic Analog.

BUG2 Logical .FALSE. BUG2 = .TRUE. for a more detailedoutput of geometry generation.This will include the X,Y coordi-nates that define the mesh aswell as second derivatives atgrid points on the body. Exceptfor trouble shooting this data isof limited value at the Dresenttime since there is no graphicoutput.

The bulk data for flow solutions consists of a mesh

file and the streamchannel data file if quasi-3D effects are

to be calculated. The mesh file is created by QSONIC during

the mesh (grid) generation run. No further inputs are re-

quired from the user for the mesh file.

1

I 144K.

The streamchannel data file must contain a table of

streamtube thicknesses, radial positions and corresponding

X values along the streamsurface.

Name T Default Description

L CHO Real None CHO is the aerodynamic chordmultiplied by the cosine ofLAMDAO. (LAMDAO E stagger angle)

NRSP Integer None NRSP is the total number of datapoints in each of the tables ofthickness, radial position, and Xlocation. If !NRSP is 2, a lineardistribution is obtained betweenthe endpoints given. NRSP = 2was used for the study reportedherein with good results.

RM Real None Array of corresponding X loca-tions for thickness and radiusdata values. X = 0 representsthe leading edge of blade, with

0 the blade at stagger angle. Theunits can be any consistentlength scale common to.CHO, RM,RMSP and BESP. Inches were usedin this study.

RM.SP Real None Spanwise radial positions ofstreamsurface at the X locationsgiven in RM. RMSP was not usedin the current study.

BESP Real None Array of streamtube thicknessvalues at the X locations speci-fied in RM. For the study re-ported herein, at X = 0 astreamtube thickness of 1.0 wasarbitrarily selected. Thestreamtube contraction throughthe test section was similatedby reducing the thickness atX = 0, by a factor of 1/AVDR atthe trailing edge. Duval [Ref.3] explains AVDR.

145

D.3 PREPARING INPUT FILES

QSONIC was originally configured to use several input/

output devices while reading data and generating output.

The input/output devices are listed below as used by QSONIC.

I/O Unit la

2 File containing streamchannel data. This is usedonly if QUASI = TRUE..

5 Standard card input; NAMELISTS PARAM4S, INSTUF.

6 Standard printed output.

13 For mesh generation runs, coordinates of all meshpoints are written here. For flow solutions, X,

* Y, velocities, pressures and MACH are recordedfor graphic display. The program currently has nographic output capability. No user action isnecessary to create this file.

18 Used as temporary storage. No output is storedV)S here. No user action is necessary in conjunction

with this file.

23 Previously developed mesh coordinates are read infrom this file during the flow solution. After amesh generation run, the user must create this

lfile and put in it the data from I/O unit 13, sothat during the flow solution QSONIC can read inthe mesh points.

QSONIC is presently configured to operate with the CMS

system of the IBM 370 computer. This system provides a high

degree of flexibility in parameter selection. With this

system, all the input/output units previously mentioned are

on the disk space assigned to the Turbopropulsion Laboratory

(TPL). Access to QSONIC and the TPL disk space can be ob-

tained through the Director of TPL.

146

U4

The first step in using QSOITIC is the creation of the

data file necessary for the mesh generation run. This is

done using the standard procedures of the XEDIT function of

the CS operating system. Reference 14 has specific in-

structions for creating new files. The filename and file-

type for the data used in this study was UAMELIST GFCMD.

Once the data file is opened, the necessary data is input

beginning at column 2 of the virtual card. Since the varia-

bles are in namelist form, they can be input in any order.

Table D.1 is an example of the data file necessary for

* the mesh generation run. The TITLE must appear on the first

line (FORMAT = 20A4). After the TITLE, the logical and case

control parameters are input after the namelist &PARAf!S.

p o When all the case control parameters required are input the

PARAYS nam#list is closed with &END. On the next line of

the data file the bulk data for the mesh generation run is

input in namelist form, with the namelist &INSTUF. The

Hi = 100*(0.0,0.0) that appears after &INSTUF on Table D.1

was used on earlier versions of QSONIC, but is not used in

the present version. It should, however, appear in the data

file before the H2 variables (X,Y coordinates defining the

blade profile).

At this point, some discussion of the coordinates de-

fining the blade profile is warranted. Table D.2 is a

listing of the X and Y coordinates of the DCA blading used

in this study. Figure D.1 is a plot of these coordinates.

147

U

Recall that the coordinates defining the blade profile for

QSONIC must be for the blade at the stagger angle and mini-

mum X at the origin. The coordinates of Table D.2 were

translated and rotated using a coordinate transformation

routine for the HP-67 programmable calculator. These new

coordinates appear in the namelist INSTLFF on Table D.l.

Figure D.2 is a plot of the translated and rotated coordi-

nates. It is highly recommended that such a plot be made

for any new blade profiles, to ensure that the original

coordinates are translated and rotated properly.

The second step in using QSOFTIC is the creation of the

data files necessary for the flow solution run. The file

used for the flow solution in this report is on the "_PL disk

0- space with a filename/filetype of NAMLIST FLO'D. The sim-

plest way to open this data file is to use the XYDIT func-

tion, as discussed in Ref. 14, to start a new file. Then

input the same data as is in the data file for the mesh

generation run usinq the XDIT subcommand GET (filename)

(filetype). The appropriate changes and additions can then

be made to this file. Table D.3 is an example of the data

file just discussed.

Two more data files are required for the flow solution.

q The data for one of these is created by the mesh generation

run. The other file contains the strea.channel thickness

data for implementing quasi-3D effects.

q

148

After the mesh generation run, a file with the file-

name/filetype MESHGEN DATA will appear on the disk. Create

a new file with the filename/filetype MESHIN DATA. This is

most easily done by issuing the command 'XEDIT MESHIN DATA';

then use 'GET MESHGEN DATA'. This file contains the pre-

viously developed mesh coordinates.

The streamchannel data file should have the filename/

filetype of DATA5D DATA. The format for the data file is

shown below.

Virtual Card Column No. Variable Uame

J_ BLANK

2 BLANK

3 21-30 CHO

4 BLANKvie 5 36-40 NRSP

6 BLANK

7 BLANK

8

9

10

11

12 1-80 (8F10.5) RN

As needed

1-80 (8F10.5) RMSP (not used inthis study)

As needed

1-80 (8F10.5) BESP

Table D.4 is an example of the data file used in the

present study. Since NRSP = 2 was used for this study a

149

linear distribution is assumed for the streamtube thickness

values and only 2 values of RM and BESP are required; there-

fore, only 1 virtual card was required for each array.

D.4 PROGRAM OUTPUT

The output generated by QSONIC for the geometry genera-

tion run includes a printed listing (I/O unit 6) and a mesh

point file (I/O unit 13). The printed listing under the CMS

system I/O unit 6 is normally the computer terminal unless

the command 'FILEDEF 06 PRINTER' has been invoked. It is

unusual for the program to run properly the first time, so

initially it is helpful to have the printed listing appear

at the terminal. Once the program is running properly the

output should be sent to the line printer.

The flow solution run output consists of a printed

listing (I/O unit 6) and a plot data save file (I/O unit

13). Once the flow solution is running properly the printed

listing should be sent to the line printer.

Table D.5 is an example of the output generated by the

geometry generation run. Figure D.3 is a plot of the grid

output points on the blade surface, horizontal chord, pro-

duced by the mesh generation run. Figure D.4 is a plot of

the grid output points with the blade at the stagger angle.

Table D.6 is an example of the output generated by the flow

solution.

150

4- - - 1

A det;. Led explanation of the printed output for the

program QSOITIC may be found in Ref. 9.

D.5 RUNNING THE PROGRAM

The files on the TPL disk space that apply to QSONIC

are listed below:

QSONIC EXEC Al

QSONIC FORTRAW Al

QSONIC TEXT Al

NAMELIST GEOM Al

NAMELIST FLOW Al

NAMELIST GEOMD Al

NAMELIST FLOWD Al

DATA5 DATA Al

DATA5D DATA Al

QSONIC EXEC sets the input/output devices required to

read and store data. QSONIC FORTRAN7 is the source program.

To document the changes to QSONIC necessary to use the code

with the IBM 370 operating system and serve as a reference

for future users, a program listing is included at the end

of this appendix. QSONIC TEXT is the computer executable

code created when QSONIC FORTRAN is compiled. NAMELIST GEOM

and NAMELIST FLOW are the data files for the geometry gen-

eration and flow generation respectively for the example in

Ref. 9. DATA5 DATA is the streamchannel data required for

the quasi-3D solution for the example in Ref. 9.

151

NAMLIST GEOMD is the data file for the geometry cen-

eration for the DCA blading used in the study reported

herein. NAMELIST FLOWD is the file for the flow solution

for the cascade configuration used in this study.

QSONIC expects the input data to be in a file on the

TPL disk space named NAMELIST DATA. Since the first time

QSONIC is run is to develop the body centered mesh, the file

NAMELIST GEOMD must be renamed NAMELIST DATA, using proce-

dures specified in Ref. 13. Because QSO1!IC requires large

amounts of virtual memory, extra storage must be defined for

9 the code to operate. This is accomplished by issuing the

command 'DEFINE STORAGE 1504K'.

With the data file renamed and more storage defined,

pp. type 'QSONIC' to load the program. The output will appear

on the terminal screen unless FILEDEF $6 PRINTER was invoked

prior to loading the program.

After the mesh generation is complete, rename NAMELIST

DATA to NAMELIST GEOMD and change NA14ELIST FLOWD to NAMELIST

DATA. Create a data file with the filename/filetype MESHIN

U DATA. The elements of this file are the same as the elements

in the file MESHGEI! DATA that was created by the mesh gen-

eration run. The necessary input/output files are now con-

figured fQr a flow solution run. Issue the command 'OSONIC'

to begin execution.

If the program output appears at the terminal it is

possible to have some I/O error messages appear with the

152

q

output. This is because the write statements in QSONIC are

formatted for the 132 character long line of the printer.

These errors do not affect the validity of the program

output.

The explanation for any error or condition message

generated by QSONIC can be found in Ref. 9.

D.6 QSONIC UPDATE

Recently an improved version of QSONIC was reported by

NASA Lewis Research Center (Ref. 13]. The new version re-

quires less virtual memory and executes approximately 30%U

faster than the version presently in use at NPS. Also, the

output appears in a different format than is described in

this appendix. Reference 18 describes the most recent ver-sion of QSONIC in detail.

1

153

i - i-q i - i I ..

ci *

o0 0+0 0

N. v*.."f-~lw0 0z j h 0uskk% 0 00 0

PNo 00-af- 0 040.Ue *40go*0000000o-OW4- 0040o0000

ac 0. am (P-000 00~ of *on 00000000~ 0

UJO 0. 4b o. i.'~i-B .0 0 0

-I KNO m-a. -40000OP-'ANWj.-d0000000IA scu OK~'- I t- aP 9

I~~~ fac*C 0.. a4.,i-P% gO O wq4.4tg4.4~4l0IL4 ob 0 CJ4 + o. o.-o ocy 00 0 0. u a00. 4

v* a q-"-u. %0+++++%W---'wUs ftawtniU 0 0 NWWWWWLUU a. 4m,-4 04f-IwWWWWWWWWJJ""

le 0 0 &wN NQ@'nNt~q-* .0Fr-4'1.00 0 o *

J= Ua-

I - m W "-aA 0- ft vw-4v4 - -4wd V4I0wo u Wod GoW 1 0 000 0-fatab o *so0 000 0

E-I0 0 0 C L 0 0 0 0. 0. S S0 b0 - 0 0 0 e. 0 0 0 .0 0 e

I 4 -J~fqlNv -Nr--W1 'nu...'LLP 00-M ~ 0 0~ 0 000 0 0 0 0

40of* sc " 6tl4+++0 4 00+ + + ++zzoow~lI- 0OUJWWWWiuiwW 0 WWWWWLULUJWWL

-~.4 * 0 V~~i~~#A 0~ 4n I N ILLmin~ u Nat 0.Jl.a- I- ~f-rc YUCC4-$t onn0 tan CDi

I ~~4COWLOZZNU aoooo00oooZ

I.I.

154

TABLE D.2. TEST BLADE COORDINATES

X-COORD. Y-PRESS. Y-SUCT.

-0.044 0.000 0.000

-0.021 0.039

0.013 -0.042

0.178 0.007 0.142

0.400 0.067 0.244

0.622 0.120 0.333

0.844 0.164 0.413

1.067 0.207 0.480

1.289 0.242 0.538

1.511 0.271 0.584

1.733 0.293 0.620

1.956 0.309 0.649

2.178 0.320 0.664

2.399 0.324 0.673

2.622 0.324 0.671

2.844 0.318 0.660

3.066 0.304 0.640

3.288 0.284 0".607

3.511 0.260 0.567

3.732 0.229 0.515

3.955 0.191 0.453

4.177 0.147 0.380

4.400 0.098 0.298

4.621 0.040 0.200

4.844 -0.022 0.091

4.908 -0.042

4.943 0.040

4.966 0.000 0.000

155

, q

Uz

00

00%

600 CDP

* UJu- UAU 50

H +-E-04N NWWWWWO4NWe~ P-IA% + wWJUJIgjIAJW

o ~ u~m *...7kn 0.omN0 00 PN.

N I aw 0 "d u .0 4 00* *a .4.4.4.a4V%tt*o No SAW 0000000.0 01 a 900000000o

I ~ Z 4tO 1 C=WM44 WZ OR MGbf .0WN0 flw b000 wS i

0 0+++++O00o 0 0 0%0++++++++Oo~EtlA A14u c0" COWWWUW O0o.OwJUUJUww&Www

:Dj 9404 1 Q#AC .r5b0.w4.

1E-4 .. J 04,. .J n 4-a0, e o

H l WfSCN4 * . oN0oo,00 G4% 1 .poopZ & N4 0, cal in N** +~-E g0mAb*f *,dm

W 0.04 *ago N NONWIJ e Im--WJW W W1" 5 WO44 M.-

I ~ ~ ~ u %, Ie44~S Ne *04.44.=4-m

c 09A4 6umAgJ4

d 4 oft SZNowca ~ * # *

C -ZA *.JtN U 0,~ 04 Nf0 w w 0 O V40 a 4b 0.0. 4. . 0.

I w.'l No.2 ou 0&I~40000000 aa90000000000WI4o dKDU. "no4d tn + +*rt ++ +++

zz#I b CUUAULUUL UJJUAUUUad g" 0000 0 0.156.

Pqv4 t LLI 0 o.__o"_ccvvDn % ~ Q ID4~.n ~ v&

TABLE D.4. DATA FILE FOR QUASI-3D SOLUTION

STREAMLINE DATA FOR DCA1

4.8554

2

0.0 4.85500

1.00000 0.98476

157

PNO' 0.

40 ..JOJ I -* -10 C) 0O 4

to *i-o woz6 ~ 00 LU

* 40N LL. NO

LU 0-4 WCL. 0 ac

LU ~ ' in 00 0 0z 0 ('X* 0 0

0 (74 S. 40 -J

LU ~c" Lu0004

UA a. ab-'.0 ON 0 tU

JCF woo I.-4tI am o* l44

44 op-UO.. us W

m14 W Z N

C.4 zoWi- 000 ..ZZ in OZ)P

C OZA ozo 4lid 0 le

lbO0 1110

g1 r (no ON r*flqM #O 0 L 0

0 ONW0% 0 NoI-01 ciab waav oc~.u- ofr-nl~tW w

LUUU LL L

I~~~~ w O00 *MIO AoUOOOOOOOOOOOOO00#0 C 0009-0 2A. -Q.% 0. 0:) e- 00 0 nW W Pl

0 04'~ ON 0 WOZe at 09O 0 LnUal.- 40 000 Z d~

OW0 1w * 0.Z 9o 00I0 )0. " 4 as,

!U, coZ 0 op-cop* a

000 0158uI 4N N

w mO'I N0 L

04

0

0 00000000000000000000.

* uJIUaJwwwwwwwwwwo Nwwwwwwwwju

MU 0000000000000040000F49-

4c 00000000000000000000

z 00000000000000000000

0'0

E-4-

*1.4z

0 u=

159

UWWWWUJWWWWWWWWWA" 'ALLRULULUULUJUWWWWWWWWLUU

000000 50006 00000...........00

000000000too0Oooo0Ooooo0,00

*00060 00600.000 000 100 0 00

AC 4

C. "s.

z ~ cc If

!c.Zc*.4

dog- 42c',. U

zC

E-4 - -4

cc

a." 'A 7L

rQ ~ 'L

rC456.

'n UU.0

-0 ~-47.~..c.A30

4a0

-I -N . . ILI.L'. P

.. sU viC

14* *

0 000 0 0 00 0)

Q r r.. -a z. - C x~p C.C- O' C <..

£.t t..lt~l.hd P. . .... C ..... M1t

w x1 S.it. S. m~'. C m m r-N* C JI I WU i t S. c , ~dM O C C L. C. 02 . ~ C ~ Q 7 ~ . J

w. If i il $#I ts.N P

o- A C CC C C~ N

-. e ...... t3d U N~~-A 2 '" I" p1.t 7p. -4" .t 44

z .NM- - - -CC 0

9CC c e4**

Mj1 ... . .

VU 'Mo 1111111114

oomCOCCaC0C --m-2 Z ftCcyt" S ~ Ot -S.SN :

- = --~~Q 0.0-.WLd Z CC*MISFPCU

.w 'J t ,w - 4=~*MNWz -NO41 llC.ce i N -tPN.ut-~,

2 III I II I 4 NNNSP ~*.S01 NN62

G 0 1 0 0 '2 020 ')~) ..

cc . .C . .7.C .

0.4 rC

40

2 CIA

.A. wJU LO -', C -. - -- -C -'

C2

r.- ZI eg~ C44c. C GC C CC C

Uww 4c0

= - . .

u' C L U - U A

"-4 C4 ' IA

- 'U . l L&. -- 0 -I.U 4 ~ 5 . J f ~

-~~~ Z- V;"oc '' cc C 2c

* Vi U 0~ cc

02 US NN ="N~LN NN U~ N,.J 4....... ......

8. CCWtCCCO CCCC0C,LUI* 0

%PCM.I4 4.E-. 40U NN .A

- 4 *I w%0 N I

4 2- - i.N!. N-JOCA.'~ 4 0 2 NN LN

41~~ 2 -0, - ~ -4*.

~A .4 .~ *.163

~-i 0 0 0 0 0 &~ 0 '

Mce

(PC c .. C 'aC.x.. crc

0.4c .c c c cC -,

ZMJ oP *-Z 4 I.

U). YCCC

- U.4 ))U ) 2'~ N

cc ) 0

w cc coo

UP~ a l

0 .LI Li U4N t U)T. C,0 ri'. Msvf'r Nr v.' -:3.a~' 'Cfl ( .aete

26 '0. 0 .4: = int 'S. C v. C Ot.7a* ~ ~ ~ ~ 0 1( 0.'t 0 '-' 6 -NN .C3( t U ~ ' -.

P4 V%4 aaiwr .rw

4)z ac ...................aag ata tt atg tt g1 1 1 1 # f i l l

L.e O

0 a.. cc l~d ~Cf'.,tV- '-CN 7C.C

co. O c ccce cc r'~1 -4-cc dt-~U)cvQ' ccc-~,7 ~ ccf~ c TI) loc)c c c

- o~ w- Or- C. taa~gaai

~, ... .. ~oa~...a........... -Id~C : O~

a.. to. .3 U 1 it f

LI C M.aw '4c .J N .. . .. .

4 164

(a) - 7 0 0 0 0 0 0 1') ,) -.

4.-

Ce.

c,. c. - - C -----i- -~4,r,.rr-cr..... ----- -cra...,, ,c C .. qClc tCCc Q Q CC ccr

£4 .. - 6M Wt-, 40 N'l'P6. ZJ 44444J -..."'tfll.'rlnfl !MN4)v. fl4

4S.., W~~t6P a t -,rV-lat. .. l6 p

l.4 6.0 - 4 C~.....N. .. ~J*Id~flr~lI N,.~.4..r~h S.%..... .... .f, ......- i I...... ... ,.. 1.

'.cc 11 to:~C c c C ~ o~

. ... ... ..- aa.-t~~l~ .. ..ai ~ C ~ P o.....--N 0N..J 4-..Ns3-.. 4..4J 0 .4 C A --1!CcgC-C CC C C= ~ t-.Occ-crK C C.. L.N4NrcI1 % c i-a-C...c 4-- 161414-. 44;.6l

Z o c4 C.7" rrfno- 1 i-.~.i 7 co l~r. ON 44l~4 lj -. O~C-.

- cc ~ .. 6C~. .ri- .- 44.3 OC.OO .C4~......r...3.....O C Q C C5:c-

.4me. QOI

%J a. s. .4 . . ..

01 %o onV M'tm 3t 16 2 a 0 i a N J C - 3~4414,,0C...~.:aN.- rC-~.3 = ~ 4' 4 0 C ~ ~ ~ l ~ , 4 j . .~~-

.. ) c. .. .. .. .. . . .. . . .

Cc 1 0. 04*3 Zj .....

IL .41 70% t-6 Co cc 1 , _,cccoU,~.,z,.c - cc c - ,, c e* 610 a. i~Ills, 111661111111111116,

'.4

- 11116 4 4~4'0'N W 00 l~6 U'44

~4445. ~N 11' ~. -CJ~241 4

64.0nlJ 4Nl6a4 tC .J.O C1i-..C C I tl

cc ~ . - 4~C~ -~ .

MW3 won ;.cU~ 6 *~1l6

. .C.444144- N1441~

1 ~ ~ ~ cl 0 0 a 0N'4

C'C N .. ~ N N I~ ' 0 0

C -9 0 0 0 0 0 0 0 0 0 11~ ,.-

*-C'. *.t9 , ito' .4f -rz*.PA- 'T t er. eNW

..... C C .......... .... C..

C-4~

LA

99919 999i

*.re 4*' v~-.ro'..4.uJ c . .Vo9VVcaccas t l

&577p.71 V-9 9* Id.wQj~cc

ave..

4 J~~~ 0J~ '4 N1)~ '~' .2d

~166

4-)

X X)0 CC,1~05. E-4

or00

01 (d

* . 0

- f-I 0CD C

" I II I I ILl L) Ln 0a)0~' (5

CO* CD C -IG

; C; 7

I x b

167

KCD

C30(04

00

go to

0 1.4N 4J

00'-$4

4.)) 0

x (co CC .£c 1 C 441*f4 ri

1.4-~ 0

0

4. 0 >

0 41

o ~ 0

C\j U, C Coo 0 C C

16

APPENDIX E

OSONIC PROGRAM LISTING

~OOOooo00Cooooooooooooooo 00000000 0000000 0oo

0 f" 4 0.- 6040

3 _j )( *% (3 -. 0 CL 4 *o -o 1J4 s. U4;I- wZzz

LU I-~ lo Ca W. 0 * j u W44 ju 00C i -- U -~ 0-. Uk.41

0 -z 10 %- C 0U 130 w4 OALCDZ0 0 30"0 1O _K (" 9. 14ZNx W

Ki CL 4W -0 o.c oLio. o) of .p4~.lwLo 0 _j C. 4zm 0*1- C 0 CLO O.4 0 D4d _j 9 0 -41- * U.. .8 =. Z z ..JWU -1 0i u. .4 14 >0 Ii) X_* qLU.c

Motu CA CC) .- Cz W Zv ' E -asooi U o 41t o w mi.8- w 0.J-. z WW0U-

LU 0 nw -V) -9 (a.j 0. 4900w V) ""I-- r.4 -

z 0 0=49 .0 Q ~ Jz. J A c 0 0.0Wm Z-aZ.4 z4 0 _jxUC.WZ a -ia 04LS Z*W~jz

U'~ 190 U O-*CAZC W-1 $"c 0-UJC 0+(.I-

of- I- w 4g.- * wLUj _J0 aim cc0 .. C .4 OI. 4c W g ZI- 9MW 00 4> " .- ~~) c~ Poa~ 4W 391

M .) - )Jw - weQ-4.1)4 mi- .4j (a *4-

I-u) - 0 ..J 0 (~J 0 0 .J~qtni v - c a-.-4 -.- V U -r.-3- cla z cn W0 LU q W Z- W..J 9.Z 0-# .p.lQCO0 .I'-ljW

Ob-~C - 4- NCO- ZOU OWV) J ~4W~0a~U..J 0~ U.U)(49 004j N. 000-e L) -Momtf 0w OW

L .o 0 .. jW - . -. O--. ..I UJI. W -D - w.40 Z -k .0 *Jl.- U. .Je f z Z9 4ce .. i .t Joal*4v)Q O )..wt-W 0 ob WOA0.

Zw (AU 0 0 L~-1 UJw 4cn *occtud M:1 O - ps4.. .8. OLU .ju J I.- .oqct 0 i CCU (J O4 a0.12 0. O.-4q ry ~WCLn Cc43- cc . 49 0- 1W - 0.a- 4tWO U .-. NQ ujc0W - a~U .1

0U 0 0 *M o-% Ow a%.N-.3, 0Jz ftJ ftWO.. .tIOZ.J LIi U) W 4 IOZUW% P_ OwwIJ.Z s. O 0ZO.-< 4.. M c

V110 ac U ZI I-uqx4~ ZC)U ZOU)-a4%.l..Z ".8.U .'0Z-J

44 a. O)~1.JIJZ4 4W1U)S Izzmo0 1--az..jU3f.0 U 0 LU & C 1 -ebOX4- 0OC .JW 0.00W.4

W.p LU WNWU.~W WO.gmw ZWW) Z"%=WZ( LU Z 1.- CD ZO.ZCL ca .0'Woo".. 0I-t..JwOox P_ c n. JMM 0. W>f%0LI g-e)

= 0) 4 <4DWKWUZ2 -4 -MZZZZ -<in l/)"OxWI-#^CC 0. z 0 U -0. .. J0oC%&_a00OO.Lww Z..Jqc1- _cco :V 4t 4<1..K.J1I WWOOinOUL 0 cr XXX1W4.ZKI. KC-;.J

> i uOI ZWCOObwOWCOOCCW4U. -04WO0..J.1 x uu - .a u u - -.tl-

169

UL

0000000000000000000000000000000000000~ ~~.ir0

LU000000000000000 o000000000000000000000

00000O0O000O00O0O0000O000

LLI-0 z

LU P"0

0 LU -

00

x 4.u -40 40x O 4

z 4 0 O-4Z Z 0 4-zo--o j -o w - o- 234 + 4

#A 0 0 IW)P - i L --- 0 -W4 fUL

=0 - 1- 0 VAC*)C o- NU . C 0 XL*. C c .uz .4 Z"w w -Xai- W I-u.

4U.w .4 zW44ff e.. V)*4~z zjbf *u-^>. 4CO4 01-U-am W UZWM~wx co

W* - 0%% --- COo 4JM X Jl--w1

Win t. 4=- <Pincpoz 4 j wI- waco W * wW4 )(

CoLU o I-. XU 0rLL W UJmm" O4 4LU-JW

K m(J*~e W-i -2 .ZII 1702

qLX0u4

ZIJ- a * %.JU LI _

4%cau %. 00W01-.-CO-4 0 *U *4-W4U U.

OdU.) 0A w 0* -- 0 0ZDZt d 9L) 4c P- OW4V%

.9C _ _j _j S. -UO 0"".! * 0U 9 N %...J Lu *S-exO 0 0 (V) *Z4U)0 0) -.4Ux - 0#A 0,-Ju.. .-i 00+-0 4-I. cn0eV)f 4 0. IC40 6 S 0 LU . % L %0&. . W."4U. (In KX- L( n 0 - .o

0 0U j f C 0. -4 W4 XnU%. a-. r.z~r V4 ,Jl X"4 a' 1 4 0.

0-KUJ 0. U)0 0. wx 'O.0 U)

-.- 0 O0.L.J-'% OCL 004-a4 S

0d-. 0A4 (2 Z- . %. U.J%4 U. 14

%.41J.J =4j 00 -O.J.j e * oI- 0-mac~ 0 L ~q0 Ccd P4 .J)0 * .M OU.W4a 0 -ie o- 0o 4%)).4 - N

Zz I a+ - )(.60# 04"' 0 0 .5.-t4% amej~~~ 0.0.r WE-LL 40 41 %NU.- N.

Z 0.- .. O"0U)Q.V 04 0 0... 0= V a0 04jlz Of 0.0 1. ' (M o-- - 4O %.4t 004

0" .. 4W ""g COOLU -MV Cet * .:74X .Je MU)S LL U1-%N am .3ca-. ... 4 N-4 0- Z0 %%cc "o

Uc f 0-00WCy 0 "-O".Zom( -0U__ L 0 -. - f 4.4.-_JL V)'( a 0 UJU-...JW U. MC"

N - I- < .4-...5 OW.. .u. *.)C %no..U z 000 UL5-,)5 O.'--4 00sZ. 'tO 49-$4 - * 'U) 4 N.q

0- a- -90 W(-J 0 L..-. -' 0- M %i* 0- *.0~. LU a4 xi "U) ac ).W. %bZ % .- % D00 LU2 (U)nl.f -*.i-. .0 < 04 0-4 0"-~LJO 0 a

m *i 0_m.00N .. 0 %.04 4.9. O.O*Ze Z 0-z Y <CU)Z.ZZ -Z4ZZ ,<t O00w0. CCO 9U <-C *

OW Z 0 U~~ 00p .4/10.COCMW U)0 MowZ..O0% 0.

Q JCLCOJ -CKU .0 4Z - oUUWU0 - a- U . 00 - .% 9 r40 0 luJ

fl~l~%OO' 4 00 1-9rrr-~

0OL

o. - I- " x Lin LU 0 LUX

49 0 vAI-U

W. U 0 -OP4

Wn Ili ON rn-at I" fo-". (% .m

ft LU 4Z .Jc. 0. UJ0

.4c 0-u Mo-0I- s1

40 In z WZ ON .* CL 0 L4 'I

04 0 -A A 4 0..JZN4 0 ow 2 M 90 (oO-i00 _ U.1 us _>_ 0- 0-0-4

L - z >c 0 .0"S

z z .0o m a- a uC -.- O.f

.0 wo I- cc 99U 0J-wo Wn 4 CL ot 30 -fn :49t

3lm )I-.. -. L Lu .- )-.-. . fLU O -A 0 Z T- WA 41 .Z Z 00-L .00 am -Zj 1.o4 o-1 = 0 - a~~ P4O.~

0 f" 0 ox3 .4 M.M.3O 4 00 a0 . cOr 3> LU 0--LU 0

2 , 00- LU I.- sol *U 4%0 aZL,.vw * CCa

:; n "qaCa i X Z J LU4LI 2 .JA0 1- 00 v . 4" LU s- 0 a.-LU0

9-J.Z -+- -- X xU (.D. 's 0 -. w3Wa4.O w4-x u Jcr. *- LU X.. 39 4Z -wo _jLU M 3U.)I

.J 0 I-' NZ ZCWU.J . 9..1 oW z 0v*"z 04-Le-LU1~%N >*z c,0-NMZ-<XaZ3w .1x LU .J1 % %)(O LU_

Z -ZZJ=-gI3LJs *-u4N PZo4X 0 W.. Q. 04oawwn%-JW~

a- LwO %WK3Luzv.4fwL4x 9 aw"KDv" o*%t op.* wrouI.)-ar-aO.J*%%<Xo*Zmz IfIt If x 11 gg 1-.0-4 If v-40wO W-U.. ~%e

uj LU zjw 11 1 -1-Z W4ZZZZI.->zw0 I-- UO0 _5 ZZIfx &-712zL4.d) -WA 0 40 OU.CLJC0W02cc 4c a-TK.JCa.N 11 lJNv~iu4K e. Ct-K N N -XZ Cr CQI-- ~*oEZ M

l'1- Oin.DzK4-3in03 Q--.-t-K-w-Oma OODCWOU4rZWCI-u-cCO4 CCOLwZ= zoaocamou0-

,A cc JQUWQZWZZO0)OX>-"ML.m 8"-31.WLWt -- UU *4JO

IF0s-i N-i L)L

172

UL

0000000000000000000000000000000000000

~j

U IU

NNCYNmP-44u-%O S.a-10

0- O),- O - -r

114Z~~~ ~ ~ ~ ~ 0 - c ---"z"Cz 10 o o xxx xx xx xxx xx xx XV-mooz uj -"o -J". to O.

CL3:m ~ ~ qw -z1 VZ UC$

defwZZZZZZZZZZZZZZZZZZQDW WClOOO-t<-

Y -n n *I0

173w~

444tImvww o

0000000000000000000000000000000000000V) MC~

NNNNNC~NNNNNNNNNNNNNNNN Ie~NN~eJNNNNNN0000000000000000o00~o0~o0oo0o~ 00000

In

1 U.490Lu;4

j 0.--t Li

"I"2r 0C~

1- GC..I

zo j uj

-. Uac a* -- &CN

x b- W 00 -V 0CM I- 4A U P-c

CLZO~I OWt xx d C N Z At

ZZ"~~ ~ ~ ~ o-a.NO4NV4 C "jdl- O- o -A 49-Z 4

.-ow Is of- "" -sN4n 4 VP40 c WI~~~ ~ ~ g.4ro Oqw 0.. LU-wI " %*O bW b

M-"P4 2ZP U)l,- Ml 4= Jx w=-o o x-jx

I. wCO -a 0. L c~C 0 w.-~ - 1-41) 0.1). 0

_ -- N 01/) W~n ~ 174

o0L0000000000000000000000

o coo

4A

- 4o uj

zz z0. 2WIOL .

P44 .I j4

z1I 4 4_ -4 z-0 U.1 29C =c 0 3C 1

m~~ ~ ~ ~ m4-p x4 LZ (CL2 c- a% M-f -.-10

Wu t0CI0x. 0-~n 0wU Z ~ f 4A z4d4 m do 0 (A

It~ ~ ~ It awAo. " x J i- U c. L 449 Z "2W Z -4 M .40-z fC

4L In 39 4 V.. 1101 >lw oU0U) gl Q-. 44 aA ( cx z o

49 P L0 04 z X0 0*U 03 U)ccZ- -51 09 CL CI Cf. U) L m

M .4 4cA t .- t 0-4 N== "a z40.0. 0 fw 4 Z w 4 I-w. 0.. *l .0

U)U) 4 til 0 W)0 44 - I- w"- _j UU tu0 0. IU)ox U) z' W)~ WW0 0 0-0 CLI -I

V"14"" olwl n X0. m M) cgf% aco- W)CC LL 04U.

--vc U.. _ _ UPW U) M <4 0 U))wzccoz 4m- Ww W.% A QU a eW C).7yrz iv r.4 e if..J..J. L L04n4 %aIZt11> 0 Z 0. ix Q0 2u -at<fitUJU< -

N 1 C1-- N31 I-- N) aUU ON. * 1 - z1

U) .wa.w a4 J~ 0 QO 0 4"Z4 C C-0-wl--c w 4c Il 4 ~ ILI0 %.U t3 LLLR i= (-x u Z L.-

W a 40 MZ W W -- w" CM M LU/ cr(-!

U~~~ ~ WN %) 0 4Q U ~ 2 % .

C'40.. -'-. .2 .0 - Zm ~-175 i

s-a4

0nu 4%

uw. 0.

O10. LU0MU4 xn

a.W 4.ft

~Oa 0 z* LU LL

-Zac V) C 0 - 490.-u ) V 0 Qr -

-jO n 0 wN V) CCU I

OC - 6" .4yc xUfv.- U. MC% 0

O-w - Iumft 3 fLUCW

Mnif03 0 LU JC e LU "-n LUVI64CC4. mcou -4..) ZLUI

0= O I- 'ma0. 6 -9 -4 X 4 L9 cI01-4 3w ob IC O j zf cIC

"N - Z 1 -C.~ N cc 0 - . U

xrpv W) If nNW -cac 0 eLJc

04n IL N

LUq--4 N J *CO LU co --% sInU I-4 P"OI484o- 3C -t-0 cz ie a f

03- v .ej ZZ a H. c;- Z w 0 WL~L0. LIn ZQ o4*c 0 CL C4 -%

cg m0P 4 if i.U Mo CL.4 (As X) * ms+ il~b N Z ~ W LU 0o 3- X I Z4L 1; -;

N%-OZ l'v "Z L. ILy0 P 0 Qr. Nz 4 N-OIA.0 P-4 u.jJ 0o < 0 Injja ftoI- 0. 40"

<WI.W NNs4 Z w..J o 04+ - ""0 - Nws-.sW.

Muaj-4L 0 0 > C 1O - f- 0 oK4 V0IZ-WCL LU IZ Nu" 0W iL 0n~ Uo I it11oxI " ~xM-J

-zn z CV r-o40 F-4 3*'- 0 QL... - (I)) <c P" No 11 s-i *s-9Oczacz N w LUL *0C N- * sa(.D 3 1" Ni0X ZIIWX-Mwx XwZNGC z~ct *o FA0- mamm* O 4* W~ sewrtnwxm-.4 of 0 O wqw Z .J -Z Is Z I ZZZ4D wVcowo- wil 4 LLLL Z- WW2 * 4 nC AA. - * W ".4.aC.0.c.W0.uuuWz <ZW"U *** ) g 4 .. iis nsi)WOd

~-LU.Z n Zz~ 4~ 2 nin WI I i 9989 N Q-~tw~L II - ssssJLUI4 ... o0. In i

Z~n2N0I/ ~ r.I0 o .. -2.)4~- s--s~i-176 *

UL

Z u

o j 4 0

LU Of1) I

1 - 4U z 411UP .V 0 Z L

Ln.j Ui Unc V)4 w4 " -

U. ("nL 9 mj0

2 *U _J 16- l'n - U. Zfz ~ < Lu 4z AtI-

Ur 1. 0 X XI02

~44 -aca owa .. J UO1XCI 0" N49 0.-. 0 ccce sc CIO N( CC 0-0 U I Z -1 > s

Imw POO 1- +. Inb 01 U .1" U ~

~- * *L Q 4W 4L LCLu 0- LA.~ -. 0AL 1.4u.J - 4z ~ N4 1-4cc cc 1- II

'0 or.4-d~~ ZLZ Zj4. 4 .10.

4c q U 4 O -- 0." a4 J Cf. J1_'-% ey- 0J 090 0 g t-O .

co ~'4 cc .J. lU =IJW Z4U.< LU04L z4..0w LU -) 23c)v U~> 0

-z LuX + 0J 10 M . .- JO..J1W (L"U 01 --. of G~jfafw.f 0 cg o XW ga -0OC

wo -d.zm X In~U UU ZU.Z~l. 4 -oIn 11. g-o"$ 661-. ott 11 -. 0M OZ WIJZ) + xLu u 4e-- . *. - W.5 N? U jx04s-Sx'

>- VIZ 4 0L I4-. l' 11 It I--04 IL.-. 00 lII z i- D 4'-4 Ii-O fix

-"4 Via1 =11 oftoe "4 0 _I-1- ~ xxu.LL0

Lu0 .w .&U-xm x I- *0 _m at2 I. 400-

I- W(. zozo' %It)U..L LuOWC 0= 004U.0

mI Z I * .. 4 I . ~ ~ ~ 1..* *

oW * lM . 0 WLL.N t177-

000000000000000000000000000000000000000000000000

Z04 mf

o -. JO 0

LU:N >.-

I . -cc LU

w .~0 U.O4/) 0 oAJ ~. 0

*0 LU I-JLW (n0/ (3c ~0-0

Z -jUJ I-U 00

crV) LU Z "0 v. vwOwi (0164 00-..I-= 4A) L. -A< ./4ox4uI 4/ 40 NltCc) 49tII- W-j 2z U- IA *4 4W0j.e

4/)P -gv/)4 0 f. 0 F-Mal-'cc a _Z-J LL. a Ax UJO(3 =0

o 24/) s..04t) 2 I- -4< ca . c or"

Z Zi-oz LU 0 0-0 ZCYJ - -4~a 0jZI 0'- WUI-.W ..J U. I- 00(3 c 4w -W M0-."W-ftowo"- Z CI I-M _41~) 4.4

o -- Qt.n/ ~ww 0 49 2 . _Co)-ug LUL3Z %t2 NZ)0,* Z 6- C) 0 4/4 MM 0)-

o_4 04AZZ0 U. 1.- 0 cc b" COc4WJ 17 0-(*-$uZ>W4LIU. - g- I- j .3Z - O.Z ft-4 Q-%

Ns X0002W Z I- >V) 4 4 I-na- = 40.-w 00It I JA4Q40" - -4 QI Psemu.F- QN00 0(

'-. W..Lu X 04/) X -ON .(jrJ 0 N ..$ - ... LU LI a LU ZZLL teo -0

4' 4waot-ou- _4 Lut- -i Z - e4.- LZ M . . - ALIC. *4J1- -V4)y WU V) e. 4t 4 w(3..O ._J_ 3 <WW v

- -00 C1-.0L) .0. LL UL LI 0=0 6-M Q<Mlle~O-0..il- wl-ZZ..j0w4/). 0 9 LI .4cZU.. - -_Qa ox

"4 @cmLUJL- ' (/) u..Z x -J 4/)zc Z4/) -3 49 0.(;4 I dw0W-**uD.W~-o 4.4 oL 0 (. coW @."= OW..J 6.C

LU W4j<4 lDL6>4) 3c a V (D .4 ...JU.ZLI %46I 04-q + 11 . w w..w crWLJ LU C U. U.. "- 4 /%,. * . L..

-. 4x0l Z< I-LU c00 W-m0Z'-')-Z s*Jxo-.a:.. 4 XZZIIZU-00000000 U. co x> LU U ..JWu/)< 4 .muL w4w")~-~OQ0Oo0 02 L 0.1-- ZtOJ4nWaEI

a - 0 0L.0 < LWM -0 -=Lc<udtmz ti u.00 ZOL.L, 11 I nu . Wa.C a mvuL mmwm 40W

mo~ovo.*Q w 0c 61- _J_4 'CC %. e4j* -'.%..a 0 mZ =Z 444..JxxwwZ<.+-Zz

0 zo ZOl tZ>Ow UC) OWWWZC)0000

178

V~~~ wmwwmwo001100000 0000000000000000000 000000 00

000000 000

U.

0 c

Z0 N LLCL ("2 .- 3

_. 1-4 0 4_= z

4 L .u. aU *U t1- - c 0 *Uc 6. . Wq 4 .4

&6*. >-C x

ot w N U.0. -bc Qw N .U -C(7-Cf .1 Zf- 0J . 4 -1 C . 0.4ZO .4iX04 . ZL _ua-

a L 8- L@ - C CO~ 4 =4 - tA0 ) 0=00 .o f ZKO1 *3 40 6U-

ft a* zo CL. X> 4 0o . J4.4CA C J AX Cof 0~ ow q - Q cC

2W NJt0t - - V-4 X0-o

X. 0- LUU -3 ..JV" 0-a0 ZO L 0.ftl -M~ CO .6 U

J1-/) 0.o co cca . 014 4i CL -4 9

w 00 weWi %0- -N ILI0.- LU "CO.-40In00.P0.w( U.K x .j cc-0O- 0

0 Z -;X U.-XwON Ow. Z -* 0. OCN 0 0 zo U f40LLO- LWw - N WO = 9-coo - 0PO < - 4 -j. L 00 OF 0 -s6. v)(,nv4 -% ft

:-qc ue' U. o).- 6. -0 0. Z 43c OMNI- 0 140m 6. O. 6.4:00.. -=m~ N CLU 0.W LU.(f (" ~ 4 0

CnU 6. .J -- 40r'1CO CDCL.w LL _- J ft6. m 6.fWZW ft 0 L) NLu 04- LL4n Ow -P~4 -No wo,.4 Z CALL jn. ..,, ..-- 0 I

OO.0w c ft. 6.ftv)CO,4 =6. -3 - (Z oz LuN.VIC . _r U Z U. oz;;0 - t %tOCLULUO X-C K Ube('nP (3(. - -4. - 1 0 P4 -t

0.-i Vma. -. 00 -- 4u. c(CO.J 6. - SeCK Luj-.4 C.D Go - 0=O0%-J 0..J Z--& U. 0..J 6. >comc.JU. cr 1- LU of-P4=Cr. Old) LL *o)C 6. > LUNIM Z WE,)4..j0 c. .uo LU 4 4 M0wUqj 6. 6.6 WL.-Occaft .JO - - Z -Z< 4Ddc CL V. ftU I4c3 QON V_ oZ.-Kcc 3c-. D .K-If~.. * ZZ

1-K a COCL 40-MwMw -CO ',%UJCL<XV)fCc (ACd U'i U. I- -..LUNFt"..a 0.. U."0000) C.. 1-MfI.J.4 ~ sS~NNNJ4 0 0ld) *-(U"%.6.u '-,C% M KtLId))'I- - *L ccU.0

u.. wU _J~-f-- -) -LL 4C s- e- KDW)d)-.- LU Z ZZNONk Z.-4 LU.- 6.M0=0d)-wO V) crLm- 6.WWJZ%- ... 0 CL s dKcinK _CL > 6.0Vmmm0owZ mO24.J0.U-ZI-004 4 4;0 U(00o 2~i _J..0..j - ou-0 4I-.-Mi-d cc0U CUZujW~W lmd) <XOWOZO '4-0 '.%. 6q-j a.A%. I-* - LL * *

(Du 6. Q0-4>~'000- ~-.--- LLO. 41-1--- co wO -%.%.%0.COU1-'%V)C ftS0flf~ D ~ 6.0 I I

q ~ZZZ >dZ-Z-)-'.0"C1..4 Z 49 Z 0 F%*JNJOCOc. *CWO iOXZ=w.ju~j .. J .J3:L.(0 ..O..j.. 0 LU c0

KK~Z~KWUfl) WKU4w..I~w4 X U. u . zzYKKOZ1.'K1-4KK400KT .4..TKKI C fww

OC4WL OcWWc ~<C 0 0 CC LLU.ujuLu --- UOJ .UCCW -am~ -Z S.z a~e6 ZZO U) ' 0 CL -

179

U.

toL

8N

I.-

0 Q-xLi

o-- U.

Z0 z -I- -Qa A 0 LA.4 e6 Z #N* q

-' U oc L 4 1%,0 N -W U.0( 0'% *J cc 4oL 0*

a J .009 0 X - *. Q OD +*i 111" 049 o- t -u' L0 LL +L. * 4 c

4 ZNLW 4 4w . W Z + *. *. _ U.

*C~t OCDWW+0 WX m N 09-4.. 1 ( 11 if xx 0x 0 0M-ft M N.JOLI I- *x Ol *Sx -44 t 0atC

X-Z0c4 I ox ** % *4~~j sQ I- 4-~-o JJW OLIJII-54)(0-i(a~ 1-U W .4 * U

-.-v 0x..Z% u4. 44 W 10- *N 4 0 Z4 *4 * .. J 0CU. 44t-LLW(lcy....Jo OO-9L4 Q 4U C 00Z X -4 N 9-01Z+ 1P- O I- I-C4

QC~~r.LUUL~aC 4 W4-WIX- Il Z i0 00- *L *l I- "M-

444-WW j< .0oe41 -94 4 U I42XY-O4- a 11 Ue C*L I *r1~ 1- It.-.zCYoU.I-

0ZMXL444-04 *t..I4U-WW I W Z- 0L . . *L%.0Z%0~qU-Li 4 T *L KilO-O QII I I I OCULi~ I 3 I coca - ~ II. Z LL LLU.Qtw V)-- L. ULU U'4* C 4 L. II01- J qJ)II

~~~~~~~C UN)Z I-N X 0 (L IW Z.'U.uIZ .. j4 1 ICIq 44-4Z.0. 4 -~44 w U rN.JI4- I a Cwe.. ) IIU

0 0

UU

0000000000000000000000000000000000000

I.-

0 ca

P-0 -40 CO 0

CLC LLCOO 4 0%%nvdo% LU 4q .

N~-v.c M "

14ww 49-CO CI..O 0- x>

I-. .4 %. 10 494 <I

CL-LCI 4UL 4.4JIIK 4.0=w-. 08 O 0 * U)

co VV 0.4 0.W.14

-C-0-0 0.I- X INstCD& -..-.. OL 9:** a . i.

*I 4. qO O4fl0..4 2i U), 0.+(D 'tV f4~0 qp4WI"4 - 00 *MC O4,-f%4

Ao w2 gw~ U.5AWW41 W%0PW-fo If 00 ,. g0f b.-cic if00 U 1- 2 It if 2

N ~ ~ ~ ~ I P- Q40f4i J ...JuU-

~02 Ue.e-01-.O L. I 4 0 181.

0000000000000000000000000003oo~oocco000C o00QI0000000000

~z

* -0

0-

z

6.044A

OW) V)4 (OL

Z 0u 4*I1- X (3 LUU mll 4uo - =0 0 1

(n) oot X

.-V W0 LU -' r

0UU 0 0r (eL L

W U %O UJ.4 U.

LL- 4*.-i 0 u. L> 04 -. U- * -- 4 a 034 ccl ~ 4Q 0" -j4A 0 * - 4 X(4 It -. 4CO- LU Z

0. .4 I.W) 11- x VB4 ) U.-0" 0

(A (2 LU OW *Ny 4WA NY - o Iw-o go. - 0 Z.. U..m0 a W 4

x( e t- -t-4N )e4 0. x 4-t QCW 0 PQW.1o n .4 IU joz - .- I C9. CL uWu

- * If w <4 W L )C) U)P-~ * .J I-Zx -.V-) - .1LU Jcr. 0m -4-C * C(4 U)) 0-4

- ZW I- -WIJXe ol- .-.X WO 4**I- 44 -w r. XX xt W CLC%- 44I-

CL.~.w U eaW.-M efe 0.0-* oft 4CI exZX'(WC w:) u 0 a '-I-- x -44n 0-8."4 * * z

-4 C'4Q VU) )C 0-.0400 -. Do~ i,-I NO UUm6I41 '-P4 0 -M' OXCu. . 0 04 * 0 P" Ifl..% *IV o.(.( ~

1--P- .ZWZ am - W0.nt aW if -- 4% 0ft* LW.-4. 0 49

"0I-0 ~ wOZ - W *wZ 11- 0- 6c -- - 11J~ II...a-

LU 44w4<W<..4..J 4WW * C r4 U.--N a~~'Q4U)4W'OXN .J0O) Z.gIQ' Zz Z 0

Ifu-wW~.~U LLLWrCLLLLC-aCOU.OO-aOOCU.UOCOZ c ci~~ L)~co OX.) U)00...-UL ZWU 0 0

m 0%oo

P- (30 '- -

182

0000000000000coat000(09000000000000000000

0000000000000000000'e- 0000,0000

Us)

* cou a

LU LUa acO 6-

ul +) or0 A-j .-. 0 40o c o

j~~~~ 49 Po on N 44 -

*~~ ~ ~ ~ 0 n- f-7" w J

ZZYZ wU -o 0)(L4 0 1 Cie m0 g " + *C - ~ *j CLoc)4- 0 -".0 CL)

aaia% 00 GoIfW *u-N0 * to( X

.4-M-40 < 19 0-4- n.-# 0 n 0- 40* 4* a N-", of~ l..-! -n L

4 *- 0 m n V) O.- % . "R')9 ) -WfO g t. - .. LA -9 +$- on~ +0- 0.- ,-4.U) Hf P""40 4*4~ U. " ft 04 0U)." 0-U. C . 4 4I- P-w- 0. I- n-d"" CL 004. ON --- ' - o

i4' 4 *OCaL 0.4 -mO00 MX6Z c"4a%

44.4 4 Z-%O.Z% 04.. .D-H 04*10-K =i

.44 W X o.4- *4.L.-% e 0. -aJ. C.-. goLu0 .-.. 40490lW ICMC =0ZcO 0. O.4 O- or 91404 OX a -

WW-olN .CZ1- NJ .X-wo I-C'-* 09- I4.wc II . I0.-j0JZ I 0441 -. Z' I 0Zn '-.0.F.-. it0+ - 0.Z' i-JaDr40"- 0Z-.c 1 6

V4~z4Z~uj -1.-4 O* W C v-n.4q "4UU *0W--. OZ' 40 1- 0 OO I OU W .9%00c n.-immZz *ZccKD XU *P- AcW * 0OI0J * i *Z~r: * 2 LU% .:01 J2 t an~ 4 if4' Jzz. ifIflU)W%.. a+ i-a w1.m~ jrf* WOZ 11 Wj~j.0. * tIf 11 -" It-OZ *U- 11" .OZ 1 e4-.-4 COC Z e 41- ZW... JZ. MOM IL W-J M W.I'~. -*-J4wm nt-4 C4AM*U 00nP4*.D0 -a IIietw-"- x~~(-- II 9 II ZOU N II ".40Wfz 0.-ltoz Z0WU'cW * C ZOP.11mm

N tU~0 0- r\f%

183

+L 0

Z

x 00

4. I--

.ooc0 at 4t"

c4 A-J P J2L 1--

a L< -. 14

U . -~v 4

z X .O

- .U+ ~% 1

cx X 0 fi -j404!X Z4Z%.C -%%LN.*L--te o%% o a a Iw- 0

-J-J I 0-4O*-O 4w Z PlCOJvL~ .- . acm % 'OZ- . -W 4 X X * --@LUC . - +7-wo r14q4-.*0 0 0 o o c o LJJLLLiLLU OSI-l -

+4%% 0 P- I- 3 1 *NZ ZZ Z Z Z --- c rWrC " I*On cat1 490 - 0mwwpfv Co- N-,.4N 0"#4W4c N W4-x fx,-4-xx x x x xx x t~/ %

0c. *.G 1i fi . 1 Y.=-Z4W LLLLWUUUUULLOULLLJJUULJU C< . -C OCCOCOCCC CC 00-T j"=XJr xx -aozz zz zZU)04W4Z ZZ LLCCc

%.~~ ~ on40-.~

-. Z * .. 4Z I I I I HII ~Y184 w

woK4mm%

+ z'

*( - - ug 0 MN -

-4Z so 0

+44 ~o 49 -@w 0 -44*I

MMO )w 994 .40 WO~ w"- 0g-- :5(.2 N - 41-9 49I-

40 move LO * j

04 0 * *44-IN Afat £.4 44* * -4 .9Bh- woWO

Neaf 404 0-

Q* .44 we -tWa -2 LU

US~~ u-oz Z-O. 0Zo 000-03-Ui U4 Ajw tAUWU ....

N Z* ** 64140 qcz g-%%beJZ Qj DM1 - 0 emW 2bp - v

4-0*4W W6Z** amxWia't ": LL 01) U-4- 001 f -- m ab mi3s

4-w~ 1-4 -ziOt#V.D- ~204~ Ow 00 alOW0a-0 "3'4 -b . 0 *a f

C7,4 I4fl V71 o z * 4044Q N) 0 -4wCCC 1--+J z o - :: WIx* .Je aa am ZO U. j0 -f No b.. 444WEU4 Mfd.* j 4 1. 0"

0-.Z PZ A40 - 1j si *m * 04 z% gin i.J~%w-@ ON- WW9 Z Q Q4

I 0_~i "~f i-n44 I4 CA44- 44 >0

."ego* ~ wque -.u &.4 =f - z,"j"w 4 yn 0W4q-Z4 - ww 4W6 dr a -zc %. Q4U -mA 4 N 0 -1 u -

:0 4OW* j~c*d cwc 40 -w .0 - w6t~ OZ a 49C*MwOK v- L N f U-.. 49(CVl ae -U; Owj-O djM L

OWW AOONN WX94FI93cZWwW@4 XQV 0 00

wgI..jig ZNW~*W4w le -. J.~ N NL N I * X+ 0 .11

jU.LO. * gWOUwC0l.)Ulf.LLLZN 3U. 0 C. zx(

N No

'a 10. %0. .0 .

185

IA

x 0

-UQ 0 ' l-In 00 0"

o -. zU 09- Onb0 > z

a LU N I cf-1il 4c u 0 a ) 0

tI- 04 0 001zzLulk z 0 9-O. 9- =09-C

-J ~ j w- ww-- 0 z0U 9- > "0 O0000r1-0 90 Z o *L

SI- Z 49 UJLA a. cc W1Z 10 0 0 0 AO Oas u 0 ..- 0 4 U fl

CAI 0U Z3l. Ul cc 04 11111 ZI-11 1t 11

Cluj- 0 cc :D 2Y f0 " M4' -

LL1 o 4 U 0 0 L 0

P" .- it u -- WW-) 0 r4I"UUUL ZO.LUU 4-ULUUU.U ~ ) 11 XU)ILfl- 0 c 0 LI-Z LC LZZZ LLU Z Z ZZ Z

0 4 Q .CD#- "e9-000i000 00000 wCCAS0000 ..s

- ' U*.e- 4 LU liii- 0- u - w' i - - 9' ;g -' -91 II

UN . 9-. Q u99 900~- .- - - 0 - ~ - ~

CVW - 099 ~ soL1~.t~"O 9-fVOP~ 4186 9

VL .I L U ~

U.

I.-

4% L

z 0I-I

LU (+ V) 0

L9 ~ ~~~ ~ ~ 0. - LU o"a

cm a UtuL -: w C

=0 a* Cc l'- U 0 LX

0-- uje f- * 0.40-

:-=- V ~ s.i W)- o-* AmI

0 0, ft- I- 00 0

1. -0- 0419 o~u 0L 14- m $- o

inw (xw 1- 4 - a+ )4

m~ ~ it * LUC 0 - j 1 op* Z"

N. 1 s.=*- 49- *04 16- Z V"~ x- 46--4U.

LU -' o- uj W09 (.Ww 0 IM UQX - W%-0-o PA7. 0: N 1 I on '9- U)1..)of1I I 1-U) I- 1-o ; X LU 0J "aU.-

Z i UJ .. (n-.~ OOO 00 <I-- N - 0 <--ow 4I c o 011(a

.0- 191 w 0 o-WCZn.~o-4MN('*..EGD if 11 - 0 *+JU. z*1-

N--CfNl - U ( U..sIU.WWUZ .ZUZZZ'.' UW (3d LUt " =ZIt L *P-.

N cc C iO- -1- - -JO Ct '-4ILUUU.UZ LU-4Z,-.)U)fU)- - LLU * L0 UCU- 0(

NQ 0 L.-.Jr9.AN.f N usi J .uuuO-4'.4~

* OZU)O. (3LU *~~w ~ ~ ZZ-'No"4187-

0000O00000000000woo00 + +A-c0

-- L. oq+ 4nv4u

o uju~

Wjoe +4~ -0ww4 ocI-.* )-acl

0. g Z 04 -.

zx4 4 * zu)(O

Cli- 0 1 (.D0

00a. -*z --. swj. 0 0 Z Q( Mi 0.4at

ft- .4 < 0 -)W*.1*- 4 X U. ui*.*. 44~44-U6l

UJWA Noe .1 Cc~ 0.J..l ** Z 7 1-0* 0 P-ON ">>X-Ccc

00%* Z 39 * eZ(50.Z . P-- Z o 9. 0. *.. a .X)x(4

8OZ40 0 >--Cc & 00. .***

CLOI w40*0*3 l-.cu :

ZZX-ot ( .jo I <WU.* m 0Wtucx" ox~sw.r~if441-m- 4 Wu 01-001.1 us 4.)3I Z0.)oX-*ew XOW Z rZ-40 *ZZ >- -4tmjw Z W.-t-wwxxf*h"mZ ac 39 >"-a .e-eo % .- oo00 p"-jlZ PO WOZ)U.LL&A..LLLL )I

0.-1LI* 0 u I.ol WNN= 0ow I W#WWII>O'-v)~ *- = -O>-L~~l-.--~ UI-a ZZ

I-OW- 0 W-4="- *l-O * *.~ s.U.n.U * *LJ.UI4 I OXuuUVYluElFl

0.I--w4cU- I- 3.1 IJZOD (AlIn--Qc(oj( *(DI- . . . 01-O ZCU.LW dvWtv~e4II J%4X- *ZZ- o 0.OW-41.1J 44. al 11 11 If H1 11 11 11 11

~Us-.eIU)II)OC4 NIL.IL 1I If pIIM- O.0.40l ..1 C300-if )WOI-- H JiW-l.W.-O0- wIs-~

q 0-s-lJJ1-NZ=<OLLOC JIM I I.- D ln JZJ= Iil loxxxxxx x1 rr~H I-m'W1-- 0O-00.-IO 111. .~ - b~CW CL

04WL<CWWILLmfIZZ UU..LLLUJ4.)ILUAL0 -. A0L0 tLLLL<4x4r~aocoqd4 0

188

V70q(% 7 )~47(coc 0000 0 0%()004 a% a, 000000 00%000000000

~+

00 00000400 0 a000 0 00 0 0 00 0 0 0 O 00 OO14i~~.

494j- mos "4-11 t 4 ar

* r*2" U1 . z--- 4

4zx~~~ 1729 c0. - -c~dc I s a xf- " .o1'f ,)L

VHL -4r* Z44 M Lu L-11

*4A o~j ++40 M6 XO4N 0CID* ~ ~ 4C1 .4- c-A -l+o+ Z-4 ul-u -W>.411 = mft~.E). j+Iuwj o*0 0co UuX>.-"->Pc* %tX - U ~"% -:--X O.(lO tU P4 Nor' ~ ~ 't%4cc0k wn J-4 N

4I ). 4-z~~- <- - -L-4 n

MZ4 6 '0 *ia-44w 00 'A ow4

N IfIf I 4 oilIf 1 0 v)(4~m xL .J W 1 - e- -at x Coo1 -4 f11 OU ); *NN N cm4

ow = X P11 I "4(y4" mc z1W ---

U)0. .4-* ft I-f---ULv)--.Q-.-LL. JI ifU. 44o~ 0. U) I 1

x>, -P cc Zwx~.. Mw ~4V OQ O+9L.~ C. Www o* n ZZ00 LUL~ ~%%U~w- ).NXow.N3-ooLmm N NW

CC,~w44 c~u 000 Z44--*4%. 5 % I g-.(fl*4£.)L)4 V. It

U 4..,)((m N'-I&N)) w44 I0-4 4QU -2O4)) 4

).~ Z 0Z~ Z ~ .~)(j44 I189

u rz

Im-~~ I- x w

Z~~~~~- c aa c49a

X~d~zXle ~ 00 ~e~z0 %4 - - -w

.C ( a a++3 da 1 0 >

xX00 m -oU0 9wC4YY *CC (Y S~ w ul

U.W W I -- --WLU I OX>. L-ZUU I - -- l-0- CZA- 0 aq ~% I >. ex* * 0 ,- 10 1 CL * V"

~~ s-ex4.W~-ft 1 Z~N U)7 to 00 1NZ Z)%

C-)-2x. I>- _ ONO#-OOQQx> WUj ONO-OOQUX: - -- - w

uucm~~ u u1 UQ u U

~ 0*4N~ .~*~ * ~ ~ ~ **4~~ 190

0

U-1

LU

LU

-.1

0

- L WZ c ca XXX )p)'-XXxx )P, > >- N

44444 444 -0f1 U- N 0.NW

w U

x)(XZZ00 W4400000O0000Q UN

u)ntlw~n W W X .J-W t--WW WW W-J- r~J-dt. 191q.w.

D-A29 456 PRELIMINARY MEASUREMENTS AND CODE CLCULATIOS OF

FLOWI 2/2THROUGH A CASCADE OF DCA BLADING AT A SOLIDITY OF 167

U UNLRSI E (U) NAVAL POSTGRADUATE SCHOOL MONTEREY CR N D MOLLOY

UNCLASSIFIED JUN 82 F/G 21/5 L

Ehhhh~~h1"i

1iiii.,._ - =1111 *' 8 vUlll ,_o =All

L.

MICROCOPY RESOLUTION TEST CHART

MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDAROS-I963-A

NATIONAL BUREAU OF STANDAROS-1963-A

III104 28"2.5Bl' i ' I

IIIAI5 111 -- L4 Ij.....__= 112- ,....L,_. -1111 L 13 111 L .161

I'Al lIul I'll'j 21 1. 1.1 1.6=8

11111.25 ii _1111"- I 111 6

MICROCOPY RESOLUTION TEST CHART MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS-1963-A NATIONAL BUREAU OF STANDARD. 1963-A

U.U

- ... zz

ipC 4 " a.4~i~ e .e o. o. ft w o. ft ft s. a- ft o *ol -)

== =: .. =N It~0~ If 11 n

11D~ri LAW) =(A N ItN~J -dt-M =M

00wwww CCD-' 00 COWWWWXWXWWW WWWNNrQ- NWwq.~.0040..00..~..UU~lUWW~D~ WW 0.0...00..0 0000 001D(- . M

U)U) )U) )~'-e~ . 0W0.~~~~J)4U)U4j~f~flU)UV)U))4A)U))WWW .00clIEN N NN N iiii I N N N i I N NUN I 11.0..0. ~ _

u fCl NlI I III

.- N ~ 0~Z Z~'JBllU)I N N ~ N~-.fWi.-iJ Wi~)UU192IIIU

UL

-ft-

L. 6-4

a -w " a " "

w N. wa Lu-- * -1-wIb

z LL(YIL L- f .fr* U." z

- 0 -0 1 . L

cc0 ftEw "U.m-4Op-&-wa%4u. I-

o" ~ ~ ~ ~ ~ -%.j W4"4 dvr 4wa L~ qt t w U) Lu0 u) P t-- I.A -

NwLu-x~~ .- 1.-N fN I ON W4 0 . Z L("

j N 1N0u01 L~u "414 MN alut owU)a >LL a% a ~ N - wu0wso -P4 -w I IP. 1-W- -J-*W * N ~ wl 0g 11 m1 if

-e L LD C0400 00 cc2 cc co. ml i0 Z j )119~ tL. - -eLI.

woo 0 J== 4 .jX=~4.==-JXw 0at 0 ccC-- - *e LI&QwCLC ww .LU.Z CC

NL a a, Cm166L.LUL" u0 --.-. Z'-.-ZC 0Z>= L

~ 'A-~ .. ( 2OUs-0U193

L~f

000000~~-P411NNN44NNN~tJNNNNNNN~'NNNNN

z (10 N

Wa cf-JV XO

06. ,JWwW W=-i

NN -%

00U+" 1"-S.% V oo0.7 LN*e Z U..U)

us90 0 *W- - f~-2 gL

0*0 -- f N".oz-t )- oin.-J ftf afOC-mo -4- I-M+o.qx Win) 1CO..4b o. 1o-

COO 400o N+")(U0 CU LV tfw 0woc0. - UV) w- =wa6> -A( COa~

o 0 C0 eaoo ~~":v ft-4 0. '0. 00

I-Z~w U ttOWM*- LLO a -Iu)*- Z"Q-ow,,- CJZ9 *I wO Z 11-%w 1 IfI 0 -JOWJ

a>MtL Maw0 a WO *0 a

Oa..44 It 0.0~4.

.0)00 .- W0.4 0*- OOU-194S

00000000000000000000000000000000000000R0000000000

0%0. 4 Q~0. 4 .4 04Nr ~In 0.NrE~In.

U-00

z 04 0- .

* 1 *4

I.- 440a

0=cc %WICC0 x

*0 *1 -. )(a.00 0 WX 4

4 -OCC cr co

" 04 0 - fl 10-Z - 0 w.4 2

YS * LL, ,4 x 01 .v

* -cm J *- * ow-O 0 cc M0"0 d N C194.4 49D aL O99W' "O 4z .-. @0 I a 44 cr. oI.)- 70 -- M

4Lflw*4^0 -.fw: . %ff cc Z d LULL4 Lugia O IWW4C LuW8 -Z w %.r.. 0 In Pq L-4

U-.41% 41ae c .. J* - 2K ci '0 Ic 0 )e 1 L 1w 0 * NaPWW aI -,% 0 0 U. .e4J. (fl

a;I i - )(w4 LL wLL LL CC 9- COe0* genc 0 -UZOW* Z-8.- a z AA 0 . G+ w NN WLL

UZ-Ajt I0 I- u.4*a Z O -- f .- of 0 "0 l " U..Z OC hIf 1- 0

.dU4 S4S ewe" *=" 0. If#A 11 00 LU 01on-t/ 0 eLL.0 9.)

00 a4 I-WO-ph. ZZ * II Uc CA IA ZeXO VZ -. L O64 =X

I r- eWOCY~- g L- CIC-M0.@- * (7- ipUCCLL CL O UJ 09 *I1 >eV) * OWK) )(

~~~~~ ~~~ic AN-*amWm. u ~ O ot~oo~ u-W *4 N 4 z ~ 0 ~ a U C a.U U i 0k. -

w .4*~NU.-4 Lu)(l-i *LD.--~.)ZV~l ~ 0 iiI~w~w~l~~...W...WflS4 00%~4 w .~ n L X~-0f~....L X Z

u~ in u'.Z I0 L) t

ow~'-00-'I- 00~UZ.-.C I~nW U)44.195 ~

UU

'2OOOO~oOO~ooOOoOOOOOOOo~OOOOO

0 P

U.

0 Z LOU

I-- c Z 0* a

0.41- %W 0 + 0Ndu CI X*L

QUj -00M W +0 Z K4WW*jot 0 = 4 N 4 - N 0 0 "20 20U

X ft IUU N 1) 0." 0 0 +0 ~OZO !A.u. * Ow#A Z

W- OZO- X~ ZW*0* *

w W * Z1 '0K U. U). _r 1-0....j+ U K NLN -0 %zN(

S= -N II 0U I- CCUN.L Q 0 .NLO O-,4 L

I, 2 w w 7) 4 LU- I.- 4 '.i0 0 LX-OLU 1. 04- *4. m +* *f

OL 0 0I- I ow *Z ftW m -4 )( *No09L .- )ILU.-400 00>N

kw 0 0Z~w 0 -W ".Z0Z0=.'00. LU' I -pM 0 ew CO9.9 41 Zw.4.4 XP"ZX ~0*~w -

.49 N.. -'0"O P-0 SF4 *m 0Xviw~ MUI-' L >. j *N(- LU I N 00oWN w M. * -f '0 -m44t W" a

X - 0 .49 0. *KX7w . I- O %Z 0 P4Z)>~z wI-9 0. 0 9-L Z .J) onof.- e.5 S1.---'c'd .:gWK4 P" + * UJ +w.0.~ -* + OXL- *.00..J 9.

W W~ r.0% N.W if~ W). ow CW0 * Z .4.X-K( K9 4-4.

OZ KU.4LOCOW1- 0P..P I-J 0-4 9a -. -Z-Z>.J.Z0 -eZI-9-4LUXZX>) %

00) -7- Z Z N &MeZ ?. * 0-w -. I4~~940- W ..

Lu ~ ' NN m LU *.-4*+03Z=X>--4fl.-. V4f"l-L-U.J4UV)A41- 11U)Uj 9-w0:. - I- I9-LU *9-V-qWo 11 11 II 1 lif %v 11 N .. JC 0 1 j li11it c~ NMw

Vn WowU.0Lu.=K~K -J U.U.wu. .Z> KI0I0I0U.U.u.oU...J".Jn L

QUU U U U

196

UJM>

Wo 30., 0n.

ULU LL%OW LULUO'-

=M Ofl XOft-f (Dg =zi -M)

44 s-,. I I xxI

3XZ Z. ON%b %% 6.46"" Z

4~I-aL.Ww 4w

'J. Coco QWI.IC 11* -4L44 xz 44tzX U-' 464"d

NN%f%% -. 1 co N*f%%.0 21 "%%0 0 LU in-.. 0~ $--a ~ -C

12INN 014-.J.1 n-N1.~ 1A- 11l

z"* * O.W44 Z**494 -Z= Zr4pw;

* -. J.* 0.tip40"N=I-* I-Z 4c =0- 4 = v """d .w

'J)U~z 4000 Q'j=XZOO cf.6-.44OU.I-494~4 22 44W)V4ZZ -* -%waxUw

0ZK%.% UMCDO3 ZZ%%( L "4QL +C0I-- )C F.4 UJW 0 0 act-$" eIP' S *. .4 0 -"*ZRL infz.ftftqv IL 0N o +O *4"W.. **Vuw + **...p..Aine wv4tcro.. *040 o- "4 $-IN -. VMlf* * -- a.** kno-iZCO* P4ccIfl

O000NN X Z OZVr'. C0M4 -2-50 ou(- V)+ $0"v4 0i-ftofoZZ.J.J) 2w )4-LUwOO OX= -0Z VAOC== O-C*W"t~40f"

VU74(X(- 0 0 XZX Qummw =XXXX 1 If:Z ItUI-

XX(IU.L o *-"MN. 2 If * 442m1 "4=ftn 11 MWlI-)-- C( I WU I LU * .2 44 z2- 02244X- CLC -. v - #-U. .+ +WW2A e2 0*70WW I I 11 U4 .-Nu.Jr'.A I "4 .4 w,.40 -.-. 0rWN L uja

~4 0 N).a--~ N 4CID NQ.- -0N .1 I .wZ ..- 's' Z

If.~-.-~ *j 'N1AV tN4:C QV Ne. NilMOC I.-. .- 0"4-f

I .ICALVIU.L42 -044 o6-COCZ Z OuXPZU""=2O20 Z

I "4

197

Lum Nco

0 L41-0 0 at

1- L) ccM Auj0 LLL

0 l-Z - -M

0o U)0 .

LL ,-4 1-49 S

U) :C: I--

oo A 0 t 0u..A .1 oil- 221 U.

0 2-s eW uJ

a cc 4s. LU U.UJ9I0 OL U- 00- Z~ 0-. U 0 .(3 4% -)o

.J at0c-4O 1-0 ow 9."

o ZUU 02 ZM 4Wj c -M go-N I- @ -*0 *ALL =0J= L CD Wo 0 N 0

LU ~ ~ ~ ~ ~ ~ ~ 4 V) *Z -Z0*=M J Ua.N C "C

W. N. Zoo" P zI-r . w x I L0 LU W-O U. oft" + M~ccf. V) Cc= - U ."A 2

.4 Y) I- -J" 0 *o A x W < 0 (D Q I

LA '3l=tl- l. Os-') S. 0 (at 104o

LU S C oWT 00U- i- UJ"jo OJL 2r' 0 SI.40 e f"04A LD 0 M- * tft ~ < - =) .44 *4

1.4 ci -a e i . tLtv =0U "4D .4 <W 0-w 0 -W 0oiw L. M U. 0 (3 s-M *' 2 NQ Mz OU. .- =Z 1-0w.4 -u M (Do 4 LW L -

U)-o +O4W~ qA.oc c ~ o4" &^ I O- 0 0 NLU w) *2- s-2'o=*zcc w wo0 z cc w o ZW 0. N a. '.a.

ZOU CC 0 WLWQ1-OZI 0aW CL O39M

~~~~~~~~~~~~f a*I.4-s.4 2 J -LW ~ 5 . I> UO ~ ~ ~ ~ W uu CIO %J Q~-~a-4 U U)f z - -~

W 2 A5-.~O0 Ow UOI ~ U)4 ~ 0(1980

UL

LU)

1,,

at z

LU M &A-

43 49 0. 0LI. #^ UJC

4U jW P"Na.4 NU.1 Q ;3 o.4L

-4 $A zI' 4LU q0. OO XU4

r% . o-U&

II U.1 UJ CL N"t *%~ LU

m) U ) 1-L ac*0

4- U .Z-t I.-.WW 4

Q U. 4 c- -l 1- %w+. I-I U.1 N 6" U) +~ "IN Ide-1-- 9-4 44

I NU wf - " C . .wow-0-tLU0 N 0 Uj j -j~ oza- +Z0~0~ #Aolfil

9-" >, AZ N 4Ujc J 0 LU LUCLO ==g=.

N43 MC @+-rI Z 4 CL P"4 * um **c. j a. S. ob*4

40) *t 0 p U0 0 .w 0-

0494 - 9 0 ,fo1 -N NO t u>. Z , V, 0I '"4

I- 0- Uw o- . ow " -co o- I j. cc w. N- 0 .0~ LL 4_tIWW- a '-- *.' U..L a. oil a.tI-wo~w41 444N.OL

mm0 )(Utj4%wz U.1 V.J et ... z . -o'4 it- 1I -5i if oarccI.iZ *-- -- TLU uJ 0 0. If ."90SZZwww-4

"ws-a 04 '-.W "No 4 I 0 -) ~ Z~ .

N- c 04 It~0II a tNN .O a-No try-0 fO~NO N_ rk vv. u U vowJ U" w Liuu

I 00 . 00 - .I ~LU 91WI~-'--* U. *199-

LUz

z z

ao 0a

zz

+U U. a 4cI.

IP% LU o1 z d"0 0- .4 Uft 1. 0 z

zo pq* AM 0A

9-* 0 gooOZu U Z 001.0

20-dw ~4M 4

0 NU- n Z %C 1-- 01,. to. so-> ,4 9

LU z *aU *aJ i-1

.w .14 0. 41.- cc ZL 2 DQ NU- -:14 CL I~ 0"1- 0 4"-.0 Q39 "41 LUo" LL l- u

W4)-tno If 0 w l-i U.."OC 1-4 3N0 L - -- r )N" 0.1- 0 0 -49c -j a

32 ~ ,~w ZNj OZ *'(0 0.Q QU( it4 o1 '0L* L .m-i 'ccc, -0 xp"~W U) out.U L' ZL 0 N v

.jww" -W u "o. U . ft .e. G. .I Noc.o

0 . 1-M M -wtiO.J9I. LUU4wW LU-lNMa Lg- 3M ::*wm z 1..4.t *1~ 1 (De0* (8 '.44f4- 0 0: -- L

C14 ~ ~ "1. ORV m it If If 11c f9-e 4 0 e 1 fm.HV0 LU 0

uo~~ ~ ~ 0~ 1x -vvw ,-Z 04 *ic ILV)) Wa.oc 0j 0 O t-

s 0 09-0.8.0.. L ewO *s * .- GM LU Nr CC0L c w CVu)(I a *o .Dwiwi- *M 3-u 0 CL C U4

LLD I.WO.Vldl/Po 0 0 0 - - 4 00cc 19-- ~N P-I hN0 (IO OZ N0 U46)V

W L ~ U)~NN od)ZO W 0.-.-U) ~ Z U. U0% ~

200.

mo w

U-

4c -4

U. 0U..

14%b .4 I un

.1U U..

I.- ONO.ac Z

z $- - *j x

Z.4 0 V) 11 Z $:D CL It

I I ) 9 00.W U V) tiac X .n

I 'UJI- -- ) ('nvw -w~4 !It wo MN Iw o _I))H( Q' U -).s4. >- ot) O~MZ CLt. X -

*e'JOu Pw-u.-w XA4nV 4c1 m- I-0C fl**-JJ-OO 1-*Icc~. *WI inN~t-0~U Cc OZ 00149 49<IWWW- -

ILLL qf~lf.CL L(JCCC 1d- -4LC M- LL. Z - 0 -4LLLU/. 4-z9 ~~0 * -. U4Ow -dO mXICIV)U' os*) ~0 o o IuJi ..00 0

I 44w- U-UaC(D0I P.4Zmu *L w_% 02 .O4" 4 -XI- 0il

iII00 N Wv *UI M -. ou )N- e 00CII-C swIz wwi at&% itIICL.-04 1-- z 2~ 0 _W34> ..4igZ ww ow 0UA

0 UJn 0 ow WUCL4,.e O Z NI it aI dc 0" e*a LUn Z>! CI 0<0 W 0 O*WZ> dIH-0~) >ICXZC *--z Imo- Q Mc.0ewe I -)3D- COIna ec~

I 1C. ~~w C ~ 41.07 0 _.j 11 ifw~ I00.Ju.IL-i U._-acLLLU.-Z OZ u..0 ar W>LWitWI.cO.JU.U.....jw.>u.

-~-~ W41-U.W..UW w o C00

w I U COWU~ UCL) u Co

201

41- ()% -NMttA410-=ak0 F4NM#tn 10- Q4 pwwm44 Q-woOV2

LU

4c -U

LL CL

4 Za

I- Uc)

LU

6- - W. j -

ceQ 0 V) . Z*L -LoU _ - * C

M> z .. 1 UC4 Zj

-. U.-I Z 40.-, 0 +

N x U. 1)0.c-4 co 04P.-I 0 0 U. 1

.9 0t *I .J *".I.j X U LU

w Ow.. 0 CCU. X 0 Z - U)--

a.. LU 0-f .. Je. 0 0U. CL - 3J ~ 1o-. .-.

I.- io :)U 02 -qt U.Vf '"4 U) *a

x x1* 1 11 * CO42 11 wW I- I 11 11.,j IL ""o-- 0i V2r 2L< P N 04 "

Zw N- ll w. w "4 a ) 6Q - 00 0 *-0- UZ) U MU49> 4% 0 U10 LU I-49- *u.Ifl*I0-9W LU o- -

w-J-2-ZOC a-. - --. it - %..O 0Z-< C -OZU. Ill 01Ozo ?U 0 ~U.0 w COM .W.WOLL.JX) u Qcm

.0~~> CO.(3 4On.O4J.. 0_ - LU. 0. 0.ZIOU.*ew~ m.

- =0 LU u a-6I wU uuue MUM0. u

Z.- LU 2 .- 4 ~--~~*4OW. ~ ~LU02

U.

U) LU

LL 4 m k-z 0 ac 0 -.11

P" xl- U.1L4 0 ac

-U Z 0 -J U

LL cc LA UJ

U-0 tEO d LUz z - V.

0 IA 4-. -Wc ft" * .

cc -ot 0u P" -a

-q < .J- I- %0 J C-~ * 00t go a 0a

1) 0. 1--( X-4" KV U.(A *l. -i aU 0 . 0d St

O0 -M= )-w.JU 00 O~t Zcc 4 wW Zc M*vs*Ql -W OCL%

4 . . 0 041..gi- "OUKI LDV)

"-4 . -. NQ 00- " .O- aU XIIU.- z LU U. =ac- 0 Q11 cc o

Ch Un 0) V)C z MW 00 %W0ZN(JJ-~ 4 LU N(%-9 420"(J 0--du C00 -

V)0 -OI 1J 1I. - ~ *O. +z~ So 4

ccL VUt-L .W I0 41~ Sa W4.O4- *LJ0

1* 1-4 * > xO 00 0 WO -m a-r0

aCJqw4I LU N WW.%...J U)4 -. 4Q0 *

X0'. U) '3WUJ S5 0'~~- 1 4 *)nnof.7 .. f *U LU 1 i- 9O- j Ox -.. x Ox LA.lp 0" . I/)N I.- V) in-. u 0~ SO 0!1 "COX -. O W -r 0

5 .-.- 4 6 -, (L 0 *J, 4>"U 0 m Ob OC..s4W(-) *i * 0

I I IP4 LUC at LU At%. 014-ac * * 0 . . NM-(3W.1.1 % LU WI.I. t 'UJ*- .. j -4 LU cc U.I% N J~.so5 9 SO *0* 40 .- !d~ a: to

I Xx+X A%. 2 0 IIZN 1100-rn *41 - * 'N * 04.#mVO l'- 3cc

04 wLwowW - 0 LUJ OItQ- 0 11 -11I zgcl:t z --- 0I...-.0~ N Q- 0J XNZ< 11 2L)oou.O 4 4 0 Ou *u'-.0W4 z WUV)

WZ 0Ju 0.W0W-I.tUCkU.L0L C.O.OZ is I.cc

-I

I 0%

203

Uu

- 0

0. * LU

0 0I I-L>uj~ S.0

V) .16 LU Uz- 0

0." . I-- U

LU ZU% 049 a- . 0 LL.

q L. LU K -LU I

ILm- in 4

oz LU AtZmz * -U

4 e--%ILW*Z- C* Osl 0

oc 0 0- ZO 4

-~Ci 4 49Z I.I- *~ 0UD. 0 ..4 .x $--a O404 J

4s.. U I- U4%A

U 01. x Q 0 I -

4 Qt V" 004ZO UUu 004 -J-Z Z .U

W dm -- -- ~ p xaW4 0L ON..Jxf =4. icc ON I'- UJO -- CL - 0L1--

at 0.0 LUX O 0 )(. U 0IL . a Itm -1 N-O 0O ifN~ 0- 9--Z%. 0%.%4 p*w, It ..JW Z- +NU).U I-WIL I 0 0 m - I.o >Z Lej-qq 0L at )M I ,.

U Lm U NbW '4j 'XU-Z> Z Cc U0f ".w W -W j 0.w m-w 0 01 0 31 -W auo4w- co 0 ~ ~ u 9-In ILI%3 z. wU I

CL M-- - -L o -3LAm wN --. -0W00. 0.~ 0.LL -

,110 co9 U Z. 1~OL U L~U .0UK O . -I.. U 0

~ ~t4 -z ~.. .. a. . K. *~ w204.

U4

La m m

0 to-

z U .C13 z"~ 4c

0 P4

040

_j . '0 Z Z-

j 0 2 I .- N

4

4t 2j I.--

4 4 zn 1--1--

1v LL.-.0 Z .- w 0 4 7.3 w 1- U. 0-.2

U. a~ ar 4 pLU.J at -* J LU "IP 404 LUL

W.u.L X M. X( -. 2 -m&- a. U w'%04 0 -a o- 1

o"Cg M ie I- -j- "aj- 4M~-.W4Ai N aUmC Lum V)I NIOZ

*1c 241 )WOO Woa .-j "f LU 2 le t1 LU 4 *otN@

af= 0 t-) m z 0 II ulu ft Z-4- Z +- .

a4ni U 4Efl4L. 1.-. 4 2 a-U.440.. w4w a = -AU. X .)_0 4J Z4. - -:3D 0. ot 4m : 0o *")(-0

I ' U. W4Ov) -J x -AZ U 0 IJP 0 f- oW-ZIV a: at X)w (WIA I.- .- l- .1W 1-Ja1- 0 -ZwW

Wi W.b M Z NUJ.)20-4 -41-2 4Z I.-Z wmo--I 1-X 0 In .tl-)(%'.1k% X( 04 b-4 Qpw XVf)(. 0 Z )(Ctfl

-(Q )-. * -W ~ ) 0 U 0P4 .j ULOWW .5 %w0.~CM Z UZO zv L - Uf. -- % 20 in.10. N 0. w ..M -. 0 oC4 3. L a 4. X4 0 F-VIn " o

f-4 U.w <4W)-0b 0a - * * 0 NOC*t L-dU1 ~N-4I'NN..1CI-- 11 U 40 y QU W N 6 4n I x so a wWo

n. LU a" of * 1.-w.4 oW LUjv*v--4 P14 $-- ~~M w

* *~.Ji.- 4ZWZ-l- ZW-1L-.-.J In Z(N* om4AoI Z tio1wwa*P4-.I4 U- 3:U...J4C0.OC S%'0 .4 1 >. "fa -IZZN 1m- w4Wiww

lf 1-43 qCC1%OZ4Q MX(Q~I 0 2H'-mtflWAU -- j -7-- -NP - 1-M1- v4-"wmx== qmo-M% LUC Xw-. 2 .iz -. ..Zn *JM -Ww.s'(Lowanom u..0, Ou .-eLC2LL-- 04c OwO-jw~z x womm lI

* I LULL(~m - 1-a a 0--0u . "-00U.'VSU..,j 00. C) iiOagiz mu.1c3393

205

0000000000mo0W047% Q00000000000000000000001--rV-f.--w w om0w wW Ww w o o

P" Wz z.-) 0

Z2 zL.- e-00 aLN N (3~ 20 w

W O0U . u.

NJ -4'-. m- U W 0 1--Z *e W -O(WA a 4 ILl

NW4 cc J.0 -M z I--N. LU Il ft . 0 4d

COZ U-lWi 4'" ..

0-.0 V) ul* 1- LLW00 Z

z LU LU X '. . ( 4W *- QJ E) .j Cy 64- 0a- .JOL

x 4 IL LU 40 CMU)e -4L a. W=

- 4n. Lu 04z W"CZ =0 0 *4

. *LU 4iil. V4-..j P" . ox 00U. NJ Z4)( -4-.Wo0 00

~N 0~J -- cc I.(a "0 Q .owUz cc x.I- WDZ o-4 -94

NJ 0 n ~ 00 Mm== 03.-fo4 L6 -rN 4 ZJ 4- a 4-'-2 4 - . (I a 0.W~ ICL

N Ifa2 -4 (L O 4 .- 4.tI(q0 0--JZ 2j CJZ 4N Woo.W 4

* 0 * .-- D 00=.. -4O0- 0.~

lb o - 00 o v+ * CL . o- q Inww e D.

)w ..j <W- Doo"14 ow14Z Z)l~

* 2 U 0C..-. l'woj. OX< ONr.Jcc 0 J f3 M JZ Z~V) 39< -- 0.0(OI

a. .J ZO a" OL-- 9. CCl% wt0 .. WZ

W UW 0 0 -~J4 0).-244 ow.~~ - wUM-" Z0--~-.j440 Z-4J

N NY z >- w 0 @*=~W.I =)ZtWix 910 CL .lu~ac: o414-o 0 a.-~(( D .

(4.~fQ - I"- z J-< %.l..1 46 04^ mmul..)-Z D 0. < U. 4<-JWWZ< .- ZZZZZ -><u#)

Q Luur c0 0 ft0 u.4 -iol-CLM00C000 .- wLcoo-co- 0- m cc J N LWAd -J022~4

%-w* I.- o0c W x 044 3Ay4.Z220Z-LLC.cI Hz Lu Z= w oWi CoWuJ0000..joac4cctnu.-"lu - etv 1 aCO - -wuu .4

q U LJU4..)L)4J

206

I--

OL0

)PC- 0 A .

gN " . -3P" 034 ovae,( 0 .- U

OM--Po

00 = r0-00 %

O .49U. mft 44 ~04C3 -ftU. o- -D-

OoZ.m--

U.-S-10 0.) O.w WZi'c - 0J

0CM -- U. 00Z

*z0 ..m M0. 4. 0 .

"n -. 006- ox - "w0 0 04

1U.&co j -0I~- CLW I.- LUw I-I4 4 4moo e" = 00 "3 not x 4I9-Z = U.w (n 0 l 40" LU U.XP0

-- Z"OCN0 oa.L- *t. 0LI. L 4 o. V4 0oiui-.0-4- s -0. 0 IJI U U .1ou .4 LU

j.4j, j 0ut 0A UZ 0I- 0 Zt C

-1-0~ Wr0 LUL-%U 4~-. ->..I Z -,999oI W. eof ..Joo me a- %I-Z a o OII LU X N-LUU

JV-. 9, -- 0 cc %J _JL- OW410 a4 ow- K'1 O 9-I4TOZ OZO -4- U)j~ 90. 9 0.J. *1 K~. * -U m 0

%U, MO-O0f ooacy o 0? *pJI- W. 0 =- o *a CFO N O LU910>%. X -j -U wOU.. to" N1 0J if.- -41 X-4 4 0-fl'AI O

I zJUI0 w4 .J X-xc LU1 OilZ- N1-$1 1 -)

I x.~lI~0 - .Ow-O X---,N*~~K K 4LLU. 0

I 0s>0 0 (3eu.. L*j~ L *0u4L seoo wI-Il II N *I Z?-w~~wUacww6- Zt 4OC s. UIL 0..e)C-.0-NII W

I~~. r-4-- r~t

207

I+

0000000000000000000000000

Le

uzfp.4X 0f -0~ ft 4u 4.0 -tW VC .s."-t. b4

ooM 0oZ-oMo 0O 0O0. "" 0 .Ob .0s.O b00 .~00 a0O4

0f 0~)M )1 1 11if ifV)

fta z zz x x a-$>>0 0 - UUZ o c x x >)--$X X >>)-'

OMLM &&oc

O'208

Vo

U.. LL.

,.- I-Iw* *-

ftou. V L 1 U..O014 - 0 a"

u.- -. 4LL I- "A .O- U.0 ma ULI -

44 -1- *-O z* W U. 0

CMN -N I.z

(, 0,0 -oL6 a.4 -- .4 0 o4L co

C6U*A" P4%L U.. -0 ton 4v4M 1 0 -0 1W-0WNof N"~* U.0" 4- @

LIL-. -&' ~ L- O Go-d 0

U.1 ftat~w oftft'l-I49 oo 4~Y0.-' U..eZ I- Zj o

I -1- -v . -4u4.4 1fl4 LL tL~- %wU.. LLU- 4

czn +..z ,,-,- I-.-a tm-LM -w-uo 0 &A zV*4.0rodxc 4 04'- f"..--.-.' Zo --- Z-Z 0 - t- (u n 0uJ-CLO0 Mowf---'--" + "X ZOL....-.s X -v .uj 114 n -

~~~~L al~ZZs~ .1Ol li10.11 UAL. <4-WZ I 1 0ii-t"Lwu 0.0. o.0 o..Z~ -- - v--q..-..f-Z~()-wo.

4L- 4N..-j N UA 11 NAI It Nf It 1I C.0.41. *-4e4 N'N -f~f -CO Z v4 V0-0 _O=

CL W LLL 0 C. 00 U 0o0Q C0 C~ll. .Z0 .~

I - 0 0 NM

209

JU

V OO~oOO~oOoOOOOO~~o~oo~ooO~ooo~ooo)oOO%,I~~Q h O 0 0 0 0 0 .4%440 001

~~g~p~~ N N NLA.N NN4N NN400O0 0~0 0000 000 0000 000 0~00~o0 00000LO~~J v~~ L~~ ) U~~ fl U ) - "f4~lL/ )U~lfbl

zc

con I--

ujW>- Uu* * * -.

)-I- ui a

0c-

00"* * L1

.4 0 -.10 cc

9-4 000 0k'bL)0

b" Z 1X- 00 w ILit- Z-> I4I ,-

-- 0L m. + N 0

rW 00o( V)144 0 *)%- - >

0- a 1 0. I-x WU) I-- I M-tn -40 0 00$~~jvzo0 OU)00Z m-o0 -mtx fo~

0-Z eop O+ I-)L.0 L 0 '-'W .. j-.. owon t- V* 0 4-4ml0 0

0s- OL. U cOP- 4 40-o-W~x u q00Cy U) -lje, go% f)t4 0 00)UJ w

WlOUJWL- U)LL0.4<U W N 44insoww0P.(DJJoOulo~ .-.. O Nl..9z I M~l.-I-o U 11 11 11

11 I 1M00Iofll-0.+ * OIL X 22" "-4 **4k~- 000.-c:I IfI 11 A)~q 0~I 0.44PW4 0 - ofW i40 0 1 I.CF.c '11....4.4 r

>m>o"m> "oo "o~-o"W" > 'l >W M-* I o

N 0 W~Uf O.. I ~ WIM-04 1000 INNI____M a 0 -- .W0 . 0)* -~-~..

P(.D.JOW i 0.jz Z *Iu. Az>g 0--m uuu i----.u UN

II I (~6 gj~iw.. * n '. -- * 21 0w X I If N II i

0000000000000000000000000000000000000

P~ 0Q~~NM4'~ ~OP~04c~4ujO~ ~ lO' ~ Nf4W.fr0, .Nf4NN N NN N ~~l.j U'''444'f .O.CO4

0000000000 C000000000.00000000NNNNNNNNN 4N9NC NN NNNNNNNNNNNNN

00000000 cc000~00000 0 0 000000VIUatx 4k' iWWnU W4AJtIn4WU)7UI# Wi~

LZ Os x .9 -

tuL -g 0

0 0= 0 . L

0 0U 4 0

oo 1 0%. -w Z -1Wy +4c= zM L U10 0 1-

lU OW z( 0++"o*2i ~ * +-f af %XL

=1 1*tC 4O Co * 4' *P2 el. -t- a 0

- 4UP4 W %0 0 C4aWK L12u40 Ot. -a ~ 0 -. XNLL6.0

02 . Wv.4 O G <. 01 IL 0 -of

a. *c un tq 0i su IL' -Iw * 4N034* 0 P- -IC~~wv Ow -0 79 M4 U.Z M O

Czcw ~ ~ ~ ~ ~ a 0(,-v4K oo * 2 v("0 L.f10 WW2 j

Oa .d, 0 LU% -93 L4 - -tC 44U. w W0 -)- * U. 04Np0 0 bI * sat- -4 wI -. 1 tL ILz 0Mo a *

Co 0" Ol.JIL"- tnf OP.$" N. 4ASI 00 on +UJ0M- UaIzc 00- M0 K Op O .wZN :3O U.0 W.cc.43Z- W c

M v0049 0* 0Q09 (~ qb%.a& *Z0"1 Z ZOOo w lo awa0 W'J 00~~* * *a 4=fW I OWZ= 0*a -- -- 04 alptw L

-44*% 0"40 -J49 *aL -I-M( * 4 -)- 0~ *a LLaft.tt . " -CC - v0 .;O- p GI4lRu4 ~- t o1 6-a0 o- ft4P C034 ) IO 0a U. wQo

IL N faq e(~ 10 O*%.X 43 00 0-IL

11 OW* Ox It. 0w04xj-- a0 NL (D-4~-~w "Z awl""-wleUC Ja~W O W 0 4I4f-e~ -a"W aa al*m3-L 4>u 0 0 A

XIE ) 0.4 Co0 Waaa *00L*a aZ4 tL *"WOW '. w -Zw0 = w -Ui 6(3* 0.4 *e~~*~*. 4 O w.J* IWOZ w~ ~ S

0 2 ~ W~~w*I~a* ~ f * 0 . ~ *ILIL~a~ w~ wwwL3 0*~- *- ZZ 4 .0o

U) ~ ~ OwL ~ U.43 ~e0Zww 2110

000000000000020000000000000000000000000000000000

~at uooooo--.

ZU 0 4OCL -6ZO -

-A U) 04C ZL

t. 0. s- I.- 2

9L 0. oL z.2 .j N V0 I-

* "74 us -*--- ob JC(a *44 -i 0 00= I 0

Zu OM&M. Z= ..'RIL-1V -o a- U)

0. W . OC 0O 0. b.@ Z"aC U. ..4 0 -at B O

us U.; LU0 cr. .JQ. O0 uw 39 0 00Z)0. 0oo =uS IL "LIoCLU -.. :u UU4a- 3

#-LOX CL 4 UJiolNoc tL-.*)WLU

- i- I. o 0 N C w0 - 0 W43XLU XO IL O 0. CLO 00% oU)jLU 4

Lt~3 2- C00 LL2nU)49 0 4t Z *- 0. 0. =m G.=eL 0I)..I. a~.I *U 0 1- LU- L-OW V)**4 44 0 --- OX 0 0. - Z 9L 00C0C-J LL-j= IIL ccwf.mI 0 N 0A N U) 9-%%

0 *WCsw Q I-. - cmZ)- W~ w- z4 0 mm%.vnmw CL 4'

CZ f- OZ OD N- 2 = 0..00.Z A.%

e. w03.NOm( so- 0. 0 -* 0% -m~xq2 OCNZ%% 0 I-o(%(~w4pf om-. . )(% 0 U)=<Z-40w%- OD 0 %U

*%%.6nC. Wow0 CLC4C 0-. U. *4 @sov0 U)4

*;%og x cc P-".in -0 10 % IX.2 .. m.C Ln

ZO-ZCDjXW)'-Z -iS mu * inct wooouZZZW.-.X)cc 3 0 i

cmL. -2 C0L~.B 9- -

-, ~ ON 212

UU

:3 L

NNNNNNE4NNNNNNNNNNNNNNNNNNNN4JNNN

LL CL

0 --. I-

1.4 -UI-

do* (L 1-.

a)U z z= - = 00

Z WO x0. a.- z P

W 9U.( L. L a., 0 -e

W LL I- - I- " D 40 "4&4 0 a

-.1 LU OW 49 0% 0.i, c _ 0i mi -4 0 z .-CI 1-- M ZZ 0 4 CI--. Oc

Ju 0 -U-I = 4 VU)

U) 0 U.0 U. - . 0 gU NZ v o* 0U) s..4 -M w a .- 4QY I--Z -*

-1 W*Q =K- =LUO =W UYLUW Zwfn # amI O44I 0O 1

F14U -- qN ~ I- 0 II III 11--- 111

IL - If =z a OCju. 110 wC38 11 3- ZIw- LUZ , LU LU

LU(1 4N .J U. eI3D.0 L

K 4~Z~Z Z~J213

LUISO~~ -

0

CO)

z

0U) 0

IJ

z ~404 Ohl

' ' 0 LN - lc Oz 0ClU - -fw ~

(19 I.- a 000 114 X 9 9qJ~N

a N0- 0 10 ; L 0 0 o4 MU 041111- N 0-: 0 . -0 IA - 0

P- I Z 0 zjd _4 tuz 1-=

CD (.D 0 C l si- u uac- >%w.1

in I- I- -atN4fN4C11 xc ;, W -Y , W-- ifif

0 1 (I4 -0 N0Z N %wo 111- 00 1--

u N~ u N--W w N"u N -J N C W

I- -a Z IZ -- -aZ ~ 0.. - Z-4 .14LU214-Z

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOW

I. z 0

W N

W W4

cc 0 (. T

z T. U

4C.0 LU CAN-~u ItZ

Z Z _j

z 0. ft"

494 Z- l--qVu _ 0 F-*- W-

N C- 0 JN- U -2 N'CD I- OzW

4n0 cc 0-- _j W -j M

-i- cc 4o d fv UN 0SL W o"L AS.I0x o

0 w 1-J -b( p- IOwS 4 W mo OZr W ON -

.Jo CI -I. **- "0N 4K4.4

4 -0r4 Z Or- . ZJ. - a:o 0 fXO -X -K 0 4rftw N.a. z 0 NJr

-o4 N ftow I.a M0 a 10* 114a 0 + o4N 9o6

a". - - 1CL - -0 W fva W. 0 -i-=1 1 WNza NNW< 0 Lu< A We-GU N e-.N-u -04

aL -w oo a W 4 3 WW-. 0 UL. ALL-AU . -ZU49Itc r

NUN 0% uNO4 N L0 NU u

215

p oo0000000000000000000000000000000000000000000000

V

0j

LUU

LU

U).Cf. Go0

0 010

0 .1U 0 Uj

U.1 - 1

ac 0LU6 j 0. 4A LU

z -J z L.U.

- z 0

U4 LU

-A. 0) U) (Ai . 0 Uzu 0. LU49 c

wx a-,~ U)I,_

V ) p"Q 0 CAI) 3; .- V) x

7~ LU (" (L v. 0.4NCm -- tx 40 .40 MP0- co 6- X Wt N., 0M

X49 x P". NP4I--0 ~4N -OPN-i- ) 1 0 10)))p + MOO WOO U) ZZ Z

LU4 LU c 0xDe+-.c x fill W- zp"f'. <_ * >Zz %N 0 AC <( Up1U U J of) of I.JPJo 4 000 it N NP.Iu4,..

w -44 W0zl -2_ * " ZZ 0 -00 0Q 1=-ZIIX go wewZOO LJ14 -X6,00Z 0 w 4 U)..... O * Z.%J0O- .6 X qxQ -Z)- 0-4.~~ .* -wl -* - 00 ~00 CIDNIifZZZ

4A 0 LJ 1 -Z) O ZZZ til 11-0 Za-)n L4-f ZZZZ-4Nmw4W~ 40 W4-FOC -CCl 01 oLoCC ee I L0 w)e fw 000 e. llwwCCC.

Z I-" W me Z4- -in 1-- fZZ " .1 U00-4 Z~- """"N IIN I0"U~.- ).d ~ Z - <%. Mft00 W%40 U UU Z I

- . P"Z if PS)O LU4Ut0C~ 110 ".) OX . bX) x0-x -. 4-OM NU OM No-J cZ)7 Ww WWWWWWOM. .Z ~ i C

Wa LL * .JL - II X <XX f14Z(~ 4 XX JONI. -4-4 wxx xxxx.x.xjxjxJ.I..IL <8C 66 mwzzz a am=~ ggca- W= UMI. ZZNI.JJ

- -00 nUUUUQC-Z-CC"0.- -00 0 -00 a-1.1. cc 0-sc 00000000

-~0 Zn (In01 w l -Z l - Zw~( In It~fV w w w' C~w ~ w 0 ~

U 4 U 44~~1)w~-.X~O .- X)- i-)' IV t II,- 0X' .- x) )'eZ U N N ~ ~ N ~ N W 4

LU L wU- ZI ZT 4 Z i 4 Z 14 ZZ WZ216ZZ

UOUL

0

LU -

0 U)

LU L

Z Z 04 cc

l' LU a1

4c V4W IUJo LU + I CC

m 6 . L.00

cc+ I-LU 401

ft U z xI

0 0LfI

I U0 m - m )

l' 0. Z1 Zw' a .~-C 01-X--

tI cci P4 mm.' Zl-

*z I.. . Z ~~I P"= c

a( NIae -0 C3 acet 0 0 .

LU Wa Z 0 0 m+ LU * a

z I-- ZC- I- x c 1 "*'-e

IiP400 0 G. LU W) V406-0M .w Luca g-~pg * -. 0. ri- z ZWJ-$)-- s. a.eM*

1--.-Z' - 0 0 0 o OCO-- X-- -I 00.~ z ZZI wU Z W xfww Unu00 t.- XI s~)L~-LU Nm LU Ij 0~ 21Zo *XCN I MCM)lN-

I-003r~e.'dL-.W 0 =-.OP 4d) .- W * .e - . 0 -W"4-O2zz U.; of LU m -(liZ 1 3 Z NCYWZWI~l- .C0OX--0 I~'~*l I" 1-4 ) cc .00 U ".4 9ZO-4MZ~~e~r-)V0Oczm4%I P.Jrd WU * -%0- LU Z U V- o- .XU o. we..44P-4('o9 o o o

IIf If 0:ZpwdZZt9 U. Mo- N -Z UI.) I M 0,0 O 0

O.w-.Ze-Z DZW4.-. <LL. UNWX-- ww4v44wwwwI NN 114.. 11III 0 I.- * 001.-WX t _ 4% (MCD P-*-rI- 1222-I-

I 4 )J Z 2w -0wc L3 X0x 2w ZCO-J-I-i-r4WO itI LU OIL U.WCW LL 44 OMI.Lw(0 wO 0c~cww

-4 N

N u N u Ili t)Uu N Lntm'.0-.t

* 1 217

U- 0

z JLU z

-W uj

in 1% W 0 "

IJ-V -- cr 2-, 0. 0 2

4 .1 W N+.. N) CL * Z

01 0 -1 CL LZo w(DI-4wLUN Z U.u i

0 00

Z U

-v 0% 3r.0L X 0 W 2

U) <~ ZU.

z 49 *Z 0M

0 Z) U. -%lo I.-C- CL .v -4F4

-U I. >- -J W2 uN Re- z

_- s0 0 6%ZNU)Wc

.Zf P)(LU 0 t " W N W Wp .n) z2 -. ZU I.- 0L -J a .. 0 - -

M-4 .C, 4c- 4%-"plp r-4 --v-1 490 -j l-a0P"*I- ~-0f"" V

NI~f 04 V s a i v 0 <Mw++a 4~x.

4 a OCC c s .p J I- LL w 4 - - L *- e0

*o > "n: J ZP-0 * 0L* o- -.4e0- Z= 0 0M*C 4.J Z-""*"vjU)U )-4 N 4~ZZ 0

of- 41 I-"M.ZO 0C 00-UUJC r-wF4ZCC J 4 Q - ClC-4L~l0 + I---UJ> 0- Or--S-vWX- ft U

Z Z 0 m. N ) ) LU- 4w w NJ >wZ4L

cleoo -L Z4 e.4WW4 Z - Z aCNM=-4'1N =--w4 xtn3.LLLU s"""t 0o +- 19N LU 00"000 X).IW'-e1 BOXII)X>-NICL

~ C, '1I-Z 218e~g~i44J .9

(fUU1fC(%OdjqtQP ako~~~%4r04o4 rAQ_

oo0000000000000000000000000000_r

01-I-

uj

U I-z

LU LUa.z z

wjz -I

Lb * in -z 0

LU 4c A

44 4

K ~ 0

0

'Le 4Z I Iz LU LU 0.-M Il

- NJOW 0. *t 0.

0 1 c0- j Odf U I 00w.NO r.d11 N (INP-Ot". C%4_0 tc.-'wl"_4 0 *wX)Cw)->.QZZ0Z

u I. I-l-zU))(IAN wM.ox~>

m dv~~~t . MM1ZZ )I-I 11 wa a N,4of" om-.14 * ow 6 O oil -ll LU *oI.-.4i4nww cnl 11 NI 1l 1

Zi * -) 4,5 f*) 1- x o-(%i 0 0.. O"3u.4 1 o, o o ft 4L~~vw~ w4 -. o~wc .~-o -ov. 4s. 0 P-4 N~qxx xZ Z Z Z Zp%@.

N -4 fI I-I - tfw

Go Inc II~rn0

oc

z

ui-uCL

uJ

uJcr00

U.

z zCU)

0 LUcc 4A

Y-. I- U

4> -L ZU

LIN LU Z4~U. *r CL.z * u

LU CY I-- Z 0-'--4- UA Z LU w4

o M. cc " M- + -- Qr. -I-C 00(~N4.4 4 c ac I- LU

V. 4 ) x F- 0-0 0.""" W0 NJ 4j - LU ZZ I- Z X)m 1if X)X)(-M-ft B4n. -4 --% zV

NM 4 x -4 Q~ I 1-f LtUWWJ.-h- Zt 4. Lu P- N 0 LL.0 0 '-4 N-4 D 1-4 -4 00 f LU

-4 0- .4.-hfvwl +w * .- 0 D 11"-4o(Wt-H u*-I -.L - )C>.-4-JN( 1.-L u 4 .- co-JZO 1 40.4 pl 11 it 11 1 4.4+. ; I +W+. .-4top- 3491-

fn~fl 4X.-Q.- MIl,.J s -. o- .gg ) 11 WU 9-J.-N .u.)' +. LUJA.+4 ..i OX( 00"-4ft I 1wu-~~- U- I-- f-4 11 C x I <4. Z. (D

'JE Lu I- PAJV +- +4> 4M1- 15 zs.-Z( -3czif z m0all >(D)C NO$ P*v- Coco "o-f f L 0 1-11 n+ 4ifu 11 - Or kZW(L I--U =~ II'JU4 It 0J aJJ 10 10 0 U)>K I c-- >On-.ox)l>-X)- LUW Z.-Zz F-40"SOv 0-0 a

a 0 0

220

UJIL-S

I- WWL

U.1 U.U.j

LL 0 WWCe__LU

cc VRA NZ -~ -f

IL 0z W. CL O&2U uJ IL d WW z

a U. VW am W 0 P4J z

*CL 0--f-00 '- * I -0 00W I--z -ZWft zc L c 4b 0. U~L W1* 06W - ZZ '.%UZ 0.01

I 22r 04m am Of. 04~J

Z " *V I C; vC. Wo-'.-0O *N 0. z Go0 u IJ1 -40

I )( I- 0 1 9, C,,0,..22 4.W

I30vv f- I- - 1Z Z < 4O~ 00 Mo LI ,W '. Z+* 4 WI--0.-.WooOW60i~IC "s U. 224 0o 2& I- dc W

oIt~ Nm. 0 0, Wn U.U 04114-"-.4 .4% 9 z aZ -JJ-- < . C.1- MU1 ~ 2LfOOw.W 0wow ~0U0O0.0 0 a ) I-OW 00 W~~ 0-_I-I W -- c

0=4_ Wt4 jIJZ)WWg. oWO

WLCI2 X 0 1-4 o WW14<U.IL%4NJZWvIN~ut"_ZO0. * a 00- oI-I-xiOIW1 049-

P4 4.O I- I- rLU-Z4C CC 9-0 ILq~j za 24 11 I- 0.4 1 2 -4W0 .J QQCAC, Dwx~

lin OZ -oxI -4 LU ZMi WO 0.OJ 44 ~CP4ow '. OX 0M - -t-Uj z- IL X

N I 0 2ww V42 W.J.-4 O.*C11.<W=zcn-~L LUP-: %0OL-0 (rp00U)2 orz - - M

11 OI4 0.+ X Z 0W I .I - .ZW210

[ I Z-40 *(w"4l- OIJ0Z ad-i 01 -- -a1nIW .)x N 1.- N

044NEZ xfv I '...J~fI LUO W..J~ U)CCC CNIC.-pw WOM C-af= 2LZ "CinZU 009 co

Uo"4'~w'9- *+2Z- w-. 0gMC * 2

* "44,(~"4- .- W'.~.".-WII 0221

UU0U f(

0000000000000000000000000b00

.j zCL N

Go cc Cin .Lux I ~

S. 0U cmI

x in * i

W 0 -A-* COC 4 VW

z 0 MO wo (3co Z ox 0. CLCa. Ow~. ca m in Q

*U 0. 00 P* I- U.4 0 C...jv u A c

I.L. .. w ld )- W~ Ncic0- CL 04- 04 at -

4O -C WinZ acl-06t n - A 4 0 (.af

LU z~ a.il 01- am zz OA n 11 *-o UJI00(fl ML 0 WI .4 0*

.W - 04IV MC c c 0I mZ cc I 0*cc *xza.,...zo. in z 1 u..* 0

0<1%4 X~ X UGNx 1

U. O j~ OZ* I- U.. * U W 4.+,*

I -Ic4vxj% Z s-J WN W zn

4 %j..j10- 0 64LOV4j 0 WC4%J~rL 0 4J "VOCL"P..4ZI)u0.40Oi 3CJ~c 04 O.*CO.~ : C

u.P~ccmw o..jWzzi + za. *LJ%.Z 0 0O. WW O0 S CLC LU-000 - . O oevqwjt~xj)4 N% O CC CO- - _a.j .- O

ozw4Z 1% -0inU 41ra 11 - 4t kMMQI1 1,- 3 *a.j 1Ox 4x 1 11 W- 0Z% z 0 114911 00-0 *

0 ~~- ZZWWO-O -. 0 o 1gto 4ci 11*0.~ If inwo- L (30C * d'- 0Z-i Wtf -ZO*. 0W WnO

0 0U Z ~.w.. w onwi~nun*w ~ 0umcZ c .-h%%0 to-U, <'P0 II I N UI I 3 I 4

od) WWWZZ0.14 'Xa.*.-i UQ XJ~)) aI M<0-in-J QIII -4 Z 0110.

S z J~.U00~.~"ii *w~~.io uO..JO - w3 014

LIN

222

UU

0000000000000000000000000000000000000~c

zwz

zz

W 04 0Uz 4xv-C

4 ot tLU z 0

z- 1.44c

)10 0 r.

I. U. ZW z CIi I.- -Ui

a 4 - Z2""* I-o a W w L 04-9 0

U) N. cc ccw )_Y WIU) 0 to- -4 W1

4. J- wx 0. .4% 3cNcI- o=II- mo 0. l - % wL j C

9- U) 0 o1- N W4% 0-4 NAX4) 40 I9-I- (z 404 "odM f- I I0-0 0 UC)0 O 0-

Lu X-0 4 _0.L tL ti- w I- . 1U~V~~. SU. 0 4 X3 CL*+ N* -1 9 z Y J *I*1ft 1 I 0 Z a. mo< *O -ot - / w r

QWO 0 leWtZJL.IUM WZ- Jj424 - N Z IJ N Z - 4 11_4

ww *Z 0013J QNW00 WG N Iflpv 01-A I- VW

U. 4%.U~-"m 0 i.J- .41 N .. WC 0 %W %I- C L=Z

0 ON ~NON- V)UC H~UN I- EflI-k

L) U

223

0000000000000020500000000000000000

U.W1

49 4.

e. ix

LUj WU

C.9. ON00 -j

us 0 LU1

)x N 491'-. 4I UL 0 ~J--Jo IU

*z a QOI O*Z-W4q 0~ z 0 L14Z

cc2 LLlir ccZ U.0- - 0 -.11 C # 0 .

cc -4 " x XJZ -.4 0 lILC I. tu 4-ow U.C9 0 P- I LU 4AAW C7 4 F-%1 0 ~ tAWu 4 0 4 1-ZLO LU M LU C.D z 0 N --% LU

49 r- 0 c 0"-) 41.3 Z 0 Ci I aCie qc 20) zo .J- - cgqc4 4 Z-. beI-I- * Ou. CL '4(.-ZO. I.- .j 0 OwL 0. 4c

in 0 4U 4 *-- Q:) 0 4 *cc z i-z QUVx X0 z 1--z QWjO 4 44q * - N MaI UJO qm. - 4 * 0% N

S Cf racZ as U) 1 .b- c 4 4 Z~oe I -u)) wo- *N x d S S- LUN x

<NJ 0 144J * Zr.IN* ~ 44N V) at 02 Nol & zI- I L I ly -A 0~ so-OpO"-. I-e I I u.' lw0 I c

N) 0"o 11-.I LU LLU "POCu~ U)We4 -f * U).- 11WU LU- 0 ZU) MO.- N~ *WWLL%)C)( I-M ZV al.) 0- Nd04 V)(7 44 LULU * . 6 go." 04cN V ) .4-4 WW .

r-i .JW WO r44 0 - C#-O"fU)LU) QC.JZ U- .JO acc N 0 -0.LUu. 0. 0 I- '. .4 "41 * '020. LUCLINJ "'00. I- -%a" eM %%NOl-C0- a: g~dOWZ-d4O0Z: 1'J4- - OCO4 cr d~cWz-4

WPdJ -0O 44'dWQZ die* * JJ.LQ. "0.- <<-'0 ~* 0 )l- Ju-me4'-wc a 041- lIZ QIJ -Z w)- wwqw

9-w * 4 s *)NdrRO*(a.j AxNdt Z*-ON 4- 0 0O4#.I30. woI cou -4 I-ZO100 Z2 0 'a J. VOS4N1Z' to-01-OC

C.Wa-'9 *In LUS(ON=443UUjwNu%-" 0..Wa-.Zkw 9P.4) WJP-Q1.4III 39w 1-Oc4%pSrt 0- * *LCO *.0* 0 n.5 LU I-at P4 x 0 Qcx. * 0 *.00

4c:)f0f"f- MO-CC c Fu Ifl-s-N If 4 0-4I #I l.-'O'l- M=-ma0, CF.JC%0'0 $u OClmuWLuWUN 0l~33--- 11 z JO---('-WWL COLUWLUWV Of f

LL-WOO.-. N )-wjp4-,.. ez 9- 0 0 "0 uLO N .-au-O a it )-PJI- OZ 9.- QNr-w -U If UW'-U. §.5- X)~ I-- -UNJ& - "N1oiX .W.itLUWo'&. f

c -Lu poqmZ w...-Pc ZC C -~-O %-w 00.a-w.-.. "08OtACLL- QCKWU.LL..JdjZX-LLL-t.LLLZ CZ 8.~ O-'OuCL~- 8 Idujt&.U. .. 14 Z

CL sW C Qw*IUa.-..a. ULUW Rl)-O.>-p4.Ji-

p0

Qu UO. u ('JJ UL) uu

224

UU

I-.

at U=1 % 0 0 %.

0n L4 f L 4

Ii 0 WU U

% I U.I, N .-t z 2*v C 4L .. _~ * * rI, L*

-bt 01Ns -U*A ** LU ru*

loI- O ILU 4 zU *w49 4 t

Cf e.-% INo *"Ct U4 NoafI W% 0* 0. N ~ _C N * 4

-b40 PP.4X 0 6% 0 U.IJJX U -"o j. G6L4%. U% U41 IL4I J 0 lvWI-8 .A qU*,% o at S ~ ftoJ *c 14" -4

.1*cvv NZ XIIIii CLU .. Z 4%b %bp - O LL I0 o~L U c o-a dULU W*LC -Q . U-LU0

fn *D 0i-I eu% *WL I-J.v YI-U - FWAZZ 09 0 4 N ~m 1 -4Z wN N I If --_L 3%iUJW dft _fflil-4c L *GU- ~ c ALU * M-4. * C u * ILUV

0 u [email protected] Lb-0 LW% I 0.I I. -nz jn - F4 If< .o.

I .0.-.w 0. 01-wm NO$Uj N it " U UN * 11 1 ONa".1614

11_ x I- -JX--XLUtINI- I' , NI. UroryjMU e-.UWfl"4U. NI ZO j %w*~~~~a -sQLwAOi CZ 0 o zz z C

4/)N *w oc c 0<.0Uv.

4 HZ tI 1-U Iu.~ ~ LLU*0.-. *c~ c~ ,ui) I .%0

aN*~ ~ N C c UOli ILw%

* rnW4II....W..IH4 .mN~ ugu225

0000000000000000000000~00000000OO O

LU U U

O U. L

o 4

U S

_j In LU

- LU

10- P4 5-

0 0 Z L

0 "V "N UZ0 cc -- ow- LU 4c

(M) N t. 10 U LU VILU CWJ-4 * r z 6 1 ) I I.-

40N* ** 0 LUJ lc 0'0.*CL C.* U NCY* 44 CL.-C. 4 WUaz *~ Y.Ag. **~ 3d4W I-- U .

Wac* 49.Jj -L O 0 4

Og*0o. c Us uU I l N N U UCL .%%ky NvIQ%N %'bNW .% N 0

ZZ-4%%. 4o ow LWf"%% %%M _J7fl_ ..J c-OLwD.- -wAL Wi Z 1-C.L-f . Cvwp .)4 L"

6 .0JM v4..a N wi-i" ou..J -.6..e L4 '.4.-gU)C.NC.4fl Z f.p4).oC.)ZWI.W-u 6- I* CL I

otI '. 4 M* I _jz.j I ZWU-- 011% z v):)CXU 04401A .0 WU * '.E4 SM)OU) *0 6.0*0 a6. 1" ZXv- a

Z -MN y 4 N a.-J-t 14-g 1 itLU. Zp-4 z CLX-0O _jLU,11*1- A%- CC ( Af*C.UACL*t%-vN ei * CL voW 0 :)1 Iz CL

LW...Z..JSAZ 0- 0NN~~ZIn*-)IW..J. a w X-SAZ8 O)0U) 00 Z N N 94410,1) 0 NfQ0-oI .0I-fl 4z

LU cy-u-mi "uU *.of *Z I .5- LL *1.ZWOWN N # 411 -t4COC0.. Of 0s 11 4I.gjnn-I 0 Ad .-. ONz UL

ozzIzzzo 0 9I-I-ZZZZZZ %wfwCLwrat C -4N4Z0cr00000z 41 OqcwWjOOCOOc UJ-U-O..JUOZ z _ -4 0

4-t 4 4_U U NNY N 41.) N Q

226

LU iu

IL LI

V) ULU

LU AtWL

LU

W 4A

z 0 ZI * 0 <

P" at 0- cc~

cc~ I- LU qc-jIL c 0 - 1.- LU1.1.1 0 y I-- -'2It V)W 4U of 1% 4 1--

W 0 1 01"- 40 x a at II4 zo he ~J.w. U)) ~4 49 za Z le

9- * OIL a. 4 X-Zo. - .1 0 OI. (Lo U) 0 -PA 4 * W0 U)nOA " (D "O) 4z O -Z LL .xu 3 z I- z

I 0 44 * - N2- loll W 0 4 49LU - c CI .4 ZJ-) W *O- at zi 0.q

N 0 0 r-4 g- Z PQ* 4b . N U) Or 0 N-4IfII z LU I ao j e0*.-'S-e II I LU ILL) I a

wU N U).- 99W LU 000.w... %A LU -f * U)O 11 LU1.- 0 ZU) Cli- N * uswJ%)(( I--i r4 "I Zd' 09 -44 o 44d LUU 0 P .- so - 0 4z - 0 <44 LUWJ.. J U)LU wo # 0~ 0-~ UU 9L-."wwJN I. U)0 z cc1%CL _j . 1.- - of *CP '41 OZO. LU G.Z -00.JZ I--I- CL.- ac WZ00 N I-N 0MC.4 c9Y

U-NWOC U) !kL4,J04 * @49-9- )- 4- ..a *a.JW )-U

I *. 4.., 0 -wz 4 -Z2 Z* 0N - 0,.-OV-w4 cc -20 * S 0Zt- -4-N -. 1 NOPJ4<.4Z- w + -

LU 1Ao *-I U~Jo"t14Z4MQWUN-.- +CZ 0. WN11Z- 1 111,4-) LuW(OOI "-)0ft acet . 40 Ouca0 0 n-) LU C7114 I-- cfp-4XJ) *%w Ct%% 0

m LU9f- =zt-eaUciz 1 of a-U .. 2w Zan 4 = gil 09Of- ==IP-mixU,000 O*W OLULUJ(JU 1 I(D~- Z N"-.N .. J 0s-4 WW-u QOLULUW

W.O40. 11 )UNI~-g.. OZ n 0 "%% If N 6 UL WLIP%. If ...- ' is )iLU..j-1-Of~y-wt w4) to WUI."L 0-151 *@(X I-- .- 4ey (J('J. - PN4%J.-. -4- 11 LU

c --A 00W-.1K o 20 .11 Z 0 cc -' 0F I OOLLI- OWWWU..J=-U-tLwU.U1.2 02 2WP- C 00w..t9 0W LU. LIL 00"NsW 0CNt-.-).-s.W Lw NLLZ 0 0.0.-.)O.W oC.N..-.-

227

CL

-z

0 4

UR -OZ

U . Lu 0

-) of

mu.~l 0, ax

0.JI6 jLU 4D)c

LID gg 2% L.-".

a ~ u.. 4L.J Luc;.

(3 tL LWU mC-

I OWZ-4900x-m o" UC @ U--NWuj--.9 Z X 0iV ZJV 0 c ac0 a+-0Q~tz 49t C16 C6Z **u a Oij.. 40... WO.O Y

LUn ... @a Ow 0d- 7 t W4j d _NJ *WUWN )(X -1 I-. *i 1-0 -Owc =I-U

P-L -X QC O-Z ftZO VZ ...J7 U)*xWgj 0w2-4OO04 4 -UC. xx z u1W-WM ZZU-WL0 o 0 wo%~t4 LL 4 J<=c of-- c 1z I

~~~~U 0 4--Uw'O 0 I 0I ..

0Q0O I ~ 0... -J -eI a* * *(10(U~ 0 ~~CZOO IZZ.. 6'*- 0 0 L 4.J .JZ-

4RUWWNNU Q- uII II L I-I0)0. U4.

0 0(. ~)( - CJ U)~)U%..4 ~228I

UL

*~~0 O0000 0O 0000)L000

>- a 0 c3---Us

o 0L " Iz lm

I.-0 LU 0 XICJ ~ )

00 Ir w oa L Iz so

044 xz 0Io"Ni

I z 0. wx$J go

00 I- I W~- 4cfo 0 oopp 4lZ - * u.L 2z px.X. 4.

ofI 0% MO )O-wwo qm. LcUi

0- U.. LU 0ZZ oI 20

-f 2 0 -149 C.4. m

IY C ( A % 4 -1 OwI= ++2 i

L)1% C 0 . 0 a. N11. @-IC-% 490

wo M X t( 0 - 1 *) ( I I 2)C

Q -r- 0 0 *- LUZ - -wwX IIto

0.- Z*o.Z40. U 4cW 00 %W10me -4d dw

us.%S6 UUr.w L ZZ.2X-) ZL

I- ~ I--~ I. 0 01 .. 4Lw .I (40.)-

I 'LUC IA 0. N uJ -i Uo1u 00 Z4.UIL.L -is 10 2P-o LU z W- a ~ 0 ..d 2C2 O vdft - *.++o-

I L . 11 0. n t m- LU =. LAJ 0.. r'.JN. .4% Jl111 f4

ov* VI-t-4 c 04-1 2IL 0 tn 4t4 ZON ) fi) m t

I ~ ~ 0 coU( 0 0% 00%*-svJtII~ U

Q (Md N'Pd U w Q u. NZ u wZNO2Q

229

4% 44

000000000000"0 okQk0004 ko000000000000000

uj

(9

M,

u-

-A.0

409U-Z

0 00..

U-. -0 00wC OW 0~ 0 f *k

0 00 4 * L"uj 6I .40 * 1. w

"Z *.t -10 0

LO ILQ% LUJOf 0 fL0Nz Ui i O j' CO 04 4OCUA 0e

m 4Q04 -< -1 011 -u-0 c

0~~~~~ tu zotN8c0u L 0 0. 0 .XUZoL 0O~U' 01' .1

- ~.W~IA 0 OIA 0 0* nCE~~~~ ~u'-u' " ..- 4 l0

0 ''L .-. t - . ,.~1 ~230U

00090000000000000000000000co000000000000000000000

(OQOOOOYCOO OO00000000CY(37CICO 000000000(COCI 00000Y(FC

I-

I. LUI--*

LI. W)

~0 u

uLU U

to M 0

49 ) wUIx )- U

0u <)

CL 0 O0.1 U tz 40 z .0"i

Il . *O 1 -f

0. <~ @LZ .JO LU LU0 U

Z4Zoa .4 Nt (AUX I-.1 >

ac Ox- GCO 4CP" o-LUW C)qfr- U)L I 0"r410041- ZUJ4l P-Q

X4 1* 0 1- ZZ 4 NO 0. ) L~jU L 1- (30-.IU e- 4U 4 mU).. o "uxl--- Xg .. " UII41

I- U) u 0 4 * * oW 10-.Je 11 LU

LUju 191 OW U)UJ)sO-OLX o.X -A j

IX" Z1 #1 to1 0 .I0 11 11-~- ZMC , a o- c 41 i--jw -N z O zu0 U-..'e 0 0co~l a

11 M-X LL 0.0.- P- WII.4 -Z-.ZIItnU) A UJmww< N"O7* co--4N ) WO W4 ('

cc =U~ zoo'-- Z0-swL9w *CU~sW W~.

0 j O0. -fI-v-M0.OPZC WOO U. c

* 231

G 4

000000000o000o00000000000a009- uj -j

lo 4 LL-

04 LU. 49

*~ UJ nX .%dzo .Z - In

"U * 'LULU 0a-w oc- 0 0 z..W N

I - I- zWL-o C3 0

LU UAJU. 4 z-.

z I-L 0 W* O.. a a w.

0 -A V)~ 0.04WL -1- 0x %t -&OIL0 Zi 0

U4 Z. O(0 .-.. -

CL. o P. in 'S of-0-r I-- - I-- %vM .i - x %w-4,jo-w 6gJj LU .4x0 CL I- 4Z04W& )l-6. om . 0 I-oz44F- 0ow >- Lu

760 Zoo0a 0 WUZWULLWW - s- V) >.70 at us-c~a -t XW..(J:O-Z)-

0 "o-t. ca- 0 .WvPJ. .. L zX -J.JOZ :) "VVZ n 1-- 4

OF0-*0.- xv14 .. JLU - e. W I-0VX 14W'-"0 w0-ft.0&140 -X( )- LU4

az W- Z.40.OZZ44.4 41414 * x

be... 491- -4 ...aJ,.Jw o-= OP4 CC XNI-- 4 * Z LU

L-C - 1 * )(ZNef 4oZl -N Z 44 -) 1- N .fN ,U.( .044Q) -O)UNI-g-. w* 14-L e-> X N% 4a.*tco .* -14 .e'.JO .Q~ -00LU0 zcjl.0- 0 - 0 m40 0-400- .- Q00 -s .- %0 . j0* L 0 cm

CL 0ZL0 "- 0-w * .- 00L .0W0-N9 0Z9 0* m~a-% "oCZOt o~4b~O X'4. .L(N) -44 LUf-

* ~00 .Z044.-4141.JA. UJ o*. %.%.1 0"4 %'Z 01L%'.O ~ e~ z~. u4. 4.4 cr 0 a

.. %.W0-ZOOmLUO- ft*-w~Luzocn4.j14*0 XNO0)%** 0 0 cc

LUCtnZoiZz a. q.Z~Lwr- 1 4-0061-- 0 Q

M.M0- %14.ZDUu O-%£M.%. If otn=Z % >.c~ .4o 4414u.)%.CO If .1.- a M ILU0.wZZ~f~--L4LUK.4- "QJ-W OX 4 if if 11 0 0 0

Vjo ftJ0 ZOoozuJuujwjUUj -jiN~j ZZ N g-J-iww o LIJ Z~ 1CI11 l'- Uj

0Z~J.i) ZZU.Z000 LU00.1-o-M~ 0 0.

232

U. cr

U.

L W

f. IL

v4z

ZP4LUOIA 0 W

0 wo 0 l0 '4809 If V

Ic cc +V.z c CD3 z O

z - "W 10 0

I -W 0 _ 1~p

%ICCOG in - mw -W R-a4 OX O-l - OU 0 P4foa eIIz II

*1 Lu O'wZ-i 0) 0L4 0 g-

I. Z ~ z GoZ 31 ca~ x cc .0

15fm -.-. ZI -x Vm- 4. -0 UN.-. 0 0 - no0

ftI 0t I-0-.W4N+.11+ - . xfNf - .J I x -Y 00I 4 4 0 x 44. F01+Qm o40 -4kA 4 4 00%'--1 .4X-3xQ -0- 0'4A Wj 0-Q w4 .2 U0 r- W.WW WU*0b I.~ Z O .0 %0,0

oi 0 *ICNZJ.IO'C)( I r)in~oaw - Om-.- of it ~w.4~s I~ r4AOOU - - w -OI-j w

I ~ ~ X -.4I-IZO.ic = 144* 1".003.O- 4. Ipc 1-4X0.0oat OLLJ 4wow~~s*-Iw.c www'~Z 0 i e OC.

U- U. &'~t3Ein.,3CO 10 inOZ~r ( in~4C

-t -tO 0 C4 MtN N N C4N N N- N N)L)U Q- QQL)

233

UL

LL

00LUU

* 0

zz- 8-

LU 0M

LUL

U. -.4

(D l'-

CL LU I

ol 0- - 0

1 4 - t

Z. 0..j -_"X I's- LOW

CL OV. LU 0 -Ul% r <LU 0 CL 1-- 0-U -

L *0 Y Y. I- i LUZ 4 C.I 00

0* - 1 0. 0l% =-mn Ml I

if 0 0 44 011UV t 1C ~A1 0-N--4 04-- 0 0. if U.1. U)-m m -Z w >

0 ""=w in LUQ=t 0 +- 0 -0~ w - -, C OZ O--8- O 8t- -- C O so-- Z r-J "V *.ul 0

MOW ~ ~ ~ ~ L P-CLrv 4WLI- 110 0 0 100 8ZI. )WJ- U.U)4f U)U) - - '-4 0% Z ..aI 0 -" L

08- ~ ~ ~ ~ ~ ~ 0 W48 .~L ~ Z X JZX .4f~LIN0- li I0 - Z JD Z'

LU S U * ~ ~ I U N.u4.-u-Q N N0 0(N 0

.8-- 8-- *0'w ~ Zoww8- ~ -(() 234U (

a Ut

0 0 000 00 0 00 0 0 0 0 0 0 0 0 0 0 00 0 0 0ou~

IL Is'w -O-C40W>

* +- =-)-Ip Sfu

0N 00l. a+ -w 44 f

I *W 0 t-z wp

a- ac- waC C 04 -Mr W4

CL * X *. t- 0IO X1M 0. CCCY X nc0Q 0-UZ jl NO W do V NO(1

ff a ftw 0K N4 -4J WWI 04.- Z 4 049--

PI ~w-C. 0.-iiaul +.~ -W ftZ0 o N W = N9oiqI 0 0.04~h-fti 11 01 -4N OLu N LuI M0.- 11 Ntn " 1-0 11O0PJ U *zr"") xx (4 U -0-U-

-zq - LJ 14-01- MINN IL CLu.-KI

1-4 Z ow 0 W U.U.

No u N a O- -

235

V 000000000000000000000000

~ O4.OxNNNN NNN NNNN NNN NNN NNNN NNN NNNN NNN NNN

000000000000 O0 0 0 0 0 00 0 0 0 00 0 0fl4fifUxW U)))4))~jEl~fU U)U Lf 1 (

x ~ O

100w .

-00 caC0 Nzz LU 0

-. 0" U N

In OLU -U I-o- 0. P.u

z 4 O 9_*Oo"0 0 I- 1U ".1

Z w~CZL )I I,_ l ui L * a: go Xx>-z z -f-100 0z 00

ou 0 " " xgww _zz woe.62z

z v*ww- 4vo-fQ. Z4 -j o.ZWW 0 -C OLU4W0 us w"o . o . , z fZ -JU

0 z1- _ Z%-OJL -LULUO a Zj *.0 -. LU (16OLUL ~ I - 0L at '-ew .

0 C 04()1 9.W-IflXCCOC 0 N- Od.- 0 40a 10 ' rco L-.Xm lo -0000 00 * L 4:9000

"oJ 0 o."0 " w 4~A~z "n - * I "o .o"O LU L%wou

ILU .ft 6 ()- o *-mz z -I--C 0414> Z Q.0o0 ac CP44AL (kXwLdU LU 0 *i -d, a- JZ0

0- 0 8<7 s-e. b I4 .Lz(= ;C .Qal .. o ep..ix- 000444 o Iw _L 0-0 it LUco I-- i. O s-P

0 Z V W -4tp .Jw WWf-tw -gXIO -ON)( 0nwJ-- 110 c- 6

c a-i 0 (w" C.WC OWLO..'- If UL 1 01_LLLLU..ULAz a -- '0wl i0 meZ9 >pl~ox-Z-4~4z NsXx~ -oacsqo~v 0 0 -'

*~~~ ~ "410 - ~

s.C%%JL) .~ULUU) 236 Z

000000040agR0000000500000000 0.90001000000:0000000000Oc Cwp

~0

4 St

'I..

Lu

0 Nj L

Z1 0 C

0 0

0 n dO -a a 4

)w X . 0

N CL C 0 L 04U 0

-% 0i - W)z

C411C InC-Jn 0 0 LI0 WA O#OW .I -ft 4CL 0 0

n. LC4 In X.4. Z49 q a U. 0ALO 1-3a 0- 0N1- N o.ZOj.- = *- l.o 0

z I.- ~ n ft& 64 0" v4 LZf j#

IA xn 49 V)f .(V) OfOj no zI.- 0"Q fC .~ In'CnA O.f -. LU O. In-b -

0LU~t 49 4-4 OC Q.. wwO1-34N0 1 49-1.- 40-41- -Aw (( 1 VII- 0

NqI4l-0L F,..W.W. NZW qO. 4AU LL M OW 39 cc 1

:N4w)w)l WX'W) OWNC o wC mc L dwUJ 00015 g-V~ ZrJ In z - z 1-9 0.

Wu-. -39Iw44 )(InI 03 6. 6. 9 ODox 0 Z U&-11~ ~ ~ (X w~c -.. 21V m xm- 1 Z-- 0 ).Wu

.1 444.4. 4.49L -4A X(IA tn 4" 1.4 0 X~? LU

el P-U~41 WIc-W I-W- PCd0. ~.0 P" 03 - 4 1-- N O WIn V

IPN>- -*I0))IJ (r 0' *4 ael U. >.. NZ U.S cK -WW- ZZ v s.w0%XU..-U. OL.LLU 1-01*- M1- - CC 0 .- Wt "- 0 000 0.JONLO 04flw.In- Ofts.4fl I-IQ. VW~ In I-- Wp- 1- U ef400 6-

Ii 0. go -00 -0-0~ OwU.. --4. o -~it- v4 to of -ttC1m10.0404m<4<w&0. &-X<( 1- 4 Wutn0 *e 0 4

q000 NO1IZ- CC 1 NC It CC ofg I I ZIONO- X( UL "P" WW4 "w4.4.

S110 IoN IIUJ OwI4lO 4I') @1140114114 ItOtJ1 1doi 4i zQ-x NP--oo1-

IN m N N

N N OdN uu (i u t N u

237

Ux

x I.

V) *WWU

CI * I I

40 11 - Izzono z *ZLLIL

0 z0 WDI--J xzw U.1 .- 0w. 0

04 .. 04f0) N I..ceZ m..*Jfo..J,...3 0

0"4 0 -4.-0000 0PP.jo 0 * vtfv~m wwO-~ of 1 0

19 o XX)Z z * "I-c 0

LU IPU S-.w'4 am .G. "M-'. WN6 "li~

z .w- 0U.1-O Z4<0"-z P"4U 4w 4)~W~ * .1 *o-wv )0 02 1-4 .1 *OOW -L wWK)(. 0P"Wat"" JIcI- w .Zaxx(l- m1

I-0-J X(W 9LC(DWWU z - ...a I I I.a-4 0f 0 Q0 7 Zewwmc4a 0 N" 0 00wne UC 000400 W-0CC-0- 1 000 * Z24WJ o" * NN w) oo..a..jW W U) ZZZ 2 wwLIP-I--VU) 61.1. Wic aww-ft vq-4a..-..- II - ~z4WWj 0 *b OWS-._JV)LWWU ZOb -4s 000 II eZZOOCO >-." WOW .. o.4 wwc-Jvm-fj P N .. 400c OW-.JI) 4 * -f I %w GOO" U. WU If II)

04-.1-4 ..j -4N If -t4 -- w 0 1 WWWv 0 *a * OZ-% 0 M'o.o NWZU.4<U. I W . *.6 f (-.ZZZZ ZOZ do'.JI(>_ + *woact Ou * 0 C r.*- W UN~~h(.4.-AU *w . wj ow a..L * X)- *Z I_ '0M o N 0 ON -9 Q.o-.Jm(.dOOO- o s- <L4W0..wOO o S o%0'-.CIO no, a X m00oc.- PZ44wwf1-fl" ,-.. LJW 11 to to CNOCO 11 -t 4

*W-AXO440 Ow* a 44..4 No " wx o *ZZ XU. if it N o*A-'0Lo4.a<J1ll- I->--4.I00 ->X 11 gI-POOOOC)x-0 Wc%JNl'-09j-0. C~S(O 0444") v WWZ XWI~w )-wXv-.N Vn. II_ 10 C~ WLW71A.4c a0-COU.U.O0QLL00LU.Z IfLL 11 0f--LU..U.. LLWWWC.JJOZ 000>-

v40 -4

238

NO 000000000000000000000000000CM000%000000% q000000000

z0

UJO

Q -00zL

2C 0 r

a- WOO + CL -W c

.1-4 > - '0w 0 -A0.Lu 44Lu W) " 0of 0 A0 "b O

>- S.-l 4om IA L L U. -. 11X U)1 U) - - *.0 00

V) 0 'O C =Z 0 .C7 9Z 0-fIf- I- I F -4 ..J We o.-. I

4 %. Op: U)W U.. zoo I-..J

qcI 14 1-- 444 40 X.j ) 0.-% " -uI -Lu I.- Lu 1-4-- U. L -AnUc N j 0 .Jwl

.4)1-U >- LwW ww * W 0 0 Lu MOV4 ONLuIf a)( >- )1- )-1 0.31-1-C )(O% ZO)U. 1- 't )WO c~f0 0

'1 '0 X. xx>)0N0yQI*c ~+ I - b-O .

0.NV)-wo Nm )-44 V)QcrAL00OOQ 4J14 00.(%.IC 0" N)'(g-1I- 0O0*M~ w g 1 0 c.4

1 - -J ofh.. 01 JWUJU cc Of- I Zwlsz WWL ~-4Q CK4NywILu P'- U)V- .0. I-e a 0 d,Q W0 N0 0 rI.D us QLuo"-4SD 04 ~,Z.400 -1Z~I-~(DL LLW/ I.- X -x U.VUW 0-

I~~~ ).Q Go WI.)l.U No" U'IIJUUILI-* LL1-- 0U'0 U)em .uJ 0 vwf-. ).. jQ II Q LU W - f4'0.W Z I4- 0-M u 0' SC W

I NZ0.w)U-0"iLL- U. <M 1-c -N~~WNYXZ-XfU'%to44ZXU)U)W.P0U).Ju I IIWO 0+0 loOZ 110 W00I%-42

*l OZW0 "44.-41-lp-L 2T44t Ogw 1-Lu if I/w X ZZZ -CO-MX0C V)WZ,-W.-.

~.w I Aw w > 4>-- ).0-z-.JJ 04uhO~ 11 O 11 It 11 11 11 -ZU.. 11 U.XML

I -t 0D co I- (M-,U% U% "n N 0 Q %a

I - 4 d 04 -q -4 P4 .A -91CUu N NU) N Ni. N U O N N UL UUI N

239

UL

N 0 -

o 0 UC; I- LUS

7- ; 0 mu

Ma LUeL

O- Vu I- I-J4C z 0.-4 Z

nn UJ<-1 0-ai

*UL 0* - LG(ao z N- z I wL

C14 t )I> 10 j -40 O 'tO*m O3. W O .U --

-- 0 cel- -4 "Ax W

0 ~ ~ ~ ~ ~ ~ ~ fU 04-11 WUJ 0.z0 - Za0 a

l' -9 1c a. CLs-. 4Z~ ze 4 -0LU I W40m- .4.-rl cqx - l-J .J .mU .f

"4 N-93.u 0 un0 -'-494 -- 4 oft--J If4A D onunc I- f - X00' 0L- ZLCC -WLU

UJ *-> .00 -- a 0 0 - -- 4uo "V

P~ pxI>> l-V-t ZZ 0- Col. ZUR Xp-0sL-FA > 0-

N4 L-s).).- LUU -J- p 0. Nxcc -40L) O-Zac to %0 Lf 0-). (% O=L.LU N1O %%f -J b-JLUWO ~ L

N I->. If~w 0 Z - 000r'-O- Nt.O. 0 ILU '-.JJ - Mft"w)-oC *J LJ ' me(D 1J- - 9Z01 % .4fl I-U...J )( 1-0.4I

LUI-XCo *1 0-~. eb-c 0.4"4 04X * ) ..J1-LU *.4v* ,us- )no-0r -4 N41cy" w- z Z w e toqI Coq LD if( 1 41 0 CL *xi-.1 > I10LU N4)..U 0j w7*-4~z ...iI--a 49 4a .-.-. 0 - I M a <<W

In in 0 0%I . 'On'W- &~ -. ~

-4 0.*WO. '(e".O d 4W -..M Nei Nw w NNW NO N*( N( NUN- m10 ~

*"4- ~(W O .. * N*W lC, %0- ..JUCLUs240 L

ULL

00000000o00000000000000000000000

z

U

z Odu

I- on

I~CA WLwn~

z ~WIZ -Z - ~ 'Uz NZU U.0 ,"0 U.1-~ IIU 1.--.~. 'I- cc .00 U W W I Uii ww zw w

00I. Cu..0U. OCfOG. (D cmnC)-~

l'I ZCU OC4C #A CY z N>dC 0

1- 04 u UW - 00 0 -W - >aNmcLAJ~~~ ~ ~ ~ ~ NX NJI N0( . v* P q LU

0 (Lo =W AULJ ~ wrNO N.LJ 0".60% N -0 N4 41" NN 0W .II - N.-P~vz Uw U %- 1m1 bo44I - 10010 IL N"j-C%'v4n"-(L+ I-f t- f1 t

0 LU CC -- O->Uj 141 C 16t V

1 U'0*CUQCULUa tc t LUCCZ ZU WJ 4 W w +trp*V

UL

z

0

1--#

00-=

=w -"zw0WCLJ"Vwj *XL* X-I

I~ UJ LUI1- LLU %4'-jqr kt qp0 f

U) ..J..J LU .6J UJa.-IL- LP . -0

t-o* x uo -4 N §.-*x- 4.z a N WDOX )I- + C%4 UJX 04, A QM

0 *rft UU --- 1uj- O3x )N

49N #-w~' - e -49 w 0 N A.c

0 0U LU am 9 ot -. W ZU O- *fOJJU9%".UU

0) 6-W N OO -0) 0I- 4-% I-O*O( ZZ .~wx-x us Nlu UO0ZU OW4 N iuOO)(~fQV VI U) ON

P" O 4 0 a 1 ._W W.i 0. 0 *O*UL o--119=~- ff > I-yo I-I. WU-. 4t t*;I **,00

.0 ZI'.JN LUlI -- LUO 0-

)I- *-- NII- 0 M * Urn-I-I-U ww S N U -- p44U. I00@ *..JD* ()C U. **.JW= wwwl* )(ON - )- ca

-~~~~~~~~~c 0 U J **C--W Z q ~.J*~~~N Mt (In ~m.0 GO S N ~ .. S Oe .-

o y CY- NN N(.-.Z O K- ~ IO ZZN NN LU N)f WZ UCl ) WZ *JU JQ LUU

- N ~ "~ee UW eONN.-.242 iLW.6 '- .a~l-

oUo

- ~CL

40

4P

z U)

Z 0Z0

LZUxC

N U.z 1 -

M5 000 4cU) W '4

114.C 4t Nfto

P-4 I- L I- - j j

LUIC U. *.o~ CL @-ManCLa 9

IN U. "" n t - )JQAj CI-.Z * 04 0t o-A - .V OL

zI < _j 00e 0N I cc LU4 ow oZs-o %

LU U . W9- f-v J .NI -- O

W- LU ->. I- CC4A NU I to - O L

... Nocu, a t P-1 '.4 "W4u 4 o4 =J. -0 - J -WV)- Z-M- U. C5-..J cc --

z <X 0.~w Wm.w 0 U00J NJ..v4 N 0-U)1,4= Z -- 0'- 4 N)- 4X~m

I W P -i JI--= l'L. 0. ML eIfl. mw .aL0 . amIL

VI o s LU6% owu m. IP .4.i ec.0..~wnc -40..t eat

Ij ~ 5-e ...i m ..J f-NW- - -- N-0...J-.1 Qt 6449 *a"w 4 -W ateU e(DM (DO c0-4NC LL. N if 2c W-0 LUL zw N. WJJ z.W Wmc~- W ~ go"/i r 12 if U-C . D 0 itP I-o a1 -o<0I - ... .'.. -

J 4 UWN1 -w r Z ZU0X *r LL 0NC W CD0 WUa.WC aW5 XK LL' 4 - v-W L MI 4c) 05- U)LU=s J L UOcm .WL= fOIL)'

I~~~~~~~ C4 MIN '.4( Z CD 0 14J WU) K 4 Z U esU) 0 -IU)5-U .. JU)Z.1U NN

- -. 0 0Ww OL ~(D-CD..~-.C243ON

Ux

0

x "A-

.N 0 .OZM_j zotf t b - -

4 zUJL -6 -- C -o4UU U. . 4 - ' wW

cui1D V) 0.e- a n >..4P4"4.2 %.. .JC )4aL *U o 0

.40-V04A O ( 0-0o 0~-7

- OO- o""00 Z. - 0 Z -Z - <-4U-_~j -wvoLDL *LI- l'- 0"0. L1U . -Lu 2N IfIwmw.t X dLALU&ULU UJlrI-uJdZ 1 1-0M. f . N 4 s LL I-. ox s v .> . I .

4Aa oz "- 0- 00-- 0.- InZn.I-- 4c oc WI.- uJ.-0 .0I- ~W z

OUJC -n ***ac U.11- >.4A _ a.-o44 X DJ ZO ULL 44wmw C a 41C xn o4- 44- -XLU

V)~~~ ~ ~ ~ r-4. .A LUN 4 J-JJU U A c z UJUJ- * X- pto 1 -4* L t4Z LL~-- aw4.CIa-XI- 0. X* 0U Z i% LXOU). 0 1..0L MC )xzDO 1 * -o.-zo0oo Z4 = LU a- z *Z 4-

0- I- 10- f1 - -44j-J 01 *1 ww WQZ 0. . <1 41 4444 IP1 O.P I,-- I LU % 0 * X ).ZZ M- > LU I no-1-I- -ow -

rlU -W N ))L~U-1< 4x 0 Z% if U U -. I-Z_J41%_ ' CZ -0- 0 v-%~ 10 1-4U .(%J'3 eN o.)("- IL- U-.U

In -4 .0 -Wo-W If N11 ~ a1 0 U LU 1 41,11000 WZ X,~owo* K1n If0 uv-4z In if"WO too-~ LU 0.0.- IItoNr _ X *1- tw t- W- J1-1-%m- (1CX< LUor ~ ) O

NJc eN C(w... 0 )LU CDULU .0W 4- .- - X1

LA. ~ ) . w ~ ~ 4n 1 '.0 0V.4% ) -0 N ~ )* ) *.OO 4l -s(~I1 - -w I 4 - 4-L (.In (1In N4f u- CMJ In u'.J.U LUu P%-4ZC. ~

,Iw~e-ww-..400..-( ~LU1-W' (244 ~1

at UJ

OO o000000000000000000000000000

~LU v)

x. LU 0.

QLU (O

LU U.LU 0 N-i

LU4 x

Z I.& I..U.dr 0 o -

U.I U. I-$-$) LU

40 O)OX

0 r.cl UcU.4 (A V O0.a

Q 49 0 a O z fl0Ij U.1 U..- - 49 400

IL - OlLUf- U -

00 X0Z0Zc%% 0 -

49) ,-. r 1 x0 ca * Od 0n 40 ZZN w 0<r*a N4

Ii 0t %.j -4 a I-, . CI1 LU= zZ 0-pog*Z4-z* ~

.4f.o 0 0 I... PI JLiWl.Ur%~oy3w0 0)~v v" LU 4 LjOCUCU *N bI4

I xx I. .OLO u tx *- .0 0 'v t 1 I-4 ,4"iIj I-NI (X 0LVZCZU 110 LU -AU. 4 'I *CD

6- NP V-4 = Z-> 04 .. JLS -.

I-Jx- U)ZL LU >0% 49 00 -QW< ZX X~I **..J Z0(D."' - ..v4

-~ ~ ~ ~ U Q UO01. -4L~S 4

I 4U.~.4 K00245

000000000o0000000000000000000000000000000000000

000000~~~ 00 00 00 00 00 0 0 00 000 00c

I- c Qz _jc 4n

0j 0 X *0t

44 V)00.0P

4j -4 X" N .4x ~ 0Z *. 0 a0 t%

x wj z . ft 0CL x Z c n w -0x x( 0 xN 0 0.

ON s" U.S V.J UJ aco 0 - SO

1 +Z.3 -14 49 .8c . a. O) a-0 w-._blO_ " of.- ow (3 (m .0 0

3~~ -1 U nKU%% * 4 U- L N 0 Mt* *u NO OZO wOts- X 0-tP. i - j tn L "L

-Xj I-O0ftc u 044 C Nz N-- b ~ ~ acl 1 00 ~ 0* + ccc4)cc q

W IU. 04-N w4Z4 A c.4U I D.

0 1 0-0 0 *0z 0 4 0 M LAe ft OIA0

1. *4 0e" t a~ a Aa .

~ 14 a 3- P I-W W* 04%. 0 uj 'i i ".?.J w - * 0OU)W OZO 2Z 4. -aOme

+~ ON -- 4 UtnU 4 04u ut44ce " I-' 4. W% .@W%

b~~C w3eOC 4c M.%ftNU)J 4 4- U) *) v4 On7atdX L -%ow* a I + Uo.J*J M. w U. w. - UC c-%. -

W)( r'1 OMW 0W, aC W U ~ i >J 0. W O M~ 0. 0 %.-xw~ OwOAO.4 i =-3 4 L 0 - 4 N WW.o m

'49 UJI W..IN 0+ )...U)- 4 w 4 Q Z( .t ** O%0AJ%.<0 *(AMOI. 0 0 LLO4ZZ i/S Z~ x 0c Z U 'O-W. *Z "-Q'.- 0 -d 0Uzj. 40 c z- .3 00 4" *n4Aq

a. .o.It.. <.3 ... J .~w n Co. 6 V) _* x . 00-4wI0* N 4 Nc 0u 11 a " mcco LU 4 U) - o z .. eN'

4 0.Z O * oxQcSem.-Ow- 0 x. < U- 0091 F* ,X LON j1LJ3U d W Wwr.J4 UO OWZ MJ M- CA in -An 0nwOi

4u C.L) *.3. QUO u Z uu)~

~ * ww * I4' -- *)( ~ UJ 0 ~ - U 246..

wo o oo(%

"o 0- -

.6w fto 4

V-

C4 . U.1

IQ 0u I I I-

NO

d* + 04

1 (1-ca 0 0

.-- S PM - 1 w

wl'7'.'*40 -- *O

WWZnL400" 9 " d

In CC0* -o 0 In('U Z Z

coON -o W co 0--o I w Z *cc 41 4 "4I.4 1, LU U*

0 * L AL -n # *zmnzNI --%- 0 iM'94O 11 Q1v = N(a L 04-4~ 00 (a"* IiO Z V)U IQv

I.+ 0 :(a eI'4(Dz aft o 0~ %.) s-Z+

c . 0)4 .44 4 n4v I"0~~ V~.JI- U0M.W*I~U ~l I- ot If X~4I* It A% '

4 0 cc) Z~ "41 nE*-(' I11 LUW Z -aL0Z*I ~0 49fw It 4a if 'I -) >Z flw w = 0% "J)

I-m CC4 -41' 0 "4 00W M Nw 11oW"I-4 + 0if t 0 co0 0

Cc I w Z-') I90LLC If c 9In-C.W: 1 OIACM-.4U 1 WI-JLZ 0 00<4 ofWI *4 * w0 I 4 19 > Z'eW-f4~~>4 ' rZZ9

ii I- n I-mu ~0'II10'.*I..n-e4-4N 5(ac 0

I ~ ~ Z 44* ONU)I- ~~~47 I~I~--4 lz.s

LL. 00 a

2U 4

U) 0

Z -

2; 0 zL

* u~z*o U. I

S. x X -0 P" IwU z I-)@-I- _

x * 2 .- 1 0 N

a Z4 * -Lu XV

z ~g 0 _j z -f Q.VU z~- 0. J w--

LU @- 0 4 w =0. IW

z 4 Q " 00 z 0 -v~v-d 2l V) o- uo U< ) fl

-40) Q V U. co V *e.,M < 42 1* Z ) j iZ 11s-ft4 0VZ 0 014 *0.I *1

1- 34A V Q < V) u4 k-- - z xat 0LU Z 4*4 cu Zin *LI 0 . IzU 44A z Cx LL Z0.4i Z. Na L f wV

0 o. * -* 0 - 1.1 1.- -. 1

11U Z U) M- W 1 0WOZ M z z m g c'.Zat I. U Z m 0 041W UWIG. Z )x LU i-0*ag

0 --c 4 X-% Ul-O - X* o C Wm "Z X-11.-44 1 11111-MUZ IQ UwIZ w U O<Z U.- U) 4 A -Z [IL itItUILLCUL Uo WOM L QU *- A-4 N

U) 2 U)* U Z U)+ U. ~ U)- w %~~fl~4 ~ %2 .J 0 2 I *4

3U.~~~u uu U)% a. ql W W X )

- C 0)Zw 00* - 248

0

z 00

CL

0 U0 l

le 0

cc0 0

Ig U.1 U

O ob LIZ~* I ftI-- tz V

I4CC "0.+* *Q ZN

249.

O00000000000000000000000000000000000000000000000

zt0 0 0 0 0 N NN N N N ) f 0

~Z

0N

2x

IX c . W 0

W4 cc CL 0 Ln c -) N Z )- at

Z I- <00i A %I- N~

0 - f- )( >(g-N~ 00C ( .C

(3CLO~~~ K. 0 L3 m MZ4Z0L,; 0 0 0 U) - Oi

0 cu i U. -. -.1 0--NZ0.0 - 6 ) 0 0 w IIw

WU) )0 1-U. ) LL LL ~ LL 3 .0 4-

ZW .0C 0 .- @ U) LU U)U - I -NZ <-1wOOz C03N = 0 4 W 00 -0%.U)W L X OCV" sf 0 .3-4~4 ou .J

N0.. -jj- X2- 2.W Z v4 -4 N '0 L~4 v-C- XU)Uoio * 0W dN 4 W 001 .1 U ns M-aM- Of 3 31 * . ZZ

4a '4 ZK)Z 490 0 If~ -1 440 0 gLV

OXXXI v- of 4xS0zw p84 mJ 11 N,,j & U)"seOCO-604 Z47'AWIxwU 11LL U.w U..ww w cw c L 3> -4N *U UiLL

U >naI %t ItO Zn LN a

250UJ L - ~J 4

oA 0

#. W

*IC I---CN z 0 .

LU .4 C

* U.. En

Zv) o Zidt4 0 0.U . cn 4 Li, *-N W co z a -"a C

V) WZu -A q 4U En - Oa -

I N* 0 9 Z Z V) a- U. s0. o" ft -oKCL 0. Em -w

le#* OW CDn OW EA- n 0-) U. 0x I zz 0 LI -mZ-F 0.- OZ LU 0 - cc (3c "oa

o En EnJ 1-I Z&AAOWN Oz 4X W 0. 0 <I. x Ow

4Z9 . 0 v)PO a4 r UOU tIJI Vnl MLN . .

Ni 20- l- 0.v'J#Z% J -f *ZU -- j-- u z I 0 "OV 0.

W o 0( L CPnU. 11 w( LL P-n~l~ 11 O~li9Z EnI- N CL 0I'.'O l--. En

I ~ ~ ~ ( -4 0. =OwlE.." -i4 4 4M of- Za4.Za Z.0- ..0OE0mI

* ~ ~ ~ C gUL 0% W'4--C".U9En F'-64- P- U.O.eI NtUI +n- .1f4

* 2 I- ~ 40..~4~WN~ ..251 ~

VI Z - -. e.I -m -OZ D- - w WZ E -Od ..-

LUC

000000000000000000O00000000

I. L

U..U. Ll49 zjC Cx0o .0z *UOnf

V- 0)(40cl U.1 LU CA CD

4 L0 n- 0 0 CL

z ~ J CZUZ- Qq I-C at z, Uus ~ ~~ Z)U 04Qx-Mm L. LU

-X-- L> U X= 0 cW01 cc NA40.0~ ccJ cc. of 0. .zt P).j X 0.J U. LL .

;Ou Zo u 0

j .4>- 0 0 OO((D Ind - 1.U~ 49- Q 000 0

ZW14 - -1-$ 0. U..ft Z. 4 I

0 z ~ CL X)(ZZ O O1- W... X0 I.Inf j _j j* &U.JLZ~l a* ftim.- mn Qn .In$- Z i i _

M 4-w< U OWZZ 0144Q - 0 0-I- zd UJo-. O W'C _j In In Inc . ki L

P2 InOlD .Jn~ o--.JU Q Z 0 In-%-%J Z .g oe wx o.'. 9....-em0 O O NOII. -t P0w I- I.C I,4

0 0-u Cc S14U4' *0. 1C * 6 's- Z Z - -ZI 3f =~ o4 & I-- 4 2- w - ..

us WL4AIn #%A #A(..Z 0. 0.4--A o- 0-oZ _ -UNC* LAC o(" tn 3ZZ~t ow w U 2O O 04 _r %o.%u WO -40 0 4" -8 @. -(n - M 04i*:=Z " ItZ06IlL ON- Zn LU 0 0 0

* In LU Of * '-jk-4C~-8 *r jc p-x0x4 I-L .. 4 )LU Z -o.ZL W a s 0 oroU-U0. P2 1 nnnL U U U

=n0 ruow c 4A 0g M~i . o r~~ .0 W 7.. w .- 4~wqA I- I- I-m I-.In. it01- * ZI-W o-.-W = .'O Z 1-n. 0Of-.U0I-0

+0 in a mJ0 _rtf 44A~.4 .J~..

* U .Ifl)n n OI..In * N4Z..J U~*IA* f~~252-*U4

rc

'UU

V~V ItOO O OO W4OOO O OO O OO OI.-~oO~o O

I- 0~o

cz I.- -0- 2.o 4U l

lim ~ ~ U UO o W I

Z- 4U) 4 0 0. z #

4m ccw z Uel) LUz t CCie . W4c 0 0 V).

co -A -4 Zi04A 0 )U LL LU ;-

V- _ 0- -z -. Wz c"of. eg x0c 4 W . U.

I N LUA' U. a) 0" VN^* J 444 Wa.X 0 IIII Zxv 44 SEi .2 Z Z n 4oL - .L

0,~m LU S. V): O 0ICL94 0ovU) 0. I.- 400 LU WL>

Whm 00 1* W l 09 W a.M- cZ.I W Np &.u'sZO 0 W> OW N a0Ata.-- 0w-a 10.- 04 ZA -- n "c

4I cco d.% WW.""I-- LU V)--U)A L -.Z$ zow V0 LU W0

- *Ji- vo 049 Z 4 C-O J 0 w za,I fj l-uz PU4 ".U) OU ) pz '-AZD~ 44 0. m 40Av

@op--lLj t * 0W049 *.C e U i LO0- X#0L *)U. 0L U)L I U M 1- t

I.3K0ZU NN 1Zo .J JWZ4A Z LU.P 0 Z 0 11 z uu~q4A Z 0N zzjz n DOU) " -JM o-bLs.0 zl LU0 -.-zc ii

U ~-J ) W -0 ( Z WUJ. IZq 1 4-. o n CM -I IZU)Ou 0-jW .. 4 ZU N ftZU)IA P0 4z M 0I-LUI -UWKW.OI-NQ W ZW 4aLLON .W) M"UU LL N CC U) NLZ0C

IOW sei e% '' n ~I a4U O )KZ4 Z ~ ~ -- I-UJ-O U L

U)~~weI0 )4 I- 4~ U U..c~tlI253s

0000000CVC000k400000000 %T(0000000000000000000

00 0000000000.oooq4oo.oo-..4eJN 00000000N

00

zz

4

)IM -

dfo 1- -0 - - 0 -

0~ 20IO -0.0-f P"0Z

00. F- -m I. ct-*z uL. UL 4z . a-OZP - 40 "0M- - -4" pM .

U.X LU6 *z ILX =U -$.-a LV* LL W.L LU 00 %% s A L M4. L

tn- q .000 -"" CY0 J -. .J 0M-N. %Wwl-- 4U u -- j-w wQ MAWt-.12cUM CL CL.12c= w4 L Z>-Cu w CL 4

N.- 00- N 0 P"LN- 0* oo 1

wZZ .1 L I.W -Z I.)U O"I- c -<W-Z ("*v44 O w# 8Z N '-WCC W-<<X Z?4 Z 11 P% .-. 0aJC-<<= ZZ it

ZZ LX ~- 254(

Ij

001

wa ee" N

.4.Is z h

CM Nt" N'44 4

444 4..-*4

~.4 .C~ 4.4 C u 4- .I

4x~ 0 41

44 "UN us410ZL -

I-4" m"14-4. wt4.. *o w. -- .-- Cm

C3 UCC OMPIe 044N4.4c U JCO M ZIo IICL ' 1-1 M-N 44 NI- 44 act 014- .~cwA

W. 3U- la. 4w4(Ij+ . UA.Cq 4N 1JCZL C .r jsI- ZNNZ +.44 * .m-c oo w p4

.l3Ugl If.4 Z N Z W ' .N 1 llI -il1 __4-.1 qg I sst' .-U.NNod~ .44 em 'o4~jINo CJz. N Z=- IU .L.0ZO La td .1 a- 3 IL-4 -1.1 OWI UU ~ %. (DLWkV L Li- 3-.- 3.-U ~ um WW -Z P-.

.1 1 U 4J'.00 "~ 64.Z~~Mf ~ 4 .W4IU) .J. aI, QU..J 3-'N4~ 4.'~ei'*4- L .Z-I- ~ I- .N-m

I ~ %.". '.00'3 4 0 44 3 ~e0"" . I255Z

UL

U.

cc44

4UNO ~-NO

tL. 0.l -q %m

&L4oU 244 cy- Z 44LV

*JW U p" *N .4 - 6iLUOp 0 O ONr 14 W 0 :3 2o

Q 4Z.. oO ZaWrNLZ44 N.. 9 4.W0.-.i +-* 44 LUOO .

-A U 4.-OQZ4NNO.O.<4 Z444 I" j 4

U. W&&Q M~*4~~*** cmm9 N 911-agca= ifM9f"m Cq~INEq F-NN 49MM~ Ncz-- WNZ-N N(' C4 M&M.0 Wpd4 Zp-s - 8-d

04eI *Mot4~44N- ZP-.'.22 * .. 44NNW .5444c~ "Kq4 20+ +wU+ Ii. IiIN ".- W~ 4 * 0 % % O % - Ps-c

*0,.jfJ 1 ..SE% 1 V- 1 1 Z M.JZZZ * I 0= 04MFN "NV-14 I NO"4 CcO -,Z MZ 4..J44444)(4xqxx% COORR JO44OsNg4W4AOfq4AC OWN 11 NO II ""i.0' t f Nl"N-~..0E (v +9 1 40 1 +1- + If + N I- + .J I WI

X c " t # -i "1coc

256

U.

XL

m(~w4 0.

4.1>= . a U-I- -J.o o

0 1.- 0- *0 Cfq >- . (

1.0 < 4 - L

0" 0.LUZ CL CMm4 0 U. -.0. LL. LU0

UJZ 'OZ0mn U. W-0 49"a .. "4z xC

U.1Z ZZU LU *UO4 WZ O0. NJU IL

aM 0U. 64." 0 --f _j xac Zj s. OZac 0 AAL.3

I I LU LU - 42.. ..J L-.

I. cc I.- -Z =L6 Ux w U'LmCI. ac -m4 LU-4 ow sX~ 09 aC 40 LA.us W) Z U-LU . a -Z Q

49-1 21c cc cc Ix CL 0 Jc - f.U.I .J-sc -f ,e LLeULU Q~L ~-J -Q

-% 1 +e zo *0.jl -X a 0~p L.

I (D -0 -. LUi_ U) dm0 =~4 Cp M Z "*.Il 0~w to-oc -ia JAD I- # -U1 -*-ZZUN - W t C 0 a

044o A~ W MM *.1- "" P0 IL W~ 0 Uo- LULIxf* 64-1- 0- ' .4 1.- 7.JU x LU %A.) VIMJ-J Ll. z L

j44ftp 0 go 0 2tL4 04 .. s) "w "0 Z M W 0#iV' .CID - .... I-..J C L U i- 0i - 00 _j Uip- _ aws<'-I,- '-

4 - o o--j4(q Ao *j - I-I L . L i) W w .u'-afZ0-1,-O(D 0 LU9O4 Usi Z4 <O-w 4 1-1 <~l L i0 1-0

(D~~ .44- - oC v4 .4 o- Z'J ZX OU0 dW ill cc, MaaOZ LI Q .- wZOI QZI-fo~w#-: #...J .J..j- -JWwaI-X uC w u

* p4 *...J.0.-- . *(D t1 - 0z- * - U. >= 0 .. Z .J4 .0 LU -IU 0Zw ULU WOOLUo if AZ--LWc 40WuJU) Z..4 I-U)g>- jP

I oil1141-DO .. J~i"4(D(D 4 C~.~(~) .JW U-U)' 4 JW-

LU-..I~cZ .~0* -~l* *i 00IL W4 Z wZ4 "b.4vo',4 L O Z( DO 110)0

I *.IiP~ w.~- ww I. W.....-~ .W UJZI .. JU'.Z2a257U

O~oooOOOO~emomOOOOOOOOOOO(oOOOOOOOOOOOOoo

(0 a0Z

z U

op

I~Ll

>. ow wp

.d~b 0 Iaf

.; o a dW.-

z4 z *-.- "

m~ ~ .44. -Q . fJ.zzz Go owo. ON Zw..px " 0 Z fo ie>C

zL I. CU a JL. c - 1 0 e$-a- X 0 cz 4 e 0 N-WW. MOM

)1- 60-1 ILQ 0U 0- C4wz (D*J"4 I OC cc P- 0 u-L. LJ

z~ 4 ~ OX1 9 0 -1 4 Z -j A f.,CL 4w '(2 -. I.- &w ZO0 L6 Z"4~ -

F4 3 o 4A *z P4 ZU 1. _(fltV w K -jwo w4 ow"O _j 4ZZ UC.J. 11 0 1 6 LC=-1-OJ 0 t o 0

N a 1-O -O (.~wx< +*~ -.)OCZ> >--tw -~ 0 2 JJ mw31& jN0oN -xN6 MI 11 NJ It( if 11.. 9d -u )-c Cie ..J1-.-IL 1 - OIL w PaK of1.0 X0 0)-i- -.54ftw 0

Z0. ( C 0 ?QZ 31 I-1 Ow 4 Z (d oL-. C ZU. U.4 NZU. - 0 Lu E'uL* 0.u-.Uj a:U.J 0 wLS-l 4XX U 0 * )-. .JUJW 00 0

I- L00 - . WXW(I4~ ~0 ~ I-. En0258W

0 4

I-. Wan0 UJ 94M

CL 0U ("'1

LUC * LU 42C w*0o~ *0X W 0 ITI0.- 1, ..J (" o

VI IW U. 72 c N

I.-* -. NM90'I 40 U. OA U. ̂ 4

I. zW cc * .-. 4 % ft~1.1 0 qKu 49N

Ii + CIO '. -cc SNIi- t* U.0 . Ww4 4N LU

X 00 60 1- * 44 Z-DLX-CWV U. &0.4 *-. 0 9"

xx Q~j = N Z VMWr tN lif 4 -C 4p w- 02-Mfla U.(xx wUz 20.I1w 0L~ <4d I.. U.

-f W " licr x X O . ~t 1% ILLUM .t z Ww-( * z NwrV4 us 0X0(O x. )w-- 0-0 UA.4 O4NL 4 0 a

1 P 491 &WZW -%Z ZW 0 qx.4wc 0. u

OF 04 0u~ .l-U Z U. WQ 04 W4 Z 0IA 0 &. +WI ()CZ LU * C qx0. c N4e 0.

0 Jwj oac.f m-- +. t) -ic OF4 au.. -1 i O~j z~ x~ -Cco n Ii411- -camW).4)c-i

J 0 D.-.4 Wl-QL ix a>Z 4'.) - I _ 0

2 >2( U.UP( CLZM - 4- _j J>X- 0 N I6-4 )(4 4wv a U a-C cc Z %%. cc0

VC *.2 2Z-J4A 1-U.WJ EW LL~ "41.11 40~ cx W 0x 6" * C3a G.D Z0-1 II 0 211~z 0 Ci

weM X~ -M4 00 cc x0.0 0 .. U.

IZ4Ci $4WL : *4 wOO )( -i1- n <U 'l-1- Z0 UJ W NMI.f 0* >Z .JCLZ Z-0 am -I.- 4Z2 a CI O tI 42-JLW I-( x 4~ COCO P"-- U. 0.0 0 2 z% wp-#- tM Lu @-I--

lf Ww4=)%wx I*--je4 -4z t-a- Zo. = a 2 490Of ZCX>Z 49flI Ztfl M..10.6 WWu 4ZZ CL L 1 0 %. 0'c

I uOa-01wm OX&a. on 40o 0 c _j w1 _ *40 w"406_10~O.w w~ ZwWS- MU0 I.- Z ..12 z -J- LU If M W+ 1I

Iuow 3 W.0U.t2 LL)O2=.Wl U. t44 0C woo W4U. z it-Ou Zit IL-d""Q.~-- 0 WfU - LL U.U. CCUU (d)L)O WZJ MWCO t a oc

0 o4 f

259

p - 00000000000000000000000000000000000000000000000

.9 0u

Z U.LUU

Li 0

04 0

LIt* 1-- 0- -

LI* *0' MJ

u4 o- JL Me" Go Z

I- ac LU-r4Co z* 0-M s .-

1-1 ml-

-U * M 0'L0. cf Y. LJ-( O .

%Ll. %%%t m N Do. LI4 X CN 2 1 4r mmc @ c (L - 0~-cLINN IU <. LIU %kZ 1- 2lz a4

MN%-(3~t N 4 - i W .*W0m e LU 4 4 M.)1 LI OC *0

W U.1 %t" qt-O <

N =40< < = 40('%J-40 C4- c .4 -=O N%k 0 %YI L*((CrL a ON 1 ~ s4w 0 Wz L l

0 wor4c ~ &C -* I M LI .I0 4CLIc -o 4I-- ~ U - 41 11- 114 1--L L C 11 111 1I tI 11 t1 1 11 11 i M 10 i

0 z. it4 WLCl)M 110% 0 i I N 11 Mani-0 N%.'*C0C~ UJ ~ .tOCW)4 4 .DW WCWL-.04 WOO -

0~~~ (.NfI% %j U-L) l- 04 .

U. U Q.4.4~% % L~ '~~ Z260

UL

Ij z

I mn

I z A

0.4 0

I . 0 ftI

ar 0 3C c b. . .a "d

4* 11$ U 3- % tS t

Us aU Z.fsP0 Owu %

a0 L -= 11-44O 0 00Q 44 cc04 LLL c

IZ 44 . .a l t4V~M 0 Uoco 4)io C * t- wC

W4 Cau c W.CYI- LU 0r c -4%1 * t - Nin-I 00 1 4'out;C CL Z .JLw dM ZUn

W11Vdb1 ac LU (_ 4 If NQ -feoN >.* I0 0 I -

0w 0fI U0 xLw XU w w~ ce ==.a OWZ- <wo w N-

0 1* *PW 0 ewOwwm LUa OaL)w uw ZZZWW* M

*OOLWCO N0I .0 ~CfU'fl** I I- 00 J.4

-II44Z+- NW~ 4~ -~ Z 4N ~W261NU

V OOOOOOPOOOO0000000000000O00000000000000000000000

U.)

0 0

0. f-4 CL

0i w

o z

4 0

x~laC 0 c

44 uc 0

F-" 3 -t0 aZU ) P" I-4f

as 0 u0c

0 2m~u a--0 X C P*I- ox- -W-X w

00 0coM=0%wz ( 4.1V0- 0 V)I-i- U.PItf q )- * a u 0g ) C . L

ZZI-O W VI b - 4c o O1 - O- mw 00

Z U)Ce~ rZ 4L'4U on o~0 . 0 -- )( 4z I - -. IOX 4 z =

I-0 Is~

*~ I - ~

wooWOM- 0U0.4NM wooNt~' PWMtnf-wq-N~ -04

NNN-frcfglrl1- *u tA n n

U) N-000 40-u GxW ~.--u

0. 0 *%VX 4

<I- ft N 0-M0 --

w .1 c ~0 o... 0FO 4P1 >V M ) -0 uI-O

x LU W ~ OI- U1(CL '- (2)~ LUM~ J bN

M x 0 -YL

Ijc w 04 -U V4ZN 00> (a 4 U 4 w 6-. N0.I--

0.0 z 0wtor a.- w J4.Z00 .. tw 0. 0.

0. 4M( LU At.e WZmf-c . > -l

49 ~ U *-01- oo)u 03 -WLU LU An OCOZ ozI a

N .LU IOp b Zb NW 4NW I--) -4wx ". LU c . L -wO..hO . I-- wieU

o 0 10- Z) L 4.O .0ro WLI-

0" * N U - 40 I -a-MC" .

I (0 L 4A 1)3 0) *.X-N IOIX< 4b)-2 aN us Z44 * U44z N-t. o- - o o-0Z)U0

I I 4 W I.-W .v .0~ vw z O.l- 4'.0~%I -. J LU Q <U) 00 Z Z0)=-Cv0b.-~N-4 *- N Z U V) * WL d<#AWPfl NWI-U.

I 1-0 0 I- LU )(.0- 4tZX Z 01--

,i Uj X- N- 1*S4z Zw4t ZZUg-q >o.WWW WA. 1- i

It" ZZ c If -U'L of C 11 a 0uJ0I ~ ~ ~ fw cc U 410. .~-0) ~p ~ ~ ~ ~ ~ ~ . wn40 ) Z U U ZtLU-UU)oNwZ)

CCU. II U N -U-wIa C0-C0WZC=0.~000.-a0N

263

000000000000000000000000000000000000000000000000

4O'~ O~~ 00 000 000

u.,u~l~gvo 4co~~o~

* 0

0 N.4,

0 -V)x I.- I

Oz Z .OLr4C -

Nos =o, 4

4b~~I e.I- C404 -ol 0 Cc .

P x LOI l' NI NN

1 0..lk Q CfoOZDL - 0UL Q 44LU ., -C cec.1-- 0 <s -UZ - z x X 04 ZO

op*c Z0-0O4CM I D MZCMV) 0lat 0- 04 o*A40J U f JJ o . C14

M -MO oi 4 v# 4 .N 4- "06 4 00--4- osgn"C4 Loo .

0 jmI P4- W

* I-U) )-<<- I- S

1N aZ~ a~

0 N (nIt 0 I .

Z0 0 aI~ - 00 0-u .m" LI1- 4410O

~ 0. t~u.4LI264

o do Itflfl nLafa

cc NW 4 ** - w I 4cCo.N L 0. 0 1-

x N0 * J 49N 1, 1 Z 42 %b .

xI . - . - C.9 CiU do% 4 cc%.-%

x - 41 4C -%49* m I co I

4 N~ co CL-1 %(.0 1 x(Q 4 odi

U)~q - 4 LU* F -

IU 24ft s-4 a.<I-ga -2 Pe MI .~

0 4 cc P%1= 4- In Q4%.C0 4 * 00 atw * U 1.4%

I* 0 W -~ C3 -A I- 2e 20 41 ")2 .

N "0 4 a. w 0 41.'lye 90 0 -WW 0 LA. *4.

: 4 xN NA 0.0.4 " V t~

* z V dr 14 2

I~~0 24 w .U UI 2 L ccW0 LU 00 *2 41

n 4 4-*-uI U. U. IW ew0 "00"j 6 0 aft Z t 19--t2

0 2 P 0 0 40'0 . - 0 . O. 0 -

N N a a 30 0WAZ C CO 4 OU. . --Mot wII 2 4Z z 0 1.-A0 041 z z Z 41

4 "Not 4 QL-%i 9 CCIO- 0 P" I cofotI 0 .*~w% N- . 0.6- z 20 z cOw"NN

Z W~J40441 0 e g.0<Z0 *4- 0. HO .- 14 0on Pa 01 -.- .6.t* 442W *

I~~~~Z .- tu *1 .% *.-. N4-O(.,d' .. ~ 3

go in- 0*'0*.2.-.ww~C0Sfl)% CL :)z O-- Z- Z wZ LIZ X214 If ZI ~ ~ ~ L .- 4N-0-~iLU 414- = ZI--- - -4.h- i cocoa.42440-

I w ww I W O=W-4 im- N 0fw fwWz -I ftcr Z OZ J..Z 'NIIUwZpIU -L ULL4IWU 1 LLL v4NU.L4 -O CO LLI-OCC*-C .4c oil flw"I,-.U.W

- ~ ~ ~ ~ q~ L *r W%- I I4Z-4..e.L 4-1 441..lt

4 *4265

0051 000 0 00 00000000000000000Q000000000000000000

00

da

.4*a 0 u

UJCw NJ _j(

aezI- . 0 0

WJN*w 0 w-mCK~ft x

+ 4* 00 X v "

1 w*e1 0 0

i w 7 -)" - 4 -4bJu 00 - 0 J =)

0w 40- 6- K Zu M

z1~. UN 0hma r I Ow4L z':g44ww 1- 0K ) -1 -jllqzgZ X -. Je o~a 0=-4z lkw~~l. Cy " gd VU4-I- ~q

s ej [email protected] s w.. eL 4c NftNWto ~ ~ 4'- o*Ve0y vlu 0+%Jo -PN

W04KO 0e4Kee0 JNWQj.. W.. UO UU UI-.JIN.

- ~ ~ ~ ~ ~ ~ ~ ~ O ONWS4 ~0 ." dU60 *j I wjjU00o~IjaKWUZoU I4Ugaa~ ~W 0W L'.w-'-

inslilp.U W In 10 4J.~

00 KKflfl 4IlZ-.~ti ZO00 ~O.'-Z '--266K4*

CU

0000NNNNNNNN~'1wIM'~NN

.99940

.. 44a

COW I C1* 00 LU

x 00 NN% 4-..0 - N0* FQN

a4-&t4, 4 C.00

6.4 04~ 00 w 99 -

x~IL~ NN 4CC 44-__0 0.0 -c

.1040b0 44 410 %w LUft"4ch * I-

444 *4 4

Ijc~) 0. 0 NN 494: 4 0 ac mc COf1I4-. I 00Go +%I PwNia NNOP440 r440s INOCL

w0"O NX CC- N4 %W4c .. Ot0Wf4 c Os- N CLA.* V.-00jt="~~w.) b 6 f 4OXCI- -1940-m =O M X-4

*44+ ZZ0 '.a NZ Z--N "4.. 44 4" ZZ=

if 00 4N Z- 0 044NI .- N0 ftoZwot Z 11 ftN I- 1i =Z 1t~

00 ae 0000I -"-0 4-t.

* 440 0 @0 ~ s-~e267

00*5o 0000000000000000000000000000000000000000000

~u0 L

*u~ I.- N

Ch 0 % WC Y

"* w 0% C%

Wu) ~I- u

P--~~U - -f=~~~~I oc I-. f.

(M f* . 030+ I FW4*P1-4r0 G.* *O b ""V + WN C4 a

I- I- LP. a- 0*-b + +- .

ft '0W m+*" W.4 CIA-1- ++D.1 IZ49z%.Za.7 4A N "44 0 Niu £044*" N"3a

WlIWUw.M P4 42 90%m WW-4 1-I-*uj- I. -- I- 4 o 4. "wol L44 £0.4U (3 - I - " w044

wJ 0 F.42wo4CU -C ww- Us )(ov4 f -%.c46c-

V. IN We..oUM 11 -WZ.. N-J). - Z -0- .M -oz N -- tm~--Wu - 4W "1

:3 ~ ~ *%WW IMU7 94 '.'.rrf-~r4 N NC1juu~ -1-~ UJU NNW1- W a. A. N NN ft N MWw 11 - -

S"M %tWW 4 .)o. 4 I-- N N 11 < m

zq. zzwzlow IIZ O * 4 )( 4'. w OZ

I'. 4 -2 '.. * 28. -. NN 'h~(

UL

oooooooooooooooooooooooccoooooooooooo4.~00 N~ 4. N~ O" 0.-N ~ O 1>

D N

IU I- 60

>. o- CUJ dab A -RD . NI N0-

W& lI z oa- c wpfwJ

of 0 00 & 4 . O#- CP-(0 CL

IZC O-)-w10ZI- qzl- j -mm~~c

1-4-1 1- 1-+X-kZ*Z-ZI 19 f1 - fC fi 1I J7PY7Y3

I __Z CL 0 A K1

I OIt4.- N= .'. IL -4--iJWJ

00 00 5N~

I0() 00 W- (

44 'Q'~Q.N NI4~~'W-.I2609

fooItPf-fo o w m m0(%00C-

000000000000000000000 00000000000000

N "4z*

4 4

N N

49 c4

30,~ ~ ~ P4% -" W 4w-00S a~ 0 "O C0RW

1 ~.4 a+- 4. th .f co0 IAJ 00o -0 0 O.Jm uu -tOX

01 "O z

* 0iICDmj-w " ,- -- ,k Z

8-6 X 0

44 ~ 49 Ob1

00000.ator It0- t4(; aoc 0(70 00 NW~ "I. OU ofOU ~~,6ov~~~c X

-J 08.- J ... JJ.--J.- * .. JN 0 N -0- .4 -- ""-.04ujjx c

.f--Nr'mI0O-- I w- Nra~ 0oz " -zN0N 1NNNN j10"44.W LWWUL-UWZLULo am N~L 4. 0 4 4 4

270W W .

cc NO t0000OQ 4C 00

+ *401

- N 0N4-4 N a.

I9c 000 tN a-

Nxx 43 $- 0NOC I-

40 '0 ob I44 UISJ NN X*,)

+- +. ". IL-%-Ic 0.0 d- '% Q-MN

cc 0.- 0 04~ NNNO. w U-4 NN No N N W0'"NA11

014 IX * 1- Z40JU~~

I 0 0 040 0C0 P4 I CDu~oI 0 *1o N10 eJNz NOb 4I . -k

I0 40I 0NN 4Ci

.9O- cc P xe -f- 00 024 fto a.*WZ4I Ice 0I ~ 000 -%.2 z 9 =X* WLJNN *0 CIO Z- 1 -Z 1~ C400 IU-t1-.

CNNI 00- x *4 g0u.-.

P9- 00 . 40 -vw -WCL -==wI~o *00 00 9( 00 00 ILI-e Z XWVN0

w-. CV0" 9 ON: 03=o~ 0 XZ 01OZSMZjdltdw .4

'~0.0. - WIO " of 4A- ULLW.L-W

5 B~uuw- .JI --. %I. P.J f" N 0- N 0.e w4W - l~(.0 . N ~ o Nw (mw. NW NfO.tJC 110 .I

.- IX~0,. * .'J~ oI~2710

0000000000000000CO000000000000 ss0000 0 00000 00 0

0 .

0 49. k44 -01 4 4%1- IU&Z" .w-03.-W Z.

4~ru -09J.WNO uuou 0 N

-f CC.wwU J wA.-,. i~ ... .COW. *. z*. a0WZWh.. .. j3j.,.. 0 ) Z

+-- 1 U- WA x_J..Jmmw~ 0 -ft a- 0 Z

0Ww.'u- P4.a 00 V4. - .3j OlCU LA 0 .0 -A, WANWOWN .. ~ Z"4 ac -* ac.-40- 4cft014 .j iZ 0D *4 + -w6

L OUw 0 %~~P*N - %~ 0 041 LUJI.WNNCY-AM cy~--P - ZZO * -W4Z -N4% Z0C3-4LC. e-."4-LJONJ ..J

%b%. 0 -.j * g LDV440N0co0 . *%-m.0 "WON 84-4 1 0-tw-O-i 00000 cI'41 N N~ a * 4N 00)0- N N -"ZZ NN a0N --

tLjU4D-aOWWWJWWtw Z"-$II0W,.C-Jx N WA-af"4WtuZZN..-mp~

* N 'VZZ p '0 -~N4-~0Z0

0 Lnknuvqc V. a- #4Ww0 e-qiAW%%4N P a 0-049UN to -- 4 0.-J-)wft*~Z -~WftpOzZ m0-.-..-Z.Jj Ozzz of3- N VInzz3- -JO-l"

WWSLILOu.COWILL.LLO O-w0wO3-cwW~ 3WmZopx>WaqL 0SrJ)00uoWu().Ur.Sg-eUzwopN)

cc af Nmg0.0 0 N

-if4JN t AI A

272

U.L

0~~~t. OOOQOOOOOOOOOOOOOOQOOOOOOow I.L yl

0g S.UNa~0O~'O0 000000000N00000000000 004

I~~ ot _j lAzlt lI ~~0O0000O0OA0000

IU -2 (7 -0.

06- U. 04V-0 UCL OL- .Q. N3Z% I a O4-Ol LL LI No m - -- _ pw - * Z.-MU - --

0.0c 0(0- 4 +4 LU-WC P4w11-4" .111

I LU LU .... 0"a.J 22 11 0 W.-0

IIZ OZZ OC-4I-) UI) Z oV 1 4W 41*Z 44ZZ 4I-IZ Z-

LA 0n LIND tA LA0

0. W-'.Q - *-~*.0.-- 0 *02073

UW

us

W **

j - -

o Co cc

Wu x

au **

"WI01 0 P-

4"

U, I. 1. 0 N

oU 0 *44 -0

4: NOJ 0 Dzo C

ZZ%-Z 0 Woft 0* -0LA~ ON m0 j N 0O

*(I-1 4 W 0 04, X" p ,0'o) j .Q z M P4 N04-0 M~ * NO- 0

*Oqu~ p"a0U N g.~ 00.rnZ- NZ*>Lu a 4 z) o * %0. _j~.-' -. ' rW Q w oIf %r I y0 0 - If *Z4- " 1. * 4If ZOO. 041

I 'tftZW 9- o 0 o- C 0.Lu-." W ev O.- 0 ~waN.4 0.NJ. .J N - *NN 1,

0->-C4 0 & w * *-0 O 0 " 4%,C.' (D- 0-UA

4- *Z) 0 L %..4 4." . = 0 p fq4W "4 JWD *(X 1LU Lumcrc Cc:wo.tNo 0 I-j- OWCDOZ Lu 0 90 II -- maft-Z'0 002O Z

-" .4 O Nw -4-O f f1 I It W P-0 9-, 11 I.i-'4 W Z -4 "P1W ruj UWrI >G C fCLu-I C 11,.~~ 0~ 11 0%v" -* ~-V- .4 If 1-84I

0.-4'0- 0Z "o 0.2 *Inor0o.( m w .O-UU4 %Z o W L

-~~~~~ 00 0 -. 0WW0 w~I N ~ ar~~0-~~~N .4%0 Z.10 0.0 ~

U L~.-4DZ ~C~r W~ IIII I iiI, N"400274 0 .- J.e.u ..-

040sw .I, -oaomiw'tm fc ~vN ~ n%

woo OOcp o00O 0cK0000 0NNNNNNNNr(qrvdIrq~

U.1

U.1

0

M co

0 0

Ii I.

%t Z P.0L 0

j LU"0 0 * aI4 0.Atw. 0 4

Ci 00 + %

z~. -U

*40IM + . .

W. U. >.+ DO4 0m,

04 1%*Qa. w004

W. U) cc*C-%n.iLU 0+ 01- * w

Z (Da 0 * I o.(N04- IZ- o 4 o- L--c.4 UJ 09-4 0114 LLLF4% . .- + .AUU U-()~LV

aruz *QM.%*0 0. 0.4 ~dw - N+ WZ M -Z Z-f. 1__1PO__, .4 U41 -9' lLLlj.

11 wo w N0 go" *4414 LUUJJ- -+tfl P O AU I-QI-u. -ct-ac t -zoo-o CLO- to-Q 1 11 llL-4 -

o "u 40 zc Ic4LU I * I 1 0.0 0 1 o--L-J.-o LU

L.4- % U-L I-IJX.-4iJ nIt~ W..- e4~ COO '.usou

Z 14 O0*.-'* 0z I'...1

0-ceLUW'1 I -t I *JUJ 1--f-4- U.. U.ZL it to LUU ifDLJCccJLUZZ-. NZ e--N a .&-cC %0WL * I CL -*ZL

IO4 -0 .rJ..- g.Q *ud% 0.Ll

It tAa0 co co c 0I~ 4 '44ZZ ?,_II I.j 0W - ~ . L

Ow 0 '~w WrJ n g~g g nuu I4'I -a275Jj~

MM4 *U4%4-A%#~%n~%4 444444O o

0000000000000000000000000000000000000

1- 4 0.

0 Co 01-80U4u. 1-s 44x

WC4 0U 02U 1-W 6.90

ZUJ >4f00Z- us I- I--..-

0 :) X.-w I--0N.I-'c cUJ.

4n '-.0 U)V w d:3 *1 - - 1-

1-2 IU WOZ A-ACV)1 ZZU LU W 4

002L Lu JLU P0. u

-r.01- I. - Zu2 LU-

t- Ulm 4W% uju.

)0 c X04 4 W4

Q) 01 O-6WUI .1 0 . ui

-fP4J LU If 48-4w z 2 4 LUXZ I >0 fV) z44 41 44 >4

09 In00 cc9 lb P"

*ZXZ Zifl Q Oab- I-- I. - C. . * Zw

(fU ()LU 09 LU 0 0 4 0 UV. Z" 4..JW 3 1- 90.t- Zo ~ 2I*OV o ifloil aU 02 0. 2 OZ

- .*Wu O Q0 il-e0 ... 0. Me ~ 0. O )-J-10 0'' 10a* o- (. 41.0

049.J -X U.-1-f LL W4 U. V) cV LL_CLUJ UJO -%1- 4 O4q - 0 afti ~- Occe

41> .# W lU) X-w z. W.O 2 .4+4 >I.-' z Z 3 z 220 112 11 * @#.1 * 1-ZZ4

p"U ,.1-I - C Oath) 0 WISOW a a WPOVfif O"e-. 1-0.4 aw P" 0"49 P.NW. " " ,. N= - Wn '*40 m - 1

f4 Hz MLJ)l .430 w 1-..JW I-- + 0- Z 1- 0 + 9 -q I~a O'' C"3 3 Z 4=X "n <O 4 a -o 00~ O -a 41 I g 40

(.0 % W..Jif )(I LU .101- Un _j -l w 04-f- .J w f w 0+4- 0 *Ow--Oa8 WW Z X-1 n'z1 10 =s bc l--~11$1-WwzmK.j Wt.J P- 0<0 u44 0 8 L0 u U.0 U.-a-/)I U)140.mw1"O 11-0 o JDe-OU O.-na Qn)"O -0--.0j ... iz

x 4CX Ogxj 4 cO 4 40v ZQ 01-c % U U.

0 0 C) 0 0qp UWUU wuUQUUUU cm ""4UUq)U 4 fUU

276

C3

- Dew

oft of

I~o z I I-o.

*1 4>Z

.1 4 -

0-91O

.1 - I.~ 277

LIST OF REFERENCES

1. NASA Report SP-36, Aerodynamic Design of Axial-FlowConressors, edited by Irving A. Johnsen and Robert A.Bullock, 1965.

2. NACA Report 1016, Effect of Tunnel Configuration andTesting Technique on Cascade Performance, by John R.Erwin and James C. Emery, 1951.

3. Duval, David A., Evaluation of a Subsonic Cascade WindTunnel for Compressor Blade Testing, M.S. Thesis, NavalPostgraduate School, Monterey, California, 1980.

4. Rose, C. and Guttormson, D. L., Installation and Testof a Rectilinear Cascade, M.S. Thesis, Naval Post-graduate School, Monterey, California, 1964.

5. Bartocci, J. E., An Investigation of the Flow Condi-tions at the Lower Measuring Plane, and in the PlenumChamber of the Rectilinear Cascade Test Facility, M.S.Thesis, Naval Postgraduate School, Monterey, California,

yjw 1966.

6. Moebius, Richard C., Analysis and Testing to Improvethe Flow from the Plenum of a Subsonic Cascade WindTunnel, M.S. Thesis, Naval Postgraduate School, Mon-terey, California, 1980.

7. Cina, Frank S., Subsonic Cascade Wind Tunnel TestsUsing a Compressor Configuration of DCA Blades, M.S.Thesis, Naval Postgraduate School, Monterey, California,1981.

8. NASA Technical Note TN D-5427, Fortran Program for Cal-culating Transonic Velocities on a Blade-to-BladeStream Surface of a Turbomachine, by Theodore Katsanis,i 1969.

9. NASA Handout, Draft of Technical Paper, Quasi-3D FullPotential Transon:.c Blade-to-Blade Code, by CharlesFarrell, 1981, Conference on Turbomachinery Flow Analy-sis fPethods--A Status Report on Maturinr Codes, Confer-ence at NASA Lewis; Reseerch Center, 14-J.5 October 1981.

q

278

U

10. NASA Technical Paper 1493, Performance of Two-Stage FanHaving Low-Aspect-Ratio First-Stage Rotor Blading, by

7Donald C. Urasek, William T. Gorrell and Walter S.Cunnan, 1979.

11. 3052A System Library (9845A), Hewlett-Packard Company,1978.

12. Turbopropulsion Laboratory, Naval Postgraduate School,Technical Note 80-0Z, Data Acquisition Programs for theSubsonic Cascade Wind Tunnel, by D. A. Duval, August1980.

13. W. R. Church Computer Center, Naval Postgraduate School,Technical Note VM-01, User's Guide to VM/CMS at NPS,October 1981.

14. W. R. Church Computer Center, Naval Postgraduate School,Technical Note VM-05, Introduction to the XEDIT EDITOR,May 1981.

15. NASA Technical Note TN D-8431, Revised Fortran Programfor Calculating Velocities and Streamlines on the Hub-Shroud Midchannel Stream Surface of an Axial, Radial,or Mixed-Flow Turbomachine or Annular Duct, by TheodoreKatsanis and William D. McNally, 1977.

16. Turbopropulsion Laboratory, Naval Postgraduate School,Project Report NPS67-81-019PR, Uniform Inlet Conditionsfor the NPS Subsonic Cascade Wind Tunnel, by Donald M.McEligot, December 1981.

17. Pankhurst, R. C. and Holder, D. W., Wind Tunnel Tech-nique, Pitman and Sons, 1952.

18. NASA Technical Paper TP-2030, Computer Program for Cal-culating Full Potential Transonic Quasi-Three-Dimensional

* Flow Through a Rotating Turbomachinery Blade Row, byCharles Farrell, 1982.

279

w

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, California 93940

3. Department Chairman, Code 67 1Department of AeronauticsNaval Postgraduate SchoolMonterey, California 93940

4. Director, Turbopropulsion Laboratory, 15Code 67Sf

Naval Postgraduate SchoolMonterey, California 93940

5. Fan and Compressor Branch 2(ATTN: N. Sanger)Mail Stop 5-9NASA Lewis Research Center21000 Brookpark RoadCleveland, Ohio 44135

6. LCDR W. D. Molloy Jr. 2VC-5, NAS Cubi PointFPO San Francisco, California 96601

280