WE EFFECT 0‘5 EXIT CONDETIBNS @N THE
EEVELOFMENT OF AN AXESYMMETRXC
’E‘JRBULENT FREE JET

Thesis gar We Deer“ of pin. D.
HiCh‘ifiAR’ STATE UKEVEESITY
Staniey J. Kieis

2974

LIBRARY

Michigan State
University

 

This is to certify that the

thesis entitled

The Effect of Exit Conditions on the Develop-
ment of an Axisymmetric Turbulent Free Jet

presented by

Stanley James Kleis

has been accepted towards fulfillment
of the requirements for

Ph.D. Mechanical Engineering

degree in

 

 

   
 

Major professor

Date May 16, 1974

 

0-7639

 

 

ABSTRACT

The Effect of Exit Conditions on the Development
of an Axisymmetric Turbulent Free Jet

by
Stanley James Kleis

The mean flow in the near field (0 3 x/D S 10) of a submerged
axisymmetric jet emitting from a plane wall constitutes the boundary value
proble'm of interest. The solution (U(x.y). V(x.y). u'(x.y), v'(x.y).
iii-Rx”). etc.) is dependent upon the boundary conditions and Reynolds
number. For sufficiently large Reynolds numbers. the present case.
the solution is Reynolds number independent. The boundary conditions
are: the exit plane pressure (P(0.y)) and statistical measures of the
velocity at (O.y) and (x.°). the latter being zero. A postulate of the
study is that measures of the first two momentsare sufficient to specify
the exit plane velocity boundary conditions. An experimental configuration
to provide a nearly uniform mean velocity profile with a core of homo-
geneous turbulence of variable intensity and scale was developed. Eight
cases with intensity values of o. 004 S u'/U S o. 035 and integral scales
up to Lx/R = 0. 28 were investigated using conditional sampling techniques.
For each case seven radial traverses were recorded in the range 0 <.

x/D 5 10. At each data point zone averages of U. V. u'. v'. 6?. v and
the number of interface crossings were recorded for the vortical and
non-vortical modes. The integral continuity'and momentum equations
were used .to characterize U(x, r). Centerline variations of U(x.0) and
u'(x.0). and a width measure based upon the superlayer interface mean
position were used to characterize the detailed structure.

It was found that the jet exhibits an increasing momentum flux in
the near field. This result. although contrary to expectation and the
accepted assumption of ambient static pressure in a turbulent jet. seems
to be conclusive and borne out by comparison with published data. Both
integral measures, mass and momentum flux ratios, are insensitive to
exit turbulence variations . but, the detailed structure (including centerline
velocity) variations with exit conditions are systematic and explainable.

The Effect of Exit Conditions on the Development

of an Axisymmetric Turbulent Free Jet

Stanley J: Kleis

A THESIS
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

College of Engineering

1 974

@

Copyright by
STVUNIJBY'JAJAEEBBHJEBS

1974

ii

To Both Families

iii

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to Dr. John F. Foss
for his unending support and guidance throughout this and previous studies.
Appreciation is also extended to Dr. Merle C. Potter, Dr. J. Sutherland
Frame. and Dr. Gerald L. Park for serving as members of the Guidance
Committee.

The author is thankful for the financial support received from
the NASA Lewis Research Center. the Mechanical Engineering Department
and the Division of Engineering Research.

The author is also indebted to Mr. Robert Walton, Mr. Gary
Crockett and Mr. Tom Merrow for the extensive computer programming.

To his wife. Beth. the author wishes to express his sincerest
thank you for her patience and understanding.

iv

TABLE OF CONTENTS

List of Tables. . . . . . . . . . . . .
List of Figures . . . . . . . . . . . .
Nom enc lature . . . . . . . . . . . . .

SECTION

1.

2.

INTRODUCTION. . . . . . . .

1.1 Formulation of the Problem .

1.2 An Axisymmetric Jet. the Subject Flow

1.3 Literature Survey . .

1.3.1 Free Turbulent Shear Flows:

1.3.2 Turbulent Free Jets .

1.4 Technological Problems Supported by

this Research. . . . . .

1.4.1 General Numerical Solutions

1.4.2 STOL Aircraft. . . .
1.5 Scope of Investigation. . . .

EXPERIMENTAL FACILITY . . .

2.1 Flow System. . . . . . .

2.2 Traversing System . . . .

2. 3 Data Acquisition Equipment
2.3. 1 Transducers. . .

2.3.2 Signal Processing Equipment
2. 3. 3 Analog- Digital Interface . .

2. 3. 4 Digital Data Acquisition and

Control System. . . .
2. 3. 5 Discriminator Circuit.

ACCURACY. O O 0 O O O O O O 0

RESULTS AND DISCUSSION . . .

4.1 Mass Flux Distributions. . .
4. 2 Momentum Flux . . . . .
4. 3 Centerline Velocity Decay.
4.4 Centerline RMS. . . . . .
4.5 Jet Spread. . . . . . . .

CONCLUSIONS O O O O O O O O O
APPENDICES O O O O I O O O 0

Appendix A - Fully Developed Pipe Flow . . . .

Appendix B - Thermal Anemometer Calibration.

Appendix C - Exit Condition Documentation. .

Appendix D - Additional Results. .
REFERENCES 0 O O I O O O O O

Page

. vii
ix

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12

14

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15
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16
17
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. 19
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. 30
. 33
. 34
. 35

40
42
43
45

0156

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LIS T OF

Dcit Conditions .

Data Listing

Data
Data
Data
Data
Data
Data
Data
Data
Data
Data
Data
Data
Data
Data
Data

Lis ting
Listing
Listing
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0 O O O O O O O O O O O O O O O

TABLES

O O O O O O O O O O O O O O O O

Page

46
53
60

74
81
88

O O O O C O O
0‘
q

.101
.108
.115
.122
.129
.136
.143
.149

LIST OF FIGURES

Figure
1. An overall schematic of the flow system. . . . . . . .
2. Configuration to achieve controlled intensity and
scale at exit plane of axisymetric jet . . . . . . . .

3. Schematic of data acquisition facility . . . . . . . . .
4. Discriminator circuit . . . . . . . . . . . . . . . .
5. Sum or difference circuit processing . . . . . . . . .
6. Mean velocity ratio, U(0,y,0)/U(0.0.0),~and the relative

10.
11.
12.

13.
14.
15.

16.
l7.

18.
19.

20.

21.

22.

23.

intensity of the longitudinal fluctuation. u(0,y.0) for
the conditions 0.3. 5, 980. . . . . . . . . . . . . .

Mean velocity ratio, U(O,y,O)/U(0,0.0), and the relative
intensity of the longitudinal fluctuation, 11(0 .y,0) for
theconditionso.5, 20,0. . . . . . . . . . . . . . .

MassFluxRatio..................
Normalized Mass Flux Ratio for the Vortical Fluid . . .
Momentum Flux Ratio. . . . . . . . . . . . . . . .
Centerline Mean Velocity Distribution. . . . . . . . .

Centerline RMS Velocity Distribution Position of the
ViscousSuperlayer. . . . . . . . . . . . . . . . .

Mean Position of the Viscous Superlayer . . . . . . .
Excursion of the Viscous Superlayer . . . . . . . . .

Pressure Distribution in the Fully Deve10ped Pipe Flow
for the Thermal Anemometer System Evaluation . . . .

Reynolds Stress Distribution in Pipe . . . . . . . . .

Comparison of u' and v' Distributions with the Published
Results Of maer (1954). O O O O I O O O O O I O O 0

Thermal Anemometer Calibration . . . . . . . . . .
Exit Correlations 13‘ /D’= . 13. AV /D = . 052".
X =00583 xy=00580 e e e e s e e e

3:
Exit Correlations Ax/D . 014, Ay/D = . 093.
00650 O s e e e e e e e e 0

kn: = .085. Mm

Exit Correlations Ax/D = .11. /D = . 046.
xx/D=0086. Xy/D=.o7leAY e e s e 0

Exit Correlations /D = .10. /D = .052.
M/D='0580 AMx/D=sOSOOAY e e e e 0

Exit Correlations Ax/D = .097. Ay/D = . 052,
Xx/D =0083, Ay/D=.07o e s e s e e e e s s 0

vii

Page
159 .

160
161
162
163

164

165
166
167
168
169

170
171
172

173
174

175
176

177
178
179

180

181

List of Figures Continued
Figure Page

24. Exit Correlations Ax/D = . O89, AY/D = . 053,
xx/D=.075, XY/D=.O7le s e s e e e e s e e .182

25. Exit Correlations Ax/D = . 074, /D = . 049,
1x/D = .052, 13./D = .046. 19'. . . .

26. Exit Correlations A /D = . 083, [\l/D =

1x/D=.06, 1y =.05 . . .

27. Exit Correlations Ax/D = . 08, AY/D = . 059.
Ax/D = .062. xy/D = .056. O 0 e e e o e s s s e 0185

O O O O O O 183
.057,

O O O O O 184

viii

'Ut‘ou Hip-100‘!“
U

"U

faces:

5:: a
.c‘
.F
6-

o-l-oe:>etr-<t~l

NOMENC LAT UR E

jet exit dimension

radius at which lJ/Uc = 0.5
number of mode switches
voltage signal

normalized longitudinal correlation function

T
-1- S{fiflu(x+Axi/TIZ} dt
T O

 

normalized lateral correlation function
instantaneous and mean pressure

pipe flow facility radius. (3. 25 in. )
radial coordinate in pipe flow facility
time

total time of sample

skin friction velocity (Tw/p)l/2'

instantaneous. mean, fluctuating and root-mean-square
streamwise velocity components

instantaneous, mean. fluctuating and root-mean-square
radial velocity components

instantaneous, mean. fluctuating and root-mean-square
azmuthal velocity components

streamwise, radial and azmuthal coordinates
vertical direction

intermittancy factor

micro scale of turbulence

dynamic viscosity

kinematic viscosity

integral scale of turbulence

vorticity

density

shear stress

orientation of velocity vector in horizontal mid-plane;
9 5 tan"1 V/u

Subscripts

atm
c
e

n. V.

~<x£

atmospheric conditions

centerline

at the exit (x = 0)

denotes the non-vortical condition
denotes the vortical condition

at the wall (r = R)

streamwise component

lateral component

1. INTRODUCTION

At sufficiently large downstream distances, axisymmetric jets.
as well as other free shear flows, develop a self-preserving structure
which has been described by Townsend (1956) as a state of the flow. . .
"in which the conditions at the initiation of the flow are mostly irrelevant,
and the flow is geometrically similar. " The dependence of the self-
similar region upon upstream conditions appears as a shift in the apparent
origin of the jet. From a comparison of previous studies in the self-
similar region, it was believed that the shift in the apparent origin would
be evidenced by a difference in the rate of entrainment in the initial
region, see Foss and Kleis (1971). The results of the comparison also
indicated that the exit trubulence structure had possibly more influence
on the shift of the apparent origin than non-uniformity of the exit mean
velocity profile. The purpose of the present investigation is to provide
a systematic study of the influence of various exit turbulence structures
on the development of an axisymmetric turbulent free jet in the initial
region (Osx/Dle).

A new technique utilizing conditional sampling to orient the
sampling probe into the mean direction of the velocity vector of the
condition being taken was developed and used to increase the accuracy
of measurements. The’increased accuracy over conventional methods
was deemed necessary for the accurate determination of the mass flux

given the large velocity gradients of the initial region.

The traditional measures of mass and momentum flux and. also.
statistical measures of the velocity distribution were made with somewhat

unexpected results .

1. l. Formulation of the problem

The axisymmetric turbulent free jet is but one of a general class
termed "free turbulent shear flows". This class of flows contains the
general groups of jets. wakes. and free shear layers.

The outer region of a turbulent boundary layer also exhibits the
characteristics of a free turbulent shear flow; however, the near wall
region of a boundary layer is dominated by the large production of
turbulence kinetic energy associated with the steep velocity gradients
resulting from the no-slip condition. Turbulent shear flows are characterized

by the production and decay of turbulent kinetic energy due to a gradient of

l

the mean velocity profile with boundaries unrestrained by the presence

of a solid surface. Turbulent flows are governed by the conservation of
mass (continuity) and momentum equations (the latter become the familiar
Navier-Stokes equations if a Newtonian fluid is under investigation). For
the instantaneous equations, these represent a system of four equations
for the four unknowns U, V, W, and P. The solution of the instantaneous
equations requires the Specification of the initial velocity and pressure
fields at every point of the flow field (i. e. the initial conditions) as well
as the boundary conditions of the particular problem. The complete
description of the flow field would require the simultaneous solution of
three non-linear and one linear partial differential equations and a forward
stepping procedure with respect to time. The instantaneous velocity and
pressure fields are. therefore, most difficult to obtain. Also, such a
solution would constitute such a vast amount of information that it would
have to be suitably compressed for utilization in the solution of a techno-
logical problem or the description of a natural event. An alternate
approach is to represent the instantaneous velocity as a mean plus
fluctuating component and time average the equations of motion. The

averaged equations in cylindrical coordinates are:

2 2
91-1..-” Z-V-° -sav')
Md. yi 3§+Mvv :3 2%“) y y
2 sv'w- on"? w'2
'1'}? ""55? +97
(dw+ Y31V») - - s + ”2“,-le + 2 “hag-2W2) (2)
"at— v ' '55 u v 3'13? Y
_ 8wv_ DEW; £—
P'5'); 93x2 Zva
dU _ a any) a - au—v'v
9(m)--‘5§+uVU-p-5x -$a;,(yuv) $5,,

The time averaging process introduces six additional unknowns (u'.v'.w',
1117, T13, and-W). a group of terms commonly referred to as the compo-
nents of the (negative kinematic) Reynolds stress tensor. Even for the
special case in which the mean velocity gradient is zero. the correlations
'u—iFi are non-zero and the indeterminancy remains; it is a fundamental
aspect of the mathematical description of a turbulent motion. The solution
of the time averaged equations requires the specification of statistical
measures of the velocity field as boundary conditions for the particular
problem. A complete specification of the boundary conditions for the
instantaneous motion in terms of time averaged flow variables involves
not only point wise averages of the velocity field but an infinite set of
correlations between the velocities at each point in the exit plane. It is

a major premise of the present research that the statistical effect of

the boundary conditions on the development of the mean velocity field

can be satisfactorily represented by specifying i) the character of the
mean streamwise velocity profile and ii) the scales and intensity of the
fluctuating velocity components. A condition of spatial homogeneity
precludes the necessity for identifying the values of lateral or longitudinal

derivatives of these functions of the velocity field.

1. 2. An axisymmetric jet, the subject flow
The axisymmetric turbulent free jet was selected as the flow

field to be investigated because it has only two independent variables
(thus reducing the number of unknowns to seven) and it is of great
technological importance. A few of the technological problems which
are supported by this investigation are described in a following section.

The axisymmetric free turbulent jet is often described in terms
of three regions: the region containing the potential core, the developing
region and the fully developed or self-preserving region. Thepotential
core contains fluid which is bounded by intense shear layers but is
characterized by the absence of the shear layer influence upon the mean
velocity in the central portion of the jet. This region extends from the
jet exit to approximately five diameters downstream. The developing

region extends from the end of the potential core to the fully developed

region and is simply a region of transition in the sense that the jet loses
all identity with the exit conditions with the possible exception of a shift
in the apparent origin between various jets. The fully developed or self-
preserving region extends downstream from about 40 diameters. This
region is characterized by self-similarity of the velocity profiles. That
is, if the velocity profiles (mean and fluctuating) are normalized by the
centerline value and the transverse coordinate is normalized by a
properly chosen width measure (a function of streamwise distance). the
resulting profiles are independent of the streamwise coordinate.
Townsend (1956) provides a comprehensive discussion of the
nature of self-preservation and the implied interrelationship between
the velocity (U0) and length (10) scales for various shear flows. Speci-
fically, let Uo (x) and 10 (x) be the centerline velocity and a radial
distance such that U (x,y)/U (x.0) = O. 5 respectively; then U (x.y)/U (x,0) =
ftv/lo) if

10=ax+b (3)

and (10/ U0) dUo/dx = constant. A negligible streamwise pressure gradient
and the global conservation of momentum equation can be combined to show

that Uo satisfies the condition

U0 = (ax + bfl (4)

The velocity field is then specified by the normalized functions
and the functional dependence of the normalizing parameters on the
streamwise coordinate.

Numerous studies have quite adequately documented the self-
preserving region of the jet and several investigations of the regions
involving the potential core and transition zone. The present work is
exclusively concerned with the near field 0 $- x/D E 10 and with the effects
of the exit plane turbulence structure on this region. The remaining sub-
sections of the Introduction are to place this investigation in its proper
context by considering the appr0priate literature base re free shear
flows (1. 3), the technological problems supported by this research (1. 4)

and the scape of the present investigation (1. 5).

l. 3 Literature Survey

This section is a review of the literature which provides information

related to free turbulent shear flows in general and axisymmetric free

jets in particular. This section is presented in the context of the objectives
of the present investigation. Some general characteristics of free shear
flows are first discussed; pertinent characteristics of the axisymmetric

jet are then considered.

1. 3. 1 Free Turbulent Shear Flows
l. 3. l. 1. General characteristics

The important common characteristics of free turbulent shear
flows, including jets. wakes and the free shear layer between two streams
of uniform mean velocity, are: i) a sheared region where the turbulence
energy and Reynolds stresses are produced, ii) an insensitivity of the mean
flow and energy bearing eddies to the Reynolds number (if the latter is
sufficiently large) since the direct effect of viscous stresses (i. e. u VZU)
are not important in the absence of a solid boundary and iii) a thin,
contorted and three-dimensional layer bounding the fluid in fluctuating
vortical motion. The layer of (iii) is termed the viscous or laminar super-
layer and it is responsible for the diffusion of vorticity into the non-
vortical ambient fluid. In a strict sense. entrainment into the shear flow
can be defined as this vorticity diffusion process. Alternate definitions .
which may result in a quantitatively different entrainment magnitude, have
also been employed and are described below. The existence of the super
layer was first identified by Corrsin (1943), the flow field characteristics
related to it were first measured by Townsend (1949) and its detailed
characteristics and the attendant statistical behavior of this turbulent-
non-turbulent interface (superlayer) has been studied by Corrsin and
Kistler (1955). As pointed out by Corrsin and Kistler, the distinctive
characteristic between the fluid interior and exterior to the interface is the
existence of high frequency vorticity fluctuations of the interior fluid. The
gradient of vorticity is maintained ata large value due to the stretching
of vortex filaments in the vicinity of the superlayer. It is the diffusion
of vorticity by direct viscous action at the superlayer interface which is
considered to be one of the important features of free turbulent shear
layers.

The intermittent region of a turbulent boundary layer, which

exhibits the characteristics of a free shear flow, has been studied by

Kaplan and Laufer (1968). Kibens and Kovasznay (1969) and by Kovasznay.
Kibens. and Blackwelder (1970). The results of these studies indicate
the possibility of a much more orderly structure of the flow behavior
than had been previously revealed by long term average values of the
velocity. Similar studies are continuing on turbulent boundary layers
and also on turbulent axisymmetric jets; the latter are discussed below.
In addition. theoretical studies of the properties of the superlayer
have been conducted by Townsend (1970) and Phillips (1972). From these
theoretical studies. undertaken to provide some correlation of the many
experimental observations. it is suggested that the area of the superlayer
over which the diffusion of vorticity occurs is not only a function of the
large scale fluctuation resulting in the observed bulges and indentations,
but also smaller corrugations corresponding to all scales of the turbulence.
These smaller corrugations. although not so readily observable, can

result in large differences in the superlayer surface area.

1. 3. l. 2. Entrainment

The recognition of the intermittent nature of the detailed structure
in turbulent shear flows raises an interesting question as to what one
means by the word "entrainment". Historically. entrainment has meant
the process of a jet of fluid somehow "capturing" essentially quiescient
ambient fluid and imparting to it a streamwise mean velocity. The rate
at which entrainment takes place has been taken to be the rate of increase
of mass flux across planes of constant streamwise distance (x) with
increasing streamwise distance. To evaluate the mass flux across a
plane. it is mathematically necessary to integrate over the entire plane
(i. e. to infinity). This is not possible experimentally and requires an
assumption of when the mass flux becomes negligible for larger radii.
However. if one takes the presence of vorticity fluctuations as a property
of the fluid belonging to the jet, entrainment can be defined in terms of
the rate of diffusion of vorticity from the jet into the ambient fluid. Then,
the rate of entrainment is the rate of increase of mass flux of vortical
fluid across planes of constant x with increasing x. There are two
contributions to the total mass flux, the mass flux of vortical fluid and
the mass flux of potential (non-vortical) fluid. Although both quantities

are measured and reported, the historic meaning of entrainment will be

used unless otherwise noted in order to compare with other investigations.

A study of entrainment in axisymmetric jets was made by Ricou and
Spalding (1961). They used a porous cylinder surrounding the jet for
many diameters downstream and forced fluid through the porous cylinder
at such a rate that the pressure inside was that which would have existed
for the free jet. The volume flux through the porous cylinder was mea-
sured and provided a direct measurement of the entrainment rate. Based
upon the results of Ricou and Spalding, the entrainment rate in the self-
similar region of an axisymmetric jet is 0. 32. specifically

s . Q
3%— = 0.32 %"—("=°’ 161 = 2115‘ yU dy (5)
o

1. 3. 2. Turbulent Free Jets

A relatively large amount of data exists for both axisymmetric and
plane jets. Most of the experiments were conducted in the fully developed
region of the jet where the velocity field exhibits a self-preserving
character.

As shown by Wygnanski and Fiedler (1969) and Heskastad (1965).
jets may not exhibit true similarity for as much as 60 diameters (slot
widths for plane) downstream for the mean velocity profiles and up to
120 diameters for similarity of the turbulence structure. This asymp-
totic approach to the fully developed state could conceivably result in
very significant differences in the determined virtual origins with
different initial conditions. That is. small changes in the slope of the
spread measure or centerline velocity as functions of streamwise
distance at 40 or 60 diameters downstream would result in large changes
in the virtual origin.

An important aspect of the behavior of turbulent free jets in the
fully developed region is the determination of the exit properties which
influence the value of the virtual origin. This requires detailed

measurements in the near field region.

1. 3. 2. 1. The Near Field

Measurements of the pressure and velocity distributions in the near
field (from the exit to the fully developed region) have been made by
relatively few investigators. Most of the available studies were concerned

with jet noise generation, specifically. Ko and Davies (1971), Laurence

(1956). Bradshaw et al (1964). Davies et a1 (1963) and Maestrello (1973).
Consequently. their measurements are concentrated in the intense shear
layer between (or near) the potential cone and the ambient fluid and are
primarily concerned with the turbulence intensities, shear stresses and
correlation functions insofar as they relate to acoustic noise generation.
The results of these and the present study overlap and comparisons that
contribute to the present motivation are discussed. It should be noted
that the turbulence data presented for documentation purposes could be
used to investigate the effect of the exit conditions on the turbulence
characteristics related to noise generation, see Appendix D.

The region of an axisymmetric jet nearest the exit plane is
essentially the flow field described as a free shear layer where the
bounding streams are the high velocity potential core and the low (or
zero) velocity ambient flow. As such. the independent studies of the
free shear layer problem contribute to the description of a jet flow. The
phenomena of the shear layer instability and the asymptotic shear layer
structure are well understood, see e. g. Freymuth (1966) and Wygnanski
and Fiedler (1970). These phenomena are present in the jet flow of
interest but are not explicitly pertinent in terms of the larger scale
phenomena that develop in response to the axisymmetric structure of
the jet.

Several investigations have resulted in velocity profiles in the
- near field of an axisymmetric jet. Foss and Kleis (1971) made use of
these to evaluate the mass flux (by numerical integration schemes);
similarly, they also evaluated the momentum flux and used the degree
to which it was constant as a check on the data (and the integration process).
These results, and the significantly different entrainment rates which
were evidenced by them were a principal motivation for the present
investigation. On the basis of the results reported herein. it has become
evident that this motivation was ill conceived. Specifically. the momentum
flux is a monotonically increasing function in the near field and rises to
approximately 125 percent of its exit plane value at x/D = 10. Secondly,
the accurate calculation of the mass flux is a most delicate matter re-
quiring a knowledge of the mean flow direction. The procedure used
herein, to determine the separate mean flow directions for the vortical

and non-vortical conditions and executing separate mass flux calculations.

is considered to be a practical necessity. That is. this scheme alleviates
the yaw induced errors when a single time average is attempted in the
presence of a velocity vector shift of the order 130 degrees and it
accurately accounts for the direction of the time average velocity vector
which is an important factor in the accurate evaluation of the mass flux
integral.

Recognizing the difficulty of accurately determining the mass
flux by integrating a measured velocity distribution. Hill (1971) has
employed an extension of the Ricou and Spaulding technique which
ostensibly allows a local measurement of the entrainment rate. Hill
exercised considerable care in his investigation to calibrate his device
in the self-preserving region and to examine the optimum radius of the
device which introduced (and hence monitored) the entrainment flow.
However, streamwise gradients and streamline curvature effects in the
region near the nozzle cannot be accounted for in the calibration scheme.
The results of the Hill study show that the asymptotic entrainment rate
of 0. 32 was attained at approximately five diameters.

Sami (1967) and Sami et. al. (1967) have examined the near
field of an axisymmetric jet; their motivation and their.results are
similar to and hence quite pertinent to those of the present study. Their
jet was formed by pressurizing the room below their laboratory and
using a l. 0 ft. diameter hole in the floor as the jet exit. Measurements
were made of mean and fluctuating velocity and mean and fluctuating
pressure. The mean pressure was measured with a static tube and
micromanometer combination. Although the micromanometer was
capable of measurements to . 001 in. alc‘ohol, the necessary instability
of the readings due to the large pressure fluctuations raises questions
about the accuracies necessary to measure the small mean pressures

involved (on the order of 0. 007 in. water).

1. 3. 2. 2. Exit Condition Effects on Jet Development
An investigation of the effect of exit conditions on the development

of a plane jet was conducted by Oseberg and Kline (1971). The variation

of initial conditions for their study was confined to controlling the boundary
layer growth in the contraction by the use of suction and blowing. Their
study was performed in water and the hydrogen bubble technique was

used for visualizing these effects in the resulting jet flow. Their plane

10

geometry and their variation of the mean velocity as well as the turbulence
structure restricts the use of their study as a reference source for the
present investigation.

Flora and Goldschmidt (1969) provide a comparison of several
investigations which show significant variation in the computed virtual
origin. They also conducted experiments using various nozzle configura-
tions (different boundary layer growth) and varied the turbulence structure
with the use of screens and grids in the plenum. They conclude that the
calculated virtual origins are not influenced by different nozzle designs
but are a function of initial turbulence structure. All of their tests were
conducted on a plane jet and, thus, are not directly comparable to the
present study.

The present investigation is complementary to the recent study
by Crow and Champagne (1970). Their investigation was to determine
the response of an axisymmetric jet to the introduction of single fre-
quencies of excitation at the exit plane. The flow field investigated by
Crow and Champagne was basically the same as the present study subject
to different variations in exit (or boundary) conditions. Their exit
conditions were generated by a loudspeaker in the plenum chamber
adjusted such that the operating frequencies corresponded to the resonant
frequencies of the chamber. The results of their investigation indicate
that at certain "preferred modes" of excitation the jet exhibits an increase
in mass flux and more rapid centerline velocity decay than without
excitation. A more complete description of their results and a comparison

with the present investigation are included in the results section.

1. 4. Technological Problems Supported by this Research
1. 4. 1. General Numeric Solutions
As shown in the formulation of the problem, the introduction of
mean plus fluctuating velocity components and time averaging the
governing equations results in an indeterminate system of equations.
This mathematical indeterminancy plus the need for engineering calculations
of the behavior of turbulent shear flows have resulted in the develoPment
of phenomenological theories to effect a closure of the equations. A
vast literature exists for such closure schemes; the earliest of these
was the Boussinesq (1877) eddy viscosity model. The Prandtl (1925)

mixing-length model is characteristic of the models predicated upon some

11

physical notion of the behavior of the shear flow. More recent models
have attempted to eXploit the dual role of the Reynolds stress as a
significant part of the momentum equation and as a fact or in the production
of turbulence kinetic energy. A conference to compare the ability of
various models to predict the behavior of free turbulent shear flows was
recently sponsored by the NASA Langely Research Center; the conference
report provides a comprehensive description of these models and their
relative success in the calculation of selected test cases, see Birch,

et. a1. (1972). Included within the structure of the conference were
committees to recommend "critical experiments in free shear flows"

and a second committee to summarize the status of free shear flow
computations. A recommendation of the former committee was that
systematic investigations of the effect of the initial conditions (e. g. the
jet exit plane conditions) be conducted and both committees urged that

the initial conditions and the original data be documented for each inves-
tigation in order to provide reliable test cases for evaluation of the
prediction schemes. The documentation in'this report fully complies

with these suggestions.

1. 4. 2. STOL Aircraft

In the design of short takeoff or landing (STOL) aircraft it is
necessary to create a large lift at relatively low forward speeds. To
achieve such a condition several engine/wing-flap geometries have been
considered. One such geometry consists of having the exhaust of the
turbofan engine impinge at some relative angle onto the underside of the
wing. One possible benefit of this geometry is the use of the strong
streamwise vorticity produced by the impingement as a boundary layer
control mechanism. That is, the streamwise vorticity would be ducted
through the flap-gap and onto the upper surface of the flap assembly.
The flow field generated by such a geometry has been studied by Foss
and Kleis (1971). A second geometry which has been pr0posed is to
exhaust the turbofan directly onto the flap assembly. This problem is
similar to the previous one with the exception that larger included angles
are involved. The large angle oblique impingement problem is currently
being studied by Foss.

In both of the geometries it is necessary to determine the flow

12

field associated with a free turbulent axisymmetric jet in the initial region
(from the exit to ten diameters downstream). It has been shown by Foss
and Kleis (1971) that the flow field resulting from the oblique impingement
case is not measurably different than a free jet up to the streamwise
location where contact is made with the plate. Thus the free jet behavior
is important for two reasons. First, the free jet influences the ambient
fluid due to the entrainment process. The result of this influence is to
change the circulation and thus the lift of the wing section. The second
reason for studying the initial region of a free jet is that characteristics
of the free jet at the streamwise location at which impingement occurs
become the initial conditions for the oblique impingement problem.

Since different turbofan engines generate different exit conditions,
it is important to determine what effect different exit conditions have on
the development of an axisymmetric free jet. Because experimental data
indicate that the exhaust of a turbofan engine has a relatively uniform mean
velocity profile, the present investigation, restricted to uniform mean

velocity profiles, is quite relevant.

1. 5. Scope of Investigation
The present study is an experimental investigation of the effects of

different turbulent kinetic energy and integral scale on the development
of an axisymmetric turbulent free jet. The region of interest for the
present investigation is from the jet exit to 10 diameters downstream.
The range of Reynolds number is from 65,000 to 100,000. The root mean
square (RMS) of the axial velocity fluctuation (an indication of turbulent
kinetic energy) was varied from 1 to 3 percent of the exit mean velocity
and the integral scale, calculated from time auto correlations at the exit
plane of the axial velocity component, ranged from 0. 15 to 0. 3 inches.
The documentation of the exit plane conditions is given in Appendix C.
All measurements were made on a 2. 0 inch diameter jet using a thermal
anemometer with an x-wire sensing element.

Conditional sampling techniques were used to rotate the sensor into
the mean direction of the velocity vector for both the vortical and potential
condition readings in order to minimize sensor errors. Zone averages
were made of the velocity field for both the vortical and potential
conditions. The quantities measured were the mean velocity magnitude

and direction. the RMS of the axial and radial velocity components. the

13

product of the axial and radial fluctuating components (ii—=3), the fraction
of time in the zone condition and the number of condition changes during
the average.

The mass flux at various streamwise locations and the entrainment
rate which can be inferred from these measurements was a factor of
principal interest. Measures of the turbulence structure and their
relationship to the entrainment rate were also of specific interest.
Unexpectedly. but quite significantly, 1) the mass flux increase trends
are independent of the exit plane turbulence conditions except for a
streamwise change in the initiation of the asymptotic-increase-rate
location; ii) the momentum flux is not a constant in the near field but its
variation is independent of the exit plane conditions; iii) the turbulence
structure parameters do reflect the state of the exit plane turbulence

structure conditions .

2. EXPERIMENTAL FACILITY

This section describes the experimental facilities used to obtain
the quantitative data from the present investigation. Included are des-
criptions of the flow facility. traversing system. transducers, and
signal processing equipment. The discriminator circuit, which is a
signal processing piece of equipment, is described in a separate

section because it is of central importance to the data processing.

2. 1. Flow System

The flow system used for the present investigation is a minor
modification to that used by Holdeman (1970), Holdeman and Foss (1970),
and Foss and Kleis (1971). A detailed description of the flow system
with modifications is included because these reports are not of general
circulation. A schematic of the flow system is shown in Figure l.

The blower is a Buffalo Forge model 37 V volume fan powered
by a 15 horsepower D. C. motor with a i’ 1 percent positive feedback
variable speed control. On the inlet side to the blower is a fully
developed pipe flow system for comparing the results from the data
acquisition system against the known results of Laufer (1954).

Filters and a 36:1 octagonal contraction are located at the inlet
to the fully developed pipe flow system. The pipe is 7. 5 in. I. D. ex-
truded aluminium with a length to diameter ratio of 105. The pipe is
fitted with static pressure taps at every 2 ft. along the length and a
traversing probe support. Connection is made to the blower by means
of a removable section containing a screened diffuser and flow straight-
eners to minimize the upstream propagation of effects from the blower.

The main plenum chamber is connected to the blower through a
diffuser and turning vanes. The diffuser has been fitted with 30 mesh
screens for separation control. The turning vanes are of constant
radius. The flow in the plenum then passes through flow straighteners
to decrease the large scale motions and a filter to remove foreign
material and further decrease the turbulence.

As shown in Figure 2 the flow then proceeds through a toroidal
contraction to a 3. 25 in. I. D. pipe mounted such that it can be positioned
axially. At the downstream end of this 13 in. pipe, the central portion of

the flow is separated from the boundary layer portion by a concentric

14

15

2 in. I. D. copper pipe. The copper pipe is 2 in. long and is mounted
in the exit plate. The upstream end of the copper pipe is ground to a
15 degree bevel from the outside to minimize flow separation. The
excess boundary layer fluid is pulled off through a secondary plenum-
blower arrangement. It was found that the best adjustment of the
secondary plenum pressure level, to minimize separation on the 2 in.
exit pipe, was obtained with the axial movement of the 13 in. long pipe
relative to the exit plate.

The variable turbulence initial conditions were generated by
arrays of 0. 020 in O. D. tubes as shown in Figure 2. The jet tube
arrays were placed at the throat of the toroidal contraction and air was
supplied from a central high pressure (90-95 psi) compressor. The
pressure was reduced through two filter-regulators which removed
nearly all of the pressure variation. Three different grids were used
with center to center spacing of 0. 3, 0.4. and 0. 5 in. Extensive
testing showed that the scales of turbulence at the exit varied with the
mean velocity at the exit and the intensity could be varied by using

different grids .

2. 2. Traversing System

Because of the nature of the data, with the requirements of
using an x-wire hot-wire probe and taking measurements in regions
of high velocity gradients , it was necessary to construct a probe
traversing system which could be positioned accurately in the three
spatial coordinates and also rotate the x-wire array in the plane of the
wires as shown in Figure 3. To meet these requirements, a lathe bed
was used as the basic traversing mechanism. The lathe allowed 30 in.
travel in the streamwise (x) direction and the lathe cross-feed was
used to give 12 in. of travel in the y direction. The cross-feed screw
was removed and the cross-feed was driven by means of a stepping
(1. 8 degree per step) motor geared down and connected to an anti-
backlash translation screw. On top of the compound feed, which was
used for fine positioning in x, was mounted a dual worm gear drive
which moved the probe support vertically (z) and in 6. the angle in
the horizontal plane. The 6 and z movements were also driven by

stepping motors (l. 8 degree per step). The worm gear drive allowed

16

z variations of 10 in. and Ovariations of 360 degrees. It was necessary
to correct in 2 after a change was made in 6.

The x-wire hot-wire probe was mounted on a support which
allowed the wires to pivot about the axis of the worm gear drive
assembly. A Disa type 55A38 x-wire probe was slightly modified to
give a probe separation of 1/16 in. to lessen the probe wake interference
effects reported by Guitton and Patel (1969). The sensing elements were
5 pm diameter Pt-plated tungsten wire. each 1. 2 mm in length.

The entire traversing system was levelled and aligned with the
physical centerline of the flow system using an optical cathetometer.

The stepping motors for thee and z drives are Slo-Syn type
H850 and the y drive a Slo-Syn type HSSOL manufactured by Superior
Electric. One stepping motor drive unit was used for all three motors
by selecting the motor to be driven with a solenoid actuated rotary
switch driven by a square wave from the on-line computer. The
stepping motor drive unit accepts input pulses and energizes the proper
field coils in the stepping motors to rotate the motor one step (1. 8
degrees) per input pulse. This pulse was also generated by the on-line
computer, thus giving control of the probe positioning in y, z, and 8

to the computer.

2. 3. Data Acquisition Equipment

Two flow variables were measured in the present investigation.
pressure and velocity. The transducers necessary to produce an analog
voltage proportional to the two measured variables and the equipment

used to process the resulting signals are described in this section.

2. 3.1. Transducers

A two-channel Thermo Systems Inc. model 1054A thermal
anemometer was used to produce linearized response from the modified
Disa type 55A38 x-wire probe described earlier. The signal from each
channel was passed through a Thermo Systems model 1057 signal con-
ditioners for low pass filtering to eliminate aliasing errors. The
x-wire probe was calibrated with the probe axis aligned with the flow
direction; the velocity was calculated from pressure readings.

The pressure was measured using a Decker Corp. type 308

variable capacitance pressure transducer. Two transducer units were

17

used with ranges of 3. 0 in H20 = 10 volts and 0. 3 in H20 = 10 volts.
The three-inch transducer was used for the calibration of the hot wire
unit and monitoring the plenum pressure turning the data acquisition.
The three-tenths transducer was used for calibrating the hot wire and

measuring the pressure gradient in the fully developed pipe flow field.

2. 3. 2. Signal processing equipment

The analog voltage from the thermal anemometer was processed
in several ways both by analog and digital methods.

A simple sum and difference network was set up to produce a
signal proportional to either the axial or transverse velocity component
relative to the x-wire probe axis. As shown in Figure 5. this signal
was then fed into a Thermo Systems Inc. RMS meter for comparison
with the fluctuating velocity components measured and calculated with
the digital data acquisition system. The sum and difference of the
anemometer signals were also fed into a Princeton Applied Research
model 101A correlation function computer to produce autocorrelations
of the axial and radial velocity fluctuations in order to document the
various initial conditions used for the present investigation. The output
of the PAR correlator was read with the IBM 1800 computer and punched
on cards for later processing.

In addition to the commercially available equipment for signal
processing, a circuit was constructed to produce an analog signal which
could be level discriminated by the digital computer to indicate whether
the flow was vortical or nonvortical. This circuit is described in a
separate section because it is not commercially available and it is of

central importance to the conditionally sampled data acquisition.

2. 3. 3. Analog-digital interface

The analog outputs of the thermal anemometers. pressure trans-
ducers and discriminator circuit were fed through individual buffer
amplifiers with variable gain. The gain on each of the amplifiers was
set so that the maximum voltages would be below but near the 10 volt
maximum of the analog to digital converters on both the IBM 1800 and
TI 960A computers.

The actual gains of the amplifiers was determined by applying
a l. 00 volt D. C. signal to the input of each of the buffer amplifiers.

18

The outputs were then read and the inverses of the values obtained were
used to convert the indicated voltages measured by the computers to the
actual values input to the buffer amplifiers. This provided the most
accuracy with the limited resolution of the 12 bit analog to digital

converters e

2. 3. 4. Digital data acquisition and control systems

Two general purpose digital computer facilities were used in
the present investigation, an IBM 1800 system, available in the College
of Engineering and us ed for previous investigations in the fluid mechanics
research laboratory, did not have fast enough instruction execution times
to make it useful for data acquisition for the present investigation. In
order to meet the increased Speed requirements for the present investi-
gation, a TI 960A "mini-computer" was obtained.

The TI computer facility consisted of a multi-channel analog to
digital converter, real time clock, Silent 700 data terminal, card reader,
digital to analog converter and digital interface cards for communication
with the IBM 1800 computer. The four analog signals (two thermal
anemometer channels , one pressure transducer and the discriminator
circuit output) were in turn interrogated by the computer and the signals
processed.

The real time clock was used to time the data taking at a point
for the Specified time interval (usually 15 seconds per reading).

The Silent 700 data terminal was necessary for communication
with the computer. The initial positions, type of traverse, starting
and ending points for a traverse, coefficients for two fourth order
polynomial fits to the two wire calibrations, number of data points and
the time for averaging at a point were entered at the beginning of each
traverse. This information was used during the automatic "process
control" by the computer. The data terminal also provided listings of
the unprocessed data as a permanent record.

The digital to analog converter provided the square wave outputs
used to select and drive the three stepping motors for probe positioning.
They were also used to drive an x-y plotter for plotting some of the
results of the data acquisition.

A digital interface card provided two way communication between
the TI and the IBM 1800. The card had 16 input and 16 output connections

19

which allowed the transmission of one sixteen-bit word at a time. This
was done with an answer-back system such that each computer could
send or receive from the other at a maximum rate with the minimum
possibility of error. The communication was necessary because of the
lack of a peripheral device such as a card punch for the TI system.

Thus the TI system was operated in a satellite mode from the IBM 1800.
That is, the T1 was used for the actual data acquisition (typically 8 hours)
and then the stored results were transmitted to the IBM 1800 for punched
card output for later processing.

In addition to providing punched card output of the information
transmitted from the T1, the IBM 1800 was also used for two phases of
the data acquisition process. The routines used, which were developed
for the earlier investigations, were to calibrate up to four thermal
anemometer channels and to read the analog output of the PAR Correlation
Function Computer from which the routine produced listings and punched
card output.

The IBM 1800 was also utilized for the processing of the data due
to the convenience of writing processing routines in FORTRAN and the

inconvenience of using TI's version of FORTRAN on the 960A computer.

2. 3. 5. Discriminator circuit

In any conditional sampling of data, the signal upon which the
decision is made as to whether or not to include the reading in the
sample is of primary importance. For the present investigation it was
desired to produce a signal based upon the outputs of the thermal
anemometers which would indicate if the flow past the sensors was
turbulent. The property of turbulence which is desirable to use to
produce the analog signal, which is eventually level discriminated, is
the presence of vorticity fluctuations. Unfortunately, it is very difficult
to measure any of the actual vorticity fluctuations. Kovasznay. Kibbens

and Blackwelder (1970) measured a part of the instantaneous vorticity
uz , where

we‘l'sx—‘w’ ‘2'”

for the discrimination. That is, it is possible to construct a probe

consisting of two parallel wires which are normal to the flow such that

20

when the difference is taken one gets a signal proportional to approximately
BIS/By. This signal is then processed by analog circuitry to produce a
signal with a definite on-off character.
Since an x-wire probe was used for the data acquisition of e
present investigation, the alternate approach was taken of using '8? as
the signal to indicate the presence of (oz. Using Taylor's hypothesis
we can write the approximate relations
817' z _ 1 m7 (2. 2)
33? {'1' I)?
which can be obtained from the two channels of the thermal anemometer

by taking the difference of the time derivatives of the linearized signals

x.

i- ~ a -.— <2»)
where A is chosen to compensate for the difference in the gains of the
two signals.

It was found by analyzing the Fourier Transform of several
samples of data taken in the intermittent flow region of the jet at a
typical velocity (100 ft/sec)that the greatest percentage difference in
energy content at a given frequency occurred between 1 K112. and 3 KHz.
Therefore, the difference of the time derivatives was band pass filtered
at these frequencies before it was processed further. This essentially
eliminated the low frequency components associated with potential
fluctuations (caused by pressure gradients in the non-vortical fluid).

As is shown in Figure 4, this signal was then processed in two
ways. First, it was full-wave rectified to eliminate the zero-
crossings. Also, the time derivative was taken and then full-wave
rectified. This was done because the zero-crossing of a signal such
as this are points at which its time derivatives are nonzero. Thus,
if the resulting full wave rectified signals are added together there
results a signal which should be zerg only when thevoriginal signal
has sufficiently small amplitude ( g—v? = 0 and 5952- = 0 ).

The final signal was then read by the computer which made a
decision as to whether the data point was vortical or not by comparing
the signal to a specified level entered at the beginning of the traverse.

In addition to the level discrimination, the computer acted as a digital

21

filter by saving the previous two data points and requiring that there be
three consecutive readings in a new mode before it considered a mode
change to have taken place. That is, if vortical fluid has been passing
the x-wire probe and a non-vortical reading is made, then there must be
two more consecutive readings indicating non-vortical fluid before the
computer recognizes the switch from vortical to non-vortical. The same
procedure holds on making the switch from the non-vortical to the vortical
mode.

3. ACCURACY

Several factors must be considered in the estimation of the overall
bounds which can be placed on the accuracy of the results. Some of the
factors forwhich error bounds can be estimated are sensor positioning,
alignment of flow field and traversing system, analog to digital conversion
and integration scheme. In addition, several checks have been made
which indicate overall performance of the data acquisition facility and
validity of assumptions made in the data processing.

Accurate probe positioning is sepecially important in any
axisymmetric-flow field. The evaluation of the mass, momentum and
energy flux integrals weight the measured values by the radius. This
means that the points measured in the steepest velocity gradient are
weighted more heavily than the high velocity small gradient fluid near
the center. The position of the probe is then important in the accurate
determination of the function of the velocity multiplied by the weighting
parameter. For these reasons the traversing mechanism for the present
investigation was built upon a lathe bed and cross-feed. The streamwise
position (x) was selected manually with an estimated accuracy of 0. 02 in.
This was deemed adequate since the gradients in the streamwise
direction are relatively small. The lathe cross-feed was driven with
the antibacklash screws stepping motor drive system to position in the
(y) direction. The estimated accuracy for the transverse (y) direction
is 0. 001 in. The vertical and rotational drives were also driven by
stepping motors, and the accuracies are estimated at 0. 001 in. for the
vertical and 0. 5 degrees for the rotation.

Alignment of the sensor traversing system with the physical
centerline of the flow field was accomplished using the optical catheto-
meter at approximately 60 diameters downstream. The initial alignment
of the cathetometer was achieved by passing a laser beam through the
supply tube for the jet tube array, through the jet exit and onto the
opposite wall of the laboratory. The resulting accuracy of the alignment
is estimated to be 1' 0. 05 in. at 10 diameters from the exit. These
accuracies agree with the measured centerline of the flow field as
determined from the half velocity points.

The finite length of the sensor element and the unavoidable inter-

ference of the supports for the sensor element cause the response of the

22

23

x-wire sensor to be somewhat different than a simple cosine (normal
component) cooling law. To minimize the error which would occur if
such a response were assumed, the scheme of conditional sampling the
velocity field based on the output of the discriminator circuit, which
indicated the presence or absence of high frequency vorticity fluctuations,
was used to rotate the sensor until it was aligned with the mean velocity
vector for the condition. Short term time averages (0. 3 sec.) were
taken for the two wires. The velocity components along and normal to
the x-wire sensor were calculated from the two polynomials representing
the wire calibration curves. The angle of the mean velocity vector
relative to the probe axis was calculated assuming a cosine cooling law
and the probe was rotated to align with the measured mean velocity
vector direction. Since the cooling law response is somewhat different
than a simple cosine law, the procedure was repeated if the indicated
rotation was more than one degree for a maximum of four corrections.
With the x-array aligned with the direction of the mean velocity, the
probe was being used at the orientation at which it was calibrated. The
part of the flow field for which this procedure would provide significantly
. better results is in the low velocity, high relative intensity region in the
outer part of the jet. The velocity measurements in this region make
significant contributions to the mass flux integration used in determining
entrainment rates. Conventional methods of using sensors which are
not rotated into the mean velocity direction encounter significant errors
because the relative angle of the mean velocity directions between the
vortical and non-vortical fluid is as large as 130 degrees. In addition

to the errors associated with support interference, the indicated mean
velocity differs from the true value due to second and higher order
turbulence quantities as shown by Champagne (1965). Those contribu-
tions become large in the outer region of the jet for the non-vortical
fluid where the mean velocity is nearly radially inward and the potential
fluctuations are relatively large. Since the x-array was essentially
aligned with the mean velocity, the conditions of the measurement
approximate those of the calibration. Therefore, even though the
x-array still has errors associated with relatively high turbulence
intensities, the contributions of the errors to the flux quantities are

minimized when the measured velocities are rotated back into

a.

24

laboratory coordinates. As a result of these. considerations it is
believed that the scheme of aligning the sensor axis with the mean
velocity vector direction yields significantly better accuracy in deter-
mining the measured quantities (U. V, u' , v' , :17) than conventional
methods.

The errors associated with the data acquisition facility include
the resolution capability of the A/D converter and the round-off errors
of the computer during the time averaging. The A/D converter was a
12 bit converter with an input range of i 10 volts. This means that the
resolution capability was 0. 005 volts. Full advantage of this resolution
may be made for the time average of the voltage signals; however, if
this signal is squared (needed for fluctuating quantities) the resultant
quantity may contain up to 24 bits of information. This then must be
truncated to 16 bits in order to avoid overflow. The result would be a
mean square fluctuating quantity accurate to O. 04 volts, which is
adequate for mean values on the order of 10 volts. The voltages
encountered in the present investigation ranged from about 8 volts in
the center of the jet to about . 5 volts in the outer portions. This would
represent about a 10 percent error bound at the lower voltages. To
overcome this problem, software was developed to make a short-term
average (. 25 sec) to determine the approximate mean value. The
signal was then scaled up by shifting the quantities (suppressing leading
zeros) allowing for a factor of 8 overvoltage. The result was an overall
accuracy estimated to be 0. 05 percent for mean quantities and 0. 4
percent for the fluctuating quantities.

The overall performance of the thermal anemometer and data
acquisition facility was checked by making measurements in the fully
developed pipe flow facility described earlier. The calculation of
Wfrom the individual wire voltages tests all aspects of the x-wire
system and this quantity may be established by the independent measure-
ment of the pressure gradient in the fully develOped pipe flow. This
evaluation is described in Appendix A; it was found that the measured
values from the data acquisition facility agreed with those calculated
from the measured pressure gradient to within about 2 percent. This
was considered to be quite acceptable.

Although the accuracy of 2 percent for the calculation of '11-; is

25

an indication of reliable data acquisition, there are two additional types
of errors which affect the accuracy of the behavioral measures of the
jet. The first type of errors are those associated with converting the
time-averaged voltages into the desired velocity quantities. The
measured voltages were first corrected for the second order turbulence
terms as indicated by Champagne (1965). The resulting response
characteristics of the wires should then be accurate to the third order
turbulence quantities. The resulting cumulative error due to this effect
is estimated to be on the order of 0.1 percent over most of the jet. The
corrected voltages were then converted to the desired velocity measures
(U, V, u', v', T17) using the polynomials which were fit to the calibration
tables. The accuracy of the polynomial fit is shown in Appendix B.
Linearizers were used on both thermal anemometers so that the voltage
output was approximately proportional to the instantaneous velocity.

It was only assumed, however, that the response was linear over the
range of excursion of the velocity fluctuations about the mean value.

The fluctuating voltage quantities were converted to velocity using the
local slope of the calibration curve at the mean velocity point. After
being converted. the velocity profiles may be plotted or measures of ‘
the behavior of the jet computed. Some of the behavorial measures
which are commonly used are the mass flux. momentum flux and
turbulent kinetic energy flux across a plane normal to the axis of the
jet. To evaluate these flux quantities it is necessary to evaluate integrals
of the velocity, velocity squared and velocity cubed. If the assumption
could be made that the flow field were axisymmetric, it would be
permissible to make the measurements along a radial traverse and

then integrate in cylindrical coordinates. Two special tests were run

to examine the axisymmetric character of the flow. Traverses covering
the exit plane (x = 0) at all operating conditions verified that the exit
condition was uniform, and a horizontal and vertical traverse through
the centerline of the jet at 10 diameters downstream verified that the

jet was axisymmetric at 10 diameters. The integrals were evaluated
using a modified Simpson's rule. A parabola was fitted to each set of
three points. The parabola was then integrated with the weighting

function

26

AI = PM vdy ‘3'”

S y + 5/2
Y'5/Z
The accuracy of this method was checked using several different known
profiles, and the results were good.

As a result of these effects it is believed that the overall best
estimate cumulative accuracies are 2 percent for the mass flux, 5
percent for the momentum flux and 8 percent for the turbulent kinetic

energy flux values.

4. RESULTS AND DISCUSSION

The principal results of this investigation are comprised of inte-
grated functions of the velocity (mass and momentum flux distributions)
and other functions of the velocity field which characterize its detailed
structure. The format of this section follows this natural division of
the results. Additional results which are predicated upon the turbulence
quantities are presented in Appendix D, "Additional Results". Characteristic
exit plane velocity profiles are shown in Figures 6 and 7. These are to
indicate the relative uniformity of both the velocity and the intensity of

the fluctuations .

4. 1. Mass Flux Distributions

The mass flux values for eight distinct exit conditions and for
seven x/D locations in the near field of the axisymmetric jet (0(- x/DEIO)
are presented in Figure 8. These data demonstrate the negligible
importance of the exit plane conditions over the range investigated for
the determination of this aspect of the jet flow behavior. This is an
unexpected result, but it appears to be conclusive since each data point
on the graph is supported by a radial traverse encompassing 31
individual velocity measurements and 7 mass flux values are used to
establish the streamwise distribution.

Since the largest intensity (3. 6 percent) and largest scale
(A/D = 0. 13) case were obtained by creating a jet solely with the flow
induced by the jet tube array, and since it is unlikely that these condi-
tions can be made more extreme without sacrificing the longitudinal
homogeneity utilized in the definition of the exit plane conditions, the
present results are inferred to be representative of all such jet flows.
The effects of a stronger disturbance condition and the attendant
longitudinal inhomogeneity and, perhaps more significantly, the effect
of a nonuniform mean velocity profile at the exit plane cannot be
assessed from these results. An investigation of these effects is
suggested as a logical extension of the present investigation.

The slope of the mass flux distribution for x/D 2 6 is nominally

0. 31;1 this is considered to be a most significant result. For an

 

lThis slape is primarily based upon the data at x/D = 6 and 10.
The data at x/D = 8 is adversely affected by the outer limit used for the
radial traverse which is considered to have truncated the flux of non-
vortical fluid. This judgement is supported by the measured flux of
vortical fluid at x/D = 8 as discussed below.

27

28

isothermal submerged jet (the present problem), Ricou and Spalding

(1961) have established an "entrainment rate" of 0. 32, i. e. ,

sail/1C4.) = 0.32. (4. 1)
d(x/D)

 

using a procedure which is independent of detailed measurements
within the jet field. Consequently, the agreement between the present
result of 0. 31 as a conglomerate value established by eight separate
sets of measurements and the value of 0. 32 from Ricou and Spalding
supports the following conclusions:

1) The overall accuracy of the velocity measurement and the
integration procedure is approximately 1 2 percent as revealed by the
dispersion of the data points about their mean value.

2) The asymptotic rate at which ambient fluid is caused to move
across a plane normal to the streaming direction is established at
approximately 6 diameters from the exit. (Recall that the detailed
structure of the velocity field is not self-preserving before approximately
60 diameters, see Wygnanski and Fiedler (1969).)

Attaining the asymptotic mass-flux-increase rate at six diameters
downstream is compatible with the results of two previous investigations,
specifically, Hill (1971) and Crow and Champagne (1970). The study by
Hill was an extension of the Ricou and Spalding technique in which a
determination of the local value of the mass-flux-increase rate was
attempted. Although the measurements are undoubtably influenced by
the finite width of the device used to introduce the entrained air and
although the streamline curvature of the entrained flow may affect the
detailed results, the results of Hill provide substantial support for the
present data. Crow and Champagne (1970) found it necessary to replace
the entrained flow contribution to their hot-wire signal by an assumed
smooth variation from the edge of the jet to a zero forward velocity
condition since their instrumentation was not configured to provide for
flow direction measurements. (Such a refinement was not required
for the purpose of their study.) However, they similarly conclude that
the asymptotic mass-flux-increase-rate attains its asymptotic value
at x/D = 6.

The present results suggest a mass-flux-increase rate of

29

approximately 0. 21 in the region closer to the nozzle; however, the
experimental accuracy in this region is insufficient to obtain more
than an approximate value, and it is insufficient to judge whether this
rate is essentially constant up to x/D = 6 or whether a continuous
variation more accurately describes the physical phenomena. Based
upon the present results, the increase rate of 0.136 for 0 3- x/D<- 2
quoted by Crow and Champagne appears low. Similarly, the continuous
variation in the quantity reported by Hill is not supported by the present
results.

The mass flux 0f vortical fluid across a plane of constant x,
normalized on the exit mass flux, is shown in Figure 9 as a function
of x/D. As in the total mass flux, there appears to be little if any
significant deviationbetween the various cases. Although there appears
to be a decrease in the rate of diffusion of vorticity (rate of increase
in the flux of vortical fluid) for the highest intensity largest scale
cases, it is believed that this is a result of the failure of the interface
detection circuity to respond to the lower frequencies resulting from
the lower mean velocities. This error would most probably be largest
in the outer edges of the low velocity puffs or bulges of vortical fillid-
Note that the total mass flux will not incur any error due to such a
failure of the detection circuitry since the mass flux not included in
the vortical zone averages will be included in the non-vortical zone
averages. Thus the total is still essentially correct. (The improper
zone discrimination will be associated with a yaw error in the thermal
anemometer response. )

The streamwise distribution of the non-vortical mass flux provides
for an instructive comparison with respect to the total mass flux
distribution. Specifically, the rate of increase in this curve is relatively
constant; there is no pronounced increase in the slope at x/D = 6.
Consequently, the latter response in the total mass flux distribution
must be caused by the enhanced movement of non-vortical fluid. This
is a principal reason why the word "entrainment" is us ed with caution
in the non-self-preserving region. It is probably significant that this
change in the mass-flux-increase rate occurs in the neighborhood of
the termination of the unsheared core of fluid. The constant rate of

increase in the vortical mass flux implies that the diffusion of vorticity

30

phenomenon is independent of the agents causing the increase in the
total mass flux.

It is important to note that the increase in the movement of non-
vortical fluid must be associated with a significant pressure gradient
in the streamwise direction since this is the only accelerating agent
for an irrotational field. The existence of a streamwise pressure
gradient is consistent with a momentum flux which, as will be shown,

has a significant streamwise variation starting at approximately x/D = 6.

4. 2. Momentum Flux

If the static pressure in the jet interior is only negligibly
different from the atmOSpheric value, then the momentum flux past
any x location is a constant and equal to that at the exit plane of the
jet (see equation4.2). This assumption is commonly made, e. g. , see
Townsend (1956), and the constancy of the momentum flux is often
used as a measure of the accuracy of experimental data, see Sami,
et a1. (1967), Mons and Sforza (1971), and Foss and Kleis (1971)..

R 2 2 R 2 2
5 WW] - XRP‘Ydlf] = pfiU +u' )ydy] - [m N” )Vdv] (4.2)
O x=o O x=x x=x O

X‘-’O

The results of the present investigation indicate that the momentum
flux is not a constant in the initial region. Figure 10 shows a plot of
the momentum flux, normalized on the momentum flux at x/D = 0. 5,
as a function of x/D. The results show a definite rise in the momentum
flux to a value between 20 to 30 percent over the initial momentum flux
value. Since the present study concentrated upon the near field of the
jet (0 <-x/D <- 10), the downstream behavior of the momentum flux
distribution is not revealed by the data of this investigation. However,
it is expected that the momentum flux would approach a constant value
at least in the region (x/D? 40) where the mean velocity profiles attain
self-similarity. Note that a condition of self-preservation, see
Townsend (1956), would guarantee this result. Referring to Figure 10,
the momentum flux appears to be leveling off slightly from 8 to 10
diameters downstream. It would be most interesting to have measure-
ments in the developing region (10 <- x/D S 40) to examine the behavior

of the normalized momentum flux.

31

The direct measurement of the mean velocity vector (magnitude
and direction) and the turbulence intensities in the vortical and non-
vortical zones of the jet and the utilization of these values in the
construction of the mean momentum flux value, see (1), implies that
a nonconstant momentum flux value must be balanced by the integral
of the mean static pressure. The mechanism for the reduced static
pressure is revealed by the radial component of the Reynolds equation
(see Hinze, page 23. ). For an incompressible steady flow of the
axisymmetric jet, the radial component of the Reynolds equation for large
Reynolds number can be written in the following approximate form,

2 2 2
1 8 __ l 8(V +v' 1 ,2 .Z 8(uv) _ 1 8v'

If the streamwise variation Of a; is neglected, a conservative estimate,
then this equation may be integrated from outside the jet to an arbitrary
radius (y). Thus, the radial component momentum equation requires
that there must be a radial pressure gradient due to the turbulence
quantities. An attempt was made to compute the pressure from the
radial momentum equation by assuming that the azimuthal component
(w') is equal to the radial component (v') within the vortical fluid and
equal to (u') for the non-vortical fluid. These assumptions were
checked at x/D = 10 for one case; the agreement was sufficient for the
purpose of the calculation (10 percent and 15 percent respectively).

The resulting equation, in the vortical region, is

p (Y) = W‘Z/2 + pv'Z (4.4)

The mean pressure values computed by this technique were integrated

over the area of the velocity distribution. This integral value was

approximately one-half as large as the excess momentum flux, and

since the estimate of the pressure value is approximate and conser-

vative, it appears feasible that the reduced pressure effect can be of

sufficient magnitude to balance the increase in the momentum flux.
Sami, et a1. (1967) present data for the region 0 $- x/D S 20,

from which they demonstrate a balance between the mean velocity,

the turbulent intensity and the static pressure. The static pressure

effect, at the x/D = 10 station of the present evaluation, was a negative

8 percent of the exit momentum flux; this is similar to the values noted

32

above. Their turbulence intensity contribution at x/D = 10 is approxi-
mately + 9. 4 percent of the exit momentum flux and this compares with
the nominal values of 7 percent for the present study.

The essential differences between the two studies are the value

co
of S Usz, ‘-"- 1.0 and 1.18 of the exit plane value for Sami, et a1. ,
o

and the present study, respectively, and the magnitude of the pressure
force, approximately -0. O8 and -0. 25 of the exit plane value, respec-
tively. Since the results of Sami, et al. , were in agreement with the
author's a priori understanding of the jet behavior, considerable effort
was expended to establish the credulity of the increasing momentum
flux result. The most significant factor in assessing the accuracy of
the mean velocity values is the agreement with the Ricou and Spalding
result for the mass flux. The author integrated the Sami, et a1. ,
data with these results: 1) agreement with the published momentum
flux value and 2) a mass-flux-increase rate of 0. 173 for 0 <- x/D <- 10.
It is inferred that the uncertainty of the flow direction and the ambiguity
of identifying the velocity magnitude at large radius values is responsible
for the differences between the results using conventional techniques
and the results with the present data acquisition system. It is also
inferred that the indicated result of a negative pressure force equal to
approximately 25 percent of the initial momentum flux can be used as
an indication of the extreme difficulty of executing accurate static
pressure measurements in a jet flow, Although this magnitude cannot
be used to infer the detailed pressure distributions in the jet, it would
provide an integral value to assess the accuracy of the corrected
probe response.

Additional measurements which support this inferred behavior
of the jet momentum flux are provided by two studies of a plane jet.

Measurements by Miller and Comings (1957) for a plane jet show
a constant momentum flux in the fully developed region of very nearly
1.40 times the exit momentum flux. This is calculated using the fact
that their normalized velocity profiles (U/Uc versus y/b) are very

closely fitted with a gaussian profile

U/Uc = exp (_../8 (Y/blzlo .(4. 5)

33

This gives a momentum flux

j to
s. = Ufibs p exp (~1r/4 (y/b)z) dy/b = 2,; Uib. (4. 6)
Q
When normalized on the exit momentum flux this becomes

[fl/If) = (mi/0:) (b/a) A (4.7)

The values of Ué/U: and b/a presented by the authors were used to
evaluate this ratio; a nominal value of 1. 4 was obtained.

Similar results have been obtained by Clark (1974). A gradual
increase in the momentum flux ratio from 1. 0 to approximately 1. 3
was observed in the region 0 S x/a S 15.

The corresponding value for the axisymmetric jet of Wygnanski
and Fiedler (1969) is l. 24. This value assumes a "top-hat" exit profile,

a conservative estimate, and would be larger if u'2 were included.

4. 3. Centerline Velocity Decay

After considering the momentum and mass flux behavior as a
function of initial turbulence structure it would appear that there is no
significant difference in the development due to various initial turbulence
structures. It should be remembered, however, that the momentum and
mass fluxes are integral quantities and therefore cannot reveal differences
in the detailed structure of the flow. As will be shown by considering
the centerline velocity decay and spread of the jet as a function of x/D,
the mean velocity profiles epread faster (and decay faster) for the higher
intensity larger scale initial condition cases.

Figure 11 is a plot of (Uc/Ue)-1 versus x/D for all of the initial
conditions investigated. The inverse function was selected because in
the region of the jet where similarity of the velocity field holds (x/D a 40),
the centerline velocity should be proportional to (x/D)-1. That is, the
slope of this curve in the fully developed region should be 0. 167 as
reported by Flora and Goldschmidt (1969) for the axisymmetric jets
of Miller and Comings (1957) and Van der Hegge Zijnen (1958). The
results of Wygnanski and Fiedler (1965) show that the value is more
nearly 0. 20 based upon data further downstream. As is indicated in
Figure 11, the slopes of the curves vary from 0. 125 for the low intensity
small scale cases to 0. 147 for the largest intensity largest scale case
in the 03 x/D S 10 region. '

34

In addition to the cases shown, a case was run with no jet grid
present giving an intensity of 0. 4 percent and the centerline velocity
decay was the same as that for the minimum scale and intensity case.
This indicates that a lower asymptotic value for the centerline ve‘locity
decay exists for zero initial intensity and is near the value reported for
the lowest intensity cases.

The observation that the curves are diverging and the fact that'
they will eventually attain a slope equal to that of the fully developed
jet indicates the possibility of a considerable difference in the
measured virtual origins. The virtual origins are measured from

data in the fully developed region and determined from
(UC/Uefl = K (x/D - C) (4. s)

where K is the slope of the curve (about 0. 167) and C is the virtual
origin. The notation is that of Flora and Goldschmidt (1969), who have
compiled K and C values from numerous experiments. Therefore, there
are significant differences in the measured centerline velocities in the
initial region and an indication of even larger differences in this quantity
in the fully developed region at a given x/ D location as a function of

initial turbulence structure at the exit plane.

4.4. Centerline RMS
A similar influence of the exit plane condition is indicated by
the variation of the root mean square axial velocity fluctuation as a
function of x/D. Figure 12 shows the RMS velocity fluctuation normalized
by the exit velocity versus x/D. As the centerline velocity data indicated,
the higher intensity larger scale cases tend to deve10p sooner than the
lower intensity smaller scale cases. This is seen as a more rapid rise
and decay of the centerline RMS for the higher intensity and larger scales.
It was originally thought that this more rapid rise could possibly
be due to the difference in Reynolds number between the cases (6. 5 x
104 for highest intensity largest scale to l. 0 X 105 for lowest intensity
smallest scale). To determine the effect of this Reynolds number range,
one additional case was run at the lower Reynolds number with no jet
grid (0. 4 percent intensity), and it was found that the centerline
behavior agreed very well with the no jet grid case run at the highest
Reynolds number. In addition, both of the no jet grid cases were in
good agreement with the results of Crow and Champagne (1970) for

their no forcing condition.

35

The velocity fluctuation intensity results and their implication of
an upstream shift in the initiation of significant dynamic processes
in the jet are in excellent agreement with the results of Crow and
Champagne who found that an axisymmetric jet responds to certain
preferred modes of forcing. The two experiments are complementary;
they introduced single frequencies into the jet and studied the resulting
behavior. The present study involves the introducing of a wide distri-
butlon of turbulence scales and the determination of the resultant
behavior of the jet. The results of the present investigation substantiate
the results of Crow and Champagne in that the higher intensity cases
contain more energy at the preferred modes (and harmonics) and thus
should and do show a more rapid increase in centerline intensity

distribution.

4. 5. Jet Spread

It is difficult to define a meaningful measure of the jet Spread.

In the region where the flow is self-preserving, the most common
measure of jet Spread is to use the radius at which the axial velocity
component is one-half of the centerline value. (The half-velocity point
is a good indication of the relative width of the mean velocity profile
only if the velocity profiles are similar. ) The half-velocity point can
be used as a normalizing factor for the radial coordinate along with
the centerline velocity as the normalizing factor for the velocity to
reduce the velocity profiles to a single curve. This is not true for the
present case because the mean velocity profiles are not self-similar
in the initial region.

The purpose Cf defining any measure of jet Spread is to indicate
the rate at which the jet is growing in the radial direction as it proceeds
downstream. Possibly a more direct measure of radial growth would
be obtained by plotting the locus of positions of constant probability
that the fluid passing that location will be vortical at that instant.

In fact, if the probability of one-half is chos en-, then the locus of
points will indicate the mean radial position of the vortical- non-vortical
”interface. Figure 13 shows a plot of such positions as a function

of x/D for the cases investigated. This figure indicates that there is

no measurable difference in the mean position of the viscous superlayer

36

for the range of conditions investigated. This is not surprising if one
considers that the mass and momentum flux distributions were indepen-
dent of the exit plane conditions. A similar behavior of the flux
quantities indicates a similarity of the pressure effects which would
dictate the curvature of streamlines or mean Spread of the vortical '
flow.

However, as shown by Figure 14, there is a measurable difference
in the excursions of the viscous superlayer. Differences in the measured
superlayer excursions could be associated with two quite different
physical phenomena. Either the jet could be increasing in width
instantaneously followed by a narrowing of the jet, or the jet could be
whipping, i. e. , maintaining a constant width and simply moving back
and forth. Figure 14 is a plot of the radial separation between the
positions of an intermittency factor of 95 percent to that of 5 percent.

As the figure indicates, the higher intensity larger scale cases have a
wider intermittent zone than the lower intensity smaller scale cases.
The fact that the curves are essentially parallel is significant. These
results are consistant with the flow visualization studies of Crow and
Champagne (1970) and their major conclusions which is summarized
by them as:

". . . a forced axisymmetric wave amplifies owing to the linear

instability of a tap-hot jet column, saturates under the non-

linear action of a harmonic, and finally decays owing to an

essentially linear process, either mean-field changes or

eddy damping. "

Consequently, the parallel character of the curves is interpreted as
an indication of a more rapid amplification due to the presence of more
energy at the preferred modes for the higher intensity larger scale cases.

Note also that these results are consistant with the centerline
velocity decay and more rapid increase and subsequent decay of the
centerline RMS for higher intensity cases. That is, there is an increased
excursion of the superlayer interface resulting in a quicker penetration
of the so-called potential core and the resultant increase in centerline
RMS and velocity decay.

The total rate of vorticity diffusion in a given region of the jet flow

is related to but not controlled by the excursions of the superlayer as

37

revealed by the (RY ___ 0 95 - RY ___ 0 05) plots discussed above. The
local rate is related to the instantaneous Laplacian of the vorticity
evaluated at the location of the superlayer as shown by the vorticity

transport equation, viz. ,

’ " v sf}. 7-"
Dwi =wj i + v a “i (4.9)
51: axj 5xj5xj

The area of the interface in a given region of the jet is a function of
the corrugations of the superlayer, as discussed extensively by
Phillips (1972), and these corrugations are influenced by all scales of
the turbulent motion. It is instructive to note that the vortical mass
flux is insensitive to the exit plane conditions, whereas the excursion

of the superlayer shows a definite dependence upon these conditions.

5. CONCLUSIONS

The following conclusions are supported by the results of this
study. These conclusions are based upon the investigation of eight
discrete exit plane conditions involving an essentially uniform mean
velocity profile (nozzle boundary layer/diameter 5 0. 02) and turbulence
structure conditions described by 0. 004 <- u' (o, r)/U(o) S- 0. 036 and
.o75$A/n <- 0.13.

1.) The mass-flux-increase rate is negligibly influenced by the
exit plane turbulence conditions.

2.) The mass-flux-increase rate attains its asymptotic value of
= 0. 32 at approximately x/D = 6.

3. ) Separate measurement ofithe vortical mass flux demonstrates
that the total mass flux involves a significant fraction (8 20 percent) of
non-vortical fluid at x/D = 10. This suggests that the word "entrainment"
should not be used without further definition or qualification in order to
distinguish between the movement of fluid across a plane of constant x
and the diffusion of vorticity into the external fluid.

4.) Contrary to our a priori expectation, the momentum flux (the
integral over a plane of the average of the squared longitudinal velocity,
Uz +u'z) increases to approximately 125 percent of its exit plane value
at x/D = 10. This behavior is apparently not influenced by the exit
plane turbulence conditions. It is presumed that the asymptotic value
is of this order.

5. ) The increased momentum flux value must be balanced by a
net static pressure force acting differentially between the exit plane
("zero" force resulting from p(0,r)~ patm) and the x location of the
increased momentum flux. (No detailed pressure measurements were
attempted. )

6.) The influence of the exit plane conditions are revealed by
measures of the structure of the jet; specifically,

i) The centerline mean velocity and turbulence intensity
values exhibit an upstream shift in their characteristic variation as
the intensity and/or scale of the turbulence is increased.

ii) A width measure, based upon the radial distance between the
0. 05 and 0. 95 intermittency values, increases linearly with x/D for all

exit plane conditions but is an increasing function of the scale and

38

39

intensity at a given x/ D location.

7. ) The turbulence structure effects identified in 6.i and 6. ii
indicate that the exit plane conditions influence the initiation of , but
not the mechanics of, the controlling processes of the jet flow in the

initial region.

APPENDICES

APPENDIX A

FULLY DEVELOPED PIPE FLOW

As stated in the accuracies section, the overall accuracy of
the measurements of turbulence quantities was checked by making
measurements in a fully developed pipe flow facility. The measured
values of u' and v' can be compared with the published results of
Laufer (1954). Also, the total shear stress at any radius can be
computed from a measure of the pressure gradient along the pipe.

If the flow in the pipe is fully developed, i. e. there are no changes
in the velocity field with streamwise location, then a simple force
balance between the wall shear stress (7w) and the pressure drop

between two x - locations (x1 and x2) gives
2
(P2 - p1) wr - 7w ("z -xl)- 21rr

or
7w = 1‘ (P2 " P1)
2 (x2 - x1)

Because the velocity field is fully developed, the wall shear stress

 

can not vary with x, therefore the pressure gradient must be a constant.
Also, since the flow is fully developed, the radial pressure gradient

is zero (no streamline curvature), thus, the total Shear stress varies
linearly with radius. In a turbulent pipe flow, the total shear stress is
the sum of the viscous shear and Reynolds shear stresses. The viscous
shear stress is dominant at and very near the wall but becomes insigni-
ficant in comparison to the Reynolds shear stress in the central part of
the flow field. Thus, from a measure of the pressure drop along the
pipe, the Reynolds shear stress (W) can be computed. This value
can then be compared with the measured value to evaluate the accuracy
of the data acquisition facility.

The pressure drop along the fully developed pipe flow facility
was measured with an electronic pressure transducer with a full scale
sensitivity of 10 volts equal to 0. 30 inches of water. The plot of pressure
versus streamwise location is shown in Figure 15. The calculated

Reynolds stress and the measured values are shown in Figure 16. The

40

41

agreement is considered to be excellent for this difficult measurement.
The data demonstrates a "stairstep function" centered along the mean
curve inferred from the pressure measurements. The small velocities
required to obtain a Reynolds number of 5 x 104 caused a low level output
voltage from the thermal anemometer. The consequent "round-off"
error in the analog to digital conversion is considered to be responsible
for the ”non-smooth" behavior of the -ll'V/uZ curve.

The measured values of u' and v' measured in the pipe at a
Reynolds number of 41,000 are shown in Figure 17 with the results of
Laufer (1954). The results of Laufer are generally accepted as the most
accurate to date for the fully developed pipe flow and are thus us ed as a
standard of comparison.

A direct comparison with known results is important when
conducting an experimental investigation in turbulence research due to
the nature of the measurement techniques. There are several factors
which affect the reaponse of the hot-wire probe and the thermal anemo-
meter. For example, when an x-array is used, as in the present investi-
gation, the relative angle between the wires has a strong influence upon
the Reynolds stress measurement. A difference of a few degrees in the
included angle can make very large changes in the measured value. Also,
it is difficult to accurately measure the relative angle to within the
necessary accuracy. But, with a direct comparison with known results
(from pressure measurements), the cumulative effect of all such influences
can be determined.

The results for the Reynolds stress measurements are considered
to be confirmation that the data acquisition facility is quite accurate. The
differences between the measured u' and v' distributions and those of
Laufer could very well be due to differences in the flow facilities. The
present pipe flow facility certainly has a higher relative roughness than
the polished brass pipe used by Laufer. This could result in the slightly
different trends of the u' and v' data compared with the Laufer study.

APPENDIX B

THERMAL ANEMOMET ER CA LIBRATION

The calibration of the thermal anemometer used in making
turbulence measurements is a critical part of the overall accuracy.
When converting a measured voltage output of the thermal anemometers
to the corre3ponding velocity measures (U,V,u',v',uv , the accuracy of
the calibration curves (voltage versus velocity) directly affect the accuracy
of the results. The most sensitive measures to calibration errors are
the turbulence quantities.

The turbulence quantities are obtained by multiplying the mean
of the squared voltage minus the mean voltage squared by the square of
the lepe of the calibration curve. The slope of the calibration curve was
evaluated at the mean voltage point. Thus, "local” linearity of the thermal
anemometer was assumed. That is, even though linearizers were used,
the curves were only assumed to be linear over the variation of the voltage
fluctuations about the mean value of the voltage. The accurate determination
of the slope of the calibration curve is, therefore, essential for accuracy
in the turbulence quantities. For this reason, a polynomial was fitted to
the original calibration points and then the slope was found by taking the
derivative of the polynomial. A calibration curve and its corresponding
polynomial is shown in Figure 18. i This figure demonstrates the
excellent fit of a fourth order polynomial. A fourth order curve was chosen
by fitting polynomials of order 1 to 13 to a given set of data. The sum of
the squared errors was obtained and it was found that the sum of the squared
error was very nearly constant for the fourth and higher order polynomials.
Thus, because of the computer time required to complete a least square
fit, it was decided that the fourth order would be the most appropriate

polynomial to use.

42

APPENDIX C

EXIT CONDITION DOCUMENTATION

The exit conditions for the various cases used in the present
investigation are documented in this section. A description of the physical
parameters and the correSponding flow field measures are given.

The exit condition generation is described in the text. The
quantities varied were the supply pressure to the jet tube array, the
Spacing of the jet tube array and the main blower speed. These variations
resulted in different turbulence structures at the exit plane. There are
several measures of turbulence structure which were made at the exit
plane.

Both longitudinal and lateral correlation functions were computed.
From these both integral (A) and micro (X) scales were computed. The
integral scale was calculated directly as the area under the (spatial)
correlation function. The micro scales are defined as the separation
distance at which the osculation parabola, fit to the correlation curve at
zero separation, crosses the separation variable axis. That is, it
satisfies the relationship

Ax2

f=l--z—
h
x
and

2
821-52.
l.
Y

where f is the longitudinal correlation function u(x)u(x+Ax) and g is the

 

 

lateral correlation vTx)v(x+Ax). The micro scales were determined by

evaluating
x x: JTTAX

). = Ax
Y rs
for several values of x and determining the constant values of this function
near x = 0. This method minimizes the influence of small variations in
the correlation functions near zero separation.
A summary of the physical conditions and resulting exit conditions

is shown in Table C. 1. The actual correlation functions are given in

Figure 19 through 27. 43

44

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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So. 2o. ooo. So. .25. who. ooo m m.

2o. o8. 3o. moo. So. so. ooo 2 m.

So. So. o8. moo. moo. S. ooo 2 w.

o~o . o~o . omo . omo . Nmo . 3.. ooo 2 m .

ono . omo . 2o . ooo . owo . 2 . o on n .

o~o. So. moo. moo. moo. .3 . o on w.

moo . moo . omo . who . Nmo . 2... . o on. m ..

Ea: Too

1» on C025 :25 mdmoam

oo\_> oo\.s Q) Qua Q < n\ < .83on meanness onto owe

 

ssoroosoo Sufi

a .0 flash.

 

APPENDIX D

ADDITIONAL RESULTS

This section contains listings of the data obtained in the present
investigation. As a result of the general capability of the data acquisition
facility, considerably more data than was necessary to meet the direct
objectives of this study was obtained. Since this information could be
useful to other problems, e. g. , aerodynamic noise generation and ejector
studies, they are included in the spirit of the Stanford boundary layer
conference in 1968 and the Langley Working Conference on Free Turbulent
Shear Flows, 1972. This spirit is expressed by the following quote from
the report of the Committee to Recommend Critical Experiments of the
latter reference.

"The committee believes that rapid advancement of
predictive capability requires more complete reporting
of experimental data and also requires arrangements

for storage of complete original data in sliitable archives
(not merely on small published figures). "

The data for each of the exit conditions is subdivided into the
vortical and non-vortical averages. Each table contains data for one
streamwise location and one of the conditions. The velocity data is
presented in a dimensionless form, being normalized by the centerline
mean axial velocity. The values of the normalizing factors are included
in the captions. The fourth column (9) is the angle between the mean
velocity for the condition (vortical or non-vortical) and the x-axis. The
eighth column (Y0) is the fraction of time the flow is vortical. The last
column (C/T) is the number of mode switches from the vortical to the
non-vortical condition divided by the total time giving the number of

mode switches per second.

 

lFr’lee Turbulent Shear Flows, NASA Langley Research Center,
NASA SP-321, 1972 p. 659.

45

TABLE D-l DATA LISTING

Au/d =
0.130
T = 150000
V/Uc o
0.006 0.366
0.010 0.588
0.002 0.156
0.006 0.340
0.004 0.247
0.007 0.437
0.006 0.376
0.007 0.408
0.008 0.468
0.021 1.281
0.047 4.731
0.033 9.629
0.035 20.186
0.009 16.726
0.006 13.518
0.007 15.585
0.001 0.085
0.001 0.079
0.004 0.229
“00002 “00129
0.002 0.121
0.005 0.294
0.003 0.223
0.004 0.267
0.005 0.335
-0.003 '0e233
-0.035 -3.129
-0.013 ‘20936
-0.005 -2.602
“00038 “21.803

-0.010 -23.899
-0.010 '23.899

46

A/d:

0.8'52

u'/UC

0.038
0.035
0.038
0.036
0.035
0.038
0.038
0.040
0.043
0.084
0.127
0.087
0.045
0.018
0.002
0.000

0.038
0.036
0.039
0.036
0.035
0.032
0.033
0.036
0.048
0.082
0.128
0.110
0.059
0.035
0.000
0.000

(averaging time)

vfi/UC

0.031
0.030
0.032
0.032
0.031
0.032
0.032
0.034
0.044
0.084
0.125
0.074
0.023
0.012
0.001
0.000

0.032
0.030
0.031
0.031
0.030
0.029
0.029
0.030
0.032
0.056
0.119
0.078
0.028
0.015
0.000
0.000

hx/d =
0.058

X /d=:
0.658

Condition: Vortical

—— -2
uv/UC

‘00002
’00001
-0.001
”0.000
0.000
0.002
0.002
0.003
0.003
0.029
0.076
0.028
0.012
0.001
0.000
0.000

“00001
“00001
“00002
”0.001
’OeOOI
-0.000
0.000
0.000
0.002
“00012
-0.085
“00031
“0.001
-0.006
0.000
0.000

Y

0.999
0.999

'0.999

0.999
0.998
0.999
0.999
0.999
0.999
0.999
1.000
0.991
0.147
0.058
0.017
0.000

0.999
0.999
0.999
0.999
0.999
0.999
0.999
0.998
0.998
0.999
1.000
0.999
0.503
0.039
0.000
0.000

C/T

0.333
0.466
0.333
0.200
0.933
0.400
0.866
0.466
0.266
0.066
0.000
6.733
99.933
3.200
3.400
3.000

0.533
0.333
0.466
0.200
0.133
0.533
0.600
0.800
1.200
0.066
0.000
0.400

187.066

17.266
3.000
3.000

TABLE D-l Continued

47

x/d All/d = A /d = Xx/d = xy/d :-
1.500 0.130 0.052 0.058 0.058
Uc(fps) =70.190 T = 15.000 (averaging time) Condition: Vortical
I i — '2

y/d u/Uc V/Uc e 11 /UC v /Uc uv/Uc y c/r
-1.000 0.024 -0.010 -23.899 0.000 0.000 0.000 0.000 3.000
'0.933 0.027 -0.013 -25.385 0.028 0.020 -0.005 0.000 3.133
-0.866 0.071 -0.026 -20.335 0.071 0.048 -0.022 0.003 4.933
'0.800 0.136 -0.082 -30.956 0.081 0.068 -0.079 0.061 30.533
-0.733 0.156 -0.068 -23.561 0.096 0.045 -0.058 0.517 79.266
'0.666 0.240 -0.043 -10.213 0.128 0.054 -0.044 0.789 87.200
-0.600 0.371 -0.023 -3.610 0.141 0.092 -0.052 0.990 7.266
-00533 00539 “00024 '20609 00145 00120 ‘00076 00999 00133
'00466 00710 “00021 -1069“ 00136 00121 “00075 10000 00000
-0.400 0.859 -0.007 -0.474 0.112 0.101 -0.049 0.999 0.066
-0.333 0.945 0.001 0.067 0.082 0.068 -0.014 0.999 0.600
-0.266 0.974 0.005 0.346 0.058 0.044 -0.000 0.999 0.866
’00133 10003 “00001 '00070 000593 00033 “00001 00999 00800
-00066 10009 -0000“ '00235 00041 00032 '00000 00999 00533
-0.000 0.996 0.000 0.035 0.038 0.031 0.000 0.999 0.533
0.066 1.018 -0.006 -0.350 0.039 0.033 0.000 0.999 0.533
00133 10015 '00007 ’004‘96 00041 0003‘. 00002 00998 10133
0.199 1.018 -0.003 -0.177 0.042 0.037 0.002 0.999 0.866
00266 10003 “00000 “00032 00046 00095 00003 00999 00966
0.333 0.992 0.005 0.331 0.063 0.065 0.012 0.999 0.400
0.400 0.921 0.015 0.979 0.102 0.091 0.041 1.000 0.000
0.466 0.752 0.030 2.303 0.140 0.112 0.072 1.000 0.000
0.533 0.554 0.042 4.377 0.146 0.116 0.079 0.999 0.133
0.600 0.359 0.043 6.909 0.133 0.099 0.064 0.989 7.466
0.666 0.229 0.037 9.154 0.113 0.034 0.046 0.777 91.266
0.733 0.167 0.047 15.829 0.100 0.088 0.068 0.253 94.000
0.800 0.130 0.041 17.579 0.079 0.087 0.046 0.101 18.333
0.866 0.047 0.012 14.712 0.048 0.037 0.012 0.059 4.133
0.933 0.032 0.006 11.535 0.027 0.021 0.003 0.000 3.266
1.000 0.026 0.004 9.927 0.000 0.000 0.000 0.000 3.000

TAB LE D-l Continued

48

x/d Au/d = A /d = 1 /d = 1 /d -.-
3.000 0.130 0.652 03858 01058
UC (fps) = 70 .310 T = 15.000 (averaging time) Condition: Vortical
u . -—- -2
y/d U/Uc V/Uc 8 u /Uc v /Uc uv/Uc y C/T

1.250 0.030 0.007 13.852 0.018 0.013 0.001 0.000 3.133
1.166 0.055 0.006 6.630 0.047 0.041 0.004 0.136 3.333
1.083 0.109 0.018 9.605 0.064 0.071 0.010 0.011 8.266
1.000 0.139 0.085 31.390 0.056 0.079 0.088 0.082 30.400
0.916 0.191 0.064 18.545 0.092 0.068 0.066 0.299 74.666
0.833 0.233 0.047 11.464 0.111 0.015 0.049 0.720 67.133
0.750 0.296 0.043 8.369 0.115 0.075 0.048 0.912 37.466
0.666 0.390 0.043 6.321 0.135 0.094 0.064 0.986 8.266
0.583 0.504 0.043 4.890 0.145 0.105 0.073 0.999 0.400
0.500 0.643 0.038 3.381 0.147 0.110 0.074 1.000 0.000
0.416 0.783 0.029 2.181 0.139 0.105 0.064 1.000 0.000
0.333 0.895 0.020 1.332 0.113 0.090 0.044 1.000 0.000
0.250 0.985 0.016 0.958 0.080 0.072 0.023 0.999 0.400
0.166 1.012 0.010 0.613 0.056 0.055 0.007 0.998 1.000
0.083 1.007 0.008 0.506 0.048 0.044 0.002 0.998 1.600
0.000 1.004 0.011 0.664 0.048 0.041 -0.000 0.999 0.866
-0.083 0.988 0.012 0.730 0.053 0.043 -0.002 0.998 1.266
’0.166 0.967 0.009 0.538 0.069 0.056 -0.008 0.999 0.600
’0.249 0.914 .0.006 0.393 0.093 0.074 -0.023 0.999 0.333
'0.333 0.831 -0.000 -0.057 0.121 0.095 -0.044 1.000 0.000
'0.416 0.724 -0.009 -0.782 0.138 0.105 -0.061 0.999 0.066
“00499 00606 “00010 “00996 00146 00108 “00069 10000 00000
“0.583 0.491 -0.014 -l.733 0.147 0.098 -0.061 0.999 0.533
-0.666 0.382 -0.014 -2.232 0.144 0.067 -0.044 0.982 10.266
-O.750 0.293 -0.015 -3.056 0.140 0.057 -0.026 0.864 50.866
“00833 00230 “00033 “00070 00125 00070 “00030 00597 090800
-0.916 0.197 -0.038 -10.990 0.118 0.109 -0.038 0.280 70.733
“00999 00167 “00006 “20193 00113 00118 00013 00107 350933
“10083 00119 “00002 “10433 00090 00095 00009 00027 130066
“10166 00068 “00002 “30006 00070 00053 00005 00003 40866
“10250 00031 “00001 “3006‘ 00027 00021 00000 00000 30200

TABLE D-l Continued

49

X/d Au/d = A /d = 1. /d = 1. /d =
4.500 0.130 0.052 03050 0Y050
Uc(fpa) = 70.574 T = 15.000 (averaging time) Condition: Vortical

y/d u/Uc v/Uc e u'/Uc w/uc 627/ng y C/T
-1.500 0.037 -0.000 -0.163 0.031 0.026 0.001 0.001 3.533
'1.400 0.068 0.001 1.352 0.068 0.060 0.005 0.003 4.533
'1.300 0.144 -0.000 -0.140 0.107 0.114 0.020 0.027 13.733
“10200 00160 “00057 “220271 00072 00078 “00064 00157 230733
-1.100 0.191 -0.040 -11.974 0.104 0.110 -0.048 0.204 55.533
-1.000 0.237 -0.039 -9.342 0.119 0.084 -0.034 0.491 79.400
“00900 00270 “00023 “40927 00126 00066 “00029 00720 720733
-0.800 0.327 -0.012 -2.220 0.144 0.052 -0.026 0.907 35.266
'0.700 0.405 -0.009 -1.403 0.150 0.063 -0.047 0.978 11.000
-O.600 0.497 -0.011 '1.324 0.164 0.060 -0.061 0.998 1.333
-0.500 0.600 -0.014 -1.363 0.148 0.105 '0.068 0.999 0.266
'0.400 0.711 -0.014 '1.160 0.146 0.106 -0.068 1.000 0.000
~0.300 0.817 -0.012 -0.893 0.134 0.100 -0.052 1.000 0.000
'0.200 0.907 -0.007 -0.501 0.115 0.087 -0.033 0.999 0.333
'0.100 0.979 -0.004 -0.257 0.090 0.074 -0.014 0.999 0.800
-0.000 1.012 0.002 0.156 0.074 0.068 0.000 0.999 0.800
0.099 1.005 0.002 0.125 0.085 0.073 0.018 0.999 0.733
0.199 0.970 0.007 0.457 0.111 0.085 0.039 0.999 0.333
0.299 0.874 0.014 0.953 0.138 0.097 0.056 0.999 0.200
00399 00756 0002‘ 10879. 00152 00105 00070 10000 00000
00499 00667 00032 20915 100157 00107 00076 10000 00000
0.599 0.522 0.036 3.989 0.155 0.102 0.079 0.998 0.800
0.699 0.428 0.036 4.894 0.147 0.079 0.071 0.985 8.200
0.800 0.342 0.038 6.433 0.126 0.084 0.054 0.922 32.200
0.900 0.297 0.048 9.251 0.127 0.009 0.062 0.829 55.066
0.999 0.246 0.048 11.109 0.110 0.041 0.052 0.582 75.866
1.100 0.201 0.060 16.631 0.088 0.065 0.053 0.269 66.333
1.200 0.170 0.071 22.766 0.087 0.094 0.088 0.088 29.733
1.300 0.114 0.071 31.737 0.047 0.069 0.062 0.033 15.266
1.399 0.061 0.055 42.210 0.037 0.029 0.045 0.004 5.933

1.500 0.033 0.026 38.204 0.017 0.010 0.009 0.001

3.733

TABLE D-l Continued

50

x/d Au/d = A /d = xx/d = x /d =
6.000 0.130 0.052 0.058 03050
Uc(fps) =68.407 T = 15.000 (averaging time) Condition: Vortical
. . ——- -2

y/d IJ/Uc v/Uc e , u /Uc v /UC uv/Uc y C/T
1.750 0.032 0.023 36.137 0.014 0.006 0.006 0.001 3.666
1.633 0.044 0.064 55.299 0.030 0.043 0.043 0.006 5.666
1.516 0.062 0.106 59.873 0.059 0.048 0.053 0.016 9.266
1.400 0.080 0.145 61.094 0.099 0.080 0.123 0.054 18.733
1.283 0.201 0.099 26.244 0.090 0.082 0.142 0.175 49.600
1.166 0.260 0.067 14.586 0.118 0.080 0.087 0.430 75.533
1.050 0.303 0.047 8.903 0.128 0.051 0.065 0.688 72.066
0.933 0.345 0.044 7.297 0.132 0.070 0.061 0.837 48.200
0.816 0.433 0.039 5.241 0.146 0.098 0.072 0.966 15.133
0.700 0.510 0.037 4.214 0.158 0.104 0.083 0.991 5.200
0.583 0.631 0.041 3.797 0.167 0.112 0.092 0.999 0.533
0.466 0.723 0.033 2.630 0.170 0.114 0.086 1.000 0.000
0.350 0.852 0.027 1.818 0.166 0.113 0.079 1.000 0.000
0.233 0.945 0.016 1.027 0.154 0.109 0.058 1.000 0.000
0.116 0.996 0.005 0.336 0.140 0.104 0.033 0.999 0.066
06000 10011 “00000 ‘00016 00133 00104 “0.002 00999 00‘66
-0.116 0.975 -0.009 -0.573 0.141 0.108 -0.030 0.999 0.066
-0.233 0.888 -0.012 -0.836 0.156 0.112 -0.060 0.999 0.066
-0.349 0.763 -0.011 -0.896 0.161 0.115 -0.077 1.000 0.000
-0.466 0.677 -0.016 -1.356 0.169 0.100 -0.080 0.999 0.066
-0.583 0.579 -0.012 -1.198 0.175 0.074 -0.073 0.997 1.666
-0.699 0.487 -0.010 -1.176 0.159 0.078 -0.058 0.989 5.933
-0.816 0.401 -0.017 -2.478 0.147 0.063 -0.044 0.943 23.133
“0.933 00337 ”00025 ”40330 00131 000‘1 '00032 00828 5‘0533
-10050 00292 ”00038 “70‘22 001“ 0.10“ ’000“ 0.629 73.800
-1.166 0.256 -0.049 -10.828 0.146 0.130 -0.051 0.395 75.400
’10283 0.220 ‘000‘6 -1109“ 00130 0.129 “0.053 00199 50.000
-1.399 0.195 -0.014 -4.351 0.148 0.149 0.024 0.079 28.600
-1.516 0.135 -0.008 -3.731 0.111 0.111 -0.000 0.022 11.533
-1.633 0.090 0.019 12.366 0.071 0.061 0.020 0.007 5.866
-1.750 0.038 0.005 8.439 0.023 0.016 0.002 0.002 4.066

x/d
8.000

0cm») =02.270

v/d

-20000
“10866
“1.733
'10600
“10‘66
"10333
'10200
-10066
”00933
“00800
-0.666
’00533
'0.400
‘00266
-00133
“0.000
0.133
0.266
0.399
0.533
0.666
0.800
0.933
1.066
1.200
1.333
1.466
1.600
1.733
1.866
2.000

TABLE D-l Continued

.Au/d==
0.130
T = 15.000
v/Uc o
0.014 12.150
0.017 8.005
0.017 5.541
0.077 25.160
“0.046 “90811
“00059 -110025
“00047 ‘70763
-0.039 -5.816
-0.025 -3.268
“00020 ’20 212
-0001? '106‘0
-0.017 -1.372
‘00020 ”10426
-0.018 -1.186
-0.013 -0.798
-00003 ‘00193
0.005 0.311
0.019 1.194
0.029 2.046
0.033 2.676
0.034 3.149
0.039 4.097
0.040 4.783
0.048 6.553
0.055 8.745
0.068 12.999
0.094 19.692
0.150 43.055
0.103 30.670
0.079 33.138
0.039 37.205

.A /d=:

0.052

(averaging time)

tfl/U£

0.071
0.126
0.132
0.095
0.176
0.144
0.162
0.174
0.176
0.185
0.190
0.203
0.208
0.182
0.182
0.179
0.185
0.191
0.194
0.194
0.184
0.183
0.163
0.165
0.147
0.139
0.134
0.055
0.096
0.077
0.034

51

Xx/d =
0.058

Condition:

-—- -Z
v'/Uc uv/Uc

0.060
0.116
0.138
0.091
0.180
0.111
0.119
0.097
0.047
0.070
0.094
0.095
0.092
0.134
0.135
0.134
0.130
0.130
0.130
0.126
0.119
0.097
0.093
0.033
0.044
0.108
0.130
0.026
0.103
0.075
0.021

0.020
0.061
0.088
0.169
“0.060
-00059
”00048
’00048
-00048
-0.069
-00089
‘06103
“0.098
-00076
’00044
“00002
0.042
0.073
0.097
0.110
0.108
0.110
0.086
0.091
0.079
0.108
0.178
0.186
0.134
0.087
0.018

xy/d -

0.058
Vortical

‘v C/T

0.003 4.333
0.007 6.466
0.035 15.933
0.414 18.333
0.161 45.200
0.361 72.600
0.570 71.800
0.720 67.466
0.882 40.800
0.966 16.000
0.992 4.400
0.999 0.666
0.999 0.200
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
0.999 0.066
0.999 0.266
0.998 1.400
0.990 5.333
0.969 13.733
0.944 23.266
0.837 47.733
0.660 71.066
0.421 62.266
0.213 49.733
0.075 25.066
0.036 14.666
0.018 8.733
0.003 4.400

TABLE D-l Continued

52

x/d Au/q - A /d = X /d = Xy/d =
10.000 0.130 03652 03050 0.058
Uc(fps) = 52,270 T = 15,000 (averaging time) Condition: Vortical
, — -2

y/d U/UC v/Uc e u /Uc w/uc uv/Uc y C/T
2.500 0.043 0.027 31.996 0.021 0.017 0.009 0.001 3.333
2.333 0.050 0.032 32.502 0.029 0.013 0.017 0.002 3.933
2.166 0.085 0.073 40.877 0.057 0.021 0.093 0.005 5.866
2.000 0.173 0.125 35.821 0.068 0.079 0.186 0.278 10.333
1.833 0.236 0.142 31.170 0.117 0.136 0.329 0.048 18.600
1.666 0.262 0.127 25.864 0.129 0.131 0.248 0.178 31.066
1.500 0.361 0.092 14.392 0.141 0.070 0.117 0.359 57.733
1.333 0.407 0.071 9.919 0.155 0.054 0.096 0.517 75.400
1.166 0.452 0.057 7.285 0.172 0.031 0.104 0.685 67.600
1.000 0.536 0.054 5.822 0.176 0.108 0.106 0.886 39.733
0.833 0.636 0.048 4.390 0.187 0.127 0.116 0.975 12.400
0.666 0.746 0.048 3.744 0.196 0.134 0.118 0.995 2.466
0.500 0.839 0.043 2.993 0.200 0.136 0.105 0.999 0.600
0.333 0.929 0.037 2.329 0.197 0.140 0.070 0.999 0.200
0.166 0.978 0.021 1.282 0.194 0.142 0.033 0.999 0.200
0.000 0.995 0.008 0.483 0.191 0.143 -0.007 0.999 0.133
-0.166 0.947 ~0.002 -0.143 0.193 0.144 -0.058 0.999 0.066
-0.333 0.870 -0.003 -0.251 0.204 0.134 -0.087 0.999 0.266
“00499 0.788 -00006 “0.4‘6 00202 00128 -0009“ 0.997 1.600
'00666 00689 ”00006 ’00551 00209 00076 -0007‘ 00982 8.400
‘00833 00599 '00011 ”1.144 00209 0.024 “0.062 Oo9¢9 21.666
-0.999 0.524 -0.017 -1.940 0.184 0.077 -0.058 0.895 33.266
“1.166 06456 “0.044 -50518 0.193 00101 “0.057 06741 650933
-10333 0.401 “00050 ”7.173 00186 00125 “0.060 0.514 720000
‘10500 0.364 ”00078 ’120156 00192 0.184 “0.113 0033‘ 670733
-l.666 0.311 -0.076 -13.747 0.161 0.167 -0.132 0.169 45.733
~1.833 0.258 -0.077 -16.623 0.136 0.145 -0.118 0.061 22.533
“1.999 00210 -00025 -6097? 0.159 00161 “0.009 0.021 11.333
“2.166 00111 ”00010 ’5039‘ 00129 , 00118 ’00019 0.006 50800
'2.333 0.061 -0.018-17.026 0.053 0.034 -0.008 ‘0.001 3.600
”20500 000‘3 “00°17 “220‘62 00019 00010 -0.002 0.000 3.133

TABLE D-z DATA LISTING

53

x/d Au/d = A /d = x /d = x /d =
0 .500 0. 140 0.1m 0 3085 0¥065
Uc(fpa) = 86. 983 T = 15,000 (averaging time) Condition: Vortical
. . -—- -Z
y/d u/Uc v/Uc e u /uc v /Uc uv/Uc y C/T

0.000 1.021 -0.012 -0.718 0.032 0.029 -0.001 0.999 0.000
0.050 1.030 0.013 0.755 0.031 0.027 -0.000 1.000 0.000
00100 10026 ‘00002 -0011“ 0.032 00028 -0.000 10000 00000
0.150 1.023 0.001 0.061 0.035 0.028 0.000 1.000 0.000
0.200 1.013 -0.001 -0.064 0.036 0.029 0.001 1.000 0.000
0.250 1.001 0.002 0.139 '0.040 0.031 0.001 0.999 0.066
0.300 0.992 0.003 0.208 0.043 0.032 0.000 1.000 0.000
0.350 0.981 0.004 0.264 0.044 0.034 0.000 1.000 0.000
0.400 0.986 0.007 0.442 0.045 0.042 0.001 1.000 0.000
0.450 0.939 0.014 0.894 0.078 0.074 0.019 1.000 0.000
0.500 0.637 0.041 3.707 0.126 0.119 0.078 1.000 0.000
0.550 0.282 0.019 3.942 0.108 0.094 0.050 0.999 0.000
0.600 0.088 -0.054 -31.442 0.048 0.022 -0.010 0.914 41.266
0.650 0.033 0.052 57.321 0.012 0.026 0.006 0.072 93.666
0.700 0.024 0.036 56.015 0.013 0.022 0.004 -0.000 6.666
0.750 0.012 0.020 57.579 0.002 0.003 0.000 0.029 3.800
0.000 1.026 0.004 0.256 0.031 0.028 -0.001 1.000 0.000
'0.050 1.016 0.005 0.337 0.031 0.027 -0.001 0.999 0.066
-0.100 1.010 0.004 0.250 0.031 0.026 -0.001 1.000 0.000
'0.150 1.002 0.006 0.379 0.033 0.027 -0.002 1.000 0.000
'0.200 0.989 0.009 0.538 0.030 0.025 '0.001 1.000 0.000
-0.250 0.975 0.011 0.647 0.030 0.025 -0.001 1.000 0.000
-00300 0.979 00009 00527 00031 0.025 “00001 1.000 00000
’00350 00970 0.008 0.504 00036 00026 “0.000 1.000 00000
“0.400 0.963 0.009 0.591 0.052 0.030 0.000 0.999 0.000
“0.450 0.904 -0.008 -0.517 0.096 0.075 -0.036 1.000 0.000
”00500 0.567 "0.032 -30295 00129 00316 -00072 1.000 00000
“0.550 00238 '00021 -50226 00102 00075 -00026 0.999 0.133
‘00600 00102 “0000‘ “20702 0.050 00020 ”0.002 0.857 920933
'06650 0006‘ '00035 “280575 00028 00018 ’0000‘ 0.159 106.800
-0.700 0.032 -0.016 ~26.815 0.020 0.013 -0.003 -0.002 4.400
“00750 0.021 -0.008 -220‘60 00000 00000 0.000 ’00002 30000

TABLE D-Z. Continued

54

x/d Au/d = A /d = xx/d = x /d =
1.500 0.140 0.093 0.085 03065
Uc(fps) =86.983 T = 15.000 (averaging time) Condition: Vortical
! I — '2

y/d U/UC v/Uc e u /Uc v /Uc uv/Uc y C/T
'1.000 0.023 -0.009 ~22.368 0.011 0.006 -0.001 -0.001 3.133
'0.933 0.031 -0.014 ~24.227 0.024 0.008 -0.004 0.050 4.600
'0.866 0.049 -0.065 -53.242 0.015 0.041 -0.051 0.007 9.600
”00800 00069 “00084 -500489 00024 00043 ’00052 00078 #50000
-0.733 0.117 -0.094 -39.043 0.069 0.042 -0.056 0.478 117.400
'0.666 0.227 -0.043 -10.900 0.119 0.034 -0.037 0.920 42.666
-00600 00357 -0003‘ -50483 001‘2 00083 ’00050 00998 10533
'0.533 0.518 -0.027 -3.059 0.144 0.115 -0.064 1.000 0.000
-O.466 0.683 -0.017 -1.464 0.139 0.119 -0.068 1.000 0.000
'00‘00 0083‘ “00003 “00224 00120 00104 ’00057 10000 00000
'0.333 0.936 0.003 0.217 0.084 0.071 -0.025 0.999 0.000
-0.266 0.967 0.013 0.776 0.058 0.042 -0.004 1.000 0.000
-0.200 0.995 0.009 0.536 0.044 0.032 '0.002 0.999 0.066
“00133 10002 00011 00666 00037 00028 “00001 10000 00000
'0.066 1.016 0.010 0.578 0.035 0.027 -0.001 0.999 0.066
'0.000 1.029 0.008 0.472 0.032 0.028 -0.000 0.999 0.000
0.066 1.023 0.005 0.305 0.035 0.030 0.000 0.999 0.066
0.133 1.022 0.007 0.416 0.037 0.033 0.000 0.999 0.066
0.199 1.015 0.009 0.549 0.044 0.038 0.001 1.000 0.000
0.266 0.998 0.009 0.540 0.051 0.049 0.002 0.999 0.066
0.333 0.968 0.013 0.772 0.068 0.067 0.010 0.999 0.000
0.400 0.910 0.019 1.237 0.101 0.090 0.039 1.000 0.000
0.466 0.761 0.032 2.429 0.135 0.109 0.070 1.000 0.000
0.533 0.584 0.043 4.250 0.144 0.117 0.084 1.000 0.000
0.600 0.421 0.044 5.999 0.138 0.111 0.078 0.999 0.066
0.666 0.267 0.027 5.911 0.126 0.071 0.051 0.969 22.000
0.733 0.182 0.017 5.486 0.108 0.036 0.026 0.718 99.066
0.800 0.124 0.014 6.796 0.093 0.066 0.018 0.228 77.066
0.866 0.091 0.006 4.097 0.073 0.062 0.005 0.034 15.000
0.933 0.041 0.003 4.696 0.040 0.025 0.000 0.070 3.933
1 0000 00°23 00002 60916 000“ 00000 -00000 00006 “0533

TABLE D-Z Continued

55

x/d Au/d = A /d = A /d = 1. /d =
3.000 0.140 0.303 0.085 02065
Uc(fpa) =86 .400 T = 15,000 (averaging time) Condition: Vortical

y/d tJ/Uc v/Uc e u'/Uc w/uc uv/Ucz y C/T
10250 00022 00028 520095 00007 00011 00006 “00000 40200
1.166 0.031 0.043 54.312 0.010 0.022 0.014 0.002 5.733
1.083 0.061 0.085 54.254 0.045 0.036 0.049 0.052 21.733
1.000 0.123 0.060 25.958 0.071 0.063 0.070 0.211 57.400
0.916 0.178 0.035 11.333 0.109 0.075 0.046 0.504 82.866
0.833 0.252 0.029 6.680 0.126 0.038 0.048 0.881 44.866
0.750 0.334 0.036 6.230 0.135 0.076 0.065 0.982 9.266
0.666 0.432 0.046 6.154 0.147 0.094 0.081 0.998 0.733
0.583 0.539 0.050 5.399 0.147 0.110 0.080 1.000 0.000
0.500 0.653 0.044 3.925 0.151 0.110 0.078 1.000 0.000
0.416 0.777 0.037 2.792 0.142 0.104 0.064 1.000 0.000
0.333 0.891 0.027 1.736 0.120 0.090 0.047 1.000 0.000
0.250 0.967 0.017 1.063 0.088 0.074 0.028 1.000 0.000
0.166 1.006 0.015 0.854 0.059 0.057 0.010 1.000 0.000
0.083 1.022 0.014 0.799 0.048 0.046 0.003 0.999 0.133
0.000 1.022 0.008 0.495 0.045 0.041 -0.000 0.999 0.066
“00083 10011 00008 00693 00052 00043 “00004 00999 00133
“0.166 0.977 0.008 0.474 0.071 0.057 -0.013 0.999 0.000
“00249 00913 00005 00331 00101 00079 “00031 00999 00066
“00333 0082‘ “00002 “00153 00126 00099 “00051 10000 00000
“00416 00707 “00008 “0068‘ 00161 00107 “00057 10000 00000
-0.499 0.591 -0.011 -1.141 0.145 0.107 -0.059 1.000 0.000
-O.583 0.479 -0.012 '1.470 0.144 0.099 -0.054 0.999 0.066
-0.666 0.381 -0.014 -2.165 0.149 0.044 -0.042 0.996 2.533
“00750 00296 “00017 “30643 00131 00030 “00031 00958 100400
-0.833 0.213 -0.026 -7.167 ‘ 0.111 0.052 -0.026 0.763 70.800
-0.916 0.174 -0.021 -6.947 0.102 0.073 -0.023 0.492 81.066
“00999 00113 “00027 “130596 00073 00061 “00025 00513 310533
-1.083 0.092 -0.042 -24.762 0.057 ,0.054 -0.035 0.067 24.333
“10166 00071 “00031 “230667 00056 00052 “00027 00022 100933
-1.250 0.034 -0.011 -18.049 0.030 0.026 -0.006 0.000 4.000

TABLE D-Z Continued

56

x/d Au/d = Ay/d = xx/d .-.- xy/d =
4.500 0.140 0.093 0.085 0.065
Uc(fps) = 86.014 T = 15.000 (averaging time) Condition: Vortical
y/d U/Uc v/Uc e w/uc v'/Uc 537/ng y C/T
“1.500 0.046 -0.006 -8.483 0.044 0.032 -0.004 0.002 4.800
'1.400 0.086 -0.009 -6.035 0.069 0.068 -0.009 0.012 8.000
“10300 00101 “00004 “20583 00074 00076 “00000 00030 160333
“10200 00133 “00029 “120565 00082 00084 “00029 00147 380266
“10100 00161 “00026 “90254 00089 00080 “00025 00635 670200
'1.000 0.209 -0.026 -7.262 0.104 0.035 -0.022 0.652 73.666
'0.900 0.251 -0.021 -4.921 0.125 0.066 '0.028 0.865 40.466
-0.800 0.322 '0.013 -2.307 0.131 0.037 -0.031 0.973 11.600
-O.700 0.391 -0.009 -1.440 0.141 0.063 -0.040 0.996 2.266
’0.600 0.490 -0.012 ‘1.486 0.147 0.092 '0.055 0.999 0.266
“0.500 0.582 -0.007 -0.700 0.148 0.104 -0.061 1.000 0.000
“00400 00689 “00007 “00606 00150 00107 “00065 10000 00000
”0.300 0.800 '0.006 -O.482 0.142 0.104 -0.058 1.000 0.000
“00200 00901 “00003 “00216 00127 00095 “0006‘ 10000 00000
-0.100 0.974 -0.001 -0.066 0.104 0.083 -0.024 0.999 0.066
'0.000 1.009 0.001 0.106 0.086 0.076 0.000 0.999 0.000
0.099 1.001 0.009 0.555 0.094 0.077 0.019 0.999 0.000
0.199 0.948 0.011 0.710 0.121 0.087 0.041 1.000 0.000‘
0.299 0.868 0.024 1.611 0.140 0.098 0.054 1.000 0.000
0.399 0.768 0.029 2.221 0.155 0.105 0.070 1.000 0.000
0.499 0.664 0.043 3.736 0.157 0.109 0.078 1.000 0.000
0.599 0.558 0.043 4.489 0.155 0.108 0.083 0.999 0.266
0.699 0.458 0.039 4.976 0.158 0.083 0.082 0.997 1.400
0.800 0.365 0.030 4.711 0.144 0.080 0.067 0.980 10.466
0.900 0.298 0.021 4.020 0.133 0.032 0.050 0.938 22.866
0.999 0.242 0.020 4.877 0.121 0.050 0.035 0.797 53.800
1.100 0.191 0.022 6.567 0.105 0.059 0.026 0.529 70.533
1.200 0.154 0.032 11.740 0.093 0.079 0.033 0.273 57.266
1.300 0.118 0.052 23.773 0.072 - 0.073 0.058 0.095 28.333
1.399 0.063 0.047 36.938 0.043 0.044 0.044 0.011 8.133
1.500 0.036 0.037 46.071 0.020 0.008 0.019 0.002 5.200

TABLE D-Z Continued '

57

x/d Au/d = Ay/d = )‘x/d = Xy/d =
6.000 0.140 0.093 0.085 0.065
Uc(fps) .-.- 83 .088 T = 15.000 (averaging time) Condition: Vortical
u . -— -Z
y/d u/Uc v/Uc e u /Uc v /Uc uv/Uc y C/T

1.875 0.023 0.025 46.735 0.007 0.004 0.002 0.000 3.600
1.750 0.037 0.036 44.846 0.021 0.013 0.017 0.004 5.600
1.625 0.054 0.058 47.157 0.016 0.011 0.036 0.014 8.400
1.500 0.096 0.073 37.255 0.038 0.050 0.065 0.077 22.000
1.375 0.174 0.055 17.779., 0.098 0.083 0.072 0.244 50.466
1.250 0.218 0.033 8.718 0.113 0.076 0.040 0.502 65.733
1.125 0.260 0.024 5.326 0.129 0.057 0.038 0.701 63.800
1.000 0.320 0.026 4.788 0.129 0.073 0.054 0.915 29.333
0.875 0.409 0.033 4.656 0.147 0.088 0.076 0.988 6.200
0.750 0.497 0.041 4.725 0.161 0.099 0.090 0.998 0.800
0.625 0.595 0.042 4.110 0.163 0.114 0.093 0.999 0.000
0.500 0.698 0.043 3.597 0.171 0.117 0.093 0.999 0.066
0.375 0.812 0.036 2.589 0.169 0.114 0.080 1.000 0.000
0.250 0.918 0.028 1.760 0.164 0.111 0.061 1.000 0.000
0.125 0.988 0.016 0.931 0.152 0.110 0.035 1.000 0.000
0.000 1.009 0.008 0.506 0.143 0.109 -0.002 0.999 0.000
’00125 00956 0.007 0.425 00153 00116 -0004‘ 10000 00000
'00250 00862 “0.000 -00019 0.162 00119 “0.067 1.000 0.000
“0.375 0.740 -0.001 -0.123 0.168 0.117 -0.075 1.000 0.000
‘0.500 0.632 '0.003 -0.292 0.169 0.112 -0.074 1.000 0.000
“00625 00521 “00002 “00226 00168 00079 ”0.059 0.999 0.733
-0.750 0.428 -0.006 -0.805 0.156 0.067 -0.046 0.992 4.066
'0.875 0.349 -0.008 -1.365 0.150 0.045 -0.029 0.958 17.066
“1.000 00285 '06020 ”4.077 0.128 0.046 ”0.029 008‘2 ‘30666
-1.125 0.233 -0.028 -6.959 ' 0.112 0.056 -0.024 0.633 63.400
-1.250 0.200 -0.043 -12.291 0.106 0.079 -0.040 0.421 63.933
-10375 00131 “00038 “160118 00079 00065 ’00039 0.443 250‘66
-10500 00121 ‘00046 -2008‘9 00059 00060 -00038 00073 21.666
-1.625 0.074 -0.047 -32.525 0.038 ‘ 0.042 -0.041 0.017 8.733
-1.750 0.035 -0.021 ~31.219 0.027 0.011 -0.010 0.002 4.066
'1.875 0.026 -0.011 -23.973 0.008 0.006 -0.000 -0.001 3.133

x/d
8.000

Uc(fps) = 74.334

v/d

”20200
-20053
“10906
”10760
“10613
“10‘66
-10320
-10173
“1.026
-00880
”00733
-00586
-0.440
‘00293
‘00146
“00000
0.146
0.293
0.439
0.586
0.733
0.879
1.026
1.173
1.320
1.466
1.613
1.759
1.906
2.053
2.200

TABLE D-Z Continued

58

Au/d = A /d =
0.140 0. 093
T = 15.000 (averaging time)
V/Uc e w/uc w/uc
-0.014 ~24.012 0.010 0.006
-0.028 -26.564 0.052 0.038
-0.031 -18.603 0.083 0.075
.00057 “220726 00083 00075
-0.072 -21.284 0.104 0.088
-0.073 -18.987 0.103 0.081
-0.048 -10.217 0.131 0.077
-0.030 -5.351 0.142 0.054
’00019 -20950 00162 0004‘
.00011 “10382 00176 00029
-0.008 -0.894 0.180 0.092
-0000? -00636 00192 00102
’00003 ‘00294 00190 00130
-0.000 -0.045 0.191 0.136
0.002 0.177 0.185 0.137
0.010 0.579 0.183 0.137
0.021 1.248 0.188 0.134
0.027 1.719 0.194 0.134
0.036 2.604 0.198 0.132
0.044 3.634 0.188 0.130
0.041 3.986 0.196 0.108
0.037 4.167 0.176 0.108
0.033 4.507 0.163 0.076
0.031 5.009 0.155 0.039
0.031 5.841 0.140 0.061
0.033 7.255 0.122 0.042
0.061 16.660 0.115 0.087
0.070 23.333 0.089 0.090
0.064 26.878 0.070 . 0.066
0.055 54.119 0.004 0.036
0.042 57.600 0.014 0.017

Xx/a =

0.085

Condition:

-- -Z
uv/Uc

‘00000
-00028
“0.043
-0.068
”00091
”0.087
‘00051
“0.037
-00039
“06049
-0.068
-0.083
-0.090
“0.078
-0.043
0.002
0.044
0.082
0.108
0.116
0.124
0.109
0.089
0.065
0.049
0.037
0.080
0.080
0.058
0.030
0.011

x /d---
0% 65
Vortical
y ‘C/T
-0.001 3.000
0.005 5.466
0.021 10.133
0.097 16.933
0.161 35.266
0.302 52.466
0.565 59.666
0.767 49.600
0.897 31.933
0.975 10.666
0.995 2.266
0.999 0.200
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
0.999 0.000
0.997 1.866
0.991 5.133
0.956 16.000
0.847 41.066
0.696 59.733
0.521 62.666
0.257 40.600
0.106 28.466
0.084 15.000
0.002 5.466
0.000 4.333

x/d
10.000

”cu?” = 61.577

Y/d

2.500
2.333
2.166
2.000
1.833
1.666
1.500
1.333
1.166
1.000
0.833
0.666
0.500
0.333
0.166
0.000
-0.166
”00333
”00499
“00666
”00833
‘0.999
”10166
“10333
“10500
-10666
-1.833
”1.999
”20166
-2.333
“2.500

TABLE D-Z Continued

59

Ali/(1 - Ay/d =
0.140 0.093
T = 15.000 (averaging time)
V/Uc e u /Uc v /Uc
0.046 57.374 0.007 0.027
0.064 55.452 0.008 0.045
0.111 48.043 0.054 0.059
0.136 47.766 0.057 0.047
0.072 18.481 0.122 0.104
0.061 11.550 0.150 0.087
0.049 7.887 0.163 0.076
0.043 6.178 0.167 0.016
0.037 4.470 0.179 0.068
0.047 4.795 0.189 0.107
0.046 4.101 0.195 0.130
0.048 3.687 0.199 0.131
0.049 3.326 0.204 0.143
0.046 2.841 0.212 0.134
0.029 1.710 0.200 0.145
0.019 1.123 0.196 0.146
0.008 0.487 0.196 0.147
0.001 0.121 0.203 0.145
'00005 -00429 0.207 0.125
-00002 -00231 00205 00106
-0.008 -0.825 0.198 0.069
“00013 “10‘90 00188 0.036
-0.020 -2.735 0.184 0.077
-00039 ‘60089 0.171 00098
'000‘5 “80269 . 00195 00063
-00065 -130281 00135 00090
“00066 ’160323 00106 0.117
’00030 -90206 00135 00132
‘00018 ’70863 00112 00104
“0.026 “190201 00063 0.048
-0.018 -18.755 0.047 0.036

Xx/d =
0.085

Condition:

«—— -2
uv/UC

0.010
0.042
0.152
0.141
0.088
0.087
0.073
0.082
0.101
0.125
0.134
0.126
0.116
0.093
0.055
0.001
-00039
-0007?

“00089.

-0.087
”00068
‘00052
“00043
“00055
”00033
-0.073
”00096
’000“
”0.028
'00029
-0.012

Y

0.003
0.006
0.023
0.079
0.115
0.421
0.611
0.775
0.936
0.982
0.996
0.999
0.999
1.000
1.000
1.000
1.000
0.999
0.999
0.997
0.990
0.957
0.860
0.689
0.493
0.316
0.161
0.051
0.028
0.004
0.000

X d==
Y/

0.065

Vortical

C/T

4.333
5.866
11.133
23.200
27.933
61.866
63.200
50.533
18.866
8.600
2.066
0.333
0.000
0.000
0.000
0.000
0.000
0.000
0.333
1.333

' 4.333

15.400
38.000
57.666
64.600
54.000
36.000
17.533
11.333

5.333

3.733

x/d
0.500

Uc(fps) =79. 485

v/d

0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750

0.000
“0.050
”00100
"0.150
“00200
-00250
-00300
-00350
'0.400
'0.450
“00500
”00550
”00600
-00650
-00700
“00750

TABLE D-3 DATA LISTING

A/d:

0.34.

.Au/d:=
0.110
T = 30.000
v/Uc a
-0.004 -0.279
’00004 ’00254
-0.006 -0.353
“00010 ’00591
-0.010 -0.564
-0.009 -0.513
”00010 “00594
-0.012 -0.677
-0.010 -0.590
-0.007 -0.438
0.018 1.341
0.037 5.622
‘00001 “00821
“0.001 '0.948
0.001 2.094
’00002 ”60231
“00001 ”00103
-0.000 -0.041
-0.001 -0.056
-0.000 -0.050
-0.000 -0.033
-00001 -00078
-0.000 -0.038
-00000 "0.057
“0.004 “0.238
-0.028 -1.930
“00037 -‘0591
-0.019 -7.018
-0.017--11.277
“0.030 “23.879
-0.010 -26.335
-0.010 -26.335

tfl/UC

0.032
0.030
0.030
0.028
0.029
0.030
0.030
0.030
0.032
0.048
0.129
0.127
0.068
0.023
0.025
0.000

0.029
0.030
0.031
0.031
0.030
0.030
0.032
0.037
0.062
0.109
0.130
0.082
0.035
0.022
0.000
0.000

60

(averaging time)

\fl/UE

0.027
0.026
0.027
0.026
0.026
0.026
0.027
0.030
0.040
0.073
0.119
0.123
0.024
0.015
0.011
0.000

0.026
0.027
0.026
0.026
0.025
0.025
0.025
0.026
0.032
0.094

_ 0.115

0.035
0.014
0.014
0.000
0.000

Xx/d=:

0.086

Condition:

-— -Z
uv/UE

“0.003
-0.002
-00001
0.000
0.000
0.000
0.001
0.001
0.001
0.009
0.086
0.070
0.007
0.000
0.001
0.000

-00001
‘00002
-0.002
‘00002
-00001
“00001
‘00000
’00000
-00001
“0.054
-00072
-00013
”0.002
“0.002

0.000

0.000

X /d:=

03071
Vortical

Y C/T

0.999 0.433
0.999 0.433
0.999 0.566
0.999 0.533
0.998 0.866
0.999 0.733
0.999 0.700
0.999 0.833
0.999 0.800
0.999 0.033
1.000 0.000
1.000 0.000
0.925 50.733
0.270 161.400
0.002 5.133
0.000 3.000
0.999 0.200
0.999 0.800
0.999 0.466
0.999 0.333
0.999 0.733
0.998 1.066
0.999 0.666
0.999 0.600
0.999 0.466
1.000 0.000
1.000 0.000
0.975 19.866
0.391 188.466
0.041 13.066
0.000 3.000
0.000 3.000

TA B LE D- 3 Continued

x/d Au/d - Ag/d .. xx/d - xy/d =
1.500 0.110 0. 46 0.086 0.071
Uc(fpa) “79.485 '1‘ - 15.000 (averaging time) Condition. Vortical
y/d U/U V/U e u'/U v'/U {RF/U“? y C/T
C C C C C

-1.200 0.021 -0.010 -26.335 0.000 0.000 0.000 0.000 3.000
-10149 00022 ”0.010 “25.629 0.006 00001 -0.000 0.058 2.866
-1.100 00024 “00011 -250201 00007 0.002 “00000 0.105 30200
”1.050 0.026 -0.011 '24.149 0.011 0.003 -0.000 0.104 3.333
'0.999 00021 '00010 “260335 00000 0.000 0.000 00000 30000
'0.949 0.021 -0.010 -26.335 0.000 0.000 0.000 0.000 3.000
-00900 0003‘ -00015 -2‘0161 00045 0.032 “0.012 00000 3.666
-0.849 0.082 -0.038 '25.090 0.070 0.052 '0.035 0.006 6.600
‘0.800 0.129 -0.021 -9.545 0.093 0.091 '0.020 0.031 19.666
-0.750 0.151 -0.047 -17.500 0.093 0.076 -0.047 0.181 73.933
‘0.699 0.174 -0.043 ~13.854 0.105 0.071 -0.045 0.478 122.533
“0.650 0.231 -0.023 -5.710 0.124 0.034 -0.032 0.827 80.400
-00600 0.316 ”0.023 -9025? 00142 00071 “00051 0.982 11.666
“0.550 0.432 -0.031 '4.137 0.145 0.112 *0.071 0.999 0.533
'0.500 0.551 -0.034 -3.628 0.147 0.124 -0.082 1.000 0.000
'0.450 0.687 -0.031 -2.623 0.143 0.123 -0.080 1.000 0.000
-0.400 00814 -00022 ”10600 00127 00114 “0.064 00999 00066
'0.350 0.904 -0.011 ~0.716 0.102 0.090 -0.041 0.999 0.200
-00300 0.947 “00002 “00132 0.079 0.064 ”00018 00998 10200
-0.250 0.967 0.001 0.098 0.062 0.044 -0.005 0.999 0.666
-00200 00985 “00000 “00005 0.048 00033 “0.001 00998 10000
“0.150 0.989 ~0.002 '0.167 0.041 0.029 -0.002 0.998 1.066
“0.100 1.002 -0.005 '0.323 0.037 0.028 -0.003 0.999 0.800
'0.050 1.004 -0.003 -0.187 0.034 0.026 -0.002 0.999 0.800
'0.000 1.014 -0.004 -0.281 0.032 0.026 *0.002 0.998 1.266
00049 1.023 "00003 "00202 0.031 0.027 ’00001 0.998 10000
0.099 1.032 -0.006 -0.361 0.031 0.028 -0.001 0.998 1.133
0.149 1.035 -0.005 -0.310 0.030 0.030 ”0.000 0.998 1.200
0.199 1.039 -0.004 '0.225 0.032 0.033 0.000 0.998 1.133
0.249 1.036 *0.007 -0.416 0.035 0.040 0.000 0.999 0.666
00299 10028 -00009 "00543 0.040 00052 0.003 0.998 10133
00349 10012 .00011 ‘00638 00059 00072 0.015 00999 0.400
0.399 0.974 -0.008 -0.502 0.095 0.092 0.043 0.999 0.066
0.449 0.877 0.000 0.055 0.130 0.110 0.068 0.999 0.066
0.499 0.748 0.011 0.853 0.151 0.121 0.080 1.000 0.000
0.549 0.602 0.023 2.229 0.157 0.121 0.080 1.000 0.000
0.599 0.459 0.026 3.326 0.154 0.116 0.077 0.999 0.266
0.649 0.328 00023 4.055 00142 00093 00061 0.987 9.000‘
0.699 0.229 0.014 3.642 0.135 0.047 0.037 0.829 81.466
0.749 0.176 0.010 3.537 0.106 0.055 0.021 0.480 128.000
0.799 0.140 0.001 0.646 0.099 0.086 0.001 0.214 63.200
0.849 0.124 .0.000 ~0.075 0.080 0.078 -0.001 0.030 19.733
0.899 0.071 '0.002 ‘2.034 0.061 0.054 -0.001 0.005 6.266
0.949 0.030 .0.003 -7.234 0.023 0.019 '0.000 0.145 2.866
0.999 0.024 -0.002 '6.843 0.009 0.004 0.000 0.000 3.066
1.050 0.023 -0.003 -7.599 0.000 0.000 0.000 0.000 3.000
1.100 0.025 '0.003 -7.283 0.005 0.000 -0.000 0.063 4.400
10149 00023 ”00003 ”7.599 00000 0.000 0.000 00000 30000
1.199 0.024 -0.003 -7.727 0.003 0.000 ’0.000 0.028 3.400

TABLE D-3 Continued

62

x/d A/d: A/d: 1/d: x d:
3.000 03110 0.826 0.0‘86 0.1541

Uc(fps) £19,943 T = 15,000 (averaging time) Condition: Vortical
y/d u/Uc v/UC e w/uc w/uc uv/UCZ y C/T
1.275 0.030 0.007 14.020 0.026 0.002 0.001 0.000 3.133
1.200 0.073 0.021 15.900 0.060 0.055 0.019 0.006 6.200
1.125 0.101 0.048 25.512 0.059 0.064 0.036 0.029 14.066
1.050 0.108 0.071 33.350 0.051 0.067 0.062 0.074 29.200
0.975 0.169 0.047 15.584 0.092 0.074 0.052 0.256 68.400
0.900 0.186 0.025 7.675 0.106 0.037 0.035 0.757 50.066
0.825 0.257 0.025 5.687 0.117 0.059 0.041 0.866 49.200
0.750 0.334 0.025 4.437 0.139 0.068 0.056 0.972 13.933
0.675 0.427 0.022 3.050 0.147 0.093 0.065 0.997 1.600
0.600 0.534 0.024 2.642 0.156 0.109 0.075 1.000 0.000
0.525 0.644 0.020 1.790 0.155 0.109 0.070 1.000 0.000
0.450 0.771 0.013 0.980 0.148 0.108 0.068 1.000 0.000
0.375 0.878 0.006 0.433 0.131 0.098 0.057 1.000 0.000
0.300 0.970 0.006 0.401 0.098 0.084 0.035 0.999 0.066
00225 10001 ”00000 ”00016 00067 00066 00015 00999 00600
0.150 1.023 0.002 0.117 0.047 0.051 0.003 0.998 1.200
0.075 1.020 0.001 0.087 0.042 0.043 -0.001 0.998 1.400
0.000 1.011 0.001 0.110 0.044 0.040 -0.002 0.997 2.066
'0.074 0.997 0.001 0.112 0.051 0.044 '0.005 0.998 1.600
”00169 00967 00006 00359 00070 00057 ”00014 00998 10000
”00226 00921 00000 00006 00096 00076 ”00028 00999 00333
”00299 00043 ”00005 ”00607 00123 00096 ”00048 10000 00000
-0.374 0.741 -0.013 '1.057 0.141 0.108 -0.063 1.000 0.000
”00669 00643 ”00019 ”10717 00141 00112 ”00073 10000 00000
”00525 00539 ”00019 ”20104 00156 00096 ”00077 10000 00000
”00599 00440 ”00015 ”20051 00146 00100 ”00065 00998 10266
”00675 00343 ”00016 ”20765 00142 00057 ”00050 00973 140533
”00749 00267 ”00016 ”30421 00132 00037 ”00032 00860 510666
-0.824 0.216 -0.023 -6.114 0.119 0.075 -0.032 0.694 76.800
'0.899 0.173 -0.035 -11.680 0.104 0.087 -0.048 0.489 68.000
-0.974 0.160 -0.027 -9.883 0.098 0.097 -0.031 0.165 50.800
“1.050 0.145 -0.034 -13.429 0.087 0.098 -0.041 0.059 24.200
'1.125 0.080 -0.018 ~13.005 0.067 0.069 "0.021 0.007 6.400
”10199 00049 ”00011 ”120550 00066 00036 ”00008 00071 60000
“1.274 0.027 -0.009 -18.847 0.029 0.022 -0.003 0.000 3.200

TABLE D-3 Continued

63

x/d A/d: A/d-_- x/d= x/a:

«.500 o.“110 0.626 0.086 0.1671

Uc(fpg) 519.715 T = 15.000 (averaging time) Condition: Vortical

y/d u/Uc v/Uc e u'/Uc v'/Uc uv/Ucz y C/‘I‘
”10500 00041 ”00011 ”150483 00044 00035 ”00006 00033 40400
”10400 00071 ”00014 ”110657 00069 00058 ”00018 00007 50333
-1.300 0.087 -0.077 -41.598 0.037 0.005 -0.035 0.021 10.333
'1.200 0.137 -0.080 '30.292 0.050 0.056 -0.072 0.124 29.400
”10100 00171 ”00056 ”180338 00088 00072 ”00058 00211 510666
'1.000 0.217 -0.039 ~10.386 0.113 0.088 -0.043 0.492 81.000
”00900 00258 ”00036 ”80044 00135 00081 ”00052 00742 670200
-0.800 0.302 -0.015 -2.997 0.139 0.043 -0.036 0.897 39.600
-0.700 0.354 -0.047 -7.625 0.142 0.055 -0.062 0.979 10.866
'0.600 0.442 -0.044 -5.790 0.141 0.098 -0.067 0.997 1.866
”00500 00548 ”00049 ”50162 00151 00095 ”00081 00999 00200
-O.400 0.647 -0.053 -4.718 0.147 0.109 -0.080 1.000 0.000
”00300 00759 ”00052 ”30955 00138 00104 ”00065 10000 00000
”00200 00851 ”00048 ”30245 00125 00095 ”00050 00999 00066
-0.100 0.932 -0.047 -2.940 0.093 0.079 -0.025 0.999 0.733
'0.000 0.973 -0.044 -2.638 0.074 0.070 -0.008 0.998 1.600
0.099 0.980 -0.040 -2.368 0.075 0.071 0.006 0.998 1.000
0.199 0.945 -0.037 -2.298 0.101 0.082 0.026 0.999 0.400
0.299 0.873 -0.030 -1.992 0.129 0.093 0.044 1.000 0.000
00399 00760 ”00021 ”10634 00147 00101 00053 10000 00000
0.499 0.660 ~0.009 -0.866 0.154 0.105 0.060 0.999 0.066
0.599 0.549 -0.005 -0.578 0.151 0.102 0.062 0.999 0.133
0.699 0.445 -0.004 -0.636 0.148 0.092 0.058 0.998 1.000
0.800 0.354 *0.004 -0.755 0.139 0.079 0.049 0.977 12.333
00900 00286 ”00006 ”10258 00124 00051 00033 00911 330933
00999 00234 ”00000 ”00020 00116 00050 00022 00749 680066
1.100 0.179 -0.004 -1.592 0.101 0.053 0.010 0.636 54.333
1.200 0.172 0.005 1.674 0.093 0.068 0.011 0.232 60.400
1.300 0.148 0.002 1.050 0.094 0.096 0.002 0.074 26.200
1.399 0.108 0.026 13.824 0.072 0.079 0.025 0.020 10.533
1.500 0.062 0.012 11.039 0.070 0.060 0.018 0.005 5.333

TABLE D-3 Continued

64

3‘/d Au/d = Ay/d = xx/d = x /d =
0.000 0.110 0.040 0.086 0307 1
Uc(fps) =77.235 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc 'V/Uc 6 u'/UC v'/UC uv/UC2 y C/‘I‘
1.700 0.063 0.031 26.120 0.050 0.040 0.022 0.007 5.733
1.600 0.102 0.054 28.095 0.064 0.068 0.055 0.014 8.000
1.500 0.121 0.072 31.047 0.049 0.059 0.073 0.038 16.400
1.400 0.169 0.041 13.879 0.106 0.100 0.084 0.133 37.600
1.300 0.200 0.020 5.785 0.099 0.077 0.025 0.245 54.200
1.200 0.238 0.009 2.236 0.111 0.031 0.025 0.535 76.466
1.100 0.259 -0.001 "0.350 0.120 0.031 0.025 0.744 60.733
1.000 0.305 0.006 1.170 0.129 0.060 0.044 0.874 42.000
0.900 0.367 0.004 0.635 0.149 0.051 0.051 0.966 15.266
0.800 0.429 -0.001 -0.183 0.152 0.075 0.056 0.992 4.600
0.700 0.508 0.004 0.454 0.152 0.102 0.067 0.998 1.266
0.600 0.596 0.003 0.337 0.159 0.107 0.069 0.999 0.266
0.500 0.681 -0.001 -0.165 0.160 0.109 0.068 0.999 0.066
0.400 0.771 -0.007 -0.589 0.160 0.109 0.062 1.000 0.000
0.300 0.850 -0.017 ~1.191 0.153 0.106 0.054 1.000 0.000
0.200 0.924 -0.023 -l.468 0.141 0.105 0.037 1.000 0.000
0.100 0.955 -0.030 -l.843 0.128 0.102 0.013 1.000 0.000
0.000 0.952 -0.034 -2.066 0.130 0.105 -0.017 0.999 0.066
-0.099 0.913 -0.041 “2.571 0.137 0.107 -0.042 0.999 0.066
-0.199 0.838 -0.040 -2.790 0.152 0.113 -0.069 1.000 0.000
-0.299 0.757 -0.044 -3.382 0.159 0.116 -0.085 1.000 0.000
“0.399 0.676 -0.045 -3.808 0.157 0.115 -0.089 1.000 0.000
-O.499 0.566 ~0.038 -3.925 0.164 0.098 -0.091 0.999 0.266
“0.599 0.499 -0.040 -4.633 0.152 0.105 -0.078 0.997 2.000
-0.699 0.427 -0.042 -5.622 0.171 0.046 -0.081 0.989 6.000
”00799 00366 ”00045 ”70003 00151 00021 ”00070 00967 140400
”00899 00306 ”00044 ”80203 00147 00082 ”00060 00888 400133
”00999 00256 ”00051 ”110369 00131 00079 ”00058 00762 610133
”10099 00227 ”00065 ”150966 00124 00084 ”00068 00541 730533
'1.199 0.202 -0.078 ~21.267 0.110 0.086 -0.092 0.362 68.200
”10299 00168 ”00070 ”220554 00109 00109 ”00097 00167 440133
“1.399 0.141 -0.082 -30.221 0.087 0.090 '0.105 0.073 23.800
-1.499 0.090 -0.062 -34.739 0.048 0.031 -0.059 0.024 11.066
”10599 00074 ”00069 ”430032 00048 00055 ”00094 00046 70200
”10699 00050 ”00038 ”360697 00035 00021 ”00034 00003 40866

TABLE D-3 Continued

65

x/d Au/d = A /d = X /d = X /d =
8.000 0.110 0.3%. 0.386 02671
Uc(fps) '70.520 T - 15.000 (averagmg tune) Condztlon. Vortmal

y/d U/Uc V/Uc e w/uc v'/Uc uv/UCZ Y c/T
-Z.100 0.038 -0.031 “39.530 0.020 0.011 -0.012 0.003 4.600
“1.950 0.089 -0.062 -34.831 0.040 0.036 -0.065 0.010 6.733
“1.800 0.109 -0.079 -36.020 0.049 0.050 -0.095 0.022 11.333
“1.650 0.197 “00040 -110632 00106 00125 “0.071 0007‘ 24.333
'1.500 0.239 -0.058 -13.733 0.131 0.122 -0.100 0.230 41.466
“1.350 00282 “00019 -30948 00154 00137 ’00032 0.414 63.600
-1.200 0.332 '0.024 -4.141 0.171 0.115 -0.052 0.612 69.533
-10050 00389 “00009 “10406 00161 00016 “00042 0.814 54.133
“0.900 0.460 0.013 1.679 0.185 0.012 '0.049 0.955 17.733
'0.750 0.553 0.015 1.564 0.202 0.025 -0.067 0.987 6.666
-00600 00669 00018 10559 00202 00088 “00085 0.998 10000
“00450 0.774 0.021 10575 00187 0.131 ’00092 00999 0.333
“0.150 0.988 0.033 1.946 0.182 0.138 -0.040 1.000 0.000
'00000 1.026 0.045 20552 00180 00139 0.009 1.000 0.000
0.149 1.014 0.057 3.270 0.184 0.138 0.055 1.000 0.000
0.299 0.937 0.066 4.038 0.194 0.136 0.092 1.000 0.000
0.449 0.837 0.074 5.077 0.196 0.135 0.115 0.999 0.066
0.599 0.709 0.079 6.352 0.195 0.123 0.125 0.999 0.533
0.749 0.592 0.072 6.985 0.189 0.124 0.127 0.992 4.466
0.899 0.526 0.072 7.823 0.179 0.105 0.116 0.982 9.800
1.049 0.425 0.068 9.155 0.158 0.107 0.097 0.964 14.266
1.199 0.358 0.067 10.673 0.143 0.049 0.080 0.792 55.000
1.349 0.297 0.076 14.486 0.136 0.084 0.094 0.503 72.066
1.499 0.255 0.097 20.855 0.121 0.094 0.129 0.266 56.533
1.649 0.158 0.121 37.631 0.066 0.085 0.165 0.083 25.600
1.799 0.094 0.132 54.394 0.051 0.054 0.096 0.029 11.666
1.949 0.058 0.091 57.519 0.052 0.065 0.065 0.037 8.333
2.100 0.022 0.035 57.843 0.013 0.019 0.004 0.001 3.600

x/d

10.000

Uc(fps) =59.158

y/d

2.500
2.333
2.166
2.000
1.833
1.666
1.500
1.333
1.166
1.000
0.833
0.666
0.500
0.333
0.166
0.000
-00166
-00333
'00499
“00666
-00833
“00999
’10166
“1.333
”1.500
“10666
'1.833
“1.999
-20166
-2.333
“20500

T=15

v/Uc
0.035
0.041
0.071
0.168
0.126
0.054
0.041
0.025
0.019
0.022
0.017
0.020
0.017
0.009
-0.004
-00013
-00018
-0.032
“00029
’00032
-0.039
‘00049
-0.059
-00070
‘00090
'00115
-0.112
'00088
~0.086
“00026
-0.025

TAB LE D- 3 Continued

A/d:

u
0.110
.000

6’

55.118
58.983
64.717
65.222
30.176
10.188
6.782
3.786
2.492
2.369
1.658
1.604
1.232
0.572
-00254
”00782
-10172
"20162
”20193
“2.885
’40003
“50767
’80203
-10.980
-16.327
-230523
‘260895
-280033
-370509
-23.539
-2505?“

.A /H==

0.826

ufl/Ue

0.019
0.019
0.057
0.128
0.097
0.145
0.155
0.157
0.171
0.181
0.189
0.201
0.197
0.195
0.193
0.188
0.192
0.200
0.204
0.218
0.198
0.203
0.168
0.175

'0.143

0.133
0.089
0.078
0.016
0.058
0.061

66

(averaging time)

.3342 =

Condition:

— -2
v'/Uc uv/Uc

0.027
0.023
0.066
0.126
0.099
0.113
0.089
0.060
0.093
0.120
0.123
0.129
0.138
0.140
0.141
0.146
0.146
0.145
0.128
0.005
0.084
0.081
0.008
0.118
0.117
0.125
0.099
0.078

.0.024

0.048
0.038

0.008
0.007
0.039
0.127
0.198
0.074
0.075
0.067
0.084
0.106
0.111
0.114
0.091
0.061
0.026
“0.033
-00078
’00100
”00116
“00098
’0009‘
"00096
”0.073
-0.099
-0011?
“0.195
-0.145
”00101
“00144
-0.025
-0.025

1 d1:
0 .641
Vortical
Y C/T
0.000 3.266
0.001 3.666
0.007 5.933
0.028 12.533
0.080 25.533
0.239 53.533
0.515 71.800
0.699 66.133
0.868 42.200
0.954 18.466
0.986 7.733
0.996 2.066
0.999 0.400
0.999 0.066
0.999 0.066
0.999 0.133
0.999 0.200
0.999 0.200
0.998 0.733
0.993 3.800
0.968 13.933
0.910 31.000
0.773 59.333
0.585 69.933
0.385 70.200
0.207 49.066
0.096 31.333
0.038 15.800
0.018 9.133
0.003 4.666
0.001 3.800

TABLE D-4 DATA LISTING

67

x/d Au/d - Ay/d - xx/d .. xy/d -
0.500 0.100 0.052 0.058 0.050
Uc(fps) =97. 206 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc V/Uc e u'/Uc w/uc EV/ng y C/T
0.000 1.077 0.007 0.401 0.023 0.022 -0.000 0.997 2.133
0.050 1.089 0.003 0.203 0.022 0.021 -0.000 0.997 2.333
0.100 1.087 00011 00619 0.021 00021 "0.000 0.997 2.133
0.150 1.089 0.015 0.820 0.021 0.021 0.000 0.996 3.133
0.200 1.083 0.013 0.720 0.021 0.021 0.000 0.995 3.400
0.250 1.072 0.014 0.758 0.021 0.021 0.000 0.995 3.533
0.300 1.074 0.022 1.221 0.021 0.022 0.001 0.996 2.600
0.350 1.067 0.017 0.930 0.022 0.025 0.001 0.998 1.733
0.400 1.075 0.023 1.233 0.022 0.036 0.000 0.999 0.266
0.450 1.034 0.023 1.326 0.058 0.067 0.019 1.000 0.000
0.500 0.538 0.044 4.770 0.104 0.110 0.053 1.000 0.000
0.550 0.129 0.030 13.353 0.051 0.050 0.009 0.997 1.866
0.600 0.068 0.021 17.346 0.014 0.011 0.000 0.249 122.666
0.650 0.032 0.008 15.285 0.016 0.008 0.001 0.003 5.733
0.700 0.019 0.003 10.934 0.000 0.000 0.000 0.000 3.000
0.750 0.019 0.003 10.904 0.000 0.000 0.000 0.000 3.000
00000 1.050 00017 0.935 0.022 00021 -00001 0.998 1.666
~0.050 1.048 0.015 0.835 0.022 0.021 -0.000 0.998 0.933
-0.100 1.044 0.014 0.796 0.022 0.021 -0.000 0.998 1.400
-0.150 1.042 0.019 1.073 0.021 0.021 -0.000 0.997 1.733
“0.200 1.040 00016 00925 00021 00021 -0.000 0.997 2.133
-0.250 1.039 0.022 1.222 0.019 0.020 0.000 0.996 2.666
“00300 10052 00021 1.170 00019 00020 0.000 0.991 2.533
-0.350 1.047 0.021 1.159 0.020 0.020 0.000 0.996 2.800
-0.400 1.054 0.018 0.998 0.023 0.020 0.000 0.997 2.533
“00450 10042 0.007 0.405 000‘0 0.030 ”00001 00999 00266
-0.500 0.642 -0.034 -3.096 0.096 -0.098 -0.043 1.000 0.000
-0.550 0.192 -0.021 -6.371 0.066 0.061 '0.013 0.999 0.066
-0.600 0.078 -0.008 -6.494 0.018 0.005 -0.000 0.176 116.866
-0.650 0.019 -0.003 -10.744 0.000 0.000 0.000 0.000 3.000
“00700 00019 “00003 “100744 00000 00000 00000 0.000 3.000
-0.750 0.019 -0.003 -10.744 0.000 0.000 0.000 0.000 3.000

TABLE D-4 Continued

68

x/d Au/d .. Ay/d .. xx/d .. xy/d .-.
1.500 0.100 0.052 0.058 0.050
Uc(fps) =97.206 T = 15.000 (averaging time) Condition: Vortical
: -— -Z

y/d U/Uc v/uc e 11 /UC v'/Uc 11v/Uc y C/T
-1.000 0.020 -0.003 -10.197 '0.006 0.000 0.000 0.002 3.733
-0.933 0.019 -0.003 -10.744 0.000 0.000 0.000 0.000 3.000
-0.866 0.019 -0.003 -10.744 0.000 0.000 0.000 0.000 3.000
-00800 00024 “00004 -100357 00027 0.019 ’00000 00000 3.200
-0.733 0.094 -0.028 -16.660 0.051 0.040 -0.009 0.035 28.333
-0.666 0.125 ~0.031 -14.296 0.062 0.016 ~0.010 0.603 148.000
‘0.600 00250 “0001‘ ’303‘8 0010‘ 00069 ”0.026 0.997 10733
“00533 00‘93 -00021 “20511 00125 0.102 -00056 1.000 0.000
-0.466 0.786 -0.008 -0.645 0.119 0.103 -0.057 1.000 0.000
-0.400 1.014 0.011 0.646 0.076 0.063 -0.019 0.999 0.133
“00333 10044 0.019 1.046 0.047 0.027 00001 00995 20533
-0.266 1.032 0.021 1.184 0.031 0.021 0.000 0.994 4.466
-0.200 1.030 0.022 1.253 0.023 0.019 0.000 0.994 4.733
-0.133 1.026 0.019 1.102 0.021 0.019 0.000 0.995 3.466
-0.066 1.028 0.021 1.188 0.020 0.019 0.000 0.996 2.600
-0.000 1.034 0.017 0.983 0.021 0.020 -0.000 0.996 2.600
0.066 1.051 0.016 0.922 0.021 0.021 0.000 0.994 4.666
0.133 1.053 0.018 1.025 0.022 0.024 -0.000 0.995 3.733
0.199 1.068 0.021 1.171 0.024 0.031 0.000 0.994 4.466
0.266 1.060 0.022 1.227 0.029 0.043 0.001 0.995 3.133
0.333 1.057 0.022 1.198 0.042 0.066 0.006 0.998 1.000
0.400 0.994 0.024 1.404 0.101 0.105 0.054 1.000 0.000
0.466 0.799 0.032 2.336 0.140 0.123 0.087 1.000 0.000
0.533 0.570 0.049 4.984 0.149 0.124 0.080 1.000 0.000
0.600 0.343 0.051 8.460 0.135 0.106 0.059 0.999 0.533
0.666 0.180 0.048 15.063 0.107 0.039 0.047 0.901 57.733
0.733 0.111 0.070 32.399 0.062 0.023 0.046 0.214 103.533
0.800 0.063 0.070 48.031 0.018 0.002 0.046 0.018 14.200
0.866 0.019 0.018 43.949 0.010 '0.016 0.006 0.000 3.266
0.933 0.015 0.012 38.860 0.000 0.000 0.000 0.000 3.000
1.000 0.015 0.012 38.860 0.000 0.000 0.000 0.000 3.000

TABLE D-4 Continued

69

x/d Au/d = Ay/d -.- xx/d = 1. /d =
3.000 0.100 0.052 0.058 03050
Uc(fpa) = 97.086 T = 15.000 (averaging time) Condition: Vortical
y/d IJ/Uc v/Uc e u'/Uc w/uc uv/UCZ y C/T

1.250 0.016 0.012 37.889 0.008 0.004 0.000 0.000 3.066
1.166 0.032 0.024 36.879 0.026 0.016 0.011 0.002 3.733
1.083 0.075 0.075 44.812 0.007 0.024 0.050 0.013 9.200
1.000 0.085 0.095 48.447 0.024 0.037 0.065 0.074 31.133
0.916 0.123 0.093 36.944 0.054 0.013 0.082 0.317 87.266
0.833 0.187 0.064 18.984 0.104 0.025 0.069 0.707 89.400
0.750 0.270 0.046 9.785 0.129 0.063 0.055 0.950 26.666
0.666 0.380 0.040 6.124 0.140 0.097 0.062 0.997 1.666
0.583 0.510 0.036 4.138 0.151 0.108 0.072 1.000 0.000
0.500 0.657 0.036 3.211 0.152 0.110 0.078 1.000 0.000
0.416 0.796 0.032 2.322 0.145 0.110 0.075 1.000 0.000
0.333 0.936 0.029 1.824 0.117 0.097 0.055 1.000 0.000
0.250 1.008 0.025 1.444 0.076 0.077 0.024 0.999 0.600
0.166 1.035 0.024 1.362 0.047 0.055 0.007 0.997 1.533
0.083 1.034 0.023 1.300 0.038 0.038 0.000 0.994 3.933
0.000 1.027 0.022 1.274 0.037 0.031 0.001 0.993 5.600
-0.083 1.027 0.019 1.112 0.041 0.030 0.001 0.992 6.133
-0.166 1.029 0.020 1.129 0.050 0.032 0.002 0.988 8.266
-0.249 1.026 0.021 1.180 0.070 0.050 -0.004 0.994 4.533
-0.333 0.977 0.013 0.809 0.103 0.084 -0.037 0.999 0.733
-0.416 0.850 0.004 0.286 0.133 0.108 -0.065 1.000 0.000
”0.499 0.659 -00002 -00259 00196 00112 “00067 10000 00000
-00583 00502 ”00015 “10742 0.145 00107 “0.064 1.000 0.000
-O.666 0.344 -0.008 -1.468 0.137 0.077 -0.046 0.996 2.600
-0.750 0.233 -0.009 -2.361 0.126 0.028 -0.023 0.923 28.466
-0.833 0.174 -0.013 -4.356 0.109 0.074 -0.009 0.598 105.600
-0.916 0.140 -0.010 -4.421 0.088 0.071 -0.004 0.179 65.933
’0.999 00115 -00002 “10360 0.070 0.063 0.002 0.036 17.800
-l.083 0.044 -0.002 -2.785 0.052 0.033 0.000 0.002 4.266
-1.166 0.019 -0.002 -6.200 0.000 0.000 0.000 0.000 3.000
-1.250 0.019 -0.002 -6.200 0.000 0.000 0.000 0.000 3.000

TABLE D-4 Continued

70

x/d Au/d = A /d = xx/d = x /d =
4.500 0.100 0.052 0.050 03050
Uc(fps) ‘97.680 T — 15.000 (averaging time) Condition. Vortical

y/d tJ/Uc v/Uc e u'/Uc w/uc uv/Ucz y c/T
“1.500 0.027 “00001 “30178 0.036 00026 0.001 0.000 30333
-1.400 0.036 -0.004 -7.368 0.047 0.036 -0.000 0.001 3.600
“1.300 00103 .00001 “1.095 00082 00078 0.003 0.087 10.466
“1.200 00117 00002 10429 0.085 0.083 0.009 00260 29.133
'1.100 0.153 -0.002 -0.994 0.101 0.095 0.007 0.253 63.400
“1.000 0.186 -00015 -50686 00113 0.076 ”00012 0.513 86.333
-0.900 0.232 -0.014 -3.480 0.126 0.064 -0.021 0.843 54.933
'0.800 0.291 -0.014 -2.821 0.157 0.075 -0.041 0.959 20.000
‘00700 00405 “00017 “20506 00153 0.055 '00054 00998 10000
'0.600 0.512 -0.013 -1.472 0.147 0.103 -0.065 0.999 0.066
”0.500 0.630 “00006 '00596 0.148 0.108 -0006“ 10000 0.000
“0.400 0.753 0.002 0.219 0.147 0.109 -0.064 1.000 0.000
-0.300 0.888 0.010 0.700 0.130 0.103 -0.057 0.999 0.066
'0.200 0.976 0.017 1.055 0.100 0.082 -0.030 0.998 1.400
-0.100 1.008 0.020 1.159 0.073 0.062 -0.007 0.994 3.866
-0.000 10020 00018 10065 00060 00055 0000‘ 0.994 40533
0.099 1.013 0.020 1.159 0.072 0.068 0.016 0.998 1.733
0.199 0.974 0.021 1.259 0.105 0.085 0.038 0.999 0.533
0.299 0.880 0.021 1.423 0.137 0.099 0.065 1.000 0.000
0.399 0.771 0.026 1.935 0.149 0.104 0.075 1.000 0.000
0.499 0.646 0.026 2.330 0.154 0.106 0.076 1.000 0.000
0.599 0.526 0.028 3.045 0.152 0.104 0.073 1.000 0.000
0.699 0.407 0.027 3.901 0.148 0.089 0.065 0.997 1.733
0.800 0.324 0.038 6.691 0.142 0.058 0.060 0.977 11.933
0.900 0.254 0.032 7.305 0.117 0.052 0.043 0.901 41.866
0.999 0.200 0.035 10.063 0.101 0.026 0.039 0.680 79.133
1.100 0.159 0.044 15.558 0.084 0.041 0.037 0.379 79.266
1.200 0.136 0.045 18.442 0.076 0.072 0.042 0.143 42.333
1.300 0.091 0.068 36.709 0.033 0.047 0.046 0.032 13.466
1.399 0.040 0.047 49.568 0.013 0.034 0.030 0.005 5.133
1.500 0.022 0.023 45.921 0.012 0.024 0.009 0.001 3.666

TABLE D-4 Continued

71

x/d .Au/H== .A /H:= x /d== x /d==
6.000 0.100 0.052 0.058 02050
Uc(fpe) =96.899 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc V/Uc 6 u'/Uc v'/Uc uv/UCz y C/T
1.750 0.021 0.025 49.498 0.006 0.016 0.007 0.002 3.666
1.633 0.041 0.058 54.506 0.025 0.030 0.032 0.010 6.533
1.516 0.023 0.094 76.235 0.072 0.064 0.029 0.027 11.866
1.400 0.050 0.130 68.829 0.091 0.086 0.057 0.111 32.800
1.283 0.064 0.146 66.381 0.083 0.096 0.060 0.271 59.000
1.166 0.148 0.119 38.931 0.028 0.059 0.147 0.484 75.733
1.050 0.243 0.060 13.909 0.117 0.020 0.066 0.790 60.266
0.933 0.300 0.042 8.042 0.132 0.058 0.059 0.937 27.600
0.816 0.383 0.033 4.967 0.143 0.080 0.062 0.993 3.866
0.700 0.491 0.038 4.475 0.153 0.103 0.074 0.999 0.600
0.583 0.594 0.036 3.504 0.160 0.107 0.081 1.000 0.000
0.466 0.701 0.033 2.705 0.158 0.108 0.082 1.000 0.000
0.350 0.818 0.033 2.341 0.156 0.107 0.079 1.000 0.000
0.233 0.918 0.032 2.050 0.143 0.102 0.063 0.999 0.066
0.116 0.986 0.029 1.727 0.124 0.096 0.038 0.999 0.333
0.000 1.010 0.026 1.483 0.113 0.094 0.005 0.999 0.533
“00116 00989 00018 10045 00120 00099 '00023 00999 00666
-0.233 0.914 0.014 0.919 0.139 0.108 -0.050 0.999 0.066
-00349 00824 0000‘ 00340 0.148 00111 ‘00061 00999 00066
-0.466 0.699 -0.001 -0.141 0.156 0.111 -0.068 1.000 0.000
-0.583 0.577 -0.010 -1.070 0.155 0.107 -0.069 0.999 0.066
-0.699 0.471 -0.010 -1.229 0.149 0.099 -0.064 0.998 1.066
-0.816 0.394 -0.017 -2.522 0.163 0.022 -0.055 0.993 4.533
-0.933 0.298 -0.015 -3.021 0.149 0.061 -0.036 0.934 29.533
-1.050 0.242 -0.021 -5.105 0.128 0.066 -0.026 0.798 59.800
-l.166 0.198 -0.023 -6.796 0.114 0.086 -0.022 0.530 77.133
“10283 00161 '00024 -8049? 00093 00087 ‘00025 00286 630466
“10399 00155 ”00027 -100086 00098 00093 ’00024 00120 350000
-1.516 0.113 0.001 0.539 0.078 70.079 0.000 0.047 15.866
-1.633 0.065 0.015 13.181 0.057 0.051 0.016 0.009 6.000
-1.750 0.046 0.008 10.432 0.052 0.034 0.010 0.150 3.000

TAB LE D-4 Continued

72

x/d Au/d = A /d = 1. /d = 1. /d =
0.000 0.100 0.052 03058 01050
Uc(fpe) = 91.700 T = 15.000 (averaging time) Condition: Vortical
y/d tI/Uc v/Uc e w/uc v'/Uc uv/Ucz y C/T

-2.000 0.062 0.011 10.745 0.066 0.040 0.015 0.005 4.600
-l.866 0.090 -0.008 -5.085 0.072 0.075 -0.015 0.029 8.733
'1 .733 0.151 ’0.008 '3.295 0.112 0.116 '0.003 0.102 14.066
“10600 00189 “00014 '40340 00128 00127 “00003 00174 “20066
-1.466 0.201 -0.026 -7.422 0.125 0.119 -0.028 0.275 59.533
-10333 00264 '00029 -6099? 00160 00106 ’00033 00576 770266
’1.066 0.335 -0.019 -3.401 0.153 0.023 '0.042 0.914 26.466
“0.933 0.413 -0.015 -2.099 0.170 0.047 -0.060 0.977 11.733
-00800 00699 “00016 -10913 00185 00054 ’00076 00996 20200
“0.666 0.604 .0.018 -l.713 0.170 0.118 '0.084 0.999 0.466
-00533 00701 -00016 “10329 00177 00123 ‘00084 10000 00000
“0.400 0.810 -0.008 '0.602 0.174 0.125 -0.072 1.000 0.000
”00266 00897 00000 00019 00171 00126 ”00058 10000 00000
-0.133 0.978 0.006 0.360 0.166 0.127 -0.032 1.000 0.000
'0.000 1.014 0.016 0.950 0.163 0.126 0.012 1.000 0.000
0.133 0.971 0.017 1.022 0.172 0.124 0.061 0.999 0.066
0.266 0.911 0.024 1.537 0.177 0.122 0.081 1.000 0.000
0.399 0.824 0.029 2.030 0.184 0.122 0.096 1.000 0.000
0.533 0.713 0.035 2.850 0.182 0.121 0.101 1.000 0.000
0.666 0.621 0.039 3.593 0.176 0.118 0.094 0.999 0.200
0.800 0.496 0.036 4.230 0.178 0.089 0.092 0.994 3.466
0.933 0.427 0.042 5.612 0.166 0.086 0.085 0.983 9.266
1.066 0.356 0.037 6.040 0.148 0.079 0.071 0.950 21.066
1.200 0.294 0.046 9.074 0.137 0.012 0.065 0.795 54.933
1.333 0.244 0.054 12.538 0.120 0.049 0.065 0.551 70.000
1.466 0.209 0.063 16.833 0.101 0.069 0.067 0.373 67.000
1.600 0.179 0.063 19.570 0.096 0.094 0.079 0.158 38.266
1.733 0.119 0.100 40.229 0.038 . 0.043 0.099 0.077 22.000
1.866 0.068 0.062 42.487 0.030 0.027 0.052 0.457 4.133
2.000 0.055 0.052 43.635 0.017 0.021 0.035 0.008 5.800

x/d

10.000

”CK?” =70.272

Y/d

2.500
2.333
2.166
2.000
1.833
1.666
1.500
1.333
1.166
1.000
0.833
0.666
0.500
0.333
0.166
0.000
“00166
“00333
“00699
“00666
“00833
“00999
“10166
“10333
“10500
“10666
“10833
“10999
“20166
-2.333
~2.500

TABLE D-4 Continued

.Au/d=:
0.100
T = 15.000
V/Uc 9
0.025 38.740
0.039 55.349
0.110 92.491
0.142 98.585
0.138 42.725
0.102 24.696
0.078 16.137
0.057 9.697
0.049 7.104
0.050 5.915
0.045 4.450
0.047 3.732
0.042 2.942
0.037 2.347
0.028 1.643
0.013 0.791
0.006 0.366
-0.001 -0.128
“00008 “00616
“00010 “00892
“00016 “10647
-0.012 -1.478
“00016 “20009
“00029 “50159
“00025 “50663
“00060 “90153
-0.040 -10.176
0.011 3.464
0.076 36.816
-0.042 -38.801

“00026 “370620

A/d:

0.352

tfl/UE

0.019
0.016
0.095
0.102
0.021
0.110
0.135
0.141
0.159
0.185
0.201
0.198
0.200
0.193
0.188
0.182
0.185
0.191
0.193
0.203
0.204
0.206
0.179
0.169
0.145
0.152
0.144
0.136
0.048
0.043
0.023

73

(averaging tim e)

Xx/d =
0.058

Condition:

-— -z
v'/UC uv/UC

0.013
0.036
0.092
0.099
0.035
0.087
0.084
0.023
0.086
0.095
0.100
0.132
0.136
0.137
0.138
0.140
0.140
0.140
0.135
0.106
0.076
0.091
0.058
0.103
0.122
0.141
0.156
0.136

-0.058

0.024
0.013

0.013
0.019
“00013
“00035
0.182
0.157
0.121
0.077
0.082
0.108
0.120
0.117
0.108
0.086
0.055
0.013
“00038
“00070
“00091
-0.092
“00091
“00059
“00047
“00045
“00036
“00062
“00052
0.055
0.064
“00039
“00013

X /d==

03050
Vortical

Y C/ T

0.001 3.533
0.003 4.533
0.017 8.800
0.039 15.133
0.118 30.533
0.279 55.466
0.454 66.600
0.746 57.533
0.893 31.933
0.975 12.066
0.992 4.200
0.999 0.133
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
1.000 0.000
0.999 0.066
1.000 0.000
0.999 0.533
0.995 2.666
0.980 8.666
0.923 26.733
0.736 59.000
0.524 65.733
0.337 59.600
0.178 43.466
0.074 22.466
0.024 10.066
0.005 5.000
0.003 4.066

TABLE D-S DATA LISTING

74

X/d Au/d = Ay/d = )‘x/d = 1 /d =
0.500 0.097 0.052 0.083 02070
Uc(fpa) ‘10". 395 T = 15.000 (averaging time) Condition: Vortical

v/d U/Uc V/Uc 6 u'/Uc v'/Uc uv/UCZ y C/‘I'
0.000 1.131 -0.002 -0.135 0.022 0.018 0.001 0.999 0.400
0.050 1.131 -0.000 -0.016 0.005 0.018 0.001 0.999 0.200
0.100 1.128 0.003 0.188 0.008 0.019 0.001 0.999 0.133
0.150 1.116 0.004 0.213 0.011 0.020 0.002 0.999 0.133
0.200 1.097 0.004 0.253 0.011 0.019 0.002 0.999 0.266
0.250 1.085 0.002 0.134 0.018 0.019 0.002 0.999 0.066
0.300 1.091 0.002 0.136 0.013 0.020 0.001 0.999 0.066
0.350 1.079 0.003 0.174 0.018 0.027 0.001 0.999 0.066
0.400 1.077 0.000 0.027 0.022 0.044 0.003 0.999 0.066
0.450 1.050 0.003 0.164 0.073 0.100 0.043 1.000 0.000
0.500 0.712 0.035 2.885 0.127 0.125 0.090 1.000 0.000
0.550 0.305 0.051 9.620 0.110 0.113 0.053 1.000 0.000
0.600 0.111 0.015 7.920 0.046 0.022 0.004 0.995 3.600
00650 00068 “00015 “120811 00011 00016 “00000 00816 800600
0.700 0.044 0.003 4.924 0.019 0.008 0.000 0.075 75.133
0.750 0.020 0.003 10.651 0.010 0.003 0.000 -0.003 3.666
00000 10091 “00000 “00066 00021 00019 00001 00999 00200
'0.050 1.096 0.001 0.057 0.017 0.018 0.001 0.999 0.400
-0.100 1.096 -0.001 -0.052 0.005 0.019 0.000 0.999 0.133
-0.150 1.095 -0.003 -0.189 0.010 0.019 0.000 0.999 0.066
-0.200 1.082 -0.001 -0.102 0.017 ‘ 0.019 -0.000 0.999 0.066
'0.250 1.064 0.000 0.011 0.017 0.019 -0.000 0.999 0.066
-0.300 1.056 -0.000 -0.019 0.012 0.020 -0.000 0.999 0.066
-0.350 1.050 -0.001 -0.066 0.013 0.019 0.000 0.999 0.000
-0.400 1.051 -0.002 -0.131 0.020 0.019 0.001 0.999 0.000
-O.450 1.024 -0.019 -1.073 0.050 0.043 -0.007 1.000 0.000
“00500 00531 “00061 “60626 00093 00097 “00039 10000 00000
“00550 00110 “00065 “220566 00068 00032 “00007 00999 00133
“00600 00065 “00047 “650886 00018 00020 “00003 00191 1200533
-0.650 0.014 ~0.013 -41.790 0.006 0.008 -0.000 -0.004 3.333
“00700 00012 “00010 “390673 00000 00000 00000 “00002 30000
-0.750 0.012 -0.010 -39.473 0.000 0.000 0.000 -0.002 3.000

TABLE D-S Continued

75

x/<:1 Au/d = A /d = xx/d = x /d =
1.500 0.097 03552 0.033 dfiovo
UCHPS) =107,395 T = 15.000 (averaging time) Condition: Vortical

y/d u/Uc v/Uc e u'/Uc v'/Uc uv/Ucz y C/T
-1.000 0.012 -0.010 -39.473 0.000 0.000 0.000 -0.002 3.000
-0.933 0.019 -0.017 -40.738 0.012 0.011 -0.001 0.201 2.666
-00866 “.013 “00011 -390450 00004 00003 -00000 “0.001 3.133
-O.800 0.015 -0.012 ~39.130 0.009 0.009 -0.000 -0.003 3.333
'0.733 0.047 -0.044 -43.128 0.024 0.023 -0.005 0.188 44.533
-O.666 0.089 -0.053 ~30.836 0.049 0.023 '0.014 0.734 141.066
“0.600 00224 -0000? “10885 00104 00046 ’00017 0.999 0.400
'0.533 0.445 -0.003 -0.401 0.122 0.096 -0.041 1.000 0.000
“00466 00721 0.008 00682 00124 0.103 '00059 1.000 0.000
-0.400 0.948 0.020 1.243 0.089 0.072 -0.028 1.000 0.000
-O.333 1.009 0.031 1.804 0.054 0.029 0.002 0.999 0.066
‘00266 10018 00037 20122 0.032 0.022 00001 0.999 0.133
-0.200 1.017 0.030 1.737 0.023 0.020 -0.000 0.999 0.066
“0.133 1.034 0.028 1.568 0.018 0.020 '0.000 0.999 0.000
'0.066 1.035 0.032 1.801 0.019 0.020 0.000 0.999 0.000
-0.000 1.040 0.028 1.585 0.014 0.020 0.000 0.999 0.400
0.066 1.039 0.029 1.618 0.018 0.022 0.000 0.999 0.333
0.133 1.040 0.034 1.898 0.019 0.025 0.001 0.999 0.200
0.199 1.041 0.035 1.975 0.019 0.033 0.001 0.999 0.466
0.266 1.037 0.041 2.281 0.031 0.049 0.004 0.999 0.133
0.333 1.013 0.039 2.214 0.055 0.079 0.021 0.999 0.000
0.400 0.949 0.039 2.358 0.114 0.111 0.073 1.000 0.000
0.466 0.790 0.047 3.449 0.143 0.120 0.086 1.000 0.000
0.533 0.617 0.065 6.025 0.148 0.123 0.083 1.000 0.000
0.600 0.439 0.066 8.640 0.143 0.117 0.081 1.000 0.000
0.666 0.276 0.058 11.858 0.128 0.083 0.063 0.998 1.733
0.733 0.159 0.037 13.094 0.101 0.020 0.039 0.856 80.133
0.800 0.080 0.049 31.649 0.058 0.027 0.040 0.282 118.466
0.866 0.025 0.071 70.370 0.032 . 0.052 0.016 0.014 19.866
0.933 00008 00027 7200“2 0.020 00033 00006 .00000 ‘0066
1.000 “0.002 0.018 970451 00003 0.011 “00000 “00001 3.066

TABLE D-S Continued

x/d

76

Au/d - Ay/d = xx/d .-.- xy/d =
3.000 0.097 0.052 0.083 0.070
Uc(fpl) =107.659 T = 15.000 (averaging time) Condition: Vortical

y/d tJ/Uc V/Uc e u'/Uc v'/Uc uv/Ucz y C/T
1.250 0.042 0.003 5.419 0.050 0.041 0.001 0.001 4.800
1.166 0.072 0.045 31.951 0.052 0.039 0.029 0.016 11.066
1.083 0.057 0.081 54.554 0.029 0.048 0.045 0.075 31.400
1.000 0.072 0.098 53.575 0.019 0.061 0.055 0.275 72.133
0.916 0.145 0.077 27.924 0.084 0.032 0.083 0.640 90.866
0.833 0.225 0.049 12.449 0.114 0.055 0.048 0.918 39.733
0.750 0.324 0.050 8.911 0.131 0.081 0.064 0.996 2.600
0.666 0.422 0.053 7.280 0.142 0.101 0.075 0.999 0.000
0.583 0.537 0.055 5.889 0.146 0.107 0.077 1.000 0.000
0.500 0.666 0.056 4.811 0.148 0.108 0.075 1.000 0.000
0.416 0.791 0.047 3.471 0.141 0.104 0.067 1.000 0.000
0.333 0.915 0.041 2.566 0.122 0.097 0.059 1.000 0.000
0.250 0.991 0.034 1.992 0.087 0.080 0.034 0.999 0.066
0.166 1.028 0.029 1.628 0.057 0.059 0.013 0.999 0.400
0.083 1.034 0.030 1.686 0.033 0.039 0.004 0.999 0.400
0.000 1.032 0.027 1.509 0.041 0.033 0.003 0.999 0.533
-00083 10028 00029 10621 00043 0.033 0.002 0.999 00266
-0.166 1.021 0.035 1.983 0.052 0.039 0.002 0.999 0.066
-0.249 0.998 0.032 1.856 0.079 0.060 -0.011 0.999 0.066
“00333 00925 00025 10564 00115 00092 '000‘6 10000 00000
-0.416 0.791 0.020 1.497 0.139 0.111 -0.070 1.000 0.000
-0.499 0.620 0.015 1.453 0.146 0.110 -0.061 1.000 0.000
-0.583 0.469 0.005 0.717 0.141 0.100 -0.047 1.000 0.000
”0.666 0.333 00003 00566 00144 00032 -00025 00998 ' 10066
-0.750 0.213 0.002 0.664 0.127 0.056 -0.009 0.929 40.933
’00833 00152 00010 3.808 00099 00057 00006 00631 101.733
'0.916 0.109 0.008 4.444 0.080 0.062 0.008 0.208 69.733
‘0.999 00092 0.018 11.375 0.068 0.051 0.016 0.057 280‘66
-1.083 0.065 0.029 24.048 0.057 - 0.032 0.020 0.007 7.733
-10166 000‘“ 00011 140727 00052 0.026 0.008 0.002 4.666
“10250 00024 00005 120259 0001‘ 0.002 0.000 0.198 2.066

TABLE D-S Continued

77

X = — — -

/d Au/d Ay/d - xxo/d .. xy/d _

4.500 0.097 0.052 0. 83 0.070

Uc(fps) =107.653 T = 15,000 (averaging time) Condition: Vortical

y/d U/Uc v/Uc e m/uc v'/Uc uv/Ucz y C/T
-1.500 0.020 -0.011 -29.808 0.019 0.007 -0.002 -0.001 3.400
-1.400 0.063 ~0.018 -16.312 0.064 0.042 -0.020 0.008 6.866
-1.300 0.098 ~0.007 -4.495 0.073 0.063 -0.005 0.039 16.400
-10200 0.119 “00012 “6.041 00083 00074 -00012 0.177 45.533
-1.100 0.144 -0.012 -5.088 0.096 0.078 -0.009 0.348 72.800
-1.000 0.182 -0.010 -3.384 0.114 0.079 -0.010 0.664 76.600
-0.900 0.229 -0.008 -2.027 0.128 0.061 -0.015 0.896 43.066
-0.800 0.301 -0.006 -1.255 0.135 0.014 -0.026 0.983 7.733
-0.700 0.389 -0.000 -0.127 0.147 0.046 -0.035 0.999 0.266
“00600 0.991 0.005 00633 00142 0.096 -00046 00999 00000
-0.500 0.605 0.014 1.385 0.146 0.106 -0.058 1.000 0.000
-0.400 0.735 0.019 1.549 0.145 0.109 -0.066 1.000 0.000
-0.300 0.846 0.026 1.806 0.134 0.105 -0.062 1.000 0.000
“00200 00945 0.029 10807 00112 00091 “0.040 10000 0.000
-00100 10004 00027 10594 0.080 00071 ‘00010 0.999 0.133
-0.000 1.020 0.032 1.832 0.067 0.064 0.004 0.999 0.200
0.099 1.012 0.031 1.753 0.079 0.070 0.020 0.999 0.133
0.199 0.972 0.033 1.999 0.107 0.084 0.041 1.000 0.000
0.299 0.875 0.037 2.446 0.138 0.097 0.062 1.000 0.000
0.399 0.771 0.044 3.326 0.147 0.100 0.068 1.000 0.000
0.499 0.654 0.048 4.213 0.151 0.103 0.075 1.000 0.000
0.599 0.541 0.049 5.271 0.149 0.102 0.077 1.000 0.000
0.699 0.440 0.048 6.335 0.146 0.089 0.074 0.999 0.266
0.800 0.335 0.046 7.885 0.137 0.070 0.067 0.994 4.533
0.900 0.284 0.037 7.543 0.125 0.042 0.055 0.974 9.866
0.999 0.207 0.035 9.831 0.109 0.028 0.043 0.853 50.333
1.100 0.162 0.047 16.205 0.087 0.029 0.037 0.628 75.133
1.200 0.126 0.041 18.304 0.076 0.052 0.036 0.315 65.200
1.300 0.086 0.059 34.616 0.050 0.038 0.042 0.082 28.466
1.399 0.056 0.050 41.781 0.023 0.020 0.027 0.019 12.000
1.500 0.017 0.037 65.335 0.028 0.038 0.014 0.004 5.400

x/d
6.000
”cup" 106.213
v/d U/Uc
-10875 0.019
”10750 00029
-10625 00046
“1.500 0.105
-1.375 0.122
-1.250 0.152
~1.125 0.205
-10000 00253
-00875 0.328
'00750 0.420
"0.625 0.514
-0.500 0.647
-00375 0.746
-00250 00852
“00125 00954
0.000 1.001
0.125 0.989
0.250 0.903
0.375 0.798
0.500 0.684
0.625 0.560
0.750 0.449
0.875 0.365
1.000 0.294
1.125 0.219
1.250 0.180
1.375 0.116
1.500 0.090
1.625 0.024
1.750 0.005
1.875 0.002

TABLE D-S Continued

Au/d - AY/d -.-
0.097 0.052
= r in

15.000 (ave ag g time)

I 1
WUC e u /Uc v /Uc
’00014 '370179 00016 0.002
-0.011 ~21.218 0.028 0.015
-0.036 -38.517 0.032 0.019
“00027 -140464 00075 00068
~0.004 -2.117 0.081 0.075
-0000? “2.916 00096 00077
-0.013 -3.799 0.118 0.076
“00015 ’30483 00137 00070
-00011 ”20091 00148 0.028
“00006 -0087? 00155 0.052
-00000 -000‘2 00148 0.099
-0.000 -0.001 0.153 0.108
0.010 0.829 0.154 0.112
0.015 1.013 0.148 0.112
0.016 0.998 0.135 0.107
0.018 1.064 0.122 0.101
0.023 1.339 0.128 0.099
0.026 1.691 0.148 0.102
0.033 2.432 0.155 0.103
0.039 3.272 0.157 0.105
0.042 4.322 0.155 0.104
0.041 5.215 0.148 0.099
0.037 5.778 0.143 0.061
0.035 6.854 0.120 0.070
0.034 8.839 0.112 0.028
0.029 9.415 0.097 0.056
0.065 29.392 0.065 0.042
0.058 32.990 0.046 0.047
0.071 71.107 0.048 0.053
0.044 82.418 0.034 0.044
0.022 82.718 0.015 0.021

78

Xx/d :
0.083
Condition:

-—- -Z
uv/Uc

-00006
-00005
-00029
-00025
“00002
-0.006
“00016
“00026
‘0003‘
’00042
'00053
”00060
“0.065
”0.061
“00040
’00001
0.038
0.063
0.072
0.078
0.080
0.076
0.068
0.051
0.040
0.033
0.060
0.045
0.022
0.005
0.001

Vortical

Y

“00001
0.000
0.004
0.070
0.141
0.370
0.734
0.903
0.980
0.998
0.999
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
0.999
0.995
0.965
0.808
0.621
0.330
0.077
0.022
0.005

-00001

d:=
xy/

0.070

C/T

3.400
3.733
6.400
24.266
35.666
63.066
64.266
35.066
9.466
1.000
0.133
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.400
2.733
13.466
53.666
68.733
43.666
24.933
10.266
4.866
3.400

TABLE D-S Continued

79

x/d Au/d = Ay/d -- xx/d = Xy/d :-
8.000 0.097 0.052 0.083 0.070
Uc(fp0) = 98.190 T = 15.000 (averaging time) Condition: Vortical
. —- -2

y/d u/Uc v/Uc e u /Uc w/uc uv/Uc v C/T
20250 00003 00028 830172 00023 00029 00002 “00001 30666
2.100 0.010 0.034 73.663 0.029 0.037 0.008 -0.001 4.066
1.950 0.014 0.081 79.556 0.072 0.075 0.019 0.012 7.266
1.800 0.004 0.112 87.655 0.091 0.081 0.006 0.057 18.133
1.650 0.132 0.089 34.191 0.063 0.040 0.102 0.173 37.600
1.500 0.183 0.057 17.479 0.103 0.079 0.077 0.402 58.466
1.350 0.230 0.067 16.437 0.117 0.044 0.081 0.678 59.333
1.200 0.294 0.042 8.269 0.139 0.044 0.066 0.904 33.000
1.050 0.367 0.042 6.565 0.148 0.078 0.075 0.973 10.933
0.900 0.466 0.042 5.251 0.172 0.076 0.098 0.998 0.733
0.750 0.554 0.046 4.761 0.171 0.115 0.102 0.999 0.333
0.600 0.672 0.046 3.951 0.179 0.119 0.103 1.000 0.000
0.450 0.802 0.044 3.205 0.179 0.119 0.097 1.000 0.000
0.300 0.907 0.040 2.553 0.172 0.120 0.075 1.000 0.000
0.150 0.985 0.035 2.037 0.165 0.122 0.038 1.000 0.000
0.000 0.990 0.027 1.561 0.162 0.127 -0.008 1.000 0.000
“00149 00929 00022 10602 00167 00126 .00069 10000 00000
“00299 00862 00017 10203 00171 00124 ”00065 10000 00000
'00669 00731 00011 00925 00170 00120 '00065 10000 00000
'0.599 0.624 0.005 0.474 0.181 0.084 -0.059 1.000 0.000
'0.749 0.505 0.002 0.288 0.173 0.070 -0.051 0.998 0.666
-0.899 0.409 -0.002 -0.364 0.172 0.039 -0.037 0.993 4.400
-1.049 0.336 -0.007 -1.225 0.155 0.054 -0.030 0.958 17.000
*1.199 0.281 -0.013 -2.659 0.150 0.092 '0.015 0.847 39.600
‘10349 00226 “00012 “30140 00125 00078 ‘00010 00631 600666
-1.499 0.174 -0.016 -5.419 0.115 0.101 -0.016 0.310 54.200
'1.649 0.147 0.002 0.779 0.108 0.106 0.013 0.139 32.933
“10799 00124 00009 40615 00075 00078 00011 00071 200333
'1.949 0.077 0.023 17.163 0.061 0.053 0.020 0.022 9.133
-20099 00069 00022 170993 00059 00065 00016 00007 60133
'2.249 0.025 0.009 21.468 0.020 0.014 0.001 -0.000 3.400

TABLE D-S Continued

80

x/d Au/d = A /d = kx/d = xy/d =
10.000 0.097 0.052 0.083 0.070
Uc(fpe) = 84.300 T = 15.000 (averaging time) Condition: Vortical
y/d U/Uc V/Uc e u'/Uc v'/Uc uv/Ucz y C/T

-2.500 0.034 0.010 17.436 0.034 0.029 0.006 -0.001 3.600
“20333 00055 “00040 “360406 00030 00013 “00022 00613 40066
-2.166 0.079 -0.026 -18.168 0.075 0.063 -0.039 0.018 9.333
“20000 00148 “00057 “210012 00089 00079 “00069 00076 220466
‘1.833 0.176 -0.040 -12.989 0.109 0.106 -0.052 0.183 38.066
“10666 00227 “00025 “60356 00130 00105 “00026 00609 590600
-l.500 0.264 -0.026 -5.755 0.144 0.093 -0.034 0.627 61.866
'1.333 0.315 -0.016 -2.913 0.166 0.096 -0.023 0.803 47.733
-1.166 0.393 -0.015 -2.298 0.174 0.009 -0.051 0.950 17.066
-l.000 0.466 -0.004 -0.545 0.193 0.063 -0.046 0.986 5.066
“00833 00561 “00006 “00500 00205 0001‘ “00060 00996 10666
-0.666 0.670 -0.002 -0.235 0.183 0.125 -0.077 0.999 0.200
“00500 00765 00008 00605 00187 00130 “00071 10000 00000
“00333 00887 00010 00706 00186 00137 “00063 10000 00000
-0.166 0.964 0.014 0.844 0.180 0.139 -0.035 1.000 0.000
“00000 00998 00023 10354 00179 00160 00007 10000 00000
0.166 0.983 0.031 1.825 0.185 0.137 0.054 1.000 0.000
0.333 0.922 0.039 2.447 0.195 0.135 0.091 1.000 0.000
0.499 0.820 0.045 3.181 0.201 0.135 0.119 1.000 0.000
0.666 0.706 0.047 3.835 0.198 0.131 0.129 0.999 0.200
0.833 0.604 0.054 5.109 0.197 0.111 0.131 0.998 0.666
0.999 0.512 0.050 5.642 0.193 0.086 0.126 0.994 3.866
1.166 0.434 0.047 6.253 0.169 0.081 0.104 0.974 10.866
1.333 0.348 0.052 8.512 0.164 0.031 0.098 0.878 34.933
1.500 0.292 0.049 9.692 0.141 0.064 0.072 0.709 53.666
1.666 0.244 0.043 9.999 0.128 0.075 0.058 0.519 63.200
1.833 0.173 0.057 18.313 0.105 0.076 0.065 0.437 33.600
1.999 0.132 0.083 32.155 0.072 0.061 0.088 0.077 20.800
2.166 0.037 0.099 69.450 0.071 0.066 0.043 0.017 9.066
2.333 0.004 0.040 83.107 0.029 0.039 0.004 0.001 4.600
2.500 0.006 0.039 80.702 0.032 0.042 0.005 0.000 3.733

TAJKLEHD~6 ILATI11JSTTNK}

81

"/d Au/d = Ay/d = xx/d = 1. /d =
0.500 0.009 0.053 0.015 03011
Uc(fp0) =104.ozz T = 15.000 (averaging time) Condition: Vortical
y/d U/Uc V/Uc e w/uc w/uc uv/Ucz y I C/T

0.000 0.944 0.009 0.597 0.014 0.015 -0.000 0.994 4.400
00050 00967 00000 00690 00013 00015 “00000 00991 50666
0.100 0.945 0.008 0.517 0.013 0.015_ 0.000 0.991 5.600
0.150' 0.939 0.005 0.309 0.015 0.015 0.000 0.993 5.333
0.200 0.940 0.006 0.412 0.014 0.015 0.000 0.992 6.000
0.250 0.944 0.009 0.580 0.015 0.015 0.000 0.993 5.600
0.300 0.945 0.011 0.699 0.015 0.016 0.000 0.992 6.533
0.350 0.943 0.013 0.792 0.015 0.017 0.000 0.993 5.266
0.400 0.938 0.013 0.822 0.015 0.019 0.000 0.996 3.066
0.450 0.933 0.015 0.922 0.020 0.034 0.000 1.000 0.000
0.500 0.687 0.023 1.933 0.088 0.087 0.045 1.000 0.000
0.550 0.229 0.009 2.318 0.073 0.070 0.027 1.000 0.000
0.600 0.048 -0.019 -21.958 0.014 0.008 -0.000 0.704 133.333
0.650 0.036 -0.017 -25.998 0.007 0.006 '0.000 0.009 10.733
00700 00016 “00006 “200066 00000 00000 00000 00000 30000
00750 00016 “00006 “200066 00000 00000 00000 00000 30000
0.000 0.929 0.023 1.433 0.013 0.014 -0.000 0.992 5.866
“00050 00921 00027 10717 00016 00015 “00000 00995 60000
-0.100 0.912 0.027 1.751 0.016 0.015 -0.001 0.997 2.266
“00150 00900 00027 10166 00016 00016 “00000 00996 20000
-0.200 0.897 0.026 1.674 0.013 0.014 -0.000 0.994 4.800
-0.250 0.898 0.025 1.651 0.012 0.014 0.000 0.989 7.933
-0.300 0.903 0.026 1.672 0.013 0.014 0.000 0.993 4.533
-0.350 0.905 0.025 1.619 0.014 0.014 0.000 0.986 10.533
-0.400 0.909 0.023 1.454 0.020 0.015 0.000 0.993 5.066
-0.450 0.784 -0.006 -0.452 0.061 0.057 -0.013 1.000 0.000
‘“00500 00360 “00031 “50199 00076 . 00002 “00021 10000 00000
-0.550 0.071 -0.037 -27.911 0.025 0.018 -0.001 0.928 47.933
“00600 00035 “00021 “300530 00015 00009 “00001 00006 10533
-O.650 0.016 -0.009 -29.722 0.005 0.002 -0.000 0.027 3.333
-0.700 0.015 -0.009 -29.977 0.000 0.000 0.000 0.000 3.000
“00750 00015 “00009 “290977 00000 00000 00000 00000 30000

TAB LE D-6 Continued

82

x/d Au/d = Ay/d = xx/d = x /d =
1.500 0.089 0.053 0.075 01071
Uc(fps) 2104.022 T = 15.000 (averaging time) Condition: Vortical

Y/d U/Uc V/UC 6 u'/UC v'/Uc uv/UC2 y C/T
'1.000 0.015 -0.009 ~29.977 0.000 0.000 0.000 0.000 3.000
-0.933 0.015 -0.009 -29.977 0.000 0.000 0.000 0.000 3.000
-0.866 0.015 -0.009 -29.977 0.000 0.000 0.000 0.000 3.000
-O.800 0.021 -0.011 -28.196 0.013 0.005 -0.000 0.130 2.400
'O.733 0.044 -0.025 ~29.408 0.036 0.006 -0.008 0.002 5.333
“00666 00067 “00046 “340737 00036 00016 “00013 00186 1070666
-0.600 0.140 -0.024 -10.020 0.067 0.032 ~0.006 0.957 30.200
-O.533 0.314 0.000 0.163 0.098 0.075 -0.023 0.999 0.066
“00466 00570 00010 10053 00106 00089 “00036 10000 00000
-O.333 0.871 0.056 3.685 0.042 0.025 0.001 0.995 4.066
-0.266 0.871 0.057 3.758 0.026 0.016 0.001 0.987 9.666
'0.200 0.871 0.055 3.632 0.018 0.014 0.000 0.994 4.133
-0.066 0.884 0.058 3.793 0.015 0.013 -0.000 0.990 6.733
-0.000 0.960 -0.001 -0.089 0.014 0.016 -0.000 0.991 6.666
0.066 0.962 -0.001 -0.114 0.016 0.017 0.000 0.992 6.000
0.133 0.958 -0.005 -0.307 0.017 0.018 0.000 0.990 7.466
0.199 0.950 -0.003 -0.202 0.019 0.021 0.000 0.993 4.666
0.266 0.958 0.001 0.065 0.021 0.028 0.000 0.994 4.466
0.333 0.959 0.003 0.179 0.026 0.042 0.000 0.997 2.000
0.400 0.942 0.007 0.428 0.050 0.069 0.012 1.000 0.000
0.466 0.812 0.014 0.989 0.109 0.100 0.059 1.000 0.000
0.533 0.569 0.018 1.908 0.128 0.109 0.064 1.000 0.000
0.600 0.331 0.017 3.060 0.118 0.094 0.050 1.000 0.000
0.666 0.160 0.004 1.712 0.090 0.025 0.017 0.945 36.133
0.733 0.102 -0.008 -4.860 0.056 0.021 0.001 0.277 126.800
0.800 0.067 -0.039 -30.220 0.038 0.017 -0.010 0.010 10.466
0.866 0.015 -0.009 -32.827 0.000 0.000 0.000 0.000 3.000
0.933 0.015 -0.009 -32.827 0.000 ' 0.000 0.000 0.000 3.000
1.000 0.015 -0.009 -32.827 0.000 0.000 0.000 0.000 3.000

TABLE D-6 Continued

83

x/d Au/d = AY/d = xx/d = x /d =
3.000 0.089 0.053 0.075 .071
Heaps) =103.344 T = 15.000 (averaging time) Condition: Vortical

y/d u/Uc v/Uc e u'/Uc v'/Uc uv/Ucz y C/T
1.250 00017 “00010 ”300788 00012 00001 -0.000 0.000 3.133
1.166 0.025 -0.030 -50.390 0.018 0.019 -0.013 0.069 4.733
1.083 0.020 -0.084 -76.555 0.058 0.055 -0.013 0.085 10.866
1.000 0.120 0.024 11.678 0.080 0.081 0.017 0.094 38.533
0.916 0.139 0.044 17.676 0.081 0.055 0.037 0.350 95.466
0.833 0.189 0.044 13.278 0.105 0.036 0.042 0.758 86.400
0.750 0.270 0.049 10.385 0.127 0.064 0.055 0.975 12.600
0.666 0.392 0.050 7.269 0.136 0.098 0.066 0.999 0.400
0.583 0.533 0.057 6.129 0.143 0.108 0.076 0.999 0.066
0.500 0.677 0.054 4.575 0.143 0.110 0.083 1.000 0.000
0.416 0.827 0.059 4.088 0.128 0.105 0.071 0.999 0.066
0.333 0.934 0.056 3.468 0.091 0.086 0.039 0.999 0.333
0.250 0.970 0.050 2.987 0.057 0.064 0.013 0.998 1.600
0.166 0.986 0.048 2.800 0.037 0.043 0.003 0.990 7.333
0.083 0.993 0.048 2.784 0.032 0.031 0.002 0.981 13.533
0.000 0.997 0.044 2.577 0.032 0.028 0.001 0.978 15.466
-0.083 0.986 0.048 2.824 0.038 0.028 0.000 0.990 7.200
'00166 0.981 0.047 2.791 000‘? 0.032 00001 0.989 8.400
-002‘9 0.958 0.049 2.9‘6 00070 0.051 -00006 0.995 30866
-O.333 0.889 0.042 2.727 0.107 0.085 -0.037 1.000 0.000
‘0.416 0.740 0.031 2.415 0.133 0.103 -0.052 1.000 0.000
”00499 . 00569 00014 10485 00138 00104 “0.051 10000 0.000
-0.583 0.407 0.005 0.842 0.132 0.091 -0.044 0.999 0.066
’00666 00277 00007 10504 00132 00024 -00023 00988 8.133
‘00750 00180 00003 10099 00109 00062 “00004 0.782 820‘00
-00833 001‘0 “00003 '10‘35 00086 00066 '09004 00377 920066
“00916 0.115 ”00011 -50483 00072 00072 “0.011 00062 300‘00
‘0.999 0.092 “00007 -‘0898 0006‘ 00052 “00006 00011 80‘66
'1.083 0.021 -0.004 ~12.744 0.015 0.007 -0.000 0.000 3.266
'1.166 0.019 -0.004 -12.058 0.014 ' 0.008 0.000 0.000 3.066
-10250 00017 “00004 “130567 00°00 00°00 00000 700000 30000

TABLE D-6 Continued

84

x/d Au/d = Ay/d .-. xx/d = x /d =
4.500 0.009 0.053 0.015 01071
Uc(fps) = 104,.115 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc v/Uc e u'/Uc w/uc uv/Ucz y C/T
-1.500 0.017 -0.004 -13.567 0.000 0.000 0.000 0.000 3.000
'10600 00028 “00005 “100411 00033 00016 “00001 00001 30600
-10300 00051 -00015 -170061 00039 00032 -0000? 00601 40133
'1.200 0.103 -0.033 -18.019 0.054 0.061 *0.027 0.039 17.000
-1.100 0.128 -0.026 -11.670 0.071 0.079 -0.031 0.134 42.533
”10000 00153 “00012 ”60702 00088 00066 ”00015 00602 760066
'00900 00196 ”00004 “10291 00110 00066 '00012 00696 820133
*0.800 0.249 0.006 1.569 0.137 0.076 -0.014 0.916 35.466
“00100 00338 00001 00338 00133 00068 “00038 00992 50000
-0.600 0.453 0.007 0.945 0.141 0.095 -0.051 0.999 0.066
“00500 00572 00011 10161 00163 00102 ”00053 10000 00000
-0.400 0.698 0.024 2.008 0.141 0.104 -0.053 1.000 0.000
‘0.300 0.830 0.036 2.516 0.129 0.100 -0.053 0.999 0.133
“00200 00930 00060 20511 00101 00082 “00031 00998 10266
“0.100 0.977 0.045 2.657 0.072 0.062 -0.009 0.993 5.266.
-0.000 1.000 0.041 2.391 0.055 0.051 0.004 0.990 7.666
0.099 0.990 0.043 2.500 0.061 0.060 0.013 0.992 5.800
0.199 0.954 0.044 2.666 0.091 0.078 0.031 0.998 1.266
00299 00801 00067 30106 00126 00095 00058 '00999 00066
0.399 0.789 0.051 3.766 0.142 0.104 0.076 1.000 0.000
0.499 0.673 0.054 4.634 0.149 0.107 0.081 1.000 0.000
0.599 0.552 0.052 5.386 0.150 0.105 0.079 1.000 0.000
0.699 0.434 0.049 6.509 0.148 0.089 0.072 0.999 0.666
0.800 0.333 0.045 7.825 0.137 0.068 0.063 0.986 7.666
0.900 0.260 0.048 10.658 0.127 0.015 0.054 0.931 30.000
0.999 0.191 0.048 14.095 0.100 0.044 0.043 0.676 82.733
1.100 0.152 0.060 21.670 0.081 0.071 0.051 0.369 79.133
1.200 0.116 0.075 32.937 0.057 0.060 0.063 0.134 42.266
1.300 0.088 0.071 39.056 0.030 0.055 0.040 0.033 14.866
1.399 0.059 0.042 35.660 0.043 ' 0.033 0.029 0.009 7.200
1.500 0.023 0.013 29.542 0.016 0.003 0.003 0.101 2.533

TABLE D-6 Continued

85

X/d Au/d = Ay/d = xx/d = x /d =
6.000 0.009 0.053 0.075 dhovl
Uc(fpa) =102.301 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc V/Uc 9 u'/Uc v'/Uc uv/Ucz y C/T
1.750 0.022 0.012 29.276 0.015 0.004 0.003 0.001 3.600
1.633 0.039 0.046 49.363 0.008 0.012 0.020 0.008 5.933
1.516 0.047 0.103 65.391 0.053 0.012 0.030 ‘ 0.039 14.266
1.400 0.030 0.123 76.297 0.073 0.073 0.025 0.102 31.000
1.283 0.075 0.138 61.403 0.077 0.085 0.075 0.255 58.200
1.166 0.164 0.099 31.151 0.078 0.024 0.106 0.587 78.400
1.050 0.234 0.053 12.931 0.111 0.026 0.052 0.813 55.266
0.933 0.307 0.050 9.414 0.129 0.057 0.059 0.966 16.600
0.816 0.399 0.052 7.451 0.148 0.079 0.070 0.994 3.000
0.700 0.487 0.057 6.741 0.157 0.090 0.081 0.999 0.133
0.583 0.584 0.054 5.337 0.154 0.106 0.080 1.000 0.000
0.466 0.701 0.054 4.419 0.154 0.107 0.083 1.000 0.000
0.350 0.804 0.053 3.809 0.150 0.106 0.079 1.000 0.000
0.233 0.904 0.052 3.339 0.139 0.102 0.067 0.999 0.200
0.116 0.971 0.049 2.931 0.117 0.092 0.039 0.999 0.333
0.000 0.994 0.047 2.760 0.107 0.091 0.005 0.999 0.866
-0.116 0.959 0.044 2.629 0.120 0.099 -0.027 0.999 0.600
-O.233 0.876 0.035 2.300 0.140 0.107 -0.047 0.999 0.200
-O.349 0.755 0.029 2.215 0.146 0.107 -0.053 0.999 0.066
“00466 00646 00019 10701 00149 00106 “00057 10000 00000
-0.583 0.525 0.011 1.231 0.148 0.099 -0.056 0.999 0.066
“00699 00432 00006 00831 00160 00092 “00049 00999 00533
-0.816 0.328 0.006 1.134 0.134 0.050 -0.033 0.981 9.600
-0.933 0.266 -0.000 -0.163 0.121 0.032 ~0.024 0.912 35.066
“10050 00216 “00006 “10819 00120 00073 “00014 00667 730200
-1.166 0.171 -0.014 -4.853 0.090 0.078 -0.019 0.432 75.133
-l.283 0.152 0.007 . 2.875 0.095 0.093 0.013 0.189 50.666
-1.399 0.136 -0.007 -3.304 0.082 0.089 -0.009 0.091 28.533
-1.516 0.088 0.017 10.872 0.069 0.067 0.022 0.016 8.333
-l.633 0.066 0.016 13.937 0.061‘ 0.051 0.021 0.006 5.733
“10750 00033 00009 150565 00033 00024 00005 00001 30666

TABLE D-6 Continued

86

x/d A/d= A/d= x d: x d:
3.000 65039 0 .1653 025/75 0147 1
Uc(fpo) = 96.571 T = 15.000 (averaging time) Condition: Vortical
. -— -z
y/d u/uc v/Uc e u /Uc v'/Uc uv/Uc y C/T
”20100 00031 00008 L‘ol78 00028 00023 00003 0.001 30‘66'
-1.950 0.051 0.015 16.343 0.042 0.031 0.009 0.005 5.000
-1.800 0.107 0.044 22.595 0.052 0.065 0.031 0.027 10.666
-1.650 0.152 -0.025 -9.523 0.089 0.097 -0.037 0.100 28.066
-1.500 0.179 -0.020 -6.574 0.095 0.097 -0.028 0.216 48.666
-l.350 0.213 -0.010 -2.828 0.121 0.110 -0.014 0.454 73.000
-1.200 0.259 -0.021 -4.711 0.130 0.068 -0.027 0.715 61.933
-1.050 0.321 -0.018 -3.210 0.154 0.064 -0.045 0.903 33.466
-00900 0.405 .00009 ”10272 0017‘ 00036 “00056 00980 90200
“00750 00‘9# “0.009 ’10074 00175 00071 -00070 0.997 1.733
-0.600 0.622 -0.006 -O.570 0.172 0.117 -0.079 0.999 0.066
“00‘50 06734 00002 0.207 0017‘ 00121 “0.073 10°00 0.000
“00300 00849 00013 0.936 00172 00125 ”0.062 10000 0.000
“0.150 00953 00024 16480 06169 00129 “0.040 1.000 00000
-0.000 1.007 0.033 1.927 0.166 0.128 0.005 1.000 0.000
0.149 0.985 0.039 2.280 0.170 0.125 0.062 1.000 0.000
0.299 0.893 0.038 2.490 0.178 0.123 0.091 1.000 0.000
0.449 0.800 0.046 3.314 0.179 0.122 0.098 1.000 0.000
0.599 0.677 0.043 ‘3.682 0.176 0.119 0.097 0.999 0.133
0.749 0.548 0.043 4.516 0.169 0.113 0.091 0.999 0.600
0.899 0.447 0.042 5.373 0.169 0.085 0.086 0.989 5.333
1.049 0.370 0.041 6.331 0.156 0.066 0.073 0.959 19.400
1.199 0.300 0.036 6.846 0.134 0.043 0.053 0.852 46.133
1.349 0.236 0.038 9.312 0.119 0.062 0.045 0.654 62.466
1.499 0.204 0.059 16.166 0.097 0.070 0.055 0.355 62.866
1.649 0.144 0.088 31.401 ‘ 0.065 0.080 0.106 0.137 35.400
1.799 0.083 0.093 48.286 0.031 0.028 0.067 0.039 15.333
1.949 0.050 0.077 56.780 0.043 0.043 0.046 0.010 6.200
2.100 0.018 0.023 52.297 0.002 0.015 0.003 0.001 3.400

x/d

10.000

new») = 82.444

Y/d

2.500
2.333
2.166
2.000
1.833
1.666
1.500
1.333
1.166
1.000
0.833
0.666
0.500
0.333
0.166
0.000
‘00166
‘00333
“0.499
'0e666
“0.833
‘0.999
-10166
'10333
-10500
'10666
-10833
“10999
-2e166
”2.333
”20500

TABLE D-6 Continued

Ail/d =
0.089
T = 15.000
v/uc 9
0.026 71.135
0.055 80.865
0.118 102.806
0.131 54.739
0.111 34.555
0.060 14.507
0.042 8.437
0.034 5.872
0.027 3.853
0.032 3.720
0.040 3.780
0.033 2.707
0.032 2.277
0.027 1.676
0.023 1.358
0.014 0.831
0.006 0.400
-0.007 -0.485
-0.011 -0.927
-0.016 -1.484
-00018 ’1e925
-0.020 -2.646
‘00020 -3.185
-0.039 -7.237
-0.056 ~11.777
-0.079 ~19.416
‘00062 “’18.le
’00050 ”180635
-00040 “180‘58
'00010"12e8‘3
-0.010 -18.941

A./h==

0.653

1
tl/Ug

0.008
0.054
0.098
0.052
0.058
0.120
0.135
0.140
0.169
0.188
0.184
0.197
0.195
0.191
0.184
0.182
0.189
0.191
0.190
0.188
0.189
0.189
0.175
0.161
0.141
0.107
0.098
0.080
0.077
0.042
0.016

87

(averaging time)

vfi/Ué

0.009
0.075
0.090
0.036
0.075
0.090
0.075
0.063
0.061
0.083
0.124
0.130
0.134
0.136
0.141
0.141
0.141
0.137
0.132
0.126
0.087
0.039
0.086
0.114
0.112
0.084
0.098
0.081
0.082
0.037

0.012-

X d:=
o 3645

Condition:

-— -Z
uv/Uc

0.000
0.013
-00031
0.075
0.160
0.075
0.054
0.061
0.075
0.099
0.106
0.111
0.100
0.080
0.042
-0.000
-00048
‘Oe073
-00092
“0.095
-00086
-0007?
”0005“
‘0e065
”0.077
-0.087
“00081
’0005‘
“00050
-0.007
-0.000

Vortical

0.000
0.004
0.023
0.061
0.173
0.435
0.559
0.798
0.931
0.989
0.998
0.999
1.000
1.000
1.000
1.000
1.000
1.000
0.999
0.999
0.993
0.962
0.882
0.713
0.530
0.276
0.138
0.051
0.022
0.003
0.000

X
0? 71

d:

C/T‘

3.133
4.533
9.266
19.066
34.466
50.466
65.933
51.533
26.000
5.200
0.733
0.333
0.000
0.000
0.000
0.000
0.000
0.000
0.066
0.466
3.266
16.733
37.533
60.333
73.000
56.133
35.533
18.066
10.066
4.200
3.266

TABLE D-7 DATA LISTING

88

"/d Au/d - Ay/d = xx/d = xy/d =
0.500 0.074 0.050 0.051 0.046
Uc(fpa) =89. 626 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc V/Uc 6 u'/Uc v'/Uc uv/UCz y C/T
0.000 1.028 -0.014 -O.788 0.015 0.014 0.000 1.000 0.000
0.050 1.029 0.005 0.280 0.014 0.015 0.000 0.980 12.666
0.100 1.032 0.003 0.187 0.014 0.015 0.000 0.976 17.133
0.150 1.041 0.002 0.133 0.013 0.016 -0.000 0.970 19.200
0.200 1.040 0.000 0.015 0.013 0.015 -0.000 0.964 23.400
0.250 1.039 0.005 0.303 0.011 0.015 -0.000 0.962 24.400
0.300 10035 0.021 1.207 00014 00017 “0.000 0.959 25.600
0.350 1.028 0.022 1.263 0.014 0.023 -0.000 0.974 17.133
0.400 1.027 0.027 1.536 0.019 0.042 -0.001 0.997 2.066
0.450 0.975 0.021 1.237 0.085 0.089 -0.044 1.000 0.000
0.500 0.555 0.053 5.458 0.130 0.112 -0.067 1.000 0.000
0.550 0.163 0.039 13.681 0.086 0.057 -0.006 0.996 3.400
0.600 0.080 0.029 20.200 0.029 0.008 0.001 0.467 167.800
0.650 0.039 0.052 53.289 0.018 0.016 0.002 0.009 11.933
0.700 0.010 0.018 60.694 0.000 0.000 0.000 0.000 3.000
0.750 0.010 0.018 60.251 0.002 0.002 0.000 0.007 4.866
0.000 1.018 0.019 1.070 0.010 0.013 0.000 0.948 33.200
~0.050 1.018 0.018 1.068 0.010 0.013 0.000 0.951 30.933
-0.100 1.023 0.022 1.256 0.010 0.013 0.000 0.952 29.866
-0.150 1.024 0.020 1.122 0.010 0.013 0.000 0.954 29.466
-0.200 1.026 0.018 1.050 0.010 0.013 0.000 0.954 29.200
-0.250 1.029 0.017 0.949 0.011 0.013 0.000 0.956 27.733
-0.300 1.033 0.019 1.105 0.012 0.015 0.000 0.966 22.733
-0.350 1.032 0.017 0.972 0.013 0.015 0.000 0.972 19.400
-0.400 1.034 0.013 0.733 0.015 0.014 0.000 0.971 19.866
-0.450 1.026 0.007 0.404 0.034 0.023 -0.000 0.998 1.800
-0.500 0.648 -0.033 -2.996 0.095 0.098 -0.043 1.000 0.000
’00550 0019‘ “00019 “50710 00066 t 00062 “0.01‘ 0.999 00333
-0.600 0.083 -0.017 -11.911 0.029 0.017 -0.001 0.092 30.600
-00650 00020 -00005 “150399 00000 0.000 0.000 0.000 3.000
-0.700 0.020 -0.005 -15.399 0.000 0.000 0.000 0.000 3.000
-0.750 0.020 -0.005 -15.399 0.000 0.000 0.000 0.000 3.000

TABLE D-7 Continued

89

x/d Au/d - Ay/d - xx/d - xy/d =
1.500 0.074 0.050 0.051 0.046
Uc(fpe) = 89.626 T = 15.000 (averaging time) Condition: Vortical
. -— -z
y/d U/Uc v/Uc e u /Uc w/uc uv/Uc y C/T

'1.000 0.023 -0.005 ~14.123 0.011 0.001 -0.000 0.049 3.066
-O.933 0.019 -0.005 -15.399 0.000 0.000 0.000 0.000 3.000
-0.866 0.019 -0.005 ~15.399 0.000 0.000 0.000 0.000 3.000
“0.800 0.021 “00005 -15e553 00010 0e003 -0.000 OeOOO 3.066
-0.733 0.074 -0.066 -42.025 0.038 0.008 -0.025 0.040 9.400
-0.666 0.110 -0.062 ~29.532 0.055 0.015 -0.016 0.314 133.400
'0.600 06240 “00015 -30801 0.097 00057 ’OeOZI 00993 5.733
-0.533 0.468 -0.019 ~2.361 0.119 0.097 -0.053 1.000 0.000
-0.466 0.764 -0.013 ~1.019 0.113 0.097 -0.049 1.000 0.000
-0.400 0.974 0.002 0.146 0.065 0.054 -0.014 0.999 0.466
’00333 leOlB 0e013 00738 00037 00022 0.000 0.969 20.066
-0.266 1.013 0.014 0.815 0.024 0.017 0.000 0.948 32.533
'0.200 1.009 0.012 0.713 0.016 0.014 0.000 0.943 35.933
‘06133 10006 06008 00‘7‘ 00014 0001“ 0.000 0e952 30.533
'0.066 1.002 0.009 0.534 0.013 0.014 0.000 0.941 35.066
'00000 00996 00006 0.375 00012 00015 0.000 0e920 46.800
0.066 1.004 0.001 0.107 0.014 0.017 -0.000 0.953 30.800
0.133 1.005 0.008 0.466 0.016 0.020 -0.000 0.960 26.466
0.199 1.009 0.004 0.260 0.019 0.026 0.000 0.959 25.933
0.266 1.007 0.004 0.269 0.024 0.038 0.001 0.964 23.533
0.333 0.997 0.004 0.256 0.043 0.064 0.009 0.993 5.466
0.400 0.938 0.009 0.594 0.097 0.091 0.046 0.999 0.133
0.466 0.762 0.025 1.902 0.134 0.113 0.076 1.000 0.000
0.533 0.530 0.044 4.740 0.142 0.117 0.072 1.000 0.000
0.600 0.327 0.039 6.915 0.129 0.092 0.056 0.997 2.000
0.666 0.176 0.038 12.375 0.091 0.055 0.029 0.732 115.133
0.733 0.114 0.070 31.618 0.060 0.030 0.044' 0.122 67.800
0.800 0.019 0.077 75.581 0.046 0.061 0.019 0.048 7.000
0.866 0.008 0.018 66.432 0.000 , 0.000 0.000 0.000 3.000
0.933 0.008 0.018 66.432 0.000 0.000 0.000 0.000 3.000
1.000 0.008 0.018 66.432 0.000 0.000 0.000 0.000 3.000

x/d

TABLE D-7 Continued

90

Au/d= A/d= x/a: ”a:
3 .000 0.07:. 0.650 03851 02'0“
Uc(fps) = 90.915 T = 15.000 (averaging time) Condition: Vortical

y/d u/uc v/uc e u'/Uc w/vc uv/Ucz y C/T
1.250 0.008 0.021 68.976 0.008 0.013 0.000 0.000 3.066
1.166 0.005 0.027 79.369 0.021 0.026 0.001 0.001 3.400
1.083 0.000 0.086 89.890 0.072 0.075 -0.012 0.006 6.466
10000 0.006 0.135 87.287 0.103 00101 -0000! 00036 19.666
0.916 0.012 0.153 85.521 0.101 0.109 0.001 0.201 67.666
0.833 0.081 0.166 63.880 0.061 0.105 0.066 0.525 103.466
0.750 0.247 0.083 18.725 0.116 0.057 0.067 0.893 48.400
0.666 0.368 0.034 5.323 0.138 0.090 0.060 0.993 4.266
0.583 0.508 0.034 3.849 0.149 0.106 0.071 0.999 0.066
0.500 0.654 0.029 2.620 0.149 0.109 0.074 1.000 0.000
0.416 0.794 0.021 1.553 0.137 0.101 0.065 1.000 0.000
0.333 0.907 0.011 0.739 0.112 0.088 0.047 0.999 0.066
0.250 0.979 0.005 0.337 0.072 0.068 0.021 0.994 4.266
0.166 1.005 0.003 0.201 0.042 0.048 0.006 0.979 15.400
0.083 10009 “0.000 ”0.052 00033 00034 0.002 0.957 29.000
0.000 1.005 0.005 0.337 0.031 0.028 0.001 0.946 34.400
“0.083 1.007 0.008 0.477 0.036 0.026 00002 0.941 35.866
“0.166 10009 0.009 0.551 0.0‘3 00030 00002 00939 36.200
-0.249 1.004 0.010 0.590 0.061 0.043 -0.003 0.966 22.666
-0.333 0.946 0.007 0.426 0.096 0.077 -0.030 0.998 1.600
-0.416 0.814 -0.004 -0.292 0.127 0.102 -0.055 0.999 0.066
-0.499 0.637 -0.008 -0.784 0.142 0.109 -0.066 1.000 0.000
-00583 00460 ”00009 '101‘05 0.140 00100 "00062 0.999 0.066
'0.666 0.311 -0.004 -0.812 0.144 0.014 -0.035 0.986 9.266
-0.750 0.213 -0.013 -3.667 0.113 0.048 -0.017 0.792 76.333
-0.833 0.174 -0.015 -5.182 0.105 0.080 -0.009 0.448 96.533
'0.916 0.140 -0.026 -10.813 0.094 0.096 -0.026 0.083 37.400
-0.999 0.089 -0.014 -9.494 0.074 0.066 -0.013 0.008 7.666
‘10083 0.038 ”0.004 ”7.196 06042 06026 “0.001 OeOOI 3e‘66
'1.166 0.020 -0.005 -14.880 0.000 0.000 0.000 0.000 3.000
-1.250 0.020 -0.005 -14.880 0.000 0.000 0.000 0.000 3.000

TABLE D- 7 Continued

91

x/d Au/d = Ay/d = Xx/d = 1. /d =
4.500 0.074 0.050 0.051 0%046
Uc(fpa) - 90 .430 T - 15.000 (averaging time) Condition. Vortical
y/d U/Uc V/Uc 6 u'/Uc v'/UC uv/UCZ y C/T
-16500 OeOZO “00005 -140880 00000 OeOOO 0.000 0.000 30000
-l.400 0.037 -0.004 -7.236 0.043 0.029 -0.002 0.001 3.600
-1.300 0.082 0.014 9.802 0.070 0.065 0.019 0.007 6.400
-1.200 0.121 -0.047 -21.304 0.074 0.084 -0.052 0.032 15.000
-1.100 0.153 -0.052 ~18.823 0.095 0.094 -0.068 0.147 47.066
“1.000 00187 -0004? -140046 00106 0.088 “00051 00372 82.133
-0.900 0.216 -0.017 -4.491 0.125 0.083 -0.019 0.704 76.666
-0.800 0.297 ~0.016 -3.178 0.134 0.029 -0.035 0.943 21.066
’0.700 00374 ’0e014 “20243 00145 00067 '00053 0.993 3.600
”00600 0.492 ’00015 -10850 00144 00102 “0.066 00999 0.200
-0.500 0.614 -0.012 -1.164 0.148 0.109 -0.070 1.000 0.000
-00400 00757 -00008 -00658 00141 00108 “0.063 10000 0.000
-0.300 0.874 0.000 0.043 0.124 0.098 -0.050 0.999 0.066
-0.200 0.963 0.004 0.273 0.092 0.077 -0.024 0.998 1.666
’0.100 1.001 0.005 0.287 0.064 0.055 -0.002 0.987 9.600
“00000 1.005 0.003 0e214 00056 00052 OeOOS Oeqql 7.266
0.099 0.992 0.004 0.242 0.068 0.062 0.014 0.995 4.066
0.199 0.954 0.005 0.350 0.095 0.075 0.031 0.998 1.333
0.299 0.872 0.009 0.593 0.128 0.090 0.054 0.999 0.133
0.399 0.758 0.016 1.218 0.144 0.099 0.066 1.000 0.000
0.499 0.644 0.023 2.106 0.152 0.103 0.071 1.000 0.000
0.599 0.535 0.030 3.216 0.150 0.102 0.069 0.999 0.066
0.699 0.410 0.031 4.400 0.146 0.084 0.063 0.996 2.266
'0.800 00328 0.032 50581 00130 0.080 0.053 0.977 12.600
0.900 0.250 0.033 7.618 0.115 0.049 0.043 0.869 46.400
0.999 0.201 0.033 9.575 0.103 0.044 0.038 0.663 75.200
1.100 0.162 0.045 15.659 0.082 0.044 0.037 0.359 76.133
1.200 0.120 0.068 29.796 0.056 0.058 0.060 0.112 34.866
1.300 0.073 0.074 45.272 0.005 0.030 0.041 0.024 11.200
1.399 0.043 0.047 47.387 0.021 ’ 0.011 0.023 0.004 5.000
1.500 0.019 0.015 37.942 0.005 0.005 0.002 0.000 3.200

TA B LE D- 7 Continued

92

x/d .Au/d== .A /d== X /d== X /d:=
6.000 0.074 0.650 03851 0¥046
Uc(fpa) = 89.931 T = 15.000 (averaging time) Condition: Vortical

y/d u/Uc v/Uc e u'/Uc v'/UC uv/Ucz y C/T
1.750 0.023 0.022 44.404 0.009 0.013 0.004 0.001 3.733
1.633 0.029 0.047 57.935 0.027 0.039 0.026 0.005 4.666
1.516 0.044 0.090 63.757 0.059 0.049 0.046 0.036 11.933
1.400 0.058 0.120 64.280 0.072 0.070 0.050 0.068 23.666
1.283 0.104 0.123 49.783 0.062 0.065 0.106 0.193 46.733
1.166 0.174 0.097 29.285 0.078 0.005 0.107 0.471 70.800
1.050 0.238 0.051 12.208 0.117 0.043 0.062 0.749 58.200
0.933 0.294 0.032 6.204 0.126 0.054 0.051 0.919 30.066
0.816 0.384 0.036 5.425 0.148 0.068 0.066 0.989 5.266
0.700 0.480 0.035 4.222 0.147 0.099 0.068 0.999 0.533
0.583 0.582 0.032 3.204 0.154 0.104 0.071 1.000 0.000
0.466 0.692 0.029 2.439 0.157 0.105 0.074 1.000 0.000
0.350 0.796 0.022 1.627 0.150 0.102 0.068 0.999 0.066
0.233 0.895 0.018 1.158 0.137 0.097 0.055 0.999 0.400
0.116 0.969 0.013 0.769 0.120 0.090 0.038 0.999 0.800
0.000 1.000 0.011 0.650 0.104 0.087 0.007 0.998 1.533
-0.116 0.976 0.004 0.269 0.116 0.095 -0.019 0.999 0.733
-0.Z33 0.900 0.002 0.178 0.137 0.106 -0.050 0.999 0.266
'0.349 0.801 -0.004 -0.345 0.149 0.110 -0.062 1.000 0.000
'0.466 0.669 -0.007 -0.659 0.157 0.111 -0.073 1.000 0.000
-0.583 0.564 -0.013 -l.374 0.155 0.107 -0.074 0.999 0.333
‘00699 00451 ”00013 “10669 0.159 06075 -0e062 0.998 1.466
-0.816 0.364 -0.012 -1.958 0.159 0.023 -0.048 0.984 8.600
'00933 00282 -0.008 -10663 00139 00063 -00026 0090‘ 34e266
'1.050 0.231 '0.010 -2.684 0.123 0.066 -0.011 0.700 69.400
‘1.166 0.196 “0.026 '7.596 0.121 0.109 “0.029 0.424 71.066
-1.283 0.160 -0.008 -Z.945 0.108 0.109 ~0.000 0.177 42.666
-l.399 0.122 -0.023 -10.786 0.084 0.087 ~0.030 0.132 19.533
'1.516 06099 “0.030 ”170076 06076 00070 -00035 0.020 90333
°l.633 0.050 -0.019 -21.377 0.051 ' 0.044 -0.015 0.004 4.466
“1.750 00032 ‘00013 -220279 00042 00030 -00010 0.002 3e533

TAB LE D-7 Continued

93

X/d Au/d = Ay/d = kx/d = Xy/d =
8.000 0.074 0.050 0.051 0.046
Uc(fps) = 85.439 T = 15.000 (averaging time) Condition: Vortical
. — -z

y/d U/Uc v/Uc e u /UC v'/UC uv/Uc y C/T
’20000 00048 '00015 -170521 00051 00039 ’00014 00003 #0333
'10866 00085 ‘00028 ”180254 00068 00068 ”00038 00014 80333
-1.733 0.132 -0.018 -7.838 0.104 0.104 -0.022 0.033 13.466
-1.600 0.167 0.010 3.668 0.117 0.122 0.037 0.090 25.133
-1.466 0.197 -0.002 -0.849 0.137 0.140 0.027 0.220 46.066
-1.333 0.229 -0.022 -5.631 0.138 0.122 -0.020 0.433 62.400
'10200 00273 ’00025 ’50366 00145 00094 ’00033 00742 580133
“10066 00319 “0002‘ “40434 00153 00056 “00043 00877 “00200
'0.933 0.388 -0.015 -2.245 0.170 0.032 -0.055 0.971 13.466
“00800 00485 “00014 -1076? 00198 00079 “00070 00993 30733
-0.666 0.577 -0.016 -l.615 0.185 0.083 -0.087 0.999 0.600
-0.533 0.680 -0.013 -1.156 0.177 0.122 -0.091 1.000 0.000
-00400 00780 -00012 '00883 00175 00124 ‘00083 10000 00000
-0.266 0.879 -0.008 -0.549 0.170 0.127 “0.063 1.000 0.000
-0.133 0.963 -0.001 -0.106 0.163 0.125 -0.034 1.000 0.000
-00000 10000 00006 00303 00150 00122 00002 10000 00000
0.133 0.977 0.012 0.759 0.164 0.119 0.046 1.000 0.000
0.266 0.912 0.019 1.246 0.172 0.119 0.071 1.000 0.000
0.399 0.798 0.021 1.554 0.177 0.118 0.085 1.000 0.000
0.533 0.704 0.029 2.434 0.185 0.102 0.094 0.999 0.133
0.666 0.596 0.034 3.265 0.177 0.106 0.092 0.999 0.200
0.800 0.488 0.030 3.627 0.169 0.097 0.083 0.995 3.066
0.933 0.422 0.030 4.171 0.155 0.089 0.073 0.982 9.000
1.066 0.337 0.042 7.225 0.144 0.052 0.069 0.901 33.200
1.200 0.287 0.044 8.830 0.136 0.053 0.069 0.766 53.200
1.333 0.242 0.048 11.272 0.106 0.040 0.046 0.535 69.333
1.466 0.196 0.072 20.272 0.108 0.098 0.116 0.244 49.600
1.600 0.159 0.087 28.758 0.080 0.087 0.136 0.137 37.200
1.733 0.086 0.116 53.372 0.057 . 0.045 0.074 0.045 16.666
1.866 0.014 0.089 81.145 0.061 0.071 .0.017 0.012 6.800
2.000 -0.003 0.049 93.721 0.044 0.054 -0.006 0.003 4.533

TABLE D-8 DATA LISTING

94

x/d Au/d - Ay/d = 1.)/(1 - Xy/d '-
0.500 0.083 0.057 0.060 0.050
- .—. ‘ ' Condition: Vortical
Uc(fpa) — 91. 798 T 15.000 (averaging time)

y/d u/uc V/Uc e u'/Uc v'/UC {117/ng y C/T
00000 10103 “00034 -10791 00030 00014 "00000 00999 10133
0.050 1.099 -0.029 -1.547 0.019 0.015 0.000 0.999 0.866
0.100 1.097 -0.024 -1.278 0.006 0.014 0.000 0.999 0.666
0.150 1.093 -0.022 -1.167 0.014 0.015 0.000 0.999 0.533
0.200 1.091 -0.022 -l.205 0.019 0.017 -0.000 0.999 0.533
0.250 1.087 -0.024 -1.280 . 0.016 0.016 0.000 0.999 0.466
0.300 1.095 -0.034 -1.790 0.015 0.016 -0.000 0.999 0.600
0.350 1.088 -0.022 -1.203 0.026 0.021 -0.000 0.999 0.600
00400 10081 -0001? ’00913 00016 00035 00000 00999 00066
0.450 1.064 ‘-0.016 -0.908 0.055 0.078 0.017 1.000 0.000
0.500 0.698 0.024 1.991 0.125 0.121 0.080 1.000 0.000
0.550 0.226 0.013 3.307 0.088 0.080 0.032 1.000 0.000
0.600 0.058 -0.060 -45.916 0.028 0.026 ~0.006 0.940 32.733
0.650 0.035 0.030 41.277 0.013 0.013 0.001 0.164 110.000
0.700 0.017 0.017 45.035 0.009 0.009 0.000 -0.008 4.200
0.750 0.013 0.013 45.341 0.000 0.000 0.000 -0.002 3.000
0.000 1.087 -0.016 -0.876 0.014 0.014 0.000 0.998 0.666
’00050 10088 ”00019 ”10029 00018 0001‘ -00000 00998 10000
-0.100 1.084 -0.016 -0.867 0.022 0.013 0.000 0.998 0.666
90.150 1.082 -0.016 -0.855 0.010 0.013 0.000 0.999 0.466
-00200 10081 '00014 ’00749 00003 0001‘ -00000 00999 00468
“0.250 1.078 -0.014 -0.788 0.018 0.013 -0.000 0.999 0.666
-0.300 1.076 -0.016 -0.855 0.010 0.013 -0.000 0.999 0.800
-0.350 1.070 -0.017 -0.955 0.014 0.013 0.000 0.998 1.133
-O.400 1.072 -0.019 -1.016 0.020 0.014 0.000 0.999 0.466
-0.450 1.051 -0.030 -1.670 0.048 0.041 -0.008 1.000 0.000
”00500 00549 “00088 ”50076 00096 00103 “00084 10000 00000
-0.550 0.102 -0.058 -29.699 0.046 0.038 -0.003 0.999 1.066
-0.600 0.022 -0.045 -64.004 0.010 0.022 -0.001 0.072 56.133
~0.650 0.010 -0.016 -58.775 0.000 0.000 0.000 -0.002 3.000
-O.700 0.010 -0.016 -58.775 0.000 0.000 0.000 -0.002 3.000
-0.750 0.010 -0.016 ~58.775 0.000 0.000 0.000 -0.002 3.000

TAB LE D-8 Continued

95

X/d Au/d = A /d = x /d = x /d =
1.500 0.083 0.657 03660 oYoso
Uc(fpa) = 91.798 ‘1‘ = 15.000 (averaging time) Condition: Vortical
Y/d U/Uc v”Jo 6 u'/U¢ VVUC “V/Ucz Y C/T

-1.000 0.010 -0.016 -58.775 0.000 0.000 0.000 -0.002 3.000
-O.933 0.010 -0.016 -58.775 0.000 0.000 0.000 -0.002 3.000
-0.866 0.010 -0.016 -58.775 0.000 0.000 0.000 -0.002 3.000
“00800 00010 “00016 “580775 00000 00000 00000 “00002 30000
-O.733 0.026 -0.051 -62.705 0.022 0.043 -0.014 -0.009 9.266
-0.666 0.045 -0.083 -61.580 0.013 0.046 -0.016 0.386 143.600
-O.6OO 0.204 -0.023 -6.527 0.087 0.053 -0.014 0.998 2.866
“00533 00430 “00006 “00902 00122 00087 “00061 10000 00000
-O.466 0.716 0.011 0.893 0.121 0.102 -0.053 1.000 0.000
-O.400 0.972 0.031 1.833 0.078 0.066 -0.023 1.000 0.000
“00333 10022 00062 20405 0004‘ 00023 00000 00999 00533
“00266 10018 00064 20505 00027 00017 00000 00998 10000
-0.200 1.015 0.042 2.399 0.032 0.014 -0.000 0.998 1.400
“00133 10019 00069 20756 00021 00014 00000 00999 00333
-0.066 1.021 0.039 2.232 0.014 0.013 0.000 0.998 0.933
-0.000 1.022 0.037 2.075 0.022 0.014 0.000 0.999 1.133
0.066 1.022 0.037 2.091 0.009 0.015 0.000 0.998 0.933
0.133 1.026 0.037 2.079 0.022 0.017 0.000 0.998 1.066
0.199 1.030 0.037 2.106 0.006 0.021 0.000 0.999 0.666
0.266 1.027 0.038 2.126 0.022 0.032 0.000 0.999 0.666
0.333 1.020 0.041 2.336 0.030 0.054 0.004 0.999 0.333
0.400 0.981 0.042 2.489 0.076 0.085 0.033 1.000 0.000
0.466 0.814 0.053 3.728 0.127 0.114 0.075 1.000 0.000
0.533 0.567 0.064 6.494 0.142 0.125 0.086 1.000 0.000
0.600 0.350 0.049 7.992 0.135 0.102 0.072 1.000 0.000
0.666 0.166 0.026 9.178 0.098 0.042 0.030 0.945 41.666
0.733 0.100 0.029 16.501 0.072 0.040 0.021 0.371 133.800
0.800 0.054 0.040 36.838 0.040 0.005 0.020 0.005 14.000
00866 00019 00014 360391 00016 00005 00002 “00001 30333
00933 00015 00012 370866 00000 ' 00000 00000 “00002 30000
1.000 0.015 0.012 37.886 0.000 0.000 0.000 -0.002 3.000

TABLE D-B Continued

96

x/d Au/d = Ay/d = Xx/d = X /d =
3.000 0.033 0.051 0.060 32050
Uc(fp3) -.- 92.018 '1‘ -.-. 15.000 (averaging time) Condition: Vortical

y/d U/Uc W”. e u'/Uc v'/Uc 627/ng y C/T
1.250 0.015 0.012 37.886 0.000 0.000 0.000 -0.002 3.000
1.166 0.030 0.023 37.731 0.029 0.008 0.012 0.000 4.266
1.083 0.046 0.064 54.486 0.027 0.032 0.037 0.013 9.533
1.000 0.056 0.078 54.377 0.035 0.043 0.048 0.071 33.733
0.916 0.111 0.073 33.455 0.060 0.018 0.070 0.357 85.866
0.833 0.184 0.035 10.895 0.106 0.008 0.039 0.809 74.466
0.750 0.277 0.039 8.156 0.127 0.062 0.058 0.983 10.600
0.666 0.388 0.056 8.262 0.137 0.102 0.075 0.999 0.466
0.583 0.524 0.063 6.921 0.148 0.111 0.084 1.000 0.000
0.500 0.666 0.062 5.358 0.146 0.111 0.079 1.000 0.000
0.416 0.819 0.060 4.192 0.131 0.102 0.065 1.000 0.000
0.333 0.936 0.053 3.243 0.100 0.085 0.040 0.999 0.066
0.250 1.001 0.049 2.837 0.057 0.061 0.013 0.999 0.333
0.166 1.015 0.047 2.651 0.038 0.041 0.002 0.999 0.933
0.083 1.010 0.042 2.416 0.043 0.030 0.000 0.997 2.466
0.000 1.007 0.042 2.389 0.029 0.025 0.001 0.998 1.733
-0.083 1.011 0.048 2.739 0.042 0.026 0.001 0.998 1.333
-00166 10010 0.048 20725 00033 00029 00002 00998 1.066
-0.249 0.998 0.045 ‘ 2.633 0.066 0.046 -0.005 0.999 0.666
-0.333 0.938 0.036 2.244 0.099 0.079 -0.034 0.999 0.000
-00416 00796 00028 2.062 00132 00103 -0005? 10000 0.000
-0.499 0.607 0.017 1.628 0.145 0.107 -0.057 1.000 0.000
'0.583 0.449 0.004 0.580 0.140 0.096 -0.047 1.000 0.000
-0.666 0.297 -0.005 -1.065 0.139 0.021 -0.027 0.994 4.466
’0.750 0.197 -0.009 -2.617 0.110 0.051 “0.011 0.867 59.000
-0.833 0.133 -0.018 -8.006 0.085 0.056 -0.014 0.418 101.600
-O.916 0.102 -0.018 -10.245 0.075 0.054 -0.013 0.087 38.800
'0.999 00071 ‘00025 “190388 00057 00038 ‘00018 00015 10.133
-1.083 0.028 -0.009 -18.818 0.028 0.005 -0.003 -0.000 3.533
-1.166 0.018 -0.005 ~15.016 0.000 ' 0.000 0.000 -0.002 3.000
-l.250 0.018 -0.005 -15.016 0.000 0.000 0.000 -0.002 3.000

TABLE D-8 Continued

97

x/d Au/d - A /d = )‘x/d = Xy/d =
4.500 0.083 0.357 0.060 0.050
Uc(fpe) =92.255 T = 15.000 (averaging time) Condition: Vortical

y/d u/Uc v/Uc 6 u'/Uc w/uc uv/Uc2 y C/T
-l.500 0.025 -0.007 -15.985 0.022 0.008 -0.002 -0.001 3.400
-1.400 0.032 -0.009 ~15.701 0.038 0.029 -0.007 0.000 3.800
-1.300 0.072 -0.021 -16.951 0.062 0.045 -0.019 0.018 8.200
“10200 0.097 -00030 -110538 00071 00058 “0.028 0.058 22.000
~1.100 00119 “00036 -169879 00079 00063 “0.033 0.155 ‘30733
'1.000 0.145 -0.020 -8.046 0.090 0.073 -0.019 0.399 80.400
“0.900 00192 “00012 “30609 00115 00080 -00016 0.745 71.866
-0.800 0.260 -0.003 -0.855 0.130 0.051 -0.017 0.951 22.400
-0.700 0.361 -0.001 -0.187 0.149 0.041 -0.034 0.997 2.266
“00600 0.474 0.006 0.803 0.1‘3 00097‘ ’00049 0.999 0.066
'0.500 0.599 0.017 1.659 0.148 0.105 -0.057 1.000 0.000
“0.400 0.740 00028 20224 0014‘ 00107 “0.061 1.000 0.000
”00300 00867 0.037 20476 0.125 00097 ‘000‘9 00999 00000
-0.200 0.963 0.039 2.318 0.094 0.076 -0.026 0.999 0.266
“00100 1.000 0.043 20507 00065 0.055 ’00004 00999 00733
-0.000 10009 0.0‘7 20687 00049 000‘9 00003 0.998 0.133
0.099 1.000 0.042 2.428 0.063 0.059 0.011 0.998 0.933
0.199 0.969 0.045 2.663 0.093 0.075 0.029 0.999 0.200
0.299 0.890 0.049 3.185 0.123 0.091 0.051 1.000 0.000
0.399 0.790 0.058 4.236 0.140 0.100 0.065 1.000 0.000
0.499 0.655 0.057 4.982 0.151 0.108 0.081 1.000 0.000
0.599 0.538 0.060 6.373 0.152 0.108 0.086 1.000 0.000
0.699 0.422 0.050 6.828 0.143 0.101 0.079 0.999 0.533
0.800 0.321 0.042 7.494 0.135 0.075 0.066 0.990 6.200
0.900 0.249 0.038 8.758 0.115 0.061 0.047 0.934 29.733
0.999 0.176 0.042 13.683 0.097 0.023 0.040 0.687 74.933
1.100 0.143 0.043 17.036 0.081 0.047 0.035 0.406 76.600
1.200 0.100 0.049 26.285 0.064 0.052 0.043 0.166 47.400
1.300 0.062 0.060 44.332 0.016 0.024 0.034 0.032 14.066
1.399 0.025 0.031 50.919 0.008 ‘0.015 0.009 0.075 5.266
1.500 00013 00020 55.709 0.005 0.012 0.003 “00001 30333

TAB LE D-8 Continued

98

X/d Au/d = Ay/d -.- xx/d = x /d =
6.000 0.003 0.051 0.060 dZoso
Uc(fpe) = 91.554, T = 15.000 (averaging time) Condition: Vortical
y/d U/Uc v/Uc e u'/UC v'/Uc uv/Ucz y C/T
10750 06012 0.023 62.069 0.006 0.013 00003 “00001 30‘00
1.633 0.012 0.052 77.008 0.038 0.051 0.012 0.003 5.333
1.516 0.007 0.078 84.864 0.057 0.059 0.009 0.027 12.200
1.400 0.012 0.109 83.529 0.075 0.078 0.010 0.091 24.800
1.283 0.077 0.118 56.933 0.066 0.082 0.084 0.288 58.333
1.166 0.170 0.052 17.167 0.092 0.054 0.051 0.524 72.933
1.050 0.232 0.043 10.630 0.119 0.016 0.053 0.827 49.800
0.933 0.291 0.044 8.581 0.130 0.062 0.062 0.956 20.933
0.816 0.384 0.052 7.697 0.143 0.084 0.077 0.995 2.533
0.700 0.482 0.059 7.014 0.147 0.105 0.084 0.999 0.266
0.583 0.589 0.063 6.157 0.155 0.110 0.089 1.000 0.000
0.466 0.703 0.064 5.273 0.154 0.108 0.083 1.000 0.000
0.350 0.814 0.062 4.359 0.146 0.103 0.071 1.000 0.000
0.233 0.917 0.060 3.800 0.129 0.094 0.050 0.999 0.000
0.116 0.983 0.058 3.378 0.106 0.086 0.024 0.999 0.200
0.000 0.999 0.058 3.342 0.100 0.086 0.000 0.999 0.133
-0.116 0.958 0.052 3.111 0.118 0.094 -0.029 0.999 0.133
-00233 06875 00046 30009 0.141 00103 -00050 10000 00000
-003‘9 00769 0.035 26665 00153 00109 “00061 1.000 00000
-0.466 0.631 0.031 2.884 0.158 0.106 -0.060 1.000 0.000
-00583 0.529 00013 20016 0.152 06100 “00053 00999 0.066
-O.699 0.415 0.011 1.654 0.164 0.029 -0.035 0.997 1.933
”0.816 00330 “00001 “0.207 00145 00015 -0002? 06983 86533
-0.933 0.275 -0.004 -1.021 0.132 0.041 -0.018 0.927 26.666
-1.050 0.206 -0.011 -3.294 0.118 0.086 -0.016 0.729 64.800
-1.166 0.158 -0.018 -6.616 0.103 0.074 -0.020 0.402 71.066
“1.283 0.133 .00033 -140288 0.080 0.070 “0.033 00207 33.666
“1.399 00098 “00038 ”210619 00060 00048 -00030 0.073 23.266
'1.516 0.077 -0.039 -26.934 0.052 0.044 -0.033 0.019 10.000
-1.633 0.042 -0.020 ~26.209 0.038 ’ 0.027 -0.014 0.003 5.066
‘10750 0.023 .00010 ”240855 00013 06007 “0.002 -00000 3.533

TABLE D-8 Continued

99

x/d Au/d = Ay/d -.- xx/d = x /d =
10.000 0.003 0.057 0.000 01050
Uc(fpe) = 75.526 T = 15.000 (averaging time) Condition: Vortical

y/d U/Uc V/Uc e w/uc w/Uc uv/Ucz y C/T
2.500 0.018 0.031 59.060 0.009 0.016 0.004 0.000 3.666
2.333 0.026 0.041 57.498 0.010 0.035 0.022 0.004 4.933
2.166 0.007 0.077 84.261 0.068 0.076 0.008 0.009 6.133
2.000 -0.007 0.111 93.820 0.079 0.088 -0.007 0.022 11.466
1.833 -0.007 0.160 92.553 0.098 0.107 -0.021 0.132 32.666
1.666 0.074 0.182 67.812 0.084 0.123 0.078 0.286 53.200
1.500 0.244 0.066 15.251 0.128 0.079 0.095 0.508 64.066
1.333 0.319 0.053 9.513 0.148 0.018 0.084 0.810 47.533
1.166 0.393 0.047 6.843 0.159 0.077 0.090 0.943 20.533
1.000 0.489 0.057 6.713 0.180 0.085 0.120 0.986 5.866
0.833 0.587 0.061 6.023 0.194 0.115 0.139 0.998 1.133
0.666 0.693 0.067 5.569 0.190 0.136 0.132 0.999 0.133
0.500 0.820 0.072 5.071 0.192 0.137 0.118 0.999 0.000
0.333 0.924 0.072 4.458 0.192 0.138 0.091 1.000 0.000
0.166 0.981 0.061 3.588 0.186 0.140 0.053 1.000 0.000
0.000 0.998 0.052 2.997 0.181 0.140 0.007 1.000 0.000
“00166 0094‘ 0004‘ 2067‘ 00189 001‘0 “000‘3 10000 00000
-0.333 0.861 0.032 2.173 0.191 0.137 -0.068 0.999 0.066
“00‘99 00130 00021 10689 00206 00106 “0007‘ 00999 00133
“00666 00623 00017 10597 00189 00107 “00070 00999 00500
-0.833 0.525 0.007 0.834 0.208 0.064 -0.050 0.995 2.533
'“00999 00938 “00001 “00207 0019‘ 00069 “00093 00975 110‘00
“10166 00364 “00008 “10313 00162 00048 “00031 00913 200333
-1.333 0.286 -0.020 -4.099 0.154 0.078 -0.028 0.687 61.733
“10500 00251 “00042 “90659 00135 00103 “000‘9 00597 640000
-1.666 0.205 -0.055 -15.143 0.120 0.096 -0.069 0.305 54.666
“10033 00172 “000‘? “150279 00108 00090 “00051 00138 3‘0333
“10999 00118 “00000 “100661 00072 00072 “0004‘ 00055 150866
“20166 00060 “00010 “100230 00051 0.045 “00012 00009 70133
-2.333 0.050 -0-008 -9.402 0.047 ' 0.930,"-0.007 0.005 4.933
'2.500 0.043 -0.009 -12.007 0.050 0.040 -0.008 0.002 3.733

TABLE D-8 Continued

59.071

100

x/dl Au/d = A /d = x /d = x /d =
0.000 0.003 0.057 03000 01050
Uc(fpa) = 87.644 T = 15.000 (averaging time) Condition: Vortical
y/d u/Uc v/uc e u'/Uc v'/Uc uv/Ucz y C/T

“20100 00026 “00011 “230506 00019 00008 “00002 “00001 30333
“10960 00047 “00023 “260415 00050 00035 “00026 00005 50133
-1.820 0.063 -0.030 ~26.105 0.048 0.042 -0.027 0.009 6.733
“10680 00122 “00052 “230172 00074 00061 “00049 00054 180333
-1.540 0.158 -0.034 -12.467 0.102 0.090 -0.039 0.177 42.466
“10400 00186 “00036 “100961 00113 00081 “00039 00374 620733
“10260 00228 “00023 “50777 00128 00079 “00027 00728 470133
“10120 00276 “00012 “20639 00136 00063 “00023 00842 440866
“00980 00347 “00002 “00360 00162 00072 “00021 00961 160533
-0.840 0.434 0.003 0.424 0.177 0.015 -0.044 0.992 4.400
-0.700 0.531 0.009 1.041 0.181 0.068 -0.057 0.999 0.333
*0.560 0.635 0.017 1.602 0.173 0.116 -0.072 0.999 0.066
“00420 00750 00025 10969 00173 00120 “00066 10000 00000
-0.280 0.879 0.031 2.065 0.171 0.123 -0.058 1.000 0.000
“00140 00960 00041 20456 00162 00123 “00033 10000 00000
'0.000 0.991 0.048 2.776 0.158 0.122 0.006 1.000 0.000
0.139 0.979 0.058 3.402 0.160 0.119 0.043 1.000 0.000
0.279 0.900 0.060 3.847 0.174 0.120 0.083 1.000 0.000
0.419 0.807 0.066 4.737 0.178 0.122 0.101 1.000 0.000
0.559 0.679 0.063 5.331 0.178 0.123 0.112 0.999 0.000
0.699 0.573 0.061 6.097 0.170 0.120 0.111 0.999 0.333
0.839 0.467 0.054 6.682 0.168 0.097 0.104 0.995 2.400
0.979 0.379 0.045 6.792 0.155 0.083 0.087 0.981 9.266
1.119 0.315 0.038 6.938 0.132 0.054 0.061 0.943 19.400
1.260 0.247 0.037 8.491 0.120 0.053 0.048 0.761 54.933
1.399 0.204 0.044 12.194 _0.108 0.057 0.047 0.525 67.200
10540 00169 00046 150450 00100 00081 00053 00295 550533
1.679 0.113 0.070 31.635 0.062 0.057 0.068 0.090 24.800
1.820 0.078 0.065 39.937 0.034 0.040 0.044 0.029 12.133
1.959 0.030 0.035 49.646 0.012 0.009 0.014 0.006 5.333
2.100 0.016 0.027 0.008 0.020 0.006 0.000 3.666

TABLE D-9 DATA LISTING

101

x/d Au/d = Ay/d = xx/d = xy/d =

0.500 0.130 0.052 0.058 0.058

Uc(fp0) :70. 190 T = 15.000 (averaging time) Condition: Non-Vortical

——- -Z
1 1

y/d u/Uc v/Uc 6 u /Uc v /Uc uv/Uc y C/T
0.000 0.207 0.018 5.094 0.389 0.030 0.107 0.000 0.533
0.050 0.119 0.009 4.741 0.299 0.032 0.094 0.000 0.266
0.100 0.170 0.012 4.327 0.366 0.027 0.092 0.000 0.400
0.150 0.173 0.015 5.256 0.373 0.034 0.121 0.000 0.400
0.200 0.218 0.016 4.416 0.411 0.025 0.092 0.000 0.533
0.250 0.196 0.017 5.173 0.395 0.033 0.120 0.000 0.600
0.300 0.190 0.014 4.252 0.382 0.025 0.088 0.000 0.600
0.350 0.218 0.018 4.731 0.412 0.028 0.104 0.000 0.600
0.400 0.191 0.018 5.378 0.385 0.034 0.123 0.000 0.466
0.450 0.026 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
0.500 0.026 -0.002 '5.220 0.000 0.000 0.000 0.000 0.000
0.550 0.084 -0.024 -16.062 0.057 0.027 -0.003 0.003 3.200
0.650 0.035 -0.046 ~53.020 0.006 0.010 -0.000 0.996 5.733
0.700 0.019 -0.048 -68.065 0.002 0.006 -0.000 0.999 3.066
0.750 0.010 -0.046 -77.626 0.001 0.004 -0.000 1.000 3.000
0.000 0.146 0.011 4.463 0.339 0.028 0.094 0.000 0.400
“00050 00164 00012 40364 00352 00028 00069 00000 00400
“00100 00164 00011 40162 00352 00025 00083 00000 00400
“00150 00191 00017 50106 00383 00033 00113 00000 00533
“00200 00257 00022 40931 00429 00027 00100 00000 00733
“00250 00162 00014 50047 00346 00031 00104 00000 00600
-0.300 0.250 0.018 4.297 0.417 0.022 0.077 0.000 0.733
-0.350 0.187 0.017 5.345 0.374 0.033 0.116 0.000 0.533
‘0.400 0.182 0.015 4.816 0.364 0.029 0.099 0.000 0.466
'0.450 0.026- -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
'0.500 0.026 -0.002 ~5.220 0.000 0.000 0.000 0.000 0.000
-0.550 0.048 0.005 6.853 0.047 0.022 0.009 0.000 0.533
-0.600 0.082 0.029 19.749 0.020 0.019 0.001 0.425 190.533
-O.650 0.065 0.040 31.891 0.010 0.012 0.000 0.969 29.066
“00700 00040 00046 480609 00005 00009 00000 10000 30000
-0.750 0.044 0.057 52.660 0.004 0.005 0.000 1.000 3.000

x/d
1.500

Uc(fpa) = 70. 190

y/d

‘10000
“00933
-0.866
-0.800
“0.733
‘00666
“00600
“00533
“00466
’0.400
’00333
”00266
'00200
‘00133
-0.066
'00000
0.066
0.133
0.199
0.266
0.333
0.400
0.466
0.533
0.600
0.666
0.733
0.800
0.866
0.933
1.000

TAB LE D-9 Continued

.Au/H==
0.130
T = 150000
V/Uc a
0.050 62.815
0.058 70.786
0.067 70.683
0.073 69.043
0.093 59.784
0.076 36.486
0.090 34.630
“0.000 ’10839
”00002 “5.220
“00000 -0092“
0.011 2.343
0.021 3.408
0.022 3.301
0.017 3.989
0.016 3.332
0.018 4.793
0.018 2.499
0.012 4.209
0.019 4.143
0.007 3.235
0.010 4.248
0.004 4.791
-0.000 ’10568
“0.002 “‘0157
-0.027 -21.461
“00033 ‘150359
-0.021 ~17.423
-0.033 -32.662
-0.032 -41.840
-0.036 -50.254
-0.038 -56.776

tU/UE

0.003
0.003
0.004
0.004
0.021
0.034
0.070
0.023
0.000
0.127
0.437
0.472
0.482
0.428
0.440
0.404
0.495
0.354
0.445
0.321
0.326
0.158
0.000
0.029
0.069
0.043
0.035
0.018
0.009
0.003
0.003

10.2

(averaging time)

‘fl/UE

0.006
0.008
0.017
0.026
0.030
0.033
0.053
0.011
0.000
0.013
0.025
0.020
0.017
0.023
0.021
0.028
0.021
0.028
0.022
0.023
0.034
0.031
0.000
0.011
0.030
0.027
0.015
0.002
0.009
0.006
0.005

X /d==

x
0.058

Condition:

—-2
uv/UE

0.000
0.000
0.000
0.002
0.002
0.002
0.022
0.002
0.000
0.013
0.009
0.020
0.010
0.064
0.040
0.103
-0.030
0.087
0.076
0.062
0.074
0.050
0.000
-0000:
"00014
0.002
”00001
'00002
”00001
’00000
-0.000

224.1:

Non-Vortical

Y

1.000
0.999
0.941
0.852
0.568
0.134
0.007
0.000
0.000
0.000
0.000
0.001
0.001
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.003
0.198
0.495
0.962
0.850
0.999
1.000

C/T

3.000
3.133
8.066
44.333

113.533

65.333
6.000
0.066
0.000
0.066
0.800
1.200
1.400
0.733
0.733
0.666
1.266
0.400
0.733
0.400~
0.400
0.066
0.000
0.066
2.733

88.600

65.533

19.933
3.733
3.133
3.000

TABLE D-9 Continued

103

x/d Au/d = Ay/d = Xx/d = Xy/d =

3.000 0.130 0.052 0.058 0.058

Uc(fpg) .-. 70 .310 T = 15,000 (averaging time) Condition: Non-Vortical

v -——. -Z
I I

y/d U/Uc v/Uc 6 u /Uc v /Uc nv/Uc Y C/T
1.250 0.022 -0.038 -59.818 0.002 0.006 -0.000 0.999 3.400
1.166 0.017 -0.041 -67.537 0.006 0.012 -0.001 0.908 4.133
1.083 0.030 -0.052 -60.105 0.001 0.016 -0.003 0.969 14.066
1.000 0.040 -0.055 -53.717 0.017 0.019 -0.004 0.907 33.000
0.916 0.083 -0.053 -32.467 0.037 0.017 -0.004 0.673 81.933
0.833 0.119 -0.043 -19.992 0.047 0.021 -0.000 0.338 87.066
0.750 0.145 -0.045 -17.564 0.052 0.032 0.002 0.097 41.933
0.666 0.168 -0.048 -16.122 0.072 0.040 -0.007 0.010 6.800
00583 0.045 “00010 ‘120823 00068 0.017 ’00005 00000 00266
00500 00025 -0000? ‘160264 00000 00000 00000 0.000 00000
0.416 0.049 -0.001 -1.614 0.159 0.039 0.062 0.000 0.066
0.333 0.049 -0.001 -1.935 0.157 0.037 0.059 0.000 0.066
0.250 0.146 0.010 4.069 0.337 0.044 0.138 0.000 0.400
0.166 0.124 0.006 3.140 0.311 0.040 0.120 0.000 0.333
0.083 0.074 0.000 0.017 0.227 0.033 0.072 0.000 0.200
0.000 0.317 0.018 3.407 0.463 0.022 0.070 0.000 0.866
“00083 00172 00006 20106 00367 0.025 0.082 0.000 0.466
“00166 00310 00010 1.963 00455 00025 0.009 00000 00866
-0.249 0.113 0.000 0.334 0.281 0.020 0.055 0.000 0.266
'0.333 0.025 -0.007 -16.264 0.000 0.000 0.000 0.000 0.000
“00‘16 00025 “00007 “160264 00000 00000 00000 00000 0.000
-00499 0.037 ’0000‘ '6052‘ 06055 0.017 00008 0.000 0.133
'0.583 0.088 0.003 1.970 0.100 0.028 0.014 0.001 1.200
-0.666 0.150 0.065 23.592 0.079 0.042 0.015 0.012 8.066
-0.750 0.128 0.067 27.610 0.043 0.031 0.004 0.117 48.133
-0.833 0.096 0.053 29.151 0.041 0.028 0.006 0.348 76.333
-0.916 0.083 0.050 31.152 0.033 0.018 0.007 0.674 73.000
’0.999 0.063 00040 320606 00025 00008 0.007 00877 37.866
-1.083 0.045 0.043 43.621 0.010 0.011 0.003 0.978 11.066
-10166 00°32 00050 570223 00001 00012 00001 0.996 50000
“1.250 0.015 0.045 10.107 0.003 0.008 00000 0.999 30333

TAB LE D-9 Continued

104

x/d Au/d - Ay/d - xx/d - xy/d =

4.500 0.130 0.052 0.058 0.058

UCHPB) =7o.57l. T = 15,000 (averaging time) Condition: Non-Vortical

t | —'- '2

y/d U/Uc v/Uc e u /Uc v /Uc uv/Uc y C/T
“1.500 0.009 0.049 79.435 0.008 0.012 0.000 0.997 3.733
“1.400 0.004 00057 850320 0001‘ 00020 0.000 0.990 60133
'-1.300 0.011 0.066 80.070 0.023 0.032 0.001 0.955 17.000
-1.200 0.018 0.077 76.434 0.020 0.037 0.002 0.880 36.266
-1.100 0.041 0.090 65.503 0.023 0.043 0.009 0.747 58.200
-1.000 0.096 0.075 38.163 0.037 0.029 0.009 0.505 76.933
'0.900 0.114 0.050 23.639 0.056 0.028 0.011 0.255 63.066
-O.800 00149 00068 2‘0“63 00047 0.035 0.002 00098 380733
'06700 00177 00080 240518 00059 00043 0.003 00020 11.600
-0.600 0.078 0.042 28.151 0.089 0.056 0.043 0.001 1.400
-0.500 0.035 0.015 23.260 0.042 0.027 0.010 0.000 0.133
‘0.400 0.060 0.007 7.127 0.165 0.010 -0.016 0.000 0.133
-0.300 0.025 0.009 19.971 0.000 0.000 0.000 0.000 0.000
-0.200 0.227 0.020 5.105 0.393 0.024 0.045 0.000 0.733
-0.100 0.642 0.032 2.902 0.446 0.038 0.046 0.003 2.933
-0.000 0.384 0.020 2.994 0.499 0.032 0.006 0.001 1.000
0.099 0.240 0.022 5.337 0.427 0.036 0.111 0.000 0.666
0.199 0.101 0.015 8.694 0.277 0.055 0.152 0.000 0.200
0.299 0.027 -0.000 -1.548 0.000 0.000 0.000 0.000 0.000
0.399 0.035 -0.000 -0.961 0.054 0.002 0.000 0.000 0.066
0.499 0.036 -0.000 -0.141 0.062 0.005 0.002 0.000 0.066
00599 00098 “00013 -70771 00111 00035 “0.016 00001 1.400
00699 00183 -00022 “7.091 00096 0.044 “0.002 00012 70333
00800 0016“ -0006“ -210259 00061 0.036 0.001 00078 326866
00900 0.145 -000‘8 -180477 00052 00031 00002 0.211 64.133
0.999 0011‘ ’00033 -160353 06053 0.024 ”0.001 00‘27 750‘66
1.100 0.101 -0.019 -10.656 0.044 0.013 0.000 0.750 60.533
1.200 0.075 -0.048 -32.795 0.035 0.006 -0.009 0.851 43.866
1.300 000‘2 -00045 “‘60909 0.016 0.012 ”00005 0.969 1‘0‘00
1.399 0.031 -0.039 -51.363 0.009 0.011 -0.003 0.891 7.000
1.500 00023 -000“3 '610567 00002 0.011 “0.001 0.996 4.400

TAB LE D-9 Continued

105

x/d An/d = Ay/d = kx/d = Xy/d -

6.000 0.130 0.052 0.058 0.058

Uc(fpe) = 68 .407 T = 15.000 (averaging time) Condition: Non-Vortical

y/d U/Uc v/Uc e u'/Uc v'/Uc uv/Ucz y C/T
10750 00023 “00046 -630583 00008 00015 “00002 00899 40733
10633 00026 “00052 “630831 00007 00019 -00004 00922 50666
1.516 0.042 -0.054 -52.539 0.014 0.018 -0.006 0.970 12.533
1.400 0.075 -0.059 ~38.313 0.035 0.016 -0.012 0.882 36.266
1.283 0.108 -0.042 -21.377 0.049 0.002 -0.004 0.778 55.533
10166 00138 -0002? -1100‘5 00057 00012 -00000 00586 730800
1.050 0.154 -0.033 -12.188 0.057 0.030 0.002 0.366 72.133
00933 00168 “00049 “160402 00076 00038 -00002 00135 420533
0.816 0.207 -0.059 -15.877 0.074 0.044 0.002 0.052 24.000
00700 00207 ”00071 “190081 00102 00054 “00026 00012 70333
0.583 0.127 -0.030 -13.516 0.150 0.051 -0.030 0.001 1.200
0.466 0.066 -0.007 -6.863 0.143 0.026 0.020 0.000 0.200
00350 00061 '00008 -80233 00162 00023 00022 00000 00133
0.233 0.085 -0.002 -1.364 0.264 0.041 0.104 0.000 0.133
0.116 0.136 0.005 2.272 0.341 0.047 0.157 0.000 0.266
00000 00056 “00005 ’50084 00189 00039 00073 00000 00066
-0.116 0.057 -0.008 -8.786 0.191 0.014 0.025 0.000 0.066
-0.233 0.028 -0.011 -21.363 0.000 0.000 0.000 0.000 0.000
-0.349 0.028 -0.011 ~21.363 0.000 0.000 0.000 0.000 0.000
-O.466 0.043 -0.007 -10.100 0.070 0.016 0.011 0.000 0.200
-0.583 0.170 0.010 3.546 0.167 0.038 0.027 0.002 1.666
-0.699 0.079 0.036 24.554 0.104 0.047 0.038 0.001 0.866
‘00816 00197 00072 2000‘2 00072 00037 00005 00062 270800
“00933 00166 00060 190806 00055 00032 0000‘ 0017‘ ‘90533
-1.050 0.145 0.053 20.068 0.055 0.025 0.007 0.375 72.200
-1.166 0.117 0.033 16.149 0.056 0.009 0.009 0.594 62.000
-1.283 0.111 0.026 13.402 0.051 0.026, 0.009 0.789 53.066
-1.399 0.076 0.031 22.291 0.036 0.022 0.009 0.949 17.866
-10516 00049 00042 «00533 00016 00010 00005 00981 90000
'10633 00036 00043 50.045 00002 00013 00003 00996 40‘00
-1.750 0.034 0.041 49.759 0.007 0.012 0.001 0.742 3.000

x/d
8.000

Uc(fp3) =620270

y/d

-20000
-10866
-10733
-10600
-10466
-10333
”10200
“10066
-0.933
“00800
-00666
-00533
-00400
-00266
”00133
-00000
0.133
0.266
0.399
0.533
0.666
0.800
0.933
1.066
1.200
1.333
1.466
1.600
1.733
1.866
2.000

TABLE D-9 Continued

All/d = A /d =
0.130 0.652
T = 15-000 (averaging time)
\r/Uc 9 w/uc v'/Uc
0.059 61.648 0.011 0.020
0.070 69.502 0.020 0.028
0.093 80.049 0.032 0.045
0.108 68.647 0.031 0.056
0.105 49.103 0.031 0.048
0.063 24.625 0.071 0.023
0.047 15.956 0.075 0.002
0.051 13.884 0.071 0.036
0.076 18.177 0.072 0.047
0.106 23.075 0.080 0.052
0.083 18.908 0.157 0.064
0.042 19.888 0.168 0.072
0.011 6.738 0.212 0.051
0.007 7.178 0.165 0.010
0.009 10.684 0.106 0.021
0.006 10.280 0.000 0.000
0.006 10.280 0.000 0.000
0.004 4.545 0.083 0.011
0.005 3.952 0.118 0.016
0.002 1.795 0.130 0.028
-0.040 -10.253 0.159 0.056
'00096 ”180625 00107 0005‘
-00070 '160610 00091 00047
‘00037 -140‘28 0010‘ 000‘2
-0.037 -11.099 0.072 0.023
“00023 “80257 00064 00027
-0.019 -8.413 0.063 0.023
-0.087 ~41.461 0.047 0.033
“00066 “#70749 0002‘ 00022
.0005? “#80894 00017 00015
-0.049 -51.032 0.009 0.010

106

ofi'b/sde =

Condition:

-—- -2
uv/ Uc

0.003
0.004
0.002
0.012
0.024
0.039
0.015
0.002
0.002
0.005
0.052
0.091
'00011
0.010
0.022
0.000
0.000
-0.008
“00006
“0001‘
’00053
0.000
-00003
”00016
0.002
0.003
0.000
"00019
“00013
”00008
‘00004

x/d
o¥osa

Non-Vortical

7

0.995
0.991
0.962
0.878
0.778
0.612
0.460
0.281
0.121
0.051
0.009
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.005
0.022
0.083
0.123
0.387
0.670
0.834
0.783
0.959
0.980
0.996

C/‘I‘

5.333
5.866
14.066
33.400
50.400
58.466
63.133
67.800
42.333
21.533
5.400
0.733
0.333
0.066
0.066
0.000
0.000
0.133
0.333
0.466
3.533
11.266
32.600
34.400
68.666
65.933
43.933
42.133
15.400
9.133
4.600

TABLE D-9 Continued

107

x/d Au/d = Ay/d = kx/d = 1. /d =

10.000 0.130 0.052 -0.058 0.058

Uc(fpa) = 520270 T = 150000 (averaging time) Condition: Non-Vortical

——— -Z

y/d U/Uc V/Uc 9 u'/Uc v'/Uc uv/Uc y C/‘I‘
20500 00047 “00050 ‘070087 00007 00007 “00002 00999 30066
2.333 0.054 -0.048 -41.437 0.012 0.005 -0.003 0.999 3.400
2.166 0.069 -0.049 ~35.411 0.029 0.015 -0.009 0.915 5.400
2.000 0.097 -0.052 -28.212 0.049 0.026 -0.017 0.967 14.200
10833 00137 '00032 "130381 00067 00036 “00007 0092‘ 260333
1.666 0.163 -0.028 -9.866 0.078 0.031 '0.001 0.847 40.666
10500 00182 .00026 “80218 00081 00025 00003 00723 550666
1.333 0.231 -0.041 -10.175 0.082 0.042 0.008 0.498 76.000
1.166 0.255 -0.053 -ll.731 0.090 0.044 0.005 0.287 65.800
10000 00300 “00074 “130865 00099 00061 00011 00130 450666
0.833 0.336 -0.094 ~15.770 0.129 0.063 0.003 0.029 14.933
0.666 0.306 -0.081 -14.818 0.195 0.088 -0.048 0.007 4.666
0.500 0.219 -0.042 ~11.024 0.221 0.070 '0.078 0.002 1.600
0.333 0.126 -0.018 -8.371 0.212 0.045 -0.016 0.000 0.533
0.166 0.076 -0.013 -9.782 0.134 0.029 -0.013 0.000 0.200
00000 00092 “00011 -7030? 00217 00031 00020 00000 00200
-0.166 0.074 -0.002 -1.929 0.155 0.044 0.064 0.000 0.200
-0.333 0.213 0.028 7.650 0.243 0.069 0.106 0.001 1.200
‘00499 00221 00030 709‘2 00231 00066 00103 00002 10666
'0.666 0.302 0.083 15.396 0.195 0.035 0.077 0.011 6.533
-O.833 0.322 0.101 17.547 0.107 0.066 -0.004 0.038 17.133
-0.999 0.284 0.072 14.292 0.087 0.053 0.000 0.158 47.333
-l.l66 0.247 0.064 14.635 0.082 0.049 0.002 0.325 68.666
-1.333 0.224 0.046 11.750 0.083 0.028 0.007 0.500 76.066
-1.500 0.183 0.035 10.924 0.089 0.059 0.023 0.699 58.866
~1.666 0.163 0.028 10.002 0.083 0.055 0.021 0.829 40.266
“10833 0012‘ 00031 140148 00068 00055 00022 00943 200733
-10999 00105 00026 130976 00052 00035 00011 00980 90933-
‘20166 00084 00032 210034 00036 00029 00010 00990 70133
~2.333 0.069 0.042 31.419 0.020 0.011 0.006 0.996 4.333
'2.500 0.050 0.048 43.920 0.005 0.006 0.002 0.999 3.133

x/d
0.500

Uc(fpg) = 86. 983

v/d

0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750

0.000
“00050
“00100
“00150
“00200
“00250
“00300
“00350
'0.400
“00450
“00500
“00550
“00600
“00650
“00700
“00750

TAJILEKD-lOILATAsIJSTENG}

Au/d =

0.140

T = 150000

v/Uc 9
0.003 5.032
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.003 4.755
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 3.911
-0.033 -35.920
-0.056 -73.777
“00042 “870‘31
-0.052 -92.198
0.001 4.534
0.002 4.449
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.003 5.343
0.001 4.534
0.001 4.534
0.002 5.396
0.027 28.458
0.043 43.622
0.047 44.089
0.049 59.766

.A /d==

Y

0.093

0.124
0.000
0.000
0.000
0.000
0.117
0.000
0.000
0.000
0.000
0.000
0.006
0.021
0.006
0.003
0.003

0.000
0.115
0.000
0.000
0.000
0.000
0.000
0.000
0.116
0.000
0.000
0.014
0.021
0.015
0.007
0.005

108

(averaging time)

tfl/UE

0.012
0.000
0.000
0.000
0.000
0.010
0.000
0.000
0.000
0.000
0.000
0.002
0.020
0.018
0.017
0.008

0.000
0.008
0.000
0.000
0.000
0.000
0.000
0.000
0.013
0.000
0.000
0.004
0.016
0.015
0.008
0.006

Condition:

-—— -Z
v'/Uc uv/Uc

0.015
0.000
0.000
0.000
0.000
0.012
0.000
0.000
0.000
0.000
0.000

“00000
“00003
“00000
“00000

0.000

0.000
0.009
0.000
0.000
0.000
0.000
0.000
0.000
0.015
0.000
0.000
0.000
0.002
0.001
0.000
0.000

Xy/a:=
0.065

Non-Vortical

Y

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.123
0.736
0.590
0.999

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.118
0.677
0.997
0.999

C/T

0.066
0.000
0.000
0.000
0.000
0.066
0.000
0.000
0.000
0.000
0.000
0.066

70.733
167.933
10.466

3.533

0.000
0.066
0.000
0.000
0.000
0.000
0.000
0.000
0.066
0.000
0.000
0.133

83.800
154.400

7.400
3.000

x/d
1.500

UCHPE) = 86.983

y/d

“10000
“00933
“00866
“00800
“00733
“00666
-O.6OO
-O.533
“00466
“00400
“00333
“00266
“00200
“00133
-0.066
-0.000
0.066
0.133
0.199
0.266
0.333
0.400
0.466
0.533
0.600
0.666
0.733
0.800
0.866
0.933
1.000

U/CQ

0.025
0.015
0.018
0.034
0.060
0.079
0.039
0.020
0.020
0.020
0.032
0.020
0.037
0.023
0.023
0.037
0.023
0.037
0.023
0.023
0.036
0.023
0.023
0.023
0.032
0.080
0.060
0.019
0.008
0.007
0.000

TABLE D- l 0 Continued

Au/d ..
0.140
T = 15.000
'V/UE (3
0.044 60.096
0.054 73.671
0.059 72.861
0.063 61.579
0.055 42.237
0.038 25.803
0.019 26.390
0.010 27.634
0.010 27.634
0.010 27.634
0.011 19.900
0.010 27.634
0.003 4.790
0.001 4.534
0.001 4.534
0.003 4.790
0.001 4.534
0.003 5.516
0.002 5.952
0.002 5.952
0.003 5.833
0.002 5.952
0.002 5.952
0.002 5.952
0.000 1.220
“00046 “300229
-0.058 ~44.153
“00069 “680373
-0.059 -82.275
-0.050 -81.580
-0.038 ~89.738

A, =
Y/d
0.093

tfl/Ué

0.005
0.004
0.006
0.013
0.024
0.042
0.041
0.000
0.000
0.000
0.104
0.000
0.120
0.000
0.000
0.122
0.000
0.125
0.000
0.000
0.119
0.000
0.000
0.000
0.043
0.049
0.028
0.011
0.005
0.001
0.001

109

(ave raging time)

\fl/UE

0.007
0.009
0.014
0.019
0.024
0.028
0.024
0.000
0.000
0.000
0.010
0.000
0.011
0.000
0.000
0.011
0.000
0.010
0.000
0.000
0.011
0.000
0.000
0.000
0.011
0.035
0.028
0.028
0.018
0.011
0.013

Condition:

-—— -2
uv/Ué

0.000
0.000
0.000
0.001
0.003
0.007
0.007
0.000
0.000
0.000
0.009
0.000
0.013
0.000
0.000
0.013
0.000
0.013
0.000
0.000
0.013
0.000
0.000
0.000
“00002
“00012
“00005
“00002
“00000
-0.000
0.000

0¥065

Non-Vortical

Y

0.999
0.998
0.982
0.846
0.372
0.064
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
“00000
0.000
“00000
0.000
0.000
-0.000
0.000
0.000
0.000
0.000
0.000
0.020
0.255
0.398
0.956
0.995
0.585

C/T'

3.000
3.800
13.266
67.133

110.266

39.533
1.000
0.000
0.000
0.000
0.066
0.000
0.066
0.000
0.000
0.066
0.000
0.066
0.000
0.000
0.066
0.000
0.000
0.000
0.266

17.400

96.733

51.400

24.666
5.733
2.000

y/ d

1.250
1.166
1.083
1.000
0.916
0.833
0.750
0.666
0.583
0.500
0.416
0.333
0.250
0.166
0.083
0.000
’00083
-00166
“00249
'00333
'00‘16
-00499
-00583
“00666
“00750
-00833
”0.916
'0.999
“10083
“10166
-10250

x/d
3.000

Uc(fpa) = 86 .400

TABLE D- 10 Continued

Au/d -

0.140

T = 15.000

v/Uc 6
-0.045 -87.913
’00050 ’86.613
-0.060 -83.363
-0.069 -75.781
-0.075 -56.655
-0.063 -61.393
-0.059 ~36.322
‘00027 "0034‘
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.003 4.672
0.003 5.188
0.001 4.534
0.002 6.003
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.001 4.534
0.023 25.590
0.049 28.994
0.039 25.721
0.045 32.884
0.038 34.100
0.034 35.875
0.031 35.648
0.036 66.828

Ay/d =
0.093

tU/U£

0.007
0.008
0.008
0.009
0.024
0.039
0.058
0.042
0.000
0.000
0.000
0.000
0.000
0.000
0.130
0.119
0.000
0.116
0.000
0.000
0.000
0.000
0.000
0.055
0.050
0.040
0.027
0.021
0.015
0.010
0.003

(averaging time)

Condition:

— -z
v'/Uc uv/UC

0.012
0.016
0.020
0.023
0.030
0.033
0.044
0.032
0.000
0.000
0.000
0.000
0.000
0.000
0.011
0.013
0.000
0.007
0.000
0.000
0.000
0.000
0.000
0.027
0.033
0.025
0.019
0.012
0.008
00004
00011

0.000
-0.000
“0.000
-00001
“0.004
’00009
-0.019
'00013

0.000

0.000

0.000

0.000

0.000

0.000

0.016

0.015

0.000

0.007

0.000

0.000

0.000

0.000

0.000

0.012

0.010

0.005

0.003

0.003

0.002

0.001

0.000

d,=
xy/

0.065

Non-Vortical

Y

0.993
0.888
0.886
0.723
0.378
0.121
0.014
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
.00000
0.000
“0.000
0.000
0.000
0.000
-00000
0.000
0.052
0.189
0.522
0.807
0.924
0.984
0.659

C/T

6.133
10.000
30.466
61.733
83.666
46.666

9.466

0.666

0.000

0.000

0.000

0.000

0.000

0.000

0.066

0.066

0.000

0.066

0.000

0.000

0.000

0.000

0.000

1.400
24.266
61.000
82.466
51.800
24.600

7.800

3.866

TAB LE D-10 Continued

111

x/d Au/d = A /d = xx/d = x /d =

4.500 0.140 03693 0.085 dKObs

Uc(fpa) = 86.014 T = 15.000 (averaging time) Condition: Non-Vortical

y/d u/uc v/urc e w/uc w/uc uv/Ucz v c/T
'1.500 0.019 0.045 66.751 0.000 0.010 0.000 0.994 4.600
“1.400 00018 0.048 690419 00007 0.014 0.001 0.973 10.133
“1.300 00032 0.050 57.492 0.006 00018 0.004 00933 21.733
-1.200 0.045 0.053 49.671 0.017 0.019 0.004 0.835 40.266
‘1.100 0.056 0.044 38.337 0.033 0.023 0.010 0.377 50.800
”1.000 00091 00041 2‘0462 00038 0.018 0.005 0.344 67.000
‘0.900 0.095 0.045 25.499 0.048 0.028 0.007 0.147 45.600
-0.800 0.102 0.056 28.850 0.059 0.034 0.014 0.035 15.466
-O.700 0.051 0.027 28.385 0.063 0.032 0.016 0.001 1.333
-0.600 0.028 0.020 36.356 0.037 0.024 0.008 0.000 0.333
-0.500 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
-00400 00019 00014 370392 00000 00000 00000 0.000 00000
-0.300 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
-0.200 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
-0.100 0.030 0.015 27.043 0.101 0.010 0.009 0.000 0.066
-0.000 0.044 0.016 20.879 0.152 0.014 0.020 0.000 0.133
0.099 0.032 0.016 27.082 0.113 0.016 0.018 0.000 0.066
0.199 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
0.299 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
0.399 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
0.499 0.019 0.014 37.392 0.000 0.000 0.000 0.000 0.000
0.599 0.019 0.014 37.392 0.000 0.000 0.000 -0.000 0.000
0.699 0.062 0.023 20.678 0.078 0.022 0.011 0.001 1.200
0.800 0.097 -0.054 ~29.470 0.066 0.042 -0.019 0.015 8.733
00900 0.099 -00055 “29027‘ 0.056 00036 “0.012 0.070 27.266
0.999 0.093 -0.048 -27039‘ 0.047 00029 “0.007 0.183 52.933
1.100 0.076 -0.054 -35.860 0.032 0.021 -0.004 0.467 66.400
1.200 00056 “00059 -960093 00023 00021 ’0000‘ 0.700 560‘00
1.300 0.038 '0.056 -55.830 0.012 0.020 -0.003 0.866 35.266
1.399 0.011 -0.052 -77.180 0.011 0.019 -0.001 0.939 12.666
1.500 0.012 -0.046 -75.235 0.008 0.014 -0.000 0.990 6.333

TABLE D-lO Continued

0.001

112

x/d Au/d = Ay/d = xx/d = Xy/d =

6.000 0.140 0.093 0.085 0.065

Uc(fpg) = 83 .088 '1‘ = 15.000 (averaging time) Condition: Non-Vortical

-—— -Z

Y/d U/Uc V/Uc 8 u'/Uc v'/Uc uv/Uc Y C/T
1.875 0.012 -0.047 ~75.256 0.007 0.011 -0.000 0.998 3.533
1.750 0.014 -0.055 -75.349 0.008 0.016 -0.000 0.986 7.266
1.625 0.013 -0.058 -77.387 0.010 0.022 -0.001 0.912 11.866
1.500 0.020 -0.069 -73.371 0.014 0.027 -0.002 0.890 28.800
1.375 0.055 -0.074 -53.467 0.016 0.027 -0.007 0.746 52.466
1.250 0.089 -00061 ’340472 00041 00027 -00007 0.446 62.000
1.125 0.097 -0.070 -35.963 0.045 0.031 -0.008 0.325 62.866
1.000 0.124 -0.065 ~27.543 0.068 0.040 -0.015 0.065 27.133
0.875 0.092 -0.048 -27.625 0.082 0.046 -0.031 0.006 4.666
0.750 0.063 -0.032 ~27.362 0.078 0.042 -0.030 0.002 1.266
0.625 0.027 -0.013 -26.022 0.028 0.012 -0.003 0.000 0.066
00500 00024 “00011 ‘260326 00000 00000 0.000 ‘00000 0.000
00375 0.024 “00011 ‘260326 00000 00000 0.000 00000 0.000
0.250 0.024 -0.011 -26.326 0.000 0.000 0.000 0.000 0.000
00125 0002“ ’00011 “260326 00000 00000 00000 00000 0.000
0.000 0.039 -0.013 -18.257 0.136 0.010 -0.014 0.000 0.066
-00125 00024 “00011 -260326 06000 0.000 0.000 0.000 0.000
-0.250 0.024 -0.011 ~26.326 0.000 0.000 0.000 0.000 0.000
-0.375 0.024 -0.011 -26.326 0.000 0.000 0.000 0.000 0.000
'0.500 0.024 -0.011 -26.326 0.000 0.000 0.000 0.000 0.000
-00625 000‘4 0.006 70963 00053 00016 00006 0.000 00533
-00750 0.115 00052 240239 00091 00048 00030 0.010 50066
”00875 00121 0.058 25.633 0.068 00039 00014 0.038 16.466
'1.000 0.117 0.051 23.418 0.053 0.031 0.007 0.179 48.466
-10125 00096 00042 230798 00043 0.023 00005 00‘29 60.600
-l.250 00091 00037 220097 00037 00004 0.005 0.643 58.333
“1.375 0.077 0.032 22.560 0.031 0.001 0.004 0.835 37.533
”1.500 00060 00027 2‘0592 0.024 0.011 0.003 0.936 17‘000
-1.625 0.040 0.038 43.730 0.010 0.003 0.002 0.986 6.933
”1.750 0002‘ 00033 540072 00007 00010 00001 0.610 3.000
‘10875 00020 0.040 62.999 00005 00000 0.999 30133

TABLE D-10 Continued

113

X/d All/d = A /d = x /d = x /d g

a .000 0.140 03693 03‘085 oYObs

Uc(fpa) = 740334 T = 150000 (averaging time) Condition: Non-Vortical

y/d U/Uc v/uc e uo/Uc w/Uc uV/UCZ y C/T
-2.200 0.020 0.050 67.360 0.000 0.007 0.000 0.999 3.000
“2.053 00022 00052 660708 00008 0.017 00002 0.827 40466
-1.906 0.033 0.066 63.489 0.014 0.025 0.005 0.973 10.400
-10760 0.053 00063 490736 00017 00023 0.010 0.882 17.933
“1.613 0.074 0.038 27.405 0.045 00001 0.011 00577 2‘0333
-1.466 0.112 0.037 18.685 0.047 0.012 0.005 0.664 47.666
-10320 00138 00040 160255 00055 00023 00005 00440 620600
“10173 001‘9 00045 160895 00065 00029 00007 00252 53.600
'1.026 0.147 0.055 20.827 0.079 0.041 0.016 0.087 28.200
“0.880 0.159 0.078 26.350 0.094 0.051 0.028 0.031 13.266
-00733 0.081 00036 2‘0311 00102 0.052 0.045 0.001 1.466
'0.586 0.039 0.016 23.232 0.050 0.025 0.012 0.000 0.133
“0.440 0.030 0.012 21.988 0.000 0.000 0.000 0.000 0.000
-0.293 0.032 0.002 4.534 0.000 0.000 0.000 0.000 0.000
-0.146 0.032 0.002 4.534 0.000 0.000 0.000 0.000 0.000
'0.000 0.032 0.002 4.534 0.000 0.000 0.000 0.000 0.000
0.146 0.032 0.002 4.534 0.000 0.000 0.000 0.000 0.000
0.293 0.032 0.002 4.534 0.000 0.000 0.000 0.000 0.000
0.439 0.032 0.002 4.534 0.000 0.000 0.000 0.000 0.000
0.586 0.055 -0.003 -4.036 0.089 0.029 -0.018 0.000 0.466
0.733 0.069 -0.024 -19.053 0.097 0.051 -0.037 0.000 0.866
0.879 0.104 -0.045 -23.479 0.098 0.055 -0.044 0.005 3.533
1.026 0.149 -0.066 -23.886 0.099 0.051 -0.034 0.033 14.466
1.173 0.148 -0.060 ~22.236 0.079 0.037 -0.017 0.132 39.533
1.320 0.140 -0.064 -24.599 0.059 0.033 -0.008 0.309 59.400
1.466 0.125 -0.064 -27.394 0.052 0.027 -0.007 0.494 61.733
1.613 00098 “00057 -300244 000‘1 00017 “00008 0.777 “1.666
1.759 0.078 -0.051 -33.213 0.032 0.009 -0.009 0.890 24.466
1.906 0.047 -0.061 -52.428 0.005 0.019 -0.006 0.957 13.466
2.053 0.032 .0.060 -61.957 0.004 0.021 -0.003 0.981 8.866
2.200 0.031 -0.052 -59.222 0.008 0.014 -0.002 0.993 5.066

TABLE D- l 0 Continued

114

x/d A /d = Ay/d = Xx/d = Xy/d =

10.000 0.140 0.093 0.085 0.065

Ucupg) = 61.577 '1‘ = 15.000 (averaging time) Condition: Non-Vortical

-—— -Z

y/d U/Uc v/Uc e uv/UC w/Uc uv/Uc Y C/T
2.500 0.035 -0.060 -59.521 0.010 0.016 -0.003 0.994 4.600
20333 00043 ”0.069 “57.966 0.010 00024 -00006 0.987 8.400
2.166 0.044 -0.078 -60.718 0.015 0.036 -0.012 0.792 13.933
2.000 0.053 ”00094 '600358 00010 0.038 -00011 00909 22.533
1.833 0.119 -0.076 -32.685 0.052 0.020 -0.018 0.756 45.266
1.666 0.128 -0.069 -28.205 0.068 0.032 -0.019 0.486 49.800
1.500 0.170 -0.074 ~23.576 0.068 0.031 -0.011 0.416 60.266
1.333 0.172 “00079 ’240783 00083 0.043 -00020 0.222 47.600
1.166 0.194 -00088 ”240601 00103 0.055 “0.030 0.076 250266
10000 00176 “00079 -240278 00137 00066 '00059 00014 70200
0.833 0.118 -0.058 -26.246 0.140 0.074 -0.092 0.002 1.466
0.666 0.062 -0.032 ~27.324 0.096 0.055 -0.049 0.000 0.400
0.500 0.051 -0.023 ~24.563 0.080 0.038 -0.029 0.000 0.200
0.333 0.038 0.003 4.534 0.000 0.000 0.000 0.000 0.000
0.166 0.038 0.003 4.534 0.000 0.000 0.000 0.000 0.000
0.000 0.038 0.003 4.534 0.000 0.000 0.000 0.000 0.000
-0.166 0.038 0.003 4.534 0.000 0.000 0.000 0.000 0.000
-0.333 0.055 0.010 10.972 0.084 0.042 0.034 0.000 0.200
'00‘99 0.046 0.007 80799 00048 0.025 00012 00000 0.133
-0.666 0.107 0.026 14.042 0.146 0.057 0.061 0.001 1.066
'00833 00191 00044 130221 001‘“ 00055 0.048 00013 6.266
'0.999 0.182 0.072 21.555 0.112 0.055 0.038 0.039 15.800
-1.166 0.187 0.072 21.233 0.086 0.045 0.016 0.117 33.466
-1.333 0.178 0.051 15.950 0.085 0.035 0.012 0.247 53.066
“1.500 0016‘ 0.049 16.782 0.064 0.020 00009 00509 61.000
“1.666 0.143 0.040 15.946 0.062 0.021 0.009 0.734 45.866
-1.833 0.122 0.031 14.535 0.057 0.034 0.010 0.849 31.600
-l.999 0.093 0.055 30.702 0.043 0.015 0.016 0.935 20.466
-20166 00065 0.054 39.893 0.024 0.007 00010 00977 90133
-2.333 0.053 0.059 48.128 0.011 0.012 0.007 0.991 5.600

x/d
0.500

”CUP” =79. 485

y/d

0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750

0.000
-00050
-00100
‘00150
-00200
-00250
“00300
-00350
'0.400
'0.450
“00500
‘00550
'00600
'0.650
‘00700
“0.750

Au/d -
0.110
T = 30.000
v/Uc o
0.017 4.412
0.017 4.315
0.013 4.485
0.018 4.516
0.020 3.462
0.017 3.474
0.016 3.921
0.018 4.242
0.014 4.316
-0.002 -50705
-0.002 -5.705
‘00002 “50705
-0.022 ~16.360
-0.044 -45.330
“00047 “650579
'00043 “73.339
0.018 4.895
0.010 5.055
0.021 4.454
0.017 5.327
0.019 4.404
0.017 4.841
0.023 3.911
0.019 3.087
0.013 5.569
-0.002 -5.220
-0.002 -5.220
0.025 15.588
0.037 27.777
0.036 47.620
0.061 66.269
0.052 74.912

TABLE D-ll DATA LISTING

.Ay/d==
0.046

tfl/Uz

0.420
0.424
0.376
0.429
0.482
0.464
0.434
0.440
0.392
0.000
0.000
0.000
0.026
0.010
0.004
0.003

0.410
0.307
0.444
0.378
0.424
0.393
0.464
0.464
0.336
0.000
0.000
0.036
0.015
0.011
0.005
0.005

‘115

(averaging time)

Xx/d==
0.086

Condition:

-—- -Z
\N/Ué uv/Ué

0.020
0.020
0.026
0.021
0.013
0.013
0.017
0.020
0.024
0.000
0.000
0.000
0.017
0.013
0.009
0.007

0.024
0.031
0.019
0.029
0.020
0.024
0.014
0.012
0.034
0.000
0.000
0.026
0.016
0.017
0.010
0.008

0.079
0.078
0.092
0.086
0.020
0.033
0.062
0.071
0.083
0.000
0.000
0.000
’00000
-0.000
“0.000
’00000

0.096
0.096
0.068
0.107
0.070
0.090
0.034
’00001
0.111
0.000
0.000
0.005
0.001
0.001
0.000
0.000

X /d:=

0’2071

Non-Vortical

Y

0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.065
0.709
0.995
0.895

0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.000
0.000
0.000
0.012
0.594
0.648
1.000
1.000

C/T

0.600
0.633
0.400
0.600
0.933
0.766
0.700
0.800
0.466
0.000
0.000
0.000
48.533

166.233

7.266
2.766

0.666
0.333
0.733
0.466
0.733
0.666
1.266
1.200
0.333
0.000
0.000
10.200

193.200

30.600
3.000
3.000

TABLE D-ll Continued

116

x/d Au/d = Ay/d = xx/d = x /d =

1.500 0.110 0.046 0.086 diovl

Uc(fpe) = 79.485 '1‘ = 15.000 (averaging time) Condition: Non-Vortical

y/d U/UC V/Uc e u'/Uc v'/UC uv/Ucz y C/T
-l.200 0.006 0.050 82.145 0.001 0.005 -0.000 1.000 3.000
-1.149 0.006 0.049 82.792 0.002 0.004 ~0.000 1.000 3.000
'1.100 0.005 0.045 83.065 0.002 0.004 0.000 1.000 3.000
-1.050 0.005 0.046 83.698 0.002 0.007 -0.000 1.000 3.000
-00999 00007 00046 810345 00002 00005 00000 10000 30000
“0.949 0.006 0.054 82.987 0.003 0.007 -0.000 0.999 3.066
'0.900 0.008 0.058 81.814 0.003 0.010 0.000 0.998 4.200
-00049 00013 00069 790419 00004 00016 00000 00982 120200
-0.800 0.018 0.073 75.667 0.007 0.022 0.000 0.914 39.333
-0.750 0.031 0.087 70.317 0.014 0.028 0.001 0.712 95.933
“00699 00065 00086 520908 00022 00031 00003 00399 1170066
'0.650 0.061 0.046 36.908 0.047 0.039 0.014 0.063 32.466
-0.600 0.113 0.082 36.039 0.045 0.038 0.003 0.014 11.000
“00550 00028 00017 320204 00032 00021 00006 00000 00200
'0.500 0.029 0.000 1.216 0.039 0.018 0.007 0.000 0.066
-O.450 0.023 -0.002 *5.220 0.000 0.000 0.000 0.000 0.000
-0.400 0.023 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
’0.350 0.044 0.000 0.685 0.140 0.016 0.023 0.000 0.066
‘0.300 0.159 0.007 2.730 0.345 0.021 0.051 0.000 0.400
’00250 00342 00018 30015 00063 00022 00001 00001 10133
-0.200 0.321 0.018 3.275 0.459 0.018 0.017 0.001 1.133
-00150 00210 00010 50120 00‘01 00030 00099 00000 00600
“0.100 0.389 0.019 2.926 0.476 0.014 -0.013 0.001 1.266
“0.050 0.186 0.016 5.142 0.380 0.027 0.099 0.000 0.533
“00000 00350 00022 30616 00‘74 00012 00020 00001 10133
0.049 0.213 0.017 4.570 0.407 0.022 0.082 0.000 0.600
00099 00426 00021 20858 00‘95 00016 ’00023 00001 10333
0.149 0.383 0.023 3.466 0.491 0.014 0.009 0.001 1.200
00199 00405 00019 20752 0049‘ 00019 ”00024 00001 10066
0.249 0.449 0.017 2.273 0.497 0.024 -0.049 0.001 1.333
0.299 0.286 0.020 4.091 0.455 0.026 0.056 0.000 0.933
0.349 0.214 0.019 5.169 0.407 0.033 0.104 0.000 0.533
0.399 0.047 0.002 2.996 0.161 0.029 0.048 0.000 0.066
00449 00023 .00002 “50275 00000 00000 00000 00000 00000
0.499 0.023 ~0.002 -5.275 0.000 0.000 0.000 0.000 0.000
0.549 0.023 -0.002 -5.275 0.000 0.000 0.000 0.000 0.000
0.599 0.026 -0.003 -8.241 0.021 0.011 -0.002 0.000 0.066
00649 00108 -00081 “370042 00064 00040 ”00014 00007 60133
00699 00087 “00065 “370050 00042 00028 -00005 00084 ‘80‘00
00749 00060 -00066 “470806 00026 00022 “00002 00025 1200066
00799 00036 “00059 '580240 0001‘ 00019 ”00002 00810 760333
00849 00021 '00053 '670779 00001 00016 “00001 00947 260933
0.899 0.014 -0.049 -73.363 0.003 0.013 -0.000 0.955 10.066
0.949 0.010 -0.044 -76.671 0.001 0.008 —0.000 0.998 3.466
0.999 0.008 -0.043 -7a.227 0.002 0.005 -o.000 0.999 3.066
10050 00007 ‘00040 ”790773 00002 00004 “00000 10000 30000
10100 00004 -00041 ’830582 00001 00004 ”00000 10000 30000
1.149 0.005 -0.040 -81.811 0.001 0.003 0.000 1.000 3.000
1.199 0.007 -0.030 -79.302 0.001 0.003 -0.000 1.000 3.000

TABLE D-l 1 Continued

117

x/d .Au/d:= .A /a== Xx/d== x /d:=

3.000 0.110 0.040 0.086 01071

Uc(fpe) :79 .948 T = 15.000 (averaging time) Condition: Non-Vortical
y/d U/Uc V/Uc e u'/Uc w/uc W/U 7‘ y c/r
1.275 0.010 -0.040 -75.673 0.002 0.007 -0.000 0.998 3.466
1.200 0.016 -0.045 -70.641 0.006 0.014 -0.001 0.985 9.000
1.125 0.018 -0.043 -67.268 0.006 0.018 -0.002 0.773 13.666
1.050 0.035 -0.055 ~57.781 0.014 0.021 -0.004 0.860 44.800
0.975 0.058 -0.061 -46.363 0.028 0.021 -0.004 0.639 78.800
0.900 0.079 ~0.065 -39.497 0.036 0.023 -0.004 0.405 90.666
0.825 0.109 -0.056 -27.222 0.043 0.027 -0.000 0.159 59.200
0.750 0.143 -0.063 ~23.790 0.053 0.034 -0.002 0.022 14.200
0.675 0.072 -0.035 -25.987 0.074 0.039 -0.021 0.002 1.733
00600 00026 “00015 290065 00036 00021 “00007 00000 00133
00525 00034 “00016 “250272 00063 00023 “00014 00000 00133
0.450 0.020 -0.011 -28.487 0.000 0.000 0.000 0.000 0.000
0.375 0.045 -0.007 -9.012 0.164 0.026 0.043 0.000 0.066
0.300 0.278 0.012 2.540 0.420 0.028 0.094 0.000 0.733
0.225 0.329 0.025 4.445 0.467 0.023 0.060 0.001 1.200
00150 00439 00024 20918 00493 00020 “00020 00001 10666
00075 00576 00018 10817 00480 00025 “00070 00002 10933
0.000 0.420 0.020 2.779 0.487 0.018 -0.026 0.001 1.400
-0.074 0.433 0.023 3.156 0.478 0.020 -0.012 0.001 1.666
-0.149 0.258 0.011 2.568 0.436 0.015 0.007 0.000 0.866
“00224 00160 00010 30590 00349 00023 00065 00000 00400
-0.299 0.044 -0.000 -0.708 0.140 0.011 0.015 0.000 0.066
-0.374 0.036 -0.001 -2.893 0.085 0.011 0.002 0.000 0.066
-0.449 0.023 -0.002 -5.825 0.000 0.000 0.000 0.000 0.000
-0.525 0.031 -0.000 -0.905 0.037 0.009 0.002 0.000 0.133
-0.599 0.082 0.020 13.588 0.080 0.035 0.022 0.001 1.466
-0.675 0.132 0.071 28.563 0.053 0.039 0.005 0.022 13.000
-0.749 0.111 0.064 30.189 0.037 0.029 0.004 0.152 57.200
-0.824 0.092 0.058 32.330 0.032 0.026 0.003 0.374 90.866
-0.899 0.054 0.039 35.693 0.030 0.023 0.007 0.446 47.400
'0.974 0.055 0.048 40.963 0.019 0.018 0.004 0.866 41.133
-1.050 0.038 0.049 52.255 0.008 0.017 0.003 0.943 20.666
-1.125 0.024 0.046 62.623 0.002 0.013 0.000 0.988 6.800
-1.199 0.018 0.051 70.224 0.005 0.012 0.000 0.997 4.200
-1.274 0.007 0.057 82.146 0.002 0.009 0.000 0.999 3.400

x/d
4.500

Uc(fpl) =79.716

v/d

“10500
“10400
“10300
-1.200
“10100
“10000
-O.900
“00800
“00700
-0.600
“00500
“00400
“00300
“00200
“00100
-0.000
0.099
0.199
0.299
0.399
0.499
0.599
0.699
0.800
0.900
0.999
1.100
1.200
1.300
1.399
1.500

0/ Uc
0.006
0.010
0.009
0.020
0.055
0.095
0.123
0.087
0.110
0.075
0.026
0.024
0.024
0.107
0.086
0.394
0.165
0.137
0.135
0.045
0.024
0.042
0.091
0.149
0.118
0.092
0.073
0.045
0.019
0.005
“00007

TABLE D-l 1 Continued

Au/d :-
0.110
T = 15.000
v/Uc a
0.041 80.900
0.050 78.786
0.049 79.137
0.068 72.893
0.077 54.316
0.056 30.682
0.031 14.264
0.120 54.239
0.040 20.091
0.030 22.296
“00002 “40527
“00002 “50220
“00002 “50220
“00003 “10948
0.001 0.889
0.005 0.809
0.011 3.978
0.014 6.146
0.015 6.389
0.002 3.135
“00002 “50220
“00008 “110402
-0.020 -12.817
“00100 “340118
-0.071 -30.993
-0.066 -35.535
“00056 “370855
“00059 “52066‘
-0.053 -70.176
-0.037 -81.840
~0.038-100.718

.Ay/d==

0.046

tfl/UE

0.005
0.012
0.011
0.017
0.012
0.036
0.039
0.035
0.076
0.076
0.011
0.000
0.000
0.270
0.233

..o.433

0.361
0.319
0.314
0.138
0.000
0.066
0.090
0.065
0.049
0.042
0.036
0.022
0.010
0.011
0.009

118

(averaging time)

Xx/d.=
0.086

Condition:

-—— -2
v'/Uc uv/Uc

0.009
0.016
0.026
0.031
0.033
0.022
0.027
0.045
0.038
0.038
0.001
0.000
0.000
0.017
0.011
0.033
0.028
0.039
0.043
0.030
0.000
0.022
0.035
0.037
0.029
0.026
0.022
0.021
0.022
0.017
0.011

0.000
0.000
0.001
0.003
0.010
0.006
0.002
0.006
0.016
0.020
0.000
0.000
0.000
“00032
0.020
“00094
0.074
0.119
0.123
0.042
0.000
“00012
“00018
“00008
“00002
-0.002
“00004
“00006
“00004
“00001
0.000

X /d==
03'071

Non-Vortical

7

0.999
0.990
0.620
0.875
0.712
0.464
0.253
0.061
0.010
0.002
0.000
0.000
0.000
0.000

0.000,

0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.002
0.014
0.072
0.299
0.538
0.753
0.900
0.639
0.995

C/T

3.400
6.200
12.933
34.200
62.933
78.866
67.533
27.666
6.533
1.666
0.066
0.000
0.000
0.266
0.200
1.333
0.466
0.333
0.333
0.066
0.000
0.266
1.933
9.000
31.133
73.866
77.666
59.133
30.933
7.000
4.800

x/d
6.000

Uc(fps) = 77.235

Y/d

1.700
1.600
1.500
1.400
1.300
1.200
1.100
1.000
0.900
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
“0.099
-00199
“0.299
“00399
”00499
“00599
'0.699
-00799
“00899
'0.999
“10099
“10199
‘10299
-10399
“1.499
-10599
-10699

TABLE D-ll Continued

Au/d =

T‘= 15

v/Uc

0.110

.000
6

'000‘3-1110964
”0.044-113.241

“0.046-125.123
-0.044-145.479
“00068 '42.067
-0.063 ~36.375
-0.052 -29.607
”00065 -250261
”00082 “26.734
-0.075 -25.365
-0.018 ~18.692
‘00011 ”16.686
-0.007 -16.116
”00007 “160116
“0.007 “16.116
-0.003 -4.540
0.001 0.996
-0.007 -16.116
-0.007 -16.116
-0.007 -16.116
-0.007 -16.116
-0.007 -16.116
‘00003 “3.953
0.023 14.300
0.049 17.067
0.035 11.909
0.030 12.315
0.009 4.101
-0.005 -2.770
-0.019 -11.389
-0.033 -23.585
-0.068 -43.914
-0.054 -59.819
0.062 82.989
0.055 83.327

Ay/d =
0.006

ufl/Ué

0.012
0.014
0.006
0.027
0.037
0.045
0.062
0.055
0.067
0.093
0.070
0.054
0.000
0.000
0.000
0.154
0.259
0.000
0.000
0.000
0.000
0.000
0.082
0.106
0.080
0.054
0.057
0.049
0.046
0.043
0.039
0.024
0.005
0.017
0.011

119

(averaging time)

Condition:

-— -Z
v'/Uc uv/Uc

0.015
0.018
0.019
0.018
0.021
0.027
0.033
0.033
0.035
0.049
0.033
0.018
0.000
0.000
0.000
0.023
0.038
0.000
0.000
0.000
0.000
0.000
0.016
0.039
0.042
0.034
0.031
0.026
0.010
0.012
0.022
0.003
0.020
0.026
0.017

0.001
0.002
0.004
0.008
’00011
-0.007
“06012
0.001
-00001
-00012
“0.017
-0.008
0.000
0.000
0.000
0.034
0.097
0.000
0.000
0.000
0.000
0.000
0.007
0.032
0.010
0.001
0.004
0.001
’00000
”0.002
-0000?
'00009
-0000?
0.000
0.000

ky/d:=
0.071

Non-Vortical

V

0.988
0.883
0.929
0.709
0.652
0.408
0.171
0.111
0.033
0.010
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.011
0.037
0.109
0.220
0.472
0.576
0.821
0.916
0.958
0.976
0.950

C/T

6.600
9.133
21.333
60.333
70.800
67.533
45.133
41.400
16.533
5.933
0.733
0.133
0.000
0.000
0.000
0.066
0.133
0.000
0.000
0.000
0.000
0.000
0.666
1.000
6.733
18.133
42.266
59.466
71.200
61.333
42.400
26.800
15.533
10.666
5.200

x/d
8.000

Uc(fps) = 70.520

v/d

-Z.100
-10950
“10800
-10650
”10500
”10350
-10200
-1.050
-0.900
-00750
-O.600
“00450
’00300
“00150
-0.000
0.149
0.299
0.449
0.599
0.749
0.899
1.049
1.199
1.349
1.499
1.649
1.799
1.949
2.100

TABLE D-ll Continued

ALI/d -, AY/d =
0.110 0.046

T = 15.000 (averaging time)

I l
V/Uc 8 u /Uc v /Uc
0.056 85.224 0.013 0.016
0.069 85.372 0.020 0.030
0.073 79.622 0.027 0.035
0.088 65.257 0.029 0.045
0.081 41.944 0.036 0.037
0.076 31.612 0.051 0.022
0.067 24.319 0.058 0.033
0.078 23.848 0.065 0.043
0.105 26.003 0.077 0.054
0.075 28.189 0.118 0.068
0.067 28.589 0.143 0.086
0.016 21.493 0.079 0.035
0.004 5.511 0.064 0.045
-0.002 -5.220 0.000 0.000
0.006 4.503 0.266 0.043
‘00002 “50220 0.000 00000
-0.002 -5.220 0.000 0.000
0.001 1.875 0.125 0.025
’0000‘ -30223 00118 0.027
“0.055 -1707‘6 00143 0005‘
”00067 ’150765 00119 00049
“00061 -150082 00081 0.045
-00045 ’130518 00074 0.034
”0.035 “11.955 0.068 00029
-0.021 -10.237 0.060 0.008
”00017 '100623 00051 00033
-0.056 -65.363 0.002 0.032
'00060 “800635 00017 00027
'000‘9 -820760 00011 00015

120

kx/d==
0.086

Condition:

-—- -Z
uv/ Uc

0.000
-0.000
0.001
0.012
0.022
0.031
0.011
0.011
0.012
0.060
0.104
0.026
0.029
0.000
0.107
0.000
0.000
0.029
“00019
-0.044
-0001!
0.009
0.005
0.003
0.000
”00003
-00008
’00002
“00000

01071

Non-Vortical

Y

0.996
0.986
0.968
0.897
0.778
0.606
0.423
0.188
0.052
0.006
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.004
0.018
0.090
0.250
0.476
0.701
0.923
0.604
0.937
0.997

C/T

4.600
7.800
13.333
27.666
48.666
65.400
70.200
51.000
20.800
3.266
1.066
0.133
0.066
0.000
0.133
0.000
0.000
0.133
0.533
2.600
9.533
32.000
63.133
76.066
51.066
23.733
16.333
12.133
4.133

x/d
10.000

Uc(fpa) =59.158

Y/d

2.500
2.333
2.166
2.000
1.833
1.666
1.500
1.333
1.166
1.000
0.833
0.666
0.500
0.333
0.166
0.000
”00166
“00333
”00‘99
“0.666
-00833
‘0.999
-10166
“10333
-10500
-10666
-1.833
”10999
‘20166
-20333
“20500

TABLE D-ll Continued

Au/d -
0.110
T = 15.000
V/Uc 9
-0.061 -88.927
‘OoOb? “92.038
-0.082 ~88.440
”00087 ’890059
“00112 “75.004
-0.115 “49.495
-0.085 ~26.668
-0.081 -21.546
-0.083 -22.666
-0.075 -15.257
-0.118 ~21.765
-0.084 -18.518
”00024 .170690
-0.018 -19.020
“0.020 “160166
’00018 ”160388
“00012 ‘100562
0.014 12.131
0.033 13.034
0.082 19.418
0.083 15.757
0.056 15.135
0.031 8.353
-00003 “00986
-0.022 -8.415
“00026 “14068‘
'000‘5 -240331
0.084 58.740
0.070 59.744
0.060 51.384
0.055 55.099

A, =
Y/d
0.046

uU/UE

0.016
0.023
0.034
0.031
0.027
0.040
0.075
0.078
0.103
0.089
0.121
0.202
0.163
0.108
0.156
0.134
0.130
0.110
0.181
0.164
0.111
0.097
0.080
0.069
0.068
0.068
0.051
0.029
0.013
0.011
0.008

121

(averaging time)

Xx/d:=
0.086

Condition:

——— -Z
v'/Uc uv/Uc

0.019
0.029
0.042
0.044
0.054
0.044
0.035
0.038
0.053
0.060
0.069
0.075
0.035
0.028
0.030
0.012
0.022
0.067
0.066
0.073
0.066
0.052
0.037
0.040
0.004
0.028
0.027
0.047
0.032
0.021
0.013

-0.000
-0.000
”0.002
”00001
-00012
-00025
-0.005
”00003
“0001‘
0.007
-0.006
-0.091
-00013
0.008
“00007
“00000
0.028
0.074
0.095
0.078
0.006
0.012
0.003
'00000
-00006
-00012
“00015
0.017
0.009
0.008
0.002

Xy/d =
0.071

Non-Vortical

Y

0.996
0.989
0.969
0.858
0.844
0.713
0.491
0.312
0.140
0.028
0.016
0.004
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.006
0.026
0.090
0.205
0.387
0.645
0.555
0.908
0.947
0.971
0.992
0.999

C/‘r

4.200
6.333
14.133
20.533
39.400
58.133
72.933
70.666
41.933
13.200
9.600
3.066
0.333
0.133
0.200
0.133
0.200
0.200
0.933
3.800
11.733
30.066
52.733
71.866
62.266
29.133
26.000
19.066
11.533
5.200
3.400

TABLE D-lZ DATA LISTING

122

x/d .An/d:= .Ay/d:= Xx/d== x /d==

0.500 0.100 0.052 0.053 01050

Uc(fpa) :97. 206 T = 150000 (averaging time) Condition: Non-Vortical

y/d u/Uc V/Uc 6 u'/Uc v'/Uc UV/Ucz Y C/T
0.000 0.511 0.029 3.272 0.484 0.009 -0.012 0.002 1.866
0.050 0.532 0.035 3.830 0.483 0.009 0.014 0.002 2.333
00100 00841 00031 20159 00433 00023 ”00085 00004 “0133
00150 00791 00035 20565 00442 00017 “00055 0000“ 30400
0.200 0.767 0.039 2.909 0.445 0.013 -0.033 0.004 3.600
0.250 0.655 0.037 3.286 0.462 0.009 -0.007 0.003 2.800
0.300 0.589 0.039 3.816 0.469 0.010 0.014 0.003 2.600
0.350 0.591 0.038 3.723 0.471 0.010 0.011 0.002 2.266
0.400 0.212 0.026 7.089 0.412 0.035 0.142 0.000 0.533
0.450 0.019 ~0.000 -2.443 0.000 0.000 0.000 0.000 0.000
0.500 0.019 -0.000 -2.443 0.000 0.000 0.000 0.000 0.000
0.550 0.048 0.004 4.922 0.042 0.016 0.002 0.001 1.600
0.600 0.050 0.000 0.595 0.011 0.007 0.000 0.522 155.066
0.650 0.055 0.005 5.889 0.012 0.005 0.000 0.988 12.000
0.700 0.045 0.016 19.752 0.007 0.004 0.000 1.000 3.000
0.750 0.024 -0.035 -54.600 0.004 0.004 -0.000 1.000 3.000
0.000 0.391 0.034 5.013 0.475 0.014 0.058 0.001 1.066
-00050 00559 00035 30658 0046‘ 00010 00007 00002 20066
-0.100 0.538 0.034 3.697 0.467 0.009 0.008 0.002 1.933
'0.150 0.578 0.037 3.691 0.459 0.009 0.009 0.002 2.400
“00200 0051‘ 00035 3092“ 00467 00008 00°15 00002 10866
'0.250 0.598 0.037 3.549 0.455 0.009 0.004 0.002 2.466
-0.300 0.557 0.037 3.865 0.462 0.010 0.015 0.003 2.466
-O.350 0.725 0.035 2.822 0.432 0.011 -0.025 0.003 2.866
“00300 00733 00035 20778 00‘38 00011 ”00028 00003 30133
-0.450 0.043 0.003 4.453 0.158 0.027 0.043 0.000 0.066
-0.500 0.019 -0.000 “2.879 0.000 0.000 0.000 0.000 0.000
-0.550 0.019 -0.000 -2.879 0.000 0.000 0.000 0.000 0.000
-00600 00071 00004 30868 00013 00005 00000 00776 1280333
-0.650 0.063 0.004 3.740 0.011 0.002 0.000 0.974 2.933
-O.700 -0.009 0.070 97.664 0.004 0.008 -0.000 0.999 3.466
-0.750 0.009 0.056 80.483 0.002 0.007 -0.000 1.000 3.000

x/d
1.500

v/d

“10000
“00933
“00866
“00800
-O.733
-0.666
“00600
“00533
“00466
-0.400
“00333
“00266
“00200
“00133
“00066
“00000
0.066
0.133
0.199
0.266
0.333
0.400
0.466
0.533
0.600
0.666
0.733
0.800
0.866
0.933
1.000

TABLE D-12 Continued

Au/d = A /d =
0.100 03052

T = 15.000 (averaging time)

c u
v/Uc e u /Uc v /Uc
0.054 85.178 0.002 0.005
0.059 96.565 0.003 0.006
0.062 101.326 0.003 0.008
0.068 92.759 0.005 0.009
0.063 89.000 0.009 0.016
0.076 68.407 0.017 0.023
0.026 67.213 0.017 0.033
0.001 4.118 0.000 0.000
0.001 4.118 0.000 0.000
0.005 4.545 0.217 0.028
0.035 2.601 0.421 0.020
0.034 2.396 0.391 0.018
0.034 2.478 0.399 0.018
0.032 2.309 0.396 0.018
0.035 3.628 0.460 0.008
0.037 3.078 0.434 0.012
0.036 3.136 0.447 0.011
0.039 3.581 0.459 0.010
0.039 3.003 0.436 0.018
0.036 3.721 0.471 0.018
0.030 7.549 0.422 0.041
0.003 4.750 0.163 0.032
-0.001 -4.370 '0.000 0.000
“00001 “40370 00000 00000
“00002 “9062‘ 00032 00011
-0.032 -19.484 0.030 0.022
“00036 “280487 00021 0001‘
-0.037 ~36.201 0.013 0.011
“000“ “540615 00007 00009
-0.049 -58.484 0.004 0.006
-0.045 “5‘0021 0000‘ 0000‘

123

Xx/d==
0.058

Condition:

-—— -Z
uv/Ué

-0.000
“00000
-0.000
“00000
-0.000
0.000
0.005
0.000
0.000
0.061
“00039
“00038
“00044
“00051
0.006
“00020
“00011
0.003
“00033
0.011
0.156
0.052
0.000
0.000
“00000
-0.000
“00001
“00001
“00000
“00000
“00000

X /d==
01050

Non-Vortical

Y

1.000
1.000
1.000
0.997
0.839
0.136
0.000
0.000
0.000
0.000
0.005
0.007
0.005
0.004
0.003
0.004
0.003
0.003
0.004
0.002
0.000
0.000
0.000
0.000
0.000
0.081
0.636
0.967
0.998
1.000
1.000

C/T

3.000
3.000
3.000
5.266
86.533
78.266
0.200
0.000
0.000
0.133
3.533
5.266
4.333
4.066
2.533
3.466
3.066
3.000
3.866
2.333
0.733
0.066
0.000
0.000
0.200
54.266

133.600

22.666
4.000
3.000
3.000

x/d
3.000

Uc(fpa) = 97.086

v/d

1.250
1.166
1.083
1.000
0.916
0.833
0.750
0.666
0.583
0.500
0.416
0.333
0.250
0.166
0.083
0.000
“00083
-0.166
“00269
“00333
“00616
“00699
“00563
“00666
“00750
“00833
“00916
-0.999
“10063
“10166
“10250

U/ Uc

0.020
0.024
0.023
0.033
0.049
0.072
0.104
0.038
0.013
0.019
0.019
0.040
0.187
0.565
0.830
0.848
0.925
0.893
0.699
0.182
0.019
0.019
0.023
0.074
0.092
0.066
0.051
0.034
0.027
0.025
0.021

TABLE D- 1 2 Continued

Au/d .. Ay/d -
0.100 0.052

T = 15.000 (averaging time)

I 0
WUC e u /Uc v /Uc
“00038 “610753 00003 00006
“00043 “600543 00004 00008
-0.042 -60.683 0.004 0.012
-0.055 -58.914 0.011 0.017
“00054 “470396 00022 00018
“00048 “330523 00036 00023
-0.058 -29.167 0.039 0.027
“00029 “370256 00047 00031
“00013 “450755 00000 00000
-0.001 -5.220 0.000 0.000
“00001 “50220 00000 00000
0.001 2.326 0.141 0.025
0.025 7.750 0.387 0.043
0.031 3.174 0.465 0.019
0.037 2.556 0.395 0.029
0.035 2.368 0.380 0.027
0.024 1.528 0.330 0.036
0.027 1.742 0.349 0.034
0.022 1.826 0.433 0.023
0.010 3.363 0.377 0.016
-0.002 -6.650 0.000 0.000
-0.002 -6.650 0.000 0.000
“00000 “00922 00026 00012
0.016 12.184 0.064 0.029
0.051 29.334 0.030 0.027
0.054 39.704 0.022 0.022
0.059 48.909 0.015 0.021
0.054 57.337 0.008 0.015
0.044 58.864 0.004 0.009
0.053 64.947 0.004 0.009
0.047 65.760 0.002 0.005

124

Condition:
__. -z
uv/Ué

-0.000
-0.000
“00001
“00001
“00002
“00005
“00002
-0.013
0.000
0.000
0.000
0.032
0.163
-0.008
“00055
“00064
“00065
“00061
“00050
0.040
0.000
0.000
0.003
0.013
0.002
0.003
0.003
0.000
0.000
0.000
0.000

X =
Y/d
00050

Non-Vortical

Y

0.999
0.997
0.971
0.870
0.610
0.244
0.031
0.001
0.000
0.000
0.000
0.000
0.000
0.002
0.004
0.008
0.010
0.009
0.004
0.000
0.000
0.000
0.000
0.002
0.083
0.427

00729’

0.955
0.995
0.999
1.000

C/T

3.333
4.200
14.266
44.466
93.466
81.733
19.933
0.866
0.000
0.000
0.000
0.066
0.533
2.133
3.933
6.400
8.333
7.333
3.600
0.466
0.000
0.000
0.066
2.133
33.600

105.800

73.066
21.200
5.000
3.466
3.000

TABLE D-lZ Continued

125

x/d Au/d = A /d = xx/d = Xy/d =

4.500 0.100 0.052 0.058 0.050

Uc(fpe) =97.680 T = 15.000 (averaging time) Condition: Non-Vortical

-—— -2
l 1

y/d u/uc v/Uc e u /UC v /UC uv/Uc y C/T
'1.500 0.014 0.044 71.557 0.002 0.009 0.000 0.998 3.600
-1.400 0.015 0.055 74.261 0.002 0.010 0.000 0.994 5.200
“10300 00011 00056 780397 00007 00016 00000 00973 120600
“10200 00011 00066 790824 00002 00023 00000 00865 390200
-1.100 0.025 0.075 71.108 0.007 0.029 0.001 0.668 72.533
-1.000 0.058 0.077 52.809 0.020 0.030 0.004 0.393 86.466
“00900 0009“ 00064 340066 00034 00027 00006 00176 610600
-0.800 0.120 0.067 29.042 0.041 0.031 0.003 0.026 15.600
-0.700 0.070 0.032 24.437 0.076 0.034 0.022 0.001 1.066
“00600 00019 “00001 “50220 00000 00000 00000 00000 00000
-0.500 0.019 -0.001 -5.220 0.000 0.000 0.000 0.000 0.000
-0.400 0.019 -0.001 -5.220 0.000 0.000 0.000 0.000 0.000
-0.300 0.041 0.000 1.238 0.148 0.017 0.024 0.000 0.066
“0.200 0.433 0.016 2.192 0.474 0.021 -0.055 0.001 1.400
-0.100 0.832 0.023 1.596 0.393 0.031 -0.057 0.005 4.400
“00000 00763 00033 20511 00416 00025 “00036 00005 40600
0.099 0.521 0.042 4.608 0.473 0.023 0.043 0.002 2.133
0.199 0.177 0.028 9.215 0.370 0.050 0.178 0.000 0.466
0.299 0.019 0.000 1.716 0.000 0.000 0.000 0.000 0.000
0.399 0.019 0.000 1.716 0.000 0.000 0.000 0.000 0.000
0.499 0.019 0.000 1.716 0.000 0.000 0.000 0.000 0.000
0.599 0.023 -0.000 -1.920 0.027 0.009 -0.002 0.000 0.066
0.699 0.044 -0.023 -27.335 0.056 0.035 -0.018 0.001 0.666
0.800 0.136 -0.053 -21.386 0.050 0.034 -0.000 0.018 11.933
0.900 0.107 -0.048 -24.328 0.041 0.026 -0.000 0.113 46.533
00999 00084 “00038 “260652 00033 00020 “00000 00368 830666
1.100 0.065 -0.030 -24.605 0.031 0.014 -0.002 0.575 67.800
1.200 0.057 -0.028 -25.964 0.024 0.005 -0.002 0.848 43.066
1.300 0.045 '0.026 ~30.192 0.017 0.002 -0.001 0.958 16.666
10399 00024 “00037 “560588 00005 00010 “00001 00987 70533
1.500 0.024 -0.037 -56.162 0.004 0.007 -0.000 0.998 3.666

TABLE D- l 2 Continued

x/d Au/d '2 Ay/d = Xx/d = 1 /d =

6.000 0.100 0.052 0.058 61050

Uc(fps) = 960399 T = 15-000 (averaging time) Condition: Non-Vortical

y/d tJ/Uc v/Uc e u'/Uc v'/Uc uv/UcZ y C/T
1.750 0.016 -0.038 -66.575 0.005 0.010 -0.000 0.996 4.000
1.633 0.013 -0.042 -72.186 0.010 0.014 -0.001 0.987 7.133
10516 00023 “00048 “630719 00004 00016 “00002 00950 160333
1.400 0.033 -0.051 “56.837 0.011 0.019 -0.005 0.864 37.066
1.283 0.064 -0.051 -38.692 0.030 0.018 -0.004 0.657 65.333
10166 00095 “00045 “250608 00038 00021 “00001 00390 780600
1.050 0.112 -0.044 -21.775 0.042 0.026 -0.000 0.179 56.333
0.933 0.129 -0.052 ~22.009 0.056 0.030 -0.002 0.039 18.600
0.816 0.122 -0.065 -28.137 0.076 0.045 '0.017 0.006 4.533
0.700 0.053 -0.026 -25.949 0.102 0.041 -0.011 0.000 0.600
0.583 0.022 -0.013 -30.328 0.039 0.013 -0.005 0.000 ‘0.066
0.466 0.020 -0.001 '5.220 0.000 0.000 0.000 0.000 0.000
0.350 0.020 -0.001 '5.220 0.000 0.000 0.000 0.000 0.000
0.233 0.045 0.005 6.339 0.166 0.044 0.073 0.000 0.066
0.116 0.069 0.008 6.688 0.230 0.043 0.098 0.000 0.133
0.000 0.141 0.019 7.646 0.343 0.044 0.145 0.000 0.333
“00116 00143 00015 60288 00368 00034 00115 00000 00333
'0.233 0.042 0.001 2.218 0.149 0.015 0.023 0.000 0.066
“00349 00020 “00000 “20529 00000 00000 00000 00000 00000
-0.466 0.020 -0.000 -2.529 0.000 0.000 0.000 0.000 0.000
-0.583 0.020 -0.000 -2.529 0.000 0.000 0.000 0.000 0.000
-0.699 0.054 0.034 32.748 0.075 0.058 0.039 0.001 0.800
'0.816 0.128 0.071 29.149 0.077 0.043 0.022 0.007 4.666
“00933 00115 00073 320266 00061 00031 00006 00065 270666
“10050 00090 00053 300735 00062 00029 00008 00191 550533
-1.166 0.080 0.050 31.916 0.031 0.021 0.006 0.518 78.466
“10283 00069 00068 350166 00025 00015 00008 00767 560333
-l.399 0.043 0.048 48.092 0.012 0.017 0.003 0.919 25.333
-1.516 0.030 0.050 58.573 0.007 0.018 0.003 0.948 17.800
“1.633 0.023 0.050 65.181 0.006 0.014 0.001 0.984 7.866
-1.750 0.014 0.049 73.111 0.002 0.011 0.000 0.995 4.400

x/d
8.000

Uc(fpa) = 91.100

y/d

“20000
-10866
-1 .733
-10600
”10466
-10333
'16200
-10066
-00933
-00800
-00666
-06533
-O.400
-06266
‘06133
.00000
0.133
0.266
0.399
0.533
0.666
0.800
0.933
1.066
1.200
1.333
1.466
1.600
1.733
1.866
2.000

TABLE D-ll Continued

Au/d .. Ay/d ..
0.100 0.052

T = 15.000 (averaging time)

I I
'v/UE (3 tl/Ue ‘r/UE
0.057 73.612 0.009 0.017
0.065 78.367 0.018 0.027
0.075 72.622 0.003 0.030
0.082 68.919 0.017 0.036
0.075 46.914 0.024 0.032
0.065 31.883 0.043 0.026
0.061 24.641 0.048 0.031
0.069 24.852 0.050 0.034
0.085 25.800 0.061 0.042
0.071 28.499 0.108 0.059
0.028 33.050 0.063 0.055
0.009 24.089 0.000 0.000
0.010 14.388 0.139 0.009
0.009 24.089 0.000 0.000
0.009 24.089 0.000 0.000
0.009 24.089 0.000 0.000
.00002 -50220 0.000 00000
-00002 ‘50220 0.000 00000
-0.002 -5.220 0.000 0.000
”00002 -50220 00000 06000
-0.007 -6.847 0.100 0.020
-0.052 -18.895 0.129 0.057
.0007? -220016 00095 0.051
“00061 -20057‘ 06°60 0.035
'00052 -210180 0605‘ 00025
‘000‘5 “210568 06050 0.013
'000‘0 ’226833 06042 00014
-0.034 -24.427 0.036 0.013
.000‘5 -‘00‘99 0.026 0.011
-000‘1 -‘70‘62 00013 0.008
“00039 “526939 09006 0.010

127

0.000
0.001
0.002
0.005
0.013
0.012
0.005
0.004
0.005
0.052
0.031
0.000
0.009
0.000
0.000
0.000
0.000
0.000
0.000
0.000
-00012
-000‘7
“06004
.00000
“0.003
-00005
“0.003
“0.005
-0.006
-0.005
-00002

X /d:=
0.050

Non-Vortical

Y

0.990
0.959
0.901
0.814
0.673
0.461
0.233
0.109
0.026
0.004
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.003
0.016
0.068
0.232
0.416
0.637
0.841
0.904
0.968
0.991

C/T

5.800
13.466
19.266
41.333
61.933
72.400
55.333
35.333
13.000

2.733

0.333

0.000

0.066

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.400

2.733

8.733
27.800
61.266
72.333
63.000
40.333
27.800

8.533

5.933

x/d

10.000

Heaps) = 473.272

Y/d

2.500
2.333
2.166
2.000
1.833
1.666
1.500
1.333
1.166
1.000
06833

0.666.

0.500

0.333

0.166

0.000
-00166
“00333
-00499
'06666
'00833
.‘00999
“10166
“10333
“10500
‘10666
“10833
-10999
“20166
”2.333
’20500

U/ Uc

0.028
0.031
0.036
0.058
0.091
0.119
0.138
0.161
0.192
0.227
0.128
0.072
0.025
0.028
0.028
0.028
0.028
0.028
0.027
0.057
0.154
0.200
0.177
0.163
0.140
0.119
0.098
0.068
0.048
0.035
0.026

TABLE D-lZ Continued

.Au/d==

T= 15

v/Uc
-00045
-0.049
-00056
-0.053
-00041
-0.032
“00038
-0.048
”00075
-0.085
'00042
-0.021
“00011
-0.002
-00002
-0.002
'00002
“00002
0.004
0.015
0.077
0.086
0.089
0.070
0.062
0.056
0.053
0.050
0.051
0.057
0.062

0.100

.000
6

‘580100
-57.261
-57.012
“42.178
~24.538
-150037
”150343
-160881
-21.307
-200673
-180255
-16.845
-23.346
-5.220
“50220
’50220
“50220
“50220
8.381
15.054
26.681
23.321
26.715
23.274
23.893
25.216
28.377
36.520
47.065
57.989
66.678

A, =
Y/d
0.052

0.004
0.002
0.009
0.026
0.045
0.055
0.057
0.066
0.070
0.090
0.140
0.128
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.099
0.142
0.103
0.065
0.058
0.057
0.053
0.044
0.027
0.012
0.004
0.005

128

(averaging time)

tfl/UE

\fl/Ué

0.009
0.015
0.020
0:010
0.006
0.014
0.025
0.034
0.042
0.049
0.051
0.032
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.039
0.076
0.047
0.041
0.040
0.016
0.006
0.013
0.010
0.017
0.017
0.016

Xx/d==
0.058

Condition:
-——- -Z
uv/Uc

“00001
“00003
‘00007
?00011
-0.006
“06003
-06000
-0.000
0.001
“06007
’000‘5
’00028
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.036
0.090
0.026
0.006
0.004
0.017
0.017
0.019
0.013
0.006
0.002
0.001

X =
Y/d
0.050

Non-Vortical

Y

0.999
0.989
0.967
0.931
0.809
0.691
0.485
0.252
0.081
0.023
0.003
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.005
0.018
0.079
0.210
0.401
0.639
0.782
0.936
0.976
0.957
0.996

C/T

3.400
6.533
12.600
20.200
40.866
55.933
68.200
58.733
30.266
11.866
1.733
0.400
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.266
3.066
9.333
26.600
56.133
68.133
59.000
43.733
18.733
9.666
4.933
4.533

x/d
0.500

Uc(fpe) = 107. 895

Y/d

0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750

0.000
-00050
‘00100
-00150
-00200
“0.250
“00300
-00350
-0.400
-0.450
'00500
'00550
“00600
-00650
“0.700
-00750

U/U

C

0.083
0.075
0.095
0.075
0.089
0.119
0.045
0.030
0.030
0.016
0.016
0.016
0.039
0.043
0.012
0.000

0.045
0.104
0.088
0.059
0.045
0.044
0.058
0.044
0.044
0.016
0.016
0.016
0.071
0.039
0.036
0.003

TABLE D-13 DATA LISTING

.A /d:=
81052

= 15.000 (averaging time)

.Au/d==
0.097
T
'v/Ue £9
0.007 4.931
0.006 5.084
0.008 5.068
0.006 5.117
0.007 4.981
0.012 5.836
0.004 6.204
0.003 6.912
0.003 6.799
0.002 7.722
0.002 7.722
0.002 7.722
.00000 '00654
“00053 -500933
“00065 ’7808“4
-0.051 ~89.330
0.004 5.412
0.009 5.015
0.009 6.040
0.006 6.343
0.005 6.829
0.005 6.733
0.006 6.467
0.005 6.720
0.005 6.584
0.002 8.069
0.002 8.069
0.003 11.340
0.008 6.651
0.058 56.056
0.051 54.489
0.064 86.725

tfl/UE

0.265
0.250
0.285
0.249
0.273
0.316
0.173
0.123
0.123
0.000
0.000
0.000
0.034
0.020
0.004
0.003

0.177
0.297
0.270
0.211
0.173
0.171
0.206
0.171
0.168
0.000
0.000
0.000
0.016
0.005
0.006
0.002

129

0.021
0.020
0.023
0.020
0.021
0.028
0.015
0.012
0.012
0.000
0.000
0.000
0.006
0.025
0.015
0.009

0.016
0.023
0.024
0.020
0.018
0.017
0.020
0.017
0.016
0.000
0.000
0.000
0.004
0.007
0.009
0.005

Xx/d:=

0.083

Condition:

-—’ -Z
v'/Uc uv/Uc

0.055
0.051
0.066
0.051
0.059
0.088
0.027
0.015
0.014
0.000
0.000
0.000

-0.000
“0.005
’00000
“0.000

0.029
0.070
0.066
0.042
0.031
0.029
0.042
0.029
0.027
0.000
0.000
0.000
0.000
0.000
0.000

-0.000

Y

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.005
0.405
0.845
0.997

0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000

“0.000

0.715
0.997
0.999
0.999

xfiéii3

Non-Vortical

C/T

0.266
0.333
0.333
0.266
0.400
0.466
0.133
0.066
0.066
0.000
0.000
0.000
4.266

145.133
121.800

7.333

0.133
0.400
0.333
0.200
0.133
0.133
0.266
0.133
0.133
0.000
0.000
0.000

141.866

7.133
3.000
3.000

TAB LE D-1 3 Continued

1.3“

x/d Au/d = A /d = Xx/d = X /d =
1.500 0.097 31052 0.003 0.070
Uc(fps) = 107.895 . T = 15.000 (averaging time) Condition: Non-Vortical
y/d U/Uc v/Uc e u'/Uc v'/Uc uv/Ucz y C/T
“10000 00006 00052 820438 00002 00006 00000 0.999 3.000
-0.933 0.005 0.047 82.854 0.002 0.005 0.000 1.000 3.066
'0.866 0.016 0.059 74.314 0.004 0.011 0.000 0.999 3.000
-00800 00018 00063 7‘0141 00006. 00011 0.000 06997 5.800
-0.733 0.018 0.069 74.851 0.009 0.020 0.000 0.824 112.666
“0.666 00041 0.055 520909 00023 0.028 0.005 0.048 64.733
-0.600 0.008 0.014 59.779 0.000 0.000 0.000 -0.000 0.000
-0.533 0.008 0.014 59.779 0.000 0.000 0.000 0.000 0.000
-0.466 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
-0.400 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
-0.333 0.016 0.001 5.341 0.000 0.000 0.000 -0.000 0.000
-00266 0.075 00007 505‘0 06240 00022 0.053 0.000 00266
“00200 0.059 00006 50798 00208 0.021 0.043 0.000 0.200
“00133 06045 0000‘ 56634 00171 0.017 0.029 0.000 00133
'0.066 0.030 0.002 5.342 0.119 0.011 0.013 0.000 0.066
'0.000 0.113 0.013 6.958 0.302 0.033 0.099 0.000 0.533
0.066 0.099 0.013 7.647 0.280 0.033 0.092 0.000 0.400
0.133 0.044 0.006 8.984 0.167 0.023 0.039 0.000 0.200
0.199 0.126 0.018 8.101 0.318 0.041 0.128 0.000 0.600
0.266 0.032 0.005 9.191 0.127 0.017 0.022 0.000 0.066
0.333 0.029 0.004 9.111 0.115 0.015 0.017 0.000 0.066
0.400 0.016 0.003 10.459 0.000 0.000 0.000 0.000 0.000
0.466 0.016 0.003 10.459 0.000 0.000 0.000 0.000 0.000
0.533 0.016 0.003 10.459 0.000 0.000 0.000 0.000 0.000
0.600 0.016 0.003 10.459 0.000 0.000 0.000 0.000 0.000
0.666 0.035 0.002 3.252 0.038 0.008 -0.000 0.001 1.466
0.733 0.067 -0.021 ~17.631 0.036 0.019 -0.004 0.098 64.666
0.800 0.045 “00045 -‘50017 00016 0.018 -0000! 0.630 128.566
0.866 0.034 -0.045 -52.787 0.010 0.014 -0.001 0.941 39.133
0.933 0.026 "00055 “646391 00005 00010 “0.000 0.996 50133
1.000 0.021 -0.045 -64.111 0.005 0.009 -0.000 0.999 3.066

TABLE D-l3 Continued

131

X/d Au/d = Ay/d = Xx/d = 1. /d =
3.000 0.097 0.052 0.083 0.070
Uc(fP3) =107.659 T = 15.000 (averaging time) Condition: Non-Vortical
c 0 — '2
y/d u/uc V/Uc e u /Uc v /Uc uv/uc y C/‘I'
1.250 0.023 -0.043 -61.433 0.004 0.009 -0.000 0.992 5.400
10166 0.021 ”00044 '640037 00003 0.013 ”0.000 00964 15.800
1.083 0.027 -0.055 -63.301 0.007 0.018 -0.001 0.866 42.933
1.000 0.041 -0.058 -54.893 0.016 0.021 -0.002 0.641 83.266
0.916 00057 “00048 “390887 00021 00023 ’00003 06292 860466
00833 0.073 .000‘2 -300314 00041 00028 “06007 06051 290933
00750 00042 '00025 ’310557 00047 00032 “00013 00002 10866
0.666 0.020 -0.011 ~28.250 0.029 0.018 -0.005 0.000 0.200
0.583 0.014 -0.007 -27.617 0.000 0.000 0.000 0.000 0.000
0.500 0.014 “00007 ‘270617 00000 06000 0.000 0.000 00000
0.416 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
0.333 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
0.250 0.016 0.001 5.341 0.000 0.000 0.000 -0.000 0.000
00166 0.045 0.00“ 5.992 00172 00019 00032 -0.000 00133
0.083 0.116 0.010 5.236 0.309 0.026 0.079 0.000 0.533
0.000 0.073 0.007 5.920 0.241 0.024 0.059 0.000 0.266
-0.083 0.045 0.004 5.797 0.174 0.018 0.031 0.000 0.133
-0.166 0.101 0.010 6.019 0.289 0.029 0.083 0.000 0.400
-O.249 0.045 0.004 5.395 0.171 0.016 0.027 0.000 0.133
-0.333 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
'0.416 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
'00‘99 00°16 00°01 503“1 00000 0.000 00000 00000 0.000
-0.583 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
-0.666 0.039 0.008 11.942 0.051 0.018 0.007 0.000 0.866
'0.750 0.075 0.040 28.359 0.044 0.028 0.008 0.043 29.600
'0.833 0.065 0.037 29.930 0.031 0.022 0.004 0.311 88.666
-0.916 0.044 0.056 51.708 0.014 0.019 0.001 0.729 78.133
-0.999 0.027 0.066 67.197 0.009 0.018 0.001 0.898 37.866
-1.083 0.022 0.064 70.869 0.006 0.012 0.000 0.983 9.733
-1.166 0.017 0.056 72.604 0.004 0.012 0.000 0.995 4.466
-1.250 0.019 0.057 71.634 0.003 0.006 0.000 0.999 3.333

TABLE D-l3 Continued

132

x/d Au/d - Ay/d .. xx/d - xy/d -.-
4.500 0.097 0.052 0.083 0.070
Uc(fps) =107.653 T = 15.000 (averaging time) Condition: Non-Vortical
v c — '2'

y/d u/uc v/Uc e u /Uc v /Uc uv/Uc y C/T
-1.500 0.014 0.046 72.463 0.002 0.007 0.000 0.998 4.000
-1.400 0.014 0.058 76.272 0.004 0.011 0.000 0.981 8.933
-l.300 0.018 0.058 72.682 0.003 0.015 0.000 0.951 17.200
-1.200 0.022 0.061 70.222 0.004 0.021 0.001 0.811 46.066
-1.100 0.049 0.061 51.204 0.017 0.022 0.003 0.625 71.333
-1.000 0.054 0.057 46.856 0.024 0.025 0.004 0.347 76.933
'0.900 0.052 0.036 34.817 0.042 0.029 0.009 0.060 26.533
-0.800 0.081 0.052 32.415 0.052 0.036 0.013 0.022 11.466
“0.700 0.025 0.018 360248 00039 00029 0.010 0.000 0.533
-00600 0.018 06002 70083 0.017 00007 06001 0.000 0.066
-0.500 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
“06400 06016 00001 503‘1 00000 00000 00000 0.000 0.000
-0.300 0.016 0.001 5.341 0.000 0.000 0.000 0.000 0.000
.00200 00016 0.001 50341 0.000 00000 0.000 0.000 06000
-0.100 0.030 0.003 6.316 0.117 0.007 0.008 0.000 0.066
-0.000 0.059 0.008 7.893 0.207 0.028 0.056 0.000 0.200

0.099 0.016 0.002 8.329 0.000 0.000 0.000 -0.000 0.000

0.199 0.016 0.002 8.329 0.000 0.000 0.000 0.000 0.000

0.299 0.016 0.002 8.329 0.000 0.000 0.000 0.000 0.000

0.399 0.016 0.002 8.329 0.000 0.000 0.000 0.000 0.000

0.499 0.016 0.002 8.329 0.000 0.000 0.000 0.000 0.000

0.599 0.016 0.002 8.329 0.000 0.000 0.000 0.000 0.000

0.699 0.021 0.001 3.669 0.025 0.006 -0.001 0.000 0.133

0.800 0.043 -0.019 -24.266 0.052 0.028 -0.012 -0.000 1.400

0.900 00083 “00052 -260715 00051 00031 “0.010 00038 170000

00999 00079 -00036 “2‘0259 000‘1 0002‘ -00005 0.124 46.400

1.100 0.067 -0.036 -28.593 0.029 0.018 -0.003 '0.357 75.333

1.200 0.060 -0.035 -30.282 0.023 0.013 -0.002 0.659 64.800

1.300 0.038 -0.038 -44.506 0.015 0.013 -0.002 0.839 40.066

1.399 0.021 -0.040 -61.822 0.003 0.013 -0.001 0.950 17.800

1.500 0.014 -0003? '680077 00006 0.011 “00000 00993 50666

TABLE D-l3 Continued

133

x/d Au/d - Ay/d - xx/d .. xy/d _
6.000 0.097 0.052 0.083 0.070
Uc(fps) = 106.213 ‘1‘ = 15.000 (averaging time) Conditzion: Non-Vortical
e c — "

y/d U/Uc V/Uc 9 u /Uc v /UC uv/Uc Y C/T
‘1.875 0.012 0.047 75.066 0.002 0.007 0.000 0.998 3.466
“1.750 0.009 0.042 77.180 0.000 0.009 0.000 0.996 4.133
“10625 00013 0.055 750882 00005 0.016 0.000 0.971 12.400
-1.500 0.018 0.064 73.857 0.007 0.021 0.001 0.906 24.933
'1.375 0.037 0.069 61.852 0.013 0.025 0.003 0.767 49.800
"1.250 00049 0.069 54.360 0.020 00027 0000‘ 0.526 67.000
-1.125 0.049 0.049 45.550 0.037 0.034 0.010 0.148 37.933
-1.000 0.087 0.054 32.208 0.047 0.031 0.010 0.083 32.266
“0.875 0.092 0.052 29.446 0.067 0.039 0.020 0.016 8.666
-0.750 0.033 0.022 33.693 0.054 0.036 0.017 0.000 0.666
”0.625 00022 06013 316801 OOO‘Z 06021 0.008 0.000 00133
*0.500 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000
-O.375 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000
“00250 0.018 00001 50341 00000 0.000 0.000 0.000 0.000

0.000 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000

0.125 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000

0.250 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000

0.375 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000

0.500 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000

0.625 0.018 0.001 5.341 0.000 0.000 0.000 0.000 0.000

0.750 0.026 -0.000 -1.489 0.034 0.012 '0.003 0.000 0.266

0.875 0.069 -0.031 -24.608 0.070 0.039 -0.021 0.004 2.800

1.000 00092 “00048 “270832 00056 0.033 ’00012 0.050 20.333

1.125 0.086 -0.042 ~26.335 0.043 0.025 '0.005 0.154 47.066

1.250 0.080 ~0.035 -23.484 0.034 0.018 -0.003 0.389 71.466

1.375 0.063 ~0.033 ~27.656 0.026 0.015 -0.002 0.664 60.800

1 .500 00046 ’00039 “'40. 112 0.019 00012 -06003 0.846 370‘00

1.625 0.032 -0.038 -49.921 0.009 0.012 -0.002 0.960 13.000

1.750 0.016 -0.030 -61.349 0.003 0.014 -0.001 0.629 4.400

1.875 0.012 -0.038 ~72.269 0.004 0.008 '0.000 0.998 3.466

TABLE D-13 Continued

134

x/d Au/d = Ay/d = Xx/d = X /d =

8.000 0.097 0.052 0.083 3.070

Uc(fps) = 93.190 T = 15.000 (averaging time) Condition: Non-Vortical

n . -—— -Z

y/d U/Uc V/Uc 6 u /UC v /Uc uv/Uc y C/T
2.250 0.015 -0.038 -68.109 0.008 0.010 -0.000 0.998 3.666
2.100 0.017 -0.044 -68.631 0.008 0.014 -0.001 0.989 6.800
r.950 0.024 -0.050 -64.066 0.009 0.019 ~0.002 0.961 12.400
1.800 0.029 -0.043 -55.459 0.009 0.025 -0.006 0.590 18.400
1.650 0.055 ~0.058 ~46.370 0.023 0.022 -0.006 0.752 49.066
1.500 0.085 -0.042 ~26.606 0.038 0.022 -0.004 0.469 60.333
1.350 0.097 -0.048 -26.l75 0.045 0.024 -0.006 0.322 60.933
1.200 0.076 -0.033 “23.460 0.067 0.034 -0.016 0.031 14.600
1.050 0.123 -0.060 -26.124 0.083 0.044 -0.025 0.019 9.733
0.900 0.074 -0.029 ~21.572 0.092 0.043 *0.031 0.004 2.200
0.750 0.041 -0.013 -18.291 0.078 0.034 -0.016 0.000 0.400
0.600 0.020 -0.004 -13.015 0.000 0.000 0.000 0.000 0.000
0.450 0.020 -0.004 -13.015 0.000 0.000 0.000 0.000 0.000
0.300 0.020 -0.004 -13.015 0.000 0.000 0.000 0.000 0.000
0.150 00020 “06004 ‘130015 00000 00000 00000 0.000 06000
0.000 0.020 -0.004 -13.015 0.000 0.000 0.000 0.000 0.000
'0.149 0.020 -0.004 '13.015 0.000 0.000 0.000 0.000 0.000
“0.299 00021 06001 563“! 0.000 00000 00000 00000 00000
-00449 00021 06001 5.341 0.000 00000 00000 00000 00000
-0.599 0.021 0.001 5.341 0.000 0.000 0.000 0.000 0.000
-0.749 0.049 0.010 11.956 0.080 0.026 0.017 0.000 0.533
“0.899 00070 00039 290298 00088 00048 0.036 0.001 2.066
-1.049 0.115 0.071 31.782 0.070 0.046 0.022 0.033 15.400
-1.199 0.110 0.057 27.401 0.056 0.033 0.012 0.139 42.933
'1.349 0.101 0.050 26.598 0.045 0.021 0.010 0.342 64.000
“1.499 00090 00048 280332 00035 00018 0.006 0.598 57.133
'1.649 0.062 0.052 40.324 0.023 0.016 0.008 0.830 37.733
-1.799 0.040 0.051 52.023 0.011 0.018 0.004 0.922 19.800
-10949 0.020 00064 720816 00003 00017 00001 00971 80666
’2.099 0.014 0.057 76.021 0.007 0.016 0.000 0.987 6.266
”20259 0.001 0.045 87.526 0.005 00020 00000 0.590 20800

TABLE D-13 Continued

135

x/d Au/d = A /d = Xx/d = X /d =
10.000 0.097 3.052 0.083 0.070

Uc(fpa) = 84.300 '1‘ = 15.000 (averaging time) Condition: Non-Vortical

y/d u/uc v/Uc e “V". w/uc uv/Ucz v C/T
'2.500 0.002 0.066 88.238 0.012 0.020 0.000 0.991 5.800
“20333 00005 06067 856144 00013 00022 0.000 0.986 8.333
“20166 00011 00084 826069 00011 00031 0.001 0.937 16.800
“2.000 0.019 0.088 77.401 0.019 0.038 0.003 0.858 30.666
“1.833 00041 0.091 650353 00001 00044 0.010 06658 39.333
-1.666 0.104 0.071 34.467 0.042 0.028 0.013 0.558 59.000
-1.500 0.116 0.067 30.079 0.051 0.029 0.013 0.382 61.666
-1.333 0.129 0.061 25.513 0.058 0.032 0.012 0.229 50.200
-1.166 0.106 0.053 26.655 0.087 0.046 0.030 0.047 17.600
’1.000 06148 0.070 250342 00110 00057 00044 00016 7.933
-00833 0.072 00043 310368 00095 0.054 0.043 00003 10933
-0.666 0.024 0.019 39.142 0.033 0.020 0.005 0.000 0.133
”0.500 0.019 00016 406714 00000 00000 0.000 00000 0.000
-0.333 0.019 0.016 40.714 0.000 0.000 0.000 0.000 0.000
-O.166 0.019 0.016 40.714 0.000 0.000 0.000 0.000 0.000
-0.000 0.019 0.016 40.714 0.000 ~0.000 0.000 0.000 0.000
0.166 0.019 0.016 40.714 0.000 0.000 0.000 0.000 0.000
0.333 0.019 0.016 40.714 0.000 0.000 0.000 0.000 0.000
0.499 0.019 0.016 40.714 0.000 0.000 0.000 0.000 0.000
00666 0.022 0.019 ‘10285 00029 0.028 00008 ’0.000 06066
0.833 0.047 -0.010 -12.379 0.070 0.031 -0.020 0.000 0.466
00999 0.100 '000‘2 ”22.924 0.111 0.054 '00051 00003 2.666
1.166 0.149 -0.068 ~24.748 0.097 0.051 -0.033 0.028 12.333
1.333 0.140 -0.061 -23.677 0.074 0.041 -0.014 0.093 28.600
1.500 0.124 -0.050 -21.917 0.055 0.030 -0.006 0.295 56.666
1.666 0.113 -0.045 -22.009 0.049 0.018 -0.006 0.492 62.800
1.333 06095 -00042 “230870 00041 00003 -00006 0.7‘3 56.866
1.999 0.075 -0.041 -28.553 0.033 0.004 -0.006 0.874 27.866
2.166 0.051 -0.048 -43.272 0.017 0.011 -0.007 0.948 16.800
2.333 0.043 -0.041 ~43.455 0.011 0.010 -0.003 0.988 7.000
20500 0.041 -00039 -430806 00008 00008 ‘00001 0.995 ‘0066

TABLE D-l4 DATA LISTING

,136

x/d Au/d = Ay/d = Xx/d = X /d =
0.500 0.089 0.053 0.075 0.071
Uc(fps) =104. 022 T = 15.000 (averaging time) Condition: Non-Vortical
1 u "— '2
y/d U/Uc v/Uc 6 u /Uc v /Uc uv/Uc y C/T
0.000 00644 00023 20104 06395 00011 ’00032 0.004 3.466
0.050 0.804 0.018 1.344 0.330 0.020 -0.060 0.008 6.666
00100 0.707 00021 10716 00375 00015 ‘00048 0.006 4.333
0.150 0.798 0.016 1.174 0.326 0.023 -0.070 0.007 6.000
0.200 0.802 0.021 1.548 0.328 0.020 -0.058 0.008 6.600
0.250 0.605 0.027 2.574 0.405 0.010 -0.025 0.006 5.266
00300 06802 00021 10520 00328 00021 “0.059 0.007 66133
0.350 0.779 0.022 1.685 0.340 0.018 -0.049 0.006 5.600
0.400 0.510 0.028 3.159 0.423 0.008 -0.009 0.002 2.400
0.450 0.018 “0.001 -3.680 0.000 0.000 0.000 0.000 0.000
0.500 0.018 -0.001 '3.680 0.000 0.000 0.000 0.000 0.000
0.550 0.018 -0.001 -3.680 0.000 0.000 0.000 0.000 0.000
0.600 0.031 -0.019 -32.248 0.010 0.008 -0.000 0.215 98.933
0.650 0.016 -0.033 -63.872 0.003 0.005 -0.000 0.982 17.333
0.700 0.005 -0.040 -82.262 0.002 0.007 -0.000 1.000 3.000
0.750 -0.003 -0.037 ~94.683 0.001 0.004 0.000 0.999 3.066
0.000 0.751 0.030 2.321 0.345 0.013 -0.032 0.006 5.466
'0.050 0.539 0.034 3.691 0.409 0.007 0.007 0.003 3.333
-0.100 0.574 0.034 3.432 0.400 0.008 -0.000 0.003 2.800
-0.150 0.547 0.035 3.705 0.397 0.007 0.007 0.003 2.933
-0.200 0.749 0.035 2.732 0.319 0.013 -0.029 0.006 5.066
-0.250 0.853 0.029 1.989 0.203 0.015 -0.019 0.010 8.066
'0.300 0.881 0.031 2.041 0.152 0.014 -0.012 0.011 8.466
“0.350 0.680 0.033 2.825 0.362 0.009 -0.016 0.007 6.000
-0.400 0.570 0.032 3.210 0.396 0.008 -0.003 0.003 3.066
-O.450 0.018 -0.001 '3.798 0.000 0.000 0.000 0.000 0.000
"0.500 0.018 -0.001 -3.798 0.000 0.000 0.000 0.000 0.000
-0.550 0.066 ~0.008 -7.362 0.016 0.010 0.000 0.045 33.800
-0.600 0.050 -0.028 -29.391 0.012 0.007 -0.000 0.901 4.066
“0.650 0.047 0.007 9.103 0.006 0.001 0.000 1.000 3.000
'0.700 0.039 0.035 42.083 0.004 0.005 0.000 1.000 3.000
'0.750 0.028 0.037 52.220 0.007 0.009 0.000 0.894 2.933

TABLE D-14 Continued

1’37

x/d Au/d .. Ay/d - Xx/d - Xy/d =
1.500 0.089 0.053 0.075 0.071
Uc(fpa) = 104. .022 T = 15,000 (averaging time) Condition: Non-Vortical
1 g — -Z
y/d u/Uc v/Uc e u /Uc v /Uc uv/Uc y C/T
'1.000 0.016 0.042 68.993 0.001 0.004 0.000 1.000 3.000
-O.933 0.019 0.035 60.839 0.001 0.003 0.000 1.000 3.000
’00866 00025 00044 590560 00004 00007 00000 00968 30266
“00800 00026 00042 580079 00003 00006 00000 10000 20600
-0.733 0.031 0.052 59.064 0.005 0.008 0.000 0.990 9.600
-0.666 0.045 0.054 49.939 0.011 0.015 0.000 0.638 136.066
-0.600 0.073 0.038 27.626 0.021 0.020 0.000 0.022 16.866
~0.533 0.016 0.006 22.462 0.000 0.000 0.000 0.000 0.000
-0.466 0.018 -0.001 ~5.220 0.000 0.000 0.000 0.000 0.000
-0.400 0.018 -0.001 -5.220 0.000 0.000 0.000 0.000 0.000
'0.333 0.572 0.048 4.835 0.380 0.017 0.039 0.004 3.066
-0.266 0.829 0.057 3.997 0.193 0.016 0.003 0.014 11.000
’00200 00827 00055 30807 00192 00011 “00002 00009 70533
'0.133 0.607 0.053 5.025 0.368 0.013 0.040 0.004 3.666
-00066 00121 00059 “0705 00325 00010 00012 00006 50333
'0.000 0.936 -0.002 -0.124 0.172 0.023 -0.033 0.011 9.066
0.066 0.774 0.012 0.939 0.363 0.022 -0.074 0.008 6.666
0.133 0.575 0.014 1.493 0.417 0.016 -0.054 0.005 4.066
0.199 0.727 0.018 1.468 0.378 0.023 -0.070 0.005 4.400
0.266 0.709 0.018 1.496 0.384 0.021 -0.055 0.005 4.466
0.333 0.479 0.028 3.362 0.434 0.021 '0.005 0.002 1.866
0.400 0.018 ~0.001 -4.243 0.000 0.000 0.000 0.000 0.000
0.466 0.038 0.003 4.528 0.138 0.028 0.038 0.000 0.066
00533 00018 '00001 -402‘3 00000 00000 00000 00000 00000
0.600 0.018 -0.001 -4.243 0.000 0.000 0.000 0.000 0.000
00666 00072 “00040 ‘290‘41 00031 00020 ’00000 0003‘ 250066
0.733 0.042 -0.043 -45.792 0.015 0.014 -0.001 0.601 144.133
0.800 0.024 -0.044 -61.129 0.006 0.010 -0.000 0.981 15.200
0.866 0.010 -0.032 ~72.158 0.003 0.009 -0.000 0.805 2.533
00933 00009 ”00039 “750905 00002 00005 “00000 10000 30000
1.000 0.004 -0.049 -84.693 0.002 0.010 -0.000 0.965 3.333

TAB LE D' 1 4 Continued

138

x/d Au/d - Ay/d - Xx/d - Xy/d -

3.000 0.089 0.053 0.075 0.071

Uc(fpa) =103.a¢.4 T = 15,000 (averaging time) Condition: Non-Vortical

u t — '2

y/d U/Uc v/uc e u /Uc v /Uc uv/Uc Y C/T
10250 00001 '00040 “070690 00001 00006 “00000 00999 30133
1.166 0.001 -0.046 -87.821 0.000 0.009 -0.000 0.998 4.000
1.083 0.018 -0.049 -69.604 0.003 0.013 -0.000 0.980 11.066
1.000 0.030 -0.049 ~58.178 0.010 0.016 -0.002 0.861 49.400
0.916 0.045 -0.048 -46.688 0.019 0.016 -0.002 0.618 95.933
00833 00079 “00043 “280021 00032 00019 “00000 00181 710733
0.750 0.108 -0.040 -20.458 0.046 0.026 -0.001 0.019 10.533
0.666 0.028 -0.012 ~23.725 0.043 ‘ 0.017 -0.006 0.000 0.266
0.583 0.016 -0.007 -25.302 0.000 0.000 0.000 0.000 0.000
0.500 0.016 -0.007 -25.302 0.000 0.000 0.000 0.000 0.000
0.416 0.016 -0.007 -25.302 0.000 0.000 0.000 0.000 0.000
0.333 0.041 0.004 6.607 0.154 0.041 0.063 0.000 0.066
0.250 0.402 0.057 8.110 0.443 0.040 0.156 0.001 1.666
0.166 0.911 0.054 3.411 0.290 0.029 -0.020 0.009 7.466
00083 00949 00053 3.245 00255 00028 “00017 00016 110800
00000 00901 00049 30029 00254 00029 “00000 00017 120333
-0.083 0.911 0.050 3.170 0.291 0.027 -0.031 0.012 9.733
-0.166 0.785 0.055 4.010 0.381 0.022 -0.036 0.009 7.866
“00249 00725 00042 30340 00400 00022 00004 0000‘ 30600
-0.333 0.037 0.000 1.511 0.132 0.013 0.016 0.000 0.066
'0.416 0.018 -0.000 ~3.114 0.000 0.000 0.000 0.000 0.000
-0.499 0.018 -0.000 -3.114 0.000 0.000 0.000 0.000 0.000
'0.583 0.027 0.003 7.897 0.038 0.022 0.007 0.000 0.200
-0.666 0.072 0.061 40.293 0.041 0.037 0.009 0.006 5.000
“00750 00074 00060 380969 0002‘ 00025 00002 00178 730533
“00833 00047 00059 510093 00016 00022 00001 00616 1010466
“0.916 0.026 0.059 66.224 0.007 0.018 0.000 0.893 42.800
’0.999 0.016 0.059 74.606 0.005 0.011 0.000 0.982 10.533
-1.083 0.007 0.047 80.676 0.002 0.008 0.000 0.998 3.800
-1.166 0.001 0.050 88.785 0.002 0.007 -0.000 0.999 3.066
“10250 00002 00043 860213 00002 00006 “00000 10000 30000

TABLE D-14 Continued

x/d ‘Au/d== .Ay/d:= xx/d== 1 /d:=
4.500 0.089 0.053 0.075 0.071
Uc(fpe) = 104.115 ‘1‘ = 15.000 (everaging time) Condition: Non-Vortical
I I — '2

y/d u/uc v/uc e u /uc v /Uc uv/Uc v C/T
-1.500 -0.003 0.046 94.184 0.002 0.005 -0.000 0.999 3.200
-1.400 -0.002 0.043 93.586 0.002 0.010 -0.000 0.949 4.400
-1.300 -0.002 0.049 92.675 0.008 0.014 -0.000 0.981 9.400
-1.200 -0.003 0.059 93.180 0.009 0.021 -0.000 0.926 24.466
-1.100 0.002 0.071 88.144 0.008 0.027 -0.000 0.776 60.066
~-1.000 0.029 0.074 68.827 0.008 0.029 0.002 0.580 83.400
-00900 00062 00074 500222 00025 0.028 00002 00240 740733
‘00600 00100 00067 330880 00032 00030 00002 00053 270133
'00700 00101 00055 280676 00057 00038 00014 00007 40533
-O.600 0.026 0.001 3.091 0.037 0.017 0.005 0.000 0.133
-0.500 0.018 -0.001 -5.220 0.000 0.000 0.000 0.000 0.000
-0.400 0.018 -0.001 '5.220 0.000 0.000 0.000 0.000 0.000
-0.300 0.038 0.000 1.117 0.134 0.016 0.020 0.000 0.066
'0.200 0.309 0.026 4.912 0.438 0.018 0.054 0.001 1.000
-0.100 0.740 0.029 2.257 0.407 0.026 -0.009 0.005 5.066
'00000 10019 00041 20319 0004. 00036 0.001 00014 110666
0.099 0.779 0.067 4.925 0.397 0.025 0.005 0.007 5.666
0.199 0.412 0.059 8.172 0.454 0.041 0.167 0.001 1.466
0.299 0.107 0.024 12.948 0.286 0.069 0.196 0.000 0.266
0.399 0.018 0.000 0.480 0.000 0.000 0.000 0.000 0.000
0.499 0.018 0.000 0.480 0.000 0.000 0.000 0.000 0.000
0.599 0.018 0.000 0.480 0.000 0.000 0.000 0.000 0.000
0.699 0.051 ~0.005 -5.640 0.077 0.016 -0.008 0.000 0.600
0.800 0.117 ~0.052 ~24.223 0.059 0.034 -0.008 0.009 6.200
0.900 0.110 -0.043 -21.226 0.042 0.025 -0.000 0.070 32.600
0.999 0.089 -0.039 -23.757 0.036 0.018 -0.001 0.239 72.466
1.100 0.068 -0.030 -24.224 0.031 0.013 '0.002 0.545 78.400
1.200 0.051 -0.031 -3l.222 0.022 0.007 -0.002 0.822 50.733
1.300 0.040 -0.032 ~38.738 0.015 0.009 -0.001 0.880 17.333
10399 00030 “00032 “460554 00007 00007 -00001 00988 70333
10500 00021 .00030 ’460255 00005 00005 -00000 00996 30400

v/d

1.750
1.633
1.516
1.400
1.283
1.166
1.050
0.933
0.816
0.700
0.583
0.466
0.350
0.233
0.116
0.000
-00 116
“00233
“00349
“0.466
“00583
”00699
“00816
“0.933
‘10050
“10166
-10283
”1.399
“10516
-10633
-10750

x/d

6.000

UCHPS) =102.301

TABLE D-14 Continued

Au/d -

0.089

T = 15.000

V/Uc 8
-0.031 -51.267
-0.034 -50.446
-0.040 -52.490
-0.046 -48.302
-0.050 -38.727
-0.036 -21.602
-0.032 -16.283
“0.049 ”19.804
-0.037 -20.038
’00007 “100210
“00001 ”50220
“00001 “5.220
-0.001 -5.220
0.003 5.019
0.015 7.850
0.030 7.169
0.014 7.537
0.008 5.839
-0.000 ’10432
-0.000 -1.432
0.002 5.036
0.033 20.936
0.076 32.670
0.062 29.677
0.049 28.852
0.050 37.229
0.047 42.653
0.052 57.617
0.051 71.858
0.051 78.746
0.047 87.374

AY/d :
0.053

cfl/Uc

0.004
0.006
0.007
0.017
0.028
0.038
0.041
0.052
0.088
0.069
0.000
0.000
0.000
0.153
0.308
0.432
0.296
0.255
0.000
0.000
0.026
0.087
0.047
0.039
0.032
0.025
0.018
0.012
0.011
0.004
0.001

(averaging time)

Condition:

-—— -Z
v'/Uc uv/Uc

0.006
0.008
0.014
0.016
0.017
0.020
0.024
0.031
0.038
0.020
0.000
0.000
0.000
0.035
0.046
0.041
0.039
0.030
0.000
0.000
0.017
0.047
0.038
0.027
0.024
0.020
0.017
0.023
0.018
0.012
0.009

“00001
-0.001
“00003
"'O .004
'00005
-00000
0.000
0.001
”0.019
“00008
0.000
0.000
0.000
0.053
0.141
0.155
0.114
0.073
0.000
0.000
0.004
0.035
0.007
0.006
0.003
0.005
0.004
0.003
0.001
0.000
-0.000

X /d:=

0.071

Non-Vortical

Y

0.992
0.988
0.940
0.826
0.605
0.371
0.168
0.029
0.005
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.002
0.019
0.097
0.313
0.606
0.829
0.782
0.963
0.992
0.997

C/T

5.533
6.133
20.800
41.933
72.533
74.266
52.866
14.800
3.266
0.400
0.000
0.000
0.000
0.066
0.266
0.600
0.266
0.200
0.000
0.000
0.066-
1.533
11.200
40.800
72.666
72.400
44.400
25.533
13.800
5.666
3.733

y/d

“20100
‘10950
’10800
“10650
'1e500
-10350
’10200
-10050
-00900
“00750
“00600
“0.450
'00300
’00150
”00000
0.149
0.299
0.449
0.599
0.749
0.899
1.049
1.199
1.349
1.499
1.649
1.799
1.949
2.100

x/d

8.000

06“?!) = 96.571

TAB LE D- l 4 Continued

Xx/d:=
0.075

Condition:

-—- -Z
v'/UC uv/Uc

.Au/d- .Ay/d=:

0.089 0.053

T = 15.000 (averaging time)

I
V/Uc 6 u /Uc

0.052 97.999 0.004 0.010
0.059 101.741 0.009 0.017
0.058 100.034 0.016 0.023
0.066 97.064 0.014 0.030
0.076 96.040 0.010 0.033
0.095 77.981 0.010 0.045
0.092 43.517 0.036 0.036
0.083 31.433 0.046 0.038
0.070 19.364 0.070 0.041
0.035 20.113 0.114 0.051
0.006 12.623 0.052 0.030
0.002 5.881 0.000 0.000
0.002 5.881 0.000 0.000
0.002 5.881 0.000 0.000
0.002 5.881 0.000 0.000
0.002 5.881 0.000 0.000
0.010 11.960 0.176 0.051
0.002 5.881 0.000 0.000
0.003 5.644 0.063 0.007
-o.012 -8.163 0.115 0.023
-0.081 -25.131 0.096 0.046
‘00075 -250502 00061 00037
-0.054 ’21.268 0.052 00030
‘000‘0 '20006‘ 0.051 00021
.00040 “230983 00041 00003
-00048 “37.085 0.030 0.009
-0.044 ~46.086 0.018 0.013
'000‘1 '5‘. 3’96 00007 00013
-0.038 -56.897 0.003 0.009

-0.000
‘00001
”00001
“0.002
“00003
0.001
0.008
0.005
0.005
0.045
0.015
0.000
0.000
0.000
0.000
0.000
0.091
0.000
0.003
-00016
“0.012
-0.005
“00001
“0.003
'00005
-00009
“0.005
-00003
“06001

d1:
xy/

0.071

Non-Vortical

Y

0.997
0.987
0.962
0.854
0.788
0.492
0.252
0.095
0.016
0.003
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.008
0.050
0.146
0.327
0.644
0.811
0.936
0.981
0.993

C/T

3.800
7.133
14.800
23.666
44.600
61.866
61.000
34.200
9.266
1.933
0.066
0.000
0.000
0.000
0.000
0.000
0.066
0.000
0.066
1.066
4.733
21.400
45.466
62.133
62.866
43.666
20.600
8.666
4.666

TABLE D-l4 Continued

x/d Au/d = Ay/d = xx/d = x /d .-.
10.000 0.089 0.053 0.075 3.071
Uc(fpe) = 82.444 T = 15.000 (averaging time) Condition: Non-Vortical
-—— -Z
y/d, U/Uc V/Uc 8 u'/Uc v'/Uc uv/Uc y C/T

20500 00016 “06043 ‘680810 00008 00012 ’00001 0.957 4.200
20333 0.015 “00051 “730599 00014 0.018 -06002 00989 6.133
2.166 0.019 -0.058 -71.183 0.016 0.025 -0.003 0.908 12.066
2.000 0.040 -0.070 -60.244 0.012 0.029 -0.007 0.893 27.400
1.833 0.077 -0.066 -40.808 0.039 0.025 -0.007 0.766 44.866
1.666 0.111 -0.068 -31.579 0.049 0.025 -0.005 0.548 66.066
1.500 0.130 -0.067 -27.370 0.055 0.027 -0.006 0.409 68.800
1.333 0.163 -0.077 -25.426 0.064 0.035 -0.003 0.171 50.933
1.166 0.187 -0.082 -23.781 0.070 0.041 0.001 0.051 20.133
1.000 00198 -00065 -18036‘ 0.112 00051 -06026 00013 7.600
0.833 0.093 -0.028 -16.678 0.127 0.047 -0.037 0.001 1.000
0.666 0.046 -0.016 -19.475 0.079 0.031 -0.020 0.000 0.200
0.500 0.025 -0.009 ~20.556 0.000 0.000 0.000 0.000 0.000
0.333 0.025 -0.009 -20.556 0.000 0.000 0.000 0.000 0.000
0.166 0.025 -0.009 ~20.556 0.000 0.000 0.000 0.000 0.000
0.000 0.025 -0.009 -20.556 0.000 0.000 0.000 0.000 0.000
-0.166 0.025 -0.009 -20.556 0.000 0.000 0.000 0.000 0.000
“00333 00044 '00003 -40224 00090 00029 00026 0.000 00133
”00499 00035 00000 10‘79 00058 00023 00013 0.000 0.066
-0.666 0.059 0.007 7.551 0.092 0.033 0.027 0.000 0.333
-0.833 0.107 0.022 12.074 0.125 0.043 0.041 0.002 1.666
-0.999 0.183 0.099 28.535 0.083 0.051 0.016 0.023 11.933
-1.166 0.176 0.069 21.426 0.063 0.040 0.005 0.106 36.200
-1.333 0.157 0.063 21.999 0.058 0.024 0.009 0.243 59.133
'1.500 0.132 0.035 14.085 0.055 00016 00006 0.461 670533
'10666 0.108 00065 31.234 0.045 00022 0.016 00661 590333
-10833 0009‘ 00040 230431 00032 00019 00012 0.826 31.733
-1.999 0.067 0.030 24.313 0.032 0.022 0.009 0.944 18.200
-2.166 0.066 0.025 20.645 0.030 0.016 0.006 0.865 9.066
“20333 00036 0002‘ 270833 00012 00001 00001 0.941 4.266
-2.500 0.038 0.027 35.567 0.006 0.004 0.000 0.999 3.133

x/d
0.500

Ucmn) = 89. 626

v/d

0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750

0.000
'0.050
“00100
“00150
'00200
“00250
“00300
“00350
“00400
-00450
‘00500
”00550
-00600
“00650
“00700
“00750

0.045
1.001
1.027
1.038
1.037
1.038
1.028
1.033
0.651
0.020
0.020
0.062
0.062
0.048
0.029
0.022

1.011
1.019
1.022
1.025
1.021
1.027
1.031
0.975
1.007
0.418
0.020
0.022
0.066
0.054
0.051
0.038

TABLE D-lS DATA LISTING

.Ay/d=:
0.050

Xx/d.=
0.051

Au/d -

0.074

T = 15.000

v/UC o
-0.002 -2.735
0.016 0.935
0.013 0.741
0.017 0.942
0.018 0.997
0.013 0.732
0.016 0.930
0.015 0.872
~0.006 -0.587
0.002 6.365
0.002 6.365
-0.011 -10.751
-0.019 -17.638
“00031 “320788
“000‘“ “55081?
-0.037 -58.998
0.018 1.023
0.020 1.128
0.022 1.237
0.019 1.106
0.018 1.021
0.020 1.147
0.016 0.904
0.021 1.265
0.017 1.014
0.028 3.956
“00001 '40101
-0.001 -3.658
0.008 7.705
0.014 15.120
0.018 19.297
0.017 24.914

u.'/Uc

0.158
0.176
0.012
0.010
0.011
0.011
0.012
0.016
0.450
0.000
0.000
0.044
0.014
0.010
0.005
0.002

0.008
0.009
0.009
0.008
0.008
0.010
0.010
0.228
0.170
0.483
0.000
0.013
0.015
0.008
0.010
0.007

(averaging time)

Condition:

-—- -Z
v'/UC uv/Uc

0.025
0.021
0.014
0.014
0.015
0.014
0.015
0.021
0.028
0.000
0.000
0.024
0.010
0.007
0.009
0.004

0.012
0.012
0.012
0.011
0.012
0.012
0.012
0.019
0.017
0.011
0.000
0.001
0.006
0.003
0.003
0.003

143

’00039
0.030
0.000

“00000

-0.000

-0.000

“00000

-00000
0.098
0.000
0.000

-00005

-0.000

-0.000

“00000

“00000

0.000
0.000
0.000
0.000
0.000
0.000
0.000
“00029
'00019
0.017
0.000
0.000
0.000
0.000
0.000
0.000

X /d:=
8C046
Non-Vortical
v C/T
0.000 0.066
0.025 17.200
0.036 24.466
0.031 22.200
0.026 17.600
0.037 25.466
0.042 28.266
0.020 14.733
0.002 2.200
0.000 0.000
0.000 0.000
0.002 2.533
0.516 176.333
0.974 25.066
0.999 3.000
1.000 3.000
0.054 34.533
0.057 35.533
0.037 25.533
0.044 29.866
0.053 36.533
‘00037 240600
0.040 26.800
0.019 14.400
0.022 16.133
0.001 1.466
0.000 0.000
0.000 0.066
0.914 49.933
1.000 3.000
1.000 3.000
0.941 2.933

x/d
1.500

Ucupa) = 89.626

v/d

-1.000
“00933
“00866
“00800
“00733
“00666
“00600
“00533
“00466
“00300
“00333
“00266
“00200
“00133
“00066
“00000
0.066
0.133
0.199
0.266
0.333
0.400
0.466
0.533
0.600
0.666
0.733
0.800
0.866
0.933
1.000

U/ Uc
0.000
0.000

“00001

“00004

“00015
0.008
0.084
0.019
0.019
0.292
1.009
1.010
1.008
1.004
1.002
0.997
1.000
1.007
1.009
1.000
0.835
0.042
0.020
0.020
0.081
0.101
0.071
0.050
0.039
0.023
0.018

A

T = 15

‘v/UE

0.054
0.041
0.050
0.061
0.074
0.090
0.042
0.007
0.007
0.014
0.007
0.010
0.007
0.008
0.009
0.009
0.006
0.002
0.006
0.006
0.029
0.003
-0.001
-0.001
-0.010
-0.015
-0.022
“00026
-0.033
“0004‘
-0.035

TABLE D- 1 5 Continued

u/d =

0.074

.000
6

89.039
88.884
91.687
94.459
101.480
84.747
26.703
22.196
22.196
2.910
0.408
0.579
0.446
0.503
0.558
0.542
0.363
0.122
0.358
0.372
2.020
5.002
“30549
“30549
“60990
“8056‘
“170907
“270665
-40.105
~61.670
-63.213

.Ay/d:=
0.050

tH/Ue

0.003
0.002
0.003
0.005
0.011
0.019
0.059
0.000
0.000
0.440
0.035
0.022
0.016
0.013
0.012
0.012
0.013
0.015
0.019
0.023
0.348
0.147
0.000
0.000
0.072
0.034
0.022
0.013
0.008
0.004
0.003

(averaging time)

Condition:

-—- -Z
\N/Ue uv/Ug

0.003
0.011
0.007
0.011
0.018
0.026
0.035
0.000
0.000
0.015
0.022
0.016
o.q13
0.013
0.013
0.014
0.015
0.019
0.023
0.032
0.035
0.032
0.000
0.000
0.025
0.023
0.013
0.003
0.006
0.006
0.004

144

“00000
-0.000
“00000
“00000
“00000
“00000
0.012
0.000
0.000
“00001
0.000
0.000
0.000
0.000
0.000
0.000
-0.000
0.000
0.000
0.001
“00038
0.047
0.000
0.000
“00008
0.001
“00000
-0.000
“00000
“00000
-0.000

xy/d._

0.046
Non-Vortical

Y ‘C/T'

1.000 3.000
0.785 2.400
1.000 3.000
0.998 3.866
0.880 69.266
0.210 103.933
0.004 3.533
0.000 0.000
0.000 0.000
0.000 0.800
0.024 17.466
0.047 31.466
0.055 34.333
0.061 38.666
0.053 34.400
0.066 39.800
0.053 33.533
0.042 27.000
0.044 29.333
0.037 24.733
0.005 4.866
0.000 0.066
0.000 0.000
0.000 0.000
0.002 1.866
0.228 108.933
0.817 85.066
0.987 10.666
0.999 3.333
1.000 3.000
1.000 3.000

TABLE D-l 5 Continued

145

x/d Au/d = Ay/d = Xx/d = 1. /d =
3.000 0.074 0.050 0.051 8.046
Uc(fpe) = 90.915 '1‘ = 15.000 (averaging time) Condition: Non-Vortical
o I """' '2'
y/d u/uc v/Uc o u /Uc v /Uc uV/Uc y C/T
1.250 0.017 -0.040 -66.230 0.003 0.006 -0.000 0.999 3.066
1.166 0.021 -0.050 -66.684 0.004 0.010 -0.000 0.998 3.933
1.083 0.017 -0.053 ~71.481 0.003 0.014 -0.001 0.984 10.066
10000 00020 “00049 “670314 00012 00024 “00002 00645 220400
0.916 0.052 -0.065 -51.295 0.022 0.023 ~0.004 0.688 85.000
0.833 0.083 -0.058 -34.863 0.037 0.021 -0.003 0.345 96.800
00750 00122 “00051 “220867 00046 00026 00000 00055 290533
00666 00106 “00031 “160102 00091 00037 “00015 00003 20666
0.583 0.022 -0.012 -29.201 0.032 0.015 -0.004 0.000 0.066
0.500 0.018 -0.010 -30.103 0.000 0.000 0.000 0.000 0.000
0.416 0.018 -0.010 -30.103 0.000 0.000 0.000 0.000 0.000
0.333 0.274 0.008 1.739 0.412 0.020 0.054 0.000 0.800
0.250 0.756 0.035 2.660 0.395 0.032 -0.000 0.005 4.533
0.166 0.984 0.014 0.821 0.168 0.037 -0.018 0.021 16.933
0.083 1.010 0.005 0.298 0.032 0.029 0.001 0.036 24.666
0.000 1.007 0.003 0.182 0.032 0.026 0.001 0.046 30.600
-0.083 1.007 0.008 0.461 0.035 0.027 0.002 0.055 34.666
“00166 10016 00012 00730 00041 00028 00002 00059 370600
-0.249 1.005 -0.005 -0.303 0.047 0.029 0.001 0.036 25.333
“00333 00659 00006 00512 00656 00032 “00111 00002 20133
-0.416 0.063 -0.000 -0.167 0.201 0.013 0.016 0.000 0.133
-0.499 0.020 -0.002 -7.490 0.000 0.000 0.000 0.000 0.000
-0.583 0.033 0.002 3.791 0.042 0.019 0.007 0.000 0.266
-0.666 0.126 0.065 27.390 0.052 0.035 0.007 0.009 7.666
-0.750 0.092 0.050 28.623 0.040 0.029 0.005 0.172 70.733
““0833 0.070 00051 360222 00023 00022 00003 00616 970333
-0.916 0.050 0.055 47.725 0.013 0.018 0.002 0.909 39.266
-0.999 0.034 0.050 55.746 0.006 0.016 0.001 0.979 12.266
-1.083 0.027 0.058 64.419 0.005 0.010 0.000 0.997 4.400
-1.166 0.019 0.049 68.585 0.003 0.008 0.000 0.999 3.066
-1.250 0.017 0.055 72.736 0.003 0.007 0.000 0.996 4.000

TABLE D-15 Continued

x/d Au/d - Ay/d = Xx/d = 1. /d =

4.500 0.074 0.050 0.051 31046

Uc(fpe) = 90 .430 T = 15.000 (averaging time) Condition: Non-Vortical

y/d u/uc v/Uc e u'/Uc w/uc 117/027' y C/T
-1.500 0.009 0.050 78.702 0.002 0.007 0.000 0.999 3.066
-1.400 0.013 0.053 75.816 0.001 0.012 0.000 0.998 4.066
-1.300 0.016 0.054 73.563 0.004 0.015 0.000 0.990 6.866
*1.200 0.022 0.068 72.058 0.009 0.024 0.001 0.939 23.600
“10100 00033 00068 630679 00005 00030 00006 00793 “80400
'1.000 0.060 0.070 49.341 0.016 0.030 0.010 0.602 82.266
-0.900 0.102 0.059 30.108 0.037 0.023 0.008 0.230 64.066
“00800 00115 00063 200959 00042 00032 00003 00075 280000
~0.700 0.110 0.050 24.305 0.069 0.043 0.018 0.005 4.066
'0.600 0.034 0.016 25.016 0.046 0.037 0.016 0.000 0.266
“00500 00020 “00001 “50220 00000 00000 00000 00000 00000
“0.400 0.020 -0.001 '5.220 0.000 0.000 0.000 0.000 0.000
“00300 00113 00006 20648 00297 00018 00067 00000 00266
'0.200 0.671 0.002 0.174 0.426 0.037 -0.106 0.003 2.800
-0.100 0.875 0.003 0.217 0.344 0.042 -0.089 0.007 6.400
0.099 0.413 0.035 4.847 0.479 0.022 0.054 0.002 2.266
0.199 0.314 0.041 7.438 0.450 0.040 0.153 0.001 1.200
0.299 0.065 0.009 8.582 0.208 0.045 0.093 0.000 0.133
0.399 0.020 -0.000 -1.356 0.000 0.000 0.000 0.000 0.000
00699 00031 “00002 “60267 00051 00011 “00006 00000 00133
0.599 0.020 -0.000 -1.356 0.000 0.000 0.000 0.000 0.000
0.699 0.077 -0.008 -6.282 0.086 0.025 -0.010 0.001 1.200
0.800 0.143 -0.060 -22.755 0.068 0.033 -0.001 0.020 11.466
00900 00113 “00065 “210193 00062 00026 00000 00103 600133
0.999 0.095 -0.039 -22.418 0.039 0.018 -0.001 0.342 81.066
1.100 0.071 -0.032 -24.114 0.031 0.014 -0.001 0.643 65.066
1.200 0.062 -0.031 -26.569 0.025 0.002 -0.002 0.855 42.133
1.300 0.041 -0.032 -37.903 0.016 0.003 ~0.003 0.961 15.533
10399 00029 “00029 “650696 00008 00006 “00001 00990 60666
1.500 0.027 -0.033 -50.577 0.005 0.006 -0.000 0.998 3.466

TABLE D-15 Continued

.147

x/d Au/d .. Ay/d .. xx/d - xy/d =
6.000 0.074 0.050 0.051 0.046
Uc(fpe) - 89.931 T - 15.000 (averaging time) Conditgon. Non-Vortical
y/d u/uc v/Uc e u'/Uc v'/Uc uv/Uc y C/T
1.750 0.020 -0.033 -58.393 0.002 0.007 -0.000 0.999 3.266
1.633 0.020 -0.039 -62.971 0.006 0.012 -0.002 0.984 7.666
1.516 0.024 -0.043 -60.711 0.004 0.018 -0.003 0.837 14.066
1.400 0.036 ~0.054 -56.297 0.013 0.020 -0.005 0.858 34.866
1.283 0.064 -0.050 -38.117 0.030 0.014 -0.007 0.694 60.066
1.166 0.096 -0.041 -23.431 0.039 0.016 -0.002 0.412 72.800
1.050 0.114 -0.039 -18.889 0.044 0.024 -0.000 0.244 62.200
0.933 0.133 -0.061 ~24.792 0.046 0.030 -0.000 0.053 23.600
00816 0013‘ “00053 “210671 00086 00046 “00023 00005 30533
0.700 0.069 -0.029 -22.972 0.090 0.042 -0.027 0.001 1.133
0.583 0.020 -0.008 ~23.985 0.000 0.000 0.000 0.000 0.000
0.466 0.034 -0.000 -1.637 0.083 0.008 0.004 0.000 0.066
0.350 0.046 0.004 5.108 0.164 0.039 0.065 0.000 0.066
0.233 0.046 0.003 4.273 0.161 0.034 0.056 0.000 0.066
0.116 0.218 0.028 7.553 0.420 0.044 0.174 0.000 0.600
0.000 0.232 0.024 5.985 0.421 0.033 0.111 0.000 0.600
“00116 00139 00015 60336 00335 00036 00104 00000 00333
-0.233 0.022 0.000 0.445 0.000 0.000 0.000 0.000 0.000
“0.349 0.022 0.000 0.445 0.000 0.000 0.000 0.000 0.000
“00666 00022 00000 00665 00000 00000 00000 00000 00000
-0.583 0.030 0.004 8.338 0.037 0.022 0.007 0.000 0.133
“00699 00072 0002‘ 160916 00086 00037 00026 00001 10333
“00616 00137 00066 250096 00057 00060 00009 00022 110933
-0.933 0.117 0.056 25.743 0.041 0.029 0.003 0.130 43.266
-1.050 0.073 0.032 24.094 0.049 0.025 0.009 0.165 33.200
-1.166 0.089 0.045 26.803 0.034 0.013 0.007 0.585 70.466
'1.283 0.064 0.038 30.571 0.027 0.005 0.007 0.768 41.800
“1.399 0.048 0.041 40.515 0.015 0.012 0.004 0.940 18.666
-1.516 0.030 0.046 56.977 0.002 0.016 0.002 0.928 11.400
-1.633 0.022 0.048 65.070 0.007 0.013 0.001 0.993 5.333
-1.750 0.012 0.050 75.978 0.002 0.008 0.000 0.990 5.066

TABLE D-l 5 Continued

148

x/d .Au/a:= ‘Ay/a== Xx/d:= X /H:=
8.000 0.074 0.050 0.051 0.046
Ucap.) = 85.439 '1‘ = 15.000 (nvoraging time) Condition: Non-Vortical
y/d U/Uc V/Uc 6 \N/Uc w/Uc uv/Ucz Y C/T
-2.000 0.007 0.061 82.769 0.012 0.018 0.000 0.995 4.866
“10866 00009 00068 820531 00016 00023 00000 00984 70666
-1.733 0.011 0.069 80.929 0.019 0.030 0.001 0.904 15.066
-1.600 0.026 0.082 72.234 0.016 0.039 0.004 0.777 33.666
-1.466 0.044 0.090 63.885 0.014 0.039 0.006 0.721 52.800
-1.333 0.090 0.081 41.956 0.032 0.034 0.013 0.469 64.200
-1.200 0.125 0.066 27.935 0.045 0.030 0.008 0.339 68.200
-1.066 0.141 0.065 24.981 0.049 0.034 0.003 0.187 52.533
-0.933 0.143 0.072 26.880 0.073 0.045 0.017 0.036 15.066
-0.800 0.145 0.091 32.222 0.091 0.057 0.036 0.006 3.933
-0.666 0.088 0.041 25.038 0.112 0.054 0.049 0.001 1.133
-0.533 0.028 0.014 26.791 0.035 0.024 0.008 0.000 0.066
-0.400 0.023 0.010 24.668 0.000 ‘ 0.000 0.000 0.000 0.000
-0.266 0.025 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
-0.133 0.025 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
-0.000 0.025 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
0.133 0.025 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
00266 00025 “00002 “50220 00000 00000 00000 00000 00000
0.399 0.025 -0.002 -5.220 0.000 0.000 0.000 0.000 0.000
0.533 0.029 -0.004 r-8.631 0.025 0.014 -0.003 0.000 0.066
00666 00101 “00016 “90039 00126 00037 “00025 00001 10133
0.800 0.134 -0.063 ~25.299 0.116 0.056 -0.050 0.004 2.600
00933 00186 “00083 “260195 00065 00041 “00006 00019 90600
1.066 0.160 -0.066 -22.430 0.057 0.034 0.000 0.082 29.666
10200 00129 “00056 “230680 00050 00029 “00001 00222 690200
10333 00119 “00061 “190035 00067 00025 “00000 00676 660000
1.466 0.091 -0.031 -19.179 0.045 0.021 -0.007 0.672 ’45.466
1.600 0.076 -0.032 -23.324 0.038 0.019 -0.006 0.869 31.133
10733 0004‘ “00068 “470767 00019 0001‘ “00006 00933 180333
1.866 0.035 -0.045 -52.366 0.008 0.012 -0.005 0.979 8.933
2.000 0.032 -0.038 -50.200 0.007 0.007 -0.002 0.990 5.466

x/d
0.500

Uc(fpe) = 91. 798

v/d

0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
0.450
0.500
0.550
0.600
0.650
0.700
0.750

0.000
“00050
“00100
“00150
“00200
“00250
“00300
“00350
“00400
“00450
-0.500
“00550
-0.600
“00650
“00700
“00750

U/Uc

0.130
0.169
0.175
0.124
0.094
0.190
0.231
0.049
0.034
0.019
0.019
0.019
0.028
0.006

“00002
-0.001

0.228
0.191
0.273
0.179
0.139
0.131
0.202
0.257
0.108
0.019
0.019
0.020
0.047
0.032
0.006
0.026

.Au/d:=
0.083
T = 150000
v/uc 9
0.007 3.296
0.009 3.212
0.011 3.698
0.008 3.758
0.006 4.105
0.012 3.879
0.012 3.081
0.004 5.001
0.003 5.242
0.002 6.590
0.002 6.590
0.002 6.590
-0.031 -48.113
“00057 “830388
“00051 “920554
-0.047 -91.546
0.012 3.244
0.011 3.454
0.015 3.147
0.011 3.668
0.009 3.851
0.009 3.984
0.012 3.529
0.013 2.925
0.006 3.669
0.001 5.341
0.001 5.341
0.001 4.942
“00068 “450399
0.052 57.998
0.066 84.363
0.059 66.174

TABLE D-16 DATA LISTING

.A /d:=

Y

0.057

0.337
0.380
0.387
0.327
0.279
0.400
0.433
0.182
0.128
0.000
0.000
0.000
0.011
0.004
0.003
0.002

0.431
0.402
0.457
0.390
0.346
0.335
0.409
0.445
0.302
0.000
0.000
0.010
0.009
0.004
0.002

0.002 '

(averaging time)

\fl/UE

0.014
0.015
0.019
0.016
0.015
0.021
0.016
0.012
0.007
0.000
0.000
0.000
0.016
0.017
0.008
0.007

0.017
0.018
0.016
0.019
0.019
0.019
0.019
0.015
0.015
0.000
0.000
0.001
0.010
0.006
0.005
0.004

Xx/Ht=
0.060

Condition:

-— -z
v'/Uc uv/Uc

0.049
0.056
0.072
0.052
0.042
0.082
0.066
0.022
0.009
0.000
0.000
0.000

-0.001
“00000

0.000
0.000

0.073
0.072
0.074
0.075
0.065
0.064
0.077
0.064
0.046
0.000
0.000

“00000
“00000

0.000

“00000

0.000

Y

0.000
0.000
0.000
0.000
0.000
0.001
0.001

-0.000

0.000
0.000
0.000
0.000
0.093
0.712
0.992
0.999

0.001
0.000
0.001
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000

50.000

0.930
0.999
0.999
0.999

X /d==
3.050

Non-Vortical

C/T

0.466
0.666
0.733
0.466
0.333
0.866
0.933
0.133
0.066
0.000
0.000
0.000

53.800
152.533
15.600

3.600

0.933
0.800
1.200
0.666
0.533
0.466
0.800
1.466
0.400
0.000
0.000
0.066

51.266

3.333
3.000
3.000

x/d
1.500

Uc(fp8) = 9 10 798

Y/d

“10000
“00933
“00866
“00800
“00733
“00666
“00600
“00533
-0.466
-O.4OO
“00333
“00266
“00200
-O.133
“00066
“00000
0.066
0.133
0.199
0.266
0.333
0.400
0.466
0.533
0.600
0.666
0.733
0.800
0.866
0.933
1.000

TABLE D-lb Continued

Au/d -

0.083

T'= 15.000

v/Uc o
0.048 75.172
0.039 86.337
0.054 82.854
0.051 85.403
0.057 73.418
0.049 43.867
0.019 45.591
0.001 5.341
0.001 5.341
0.001 5.341
0.005 5.509
0.018 5.647
0.013 5.673
0.020 5.353
0.027 5.897
0.021 6.851
0.020 6.722
0.033 6.193
0.022 6.667
0.015 7.229
0.014 8.009
0.003 10.217
0.003 10.217
0.003 10.217
0.003 10.217
“00038 “330359
-0.044 ~42.419
-0.041 -54.800
“000‘! “580810
-0.037 ~62.390
“000“ “670162

Ay/d =

0.057

0.001
0.002
0.003
0.003
0.007
0.021
0.020
0.000
0.000
0.000
0.207
0.384
0.336
0.411
0.440
0.376
0.372
0.455
0.388
0.315
0.288
0.000
0.000
0.000
0.000
0.035
0.017
0.007
0.006
0.003
0.003

vfi/U

(averaging time)

tfl/UE

C

0.005
0.005
0.006
0.010
0.012
0.020
0.015
0.000
0.000
0.000
0.019
0.034
0.031
0.032
0.037
0.038
0.037
0.040
0.039
0.035
0.037
0.000
0.000
0.000
0.000
0.026
0.017
0.013
0.010
0.006
0.006

150

Condition:

-—— -Z
uv/Uc

0.000
0.000
0.000
0.000
0.000
0.003
0.002
0.000
0.000
0.000
0.040
0.129
0.103
0.134
0.162
0.145
0.139
0.181
0.149
0.109
0.104
0.000
0.000
0.000
0.000

-0.007
“00002
-0.000
-0.000
“00000
“00000

0.050

Non-Vortical

Y

0.999
0.999
0.999
0.999
0.965
0.361

“00001

0.000
0.000
0.000

“00000

0.000
0.000
0.001
0.001
0.000
0.001
0.002
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.018
0.564
0.963
0.999
0.999
0.999

C/T

3.000
3.000
3.000
3.466

33.533
139.200

0.466
0.000
0.000
0.000
0.200
0.866
0.533
1.066
1.333
0.733
1.000
1.800
0.866
0.533
0.400
0.000
0.000
0.000
0.000

22.933
133.600
28.266

3.866
3.000
3.000

TAB LE D-16 Continued

151

x/d Au/d = Ay/d = Xx/d = Xy/d =

3.000 0.083 0.057 0.060 0.050

Ucups) = 92.018 T = 15.000 (averaging time) Condition: Non-Vortical

-—— -Z
I I

y/d U/Uc V/Uc e u /Uc V /UC uv/Uc Y C/T
1.250 0.015 -0.041 -69.492 0.003 0.006 “0.000 0.999 3.333
1.166 0.017 -0.046 -69.538 0.002 0.008 -0.000 0.997 4.200
1.083 0.018 -0.049 -69.549 0.002 0.013 -0.000 0.975 12.533
1.000 0.022 -0.051 '65.958 0.005 0.018 “0.001 0.845 53.533
0.916 06040 “00060 -560278 00017 00023 “0.002 00546 92.933
0.833 0.043 -0.034 ~38.210 0.032 0.027 -0.007 0.076 35.666
0.750 00065 ”00047 -360070 06046 00035 ”00012 0.014 100‘00
0.666 0.024 -0.017 -34.299 0.033 0.021 -0.006 0.000 0.333
00583 00015 .00011 ”350495 00000 00000 00000 00000 0.000
0.500 0.019 0.001 5.341 0.000 0.000 0.000 0.000 0.000
0.416 0.019 0.001 5.341 0.000 0.000 0.000 0.000 0.000
0.333 0.034 0.003 6.544 0.126 0.017 0.022 0.000 0.066
0.250 0.047 0.005 6.373 0.172 0.021 0.036 -0.000 0.133
0.166 0.159 0.022 8.165 0.356 0.044 0.157 0.000 0.666
0.083 0.220 0.028 7.278 0.407 0.045 0.181 0.000 1.400
0.000 0.312 0.036 6.731 0.454 0.045 0.199 0.002 1.800
‘0.083 0.141 0.018 7.627 0.338 0.041 0.137 0.000 0.666
'00166 00350 0.038 60277 0.467 00043 0.189 00002 16933
~0.249 0.103 0.011 6.184 0.283 0.025 0.070 0.000 0.400
‘0.333 0.032 0.003 6.119 0.115 0.002 0.002 0.000 0.066
'0.416 0.019 0.003 9.653 0.000 0.000 0.000 0.000 0.000
‘03499 0.019 0.003 9.653 0.000 0.000 0.000 0.000 0.000
‘0.583 0.019 0.003 9.653 0.000 0.000 0.000 0.000 0.000
“00666 0004‘ 00033 36.937 0.048 0.033 0.013 00001 20266
-O.750 0.070 0.040 29.582 0.035 0.024 0.005 0.121 56.066
-O.833 0.068 0.040 30.522 0.024 0.017 0.003 0.564 100.733
'0.916 0.048 0.046 43.741 0.013 0.013 0.001 0.899 41.466
'0.999 0.034 0.050 55.819 0.006 0.009 0.000 0.985 8.600
“10083 0.029 0004‘ 56.473 0.005 00007 0.000 00973 3.666
'1.166 0.019 0.037 62.252 0.004 0.006 0.000 0.999 3.066
'1.250 0.021 0.039 61.658 0.003 0.005 0.000 0.999 3.000

TABLE D- l 6 Continued

152

x/d Au/d = Ay/d = )‘x/d = Xy/d =
4.500 0.083 0.057 0.060 0.050
UCUPB) = 92,255 '1‘ -.- 15,000 (averaging time) Condition: Non-Vortical
-—— -Z
y/d U/Uc v/Uc 6 uI/Uc w/Uc UV/Uc Y C/T
-10500 00017 00039 650892 00002 00005 0.000 0.999 3.000
“1.400 0.017 0.040 66.906 0.004 0.008 0.000 0.998 3.333
-1.200 0.022 0.055 67.418 0.006 0.017 0.001 0.937 22.133
-1.100 0.035 0.056 57.683 0.008 0.021 0.003 0.816 48.533
-1.000 00064 00050 380140 00024 00020 0.003 0.553 80.133
-0.900 0.075 0.042 29.595 0.033 0.024 0.004 0.260 73.533
'0.800 00078 00047 31.070 0.044 0.030 0.008 0.057 26.266
-0.700 0.037 0.030 38.608 0.043 0.036 0.014 0.001 1.200
-0.600 0.018 0.014 37.587 0.023 0.021 0.004 0.000 0.066
-0.500 0.015 0.011 37.128 0.000 0.000 0.000 00000 0.000
-O.400 0.015 0.011 37.128 0.000 0.000 0.000 0.000 0.000
“00300 00027 00012 240044 00098 00002 0.001 0.000 0.066
-0.200 0.099 0.019 10.893 0.261 0.024 0.057 0.000 0.466
-0.100 0.133 0.015 6.545 0.328 0.033 0.102 0.000 0.666
”0.000 0.233 0.027 6.715 0.411 000‘2 00172 0.001 1.200
0.099 0.177 0.025 8.197 0.375 0.048 0.178 0.000 0.933
0.199 0.032 0.007 12.952 0.118 0.020 0.023 '0.000 0.066
0.299 0.019 0.005 15.269 0.000 0.000 0.000 0.000 0.000
0.399 0.019 0.005 15.269 0.000 0.000 0.000 0.000 0.000
0.499 0.019 0.005 15.269 0.000 0.000 0.000 0.000 0.000
0.599 0.019 0.005 15.269 0.000 0.000 0.000 0.000 0.000
0.699 0.032 0.002 4.091 0.044 0.010 -0.003 0.000 0.466
0.800 0.071 '06035 -26046‘ 0006‘ 00034 “00017 0.003 3.133
0.900 0.081 -0.045 -29.141 0.046 0.030 -0.008 0.044 22.800
0.999 0.052 -0.029 -28.992 0.038 0.023 '0.007 0.135 43.733
1.100 0.061 -0.041 -34.016 0.025 0.017 -0.003 0.556 75.000
1.300 0.031 -0.040 -52.559 0.007 0.012 -0.001 0.951 18.200
1.399 0.021 -0.036 -59.052 0.003 0.010 -0.001 0.986 8.133
1.500 0.015 -0.035 -65.607 0.004 0.008 -0.000 0.997 4.066

TABLE D-16 Continued

153

x/d Au/d .. Ay/d .. xx/d - xy/d ..

6.000 0.083 0.057 0.060 0.050

Hem”) = 91.55:. T = 15.000 (averaging time) Condition: Non-Vortical

y/d u/uc v/uc 6 WUC v'/Uc unr/Uc2 v c/T
1.750 0.016 -0.034 -64.487 0.004 0.009 -0.000 0.995 4.333
1.633 0.014 -0.038 -70.032 0.009 0.012 -0.000 0.987 7.733
1.516 0.015 -0.047 -7l.366 0.009 0.018 -0.001 0.951 16.133
1.400 0.019 -0.042 -65.080 0.008 0.024 -0.002 0.552 18.066
1.283 0.040 -0.060 -56.279 0.017 0.023 -0.003 0.667 62.600
1.166 0.072 -0.049 -34.411 0.034 0.023 -0.004 0.362 68.333
10050 00087 ”00038 “280987 00047 00028 -0000? 00124 440400
00933 00088 “000“9 “290016 00057 00036 -00013 00020 120666
0.816 0.059 -0.035 -30.451 0.066 0.041 -0.021 0.003 2.133
00700 00022 -00012 “280395 00023 00014 “00003 00000 00133
0.583 0.018 -0.009 -28.507 0.000 0.000 0.000 0.000 0.000
00‘66 00018 “00009 “280507 00000 00000 00000 00000 00000
0.350 0.018 -0.009 ~28.507 0.000 0.000 0.000 0.000 0.000
0.233 0.047 -0.009 ~11.004 0.177 0.006 0.006 0.000 0.133
00116 00124 -0000? -30545 00325 00015 00018 00000 00366
0.000 0.110 -0.011 -5.972 0.308 0.011 -0.021 0.000 0.400
-0.116 0.035 0.002 4.591 0.132 0.017 0.023 0.000 0.066
-0.233 0.020 0.000 2.261 0.000 0.000 0.000 0.000 0.000
*0.349 0.020 0.000 2.261 0.000 0.000 0.000 0.000 0.000
”00‘66 00020 00000 20261 00000 00000 00000 00000 00000
-0.583 0.025 0.003 7.515 0.031 0.016 0.005 0.000 0.133
-0.699 0.049 0.008 9.484 0.066 0.020 0.010 0.000 0.933
”00816 00090 00041 2‘0650 0006‘ 00036 00016 0001‘ 80333
-O.933 0.089 0.042 25.532 0.046 0.028 0.007 0.095 34.600
‘1.050 0.078 0.043 28.826 0.034 0.020 0.004 0.341 70.466
-1.166 0.075 0.034 24.629 0.030 0.016 0.002 0.548 70.466
-1.283 0.069 0.036 27.470 0.026 0.007 0.004 0.789 47.866
-1.399 0.048 0.033 34.723 0.018 0.005 0.003 0.881 21.533
-1.516 0.028 0.035 51.399 0.006 0.008 0.001 0.977 9.066
-1.633 0.023 0.040 60.186 0.003 0.008 0.000 0.993 5.066
-1.750 0.019 0.036 61.821 0.002 0.006 0.000 0.998 3.600

TAB LE D- 16 Continued

x/d Au/d = Ay/d = xx/d _ xy/d -

8.000 0.083 0.057 0.060 0.050

Ucifps) = 87.644 '1‘ .-.- 15.000 (averaging time) Condition: Non-Vortical

y/d u/uc v/UC e u'/UC v'/UC uv/Uc y C/T
-20100 00023 00039 590476 00008 00013 00001 00700 30333
”1.960 0.019 0.051 69.320 0.006 0.013 0.001 0.990 5.266
‘1.820 0.023 0.054 66.821 0.007 0.017 0.001 0.973 9.933
-l.680 0.027 0.061 66.280 0.015 0.025 0.004 0.918 20.533
-10540 00070 00063 420297 00027 00023 00008 00772 440733
-1.400 0.076 0.052 34.838 0.032 0.018 0.008 0.638 55.400
'10260 00102 00046 240471 00044 00024 00006 00368 650933
“10120 00109 00050 240634 00052 00028 00009 00174 460533
'0.980 0.118 0.056 25.519 0.068 0.038 0.016 0.048 19.066
'0.840 0.100 0.057 30.003 0.089 0.056 0.040 0.005 3.466
-O.700 0.047 0.031 33.146 0.066 0.043 0.027 0.001 0.866
-00560 00019 00013 330929 00000 00000 00000 '00000 00000
-O.420 0.019 0.013 33.929 0.000 0.000 0.000 0.000 0.000
“00280 00023 00002 50341 00000 00000 00000 00000 00000
-00140 00023 00002 50341 00000 00000 00000 00000 00000
-0.000 0.023 0.002 5.341 0.000 0.000 0.000 0.000 0.000
0.139 0.023 0.002 5.341 0.000 0.000 0.000 0.000 0.000
0.279 0.023 0.002 5.341 0.000 0.000 0.000 0.000 0.000
0.419 0.023 0.002 5.341 0.000 0.000 0.000 0.000 0.000
0.559 0.028 -0.000 -1.093 0.037 0.022 -0.008 0.000 0.066
0.699 0.027 0.000 1.747 0.031 0.012 -0.003 -0.000 0.133
0.839 0.072 -0.036 -26.627 0.077 0.049 -0.027 0.004 2.466
0.979 0.114 -0.054 -25.240 0.081 0.042 -0.022 0.012 7.266
1.119 0.110 -0.054 -26.185 0.061 0.036 -0.012 0.069 25.466
10260 00104 ‘00053 “260962 00050 00029 ’00007 00197 500066
1.399 0.092 -0.040 -23.846 0.039 0.021 ‘0.003 0.465 65.200
1.540 0.074 -0.04O ~28.755 0.030 0.015 -0.003 0.730 50.400
10679 00057 “00043 ”370258 00025 00011 “00007 00829 380733
10820 00036 ”00044 -510113 00009 00017 -00004 00942 180200
10959 00030 “00040 ”520562 00003 00011 “00002 00990 50666
2.100 0.027 -0.036 -53.383 0.002 0.008 -0.000 0.998 3.800

TABLE D-l6 Continued

155

x/d Au/d - Ay/d - xx/d .. xy/d -

10.000 0.083 0.057 0.060 0.050

Uc(fpa) = 75 .5 26 T = 15,000 (averaging time) Condition: Non-Vortical

y/d tI/Uc V/Uc 6 u'/Uc v'/Uc uV/Ucz Y C/T
20500 00027 -00038 '560038 0000‘ 00009 “00001 00920 30266
20333 00023 -0004? -630533 00012 00015 ”00002 00987 60400
2.166 0.030 -0.053 -60.603 0.005 0.020 -0.002 0.977 10.133
2.000 0.057 -0.051 -42.049 0.023 0.018 "0.008 0.913 24.200
1.833 0.085 -0.045 ~28.186 0.039 0.011 -0.008 0.800 42.733
10666 00099 -0004? ’250820 00044 00008 ”00009 00653 550733
1.500 0.119 -0.054 -24.416 0.052 0.024 -0.008 0.403 60.866
10333 00130 “00059 “260594 00064 00036 -00009 00203 480466
1.166 0.151 -0.062 -22.608 0.084 0.044 -0.017 0.059 21.600
1.000 0.134 -0.075 -29.478 0.099 0.059 -0.040 0.016 7.266
0.833 0.078 -0.026 -18.814 0.104 0.047 -0.042 0.001 1.200
0.666 0.033 -0.007 -12.475 0.048 0.011 -0.005 0.000 0.066
0.500 0.033 -0.008 ~14.054 0.044 0.018 -0.007 0.000 0.066
0.333 0.028 0.002 5.341 0.000 0.000 0.000 0.000 0.000
0.166 0.028 0.002 5.341 0.000 0.000 0.000 0.000 0.000
0.000 0.028 0.002 5.341 0.000 0.000 0.000 0.000 0.000
-00166 00028 00002 50361 00000 00000 00000 00000 00000
“00333 00028 00002 50361 00000 00000 00000 “00000 00000
-0.499 0.028 0.002 5.341 0.000 0.000 0.000 -0.000 0.000
”00666 00066 00008 100606 00073 00026 00017 00000 00333
-0.833 0.100 0.052 27.722 0.104 0.059 0.045 0.004 2.800
-00999 00148 00066 260156 00105 00055 00036 00016 60666
-1.166 0.138 0.062 24.200 0.071 0.035 0.016 0.130 35.400
-1.333 0.127 0.055 23.596 0.056 0.032 0.007 0.253 54.733
“10500 00123 00043 190309 00052 00020 00007 00465 650733
-1.666 0.100 0.037 20.403 0.043 0.019 0.008 0.742 46.600
-1.833 0.092 0.033 20.125 0.040 0.021 0.008 0.866 30.266
-1.999 0.070 0.047 33.780 0.027 0.010 0.008 0.936 17.333
-2.166 0.061 0.043 34.972 0.018 0.009 0.004 0.977 8.866
-2.333 0.048 0.035 36.174 0.012 0.003 0.001 0.994 4.733
-2.500 0.037 0.041 48.224 0.010 0.011 0.001 0.864 3.066

LIST OF REFERENCES

7 . REFERENCES

Alexander, L. G. , Baron, T. , and Comings, E. W. (1953),
Transport of Momentum, Mass and Heat in Turbulent Jets,
University of Illinois, Engineering Experiment Station, Bul. 413.

 

Birch, S. F. and Eggers, J. M. (1972), "A critical review of the
experimental data for developed free turbulent shear layers,"
Free Turbulent Shear Flows, Vol. I, NASA SP-321.

 

Bradshaw, P. , Ferris, D. H. , and Johnson, R. F. (1964);
"Turbulence in the noise-producing region of a circular jet, "
Journal of Fluid Mechanics, Vol. 19. p. 519.

 

Champagne, F. H. (1965), Turbulence Measurements with
Inclined Hot-Wires, Boeing Scientific Researcli Laboratories,
Bocument D1-82-(Y49l, Report No. 103.

 

Clark, A. R. (to be completed), Effect of Initial Conditions on
the Near Field of a Plane Turbulent Jet, M S. Thesis,
Department of Mechanical Engineering, University of Houston.

Corrsin, S. , and Kistler, A. L. (1955), Free-Stream Boundaries
of Turbulent Flows, NACA Report No. 1244.

 

Crow, S. C. , and Champagne, F. H. (July 1970), Orderl
Structure in Jet Turbulence, Boeing Scientific Research
laboratories , BocumentTF-8Z-O99l.

Davies, P. O. A. L. , Fisher, M. J. , and Barratt, M. J. (1963);
"The characteristics of the turbulence in the mixing region
of a round jet, " Journal of Fluid Mechanics, Vol. 15, p. 337.

Flora, J. J. , and Goldschmidt, V. W. (1969); "Virtual origins
of a free plane turbulent jet," AIAA Journal, Vol. 7, No. 12.

Foss, J. F. , and Kleis, S. J. (1971); A study of the round-
jet /p1ane-wa11 flow field, NASA Annual Report Grant No. NOR
233-004-063.

Guitton, D. E. , and Patel, R. P. (1969); An Experimental Study
of the Thermal Wake Interference Betweentlosely Spaced
Wires of an Y-type Hot-Wire Probe, Mefianical Engineering
Résearch Laboratories, McGill University, Report No. 69-7.

Heskestad, G. (1965); "Hot-wire measurements in a plane turbulent
jet," Trans. ASME, Journal of Applied Mechanics, Vol. 32,
Series E, No. 4.

Hill, B. ‘J. (1971); "Measurements of local entrainment rate in
the initial region of axisymmetric turbulent air jets, " Journal
of Fluid Mechanics, Vol. 51.

 

Hinze, J. O. (1959); Turbulence, New York, McGraw Hill.
156

157

Holdeman, J. D. (1970); The Initiation, Development, and Decay
of the Secondary Flow in anTncompressible Turbulent Bounded
Jet, Ph. D. Thesis, Mechanicafiigineering Department,
Michigan State University.

 

Holdeman, J. D. , and Foss, J. F. (1970); The Initiation, Develpp-
ment, and Decay of the Secondary Flow in an Incompressible
Turbulent Bounded Jet, Harry Diamond Laboratories, Progress
Report No. 2, Grant DAAG-39-68-C-OO34.

 

 

Kaplan, R. E. , and Laufer, J. (1968); The Intermittantly Turbulent
Region of the Boundary Layer, University ofSouthern Califirnia,
Department of Aerospace Engineering, USCAE 110.

 

Kibens, V. , and Kovasznay, L. S. G. (June 1970); Detection of
the Turbulent-Non-Turbulent Interface, The Johns Hapkins
University, Departm ent of Mechanics .

Kibens, V. , and Kovasznay. L. S. G. (1969); The Intermittent
Re ion of a Turbulent Boundary Layer, U.S. Army Research
aiice, Dufliam, Report No. I, Dm-124-ARO-D-3l3.

Kistler, A. L. (1952); The Vorticity Meter, M. S. Thesis, The
Johns Hopkins University.

Ko, N. W. M. , and Davies, P. O. A. L. (1971); "The near field
within the potential cone of subsonic cold jets, " Journal of
Fluid Mechanics, Vol. 50, Part 1, p.49. ,

 

Kovasznay. L. S. G. , Kibens, V. , and Blackwelder, R. F. (1970);
"Large-scale motions in the intermittent region of a turbulent
boundary layer," Journal of Fluid Mechanics, Vol. 41, Part 2,
p. 283.

Laufer, J. (1954); The Structure of Turbulence in Fully Developed
Pipe Flow, NAG—Report No. 1174.

 

Laurence, J. C. (1956); Intensity, Scale, and Spectra of Turbulence
in Mixing Rggion of Free Subsonic Jet, NACA Report 1292.

 

Maestrello, L., "On the relationship between acoustic energy
density flux near the jet and far field acoustic intensity, "
AIAA Paper No. 73-988.

Miller, D. R. , and Comings, E. W. (1957); ”Static pressure
distribution in the free turbulent jet, " Journal of Fluid Mechanics,
Vol. 3, Part 1.

Mons, R. F. , and Sforza, P. M. (1971); Turbulent Heat and Mass

Transfer in Axis mmetric Jets, Polytechnic Institute of
BrooEIyn, PIBAE Report No. '71-14.

 

158

Oseberg, O. K. , and Kline, S. J. (1971); The Near Field of a
Plane Jet with Several Initial Conditions , Stanford University,
Department of Mechanical Engineering, Report MD-28.

 

Phillips, 0. M. (1972); "The entrainment interface," Journal of
Fluid Mechanics, Vol. 51, Part 1.

 

 

Ricou, F. P. , and Spalding, D. B. (1961); ”Measurements of
entrainment by axisymmetric turbulent jets , " Journal of
Fluid Mechanics, Vol. 11, Part 1, p.21.

 

Sami, S. (1967); "Balance of turbulence energy in the region of

jet-flow establishment," Journal of Fluid Mechanics, Vol. 29,
Part 1, p. 81.

Sami, S. , Carmody, T. , and Rouse, H. (1967); ”Jet diffusion in
the region of flow establishment, " Journal of Fluid Mechanics,
Vol. 27, p.231.

Townsend, A. A. (1956); The Structure of Turbulent Shear Flow,
Cambridge University Press, Cambridge, England.

Townsend, A. A. (1970); "Entrainment and the structure of
turbulent flow," Journal of Fluid Mechanics, Vol. 41 , Part 1,
p. 13.

Van der Hegge Zijnen, B. G. (1958); Measurements of the Velocity
Distributions in a Plane Turbulentfit a Air, Appfied
Scientific Research, SecTzon A, Vol. 7, No. 4.

 

Wygnanski, I. , and Fiedler, H. (1969); "Some measurements in
the self-preserving jet," Journal of Fluid Mechanics, Vol. 38,
Part 3.

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O 3.! 0.14 0. 01

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o 2.0 0.10 0.06

I 2.! 0.10 0.08

A 1.4 0.09 0.07

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I. I l. 5 0.08 0.06

 

 

 

 

 

Figure 8. Normalized Mass Flux

3.5

3.0

2.5

1.5

1.0

167

 

 

   

 

 

 

 

 

{ symbol u'/V. A/D A/D
O 3.6 0.13 0.06
A 3.1 0.14 0.07
v 3.0 0.11 0.08
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O 2.1 0.10 0. 08 ‘
A I.‘ 0. .
v I. l 0. v
I I. 5 0. o
0 I 2 3 4 5 6 7 0 9 IO

Figure 9.

Normalized Mass Flux Ratio for the Vortical Fluid

168

 

 

 

 

 

 

symbol \.1'/V'3 A/D A/D
0 3.0 0.13 0.06
.1 3.1 0.14 0.07
v 3.0 0.11 0.00
o 2.0 0.10 0.06
s 2.1 0.10 0.08
s 1.4 0.09 0.01
1-3"' v 1.1 0.00 0.05
g 1.5 0.08 0.00 . v
A
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A
1.0 O
V
v .
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O - Z V 4 6 i 10
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Figure 10. Normalized Momentum Flux

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2.5

2.0

1.5

1.0

0.5

 

169

 

 

symbol u'/V.

3.1
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1.4
1.2
1.5

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A/D

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0.11
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0.10
0.09
0.08
0.08

l/D
0. 06
0. 01
0. 00
0. 06
0. O8
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o. 05
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Figure 11. Centerline Mean Velocity Distribution

170

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F

 

 

 

 

 

 

 

 

symbol \1'/Ve A/D A/D
o 3.6 0.13 0.06
s 3.1 0.14 0. 07
v 3.0 0.11 0.08
o 2.0 0.10 0.06
O 2.1 0.10 O. 08
A 1.4 0. 09 0.07
v 1. I. 0.08 0. 05
o 1. S 0.08 0.06
0 1 1 1 . 1 1 . 1 .
0 2 4 f 6 8 Id 12 T4

x/D

Figure 12. Centerline RMS Velocity Distribution

171

 

 

 

 

 

 

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o 3.6 0.13 0.06 .
A 3.1 0.14 0.07
v 3.0 0.11 0.08
o 12.0 0.10 0.06 x
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V 1.2 0.08 0.05 8
g 1.5 0.08 0.00
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0.5 1 1 1 1- 1
0 .5 1.5 3 4.5 6 8 10
x/D

Figure 13. Mean Position of the Viscous Superlayer

172

 

       

 

 

 

 

 

 

symbol u'/Ve A/D A/D
o 3.6 0.1.1 0.06
11 3.1 0.14 0.07
1.0 v 3.0 0.11 0.08 A
F- 0 2.0 0.10 0.06 v
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g 1.5 0
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F
D
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008 l I fi l ‘ g
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x/D -

Figure 14. Excursion of the Viscous Superlayer

avg

my“:

3.0

2.0

I.“

0.5

173

l I l L

 

 

24 48 72 96
x/D
Figure 15. Pressure distribution in the fully

developed pipe flow for the thermal
anemometer system evaluation

120

174

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2.5 "
A - u'/vt Laufer
Q - v'/vt Laufer
A - u'/vt measured
- I
2.0 1- Q v/vt measured
A
A
A
A
1.5 .. i ‘
A A
A A
AA
loo 1- A A . .
A C C
A O O o O 0
AA . Q3 0
A
a . C O O O
0 o O O
0.5 b
o 1 l l l 1
0 0.2 0.4 0.6 0.8 1.0
r/R

Figure 17. Comparison of u' and v' distributions with
the published results of Laufer (1954)

176

0030.33.00 non-08053.3. #08033. .3 ondmwh

 

333 m
0.0 o.w cg. o6 o.m 0.0 o.m o.~ o.“ o
11 a 0 1 q q _ a .
1 cm
L 3.
:00;
1 cm
1 on:
13809309 ..1 ..l 1..
800
1 03

 

l.

l.

 

177

 

o "3‘15" . 5
Ax/D
F.

 

 

Figure 19.

v". ‘. 0.0.0....00..Oo.000......00 5

Ax/D

Exit correlations A /D = .13, Ay/D = .052

xx/D = .058, N/D 2.5.058

178

LOF.’

 

1.0L

 

o ....-

“5‘ WWW“ *"T‘U‘J

 

Figure 20. Exit correlations Ax/D = .14, Ay/D = . 093
xx/D = .085, )‘l/D = .065

179

1.0 -

 

1.01-

 

L ‘A‘ '
0 '

Ax/D

000.. o..............o..0005

Figure 21. Exit correlations Ax/D = . 11, Ay/D = . 046
xx = 0086, xy = 0071

180

1.0!-

 

 

0 '50....o.o.o ......... ...--..QOoouoW 5

Ax/D

 

 

Figure 22. Exit correlations Ax/DS=.10,-Ay/D = .052
, xx/Ds. .058 ly/D=

181

 

0 —* A "......2—2"W
0 0.5

 

1.01.

 

0 A." Jfirflfl.o:.0.......:.~.'..'... .. .. . a. 5

Ax/D

Figure 23. Exit correlations Ax/D = . 097, Ay/D = . 052
xx/D = . 083, Ly/D = .07

182

 

 

 

 

1.0?“
f
0 "-...._L - f
0 " It: I 5
Ax/D
1.0}.-
g
0 A:....00000300000000fi0ir5
Ax/D

Figure 24. Exit correlations Ax/D = , 089, Ay/D = . 053
Xx/D = - 075. xy/D = . 071

 

183

 

 

 

 

 

1 0T ,
f
0 ooo~.¢o..~..~...
0 w"'1ul"m't)':‘5
Ax/D
l. OW.
g
0 ..L-m- - --‘“- “44- - ~- f 3
0 0. 5
Ax/D

Figure 25. Exit correlations Ax/D = . 074, Ay/D = . 049

Mm s .052. xy/D = .046

184

 

 

 

....
O ......."‘O~oo-..
g A; A A ——'°LW
L? 0. 5
Ax/D
1. Oil.
8
0‘.
0 “...:QOOOOQOOOOOOOQQQmOOOQ~m__._ - v “A i

 

 

 

Ax/D

Figure 26. Exit correlations Ax/D = . 083, Ay/D = . 057
ix/D = .062, *y /D s .056

185

1.0F .

 

 

LOF

 

Figure 27. Exit correlations Ax/D = .08, /D = .059.
xx/D = .062, xy/D = .056 A7