TABLE OF CONTENTS

Page

LIST OF TABLES ......................... v

LIST OF FIGURES .......................... vi

NOMENCLATURE .......................... xi

CHAPTER i INTRODUCTION ..................... i

I.i Overview ...................... I

1.2 Similar prior work ................. 2

1.3 The current experiment ............... 3

CHAPTER 2 EXPERIMENTAL EQUIPMENT AND PROCEDURES ......... 5

2.1 Experimental Facility ................ 5

2.1.1 Tunnel ...................... 5

2.1.2 Traverse system .................. 8

2.1.3 Forcing System .................. 8

2.2 Measuring Equipment ................. 9

2 2.1 Pressure measurements ............... 9

2 2.2 Anemometry .................... 9

2 3 Data Acquisition System ............... ii

2 3.1 Computer system .................. II

2 3.2 Primary A/D .................... 12

2 3.3 Phase pickup ................... 12

2.4 Data Processing ................... 13

2.4.1 Single Wire .................... 13

i
2.4.2 CompactVorticity Probe .............. 14

2.4.2.1 Calibration ................... 14

2.4.2.2 Processing ................... 16

2.4.2.2.1 Determination of the u,v components ...... 16

2.4.2.2.2 Accuracy ................... 17

2.4.3 PhaseAveraging .................. 17

CHAPTER3 CHARACTERIZATION OF THEEXPERIMENTALCONDITIONS.... 19

3.1 Boundary Layer ................... 19

3.1.1 Bleed setting procedure .............. 19

3.1.2 Turbulent Characteristics ............. 20

3.1.2.1 At separation .................. 20

3.1.2.2 Prior to separation ............... 22

3.2 Forcing system ................... 23

3.2.1 Forcing frequency ................. 23

3.2.2 Effect of the forcing on the flow ......... 24

3.2.2.1 U 0 - 0 Data ................... 24

3.2.2.2 Perturbations of the separating boundary

layer ...................... 25

3.3 Entrainment ..................... 27

3.4 Probe Positioning .................. 27

CHAPTER 4 RESULTS AND DISCUSSION .......... ...... 29

4.1 Response of the upstream boundary layer to the

forcing input .................... 29

4.2 The Velocity Field in the Neighborhood of the

Separation Lip ................... 30

li
4.2. i Meanvelocity profiles for the unforced

condition ..................... 30

4.2.2 Meanvelocity profiles for forced condition .... 30

4.2.3 Kinematic Reynolds stress in the separating

shear layer .................... 32

4.3 Evolution of the unforced and forced shear layers 32

4.3.1 Meanvelocity profiles .............. 32

4.3.2 Phase averaged data ................ 34

4.4 Response of the entrainment field to the forcing

input ........................ 39

CHAPTER 5 CONCLUSIONS ...................... 42

APPENDIX A EFFECT OF WALL CONTACT ON HOT-WIRE CHARACTERISTICS 129

APPENDIX B DROP TEST CALIBRATION TECHNIQUE .......... 132

APPENDIX C ZERO MEAN FLOW PRESSURE MEASUREMENTS ........ 135

APPENDIX D NUMERICAL DATA ................... 136

LIST OF REFERENCES ....................... 182

iii
LIST OFTABLES

Table

I - Forcing Amplitude Measures ..................

A.I - Wall Contact Calibration Results .............

D.I - No Flow Hot-wire MeanVelocities .............

D.2 - No Flow Hot-wire RmsVelocities .............

D.3 - No Flow Microphone MeanVoltages ...........

D.4 - No Flow Microphone RmsVoltages . . ...........

D.5 - CompactProbe u (x/00-1.O) ................

D.6 - CompactProbe u (x/00-1.O) ................

D.7 - CompactProbe _ (x/80-1.O) .................

D.8 - CompactProbe v (x/00-1.0) ................

D.9 - CompactProbe u'v' (x/00-1.0) ..............

D.10 CompactProbe u (x/80-3.0) ...............

D.II - CompactProbe u (x/80-3.0) ...............

D.12 CompactProbe _ (x/00-3.0) ...............

D 13 CompactProbe v (x/80-3.0) ............. • •

D 14 - CompactProbe u'v' (x/00-3.0) ..............

D 15 Meanvelocity straight wire results ..........

D.16 - RMSvelocity straight wire results ..........

D.17 - Entrainment Field u (0--60 °) ..............

D.18 - Entrainment Field u (0--60 °) ..............

D.19 - Entrainment Field v (8--60 °) ..............

Page

25

131

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

161

171

172

173

iv
D.20 - Entrainment Field _ (0--60 °) .............. 174

D.21 Entrainment Field u'v' (8--60 °) ............. 175

D.22 - Entrainment Field u (8--45 °)

D.23 - Entrainment Field u (8--45 °)

D.24 - Entrainment Field v (0--45 °)

D.25 Entrainment Field _ (8--450)

D.26 - Entrainment Field u'v' (8--45 °)

D.27 Entrainment Field u (8--90 °)

D.28 - Entrainment Field u (8--90 °)

D.29 - Entralnment.Field J (8--90 °)

D.30 - Entrainment Field v (9--90 °)

.............. 176

.............. 176

.............. 177

.............. 177

............. 178

.............. 179

.............. 179

.............. 180

.............. 180

D.31 - Entrainment Field u'v' (8--90 °) ............. 181

V
LIST OF FIGURES

Figure Page

I - Separation lip geometry for Fiedler and Mensing [1986] .... 44

2 - Plan view of experimental facility .............. 45

3 - Test section ......................... 46

4 - Schematic Representation of the Traverse System ....... 47

5 Boundary Layer Development Section .............. 48

6 Entrainment Throttling Chamber Detail ............ 49

7 Entrainment Flow Conditioning ................ 50

8 Schematic Representation of the Traversing Mechanism ..... 51

9 Forcing Piston Detail ..................... 52

I0 Forcing Piston Side View .................. 53

Ii - Forcing Piston Isometric View ................. 54

12 - Typical hot-wire ...................... 55

13 Modified wire mounting for boundary layer surveys ...... 56

14 - Schematic presentation of Compact Vorticity Probe ...... 57

15 - Data Taking System ..................... 58

16 - Optical phase pickup and conditioning circuit ........ 59

17 - Raw calibration versus fitted 7-f(_) curve ......... 60

18 - Clauser Plot of unforced BL at x/00 - 0.0 .......... 61

19 - Clauser Plot of forced BL at x/00 - 0.0 ........... 62

20 - Boundary layer mean profile at x/000-0.0 .......... 63

21 - Boundary layer momentum thickness .............. 64

vi
22 - Boundary layer friction velocity

23

24

25

26

27

28

.............. 65

Power spectrum of piston acceleration (z-O.0) ........ 66

Power spectrum of piston acceleration (z--h/2) ....... 67

Power spectrum of piston acceleration (z-+h/2) ....... 68

Hot-wire Response to Forcing with no Flow 4 - 0 ....... 69

Hot-wlre Response to Forcing with no Flow 4 - 90 ...... 70

Hot-wire Response to Forcing with no Flow 4 - 180 ...... 71

29 - Hot-wire Response to Forcing with no Flow 4 - 270 ...... 72

30 - Entrainment Setting Procedure ................ 73

31 - Boundary layer mean profile at x/00--5.0 .......... 74

32 - Comparison of phase averaged min/max U+ Y+ at x/80 - -5.0 75

33 - Comparison of phase averaged min/max U+ Y + at x/O 0 - -20.0 76

34 - Streamwise data sampling locations ............. 77

36 - Phase averaged v/U 0 at 4-0.0 ................ 79

37 - Phase averaged _/U 0 at 4-90.0 ................ 80

38 - Phase averaged v/U 0 at 4-180.0 ............... 81

39 - Phase averaged v/U 0 at 4-270.0 ............... 82

40 - Phase averaged 6u at y/O 0 - 0.0 ............... 83

41 - Phase averaged 6v at y/80 - 0.0 ............... 84

42 - Phase averaged 6u at y/O 0 - -1.02 .............. 85

43 - Phase averaged 6v at y/O 0 - -1.02 .............. 86

44 - Phase averaged 6u at y/80 - -3.06 .............. 87

45 Phase averaged 6v at y/80 - -3.06 .............. 88

46 - Phase averaged'6u at y/80 - -9.36 .............. 89

47 Phase averaged 6v at y/80 - -9.36 .............. 90

vii
48 - Forced velocity componentintensity relationships ...... 91

49 - u'v' in the separating boundary layer .......... 92

50

51

52

53 Meanvelocity profiles at x/80 - i

54 - Meanvelocity profiles at x/80 - 3

55

56

57

58

59

Unforced Shear Layer Isotachs ................ 93

Forced Shear Layer Isotachs ................. 94

Forced Shear Layer Isotachs (Fiedler and Mensing [1985]) 95

Meanvelocity profiles at x/80 - 5

• ° ° • ° ° • ° ° ° ° • • 96

97 • • • • ° • • • • • • ° •

98 • • • • ° • • ° • • • • •

Mean velocity profiles at x/80 - I0 ............. 99

Mean velocity profiles at x/80 - 15 ............ I00

Mean velocity profiles at x/90 - 25 ............ I01

Mean velocity profiles at x/80 - 40 ............ 102

60 - Mean velocity profiles at x/O 0 - 60 ............ 103

61 - Mean velocity profiles at x/80 - 77 ............ 104

105

62 - Mean velocity profiles at x/80 - 115 .........

106

63 - Mean velocity profiles at x/80 - 153 ...........

107

64 Mean velocity profiles at x/60 - 192 ..........

65 Mean velocity profiles at x/80 - 230 .......... 108

66 Unforced condition velocity histogram at x/80 - 60 .... 109

II0

67 6u versus phase contours at x/80 - 1 .........

Iii

68 6u versus phase contours at x/80 - 3 ..........

112

69 6u versus phase contours at x/80 - 5 .........

70 - 6u versus phase contours at x/80 - I0 ......... 113

71 - 6u versus phase contours at x/O 0 - 15 ......... 114

72 - 6u versus phase contours at x/80 - 25 ........... 115

viii
73 - 6u versus phase contours at x/80 - 40

74 - 6u versus phase contours at x/80 - 60

75 - 6u versus phase contours at x/80 - 77

76 - 6u versus phase contours at x/80 - 115

77 - 6u versus phase contours at x/80 - 153

6u versus phase contours at x/00 - 192

6u versus phase contours at x/80 - 230

• ° ° • • ° ° ....

• ° ° ° ° ° • ....

78

79

80 Determination of disturbance phase location ........

81 Convection speed in the developing shear layer ......

82 Width measures in the developing shear layer .......

83 Entrainment field velocity vectors ............

84 - Schematic representation of entrainment mass flux .....

116

117

118

119

120

121

122

123

124

125

126

127

ix
Y

+

Y

lateral coordinate

lateral coordinate in wall units

transverse coordinate

GREEK SYMBOLS

angular acceleration

7 angle in the XY plane between velocity vector and axis or X

array probe

6u,6v velocity fluctuation see (13)

w

6 boundary layer displacement thickness

hot-wire voltage ratio

offset hot-wire voltage ratio

8 momentum deficit thickness or angular position

8 0 momentum deficit thickness at separation

v kinematic viscosity

locally scaled perturbation level, see (14)

4 phase angle

angular acceleration

width measure of the forced shear layer, see (17)

SPECIAL SYMBOLS

I

()

()

(< >)

( )f

time average of the quantity ( )

rms of the fluctuating quantity ()

phase average of the quantity ( )

the quantity ( ) for the forced condition

x
Nomenclature

A,B,n

A

e

C0..C n

cf

f

E

Q

Q3

Q4

R o

S t

U r

U'(_)

U +

U

T

Uo

V t

V'(_)

V

e

w

P

x

x o

coefficients for Collis and Williams equation

piston amplitude

polynomial coefficients

local skin friction coefficient

frequency

hot wire voltage

velocity at hot-wlre

velocity on wire 3

velocity on wire 4

Reynolds number based on 9

Strouhal number

streamwise velocity fluctuation

u' at phase angle 4

streamwise velocity in.wall units

friction velocity

free Stream velocity

lateral velocity fluctuation

v' at phase angle 4

entrainment velocity

piston width

streamwise coordinate

virtual shear layer origin
INTRODUCTION

I. I Overview

Forcing and its effect on fluid flows has becomean accepted tool

in the study and control of flow systems. It has been used both as a

diagnostic tool, to explore the development and interaction of

coherent structures, and as a method of controlling the behavior of

the flow. A numberof forcing methods have been used in order to provide a perturbation to the flow; amongthese are the use of an oscillating trailing edge, acoustically driven slots, external acoustic

forcing, and mechanical piston methods.

There have been numerousstudies into the effects of forcing on

free shear layers. Substantial information can be found in the review

articles (e.g. Fiedler [1988] and Hussaln [1986]) and in the original

publications which they cite.
The investigation presented here documents the effect of a planar

mechanical piston forcing on a single stream shear layer; it can be

noted that this is one of the lesser studied free shear layers. The

single stream shear layer can be characterized by its primary flow

velocity scale _ and the thickness of the separating boundary layer

00 . The velocity scale U0 is constant over the length of the flow

field; 0(x) can be used as a width scale to characterize the unforced

shear layer. In the case of the forced shear layer the velocity field

is a function of phase time and definition of a width measure becomes

somewhat problematic.

1.2 Similar prior work

The effects of sinusoidal forcing of the separating boundary

layer in a single stream shear layer have been studied by Fiedler and

Mensing [1985] and Disimile [1986]. An acoustic forcing mechanism was

used in the Fiedler and Mensing study; the acoustic wave was applied

_to the separating boundary layer through a wave guide channel. Two

separate trailing edge geometries were used in their study, see Figure

I. The separating boundary layer for their study had an R 0 value of

830. Experimental observations of the resulting large scale motions

included both hot-wire measurements and smoke visualizations.

Hot-wire measurements in the shear layer indicated maximum _ levels at

St-(x-x0)f/U0 _ i. This result, combined with the flow visualization

data, suggests that the large scale coherent motion has its maximum

organization at this location. A comprehensive evaluation of the
effect of forcing frequency and amplitude effects on the shear layer

is provided by the Fiedler and Mensing study.

The Disimile investigation, which was executed on the same apparatus as the current study, used a mechanically driven piston to

provide a low amplitude forcing of the separating boundary layer. Expressing the forcing piston amplitude as A(t) - A 0 cos _t, the Disimile investigation was performed using A 0 - 0.76 mm, or A0/80 _ 0.12.

The Disimile study revealed the formation of a large scale coherent

motion and documented its translation properties in phase time. A

negligible influence by the forcing input on the separating boundary

layer was indicated.

1.3 The current experiment

The study documented here, which was designed to build upon the

previous investigations, was to examine the effect of large amplitude

forcing at separation on the separating boundary layer. The effects

of forcing on the developing shear layer constituted the second phase

of the present study. A third phase of the work was to examine the

behavior of the entrainment field for the shear layer, and its

response to the strongly forced shear layer.

The experimental approach taken was to provide a large amplitude

forcing to a large separating boundary layer. In particular, a forcing amplitude of A0/80 - 0.58 was used with a separating boundary

layer characterized by R0(0) - 5500. and 80 - 6.5 mm. Phase averaged
4

measurements, using a single hot-wire anemometer, were performed

throughout the development region of the shear layer and the upstream

boundary layer. Planar velocity vector measurements in the entrain-.

ment region were provided through the use of a 4 wire probe. As a

result of the large physical dimension of the separating boundary

layer (0 0 - 6.5 mm) a 4 wire probe was able to be used to examine the

planar velocity field just downstream of the separation lip.
2

EXPERIMENTAL EQUIPMENT AND PROCEDURES

2.1 Experimental Facility

2.1.1 Tunnel

The tunnel used for the present study was a single stream shear

layer suction tunnel, a plan view of which is presented in Figure 2.

The test section for the tunnel was subatmospheric, with the open

volume of the laboratory between the fan exit and the inlet to the

tunnel serving as a settling chamber for the return flow. The test

section for the tunnel is shown in Figure 3, with a 0.5m x 0.8m core

flow exiting into a 1.7 m x 0.8 m x 3.0 m test section. (The height

for the entire area shown in Figure 3 was a constant 0.8 m.) The tunnel was equipped with a glass wall over the entire length of the test

section which enabled optical positioning methods to be used to locate

the probe. The test section, downstream of the separation step (at

x - 0.0) was equipped with a movable floor traversing mechanism, as

shown schematically in Figure 4.
The prime mover for the tunnel was a Chicago 30.5 SQAairfoil fan

powered by a 15 Hp variable speed DCmotor. The motor was equipped

with a tachometer feedback control system which maintained the motor

speed to within ± 0.5% of the set value.

Flow conditioning upstream of the test section was provided by

three two-dimensional contractions with an overall contraction ratio

of 22.6 to i. Additional conditioning was provided by turbulence

manipulators downstream of the first two contractions. These manipulators consisted of a 3.175 mm diameter honeycomb with an I/d ratio of

8, and a set of 30 mesh screens spaced 12.7 mm apart. A final asymmetric contraction, to the boundary layer development section,was

placed downstream of the manipulators.

The boundary layer development section, as shown in Figure 5,

conditions the boundary layer upstream of the separation lip. This

conditioning takes the form of removing the upstream boundary layer

formed during the last contraction through use of a separate bleed

fan. This low momentum fluid was extracted using a splitter plate as

shown in Figure 5. The plenum downstream of the splitter plate exhausted into the receiver through a Buffalo Forge 37v fan. This fan

was driven by a 3 Hp A/C constant speed motor through an adjustable

speed belt drive allowing the adjustment of the bleed flow.

A distributed roughness trip mechanism, consisting of 609. nun of

16 grit sandpaper, was employedl This trip method was based on the
work by Klebanoff and Diehl [1951]. The distributed roughness was

followed by 1290. mmof smoothwall. The final 655. mmof wall consisted of white formica covered particle board providing a surface

with the following desirable characteristics;

a) A low surface roughness; which minimized wall roughness

effects on the developing boundary layer.

b) A non-conductlng surface; which provided desirable heat

transfer properties. When operated near a conducting surface the

heat loss from a hot-wire anemometer will give rise to significant errors in measurement. Usage of a non-conducting surface

such as formica covered particle board minimizes this effect.

c) A white smooth surface; which enabled an optical

wlre-shadow positioning method to he used to accurately determine

the position of the hot-wire when near the wall.

In contrast with many single stream shear layer facilities, the

facility used in this study had the attribute of being able to both

condition and to have control over the fluid stream entrained by the

shear layer. The entrained fluid was taken from the open laboratory

volume through filter media and into a settling chamber. One wall of

the settling chamber consisted of a series of throttle modules, which

allowed for the control of the flow rate through the use of a sliding

throttle plate as shown in Figure 6. The flow passed through the

throttle modules, then through a coarse screen, a contraction to the
0.8 m test section height, and into a honeycomb and fine

bulence manipulators; see Figure 7.

2.1.2 Traverse system

screen turThe probes were positioned by means of a 3 axis traversing system, shown schematically in Figure 8. This traverse consisted of a

rack and pinion drive in the X direction, a screw feed drive in the Y

direction, and a worm gear drive in the 8 direction. Each axis was

driven through stepper motors under computer control. The resolution

in the X, Y, and 0 directions were .8 mm, .01 mm, and .02 degrees

respectively.

2.1.3 Forcing System

Forcing of the separating shear layer was provided by a motor

driven piston forcing mechanism. The basic mechanical system was employed in previous research of lower amplitude forcing effects; see

Dislmile [1984] and Figure 9. The piston was belt driven using a constant speed (1760 RPM) 1 Hp AC motor and variable pitch pulleys. The

piston motion was obtained using an eccentric as shown in Figure I0.

The time dependant position of the piston can be written as:

A - A0 × cos(4) (I)

Where 4 is the angular position of the rotating shaft.
This study was performed using an amplitude A 0 - 3.84 mm and a

frequency of 16.1 Hz. Phase information was obtained through use of

an optical pickup on the forcing piston drive shaft as shown in Figure

II.

2.2 Measuring Equipment

2.2.1 Pressure measurements

Pressure measurements were made using an MKS baratron model 310 1

Torr pressure transducer and 170M 6-C amplifier. The overall uncertainty for all pressure measurements is ±.08% of indicated plus

±.00001 Torr.

2.2.2 Anemometry

All hot-wire measurements in this study used locally fabricated

hot-wires and probes. A typical straight wire is shown in Figure 12.

The wire itself is 5 micron tungsten with an overall length of 3 mm

and an active length of I mm. The inactive portions of the wire are

copper plated to a nominal diameter of 50 microns. The wires were

mounted on the tips of jewelers broachs, the plating as well as the

small diameter prongs lead to minimal interference effects. The measurements were all performed with the wires operated in the constant

temperature mode at a nominal overheat of 0.7.

Two types of probes were used in this study, single wire probes

and a compact vorticity probe. The single wire probes consisted of a
I0

single wire as described above, operated with the wire parallel to the

Z axis. A modified wire mounting was used for the wires involved in

the boundary layer measurements. Specifically, the wire was mounted

on the side of the tip of the broachs, rather than the end of the

broachs; see Figure 13. This allowed the active portion of the wire

to be brought closer to the wall.

The compact vorticlty probe is a 4 wire probe allowing for the

resolution of velocity components and gradients in a single plane.

The probe is shown schematically in Figure 14 and consists of a single

X array, with the addition of two straight wires. The individual

wires are as described above.

As can be seen from Figure IA, the overall size of the measure2

ment area is I mm normal to the mean flow. Although no large scale

model studies have been performed on this probe to determine possible

prong interference effects, results up to the time of this writing indicate that such effects are minimal. Measurements at various orientations in the calibration stream return the correct values given the

probe orientation. In addition measurements of the thermal interference between wires, obtained by running all possible on and off combinations of wires while the probe is in the calibration stream, show

no thermal interference between wires.

Two types of anemometers were used in this work; these were the

DISA model 55M01 and the TSI model 1755. In both instances the
ii

nominal output was approximately 4.5 volts at the free stream speed of

13 mps. Electrical noise levels for both types of anemometers were

approximately I millivolt rms. Frequency response for the anemometry

was approximately 20 KHz at 13 mps.

2.3 Data Acquisition System

2.3.1 Computer system

The computer system used for both the data taking and all data

processing was a DEC 11/73 microcomputer; this system is shown

diagrammatically with the associated data acquisition and laboratory

interface hardware in Figure 15. This computer consisted of the central processing unit, two RD-53 70 megabyte hard disk drives, a 90

megabyte TkS0 tape drive, an AXVIIC A/D, a KWVIIC programmable clock,

a DRVIIJ digital interface, a DRVIIW DMA interface, and miscellaneous

other serial and networking interconnects.

The AXVIIC A/D provided limited sampling capability which was

used primarily for monitoring the tunnel speed and other experimental

parameters prior to the actual data taking.

The DRVIIJ digital interface and KWVIIC programmable clock, in

conjunction with a custom built stepper motor translator and driver

system provided computer control over the traversing system.
12

2.3.2 Primary A/D

The primary A/D used for the experimental work was a TSI IFA200

12 bit simultaneous sample i0 channel unit. This A/D was configured

to provide an input signal range of 0 to +5 volts, giving a least significant bit level of 1.22 millivolts. The IFA200 is a self contained

unit providing it's own internal clock and sampling circuitry. Interface to the 11/73 computer was through a DRVIIW DMA interface, providing a maximum single channel sample rate of 50 KHz, and a total

throughput of 250 thousand samples per second. The IFA200 used was a

true simultaneous sample A/D, consisting of I0 independent A/Ds which

were driven by a common sample signal. An analog delay adjust in the

sample signal was provided, and for all data in this study the A/D was

calibrated to provided a channel to channel sample uncertainty

equivalent to a 0.0001 mm convection length at the typical free stream

velocity of 13 mps.

2.3.3 Phase pickup

The phase trigger used to conditionally sample the forced data in

this study was provided by means of a metal tab passing between the

sensing elements of an optical pickup, see Figure ii. This arm was

mounted at a radius of I00 mm giving a mechanical positional uncertainty of approximately 0.2 degrees.

An electrical schematic of the pickup and conditioning circuit is

shown in Figure 16. The electrical output from the pickup is
13

amplified, fed into a one-shot multivibrator, buffered to standard TTL

levels and fed to the IFA200 A/D. The one-shot multivibrator is used

to provide a positive output duration of approximately 30% of the

forcing period. The overall uncertainty caused by the electrical system is negligible for the forcing period used.

2.4 Data Processing

2.4.1 Single Wire

The hot wires were all calibrated in the low disturbance free

stream flow of the tunnel. The physical location x - 150. mm and

y - -250. mm was used for the calibrations. The calibration data were

obtained as the mean of 2000 samples taken at 200 Hz. A single callbration data set consisted of measurements at 7 or more speeds ranging

from 1.0 to 13.5 mps. A pitot static tube was used in conjunction

with the MKS baratron pressure transducer to provide the reference

velocity.

The calibration data were used to define the coefficients (A,B,n)

in the modified Collis and Williams relation,

E2 _A+BxQ n (2)

where E is the measured wire voltage and Q is the tunnel speed.These

A, B, and n were values determined by using an ordinary least squares

method to determine A and B given n, and minimizing that relation as a
14

function of n.

All processing of the anemometry data was executed by first converting the measured voltages to velocities using the calibration constants on a data point by data point basis, and then performing

statistical processing on the resulting velocities.

2.4.2 Compact Vorticity Probe

2.4.2.1 Calibration

The calibration of the compact vorticity probe was also executed

in the low disturbance free stream flow of the tunnel at X - 150. nun

and Y - -250. mm using a pitot static tube and the Baratron pressure

transducer as a velocity reference. Sampling details for a single

calibration point were the same as those used for a straight wire;

however, as a result of the processing algorithm used, the calibration

data were required at a number of angles (8) with respect to the flow.

These data were taken at angles from -36 ° to +36 ° in 6 ° steps.

Since small differences in the velocities measured by the wires

can translate into large gradients because of the compact size of the

probe, improved calibrations were obtained by using one of the

straight wires rather than the pressure transducer as a velocity

reference. This was accomplished by first fitting A,B,n values to the

two straight wires for all angles, then selecting the wire with the

minimum standard deviation (based on velocity) and using the resulting
15

coefficients for that wire along with the calibration data to generate

the calibration velocities for the other three wires of the probe.

Calibration constants were then determined for all wire and angle combinations using the new velocities.

The variation in the hot wire response with respect to flow angle

was modeled by defining a voltage ratio [ as follows:

[ - z(v) / E(O) (3)

where E(7) is the hot-wire voltage at the probe angle 7 and E(0) is

the hot-wire voltage at the probe angle of 0. This function is nonlinear and strongly speed dependant. At any given speed the function

can be modeled as a polynomial. Since the function has an inflection

around f-l.O, it is advantageous to redefine the voltage ratio as an

offset value:

. - E(v) / Z(O) - l.O (4)

which allows 7 to be accurately modeled as a rational polynomial of

the form:

4

7 - C5_5 + C4_ + C3 _3 + C2 W2 + CI_ + CO (5)

where C5,C4,C3,C2,CI,C 0 are fitted coefficients. Typical rms values

of this fit are 0.3 ° . Representative calibration data and fitted
16

curves are shown in Figure 17.

Since equation 5 is a strong function of velocity, see Figure 17,

a separate set of coefficients were determined at 51 discrete speeds

equally spaced over the range from the minimum to the maximum calibration speed. The _ value at each speed and angle is computed from calculated voltages using the A,B,n values for the wire at that angle and

the arbitrary speed.

2.4.2.2 Processing

2.4.2.2.1 Determination of the u,v components

The x and y velocity components of the flow (u and v) can be computed by knowing the velocity magnitude in the xy plane, and the indicated velocity from one of the slant wires. The velocity magnitude

was taken as the average of the indicated velocities from the two

straight wires, Q3 and Q4" Once this velocity had been determined,

the flow angle 7 could be computed from either of the slant wires. In

practice the angle was computed using both of the slant wires, and

this angle was compared to the calibrated angle range. If the indicated angles were both within the calibrated range, (-36 ° < 7 < +36°),

the average is used. If only one computed angle was outside of the

calibration range the value which lay within the calibration range was

used. If both angles lay outside the calibration range the 7 - f(w)

polynomial for the wire most normal to the flow was extrapolated to

yield the angle, and the point was marked as suspect.
17

Since the response of the vertical wires does, to a slight degree, depend on the flow angle, two calculations were made for each

wire at each point in the data set. For the second calculation the

angle information from the first calculation was used to determine the

calibration constants A(_), B(7), and n(7) to be used in the determination of Q3 and Q4"

2.4.2.2.2 Accuracy

The accuracy of the processing algorithm was verified for each

set of experimental data by processing time series data taken in the

free stream during calibration. In all cases the computed flow angles

were within 0.5 ° of the physical probe angle.

The validity of the extrapolations of the _ - f(_) relation were

verified by taking time series data in the calibration stream at probe

angles with respect to the flow direction of ±6 ° beyond the normal

calibration range. The extrapolated values, so computed, were accurate to within ±i.0 =.

2.4.3 Phase Averaging

Phase averaged data acquisition was performed by sampling both

the analog input channels of interest and the conditioned phase signal

from the forcing mechanism optical pickup at a high data rate.The

resulting time series was then divided into intervals based on the

pickup signal. Each of these intervals, representing one forcing
18

period, was then divided into 16 equally spaced intervals and the

phase average sample extracted from the time series at these points.

As an example consider a block of data where the leading edge of the

pickup signal occurred at data points i and 384. Dividing the forcing

period into 16 intervals, only points I, 25, 49... would be saved;

corresponding to phase locations of 0., 22.5, 45.0... degrees.

For this study, data were taken at 5000 samples per second, and

the mean forcing period was 62 milliseconds. This gives an uncertainty of ± 0.6 degrees in any specific phase value due to the sampiing rate. Since the subdivision of the intervals over which the phase

averaging was performed was based on one revolution of the arm, uncertainties due to long term, (time scales greater than one forcing

period) variations in motor speed were eliminated. In addition this

method allowed for accurate monitoring of the actual motor speed,

since the length of each period sampled is also saved. For all of the

data presented in this thesis, the variation in the periods was on the

order of the sampling time of 0.2 milliseconds, or 0.3% of the mean

period.
CHARACTERIZATION OF THE EXPERIMENTAL CONDITIONS

3.1 Boundary Layer

3.1.1 Bleed setting procedure

The boundary layer formed during the final contraction was

removed through a bleed slot as shown in Figure 5. The initial attempt at a setting for the bleed port flow rate was accomplished

visually by using tufts at the bleed port; those observations proved

difficult to interpret with the desired precision. In an attempt to

achieve a better bleed setting, velocity profiles were taken just

upstream of the bleed slot using a single hot-wire probe. The bleed

flow was then adjusted to yield a locally symmetric velocity profile

about the leading edge of the splitter plate. Upon examination of the

boundary layer profiles at the separation lip, it was found that this

approach yielded too large a bleed flow, and a distorted downstream

velocity profile.

19
20

The final approach taken to set the bleed flow was to adjust the

bleed flow rate such that the an optimum turbulent boundary layer profile was obtained at the separation lip.

3.1.2 Turbulent Characteristics

3.1.2.1 At separation

The boundary layer data were plotted in law of the wall coordinates, U + and Y+;

U+ - u__ (6)

U

f

+ YUr (7)

y -- _

V

U - U0[_] I/2

(8)

The local skin friction coefficient (Cf - _w/O.5pU_) was

determined from a Clauser [Clauser 1951] plot. The momentum thickness, 8

was determined from

0 - I- dy (9)

W

and the displacement thickness, 6 was determined from
21

6*f0[ - i- dy (i0)

Clauser plots for the separating boundary layer are presented for

the unforced case in Figure 18 and for the forced case in Figure 19.

The resulting Cf values were 2.95xi0 -3 for the unforced case and

3.03xi0 "3 for the forced case. The unforced boundary layer had a

momentum thickness at separation (00 ) of 6.72 mm, with a displacement

thickness 6 of 9.11 m, yielding a shape factor of 1.36. For the

forced condition 00 was equal to 6.02 mm and 6 was equal to 8.21 mm

yielding a shape factor of 1.36. U at separation was 0.485 for the f

unforced condition and 0.492 for the forced condition. In addition

turbulent intensity measurements in the boundary layer yielded a

imum value for u'/Uf equal to 2.65 in the unforced case.

max -

Mean profiles for the separating boundary layer, for both theunforced and forced condition, were plotted in law of the wall coordinates (u+,y +) [Coles 1962] as shown in Figure 20. As indicated in the

figure, the data show very good agreement with the law of the wall,

I +

U+ 5.6 lOgl0 y + 4.9 (ii)

over the log law region. This agreement, along with a shape factor of

approximately 1.4 and a u'/U T value of approximately 2.5 indicate an

equilibrium turbulent boundary layer [Hussain 1983].
22

3.1.2.2 Prior to separation

The momentum thickness 0 and friction velocity (Ur) for the"

developing boundary layer are shownin Figure 21 and Figure 22. As

indicated in Figure 21 the boundary layer follows the expected pattern

of growth up to a streamwise location of x/00 - -i.0. A decrease in

the momentum thickness is indicated at the separation lip; this effect is presumably due to acceleration at the separation lip.

The boundary layer growth rate, (dS/dx), can be related to the

wall friction coefficient for an equilibrium boundary layer as:

cf " 2 d_O8 dx (12)

This comparison was made with the experimental data over the

range -30 < x/80 < -i.0 and found to be in poor agreement. Given the

limited streamwise span of the data, accurate resolution of dS/dx

would have required a determination of 0 to a precision not possible

with the experimental configuration used. The uncertainty in the

determined 8 values is hypothesized to be the cause of the poor agreement of the data applied to (12).
23

3.2 Forcing system

3.2.1 Forcing frequency

The forcing frequency for this study was chosen based on the

prior work of Mensing and Fiedler [1985]. Their studies showed a maximum intensity of _ at a saturation length X s, defined as Xs - f/Uo'

approximately equal to i. The forcing frequency used in this study,

16.2 Hz, was chosen based on this criteria to give a saturation location of 0.8 m, or 30% of the test section length. The resulting

Strouhal number based on the separating boundary layer thickness,

(f00/U0), was 0.0081. The natural frequency of the shear layer, as

exhibited by fluctuations in the entrainment field, was 3.5 Hz or

fg0/U 0 - 0.0018; see Foss et.al. [1987].

The data sampling and processing method provided data on every

forcing period taken during this study. The rms fluctuations of the

period were below the measurement uncertainty involved in the sampling

(0.2 msec).

The frequency domain content of the forcing system was examined

by placing piezo-electric accelerometers on the forcing piston at a

variety of locations. Power spectra of the measurements taken at the

piston center, and either extreme end are shown in Figure 23 through

Figure 25. As indicated the piston motion has little harmonic content

at the center of travel. A small amount of energy is found in
24

harmonics at either end; presumably

deflections of the forcing piston.

3.2.2 Effect of the forcing on the flow

these are a result of minor

An accurate determination of the forcing level, by a given forcing apparatus, is one of the major problems in experimental work on

forced flows. For the present study, two approaches were taken to accurately quantify the effect of the forcing on the separating boundary

layer. Measurements were made with no primary flow in order to isolate the effect of the piston forcing on the air mass in its neighborhood, and measurements were made in the separating boundary layer

under nominal test conditions.

3.2.2.1 U 0 - 0 Data

Both velocity and pressure measurements were made in the

neighborhood of the separation lip with no mean flow. Velocity measurements were made using a single wire hot-wire anemometer; pressure

measurements were made utilizing a microphone and pinhole chamber arrangement.

For

a drop-test calibration technique;

information on this technique.

taking orientation, (with respect

the hot-wlre measurements, calibrations were performed using

see appendix Appendix B for more

The wire was calibrated in the data

to the gravitational field), in

order to minimize the error introduced by the natural convection field
25

of the hot-wire. The results of the

presented in Figure 26 through Figure 29;

therein are in units of meters per second,

hot-wire measurements are

the velocity data presented

and the coordinates are

non-dimensionalized with respect to the piston width (Wp). As expected, there is a strong shadow effect of the separation lip.

Results for x>Osuggest a strong jet pumping effect which generated a

mean entrained velocity in the -y direction.

The technique used for the pressure measurements is documented in

Appendix C, and tabular results are presented in Appendix D. The data

showed no significant change in the amplitude of the rms pressure

fluctuations over the measurement domain; the technique used apparently registered the acoustic wave generated by the piston.

3.2.2.2 Perturbations of the separating boundary layer

The forcing amplitude can be characterized by three

non-dimensional velocity measures; the rms velocity of 'the piston,

the magnitude of the imposed velocity in the direction of piston motion, or the velocity change at some point in the separating boundary

layer. Specifically, all of these velocities can be

non-dimensionalized with respect to the free stream velocity. The

forcing levels for the current study were large with respect to the

prior work of Disimile [1984], and corresponded to the larger amplitudes used by Fiedler and Mensing [1985]. Specific levels are shown

in Table I.
26

Table i - Forcing Amplitude Measures

Forcing Measure Amplitude

Vpiston/t/0 0.021

vf/U 0 0.015

-2-2 1/2

(vf+uf) /U 0 0.045

As would be expected, there is some attenuation from the piston

face velocity to the induced v velocity (vf) in the separating boundary layer. The large difference in the maximum velocity change in

-2-2 1/2

the flow ((vf+uf) /U0) relative to the magnitude of the induced v

velocity (_f/U0) should be noted.

If the physical size of separating boundary layer is relatively

small, for example 80 - 1.14 mm in the Fiedler and Mensing [1985]

study, hot-wire velocity measurements are limited to those which can

be made with a single wire probe. Since a single wire probe resolves

a planar velocity magnitude, an important distinction should be made

between the total induced velocity change and the induced velocity

change in the transverse direction; the former being larger due to

steerage of the sharp velocity gradient near the wall. As indicated

in Table i, for the present study the ratio of total to transverse induced velocity fluctuation was 3 to i.

Due to the small physical size of the separating boundary layer

in other studies magnitudes are often expressed using the former

measure since only single hot-wire probes can be utilized. This
27

should be clearly delineated from the magnitude of the induced v velocity, the former being muchlarger in magnitude due to steering of the

sharp velocity gradient near the wall.

3.3 Entrainment

The throttle plates were adjusted to give a "natural" shear

layer, or dU/dX _ 0.0. The value of dU/dX was determined from measurements of u in the high speed nonvortical flow at two streamwise locations as indicated in Figure 30. The resulting value of dU/dX

represented a velocity defect over the indicated range of less than 1%

of the free stream velocity.

3.4 Probe Positioning

Determination of the probe position for the data taken in the

boundary layer and near the separation point for the shear layer is

critical due to the steep velocity gradients in the Y direction.

A preliminary attempt to verify the wire location by heat

transfer to the wall was attempted. However, due to the minimal

thermal effect provided by the wall it proved robe difficult to

approach the wall close enough to get an accurate position and still

not come in physical contact with the wall. A number of calibration

tests showed that coming in contact with the wall, even slightly, altered the characteristics of the wire; see Appendix A.
28

The final positioning method used in the case of the straight

wires for the boundary layer and near separation point data was an

optical one. A point light source was used to illuminate the wire at

an angle of approximately 14 degrees. When the wire was near the wall

it then cast a shadow which could be measured through use of a sighting device viewing normal to the wall. This allowed the wire to be

accurately positioned to 0.2 mm from the wall surface. In each case

the wire was placed slightly closer to the wall than this, then the

traverse was driven so as to move the wire away from the wall until

any mechanical play in the traversing system had been taken up. The

amount of play was nominally .2 mm.

For positioning of the compact vorticity probe the wall shadow

approach could not be used due to the construction of the probe. For

the runs using the compact vorticlty probe, the probe was positioned

by placing it directly behind the separation step at X - 5. mm and

Y - 0. mm. The Y location was ascertained by means of a sighting

device positioned directly downstream of the separation point.
4

RESULTS AND DISCUSSION

4.1 Response of the upstream boundary layer to the forcing input

Mean velocity distributions, u(y), were obtained in the boundary

layer region for -30 S x/80 s 0. These data were evaluated using the

Clauser chart technique (Clauser [1954]) to determine the wall shear

stress; see Figure 22. As shown in Figure 20, the mean velocity profile at the separation point for the forced and unforced conditions

were only slightly different. However, at x/80 - -5 the mean profiles

for the forced and unforced conditions were essentially the same; see

Figure 31. The effect of the forcing at x/80 - -5 was, however, still

visible as a difference in the phase averaged values; see Figure 32.

Farther upstream, at x/80 - -i0, the effect of the forcing is minimal;

see Figure 33.

29
30

4.2 The Velocity Field in the Neighborhood of the Separation Lip

4.2.1 Meanvelocity profiles for the unforced condition

Velocity distributions for the forced and unforced conditions,

u(y) and v(y), were obtained for the separating flow at x/00 - I and

x/80 - 3; see Figure 34. The mean velocity profile of the transverse

velocity component for the unforced condition, v(y), is presented in

Figure 35. As indicated in the figure, the transverse velocity has a

mean positive value near y - 0, and the magnitude is greater at

x/80 - 3 than at x/00 - i. This behavior is apparently the result of

the cavity formed by the piston and bounding plate assembly, which

creates a low pressure region on the downstream side of the separation

lip.

4.2.2 Mean velocity profiles for forced condition

Mean velocity profiles of the transverse velocity component for

the forced condition, <_>(y), are presented in Figure 36 through Figure 39. Also shown for reference on these figures is the physical

geometry of the forcing piston for the indicated phase condition. As

indicated in Figure 36, at 4 - 0° the piston is fully extended towards

the flow, <v> is larger than the unforced case, and the difference is

more pronounced at x/00 - 3 than at x/00 - I. As the piston retracts

through 4 - 90° to 4 - 180° , Figure 37 and Figure 38, the difference

between <_> and _ is increased. At _ - 270 °, Figure 39, the piston is

at its maximum velocity in the -y direction and while <v> = _ at
31

xlOo = 1,

x/00 - 3.

there is still a significant increase of <_> over _ at

In order to better identify the phase behavior of the forcing on

the flow, a velocity difference 6u can be defined as:

6u = <u(x,y,_)> - <u(x,y)> (13)

where <u(x,y)> is the average over all phase angles.

To clarify the response of the separating shear layer to the

forcing input, 6u and 6v are plotted as a function of the phase angle

_; see Figure 40 through Figure 47. At y/00 - 0, Figure 40 and Figure 41, _u is much larger than _v as a result of the lateral displacement of the fluid with a large velocity gradient. At y/e 0 - -i _u has

decreased with respect to _v and the difference between _u at x/60 - i

and at x/00 - 3 has been reduced. At y/00 - -3 the magnitudes of

_u and 6v are approximately equal and show little change from x/00 - I

to X/Co-3. In the outer edge of the forming shear layer, y/e 0 - -9.5,

6u is nearly zero while 6v indicates a strong influence of the forcing. These data suggest a lateral displacement of the separating

boundary layer in the _+y direction by the action of the forcing. This

hypothesis leads to the definition of the quantity (, defined as

£u (14)

( - £v d<u>

dy
32

which was computed for both the x/80 - i and x/90 - 3 locations; see

Figure 48. For an idealized condition of a lateral displacement of a

velocity gradient _ should be a constant. As indicated in Figure 48,

f is approximately constant for i _ x/00 _ 8.

4.2.3 Kinematic Reynolds stress in the separating shear layer

The kinematic Reynolds stress distribution for the separating

flow, along with data for an equilibrium turbulent boundary layer

(Klebanoff [1954]), are presented in Figure 49. As indicated in the

figure there is little change in the high speed region, both the data

at x/90 - I and x/80 - 3 are in good agreement with an equilibrium

boundary layer. In the region -4 s y/80 s -0.5 the relaxation of u'v'

as a result of the removal of the wall is indicated; the increase of

u'v' in the region -0.5 s y/80 s I for the evolving shear layer can

also be seen.

4.3 Evolution of the unforced and forced shear layers

4.3.1 Mean velocity profiles

Mean and phase averaged velocity data were obtained using single

wire measurements for the region I _ x/00 _ 230. Isotachs for the unforced conditions are presented in Figure 50 and Figure 51, along with

similar amplitude results from the Fiedler and Mensing [1985] study.

As can be seen from the figures, the strongly forced shear layer exhibits a stepped growth rate, with a plateau at 1.0 < (X-Xs)f/U 0 <1.5.

It is pertinent to note the qualitative agreement between the current
33

study, (ie. Figure 51), and the prior work by Fiedler and Mensing

[1985], (ie. Figure 52). In the latter case the strong levels of

forcing led to a premature separation of the boundary layer which was

not present in the current study.

Mean velocity profiles for the single wire data; average unforced, long term average forced, and minimum and maximum phase average forced, are presented in Figure 53 through Figure 65. The trends

in these data are most easily seen in the large x/80 data where the

differences between the long term averaged forced data and the unforced data, along with the differences between the minimum and maximum phase averaged values of the forced data, are quite apparent.

Little effect of the forcing is seen in the mean profiles at x/90 - I;

the gradual evolution between this location and that of x/80 - 230 can

be easily traced from the figures.

The minimum and maximum values for the forced condition exhibit a

dramatic acceleration and deceleration characteristic on the high

speed side of the shear layer in the downstream region; see Figure

60. It is inferred that the accelerated state is similar to the "inviscid acceleration past an obstruction" since the phase averaged

velocity values, <_> are significantly larger than U 0. The data for

the unforced condition (at the same streamwise location as Figure 60),

indicate the lack of a similar effect; see Figure 66. The corresponding minimum values for the forced condition are are also

inferred to represent pressure effects.
34

4.3.2 Phase averaged data

The evolution of characteristics in the forced flow field can be

readily seen from phase averaged isotachs of the single wire data.

Plots of 6u (as defined in 13) versus the phase angle 4 are presented

in Figure 67 through Figure 79. The characteristics of these data can

be plausibly related to the forcing effects as noted in the following:

a) For the region downstream of the separation lip,

I _ x/00 S 5, Figure 67 to Figure 69, the positive (4 = 120)

and negative (4 = 270) locations represent the effects of

the piston motion in the +y and -y directions respectively.

The primary effect of the forcing at this point is a steering of the large mean velocity gradient; as shown in the

figure the influence region is quite limited in the y direction. At x/80 - 5, the appearance of isolated correlation

contours in phase space can be noted. For the sake of

brevity these will be referred to simply as correlation contours in the following discussion.

b) For i0 S x/80 _ 25, Figure 70 to Figure 72, the positive and

negative correlation contours are better defined and the region of influence is wider. At x/80 - 25 the centroid of

the correlation contour is located closer to the high speed

side of the shear layer than it was at x/80 - i0.
35

c) For 40 S x/00 S 77 (Figure 73 to Figure 75), the magnitudes

of the correlation contours reach a maximum and the formation of correlation contours of opposite sign on the low

speed side of the shear layer is first noted. The correlation contours on the high speed side of the shear layer will

be referred to as the primary correlation contours, while

those on the low speed side will be referred to as the

secondary correlation contours.

d) For 115 s x/80 _ 153 (Figure 76 to Figure 77), the primary

correlation contours have migrated farther in the direction

of the high speed side; the intensity of the primary correlation contours has continued to decrease, while that of

the secondary correlation contours has increased.

e) For 192 s x/00 _230, Figure 78 to Figure 79, the intensity

of the primary correlation contours has dropped below that

of the secondary correlation contours; the secondary correlation contours dominate the field.

The distinctive feature of the correlation contours allow a convection velocity to be defined at a given downstream location. Specifically the phase shift between the correlation contour peaks at two

x/80 locations, see Figure 80, can be related to a time difference using the forcing period as follows:
36

t2-tl - [ _2-_I 36----6-+ 360 n ] x _f (15)

where n is an integer number of forcing periods. If the data locations are sufficiently close together, as is the case in the current

study, n is 0. From this time difference and the spatial distance

between the data sampling locations, a convection velocity for the

disturbance can be defined as:

X2-X I

u (16)

c t2-t I

Using these procedures, the convection speed was determined for

the data locations x/80 a 15; see Figure 81. The increasing U c

values as function of x/80 are rational considering the previously

noted migration of the primary disturbance towards the high speed side

of the shear layer.

The width of the disturbance region A(x) can be arbitrarily defined using the integral quantities

I 16ul(y-yc)2 dy d4

A2 - 0 -_ (17)

2_

_0 J -

where Yc is the centroid of the disturbance field, as defined in (18).
YC --

2_

0 -_

2_

0 -_

37

(18)

The data for A/e 0 as a function of x/00 are presented in Figure

82 along with the growth rates of 6(x) for the forced and unforced

conditions.

Empirically, the growth of the disturbance field can be described

as a power law relationship:

_180 - 0.0063 (x/eo)1"64 (19)

for 0 _ x/e 0 S 60.0 and as a linear relationship:

&/80 - 0.0784 x/80 0.319

(20)

for 77 s x/80 _ 192.

The discontinuity of the growth rate at x/80 _ 60 is apparently

related to the indicated saturation (le. the peak 6u value) at this x

location. The indicated linear growth rate is nominally the same as

the growth rate of 8(x) over the same domain.
38

Fiedler and Mensing [1985] also observed a saturation effect;

theirs was defined in terms of the maximumof the transverse velocity

components. Defining this streamwise location as Xs, their result

showed that for a forcing level which was comparable to that used in

the present study,

f(Xs-X 0)

U 0

0.75 (21)

where x 0 was defined as a virtual origin. This virtual origin was defined from their data of x - x (f) at a given amplitude It was obS S

served that (l/f) is a linearly increasing function of x . An

s

extrapolation of this relationship to (I/f) _ 0 defined the x0 value

for the given forcing amplitude.

An apparent origin cannot be determined herein since a single

frequency was used in the present study. In order to compare the two

investigations, it can be assumed that only kinematic effects are

represented in the f, Xs, and U 0 relationships and a comparison of the

values (fxs/U0) can be made for "equivalent" forcing amplitudes.

The present observations permit the maximum value of

-2uf + -2vf ]1/2 / U 0 - 0.045 (22)

to be determined at x/00 - I. Similarly, Fiedler and Mensing [1985]

present data from a single hot-wire immediately downstream of the
39

slot. Their values of (0.065) and (0.0065) bracket those of the

present study.

Defining a saturation length for the current study based on the

maximum6u values results in a value of x - 0.5 m. Hence,

s

fx

s 0.62.

U 0

(23)

Using the Fiedler and Mensing [1985] (I/f) = x s results and interpolation for the forcing amplitude parameter, a frequency of 13.2

Hz is estimated for the saturation length of the current study:

0.5 m. The corresponding fxs/U 0 value is 0.60.

The striking agreement between these two results, in spite of the

significant differences in the forcing geometries and in the Reynolds

numbers of the separating boundary layers (5500 cf 830), supports the

assumption that the forcing process is kinematic in character.

4.4 Response of the entrainment field to the forcing input

Velocity vector measurements of the entrained flow were performed

in the region i00 _ x/80 _ 200 for both the unforced and forced conditions. The data for the unforced condition and the mean forced condition are presented in the form of a velocity vector plot in Figure 83.

As indicated in that figure, there is a noticeable mean steering effect of the entrained fluid beyond the active, (ie. vortical), shear

layer. Prior investigations in the same facility, All et.al. [1985],
40

verified a uniform velocity at the exit of the entrainment

ing section, i0 < x/00 < 420, for the unforced condition.

served meansteering is consistent with other observed data

facility as discussed in the following.

conditionThe obfor the"

An evident feature of the isotachs for the forced shear layer is

their greater width on the low speed side of the shear layer. This

clearly suggests that a greater mass flux exists at a given downstream

location. Other evidence, however, does not support this interpretation. Specifically, with the fan motor set to a fixed operating

speed, it was observed that the free stream velocity of the primary

flow (U0) remained unchanged between the unforced and forced conditions. Since the U 0 value is dictated by the pressure difference from

the atmosphere to the test section and since the constancy of the: i)

pressure rise from the receiver (ie., the domain that receives the

flow from the test section and delivers it to the fan) to the atmosphere and ii) the fan rpm, dictate a constant operating point on the

characteristic curve, it is inferred that the volume flow rate through

the fan is a constant. It is therefore concluded that the magnitude

of the entrainment flow rate into the test section is not affected by

the forcing.

These separate observations can only be compatible if there is a

significant steering effect of the entrainment streamlines as shown

schematically in Figure 84. Specifically, with forcing, the

entrainment fluid is added to the active shear layer and the flux of
41

vortical fluid at a given x/60 value is larger than that of the unforced case. Similarly, the streamline trajectories of the unforced

case deliver a significant volume flow rate of non-vortical fluid past

a given x/00 plane, shownas _m in Figure 84

As a result of experimental difficulties, identified below, quantitative measures of the steering could not be obtained to verify the

above hypothesis, However, the qualitative trends of the data are apparent, and they support the proposed flow model of Figure 84.

Previous flow visualization measurements in the entrainment region, Foss [1987], indicated a mean flow angle for the entrained fluid

of approximately 60 ° . Based on this data, quantitative measurements

were made in the entrainment region using a compact vorticlty probe

oriented at an angle of 60 °. Additional surveys were made at probe

orientations of 45 ° and 90 ° . The resulting data indicated a strong

steering effect, causing the measured velocity to tend to be aligned

with the probe body. This effect could be caused by aerodynamic influence of the probe body, momentum wake effects of the wire support

prongs, thermal wake interference between the wires, or perhaps a combination of all three. The exact cause of this effect is not clear at

the time of this writing.
5

CONCLUSIONS

A relatively small perturbation of the separating boundary layer

evolves into a strong perturbation of the developing shear layer.

The effect of the forcing on the separating boundary layer for

the geometry of the current study is twofold: i) A lateral displacement of the mean velocity profile for y/0 0 > I and ii) an unsymmetrical widening effect for y/8 0 < 0. For the region 0 < y/0 0 < I a

combination of these effects is inferred.

For equivalent forcing amplitudes, the qualitative evolution of

the shear layer is consistent with the prior work of Fiedler and Mensing [1985]; specifically, quite similar values of (fxs/U 0) were observed in spite of quite different values of the forcing methods and

separation lip geometries.

42
43

Phase averaged variations (6u) about the meanvalues of forced

flow (6u) exhibit closed contours in phase space. A convection velocity of the closed contours can be computed from the phase shift

between two axial locations (see Figure 81). A width measure of the

disturbance field can be defined as a moment of 6u in phase space (see

Figure 82). The apparent motions of the closed contours are consistent with the trends observed for the computed convection velocity.

The entrainment region outside the active shear layer exhibits a

mean steering of the flow field for the forced condition relative to

the unforced condition. This mean steering is consistent with other

observed data for the facility.

The well documented conditions at separation for this study,

specifically the detailed measurements of u and v as a function of

forcing phase angle, should provide a good test case for numerical

simulations.
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X, = 153.8 8 _p, = 249.

Figure 80 Determination of disturbance phase location
_30.00()]--,_--,--_- 3 • ,- ,.._ , . !

40.000 1

20.000-

0.000

-20.000.

I

I

-40.000 ..... I ..... _ .... ", = ..... i ..... I .....

0.0 60.0 120.0 180.0 240.0 3,00.0 360.0

X I = 115.4 8 91 = 55.

>-

60.000 ..... I ..... ,,' .... i ..... i ..... i .....

I

I

4o.ooo. • I

I

I

20.000. -o.ole

0.000

-20.000.

-40.000.

0.0 60.0 120.0 180.0 240.0 300.0 360.0

X= = 153.8 8 _, = 249.

_P

Figure 80 - Determination of disturbance phase location
124

i I I I I i I I

o o

0_ f',-

d d

' ' I '

0

d

0n/:n

I I i I I I

o

I.f'}

d

.,r,t)

0

--0

0

-0

0

- _

_u

0

o >

X _

m

0

-0 o

- >

0

o

i

0

$..4

0

0

0

d
125

o

C)

><

_0

=

0

>

cO

4.J

:3

i

¢,q

oo

I

(D
126

I I i l

l I I

d

' I ' I ' ' ' ' I ' '

7

..._ .,,_ ,w---ff

i i I I i i

0 0

d o

I i I I i I I !

0

c5

fit]

0

0

-0

0

c_

0

0

o

,--4

CD

..-i

.,4

0

0

0

0,-4

d

I
127

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

J

xe

l -l-l-l-l-l- F

I

Unforced Gondi t ion

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

/

1 1

X6

-1 -1- I- I- F

Forced Condi t ion

Figure 84 - Schematic representation of entrainment mass flux
APPENDICES
APPENDIX A

EFFECT OF WALL CONTACT ON HOT-WIRE CHARACTERISTICS

A hot-wire anemometer, being a thermal device, is strongly effected by the proximity of a thermally conducting wall. Even when

heat loss effects are minimized through use of a poorly conducting

wall there is appreciable heat loss to the wall at small wire-to-wall

distances. If one of the prongs, which supports the copper plated 5

tungsten wire, comes into contact with the wall, the heat loss is

strongly intensified. This effect can be used to accurately locate

the position of the wire by moving the wire towards the wall until a

sharp increase in the anemometer output is noted. This positioning

method was evaluated for the current study; it was abandoned after it

was discovered that bringing the wire into contact with the wall modified the wires characteristics.

To quantify the variation in wire characteristics, a number of

consecutive calibrations were performed with the same wire. All

calibrations were executed over a period of 3 hours, during which time

129
130

the temperature of the room remained constant to within i ° C. The

subject wire had been operated for several days, and it was operated

for over two hours in the calibration flow before the first calibration. The wall under consideration was Formica faced, and meticulously cleaned using isopropyl alcohol prior to the study. In each

case the wire was calibrated: i) one or more times in the calibration

stream, ii) positioned using the wall contact method, and iii) moved

back into the calibration stream and recalibrated. The above procedure was executed for a numberof cases; see Table A.I for the

resulting data. The calibrations indicated with a "yes" under the

heading contact in Table A.I cameinto contact with the wall prior to

the calibration.

The velocity error in Table A.I was obtained using the following

procedure. The calibration constants for the first calibration were

used to compute a reference voltage from an arbitrary reference velocity of i0.0 meters per second. The velocity error for each calibration was then evaluated as the difference between the computed flow

speed (using the reference voltage) and the reference velocity of i0.0

meters per second.
131

Table A.I ° Wall Contact Calibration Results

Std.

Run Contact A B n Dev.

A 9.041 3.769 0.41 0.007

B Yes 8.744 3.520 0.42 0.005

C 8.852 3.380 0.43 0.012

D 8.707 3.519 0.42 0.008

E Yes 8.365 3.621 0.41 0.010

F 8.648 3.336 0.43 0.009

G Yes 8.142 3.779 0.40 0.011

H 8.475 3.467 0.42 0.006

I 8.496 3.453 0.42 0.008

J 8.589 3.325 0.43 0.012

K Yes 8.247 3.621 0.41 0.009

L 8.414 3.459 0.42 0.009

Computed Velocity

velocity error

I0.00 0.00

11,98 1.98

12,11 2.11

12,09 2.09

13,00 3.00

13 09 3.09

13 14 3.14

13 23 3.23

13 28 3.28

13.37 3.37

13.36 3.36

13.48 3.48

As indicated in Table A.I, the hot-wlre characteristics underwent

a large change when the wire was brought into contact with the wall.

The mechanism behind the change is unknown. For the current study, it

was of sufficient interest to ascertain that this type of positioning

method was not usable given the experimental configuration.
APPENDIX B

DROP TEST CALIBRATION TECHNIQUE

A novel low speed calibration method was employed for calibration

of the hot-wire used in the zero free stream velocity (U0-0) study.

The general details of the calibration technique have beenpreviously

detailed, Haw [1987]. The specifics on the method used to obtain the

reference velocity for the current study are detailed in the following.

The force balance for an arm in a uniform gravitational field can

be written as

mKsin(0)_

- j (B.I)

where _ is the angular acceleration of an arm of mass m and moment of

inertia J.

132
133

Since the mechanical properties of the arm are constant all of

the constant terms can be merged into a single constant A. Adding additional constants to account for aerodynamic drag (B) and for bearing

friction (C), the resulting force balance is

- A sin(0) - B_2 C_ (B.2)

This equation of motion can be solved numerically to yield the

position and velocity at any time given the appropriate initial conditions. To improve the numerical accuracy, the equation for the

angular velocity of the arm can be expanded in terms of a Taylor

series and applied at discrete time steps to yield:

°i+l- (_ -g+ )-_+_ -_+_i t+ 0i (B.3)

_i+l" (_[ -_ + )-_ + _ _t+_i (B.4)

where the subcripts i and i+l denote the current and the subsequent

time steps and the deriviatives of the velocity are given as:

_' - _ - Asin(0) B_ 2 - C_ (B.5)

_'' - (Acos(8))_ - 2Bax_' C_' (B.6)
134

_''' - w'[Acos(0) + 2Bw'] + w[wAsin(0) = 2Bw''] - Cw'' (B.7)

The constants A, B, and C were obtained by minimizing the mean

square error in position between the numerical simulation, (from (B.3)

and (B.4)), and a series of experimentally measured data points.

Although an analytic solution was not possible, numeric results were

readily obtained using a steepest descent solution method to minimize

the mean squared positional error. The constants obtained in this

manner were used in the numerical simulation for the fall, (B.3) and

(B.4), to provide the calibration velocities.
APPENDIX C

ZERO MEAN FLOW PRESSURE MEASUREMENTS

Measurements of the pressure field induced by the piston were

made for the condition of zero mean flow (U 0 - 0). The forcing frequency was sufficiently high, and the pressures sufficiently low to

make'measurements using a conventional tap and pressure transducer

configuration impractical. A microphone, modified with a surrounding

cavity and pinhole arrangement, was used as detailed in the following.

A Bruel and Kjaer type 4166 wide response condenser microphone

was used with a locally fabricated cavity and pinhole. The microphone

had a free air response of 0 to 20 KHz and an open circuit sensitivity

of 48.6 mv per Pa. The microphone cavity consisted of a 17 mm diameter cylinder 5 mm long with a i mm hole at one end and the microphone

face (17 mm diameter) forming the other end. The resulting resonant

frequency of the chamber (1900 Hz), was well above the measurement

range of interest.

135
APPENDIXD

NUMERICALDATA

The following tables contain the primary experlmentaldata for

the current study. The data in the tables are non-dimensionalized in

the following forms:

a) The velocity measurements of the active shear layer and boundary layer are non-dimensionalized with the free stream velocity

(Uo) ; the corresponding data locations are non-dimenslonalized

with the separating boundary layer momentum thickness (00).

b) The measurements of the velocity and pressure for the no-flow

data are presented in dimensional form. The velocity measurements are given in meters per second; the pressure measurements

are given as output voltage from the

both cases the corresponding

non-dimensionalized with respect to

(Wp).

microphone amplifier. In

data locations are

the forcing piston width

136
137

Table D.I - No Flow Hot-wire MeanVelocities

X/Wp

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5 -I0.00

1.5 -23.08

-2.9 38

-I.0 - 38

.0 - 38

1.0 - 38

2.9 - 38

5.0 - 38

-5.0 -1 O0

-1.0 -1 O0

.0 -I.00

1.0 -1.00

2.9 -1.00

5.0 -1.00

-15.0 -10.00

-10.0 -10.00

-5.0 -10 O0

-1.0 -10 O0

.0 -10 O0

1.0 -10 O0

2.9 -i0 00

5.0 -I0 00

i0.0 -i0 00

Unforced

y/Wp data

.77 .044

.38 038

.00 036

-.38 037

-.77 030

-1.54 040

-3.08 029

-6.15 042

025

030

027

024

O30

034

036

029

042

039

041

041 _

033

046

024

029

032

034

025

037

032

021

018

0.0

•167

142

147

155

152

138

086

060

053

053

024

034

I00

140

086

358

022

036

062

116

087

190

018

022

021

028

036

045

067

ii0

047

Phase averaged data (at angle _)

45.0 90.0 135.0 180.0 225.0 270.0 315.0

151

133

120

113

107

098

067

052

049

051

•024

037

085

098

098

263

023

040

067

081

082

252

018

023

022

027

034

041

061

•103

•044

243

210

178

146

123

098

065

•047

047

049

030

057

163.

134

149

308

025

O59

112

098

I15

309

019

024

023

028

032

037

055

095

•042

211

191

162

139

119

095

064

047

045

048

032

058

148

132

137

356

027

062

109

I00

107

268

019

025

024

029

032

035

052

091

•040

•127

•113

•104

I01

093

080

055

045

045

048

028

042

085

087

084

305

025

046

072

072

073

285

019

025

023

028

032

036

054

097

040

•214

•167

•172

•169

154

122

O68

047

049

05O

026

039

098

135

i01

279

024

041

068

102

096

290

018

023

022

028

034

041

063

IIi

044

341

276

274

269

251

201

104

059

056

053

028

054

191

244

158

301

024

053

105

,180

147

281

018

022

021

029

038

048

074

126

051

319

261

261

261

245

204

115

066

057

054

027

050

189

244

141

297

023

052

102

183

135

243

018

022

021

028

039

049

074

123

051
138

Table D.2 - No Flow Hot-wlre Rms Velocities

X/Wp y/Wp

1.5 .77

1•5 •38

1.5 .00

1.5 -.38

1.5 -.77

1.5 -1.54

1.5 -3.08

1.5 -6.15

Unforced

data 0.0

•002

•001

•002

•004

.002

•006

•001

.005

1.5 -i0.00

1.5 -23.08

-2.9 -.38

-I.0 -.38

.0 -.38

1.0 -.38

2.9 -.38

5.0 -.38

-5.0 -I.00

-I.0 -i•00

.0 -I.00

1.0 -1.00

2.9 -1.00

5.0 -I.00

-15.0 -I0.00

-I0.0 -I0.00

-5.0 -I0.00

-I.0 -I0.00

.0 -I0•00

1.0 -I0.00

2•9 -I0.00

5.0 -i0.00

I0.0 -I0•00

•002

•002

.002

003

005

005

005

003

005

003

002

004

003

004

004

005

005

005

003

004

006

•002

•004

Phase averaged data (at angle _)

45.0 90.0 135.0 180.0 255.0 270.0 315.0

.014 016

•016 013

.017 007

.012 004

.011 004

.009 0O4

.013 007

•013 010

.011 010

•018 017

.003 003

002 002

004 003

013 004

011 010

070 095

004 004

002 .003

003 .005

015 .005

012 .008

.032 .058

.004 .004

.OO5 .O05

.008 .008

.006 .006

.007 •006

•009 •008

•017 .015

.022 .022

.024 .021

.020

.019

.012

• 008

007

0O5

OO5

007

OO8

016

OO3

0O3

O05

012

014

153

•005

•004

•007

.010

•014

.062

•004

•005

•009

.006

•005

•006

•014

.022

.019

.016

•014

•008

•007

•006

•006

•005

•006

•007

.015

O03

003

O05

010

012

II0

•005

•005

•O06

•011

.012

.131

•O04

•005

•009

•006

•005

•006

•014

.022

.018

•008

• 007

• 005

004

004

004

005

007

008

015

003

002

003

004

OO7

054

004

003

• 004

• 004

• 007

• 147

•004

•005

•OO9

•006

•005

•007

.015

.023

.020

•016

•017

•017

•012

•012

.013

.010

•008

.010

016

003

0O2

0O3

018

014

029

004

0O3

_004

.017

•015

.082

.004

.005

.008

.006

.006

.009

.018

.025

.025

.022

.023

.025

.019

.019

.018

•019

.013

.013

.018

O03

O03

005

026

018

021

O04

003

006

028

019

•044

•O04

•005

•007

•007

• 008

.011

.020

.026

.029

O25

O28

O28

019

017

014

019

015

013

018

003

O02

0O7

022

017

033

O04

OO3

OO5

O24

018

029

0O4

0O5

0O7

007

O08

011

.019

•025

.028
139

Table D.3 - No Flow Microphone Mean Voltages

X/Wp

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5

1.5 -i0

1.5 -23

-2.9

-I.0

.0

1.0

2.9

5.0

-5.0

-i.0

.0

1.0

2.9

5.0

Unforced Phase averaged data (at angle 4)

y/Wp data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

.77 2.326 .945 1.352 2.188 3.299 3.354 3.383 2.524 1.243

.38 2.327 1.028 1.409 2.193 3.259 3.288 3.333 2.477 1.329

.00 2.326 1.015 1.442 2.223 3.260 3.295 3.299 2.452 1.320

-.38 2.327 1.145 1.516 2.246 3.233 3.208 3.211 2.427 1.396

-.77 2.327 1.206 1.562 2.204 3.165 3.179 3.191 2.427 1.414

-1.54 2.326 1.274 1.664 2.303 3.178 3.102 3.073 2.349 1.459

-3.08 2.326 1.312 1.644 2.188 3.050 3.110 3.108 2.452 1.547

-6 15 2.326 1.488 1.776 2.232 3.019 2.972 2.966 2.401 1.624

O0 2.327 1.489 1.810 2.272 3.018 2.997 2.903 2.357 1.645

08 2.327 1.667 2.034 2.529 5.063 2.913 2.626 2.044 1.658

38 2.326 1.417 1.728 2.119 2.982 3.101 3.048 2.493 1.661

38 2.326 1.371 1.648 2.115 3.063 3.154 3.126 2.462 1 585

38 2.326 1.289 1.517 2.092 3.156 3.264 3.227 2.506 1,486

38 2.325 1.257 1.480 2.089 3.210 3.291 3.268 2.498 1463

38 2.326 1.293 1.487 2.115 3.202 3.240 3.262 2.439 I 462

38 2.326 1.467 1.620 2.104 3.041 3.064 3.113 2.489 1589

-1.00 2.327 1.444 1.738 2.175 2.950 3.098 3.022 2.423 1 684

-1.00 2.327 1.385 1.618 2.129 3.061 3.160 3.135 2.426 1 574

-1.00 2.327 1.338 1.553 2.080 3.143 3.218 3.162 2.471 1.527

-1.00 2.327 1.329 1.502 2.045 3.191 3.243 3.234 2.502 1.489

-I.00 2.328 1.375 1.488 2.063 3.166 3.233 3.233 2.485 1.511

-1.00 2.327 1.553 1.621 2.189 3.013 3.028 3.083 2.482 1.587

-15.0 -I0.00 2.327 1.584 1.875 2.330 3.012 2.999 2.824 2.306 1.747

-i0.0 -10.00 2.328 1.609 1.838 2.268 3.048 2.976 2.827 2.326 1.717

-5.0 -10.00 2.327 1.602 1.786 2.266 3.027 2.985 2.857 2.371 1.689

-1.0 -10.00 2.326 1.577 1.796 2.223 3.060 2.994 2.855 2.407 1.673

.0 -i0.00 2.326 1.617 1.741 2.211 3.046 2.988 2.897 2.412 1.665

1.0 -10.00 2.325 1.589 1.769 2.196 3.054 2.993 2.891 2.420 1.679

2.9 -10.00 2.325 1.617 1.759 2.182 3.036 2.986 2.893 2.425 1.684

5.0 -10.00 2.327 1.622 1.760 2.162 3.020 2.976 2.891 2.435 1.692

10.0 -10.00 2.326 1.650 1.789 2.160 2.975 2.934 2.847 2.443 1.735
140

Table D•4 - No Flow Microphone RmsVoltages

X/Wp

1.5 .77

1.5 .38

1.5 .00

1.5 -.38

1•5 -•77

1•5 -1•54

1.5 -3.08

1.5 -6.15

1.5 -I0.00

1.5 -23.08

-2.9 -.38

-i.0 -.38

.0 -.38

1.0 -.38

2.9 -.38

5.O -.38

-5.0 -1.00

-I•0 -I•00

.0 -I.00

1.0 -i.00

2.9 -I•00

5.0 -I.00

-15.0 -I0•00

-i0•0 -i0.00

-5.0 -I0•00

-I.0 -I0.00

.0 -i0.00

1.0 -I0.00

2.9 -I0.00

5.0 -i0.00

I0.0 °I0.00

Unforced

y/w data

P

•016

•017

•018

•016

•017

.016

•015

•015

.016

.016

.015

016

017

016

016

017

015

•017

•017

.017

.016

.016

•016

.016

.016

.016

.016

.017

.016

.017

.016

0.0

•292

•275

•254

.235

•240

.222

.184

•156

136

133

169

195

213

236

228

211

165

218

.235

.216

.232

•194

.120

•134

135

138

135

134

131

137

138

Phase averaged data (at angle 4)

45.0 90.0 135.0 180.0 225.0 270.0 315•0

.122

126

112

112

106

097

092

091

081

Iii

.095

.I13

.i12

.106

•i00

•095

•106

•I01

•106

.109

.097

089

092

098

O9O

083

083

073

.073

•081

.089

116

102

iii

102

108

106

099

ii0

105

i00

•103

•106

•098

.101

.097

093

107

I00

I01

093

091

099

103

108

• 092

• 099

.093

•094

.089

.089

.095

.126

.129

.128

•102

•097

•094

.091

.085

•084

.099

•089

.098

.I01

•104

•107

.090

•09O

.091

.097

•098

•098

•Ii0

•091

•088

.086

•078

.085

.075

.074

.073

.076

.199

.172

.155

.158

.151

• 140

.135

• 108

.093

.078

.115

.119

121

134

135

114

117

121

133

134

127

126

.098

•i01

.096

•I00

.093

.091

.093

.097

.097

161

140

132

126

122

114

•I01

•094

.086

.090

•102

113

119

169

164

iii

099

135

•153

•165

.137

.126

.082

.087

.080

.083

.082

.080

•076

.076

.083

195

178

170

160

156

152

•141

.123

.I05

.099

.132

147

134

169

168

137

136

150

154

166

167

136

102

107

108

•105

.i01

.098

•102

•i01

.096

171

174

140

132

126

122

102

•089

.089

•084

•087

•109

.131

.152

.137

.122

095

109

128

134

133

126

084

085

.084

.082

.083

.084

•075

•078

.082
141

Table D.5 Compact Probe u (X/eo-l•O)

x/eo y/eo

1.0 .55

1.0 .37

1.0 .18

1.0 - .00

1.0 -.15

1.0 - .28

1.0 - .43

1.0 - .66

1.0 -.82

1.0 -1.02

1.0 -1.27

1.0 -1.59

1.0 -1.98

1.0 -2.46

1.0 -3.06

1.0 -3.81

1.0 -4.74

1.0 -5.89

1.0 -7.05

1.0 -8.20

1.0 -9.36

Unforced

data 0.0

028 .038

030 .039

048 .055

211 .227

475 .488

569 .576

614 .625

650 .655

.669 .673

.685 .693

.706 .709

.724 .727

746 .752

772 .773

796 .794

830 .827

865 .865

909 .906

.948 .945

.980 .978

.996 .995

Phase averaged data (at angle 4)

45.0 90.0 135.0 180.0 225.0 270.0 315.0

038

039

054

238

508

595

640

672

686

706

•724

•739

.763

.782

.802

.837

.869

.912

.951

.980

.998

039 .062

039 .066

059 .081

254 •243

527 .521

611 .610

652 .654

680 .684

.697 .702

.717 .716

• 732 .737

.749 .752

.768 .771

.789 .792

809 .817

844 .846

879 .883

917 .922

957 .960

985 .986

.062 .054

.069 .057

.090 .078

.223 .203

.491 .461

.590 .560

.638 .615

.669 .646

.690 .669

.700 .688

.725 .709

.744 .728

764 .749

788 .773

813 .799

843 .833

880 .872

920 .915

959 .953

990 .985

999 1.001 1.004 1.002

•046

047

066

206

461

553

606

639

660

678

699

721

742

.764

.790

.824

.862

•909

.947

.979

.999

039

041

060

216

468

559

613

643

663

679

701

720

743

769

790

825

86O

9O5

944

.977

.995

1.0 -I0.51 1.001 1.000 1.002 1.003 1.006 1.008 1.007 1.004 1.001

1.0 -11.66 .999 .999 1.000 1.001 1.004 1.007 1.006 1.004 1.001

1.0 -12.81 1.002 1.000 1.001 1.002 1.004 1.007 1.007 1.004 1.002

1.0 -13.97 1.001 1.000 i.000 1.001 1.003 1.005 1.006 1.004 1.002
142

Table D.6 CompactProbe u (x/00-1.0)

x/e o

I.O

I.O

I.O

i.o

I.O

i.o

I.O

i.o

i.o

I.O

I.O

I.O

I.O

I.O

I.O

I.O

I.O

i.o

Unforced

y/80 data

.55

.37

.18

-.00

-.15

-.28

-.43

-.66

-.82

-1.02

Phase averaged data (at angle 4)

0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

0125

0125

0209

0737

0933

0814

0754

0738

0161 .0157 .0160 .0246 .0253 .0225

0160 .0158 .0167 .0236 .0275 .0235

0228 .0239 .0258 .0266 .0285 .0274

0733 .0753 .0777 .0708 .0683 .0693

0900 .0918 .0901 .0891 .0971 .1002

0803 .0802 .0747 .0771 .0816 .0865

0759 .0709 .0734 .0726 .0748 .0757

0726 .0715 .0723 .0717 .0716 .0745

0748 .0724 .0733 .0721 .0716 .0724 .0722

0734 .0744 .0731 .0712 .0716 .0710 .0730 .0726

0197 .0172

0203 .0173

0246 0250

0745 0755

0946 0948

0835 0832

0787 0781

0788 0722

0743 0748

0720

-1.27 .0712 .0713 .0700 .0697 .0695 .0712 .0723 .0727

-1.59 .0716 .0697 .0706 .0681 .0677

-1.98 .0697 .0702 .0689 .0668 .0650

-2.46 .0676 .0682 .0671 .0669 .0653

-3.06 .0669 .0664 .0648 .0642 .0650

-3.81 .0639 .0642 .0649 .0621 0620

-4.74 .0609 .0616 0606 .0600 0596

-5.89 .0560 .0563 0545 0546 0538

0727

0685 .0695 .0702 0713

0669 .0702 .0707 0692

0663 .0676 .0691 .0683

0651 .0660 .0674 0653

0616 0653 .0666 0651

0611 0595 .0623 0601

0547 0553 .0565 0542

1.0 -7.05 .0481 .0480 0480

1.0 -8.20 .0351 .0363 0350

1.0 -9.36 .0215 .0226 0211

1.0 -10.51 .0116 .0113 0116

1.0 -11.66 .0080 .0084 .0079

1.0 -12.81 .0067 .0064 .0063

1.0 -13.97 .0060 .0059 .0061

0456

0329

0204

0110

0078

0066

0060

0456

0347

0207

0111

0077

0063

0059

0480

0338

0209

0118

0077

0064

0059

0483

0351

0214

0106

0081

0063

0061

0484

0350

0198

0122

0081

0065

0058

0496

0361

0223

0125

0082

0069

0060
143

Table D.7 - CompactProbe v (x/80-1.0)

x/Oo

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

Y/80

Unforced Phase averaged data (at angle 4)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

55 .001

37 .000

18 -.001

O0 •018

15 •024

28 .016

-.43 .010

-.66 .005

-•82 .002

-i•02 •002

-1.27 •001

-1.59 -001

-I 98 - 002

-2 46 - 001

-3 06 003

-3 81 - 003

-4 74 - 003

-5 89 002

-7.05 001

-8.20 001

-9.36 -.001

•001

•001

•000

•019

•030

.021

•014

•009

•008

•007

0O6

004

OO3

003

000

000

001

000

001

000

000

1.0 -i0.51 -.001 -.000

1.0 -11.66 -.001 -.001

1.0 -12.81 -.001 -.002

1.0 -13.97 -.000 -.001

.001 -.000 -.002 -.001 -.000

.001 -.001 -.004 -.002 -.002

.000

.020 .023 .020

.032 .033 .025

.024 025 .018

.018 018 .013

•016 016 .010

.012 013 009

.012 013 008

011 011 009

010 012 008

009 010 007

007 012 008

006 .009 .008

007 .012

.006 .012

.004 .010

.005 .011

•005 .010

.005 .009

.004 .008

•003 .007

.002 .006

.003 .007

.001

.000

.000 -.003 -.006 -.005 -.003

.014 .010 .015

022 .020 .023

014 .012 .013

007 .004 .006

002 -.002 .001

003 -.003 -.001

001 -.004 -.003

001 -.004 -.003 -

002 -.007 - 004 -

001 -.006 007 -

.001 -.008 - 008 -

.000 -.008 008

.010 -.001 -.008 010 -

.010 .003 -.006 009

.009 .004 -.004 007

•010 .004 -.003 007

•011 .006 -.002 005

.009 .006 -.000 -.004

.009 .006 -.000 -.004

.008 .006 .000 -.004 -

.007 .005 -.000 -•004 -

.008 .006 .001 -.003 -

001

001

000

016

024

014

•009

004

002

002

000

002

0O2

002

OO4

005

006

005

O06

003

OO4

004

004

,004

003
144

Table D.8 - Compact Probe v (x/80-1.0)

x180 YI80

1.0 .55

1.0 .37

1.0 .18

1.0 ° .00

1.0 -.15

1.0 -.28

1.0 - 43

1.0 - 66

1.0 - 82

1.0 -i 02

1.0 -i 27

1.0 -I 59

1.0 -i 98

1.0 -2 46

1.0 -3 06

1.0 -3 81

1 0 -4 74

1 0 -5 89

i 0 -7 05

I 0 -8 20

1 0 -9 36

1 0 -I0 51

1 0 -Ii 66

1.0 -12 81

1.0 -13 97

Unforced Phase averaged data (at angle 4)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

0060

0061

0126

0561

0615

0457

0412

0391

0402

0395

0396

0401

0393

0398

0393

0381

0373

0091 .0096

0090 .0095

0156 .0154

0581 .0613

0583 .0600

0443 .0444

0409 .0408

0400 0390

0383 0394

0397 0399

0389 0393

0401 0396

0402 0390

0385 0391

0395 0384

0384 0386

0365 0359

0335 .0326

0286 0285

0221 0228

0157 0154

0100 0100

0063 0063

0050 0050

0041 0041

0325

0274

0217

0151

0093

0063

0089 .0179

0084 .0162

0156 .0184

0614 .0583

0563 0576

0430 0427

0395 0402

0392 0405

0385 0406

0387 0392

0209 0167

0210 0185

0277 0242

0585 0550

0611 0648

0468 0480

0402 0405

0401 .0395

0390 0406

0400 0391

0384

0383

0386

0396

0388

0381

0364

0330

.0274

0210

0160

0098

0063

0047 .0048

004O .OO4O

0387 .0403

0383 0409

0387 0385

0393 0401

0387 0400

0371 0371

0364 0355

0329 0323

0274 .0278

0205 0211

0387

0397

0386

0400

0402

0384

0367

0326

0287

0226

0156 0159

0093 0097

0062 0058

0048 0048

0039 0039

0119

0126

0205

0571

0619

0457

0429

0412

0392

0399

0401

0408

0413

0401

0401

0403

0368

0331

0292

0225

0156 .0146

0104 .0097

0063 .0071

0052 .0049

0040 .0041

0092

0092

0173

0572

0621

0459

0416

0411

0392

0389

0391

0377

0395

0392

0393

0385

0363

0327

0290

0215

0156

0108

0063

0050

0042
145

Table D.9 Compact Probe u'v" (X/eo-l.O)

x/e o

I.O

I.O

i.o

I.O

I.O

i.o

I.O

i.o

i.o

Unforced Phase averaged data (at angle _)

y/90 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

.55 .0005 .0006 .0008 0003 0011 .0016 .0013 0009 0007

.37 .0003 .0007 0007

.18 .0007 .0012

-.00 .0186 .0175

-.15 0188 .0141

-.28 0139 .0127

-.43 0142 .0140

-.66 0133 .0130

-.82 0148 .0140

0003 0008 .0021 .0012

0013 0013 0011 .0026 .0018

0212 0211 0192 .0205 .0181

0194 0174 0172 .0202 .0235

0134 0111 0122 .0167 .0149

0121 0118 .0137 .0145 .0127

0127 .0129 .0134 .0136 .0132

0136 .0133 .0153 .0143 .0149

0008 0006

0015 0014

0208 0196

0196 0197

0131 0167

0163 0141

0151 0119

0146 0140

1.0 -1.02 0146 .0147 0145 .0137 .0148 .0154 .0153 .0136 .0129

1.0 -1.27 0144 .0144 .0139 .0123 .0135 .0158 .0150 .0154 .0135

1.0 -1.59 0144 .0132 .0130 .0120 .0129 .0147 .0127 .0146 .0136

1.0. -1.98 0143 .0143 .0132 .0133 .0124 .0139 .0142 .0160 .0138

1.0 -2.46 0143 .0129 .0124 .0131 .0125 .0134 .0153 .0150 .0146

1.0 -3.06 .0140 .0137 .0130 .0140 .0130 .0146 .0149 .0152 .0136

1.0 -3.81 .0136 .0143 .0143 .0126 .0116 .0121 .0145 .0152 .0137

1.0 -4.74 .0126 .0123 .0108 .0118 .0119 .0122 .0123 .0129 .0128

1.0 -5.89 .0108 .0101 .0094 0101 0099 .0099 0103 0099 .0100

1.0 -7.05 _0076 .0075 .0074

1.0 -8.20 .0038 .0037 .0035

1.0 -9.36 .0014 .0014 .0013

1.0 -10.51 .0004 .0004 .0003

1.0 -11.66 .0001 .0001 .0001

1.0 -12.81 .0001 .0000 .0001

1.0 -13.97 .0000 .0000 .0000

0069

0033

0013

0003

0001

0000

0000

0072 0073

0029 0034

0012 0015

0002 0005

0001 0001

0000 0001

0000 0000

0074

0036

0014

0003

0001

0001

0000

0077 .0082

0038 .0034

0010 .0016

0003 .0004

0001 .0000

0000 .0001

0000 .0000
146

Table D.IO - CompactProbe u (X/eo-3.0)

x/e 0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3•0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

y/e 0

Unforced Phase averaged data (at angle _)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

.55 .093

37 .120

18 •199

- O0 .307

- 15 .418

28 .497

43 .579

66 .638

82 .659

-1.02 .680

-1.27 .699

-1.59 .719

-1.98 .742

-2.46 .767

-3.06 794

-3•81 826

-4.74 864

-5.89 906

-7.05 946

-8.20 975

-9.36 995

3.0 -10.51 1.001

•090

.125

.213

.327

•442

.517

•594

•642

•664

.677

.703

720

739

762

790

825

862

904

942

.974

.992

•103

•151

.233

.363

•468

.552

.612

•660

.675

.693

• 709

729

748

769

797

830

866

909

• 948

.975

.993

.120 •127

.159 .158

.257 .252

•390 .386

.505 .506

.578 .578

.644 .649

.682 .687

.697 .699

712 .720

729 .735

743 .751

759 .767

780 .789

808 .814

.839 .843

.873 .879

.913 .919

.950 .956

.979 .982

.997

.118

•144

•213

.324

441

525

597

660

687

705

726

742

764

784

814

•847

.883

.925

.962

.989

•i00

.124

•185

.280

.391

•462

.556

.627

661

683

702

727

75O

773

804

836

874

919

.957

.986

•999 1•004 1•003

•085

.112

•180

.288

.382

•467

•548

•614

648

669

692

712

734

761

791

824

863

909

948

979

998

085

117

190

296

402

483

566

623

•647

668

693

714

733

762

788

821

857

904

942

976

993

.999 1.000 1.001 1.004 1.008 1.009 1.005 1.001

3.0 -11•66 1.001 1.000 1.001 1.001 1.004 1.008 1.009 1.007 1•003

3.0 -12.81 1.002 1.001 I•000 1.001 1.004 1.007 1.009 1.007 1.003

3.0 -13.97 1.002 1•002 I•001 1.002 1.004 1.007 1.009 1.008 1.004
147

Table D.II CompactProbe u (x/00-3.0)

x/Oo

Unforced Phase averaged data (at angle _)

y/00 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

•55 .0440 .0428 .0512 .0546 .0574 .0532 .0488 .0442 .0396

•37 .0630 .0659 .0773 .0748 .0749 .0737 .0662 .0620 .0651

.18 .0899 .0975 .0987 .0974 .0981 .0998 .0917 .0905 .0910

-.00 .1068 .1128 .1150 .1057 .1108 .1162 .1129 .1079 1114

-.15 .1150 .1157 .1146 .1055 .1114 .1270 .1221 .1173 1174

-.28 .1107 .1076 .1051 .0960 .1029 .1178 .1251 .1181 1119

-.43 .0971 .0901 .0846 .0827 .0838 .1027 .1121 .1094 0984

-.66 .0804 .0770 .0764 .0734 .0740 .0804 .0897 .0850 0817

-.82 .0763 .0742 .0730 .0705 .0709 .0738 .0771 .0770 0800

-1.02 .0734 .0719 .0734 .0703 .0689 .0725 .0746 .0748 .0731

-1.27 .0724 .0696 .0712

-1.59 .0713 .0697 .0696

-1.98 .0692 .0704 .0672

-2.46 .0674 .0679 .0676

-3.06 .0656 .0642 .0668

-3.81 .0637 .0629 .0646

0694

0706

0673

0650

0641

0626

3.0 -I0.51 .0107 .0119 .0102 .0097

3.0 -ii.66 .0071 .0072 .0071 .0072

3.0 -12.81 .0058 .0060 .0058 .0058

3.0 -13.97 .0052 .0053 .0053 .0051

0698 .0684 .0720 .0725 .0718

0686 .0682 0704 0717 .0710

0654 .0671 0676 0712 .0680

0657 .0657 0663 0663 .0671

0629 .0657 0654 0659 .0660

0608 .0604 0646 0638 .0644

-4.74 .0603 .0602 .0604 .0596 .0612 .0593 0576 0606 .0619

-5.89 .0552 .0552 .0545 .0553 .0553 .0524 .0549 0552 .0546

-7.05 .0467 .0466 .0463 .0460 .0451 .0437 .0451 .0476 .0479

-8.20 .0354 .0342 .0348 .0333 0344 .0319 .0339 .0354 .0351

-9.36 .0209 .0217 .0227 .0177 0189 .0188 .0196 .0208 .0224

0103 .0106 .0103 .0109 .0104

0075 .0076 .0071 .0075 .0081

0059".0056 .0057 .0063 .0060

0052 .0052 .0054 .0054 .0054
148

Table D.12 Compact Probe _ (x/00-3.0)

x/O 0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

30

30

30

30

30

30

30

30

30

30

30

30

30

30

Unforced Phase averaged

0.0 45.0 90.0 135.0 y/# 0 data

.55 -.002

.37 -.003

.18 •004

-.00 .017

-.15 .027

-.28 027

-.43 018

-.66 010

-.82 007

-i02 005

-I 27 004

-i 59 001

-i 98 000

-2 46 - 001

-3 06 - 003

-3 81 - 004

-4 74 - 004

-5 89 - 004

-7 05 - 003

-8 20 - 004

-9 36 - 004

-I0 51 - 0O4

-II 66 - 004

-12 81 - 004

-13 97 - 003

-.002

-.003

.010

•025

.039

.036

029

018

015

013

013

010

O08

OO6

OO3

001

- 000

- 001

- OO2

- OO2

- 004

- 0O4

- 004

- 005

- 004

- .003 -

.003

.011

038

044

047

041

033

031

027

022

022

018

015

011

008

OO6

007

0O4

003

002

002

000

- 000

000

OO2

OO6

023

043

O58

057

048

042

039

037

032

029

026

022

019

016

015

012

009

OO8

OO8

OO6

OO5

OO4

O04

-.003

•000

.017

043

051

047

041

034

030

030

026

O25

021

019

016

014

012

012

011

010

0O9

OO8

0O7

0O6

006

data (at angle @)

180.0 225.0 270.0

005 -

001 -

006

017

030

032

023

012 -

007 -

008 -

006 -

002 -

000 -

000 -

001 -

001 -

002

004 -

OO6

0O5

O05

OO5

004 -

004 -

OO5

001 .001

001 -.004

001 .001

007 .016

019 .017

018 .023

010 .012

001 000

003 - 004

007 -006

011 -007

009 - 010

012 - 012

012 - 011

012 - 012

012 - 013

011 - 012

007 - 010

005 - 010

004 - 009

003 - 008

003 - 008

003 - 008

002 - 007

001 - 006

315.0

- ,001

-,001

005

019

023

027

020

010

005

004

002

000

- 003

- 003

- 007

- 007

- 007

- 007

- 008

- 008

- 008

o 007

- 008

- 007

- 006
149

Table D.13 Compact Probe _ (x/00-3.0)

x/e 0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0 -5.89

3.0 -7.05

3.0 -8.20

3.0 -9.36

3.0 -10.51

3.0 -11.66

3.0 -12.81

3.0 -13.97

Y/00

.55 .0390 .0388 .0461 .0504 .0560 .0524 .0430

.37 .0526 .0577 .0647 .0670 .0651 .0674 .0560

.18 .0747 .0807 .0868 .0854 .0833 .0806 .0736

-.00 .0864 .0942 .0973 .0948 .0951 .0907 .0869

-.15 .0875 .0888 .0878 .0862 .0821 .0885 .0902

-.28 .0770 .0749 .0741.0697 .0727 .0777 .0809

Unforced Phase averaged data (at angle #)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

0359 .0354

0485 .0521

0702 .0749

0845 .0882

0855 .0862

.0757 .0763

-.43 .0614 .0578 .0539 .0546 .0503 .0644 .0685 .0632 .0590

-.66 .0468 .0453 .0439 .0427 .0442 .0487 .0528 .0490 .0462

-.82 .0424 .0430 .0419 .0409 .0397 .0456 .0457 .0452 .0434

-1.02 .0411 .0402 .0393 .0383

-1.27 .0400 .0395 .0390 .0380

-1.59 .0402 .0396 .0388

-1.98 .0404 .0402 0393

-2.46 .0405 0388 0393

-3.06 .0391 0387 0386

-3.81 0386 0377 0386

-4.74

0387

0385

0391 0397

0382 0386

0389 0398

0385 0393

0381 0369

0368 0364 0362 0362 .0367

0416 .0425 0423 .0421

0407 .0408

0406 0407

0397 0408

0404 0410

0387 0_92

0383 0392

0367 0368

0409 .0409

0403 .0399

0407 0396

0392 0389

0397 0392

0379 0380

0364 0372

0332 0326 0325 0324 .0317 .0316 0315 0324

0279 0284 0272 0274 .0264 .0272 0283 0284

0219 0221 0222 .0212 .0212 .0214 .0210 0228

0155 0153 0157 .0134 .0148 .0145 .0149 .0145

0098 0103 0096 .0087 .0093 .0085 .0095 .0096

0062 .0060 .0062 .0064 .0061 .0062 .0064 .0062

.0048 .0048 .0048 .0047 .0048 .0048 .0050 .0057

,0039 .0038 .0038 .0037 .0037 .0038 .0037 .0040

0343

0284

0223

0157

0094

,0062

,0048

,0038
150

Table D.14 - CompactProbe u'v' (x/00-3.0)

x/e o

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0

3.0 -1.27

3.O ol.59

3.0 -1.98

3.0 -2.46

3.0 -3.06

3.0 -3.81

3.0 -4.74 0122

3.0 -5.89 .0101

3.0 -7.05 .0068

3.0 -8.20 .0038

3.0 -9.36 .0014

3.0 -I0.51 .0003

3.0 -ii.66 .0001

3.0 -12.81 .0000

3.0 -13.97 .0000

Y/_O

55 .0080 .0080 .0111 .0156 .0189 0156 .0094 .0081

Unforced Phase averaged data (at angle @)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

37 .0180 .0194 .0306 .0318 .0299

18 .0390 .0498 .0538 .0539 .0510

O0 .0547 .0659 .0753 .0597 .0606

0490 .0450

0311 .0343

0200 .0141

0096 .0137

0118 .0117

0119 .0095

15 .0542 .0543 .0565

28 .0395 .0344 .0418

-.43 .0250 .0216 0196

-.66 0152 0144 0130

-.82 0146 0129 0122

-1.02 0144 0118 0115

0292 .0185 .0128

0485 .0351 .0357

0611

0611

0397

0238

0167

0154

0133

0138

0134 .0147

0134 .0136

0135 .0145

0127 .0149

0121 .0154

0576 .0518

0582 .0562

0515 .0391

0290 .0258

0202 0190

0145 0162

0165 0155

0137 0152

0157

0146

0136

0143

0125

0141 0128 0117 .0118 .0129

0143 0139 0135 .0118 .0129

0139 0140 .0131 .0115 .0108

0144 .0136 .0i32 .0116 .0132

0136 .0123 .0132 .0114 .0121

0132 0118 .0137 .0134 .0118

,0121 .0109 .0120 .0131 .0123 .0122 .0126

,0097 .0096 .0087 .0092 .0084 .0096 .0104

0065 .0062 .0063

0037 .0040 .0033

0014 .0018 .0009

0005 .0003 .0002

0001 .0000 .0001

0000 .0000 .0000

0000 .0000 .0000

0O56

0179

0395

0583

0543

0406

0244

0154

0165

0139

0141

0128

0127

0136

0140

0133

0129

0107

0068 .0061 .0062 .0075 .0070

0037 .0031 .0036 .0044 .0036

0012 .0011 .0012 .0011 .0015

0002 .0001 .0002 .0003 .0002

0001 .0001 .0000 .0000 .0000

0000 .0000 .0000 .0001 .0000

0000 .0000 .0000 .0000 .0000
151

Table D.15 Meanvelocity straight wire results

x/e o

-30.0 -.03

-30.0 -.09

-3O.O -.15

-30.0 -.21

-30.0 -.28

-30.0 -.34

-30.0 -.43

-30.0 -.53

-30.0 -.66

-30.0 -.82

-30.0 -1.02

-30.0 -1.28

-30 0 -1.59

-30 0 -1.98

-30 0 -2.46

-30 0 -3.06

-30 0 -3.81

-30 0 -4.74

-300 _5•89

-30.0 -7.05

-30.0 -8.20

-30.O -9.36

-30.0 -I0.51

-30.0 -11.66

-30.0 -12.82

-30.0 -13.97

-30.0 -15.12

-20.0 -.03

-20.0 -.09

-20.0 -.15

-20.0 -.21

-20.0 -.28

-20.0 -.34

-20.0 -.43

-20.0 -.53

-20.0 -.66

-20.0 -.82

-20 0 -1.02

-20 0 -1.28

-20 0 -i 59

-20 0 -i 98

-20 0 -2 46

-20 0 -3 06

-20 0 -3 81

-20 0 -4 74

Unforced

y/00 data 0.0

•175

.377

.470

.515

.552

•574

•595

•617

•644

.661

.689

.707

728

751

779

805

839

879

925

961

984

990

989

990

.991

•988

.990

.200

.324

.465

•519

.542

.562

582

604

629

655

678

699

719

743

773

800

834

875

Phase averaged data (at angle _)

45.0 90.0 135.0 180.0 225.0 270.0 315.0

.151 .144

.379 .372

.473 .468

.515 •514

•552 •551

.577 578

.596 595

.617 621

.644 644

663 668

688 688

707 705

724 728

748 751

778 778

804 807

845 843

881 .881

926 .927

.961 .962

.985 .987

.991 .992

.991 .991

.992 .993

.991 .992

.989 .990

.989 .990

185 .175

327 .316

464 .462

517 .515

544 .546

561 563

583 587

604 606

628 630

651 657

679 681

697 700

721 725

743 .742

774 .773

802 .803

837 .835

873 .878

•149

•374

.472

.516

•554

.579

•600

618

645

665

687

708

730

•754

.782

.809

•843

•882

.928

•964

.986

.993

.992

.993

993

990

991

190

330

462

521

545

564

587

607

633

656

681

701

723

•751

.776

.805

.838

.879

.148

.377

.476

•522

•554

581

601

621

646

667

690

712

728

753

784

.811

•847

.883

.928

.964

.986

.993

.993

• 994

.993

.991

.991

182

329

470

522

547

567

586

613

638

,657

,680

.705

.723

.749

•777

.807

.840

.880

.169

.398

.482

.523

.557

.579

.603

•624

646

668

692

710

733

756

783

,815

.849

.887

.929

.965

.988

.993

.992

• 994

.993

.991

.991

.199

•350

.476

.523

.550

.567

.588

.612

.636

.659

.682

•704

.723

•748

.776

.806

.837

.879

.168

.399

.484

522

557

583

600

623

646

669

690

712

730

753

78O

•810

•846

.885

.927

.964

.986

.991

991

993

992

990

990

184

333

472

522

550

561

582

609

633

•654

.679

.701

.725

•747

.772

.802

.837

.879

.168

.389

.485

.522

.557

.581

601

622

646

667

688

710

731

753

780

811

845

883

.928

.962

.986

.992

.991

.992

.992

989

989

211

342

472

521

547

558

584

610

632

652

679

701

723

•746

.771

•802

.838

.875

.168

• 394

.479

.517

555

577

599

619

646

666

689

708

729

752

780

809

845

883

928

963

985

.991

.990

.992

.991

989

989

194

341

472

518

548

559

582

606

631

651

677

703

722

742

.770

.799

.837

•874
152

Table D.15 (cont'd).

-20.0 -5.89

-20 0 -7.05

-20 0 -8.20

-20 0 -9.36

-20 0 -10.51

-20 0 -11.66

-20 0 -12.82

-20 0 -13.97

-20.0 -15.12

-I0.0 -.03

-i0.0 -.09

-I0.0 -.15

-i0.0 -.21

-I0.0 -.28

-I0.0 -.34

-I0.0 -.43

-I0.0 -.53

-I0.0 -.66

-i0.0 -.82

-10.0 -1.02

-I0.0 -1.28

-10.0 -1.59

-10.0 -1.98

-10.0 -2.46

-10 0 -3.06

-I0 0 -3.81

-i0 0 -4.74

-i0 0 -5.89

-i00 -7.05

-I00 -8.20

-I0

.920

957

986

997

998

995

995

995

•991

.172

.364

•467

515

547

565

587

609

632

654

.677

.697

.719

.742

.766

.797

.832

•870

.913

.953

.982

0

920 .921 .923 .926 .924

959 .959 .960 .964 .962

986 .988 .988 .990 .989

996 .998 .999 1.000 .999

998 1.000 1.001 1.001 1 001

996

.995

•995

•996

•167

.369

.473

518

547

562

586

611

632

.653

.677

.697

.717

.744

.767

.798

.831

.870

.916

.955

.986

.997

.996

.996

.996

•141

.357

.468

.519

.551

.563

.589

.614

.635

.658

678

699

720

746

771

80O

834

872

916

•954

.986

.998

.998

.997

.997

.172

.375

.477

.526

.559

.573

.591

.615

641

663

683

7OO

727

750

.773

.802

.839

.878

.922

.957

.989

999

998

998

998

172

382

.477

.525

.556

.573

.597

.617

.639

.666

.684

.708

.729

.751

.779

.805

.839

.877

.924

.961

.990

999

998

998

998

171

382

.479

.526

•556

.573

.592

.616

640

663

685

702

725

751

.776

• 804

.836

•878

• 920

.960

.990

.922 .920

.960 .959

.988 .987

.998 .996

.999 .998

.997 .996

.997 .996

.997 .996

.997 .996

.185 .173

.385 .375

.478 .473

.522 .517

.546 .546

.567 .565

.591 .585

.613 .609

638 .634

659 .656

679 .678

700 .696

722 .719

744 .743

770 .767

.798 .796

.833 .827

.872 .871

.919 .914

.956 .954

.987 .984

-9.36 1.000 1.000 1.002 1.004 1.006 1.005 1.003 1.001

920

,959

985

996

997

996

995

995

995

167

366

468

512

. _44

.562

.587

.608

.630

.653

.672

.694

.717

.740

.764

.793

.828

.870

.913

.955

.984

.999

-I0.0 -I0.51 1.003 1.004 1.005 1.007 1.009 1.008 1.006 1.005 1.003

-i0.0 -11.66 1.003 1.002 1.004 1.005 1.006 1.006 1.004 1.002 1.002

-i0.0 -12.82

-I0.0 -13.97

-I0.0 -15.12

-5.0 -.03

-5.0 -.09

-5.0 -.15

-5.0 -.21

-5.0 -.28

-5.0 -.34

-5.0 -.43

-5.0 -.53

-5.0 -.66

-5.0 -.82

-5.0 -i.02

-5.0 -1.28

.999 1.000 1.001 1.003 1.004 1.004 1.002 1.001 1.000

.998

.997

.167

313

426

496

534

56O

585

606

627

650

673

.694

999

998

140 .141 .160

313 .315 .329

427 .434 •442

501 .504 .510

535 .543 .545

562 .565 .574

583 .588 .595

605 •611 .614

628 .633 .639

.655 .657 .661

.677 .679 .681

.693 .699 .706

.999 1.001 1.002 1.001 1.001

.999 1.000 1.001 1.001 1.000

.167

.338

•440

.517

.550

575

595

622

644

664

687

706

.158 .160

•342 .323

.445 .436

•514 .503

544 .535

572 .562

595 .587

613 .609

642 .632

659 .653

685 .678

704 .698

.999

.999

.153

.307

.425

.498

.532

558

582

604

627

649

677

691

.998

.998

.168

.325

.428

.498

.528

.558

582

602

625

644

672

692
153

Table D.15 (cont'd).

-5.0 -1.59

-5.0 -]..98

-5.0 -2.46

-5.0 -3.06

-5.0 -3.81

-5.0 -4.74

-5.0 -5.89

-5.0 -7.05

-5.0 -8.20

-5.0 -9.36

-5.O -10.51 1

-5.0 -11.66 1

-5.0 -12 82

-5.0 -13 97

-5.0 -15 12

-i.0 - 03

-i.0 09

-I.0 15

-I.0 21

-I.0 28

-I.0 34

-i'.0 - .43

-I.0 -.53

-i.0 -.66

-I.0 -.82

-I.0 -1.02

-I.0 -1.28

-i.0 -1.59

-i.0 -1.98

-I.0 -2.46

-i.0 -3 06

-i 0 -3 81

-I 0 -4 74

-I 0 -5 89

-I 0 -7 05

-I 0 -8 20

-I 0 -9 36

.719 •718 .722 .729

•741 .739 .746 .750

•769 .773 .773 .778

.798 .802 .804 .809

.832 .830 .837 .838

.870 .871 .875 .880

.914 .915 .920 .926

.953 .955 .957 .961

.985 .985 .986 .989

998

.730 .727

757 .751

783 •779

809 .807

842 .842

882 .879

925 .923

962 .963

.993 .991

.721

.746

772

802

834

875

919

959

.989

.999 1.000 1.003 1.004 1.005 1.003

715 .715

744 .741

769 .766

797 •797

833 .830

869 .866

915 .911

953 .952

984 .983

999 .998

002 1.002 1.004 1.006 1.007 1.008 1.006 1.003 1.002

002 1.002 1.003 1.005 1.007 1.007 1.005 1.003 1.002

999 1.001 1.002 1.004 1.005 I 005 i 004 1.002 1.001

999

999 1.001 1.002 1.003 1

165

306

.453

.518

•553

.575

•594

.615

.637

•661

.680

.700

•720

743

768

798

830

870

912

95O

981

997

.156

•314

.460

.523

•560

.578

.600

.619

643

665

683

704

722

741

771

800

830

872

912

.951

.982

.999 1.000 1.002 1 003 1

004 1

•144 182 191

.314 339 353

.467 482 491

529 547 548

566 579 580

585 595 597

606 619 620

630 643 641

653 662 .663

673 683 .685

689 .698 .704

710 .718 .719

732 .739 .743

751 .759 .764

779 .785 .788

808 .814 815

.835 .844 848

.871 .881 883

.917 .921 925

.953 .958 962

.985 .988 991

003 1

004 1

179

342

475

537

568

.996

588 572

609 595

.630 617

.655 639

.676 663

.693 682

.710 .702

.732 .724

.755 .747

779 .771

812 .803

844 .833

881 .873

922 .916

962 .956

991 .987

.998 1.000 1.003 1.004 1.002

003 1.001 .999

004 1.003 i 001

161 .167 169

321 .305 314

461 .447 451

518 510 515

554 550 548

566 570

585 594

608 612

633 632

657 658

675 676

695 697

717 716

743 740

.766 765

.797 793

.828 ,828

866 .865

911 .908

952 .949

983 .980

998 .996

-I 0 -i0 51 1.001 1.000 1•002 1.003 1.006 1.006 1.006 1 003 1.000

0 -11•66 1.000 1.000 1.001 1.003 1.005 1.006 1.005 1 003 1 001

999 1.001 1.003 1.004 1.004 1.002 i

998 1.000 1.001 1.003 1.003 1.001

997

172

378

524

563

586

608

998 .999 1.001 1.002 1.000

191 .228 .215 .173 .180

399 .414 .398 .368 .363

535 .538 .521 .495 .486

570 .580 .561 .538 .532

600 .601 .585 .560 .558

619 .621 .603 .584 .582

-I 0 -12.82 .998 .999

-I 0 -13.97 .999 .998

-i 0 -15.12 .999 .997

.0 -.03 .206 .185

.0 -.09 .364 .374

.0 -.15 .494 .508

.0" -.21 .540 .548

.0 -.28 .567 .575

.0 -.34 .591 .595

000

999

998

202

375

495

540

563

583
154

Table D.15 (cont'd).

.0 •43 .609

.0 -.53 .628

.0 -•66 .651

•0 -.82 .673

•0 -1.02 .693

.0 -1.28 .711

.0 -1.59 .734

0 -1.98 .755

0 -2.46 .779

0 -3.06 .806

0 -3.81 .841

0 -4.74 .876

0 -5.89 .923

0 -7.05 .960

0 -8.20 .992

.0

.615

.637

.659

.675

.695

.712

735

757

782

810

842

879

922

•961

.990

.628

.650

.672

.690

• 708

725

744

765

791

815

845

•883

.926

.964

.992

.642 .642 •624

.656 .659 .642

.678 .680 .670

• 694 .700 .687

714 .715 .705

732 .734 .726

751 .758 .746

771 .778 .769

796 .799 .795

823 .830 .823

.855 .855 •855

.891 .895 .893

• 931 •935 .936

• 971 .973 .973

.995 1.000 1.001

• 607

•628

•652

.671

.691

709

736

754

783

812

847

885

.928

.969

.998

.602 .602

.626 .625

.647 .650

.665 .668

•685 .687

.707 .707

.731 .730

.751 .753

777 .775

801 .800

841 .837

875 .875

923 .919

960 .962

994 .989

-9.36 1•006 1.005 1•007 1.009 1.012 1.013 1.011 1.008 1.005

.0 -10.51 1.010 1.008 1.009 1.010 1.014 1.016 1.015 1.012 1.009

.0 -11.66 1.008 1.007 1.008 1.009 1.012 1.014 1.013 I•011 1.008

.0 -12.82 1.005 1 006 1.007 1.008 1.010 1.012 1.012 1.010 1.007

.0 -13.97 1.005 1

.0 -15.12 1.005 1

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

1.0

i0

i0

1

1

1

1

1

1

3.0

.58

.40

.21

03

- 12

25

40

63

79

99

-1.24

-1.56

-1.95

-2.43

-3.03

-3.78

-4.71

-5.86

-7.02

-8.17

0 -9•32

0 -i0 48

051

059

056

067

132

300

518

620

652

•680

.703

.728

.753

.781

.808

.835

864

877

906

926

955

996

0 -Ii

0 -12

0 -13

0 -15

006 1.006 1.006 1.008 1•010 1.011 1 010 1,007

004 1.004 1.004 1.006 1.008 1.009 1

053

O59

063

076

145

316

522

.626

.653

.681

•707

.731

.753

.782

810

834

860

878

905

929

955

997

.063

•068

.071

.081

.151

.337

•547

.638

.668

.690

.717

.739

•764

.789

814

840

866

884

909

932

957

.058

.059

.061

.079

•164

.366

.566

.652

679

705

729

749

774

796

824

848

873

890

914

938

.960

.072

•069

.066

.086

.185

.391

.580

657

684

708

732

754

774

800

827

850

877

.890

.919

.941

•964

.084

.080

.080

.100

.179

.366

.560

645

673

698

721

746

769

793

823

846

875

889

.919

• 941

.966

.077

.077

.077

.097

.168

.333

.533

.625

.657

683

708

734

759

781

812

838

867

884

.912

.937

.963

997 1.000 1.003 1.006 1.004

63 1.004 1.003 1.004 1.007 1.009 1.010 1.010 1.007 1.005

78 1.006 1.006 1.006 1.008 1.010 1.012 1.012 1.010 1.007

94 1.006 1.005 1.005 1.006 1.008 1.010 1.011 1.009 1.007

09 1.003 1.005 1.004 1.005 1.006 1.008 1.009 1•008 1.006

58 .I00 .107 .I00 .118 .138 .137 .ii0 .086 .090

008 1 005

064 056

066 059

070 063

085 079

151 145

312 303

506 514

610 610

.647 645

.671 669

•698 701

.725 724

.748 .747

.772 .775

.805 ,802

834 831

859 860

879 878

906 906

930 928

956 956

999 996
155

Table D.15 (contrd)•

3.0 .40

3.0 .21

3.0 .03

3.0 -.12

3.0 - .25

3.0 - 40

3.0 - 63

3 0 - 79

3 0 - 99

3 0 -i 24

3 0 -i 56

3 0 -I 95

30 -2

3 0 -3

3 0 -3

3 0 -4

30 -5

3 0 -7

3.0 -8

3.0 -9

3.0 -I0

.107

152

228

298

369

464

591

642

675

702

726

752

43 774

03 803

78 830

71 846

86 904

02 934

17 987

32 1.001

.Iii

.157

.241

.316

387

483

607

657

683

703

729

749

777

805

830

847

904

933

987

113

169

262

335

409

511

620

665

687

714

736

757

783

812

838

850

906

938

989

•126

186

285

362

435

535

646

687

714

732

751

771

798

817

844

858

914

939

991

141

192

281

367

444

534

653

693

719

737

759

781

802

824

849

862

917

947

994

•141

177

255

326

400

493

615

666

700

723

744

769

795

818

847

858

920

946

998

119

163

233

298

366

460

581

637

678

704

733

758

784

811

84O

855

916

942

996

.099

146

214

283

349

447

566

628

661

692

720

745

771

8OO

828

846

908

938

991

999 1.000 1.003 1.007 1.008 1.008 1.005 1

48 1.009 1.010 1.009 1.011 1.014 1.017 1.017 1.015 I

.I00

•145

.218

•291

.358

.454

.579

632

662

689

717

743

767

801

827

841

902

933

988

000

012

3.0 -Ii.63 1.010 1.010 1.009 1.010 1.012 1.015 1.017 1.015 1.012

3.0 -12.78 1.008 1.O08 1.007 1.008 1.010 1.013 1.015 1.013 1.010

3.0 -13.94 1.007 1.007 1.006 1.006 1.007 1.010 1.012 1.011 1.009

3.0 -15.09 1.004 1.004 1.003 1.003 1.004 1.007 1.009 1.008 1.006

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

5.0

2.00 085

1.01 093

.03 329

-.96 688

-1.94 777

-2.93 821

-3.92 874

-4.90 909

-5.89 950

-6.88 976

-7.86 1.000

O53

059

365

679

768

816

867

904

946

973

996

-8.85 1.007 1.004 1

108 .130 .138 .112

107 .137 .144 .118

381 .407 .405 .349

689 .703 .715 .707

778 .784 .795 .799

823 .828 .834 .841

872 .878 .884 .891

907 .915 .920 .925

949 .952 .956 .960

974 .978 .983 .988

996 .998 1.001 1.007 1

002 1.004 1.007 1.012 i

.069

.089

.329

.687

.791

835

885

921

960

989

,008 1

014 1

.039 .030

-9.84 1.008 1.006 1.005 1.006 1.007 1.013 1.015 I

5.0 -10.82 1.007 1.005 1.004 1.004 1,006 1.011 1.014 1.012 1.009

5.0 -11.81 1.006 1.005 1.003 1.003 i

5.0 °12.79 1.004 1.004 1.001 1.001 I

5.0 -13.78 1.003 1.003 1.001 1.000 1

5.0 -14.76 1.001 1.001 .999 .999 1

5.0 -15.75 1.000 1.001 .999 .998

5.0 -16.74 1.000 1.001 .999 .998

5.0 -17.72 1.000 1.001 .999 .998

I0.0 4.00 .040 .032 .032 .043

i0.0 2.87 .041 .033 .034 .048

.066 055

.319 333

671 670

780 772

824 818

877 871

912 906

,956 950

982 976

,005 998

011 1.008

,013 1.009

005 1.009 1.012 1.011 1.008

003 1.007 1.010 1.009 1.007

002 1.005 1.009 1.008 1.006

000 1.003 1.006 1.006 1.004

999 1.002 1.005 1.006 1.004

999 1.001 1.004 1.005 1.004

.998 1.001 1.004 1.005 1.004

.044 .056 .063 .048 .037

.048 .062 .067 .047 .037
156

Table D.15 (eont'd).

i0•0 1.75

i0.0 .62

I0.0 -.51

I0.0 -1.63

i0.0 -2.76

I0.0 -3.88

I0.0 -5.01

I0.0 -6.14

I0.0 -7.26

i0.0 -8.39

I0.0

.065 .062

.237 .233

.555 .553

.748 .737

810 .801

862 .854

909 .902

950 .942

983 .977

998 .995

-9.51 1.003 1.001

I0.0 -10.64 1.004 1.002

i0•0 -11.77 1.002 1.002

I0.0 -12.89 i•001 1.002

I0.0 -14.02 1.001 1.001

I0.0 -15.15

I0.0 -16.27

I0.0 -17.40

I0.0 -18.52

15• 0 6. O0

15.0 4.73

15.0 3 •47

15.0 2.20

15.0 .93

15 0 -. 33

15 0 -1.60

15 0 -2.86

15 0 -4.13

15 0 -5.40

15 0 -6.66

15 0 -7.93

.999 1.001

.998 1.000

.998 1.000

.997 1.001

.036 .037

.037 .035

.042 .038

.082 .077

246 •229

501 470

729 704

811 794

868 854

919 906

962 954

990 986

15.0 -9•19 1.004 1.001

15.0 -I0•46 1•004 1.005

15.0 -11.73 1.006 1.006

15.0 -12.99 1.004 1.006

15.0 -14.26 1.002 1.006

15.0 -15.53 1.001 1.005

15.0 -16.79 1.001 1.005

15.0 -18.06 .999 1 005

15.0 -19.32 1.000 1

25.0

25.0

25.0

25.0

25.0

25.0

25.0

25.0

I0.00 034

8.45 034

6.91 036

5.36 041

3.81 070

2.27 169

.72 353

-.82 572

004

077

083

092

107

132

188

325

504

073

270

587

734

797

852

899

940

•975

•990

.996

•997

•997

.997

.996

.996

.996

.995

.997

.029

.029

.037

.088

• 257

.502

• 714

.793

.852

.902

•949

.979

.993

.996

.997

998

998

998

998

999

998

063

066

07O

078

095

160

299

.496

O85

304

611

750

8O6

86O

904

946

,977

.992

.996

.996

.996

.995

994

994

993

993

994

026

O28

• 040

.107

.302

.559

.730

.803

.859

•906

•949

•977

.989

992

993

994

993

993

994

994

994

044

•044

.044

.050

.079

.175

.350

.555

095

313

624

753

812

864

•909

•949

.980

.096 091

.306 247

.629 556

.778 768

.834 836

.883 884

.924 .929

.960 .969

.992 1.000

.067 .063

.219 .222

.519 .522

.752 .740

.819 .809

.872 .861

.921 .909

.961 .950

.994 .985

995

994

994

993

994

•035

.039

.052

.125

.331

.575

.753

.994 1.003 1.011 1.010 1.003

.998 1.005 1.014 1.014 1•008

.998 1.004 1.012 1.014 1.009

997 1.003 1.010 1.012 1.008

996 1.002 1.009 1.011 1.007

.999 1.006 1.008 1.006

.998 1.005 1.007 1.005

.997 1.003 1.006 I 004

.996 1.001 1.004 I 003

.997 1.001 1.004 1 004

.040 .057 .067 053

.043 .063 .073 053

.055 .077 .085 056

.136 .123 .116 082

.334 .297 •252 215

.579 .563 .474 .449

.757 .783 •714 .691

.814' .824 .857 .832 .804

.869 .878 .904 .891 .865

.918 .929 .947 943 .921

.957 .969 .985 983 .967

982 .991 1.007 1

992 .999 1.013 1

994 1.000 1.013 i

994 1.000 1.011 1

994

993

992

992

993

992

.028 023 .034

.027 .024 .038

.030 .032 .045

.042 .051 .061

.092 .iii .125

.216 .247 .270

.415 .455 •479

.613 .666 .675

011 .999

021 1.013

020 1.015

018 1.015

999 1.009 1 016 1.014

997 1.006 1.013 1.012

996 1.004 1.011 1.011

995 1.003 1.009 I•010

995 1.002 1.007 1.009

994 1.000 1.005 1.007

.053

.058

•066

.077

.121

.245

.447

.681

•073

081

093

iii

139

212

384

595
157

Table D.15 (cont'd).

25.0 -2.37 •766 .705

25.0 -3.92 .851 .843

25.0 -5.46 .914 •918

25.0 -7.01 .963 .975

25.0 -8.55 .993 1.008

25.0 -I0.I0 1.000 1.019

.698 .734 .751 .791

.811 .818 .828 .857

.883 .884 .890 .910

.944 .938 .941 .956

.983 .971 .968 .977

.997 .983 .976 .981

.987 .980 .983

.989 .981 .983

.990 .982 .982

.990 .983 .982

.992 .985 .984

.992 .985 .984

990 .983 .981

087 .081 •065

098 .089 .070

115 .102 .077

136 .117 .087

161 .135 .I01

.195 .162 .122

.249 .204 .165

.334 .271 .261

.462 .397 .403

.620 555 590

.774 727 754

.915 855 855

.997 942 924

986 960

998 972

980

.983

•985

.987

.985

.989

•065

074

O88

108

132

157

172

230

358

518

675

822

950

930 1.001 1.081 1.047

25.0 -ii.65 1.000 1.019 1.001

25.0 -13.19

25.0 -14.74

25.0 -16.29

25.0 -17.83

25.0 -19.38

25.0 -20.92

40.0 16.00

40.0 14.03

40.0 12.07

40.0 i0.I0

40.0 8.13

40.0 6.17

40.0 4.20

40.0 2.24

40.0 .27

40.0 -1.70

40.0 -3.66

40.0 -5.63

40.0 -7.60

.999 1•017 1.002

.997 1•014 1.002

•997 1.011 1.001

.996 1.010 1.002

.996 1.007 1.000

.993 1.002

.034 .055

034 .063

034 .077

036 .095

041 .108

060 .125

130 .212

264 .374

.453 .599

.661 .811

.825 .936

.997

078

O89

107

129

148

164

•219

.343

.525

.727

.890

•917 .997 1•007

•977 1.033 1.055

40.0 -9.56 1 001 1.036 1.068 1.034

40 0 o11.53 1 003 1.028 1.057 1.037

40

4O

40

40

40

40

60

60 0

60.0

60.0

60.0

60.0

60.0

60.0

60.0

60.0

60.0

60.0

60.0

60.0

0 -13.49 1

0 -15.46 1

0 -17.42

0 -19.39

0 -21.36 992

0 -23.32 994

0 24•00 .036

21.47 .035

18.95 .035

16.42 .035

13.90 .036

11.37 .041

8.84 .061

6.32 .118

3.79 .237

1.26 .396

-1.26 .590

-3.79 .781

-6.31 .922

002 1.021 1.044 1.033 1.003

000 1.013 1.032 1.026 1.003

999 1.008 1.024 1.020 1.002

998 1.003 1.017 1.015 1.001

•994 1.007 1.008

.997 1.007 1.007

.043

.044

.049

.058

.073

.097

132

2OO

310

452

630

774

872

.028 .028

.027 .030

• 031 .038

.042 .055

061 080

090 112

139 156

233 245

377 396

548 597

709 779

825 899

.998

.999

.048

.054

066

084

109

128

134

182

339

551

747

906

904 978 1.030

-8.84 .988 911

.803 .834 .792

.871 .903 .919

.929 •956 .971

.970 .996 1.010

.989 1.014 1.030

.993 1.014 1.032

.993 1.011 1.027

.991 1.006 1.021

.989 1.002 1.015

.988 1.000 1.011

989

988

983

045

047

051

.059

.072

•104

.185

.317

.490

.662

•787

.872

.930

954

964

971

973

977

978

976

.982

.072

.081

•094

113

138

167

205

268

363

.482

.604

.734

.861

.976

.998 1.009

.996 1.005

.990 .999

.025 .027

.026 .033

.032 044

.044 061

.066 084

.113 127

.213 240

.379 432

.574 626

.733 .776

.836 .869

.906 .937

951 .977

965 987

970 989

974 989

975 988

977 987

978 986

974 981

981 986

.069 .058

.076 .063

.087 .070

.102 .081

122 097

148 120

186 154

244 205

320 284

414 394

531 529

671 702

824 839

934 914
158

Table D.15 (cont'd).

60.0

60.0

60.0

60.0

60.0

60.0

60.0

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

76.9

115.4

115.4

115.4

115.4

115.4

115.4

115.4

115.4

115.4

115.4

115.4

115•4

115•4

115.4

115.4

115.4

115.4

115.4

115.4

115.4

-ii.37

-13.89

-16.42

-18•95

-21.47

-24.00

-26.52

-15.47

-13.86

-12.24

-10.63

-9.01

-7.40

-5.78

-4.17

-2.55

-.94

.68

2.30

3.91

5.53

7.14

8.76

10.37

11.99

13.60

15.22

16.83

23.58

21.37

19.17

16.97

14.77

12.57

10.37

8.17

5.97

3.77

1.56

-.64

-2.84

-5.04

-7.24

-9.44

-11.64

-13.84

-18.25,

-18.25

.999

1.000

.994

.994

.986

•988

•981

i•000

1.002

1.003

.999

.981

.938

.862

.770

.664

.559

•457

.366

.281

.203

149

099

070

052

045

040

.038

.040

.042

.046

.055

•073

.i01

.148

.205

.283

.360

448

547

658

771

867

947

985

992

992

990

.931

• 941

.949

.957

.957

.963

.962

.977

.972

• 964

• 943

.890

.823

• 749

.678

.615

.556

496

439

377

321

270

225

190

165

143

125

112

•054

•066

.081

•104

.133

.171

.222

.281

.361

.451

.550

.651

748

830

899

944

965

975

980

980

.946 1.003

.953 .997

959 .993

964 .991

963 .982

966 .982

964 .977

941 .930

934 .923

.924 .913

.909 .899

.889 .883

.846 .860

.776 .825

.699 775

613 702

537 617

468 528

403 438

346 367

297 299

251 245

209 198

174 160

147 131

126 Ii0

108 .090

.095 .077

.051 .063

.061 .071

.074 .083

.089 .094

.I15 113

.144 134

183 173

242 248

337 359

464 485

565 567

657 653

760 761

826 820

892 880

957 931

1.008 983

1.044 1.030

1.037 1.059

1.037 1.059

1.074

1.051

1.034

1.022

1.006

1.001

•991

.955

.950

.944

.934

.921

.901

.874

835

774

701

619

528

438

347

273

213

163

.128

.102

.078

.063

.077

.086

.098

.112

130

160

208

292

394

499

556

618

713

768

827

884

.944

.993

1.037

1.037

1.080 1.028

1.061 1.026

1.043 1.019

1.030 1.013

1.016 1.005

1.009 1.001

.998 .992

1.015 1.069

1.022 1.086

1.029 1.099

1.031 1.091

1.030 1 052

1 010 1 000

970 942

914 882

841 807

750 722

662 630

561 529

.451 422

.351 302

.271 209

.214 154

.172 138

.141 .131

.114 .123

.086 .I07

.071 .093

.086 .086

.096 .097

110 115

128 135

152 164

193 207

241 252

305 304

387 374

.472 444

.519 509

.585 577

.656 645

.727 720

.792 787

.852 847

.914 .899

.959 .925

.993 .947

.993 .947

.975

983

985

987

985

986

980

1.071

1.082

1.076

1.036

.978

923

870

813

752

670

588

505

424

330

245

183

151

142

132

.124

.112

.079

.092

.111

134

168

210

257

309

378

442

517

593

659

743

804

845

873

.891

.920

.920

940

952

960

966

966

972

968

1.029

1.030

1.021

.979

.913

854

795

735

683

614

547

477

410

34O

276

227

192

167

149

132

.120

.066

081

098

124

157

199

250

308

386

454

542

633

711

777

821

854

880

,901

930

930
159

Table D.15 (cont'd).

115 4 -20.45

153 8 -28.62

1538 -25.51

153,8 -22.41

153,8 -19.30

153,8 -16.19

153 8 -13.09

153.8 -9.98

153.8 -6.87

153.8 -3.76

153.8 -.66

153.8 2.45

153.8 5.56

153.8 8.66

153.8 11.77

153.8 14,88

153.8 17,98

153.8 21 09

153.8 24 20

153.8 27 30

153.8 30 41

153.8 33 52

192.3 43 46

192.3 39 45

192.3 35 43

192.3 31.42

192.3 27.41

192.3 23.40

192.3 19.38

192.3 15.37

192.3 11.36

192.3 7.35

192.3 3.33

192 3 -.68

192 3 -4.69

192 3 -8.70

192 3 -12.72

192 3 -16.73

192 3 -20.74

192 3 -24.75

192.3 -28.77

192.3 -32.78

192.3 -36.79

230.8 -44.97

230.8 -40.05

230.8 -35.13

230.8 -30.21

230.8 -25.29

990

979

982

985

992

993

982

924

.820

.703

.576

.457

.353

.271

.195

133

O90

062

O50

045

044

.978 1.026 1.047 1030

.982

.987

.990

.982

•948

.890

.822

749

688

599

514

442

343

273

219

176

153

130

110

091

.960 .948

•958 .941

.955 •933

•948 .922

•929 .908

.883 .877

.824 .837

.744 .768

671 .684

592 .602

513 .525

443 .446

367 .376

298 .312

236 .254

190 .200

158 .165

132 .135

110 .109

,090 .090

953

947

941

934

919

894

860

802

719

613

521

436

365

306

254

.201

.166

.131

•104

.085

043 .077

045

046

047

051

060

.082

.116

.182

.253

.349

.460

.585

.715

.843

.941

.982

.990

.077

.069 .070

.083 .084

.114 .113

.146 .143

.194 .184

.221 .209

.260 •244

.304 279

.341 308

.385 349

.439 420

.550 554

.686 701

.806 811

.902 894

.963 964

.074

.071

.086

.112

.141

.180

203

235

270

302

353

448

586

707

812

886

949

989 1.011 1.000

.070

.073

.088

.113

.145

.181

.208

•240

.275

.'323

.396

488

599

710

792

863

925

979

.982

.979

.985

.985

.985

.985

.987

.983

•986

989 1.017 1.019 1.000

984 1.009 1.016 1.002

990 1.006 1.010 1.001

987 1.000 1.004

981 .977 .977

982 .975 .975

982 .970 .969

971 .958 .957

948 .939 .940

997

983

982

980

974

966

.992 .952 .926

.974 .999 1.011 1

.976 1.010 1.025 1

.978 1.023 1.040 1

.985 1.031 1.036 1

.980 1.014 1.002

.959

.903

•817

•710

•584

.472

.388

.316

.271

.231

.185

.159

.124

099

082

067

O75

089

117

148

187

215

250

297

351

.434

513

601

698

772

841

904

953

975

.979

.984

• 984

.991

.966

.893

.808

.724

• 604

.467

.355

.272

.228

.203

.168

.146

.117

.097

.081

.067

.075

.089

118

151

194

226

267

322

386

459

532

605

689

767

837

894

932

949

957

968

.972

.996

947

870

799

727

629

495

378

273

216

190

160

.143

.119

•i00

.084

.071

.073

088

118

154

196

232

274

338

403

470

530

610

696

787

852

897

922

937

948

963

968

995

.994 1.001 1.001

.996 1.008 1.006

.998 1.010 1.005

.994 1.004 .991

933

004

015

024

015

976

911

843

772

715

626

516

.420

310

237

,200

,166

148

125

105

088

.075

.070

.086

117

151

197

230

275

332

383

444

500

589

701

810

886

925

943

952

958

971

974

989

992

996

988

969
160

Table D.15 (cont'd).

230.8

230.8

230.8

230 8

230 8

230 8

230 8

230 8

230 8

230 8

230, 8

230.8

230.8

230.8

230.8

-20.37

-15.46

-I0.54

-5.62

- .70

4.22

9.14

14.06

18.97

23.89

28.81

33.73

38.65

43.57

48.48

.987

•956

•862

.733

•593

•470

.359

.257

.165

•114

.075

.061

.053

.050

• 049

.916

.864

• 794

.715

.625

• 540

• 462

.396

.339

.289

.239

.195

.150

.110

.089

.913

.868

.803

.722

.638

.561

• 484

.419

.359

.297

• 243

.199

.151

.112

•089

.923

.888

.824

•725

633

558

488

429

363

303

247

200

154

111

089

.952

•914

.825

710

593

512

461

407

353

303

246

199

151

ii0

.087

.975

.917

.826

698

564

464

414

374

329

288

235

194

149

109

.088

.973

.914

.824

•708

.574

449

389

352

311

278

232

189

146

109

087

.957

.895

.815

.710

.592

.473

•401

.351

.311

.277

.230

•188

.147

•109

.087

936

876

797

715

609

508

432

371

.319

.279

.231

.188

.148

.ii0

•088
161

Table D.16 - RMS velocity straight wire results

x/0 o

-30.0

-30.0

-30.0

-30.0

-30.0

-30.0

-30.0

-30.0

-30.0

-30.0

-30.0

-30 0

-30 0

-30 0

-30 0

-30 0

-300

-300

-30,0

-300

-30.0

-30.0

Y/8 o

Unforced

data 0.0

Phase averaged data (at angle @)

45.0 90.0 135.0 180.0 225.0 270.0 315.0

03 .0739 .0576

09 .I039 .i031

15 .I013 .I052

21 .0956 .0946

28 .0888 .0874

34 .0838 .0828

- 43 .0820 .0822

-.53 .0791 .0794

-.66 0782

-.82 0777

-1.02 0770

-1.28 0746

-1.59 0737

-1.98 0725

-2.46

-3.06 .0668 .0662 .0677

-3.81 .0649 .0650 .0644

-4.74 .0589 .0600 .0599

-5.89 .0513 .0505 .0510

-7.05 .0376 .0371 0388

-8.20 .0211 .0216 0202

-9.36 .0118 .0103 0110

0519 .0536 .0545

1064 .1046 .1042

1024 .1005 .1002

0960 .0947 .0967

0887 .0875 .0886

0843 .0846 .0829

0651 .0644 .0677 .0662

1042 .I055 1056 .1048

0982 .0995 0998 .i011

0956 .0944 0924 0955

0878 .0869 0896 0866

0873 .0831 0835 0839

0825 .0816 .0830 .0815 .0820

0798 .0805 .0788 .0791 .0804

0793 .0767 .0789 .0774 .0778 .0781

0771 .0765 .0777 .0764 .0787 .0769

0774 .0754 .0780 .0746 .0748 .0762

0745 .0753 .0746 .0749 .0767 .0747

0731 .0739 .0726 .0735 .0731 .0745

0709 .0724 .0710 .0712 .0732 .0711

0694 .0696 .0707 0708 .0708 .0680 .0701

0686 .0675 0674 .0670

0817

0798

0778

0786

0756

0766

0732

0717

0700

0680

0645

0596

0511

0375

0228

0105

0650

0817

0786

0793

0770

0770

0748

0716

0713

0709

0664

0635 .0628 .0637 0639

0589 .0586 .0593 .0594

0519 0508 .0488 .0498

0385 0367 .0388 .0362

0226 0212 .0210 .0207

0118 0124 .0103 .0098

0604

0515

0373

0226

0116

-30.0 -10.51 .0070 .0076

-30.0 -ii.66 .0061 0062

-30.0 -12.82 .0054

-30.0 -13.97 .O054

-30.0 -15.12

-20.0 -.03

-20.0 -.09

-20.0 -.15

-20.0 -.21

-20.0 -.28

-20.0 -.34

-20.0 -.43

-20.0 -.53

0052

0888

0989

1003

0921

0878

0850

0829

0807

0058

0057

0054

0746

0973

0986

0927

0869

0826

0826

0793

0080

0061

0056

0055

0054

0689

0078 0082 0079

0061 0061 0060

0057 0058 0056

0056 0056 0056

0054 .0054 .0055

0711 .0671 .0733

0984 .0995 .0982 .i006

0078 0077 .0078

0061

0056

0055

0054

0692

1007

0060 0061

0056 0055

0056 0056

0054 0054

0822 0790

1023 1004

1015 .I001 .0991 .0986 .0962

0924 .0891 .0918 .0912 .0940

0889 .0863 .0875 .0889 .0867

0849 .0849 .0831 .0860 .0823

0831 .0823 .0820 .0822 .0812

0812 .0794.0791 .0811 .0802

i001

0931

0865

0841

0830

0811

1003

0897

0882

0872

0818

0799

-20.0

-20.0

-20.0

-20.0

-20.0

-20.0

-20.0

-20.0

-20.0

-20.0

-.66

-.82

-1.02

-1.28

-1 59

-1 98

-2 46

-3 06

-3 81

-4 74

0794 0785 .0782 .0792 .0776 .0793 .0791 0809 0769

0780 0766 .0760 .0762 .0764 .0770 .0784 .0790 0755

0761 .0781 .0781 .0754 .0747 .0781 .0760 .0751 0751

0755 .0752 .0750 .0737 .0758 .0749 .0760 .0768 .0751

0733 .0746 .0733 .0727

0718 .0721 .0714 .0714

0694 .0692 .0693 .0684

0664 .0681 .0672 .0683

0646 .0624 .0663 .0636

0607 .0591 .0616 .0610

0741

0712

0702

0685

0633

0607

0739 .0750 .0742 .0728

0693 .0743 .0710 .0728

0700 .0701 .0704 .0679

0672 .0666 .0703 .0677

0649 .0652 .0652 .0631

0616 .0597 .0595 .0606
162

Table D.16 (cont'd).

-20.0

-20.0 -7.05 .0429 .0420 .0442 .0420 .0408 .0414 .0421

-20.0 -8.20 .0267 .0257 .0265 .0271 .0280 .0280 .0269

-20.0 -9.36 .0139 .0150 .0132 .0143 .0142 .0142 .0145

-20.0 -i0_51 .0085 .0088 .0086 .0083 .0082 .0091 .0087

-20.0 -11.66 .0069 .0067 .0066 .0067 .0068 .0067 .0074

-20.0 -12.82 .0063 .0058 .0057 .0055 .0057 .0056 .0057

-20.0 -13.97 .0056 .0057 .0057 .0057 .0057 .0056 .0057

-5.89 .0533 .0522 .0542 .0524 .0513 .0543 .0546 .0529 .0529

0418 .0424

0263

0147

0084

0067

0057

0056

0274

0139

0087

0068

0056

0057

-20.0 -15.12 .0059 .0055 .0054 .0055 .0054 .0054 .0054 .0055

-I0.0

-i0.0

-i0.0

-i0.0

-I0.0

-I0.0

-i0.0

-i0.0

-I0.0

-I0.0

-i0.0

-I0.0

-i0.0

-I0.0

-i0.0

-I0.0

-i0.0

-10.0

-I0.0

-i0.0

-I0.0

-I0.0

0054

-.03 .0603 .0563 .0441 .0591 .0584 .0576 .0640 .0599 .0576

-.09 .1023 .1043 .0998 .1021 .1039 .1045 .1042 .1049 .1032

-.15 .0999 .0980 .0987 .0975 .0987 .1012 .0998 .0984 .1014

-.21 .0923 .0931 .0913 .0919 .0925 .0931 .0917 .0926 .0911

-.28 .0869 .0851 .0876 .0874 .0876 .0863 .0842 .0855 .0882

-.34 .0841 .0851 .0854 .0842 .0848 .0833 .0832 .0839 .0844

-.43 .0808 .0796 .0813 .0806 .0808 .0815 .0806 .0832 .0816

-.53

-.66

- 82

-I 02

-I 28

-I 59

-I 98

-2 46 .0694 .0716 .0693 .0677 .0681 .0679

0796 .0808 .0790 .0773 .0778 .0792 .0818 .0810 .0801

0784 .0793 .0783 .0786 .0747 .0788 .0767 .0789

0763 .0774 .0797 .0776 .0744 .0761 .0777 .0767

0758 .0751 .0759 .0744 .0766 .0751 .0766 .0772

0745 .0740 .0746 .0730 .0744 .0734 .0761 .0730

0735 .0731 .0730 .0726 .0707 .0715 .0723 .0713

0704 .0715 .0712 .0690 .0700 .0707 .0707 .0712

-3.06 .0677 .0672 .0680 .0657

-3.81 .0642 .0632 .0648 0631

-4.74 .0610 .0604 0618 0604

-5.89 .0541 .0539 0559 0534

-7.05 .0451 0438 0461 0457

-8.20 0313 0293 0305

-9.36 0174 0174 0177

0655 .0664

0633 .0642

0610 .0593

0542 .0528

0439 .0446

C808

0764

0766

0753

0733

0698

0689 .0702 .0702

0667 .0658 .0677

0640 .0639 .0654

0609 0607 .0624

0527 0547 .0543

0442 0453 0436

0304 0319 .0306 .0322 0318 0321

0175 .0168 .0173 .0157 0163 0173

-10.0 -10.51

-10.0 -11.66

-10.0 -12.82

-10.0 -13.97

-10.0 -15 12

-5.0 - 03

0098 0097 0094 0096 .0103 .0098 .0100 0091 0090

0070 0070 0071 .0069 .0071 .0070 .0068 0066 0071

0061 0059 .0056 .0057 .0058 .0057 .0058 0055 0056

0056 0055 .0057 .0056 .0057 .0055 .0056 .0055 0056

0052 0051 .0051 .0052 .0052 0052 .0051 .0052 .0052

0648 .0477 .0465 .0557 .0595 0570 .0587 .0566 .0642

-5.0

-5.0

-5.0

-5.0

-5.0

-5.0

-5.0

-5.0

-5.0

-5.0

-5.0

28 .0875 .0868 .0864

34 .0840 .0840 .0838

-.43 .0806 .0808 .0798

-.53 .0797 .0780 .0783

-.66 .0786 .0763 .0783

-.82 .0763 .0773 .0757

-1.02 .0753 .0760 .0763

-1.28 .0734 .0738 .0728

15 .1020 .1006 .1042 .1022

21 .0938 .0966 .0962 .0956

0881

0823

0797

09 .0967 .0982 .0966 .0979 .1009

1019

0945

0887

0829

0793

1015

1007

0961

0863 0884

0825 0842

0820 0799

0783 0788 .0761 .0777

0756 0762 .0785 .0779

0754 0762 .0747 .0748

0757 .0738 .0743 .0761

0717 .0727 .0737 .0709

0971 .0961 .i006

0999 .i020 .i028

0948 .0939 .0941

0889 .0874

0841

0801

0794

0790

0762

0740

0742

0819

0828

0808

0749

0769

0756

0742
163

Table D.16 (cont'd).

-5.0 -1.59 0729 .0720 .0711 .0707 .0714 .0721 .0725 .0731 0728

0702 .0700 .0706 .0676 .0717 .0697 0689 .0714 0709

0685 .0684 .0689 .0679 .0694 .0665 0681 .0673

0671 .0671 .0674 .0662 0659 .0671 0659 .0647

-5.0 -1.98

-5.0 -2.46

-5.0 -3.06

-5.0 -3.81

-5.0 -4.74

-5.0 -5.89

0637 .0663 .0634 .0653

0600 .0586 .0602 .0602

0547 .0532 .0525 .0530

-5.0 -7.05 .0453 .0442 .0459 .0439

-5.0 -8.20 .0312 .0310 .0311 0318

-5.0 -9.36 .0175 .0171 .0187

-5.0 -I0.51 .0095 .0084 .0087

-5.0 -11.66 .0068 .0066 0066

-I.0 - .09

-i 0 -.15

-i 0 -.21

-i 0 -.28

-I 0 -.34

-I 0 -.43

-i 0 -. 53

-i 0 - 66

-i.0 - 82

-1.0 -1 02

-1.0 -1 28

-1.0 -1 59

-1.0 -1 98

-i.0 -2 46

-I.0 -3 06

-1.0 -3 81

-I.0 -4 74

-I.0 -5.89

-i.0 -7.05

-i.0 -8.20

-5.0 -12.82 .0060 .0058

-5.0 -13.97 .0054 .0057

-5.0 -15.12 .0055 .0055

-1.0 -.03 0512 0471

0921 0925

0999 1006

0916 0896

OO58

0O57

0055

0416

0899

1007

0914

0172

0086

0066

0059

0057

0054

0553

0949

0997

0914

0658 .0625

0601 .0604

0533 .0545

0447 .0434

0297 .0307

0190 .0156

0090 0088

0068

0059

0058

0055

0601

0966

C982

0072

0059

0057

0054

0566

0978

1006

0633 .0633

0597 .0615

0523 .0551

0441 .0459 .0459

0299 .0316 .0308

0167 .0178 .0173

0093 0089 .0091

0066

0058

0056

0055

0527

0975

0986

0891 .0909 .0913

0684

0649

0649

0611

0541

0851

0820

0779

0784

0762

0752

0734

0733

0845 0868 0835 .0807 .0827 .0857

0827 0810 0795 .0798 .0798 .0807

0795 .0776 0790 .0789 .0772 .0787

0747 .0766 .0765 .0759 .0767 .0791

0769 .0735 .0758 .0755 .0752 .0744

0770 .0755 .0735 .0735 .0730 .0741

0853

0816

0793

0774

0772

0783

0747 .0722 .0722 .0738 .0730 .0729 .0761

0727 .0721 .0725 0700 .0724 .0718 .0750

0872

0823

0781

0797

0780

0753

0739

0724

0704 0733 .0719 .0703

0696 0701 .0697 .0674

0683 0660 .0674 .0678

0661 0669 .0668 .0651

0635 .0629 .0646 .0634

0595 .0604 .0597 .0579

0538 .0531 .0529 .0525

0449 .0451 .0454 .0438

0318 .0304 .0305 .0297

-1.0 -9.36 .0179 .0175 .0174 .0163

-1.0 -10.51 .0096 .0103 .0090 0087

-i.0 -Ii.66 .0065 .0070 .0066

-i.0 -12.82 .0060 .0054 .0054

-i.0 -13.97 .0058 .0055 .0055

-I.0 -15.12 .0059 .0051 .0053

.0 -.03 .0731 .0631 .0572

.0 -.09 .1018 .0973 .0972

.0 -.15 .0972 .0979 .0962

.0 -.21 .0927 .0909 .0890

.0 -.28 .0864 .0854 .0855

.0 -.34 .0828 .0830 .0824

0067

0053

0055

0053

0640

I001

0970

0696 .0699 .0714 .0707

0695 .0695 .0705 .0690

0664 .0672 .0668 .0660

0659 .0648 .0661 .0662

0622 .0644 .0644 .0635

0603 .0576 .0596 .0601

0524 .0527 .0542 .0514

0428 0439 0441 0433

0298

0178

0092

0064

0054

0055

0053

0305

0174

0098

0069

0055

0057

0053

0320

0175

0083

0067

0055

0056

0054

0324

0196

0101

0067

0054

0056

0052

0706

0714

0677

0661

0641

0602

0521

0442

0317

0182

0094

0066

0056

,0055

0053

0739

1017

0961

0898 .0876

0832 .0834

0810 .0805

0762 0679

1063 1042

0994 1005

0921 0935

0896 .0887

0809 .0849

0683 .0745

1068 .i033

0993 .0959

0927 .0928

0916 .0883

0839 .0840

0066 .0068

0063 .0059

0058 .0056

0055 .0056

0556 0550

0933 0948

1014 0994

0925 0922
164

Table D.16 (cont'd).

0

0 -.53 .0791 .0792

0 -.66 .0779 .0780

0 -.82 .0781 .0774

0 -1.02 .0755 .0753

0 -1.28 .0748 0749

-.43 .0807 .0797 0775 0774 .0793 .0803 .0818 0799 .0808

0773 .0785 .0787 .0785 0808 .0796

073i

0734

0679

0701

0652

0611

0546

0 -1.59 .0738

.0 -1.98 .0715

.0 -2.46 .0705

.0 -3.06 .0674

.0 -3.81 .0646

.0 -4.74 0617

.0 -5.89 0559

,0780

,0763

,0762

,0760

,0733

,0742

,0720

0690

,0679

0675

0627

0568

0464 .0467 .0455

0323 .0338 0322

0180

0098

0069

0062

0055

0052

0223

0240

0264

0362

0824

1223

1059

0817

0787

0759

0771

0738

0726

0710

0672

0667

0641

0612

0577

0545

0480

0271

0183

0073

0065

0060

0375

0177 .0172

0102 .0100

6070 .0065

0059 .0065

0057 .0057

0059 .0053

0197 0182

0224 0206

0220 0234

0324 0349

0753 0795

1158 1212

1107 1120

0841 0826

0792 0787

0776 0794

0772 0779

0750 0761

0727 0735

0706 0732

0691 0694

0660 0673

0632 0642

0625 0616

0580 0579

0556 0538

0477 0470

0264 0247

0176 0178

0082 0077

0067 0064

0058 0059

0403 .0385

.0 -7.05

.0 -8.20

.0 -9.36

.0 -i0.51

.0 -11.66

.0 -12.82

.0 -13.97

.0 -15.12

1.0 .58

1.0 .40

1.0 .21

1.0 .03

1.0 -.12

1.0 -.25

1.0 -.40

1.0 -.63

1.0 -.79

1.0 -.99

1.0 -1.24

1.0 -1.56

1.0 -1.95

1.0 -2.43

1.0 -3.03

1.0 -3.78

1.0 -4.71

1.0 -5.86

1.0 -7.02

1.0 -8.17

1.0 -9.32

1.0 -10.48

1.0 -11.63

1.0 -12.78

1.0 -13.94

1.0 -15.09

3.0 .58

0780 .0772 .0769 .0786

0773 .0750 .0763 .0756

0752 0743 .0749 .0764

0753 0717 .0730 0756

0728 0708 .0715 0749

0725 0718 0692 0731

0697 0692

0656 0662

0655 0646

0616 0606

0544 0546

0442 0444

0316 0299

0171 0172

0101 0092

0067 0067

0063 0064

0056 0055

0052 0053 .0051

0192 0370 .0392

0185 0323 0365

0219 0245 0309

0376 0346 0394

0875 0871 0799

1255 1192 1252

1049 0996 1051

0805 0805 0814

0755 0779 0792

0773 0766 0794

0730 0744 0760

0745 0738 0742

0715 0694 0718

0717 0716 0708

0692 0666 0672

0649 0659 0642

0625 .0624 0651

0600 .0616 0608

0581 .0566 0564

0527 .0520 .0526

0461 .0468 0461

0265 .0254

0170 .0168

0077 .0079

0065 .0064

0059 .0059

0572 .0655

0701

0668

0642

0613

0546

0453

0296

0161

0093 .0096

0070 0065

0062 0063

0055 0056

0769 .0772

0787 .0754

,0760 .0753

0751 .0755

,0726 .0745

,0707 ,0730

0683 .0700

0685 0688

0667 0629

0621 0611

0547 0547

0433 0463

0305 0309

0168 0176

0093

0078

0062

0055

0239

0179

0073

0063

0059

0604

,0696

0687

0661

0615

0566

0449

0321

0188

0096

0064

0065

0055

0051

0317

0323

0302

0404

0791

1202

1098

0841

0808

0770

0766

0776

0731

0705

0696

0649

0633

0603

0592

0530

0461

0251

0162

0076

0063

0059

0452

0052 0052

0235 0180

0243 0201

0258 .0225

0345 0368

0758 0761

1164 1178

1140 1109

0844 0857

0794 0800

0785 0792

0790 0768

0752 0768

0736 0769

0722 0728

0698 0691

0662 0648

0640 0638

0621 0601

0573 0569

0536 0537

0483 0466

0269 0262

0164 0178

0079 0078

0064 0064

0059 0060

0334 0325
165

Table D.16 (cont'd).

3.0

3.0

3.0

3.0

3.0

3 0

3 0

3 0

3 0

.40 .0489 0482 0543 0614 0626 .0623 .0564 0506 0452

.21 .0772

.03 I010

-.12 1167

-.25 1238

-.40 1267

-.63 1083

-.79 0895

-.99 0816

0789 0876

1045 1078

1160 1202

1223 1296

1232 1253

1017 1017

0862 0844

0798 .0809 .0797 .0756

0872

1095

1209

1237

1207

0972

0835 .0832

0872 0845 0882

1087

1238

1278

1230

0985

1156 1104

1235 1217

1343 1359

1379 1361

1113 1178

0917

0788

1053

I167

1256

1311

1126

0978 .0977

0817 .0814 .0841

0776

1020

1147

1259

1237

1084

0932

0802

3

3

3.0 -1.95 0738 0734 .0720

3.0 -2.43 .0702 .0708 .0721

3.0 -3.03 .0693 .0698 .0689

3.0 -3.78 .0667 .0669 .0660

3.0 -4.71 .0652 .0644 .0666

3.0 -5.86 .0587 .0588 .0585

0 -1.24 0787 0799 .0761 .0755 .0765 .0748 .0771 .0780 0808

0 -1.56 0762 0770 .0760 0752 .0726 .0739 .0762 .0751 .0773

0732 .0740 .0705 .0736 .0746 .0746

0696 .0690 .0706 .0715 .0706 0714

_0690 .0684 .0670 .0679 .0702 0698

0665 .0654 .0651 .0686 .0672 0671

0627 .0640 0655 0652 0643 0656

0571 .0569 0586 0580 0582 0583

3.0 -7.02 .0537 ,0541 .0515 .0523 .0520

3.0 -8.17 .0355 .0336 .0331 .0336 0336

3.0 -9.32 .0252 .0248 .0249 .0235

3.0 -10.48 .0113 .0105 .0111 .0115

3.0 -11.63 .0084 .0085 .0080 .0077

3.0 -12.78 .0064 .0061 .0061 .0063

3.0 -13.94 .0056 .0057 0056 .0055

3.0 -15.09 .0062 .0059 0059 0060

5.0 2.00 .0102 0135 0108 0114

0223

0103

0085

0061

0056

0059

0129

0535 0536

0337 0339

0251 0254

0098 0098

0083 0087

0061 0060

0056 0056

0061 0057

0134 0143

5.0

5.0

5.0 - .96

5.0 -1.94

5.0 -2.93

5.0 -3.92

5.0 -4.90

5.0 -5.89

5.0 -6.88

5.0 -7 86

1.01 .0306

.03 1274

0873

0713

0676

0625

0575

0498

0399

0249

0269 0342

1224 1334

0844 0836

0720 0712

0679 .0673

0632 0615

0570 0581

0492 0489

0411 0385

0251 0238

0410

1363

0808

0711

0669

0616

0562

0492

0427 ..0365 0351

1408 1419 1349

0772 0859 0976

0693 0706 0717

0665 0667 .0678

0591 0603 .0607

0548 .0566 .0562

0488 .0503 .0483

0379 .0369 .0364 .0382

0232 .0231 .0228 .0240

0534 0534

0358 0341

0225 0273

0104 0095

0090 0087

0061 0064

0056 0054

0058 0059

0109 0096

0311 0264

1253 1183

0972 0924

0720 0698

0664 0674

0609 0620

0571 0592

0484 0486

0398 0398

0250 .0266

5.0 -8

5.0 -9

5.0 -I0

5.0 -II

5.0 -12

5.0 -13

5.0 -14

5.0 -15

5.0 -16

5.0 -17

I0.0 4

I0.0 2

85 0152

84 0088

82 0073

81 0061

79 0060

78 0062

76 0062

75 0058

74 0055

72 0054

O0 0067

87 0108

0151

0094

0067

0062

0058

0057

0057

0053

0052

0051

0062

0097

0162 .0147 .0136 .0134 .0147 .0152 .0147

0087 .0084 .0086 .0089 .0088 .0088 .0096

0073 .0068 .0066 .0064 .0067 .0070 .0066

0063 .0064 .0063 .0062 0063 .0062 .0063

0057 .0057 .0057 .0056

0057 .0057 .0057 .0058

0057 .0057 .0056 .0059

0053 .0052 .0053 .0055

0050 .0051 .0051 .0051

0051 .0051 .0051 .0051

0057 .0058 .0057

0056 .0057 .0057

,0059 .0058 .0058

_0054 .0054 .0055

,0053 .0052 .0052

0051 .0052 .0052

0064 .0081 .0091 .0103 .0094 .0079 .0064

0107 .0142 .0159 .0187 .0157 .0109 .0101
166

Table D.16 (cont'd).

i0.0

I0.0

i0.0 -.51

i0.0 -1.63

I0.0 -2 76

I0.0 -3 88

I0.0 -5 01

i0.0 -6 14

I0.0 -7 26

I0.0 -8 39

I0.0 -951

i0.0 -i0 64

i0.0 -11.77

I0.0 -12.89

I0.0 -14.02

I0.0 -15.15

I0.0 -16.27

I0.0 -17.40

I0.0 -18.52

15.0 6.00

15.0 4.73

15.0 3.47

15.0 2.20

15.0 .93

15.0 - .33

15.0 -1.60

15.0 -2.86

15.0 -4.13

15.0 -5.40

15.0 -6.66

15.0 -7.93

15.0 -9.19

15.0 -10.46

15.0 -11.73

15.0 -12.99

15.0 -14.26

15.0 -15.53

15.0 -16.79

15.0 -18.06

15.0 -19.32

25.0 I0.00

25.0 8.45

25.0 6.91

"25.0 5.36

25.0 3.81

25.0 2.27

25.0 .72

25.0 -.82

1.75 .0369 0385 0501 .0507 0579 .0497 .0387 .0332 0360

1055

1220

0765

0686

0630

0558

0487

0338

0198

0107

0073

0061

0057

0058

0057

0052

0052

0050

0056

0076

0153

.62 1062

1271

0766

0680

0621

0560

0473

0334

0208

0112

0073

0063

0060

0057

0063

0053

0052

0053

0061

0089

0164

0503

1091

1326

0922

0687

0619

0550

0430

0273

0142

0087

0070

0062

0059

0065

0057

0059

0054

0053

0071

0103

0164

0421

0888

1253

1162 .I172

1172 .i150

0769 .0751

0695 .0679

0621 .0617

0552 .0544

0476 .0462

0328 0319

0189 0180

0100 0100

0070 0069

0061 0062

0056 0057

0058 0058

0057 ,0058

0051 0053

0051 0052

0052 0052

0053 0055

1218 .1240 .i004 .1053

1151 .1245 .1355 .1361

0729 .0742 .0832 0851

0657 .0653 .0657

0620 .0595 .0620

0552 .0533 .0547

0448 .0457 .0462

0312 .0288 .0304

0182 .0176 .0179

0103 .0096 0108

0071 .0071

0060 .0063

0058 0059

0058 0058

0058 0057

,0052 0051

,0053 0052

0053 0052

0072 ,0087

,0068

,0062

,0058

,0058

,0059

0053

,0053

0052

0088

_0670

,0627

0549

0464

_0322

0187

_0099

,0072

,0062

_0057

0058

0059

0052

0053

0054

0079

1038

0075

0163

0505 .0563

1092 1129

1334 1330

0976 0906

0709 0691

0626 0622

0086 .0121

0211 .0240

0698 .0724

,1232 .1202

1266 ,1276

0817 ,0800

0705 0664

0621 ,0586

0558 0547 .0531

0448 0432 .0421

0294 0285 .0255

0147 0147 .0139

0081 .0082 .0079

0067 .0068 .0067

0057 0056 .0057

0057

0057

0055

0053

0054

0071

0076

0059 .0057

0058 .0056

0056 .0054

0053 .0052

0054 .0053

0067 .0058

0069 .0068

0511

0398 0384 0403

0259 0233 0247

0117 0125 0130

0077 0076 0080

,0067 0068 0065

,0059 ,0059 0057

0059 0059 .0058

0056 0057 0058

0056 ,0055 0056

,0055 0055 ,0055

0054 0053 0054

0047 0056 0084

0052 0064 0103

0097 .0087 .0076 0120 0163

0133 .0138 .0217 0305

0253 .0463 .0665 0741

0724 .0983 .1130 1148

1204 .1303 .1350 .1305

1440 .1318 .1189 .1136

0112

0162

0278

0551

0987

1318 .1258

1271

0807

0680

0632

0576

0491

0333

0204

0113

0076

0064

0057

0059

0057

,0052

,0053

0053

,0067

0097

0159

0433

0429

0265

0133

0084

0068

0058

0060

0058

0056

0053

0054

0091 .0076

0124 .0102

0188 .0156

0314 .0317 .0264

0746 .0688 .0454

1150 .1094 .0736

1337 .1343 .1175

1143 .1181 .1320

0543

0436

0281

0136

0094

0068

0059

0061

0058

0055

0052

0053

0137 0144 0120

0266 0297 0215

0832 0650 0412

1241 .1158 0999 .1054

1258 .1312 .1305 .1383

0774 .0919 .1127 .1095

0674 .0683 .0716 .0713

0610 .0597 .0598 0635

0513 .0516 0541
167

Table D.16 (cont'd).

25.0 -2.37 .0911 1189 1059 .0882 .0800 .0748 .0740 0779 1128

25.0 -3.92 .0658

25.0 -5.46 .0554

25.0 -7.01 0420

0230

0108

0073

0063

0062

0054

0054

0054

0050

0043

0056

0076

0100

0150

0325

0746

1146

1360

1274

0858

0581

0387

0172

0097

0072

0067

25.0 -8.55

25.0 -I0.I0

25.0 -11.65

25.0 -13.19

25.0 -14.74

25.0 -16.29

25.0 -17.83

25.0 -19.38

25.0 -20.92

40.0 16.00

40.0 14.03

40.0 12.07

40.0 I0.i0

40.0 8.13

40.0 6.17

40.0 4 20

40.0 2 24

40.0 27

40.O -i 70

40.0 -3 66

40.0 -5 63

40.0 -7 60

40.0 -9 56

40.0 -II 53

40.0 -13 49

40.0 -15 46

40.0 -17 42

40.0 -19 39

40.0 -21 36

40.0 -23

60.0 24

60.0 21

60.0 18

60.0 16

60.0 13

60.0 II

60.0 8

60.0 6

60.0 3

60.0 i

60.0 -i

60.0 -3

60.0 -6

60.0 -8

0766

0563

0432

0276

0117

0077

0066

0712 .0659 .0657 .0617 .0603

0588 .0558 .0550 .0527 .0504

0451 .0413 .0382 .0352 .0342

0252 .0231 .0202 .0180 .0171

0123 .0106 .0101 .0095 .0096

0078 .0076 .0073 .0076 .0072

0065 .0061 .0061 0062 .0062

0629 0703

0059 .0061 ,0060 .0059

0054 .0055 .0055 .0057

0052 .0053 .0051 .0053

0056 .0056 0054 .0055

0053 .0052

0085 .0081

0113 .0110

0160 .0148

0230 .0216

0385 .0368

0610 .0539

0994 .0730

0051 .0052

,0069 .0062

,0090 .0077

,0116 .0088

0158 .0112

0248 .0149

0362 .0203

0527 .0325

1254 .I020

1304 .i181

1069 .1304

0714 .Ii09 1191

0520 .0688 0814

0313 .0436 .0487

0153 .0194 0243

0092 .0095 0113

0081 .0075 0078

0071 .0066 0070

0059 .0061 .0058 0061

0055 .0059 .0058 0059

0060 .0065 .0061 0059

0054 .0058 .0054 0053

0038 .0056 .0058 0062

0048 .0062 .0058 .0078

0061 .0070 .0078 .0123

0081 .0085 .0120 .0185

0104 .0118 .0205 .0319

0159 .0173 .0397 0516

0063 .0062

0056 .0057

0055 .0055

0056 0055

,0055 ,0055

0058 0054

0069 0064

0078 0078

0099 0105

0131 ,0163

0199 ,0498

0506 ,1006

32

O0

47

95

42

90

37

84 0819

32 1158

79 1277

26 1146

26 0877

79 0643

31 ..0618 .0445 .0328 0423

84 .0326 .0220 .0188 .0215

0333 .0364 .0789

0689 .0855 .1220

1078 .1248 .1434

1314 .1387 .1261

1379 .1115 .0847

1097 .0728 .0580

0519

0379

0171

0093

0071

0062

0063

0057

0055

0055

0055

0046

0057

0084

0160

0365

0754

1176

0680 .0559 .i010 .1360 .1393

0901 .I021 1344 .1401 1312

1298 .i157

0888 .0754

0615 .0548

0429 .0333

0188 .0147

0102 0094

0080

0070

0061

0055

0057

0053

0940

0666

0480

,0275

0138

,0091

0078 .0079

0068 .0071

0061 0064

0057 ,0061

0060 0063

0054 0056 .0057

0051 .0046

0066 .0057

0095 .0083

0145 0120

0259 0191

0430 0312

0586 0449

0776 0599

0544

0417

0237

0100

0070

0062

0060

0055

0052

0057

0055

0067

0100

0144

0236

0446

0800

1207

1366

1268

0845

0628

0455

0262

0118

0084

0079

0069

0062

0061

0064

0935

1025

1115

1136

0986

0632

0721 .0578 .0753

0873 .0751 .iiii

0937 .0968 .1253

1024 .1120 .1099

1047 .0963 .0641

0661 .0504 .0319

1128 1269

I133

0728

0471

0233

0115

0083

0071

0061

0056

0058

0054

0059

0074

0106

0166

0275

0427

0565

0870

1216

1228

1213

1091

0762

0369

0047 .0051

0058 .0059

0079 .0074

0100 .0088

0137 .0112

0210 .0160

0309 .0234

0456 .0377
168

Table D.16 (cont'd).

60 0 -11.37 .0153 .0157 .0150 .0147 0183 0228 .0238 .0202 .0155

60

6O

60

60

60

60

76

76.9 -13.86 .0150 .0172

76.9 -12.24 .0184 .0252

76.9 -10.63 .0254 .0416

76.9 -9.01 .0407 .0786

76.9 -7.40 0628 0955

76.9 -5.78 0894 1042

76.9 -4.17 1150 1029

0 -13.89 .0108 .0135 .0134 0120

0 -16.42 .0084 .0092 .0093

0 -18.95 .0069 .0077 .0077

0 -21.47 .0065 .0081 .0085

0 -24.00 .0061 .0068 .0069

0 -26.52 .0056 .0062 .0064

9 -15.47 .0125 .0147 0145

0170

0201

0240

0345

0607

0886

1052

0096

0079

0078

0069

0064

0145

0169

0199

0194

0267

0308

0424

0607

0118

0090

0075

0074

0067

0062

0139

0158

0189

0175

0228

0255

0322

0440

0123 .0133 .0128 .0120

0079 .0088 .0094 .0091

0064 .0069 .0074 .0075

0069 .0068 .0068 .0070

0060 .0057 .0060 .0063

0058 0057 .0056 .0058

0150

0171

0198

0233

0318

0457

0593

0766

0144 .0146 .0149

0175 .0231 .0198

0255 .0436 .0392

0461 .0726 .0737

0724 0923 .0937

0888 0965 i001

0995 1028 0984

1072 1008 0960

76.9 -2.55

76.9 -.94

76.9 .68

76.9 2.30

76.9 3.91

76.9 5 53

76.9 7 14

76.9 8 76

76.9 I0 37

76 9 II 99

76 9 13 60

76 9 15

76 9 16

115 4 23

115 4 21

115 4 19

115 4 16

1317

1367

1351

1281

1180

0983

0968 1159

0940 1148

0896 1043

0853 0900

0749 0767

0729 .0708

22

83

58

37

17

97 .0251 .0613 .0583 .0525

0858 .0566 .0910

1106 .0740 .0968

1200 0874 .1065

1248 1102 .1097

1181 1221 .1130

1027 1246 .1112

1107

1148

1179

1200

1254

1203

0831 .0620 .0583 .0855 1229 .1061 .0986

0576 .0533 .0501 .0578 1059 .0973 .0756

0392 .0445 .0416 .0445 _0834 .0890 .0570

0244 .0389 .0325 .0340 .0611 .0812 .0521

0187 .0319 .0282 .0286 .0428 .0632 .0471

0131 .0225 .0202 .0214 .0303 .0430 .0360

0112 .0188 .0159 .0169 0223 .0296 .0267

0124 .0264 .0283 .0283 0281 .0280 .0264

.0140 .0376 .0362 .0344 0340 .0339 .0347

0183 .0471 .0473 .0459 0430 .0425 .0442

1052 0946

1080 0980

1048 0936

1073 0920

1052 0842

1016 0810

0912 0715

0743 0626

0603 0541

0533 0470

0431 0382

0315 0286

0240 0227

0267 0250

0348 .0358

0456 .0455

0519 .0534 .0537 .0543 .0608

115

115

1154 10.37 .0834 .1082 .0984

115.4 8.17 .0994 .1140 .1131

115.4 5.97 .1204 .1171 .1297

115.4 3.77 .1308 .1113 .1365

115.4 1.56 .1422 .1012 1216

4 14.77 .0414 .0772 .0725 .0600

4 12.57 .0597 .0904 .0855 0756

1210

1151

1059

0960

0860

0686

0442

0270

0270

115.4 -.64 .1447 .0911

115.4 -2.84 .1405 .0804

115.4 -5.04 .1278 .0696

115.4 -7.24 .I042 .0574

115.4 -9.44 .0687 .0436

115.4 -11.64 .0428 .0350

115.4 -13.84 .0258 .0312

115.4 -18.25 .0206 .0231

115.4 -18.25 .0174 .0231

0976

1339

1471

1515

1395

1375

1291

1218

1091

1036

0961

0746

0280

0280

0586 .0619 .0655 .0693 .0728

0826 0868 .0852 .0844 .0867

1057

1328

1458

1462

1357

1348

1320

1288

1189

1080

0996

0831

0275

0275

1021 .0990 .0985 .1044

1183 1075 .1074 .1156

1332

1314

1291

1280

1297

1268

1174

1130

0981

0728

0230

0230

1194 .1174 .1238

1206 .1224 .1271

1265 .1270 .1205

1282 .1290 .1007

1266 .1252 .0750

1245 1064 .0508

1159

1005

0743

0433

0193

0193

0821 .0388

0528 .0322

0368 .0291

0273 .0248

0187 .0199

0187 .0199
169

Table D.16 (cont'd).

115.4 -20.45 .0148 .0216 .0225 .0204 .0168 0140 0154 .0161 .0175

153.8 -28.62 .0131 .0119 .0115 .0141 .0177

153.8 -25.51 .0162 .0178 .0138 .0161 .0203

153.8 -22.41 .0199 .0287 .0187 .0187 0224

153.8 -19.30 .0240 .0555 .0373 .0261

153.8 -16.19 .0339 .0932 .0647 0350

153.8 -13.09 .0532 .1263 .1068

153.8 -9.98 .0929 .1431 .1302

153.8 -6.87 .1290 .1524 1535

153.8 -3.76 .1423 .1592

153.8 -.66 .1495 .1608

153.8 2.45 .1443 1627

153.8 5.56 .1334 1640

153.8 8.66 1209 1480

153.8 11.77 1028 1250

153.8 14.88 0773 1063

1545

1579

1605

1558

1482

1342

1153

0612

0908

1294

1534

1591

1609

1517

1446

1367

1199

0289

0323

0396

0516

0785

1089

1366

1445

1432

1404

1307

1214

0214

0258

0292

0344

0398

0507

0699

0887

1028

1213

1302

1257

1208

1137

1102

0237 .0217 .0167

153.8 17.98

153.8 21.09

153.8 24.20

153.8 27.30

153.8 30.41

153.8 33 52

192.3 43 46

192.3 39 45

192.3 35 43

192.3 31 42

192.3 27 41

192.3 23 40

192.3 19 38

192.3 15 37

192.3 II 36

192.3 7.35

192.3 3.33

192.3 -.68

192.3 -4.69

192.3 -8.70

192.3 -12.72

192.3 -16.73

192.3 -20.74

192.3 -24.75

192.3 -28.77

0523

0321

0201

0152

0126

0113

0109

0877 0976 1058

0789 0807 0897

0682 0694 .0725

0575 .0566 .0594

0456 .0448 .0487

0368 .0362 .0363

0433 .0433 .0431

0127 .0540 .0537 .0553

0283 .0269 .0226

0335 .0335 .0333

0402 .0556 .0634

0639 .0875 .0989

0881 .1115 .1246

1077 .1305 .1392

1210 .1445 .1474

1269 .1541 .1522

1433 .1681 .1669

1506 .1680 .1671

1380 .1663 1702

1128 .1276

I001 .1016

0983 .0912

0892 .0831

0838 0783

0647 0660

II01 .I011

0929 .0949

0759 .0738

,0594 .0576 .0583

0489 .0486 .0485

0374 .0365 .0363

0456 .0456 .0455

0561 .0544 .0557

1429

1131

i001

0859

0791

0660

1704

1493

1366

1145

0823

0518

0305

0966 0982 .1044

0990 1039 .1095

1078 1113 .1218

1150 1280 .1425

1309 1427 .1539

1561 1633 .1626

1047 1081

1150 1179

1280 1280

1455 1405

1562 1426

1608 .1466

1745

1804

1673

1532

1404

1224

0887

0542

0280

1726 .1681 .1623 .1457

1701 1641 .1604 1441

1643

1574

1465

1232

0857

0455

0241

1647 .1542

1563 .1326

1361 0971

1030 0627

0618 0352

0339 0219

0172 0176

1289

0969

0682

0479

0365

0281

0223

192.3 -32.78 .0138 .0237 0242

192.3 -36.79 .0126 .0205

230.8 -44.97 .0125 .0109

230.8 -40.05 .0147 .0151

230.8 -35.13 .0177 .0174

230.8 -30.21 .0227 .0405

230.8 -25.29 .0320 .0762

0214

0105

0131

0170

0252

0523

0218

0192

0137

0163

0181

0232

0355

0186 0148

0153 0114

0176 0200

0206 0237

0233 0276

0289 0351

0377 .0491

0124

0100

0200

0238

0279

0386

0620

0150

0126

0177

0215

0263

0454

0760

0198

0168

0141

0170

0236

0498

0811

1496 .1370 .1575

1298 .Iiii .1346

0910 .0913 .1229

0541 .0637 .0968

0345 .0453 .0642

0245 .0364 .0447

0184 .0283 .0312

0297 .1114 .1028 .0963

0505 .1169 .1072 .0990

0688 .1203 .1105 .1085

0952 .1261 .1155 .1112

1198 .1272 .1136 .1190

1395 .1240 .1252 .1430

1536 .1329 .1497 .1708

1532 .1424 .1686 1839

0155 .0737 .0729 .0701 .0703 .0701 .0722 .0736 .0740

0197 .0885 .0896 .0849 0814 .0852 .0860 0889 0895

0551 0545

0463 0454

0371 0376

0445 0444

0552 0577
170

Table D.16 (cont'd).

230.8 -20.37 .0485 .1086 0825 0546 0497 .0746 0931 1084 .1135

230.8 -15.46 .0848 .1377

230.8 -10.54 .1277 .1578

230.8 -5.62 .1570 .1646

230.8 -.70 .1610 .1691

230.8 4.22 1582 .1659

230.8 9.14

230.8 14.06

230.8 18.97

230.8 23.89

230.8 28.81

230.8 33.73

1418 .1601

1221 .1454

0940 .1305

0661 .1252

0390 .1162

0237 .1027

230.8 38.65 .0179 .0890

230.8 43.57 .0150 .0683

230.8 48.48 .0131 .0581

i170

1454

1589

1636

1627

1633

1516

1427

1280

1157

1056

0910

0718

0578

0810

1128

1440

1528

1591

1585

1551

1423

1338

1186

1054

0926

0708

0576

0723 .1023

1097 .1290

1359 .1531

1406 .1545

1435 1395

1466 1327

1437 1266

1345 1292

1363 1288

1202 1173

1068 1051

0931 0889

0716 0727

0571 0580

1223

1467

1703

1741

1506

1296

1249

1227

1180

1144

1035

0874

0722

0568

1356 .1394

1546 .1608

1712 .1639

1776 .1751

1616 .1652

1430 .]552

1284 .1376

1201 .1237

1182 .1204

1137 .II00

1014 .0993

0859 .0868

0693 .0697

0572 .0576
171

Table D.17 = Entrainment Field u (8--60 °)

x/0 o

107 7

107 7

107 7

107 7

107 7

123 1

123 1

123 1

123 1

123 1

138.5

138,5

138.5

138.5

138.5

153.8

153.8

153.8

153.8

153.8

169.2

169.2

169.2

169.2

169 2

184 6

184 6

184 6

184 6

184 6

200 0

200 0

200 0

200 0

Unforced

y/80 data

17 54 027

25 31 012

33 07 010

40 83 010

48 59 006

20 79 021

30 00 011

39 21 011

48 42 008

57 63 003

24 04 019

34 70 012

45 36 011

56 Ol 007

66 67 002

27 29 019

39 40 013

51 5O Oll

63 61 005

75 71 003

30 54 018

44 09 013

57 65 010

71 20 005

84 75 004

33 79 019

48 79 014

63 79 010

78 80 005

93 80 006

37 04 019

53 49 014

69 94 010

86 39 004

Phase averaged data (at angle _)

0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

.033

.015

.008

•005

.003

.052

•021

010

004

006

052

018

006

005

005

037

014

•005

005

005

036

014

004

005

006

045

014

0O4

005

006

055

014

004

005

035

017

008

004

003

033

.015

008

004

005

052

019

007

0O5

O05

042

015

OO5

OO5

006

041

014

004

004

006

042

013

OO4

OO5

OO5

O53

014

O04

OO5

038

015

007

004

004

027

013

O06

004

005

045

017

007

004

005

044

017

006

004

•005

043

015

O04

004

006

040

013

004

005

005

049

014

004

005

O52

016

007

005

003

027

013

005

003

OO5

034

014

006

004

005

046

017

006

005

005

047

015

005

005

005

045

013

004

005

005

049

013

004

005

079

026

011

006

004

032

012

006

004

•005

029

013

005

004

O05

040

016

006

004

005

047

016

005

005

005

048

013

004

005

006

050

013

004

005

O95

035

015

007

003

042

015

•007

OO5

OO5

029

012

0O5

004

005

036

015

005

005

OO5

045

016

005

OO5

•O05

051

014

004

006

005

053

013

004

005

078

031

015

008

003

058

021

009

005

005

034

013

005

005

005

032

014

O05

004

O05

044

015

005

005

006

051

015

005

005

005

055

014

004

005

046

019

010

O06

003

064

024

010

005

006

044

015

006

005

OO5

O34

014

OO4

004

OO5

O4O

015

OO4

OO5

OO6

048

014

OO5

OO5

OO5

O56

014

OO4

OO6
172

Table D.18 Entrainment Field u (0--60*)

x/e 0

107.7

107.7

107.7

107.7

107 7

123 1

123 1

1231

123,1

123,1

138,5

138 5

138 5

138.5

138.5

153.8

153 8

153 8

153 8

153 8

169 2

169 2

1692

169,2

169 2

184,6

184 6

184,6

184 6

184 6

200.0

200.0

200.0

200.0

Unforced Phase averaged data (at angle _)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 y/e 0

17.54

25.31

33.07

40.83

48.59

20.79

30.00

39.21

48.42

57.63

24.04

34.70

45.36

56.01

66.67

27.29

39.40

51.50

63.61

75.71

30.54

44.09

57.65

71.20

84.75

33.79

48.79

63.79

78.80

93.80

37.04

53.49

69.94

86.39

.0243 .0351

0081 0143

0038 0079

0029 0059

0023 0054

0176 0434

0070 0169

0037 .0080

0030 .0062

.0031 .0060

.0162 .0446

.0064 .0156

.0036 .0081

.0034 .0078

.0034 .0075

0136 .0435

0058 0154

0040 0093

0040 0096

0044 0093

0129 0466

0061 0162

0047 0092

0044 0090

0054 .0099

0132 .0492

.0068 .0162

.O051 .0092

.0047 .0086

.0065 .0096

.0132 .0571

.0070 .0164

.0057 .0085

.0046 .0087

.0356

.0161

.0102

.0076

.0065

.0362

.0148

.0071

.0064

.0061

.0464

.0156

.0076

.0075

0076

0459

0163

0091

0091

0094

.0495

.0172

.0100

.0092

.0106

.0504

.0155

.0096

0091

0101

0563

0155

0089

0091

.0427

.0166

.0109

.0082

.0081

.0316

.0129

.0082

.0068

.0068

.0425

0154

0076

0071

0074

0459

0166

0087

0084

.0089

.0500

.0171

.0100

.0092

.0106

.0486

.0164

0093

0092

0102

0557

0164

0087

0092

.0538 .0569

.0162 .0180

.0105 .0101

.0078 .0074

.0072 .0062

.0337 .0379

.0144 .0159

.0090 .0092

.0080 .0086

.0075 .0073

.0381 .0356

.0142 .0140

.0077 .0082

.0073 .0077

.0077 .0077

.0466 .0439

.0158 .0156

.0082 .0079

.0080 .0077

.0083 .0078

.0524 .0510

.0166 .0159

.0094 .0087

.0088 0081

.0099 0093

0512 0533

0162 0163

0095 0096

0091 0086

0100 0097

0548 .0532

0170 .0167

0089 .0089

0095 .0090

.0546 .0511

.0194 .0195

.0107 .0100

.0068 .0063

.0059 .0049

0408 0471

0156 0167

0086 0083

0079 0071

0070 0061

0360 0377

0149 0149

0088 0089

.0084 0089

.0079 0083

.0422 .0399

.0152 .0154

.0082 .0085

.0083 .0087

.0083 .0087

.0507 .0508

.0164 .0156

0083 .0086

0077 0076

0089 0089

0539 0535

0164 0160

0086 0085

0084 0081

.0093 0090

.0538 0557

.0163 0165

.0089 .0086

.0088 .0087

315.0

.0433

.0160

.0071

.0055

.0045

.0478

.0178

.0085

0065

0060

0435

0154

0085

0084

0081

0402

0161

.0090

.0090

.0089

.0485

.0166

.0089

0083

0090

0529

0163

0087

0083

0091

0566

0161

0084

0087
173

Table D.19 Entrainment Field v (0--60 °)

x/0 o

107.7

107.7

107.7

107.7

107.7

123.1

123.1

123.1

123.1

123.1

138.5 24.04 -

138.5

138.5

138.5

138.5

153.8

153.8

153.8

153.8

153.8

169.2

169.2 44.09 -

169.2 57.65 -

169 2 71.20 -

169 2 84.75

184 6 33.79

184,6 48.79

184,6 63.79

184,6 78.80

184,6 93.80

200,0

200 0

200 0

200.0

Unforced Phase averaged data (at angle @)

y/90 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

17.54 -.047 -.094 - 088 - 099 -.120 -.120 -.099 .085 -.094

25.31 -.023 -.032 -

33.07 -.020 -.021 -

40.83 -.022 -.024-

48.59 -.024 -.028 -

20.79 - 036 -.076 -

30.00 - 021 -.036

39.21 - 022 -.028

48.42 - 024 -.031

57.63 028 -.033

038 -

027 035 -.042 -.043 -.037 -.028

028 033 -.036 -.036 -.033 -.028

030 032 -.035 -.035 -.033 -.030

072 068 -.073 -.085 -.095 -.095

031 -.033 -.039 -.047 -.052 -.051

026 -.027 -.031 -.035 -.037 -.037

029 -.029 -.031 -.034 -.035 -.035

032 -.031 -.032 -.033 -.034 -.035 -.034

054 -.066 -.065 -.053 -.037 -.031

022

024

028

085

043

033

033

033 -.083 -.081 -.076 -.074 - 072 - 076 -.082 - 084

036 -

029 -

030 -

033

079

036

034 - 033 031 -.029

034 - 034 - 033 -.032

040 -.045 -

032 - 035 -

031 - 033 -

033 034 -

077 078 -

037 039 -

029 031 -

031 032

035 035 035 -.034 -.034 034 -

087 088 -.087 -.086 -.087 -.087

041 042 -.041 -.039 -.037 -.037

033 -.034 -.033 -.032 -.031 -.030

34.70 021 -.044 -.040 -.035 -.033 -

45.36 023 -.035 -.033 -.030 -.028 -

56.01 -.027 -.034 -.033 - 031 - 030 -

66.67 -.030 -.035 -.035 - 034 - 033

27.29 -.030 -.084 -.084 - 083 - 080 -

39.40 -.023 -.045 - 045 - 043 039

51.50 -.025 -.034 -

63.61 -.029 -.034 -

75.71 -.032 - 035 -

30.54 - 028 - 088 -

023 - 039 -

027 - 032

046

036

034

035

081

042

032

033

035

087

038

031

031 -

033

027

025 037 -.038 -.039 -.040 -.040 -

029 -.030 -.030 -.031 -.031 -.031 -

032 -.032 -.032 -.032 -.032 -.032 -

034 -.034 -.034 -.034 -.034 -.034 -

37.04 -.028 -.095 -.093 -.094 -.095 -.097

53.49 -.026 -.038 -.038 -.038 -.039 -.040 -

69.94 -.030 -.030 -.030 -.030 -.030 -.030

86.39 -.033 -.033 -.033 -.033 -.032 -.032 -.032

032 -.033 -.033 -.033 -.032 -.032 -.032 -.032

035 -.035 -.035 -.035 -.034 -.034 -.034 -.035

089 -.089 -.089 -.090 -.092 - 091 -.089 -.089

039 -.038 -.037

031 - 030 - 030

032 -

034 -

095 -

040 -

030 -

032 - 032

034 - 034

096 - 096

040 - 039

030 - 030

032 033
174

Table D.20 = Entrainment Field _ (0--60 °)

x/O o

107.7

107 7

107 7

107 7

107 7

123 1

123 1

123.1

123.1

123.1

138.5

138.5

138.5

138.5

138.5

153.8

153.8

153.8

153.8

153.8

169.2

169.2

169.2

169.2

169.2

184.6

184.6

184.6

184.6

184.6

200.0

200.0

200.0

200.0

y/e o

17 54

25 31

33 07

40 83

48 59

20 79

30.00

39.21

48.42

57.63

24.04

34.70

45.36

56.01

66.67

27.29

39.40

51.50

63.61

75.71

30.54

44.09

57.65

71.20

84.75

33.79

48.79

63.79

78.80

93.80

37.04

53.49

69.94

86.39

Unforced Phase averaged data (at angle _)

data 0.0 45.0 90.0 135.0 180.0 225;0 270.0

0308 .0648

0113 .0203

0064 .0121

0044 .0091

0030 .0062

0232 .0452

0097 .0207

0059 .0110

0039 .0079

,0032 .0049

.0222 .0404

.0091 .0197

.0053 .0126

.0039 .0081

.0028 .0054

.0183 .0435

.0080 .0238

.0050 .0124

.0038 .0076

.0029 0057

.0167 0531

.0079 0219

.0052 0123

.0040 0068

,0029 0056

.0168 0612

.0083 0242

.0055 0110

.0042 0064

.0029 0054

.0160 0605

.0080 0241

.0057 0108

.0038 0065

.0535

.0214

.0144

.0100

.0067

.0490

.0202

.0110

.0078

.0048

.0477

.0194

.0119

.0078

0054

0444

0225

0124

0076

0059

0506

0228

0126

0070

0059

0611

0238

0111

0065

0055

0606

0241

0106

0065

.0545

.0235

.0151

.0105

.0073

0448

0213

0122

0083

0052

0496

0188

0112

0072

0050

0476

0228

0120

0075

0057

0509

0224

0127

0070

0057

0567

0242

0113

0066

0055

0636

0249

0105

0065

0554

0222

0149

0105

0073

0432

0226

0133

0090

0056

0501

0188

0112

0070

0050

0488

0220

0113

0071

0054

0493

0233

0127

0070

0057

0550

0244

0115

0067

0057

0618

0250

0105

0067

.0500

.0199

.0134

.0098

0069

0432

0226

0139

0095

0060

0447

0209

0118

0073

0050

0521

0211

0108

0069

0051

0513

0236

0122

0069

0056

0561

0242

0116

0067

0056

0624

0256

0106

0066

.0461 ,0448

.0184 0188

.0122 ,0113

.0089 0082

.0063 0058

.0435 0465

.0215 0198

.0136 0127

0094 0091

0061 0058

0421 0401

0219 0223

0125 0131

0079 0083

0052 .0056

0491 0469

0223 0227

0108 0113

0069 0071

0052 0052

0554 0587

0219 0226

0118 0115

0066 0064

0054 0053

0564 0578

0228 0235

0115 0113

0066 0066

0054 0053

0586 0572

0250 0256

0108 0109

0065 0066

315.0

0601

0202

0106

0081

0056

0452

0190

0118

.0085

.0052

.0385

.0213

.0131

0083

0056

0439

0233

0120

,0075

0054

0577

0226

0123

0065

0053

0595

.0235

0111

0065

0053

0585

0259

0108

0065
175

Table D.21 - Entrainment Field u'v' (0--60")

Unforced Phase averaged data (at angle _)

x/00 y/00 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

107.7 17.54- 0034-.0088-.0063-.0085-.0086-.0083-.0080- 0087- 0131

0000- 0001 .0013 .0012 .0003-.0003-.0002- 0001- 0003

0001 0005 .0009 .0011 .0006 .0001 .0000 0002

0000 0003 .0004 .0004 .0002 .0001 .0001 0001

0000 0001 .0001 .0002 .0001-.0001-.0001- 0000

0014- 0060-.0060-.0051-.0042-.0054-.0050- 0082-

0001- 0005-.0003 .0000 .0007 .0004-.0002-.0007-

0000 0001 .0002 0006 .0007 .0006 .0004 .0000

0000 0000 .0001 0002 .0003 .0003 .0001-.0001-

0000 0000 .0001 0002 0002 .0002 .0002 .0001

107.7 25.31-

107.7 33.07-

107.7 40.83

107.7 48.59

123 1 20.79-

123 1 30.00-

123 1 39.21-

123 1 48 42

123 1 57 63

138 5 24 04-

138 5 34 70-

138.5 45 36-

138.5 56 01

138.5 66 67

153.8 27 29-

153.8 39.40-

153.8 51.50

153.8 63.61

153.8 75.71-

169.2 30.54-

169.2 44.09-

169.2 57.65

169.2 71.20

169.2 84.75-

0010-.0045-.0058- 0066-

0001- 0009-.0008- 0007-

0000 0002 .0001 0002

0000 0001 .0001 0001

0000 0002 .0002 0002

0003- 0067-.0064-.0063-

0001- 0004-.0006-.0010-

0000 .0004 .0003 .0003

0059- 0040-.0035- 0045-

0003-

_0004

,0002

,0002

0078-

0009-

0002

0003 .0001 0001-

0005 .0005 0005

0002 .0003 0003

0003 .0003 0003

0086- 0082- 0049-

0008- 0008-.0002-

0003 0004 ,0005 .0005

0000 0004 .0003 .0003

0000 0004 .0004 .0003

0001- 0059-.0075-.0073-

0001- 0005-.0002-.0007-

0000 0005 .0005 .0004

0000 0004 .0004 .0004

0001 .0005 .0005 .0005

184.6 33.79-.0002-.0124-.0122- 0103-

184.6 48.79- 0000-.0010- 0005-

184.6 63.79

184.6 78.80

184.6 93.80-

200.0 37.04-

200.0 53.49-

200.0 69.94

0001 .0005

0000 .0003

0001 .0004

0000-.0150-

0000-.0010-

0001 .0005

200.0 86.39 .0000 .0003

0006

0004

0005

0165-

0004-

0005

0004

0009-

0006

0004

0OO5

0137-

0011-

0005

0004

0O02

0003

0083-

0010-

0004

0003

0004

0101-

0006-

0006

0004

0005 .0004

0143-.0127-

0005-.0007-

0005 .0005

0005 .0004

0002 ,0003

0002 ,0003

0091-,0087-

0012-,0009-

0003 .0004

0003 .0002

O004 00O4

0124- 0130-

0006- 0008-

0005 0005

OOO3 OOO3

0004

0122-

0007-

0005

0004

0001

0001

0000

0063

0008

0000

0001

0000

0052

0004

0003

0001

0002

0052

0001

0003 ,0003

0003 0003

0124- 0113

0009- 0009

,0004 0004

,0002 0003

,0004 .0004

0129-.0147

,0006-.0009

0004 0005

0003 ,0003

0004 0004

0133-0145

0010-0010

0005 0004

0003 0003
176

Table D.22 Entrainment Field u (0--45")

x/e 0

107.7

107.7

107.7

138.5

138.5

138.5

169.2

169.2

169.2

200.0

200.0

Unforced

Y/00

17.54

33.07

48.59

24.04

45.36

66.67

30.54

57.65

84.75

37.04

69.94

data 0.0

•028 .050

012 015

013 012

020 059

015 011

010 007

019 058

015 013

009 007

020 073

014 012

Phase averaged data (at angle _)

45.0 90.0 135.0 180.0 225.0 270.0 315.0

053

018

012

061

012

007

060

012

007

070

012

058

016

010

055

012

007

•064

•012

•007

•067

•013

062

014

008

047

013

007

•067

•012

.007

•068

.012

076

015

007

045

013

008

•068

.012

.007

•068

.012

092

017

007

047

013

007

064

012

.007

.071

.012

088

016

009

049

012

007

061

012

007

073

.012

.060

.013

.010

054

011

007

058

013

007

074

012

Table D.23 - Entrainment Field u (0--45")

x/e 0

107.7

107.7

107.7

138.5

138.5

138.5

169•2

169.2

169.2

200.0

200.0

Unforced

y/00 data

17.54

33.07

48.59

24.04

45.36

66.67

30•54

57.65

84.75

37.04

69.94

Phase averaged data (at angle _)

0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

O2O8

0048

0039

0114

0062

0041

0111

0070

0039

0104

0078

0380 .0325 .0348 .0379 .0432 •0441 •0451 •0443

0069 .0084 .0091 .0085 .0090 .0090 .0078 .0057

0056 .0060 .0059 .0051 .0043 .0041 .0048 .0053

0421 .0435 .0439 .0400 .0379 .0348 .0364 .0383

0071 .0071 .0067 .0070 •0074 .0077 .0072 .0072

0038 .0040 .0043 .0045 .0045 .0044 .0041 .0039

0490 .0497 .0525 .0548 •0559 .0524 .0506 .0488

0077 .0074 .0073 .0070 .0071 .0071 .0074 .0077

0042 .0043 .0043 .0043 .0044 .0044 .0043 .0042

0627 .0614 .0609 .0600 .0612 .0620 .0629 .0628

0070 .0072 .0073 .0073 .0070 .0069 .0070 .0070
177

Table D.24 Entrainment Field v (0--45*)

x/0 o

107.7

107.7

107.7

138.5

138.5

138.5

169.2

169.2

169.2

200.0

200.0

Unforced Phase averaged data (at angle _)

y/00 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

17.54 -.029 -.053 -.056 -.067 -.086 -.091 -.071 -.046 - 047

33.07 -.018 -.013 -.017 -.027 -.035 -.038 -.033 -.024 -

48.59 -.024 -.021 -.022 -.025 -.029 -.031 -.030 -.027 -

24.04 -.023 -.062 -.054 -.048 -.045 -.047 -.053 -.060 -

45.36 -.024 -.031 -.028 -.024 -.022 -.023 -.026 -.030 -

66.67 -.028 .031 -.031 -.030 -.029 -.029 -.030 -.030 -

30.54 -.024 -.061 -.064 -.064 -.063 -.061 -.058 -.058

57.65 -.027 -.025 -.026 -.027 -.027 -.026 -.025 -.024

84.75 -.030 -.030 -.030 -.029 -.030 -.030 -.029 -.030

37.04 -.026 -.061 -.059 -.061 -.062 -.064 -.065 -.064

69.94 -.030 -.023 -.022 -.022 -.023 -.024 -.024 -.024

016

023

065

032

031

059

024

030

063

024

Table D.25 - Entrainment Field _ (0--45*)

x/O o

107.7

107.7

107.7

138.5

138.5

138.5

169.2

169.2

169.2

200.0

200.0

Y/00

17.54 .0218 .0421 .0377 .0397

Unforced Phase averaged data (at angle _)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

0163

0093

0359

0122

0057

0435

0131

33.07 .0083 .0117 .0148

48.59 .0048 .0084 .0093

24.04 .0164 .0351 .0348

45.36 .0073 .0136 .0128

66.67 .0038 .0059 .0058

30.54 .0168 .0441 .0446

57.65 .0073 .0127 .0130

0404

0163

0083

0352

0120

0058

0407

0_30 .0126

84.75 .0036 .0052 .0053 .0055 .0055 .0055 0054

37.04 .0162 .0459 .0435 .0446 .0456 .0458 .0452

69.94 .0074 .0119 .0118 .0118 .0119 .0121 .0123

0373 .0339 .0327 .0349

0149 .0130 .0112 .0098

0074 .0068 .0066 .0071

0343 0369 .0375 .0364

0128 0137 0141 .0141

0060 0062 0062 0061

0413 0413 0428 0425

0123 0122 0124

0052 0052

0435 0449

0123 0121
178

Table D.26 - Entrainment Field u'v' (8--45 °)

x/e o

Unforced Phase averaged data (at angle _)

y/00 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

107.7 17.54- 0019- 0096- 0046-.0028- 0006 0005 0013- 0007- 0054

107.7 33.07

107.7 48.59

138.5 24.04-

138.5 45.36

138.5 66.67

169.2 30.54-

169.2 57.65

169.2 84.75

0001

0002

0004-

0002

0001

0004-

0003

0001

200.0 37.04-.0001-

200.0 69.94 .0004

0004

0005

0022-

0004

0002

0052-

0007

0002

0073-

0007

0008 0010

0006 0006

0031- 0050-

0004 0005

0002 0003

0052- 0034-

0007 0007

0002 0003

0068- 0107-

0007 0007

0007

0004

0050-

0006

0003

0040-

0007

0003

0069-

0007

0001-

0003

0048-

0007

0003

0058-

0007

0003

0069-

0007

0001

0003

0038-

0007

0003

0058-

0007

0003

0069-

0007

0001

0003

0025-

0007

0003

0070-

0007

0002

0067-

0007

0002

0004

0033

0006

0002

0065

0007

0002

0086

0007
179

Table D.27 - Entrainment Field u (0--90*)

x/Oo

107.7

107.7

107.7

138.5

138.5

138.5

169.2

169.2

169.2

200.0

200.0

Y/O0

17.54 - 005 - 027 -.024 - 027 - 002

33.07

48.59

24.04

45.36

66.67

30.54

57.65

84.75

37.04

69.94

Unforced Phase averaged data (at angle _)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

007 .006

001 -.002 -

006 .004 -

006 .006

006 -.005 -

011 -.011 -

006 -.006 -

005

002 -

005 -

005

006 -

006 -

006 -

009 -.010 -.009 -

014 -.015 -.015

005 -.006 -.006

005

001

011 -

002

006

007

004 -

009

013

006

012

007 -

004

011

007 -

008 -

009 -

007 -

011 -

009 -

035 038

006 010

001 003

010 - 006 -

001 001

007 - 008 -

009 -.011 -

004 -.004 -

009 .009 -

011 -.010 -

006 -.006 -

002 - 031

012 010

003 001

004 003

002 004

007 - 006

012 - 010

005 - 006

009 - 009

010 - 013

005 - 005

Table D.28 - Entrainment Field u (0--90*)

x/00

107 7

107 7

107 7

138 5

138 5

138 5

169 2

169 2

169.2

200.0

200.0

Unforced

y/00 data

17 54

33 07

48 59

24 04

45 36

66 67

30 54

5765

84.75

37.04

69.94

Phase averaged data (at angle ¢)

0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

0391

0093

0012

0264

0050

0014

0208

0028

0018

0164

0029

0452 .0496

0139 .0127

0037 .0039

0509 0502

0123 0121

0049 0050

0475 0491

0099 0097

0050 0051

0516 0509

0087 0088

0584

0127

0039

0483

0113

0052

0486

0095

0050

0491

0088

0729

0135

0044

0448

0114

0052

0493

0093

0050

0497

0089

0763

0157

0051

0429

0108

0052

0501

0098

0051

0498

0086

0704

0174

0053

0407

0106

0050

0512

0096

0052

0500

0087

0579

0172

0050

0434

0114

0049

0494

0096

0052

0508

0087

0499

0156

0044

0478

0116

0048

0471

0104

0051

0519

0088
180

Table D.29 Entrainment Field v (0--90*)

x/Oo

107.7

107.7

107.7

138.5

138.5

138.5

169.2

169.2

169.2

200.0

200.0

Y/e 0

17.54 -.097 -.135 -.131 -.150 -.177 -.186 -.171 -.156

33.07 -.024 - 037 -.034 -.036 -.041 -.047 -.050 -.047

Unforced Phase averaged data (at angle @)

data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

025 -.026 -.029 -.031 -.031 -.029 -.027

116 -.117 -.I12 -.103 -.095 -.093 -.099

039 -.036 -.034 -.034 -.036 -.039 -.041

033 -.032 -.031 -.031 -.032 -.032 -.033

113 -.115 -.i16 -.119 -.120 -.120 -.118

033 -.034 -.034 -.033 -.032 -.032 -.032

48.59 -.023 -

24.04 -.061 -

45.36 -.024 -

66.67 -.027 -

30.54 -.045 -

57.65 -.029 -

84.75 -.029

37.04 -.036

69.94 -.031 -

150

042

O25

109

042

033

114

032

032 -.032 -.032 -.032 -.032 -.032 -.032 -.032

127 -.124 -.122 -.120 -.I19 -.122 -.125 -.127

027 -.027 -.027 -.028 -.028 -.029 -.029 -.028

Table D.30 Entrainment Field _ (8--90")

x/O o

107.7

107.7

107.7

138.5

138.5

138.5

169.2

169.2

169.2

200.0

200.0

Unforced

y/80 data 0.0

17.54 .0596 .0786

33.07 .0094

48.59 .0028

24.04 .0413

45.36 .0061

66.67 .0027

30.54 .0275

57.65 .0053

84.75 .0027

37.04 .0186

69.94 .0050

0190

0063

0667

0142

0044

0683

0118

0043

0798

Phase averaged data (at angle @)

45.0 90.0 135.0 180.0 225.0 270.0 315.0

0812

0203

0068

0707

0142

0041

0693

0941

0200

0068

0738

0138

0039

0925 .0832 .0771 .0713

0196 .0182 .0181 .0179

0064 .0057 .0053 .0053

0682 .0628 .0579 .0579

0143 .0144 .0148 .0148

0040 .0043 .0046 .0047

0674 .0709 .0749 .0797 .0780

0122 .0124 .0118 .0118 .0120 .0123

0043 .0043 .0043 .0042 .0041 .0041

0750

0181

0058

0610

0144

0046

0728

0119

,0042

0808 .0783 .0753 .0742 .0763 .0761 .0783

0100 .0097 .0098 .0102 .0109 .0111 .0102 .0103
181

Table D.31 Entrainment Field u'v' (0--90")

x/0 o

Unforced Phase averaged data (at angle _)

y/00 data 0.0 45.0 90.0 135.0 180.0 225.0 270.0 315.0

107.7 17.54 .0105 .0202 0189 .0265 .0257 .0181 .0125 .0151 0226

107.7 33.07-.0002 .0002-

107.7 48.59-.0000 .0001

138.5 24.04 .0036 0100

138.5 45.36 .0000 0000

138.5 66.67-.0000- 0000-

169.2 30.54 .0012 0081

169.2 57.65-.0001

169.2 84.75 .0000

200.0 37.04-.0004

200.0 69.94-.0001

0001 .0001-.0003-.0003-.0001 .0004

0001 .0001 .0000-.0001-.0001 .0000

0133 .0157 .0132 .0073 .0020 .0013

0001 .0001 .0002 .0002 .0002 .0000-

0000 .0000 .0000 .0001 .0001 .0000-

0093 .0073 .0109 .0167 .0176 .0149

0002

0001

0034

0000

0000

0118

0005 .0004 .0004 .0002 .0003 .0002 .0003 .0004

0000 .0000 .0000-.0000-.0000-.0000 .0000 .0000

0209 .0219 .0191 .0145 .0156 .0147 .0159 .0200

0003 .0003 .0004 .0004 .0004 .0003 .0003 .0003
182

List of References

Ali, S.K., Klewicki, C.L., Disimile, P.J., Lawson, I. and Foss, J.F.

"Entrainment Region Phenomenafor a Large Plane Shear Layer", Turbulent

Shear flows V, 1985, pp. 3.7-3.12.

Clauser, G.H. [1954] "Turbulent Boundary Layers in Adverse Pressure

Gradients", Journal of Aeronautical Science, vol 21, pp 91-108.

Coles, D. [1962] "The Turbulent Boundary in a compressible fluid", Rand

Corp., Rep. R-403-PR.

Disimile, P.J. [1984] "Phase Averaged Transverse Vorticity Measurements

in an Excited, Two-dimensional Mixing Layer", Phd Thesis, Michigan State

University.

Disimile, P.J. [1986] "Phase Averaged Transverse Vorticity Measurements

in an Excited, Two-dimensional Mixing Layer", AIAA Journal, vol. 24 No.

I0, pp. 231-269.

Fiedler, H.E. and Mensing [1985] "The Plane Turbulent Shear Layer with

Periodic Excitation", Journal of Fluid Mechanics, vol 15, pp281-309.

Fiedler, H.E. [1988] "Coherent Structures in Turbulent Flows", Prog. in

Aerospace Sciences, vol. 25, pp. 231-269.

Foss J.F., Davis, E.D. Haw, R.C. and Ali S.K. [1987] "Coherent Motion

Induced Fluctuations in the Primary Transition Region of Plane Shear

Layer", Forum on Turbulent Flows, ADME FED - vol. 51, pp. 1-13.

Haw R.C., All S.K., and Foss J.F. [1987] "Gravitationally Defined Velocities for a Low Speed Hot-wire Calibration", Symposium on Thermal

Anemometry, ADME FED vol. 53, pp. 7-13.

Hussain, A.K.M.F. [1983] "Coherent Structures - Reality and Myth", Phys.

Fluids, vol. 26, pp.2816-2850.

Hussain, A.K.M.F. [1986] "Coherent Structures and Turbulence", Journal of

Fluid Mechanics,vol. 173, pp. 303-356.

Klebanoff, P.S. and Diehl, Z.W. [1951] "Some Features of Artificially

Thickened Fully Developed Turbulent Boundary Layers with Zero Pressure

Gradient", NACA Technical note 2475.

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