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364015 649951

LIBRARY

Mlchigan State
I University

 

 

 

 

 

 

 

 

 

 

 

This is to certify that the

thesis entitled

AN EXPERIMENTAL STUDY OF THE NEAR
FIELD REGION OF A FREE JET WITH
PASSIVE MIXING TABS

presented by

Doug Bohl

has been accepted towards fulfillment
of the requirements for

MS Mec ani cal
degree in ng1IIeer1ng

 

  

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Date 2361“? M}, {99 Q:

 

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MSU It An Affirmative Anton/Equal Opportunity lnotltwon
Walla-9.1

 

An Experimental Study of the Near Field Region of a Free Jet With
Passive Mixing Tabs

By

Douglas G. Bohl

A THESIS

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

MASTER OF SCIENCE

Department of Mechanical Engineering

1996

ABSTRACT

An experimental study was performed to determine the flow characteristics of a
tabbed free jet. Results were acquired in the near field (nominally 2 tab widths upstream
to 2 tab widths downstream of the exit plane) of a tabbed jet. Upstream pressure results
showed static pressure distributions in both the x- and y- directions along the top surface
of the tunnel. Hot-wi re measurements showed rapid expansion of the core fluid into the
ambient region. Two counter rotating regions of streamwise vorticity were shown on
each side of the primary tab.

An enhancement of the tabbed jet concept was proposed and tested. Specifically, two
tabs, half the scale of the primary tab, were added to the primary tab to provide
attachment surfaces for the normally occurring ejection of fluid. The secondary tabs
caused a slight increase in streamwise vorticity created from the upstream static pressure
gradient while significantly increasing the re-oriented boundary layer vorticity. The
combined pumping effect of the two counter rotating regions of vorticity caused a

significant increase in the jet expansion.

To Coreen

ACKNOWLEDGMENTS

I would like to acknowledge the guidance and support of Dr. John Foss. He has given
me the opportunities in this study and in other studies to develop my professional skills. I
know that the experiences I have had in his lab will serve me well throughout my career.

Additional acknowledgments go to NASA Lewis Research Center for the financial
support to carry out this study, and to Dr. Khairul Zaman for his continued interest in and
technical support of this work.

Finally, I would like to acknowledge the support of friends and family. They have

helped (and pushed) me to continue with my education through some difficult times.

TABLE OF CONTENTS

Greek ..................................................................................................................... :x
Symbolsxr
Definrtronsxr
1. INTRODUCTION ......................................................................................................... : 1
1.1 Previous Work]
1.2 Analytical Considerations of the Flow Field ................................................... :7
1.3 Present Studyll
2.1 Flow System15
2.2 Experimental Configuration Defimtronsl6
2.3 Data Acquisition and Processing Systemsl7
2.4 Pressure Transducers]?
2.5 Hot-Wire Anemometers Anemometers...........................................................:18
3. DATA PROCESSING METHODS AND CONSIDERATIONS ................................ :25
3.11ntroductron25
3.2 Single Sensor Calibration and Processing Algorithms .................................... :25
3.3 X-Array Calibration and Processing Algorithms............................................:26
3.4 Determination of the Use of the Single Sensor and X-Array Probes...............:3l
3.5 Streamwise Vorticity Calculations...................................................................:34
3.6 Cross-Vane Vorticity Probe34
3.7 Statistical Calculatrons35
3.8 Normalization ofData36
4. UNCERTAINTY CONSIDERATIONS ........................................................................ :43
4.] Pressure Measurements43
4.2 Hot-Wire Measurements44
5. RESULTS AND DISCUSSION53
5.1 Introduction ...................................................................................................... :53
5.2 Untabbed Jet53
5.2.1 Exit Boundary Layer Survey53
5.2.2 Upstream Pressure Drstrrbutron54
5.2.3 Velocity Magnitude ProfilesS4
5.3 Primary Tab Jet: Preliminary ResultsSS
5.3.1 Upstream Pressure Distribution ResultsSS
5.3.2 Surface Streak Results: Primary Tab Geometry......................................:56
5.3.3 Streamwise Velocity Results ................................................................... :60
5.4 Addition of the Secondary Tabs ....................................................................... :61
5.4.] Motivation for Modification ofthe Primary Tab Geometry....................:61
5.4.1 Determination ofthe Secondary Tab Orientation....................................:62
5.5 Modified Tab Geometry: Preliminary Results62
5.5.1 Upstream Static Pressure Results: Modified Tab Geometry....................:62

5.3.2 Surface Streaking Results: Modified Tab Geometry ............................. :63

5.5.3 Streamwise Velocity Results: Modified Tab Geometry........................:64
5.6 Comparison of Jet Geometries ........................................................................ :64
5.6.1 Discussion of the Static Pressure Fields ................................................. :64
5.6.2 Comparison ofthe Streamwise Velocity Frelds67
5.6.3 Lateral and Normal Velocity Results73
5.6.4 y-z plane Vector Results75
5.6.5 Shear Stress Results77
5.6.6 Qualitative Vorticity Results ................................................................... :79
5.6.7 Quantitative, Spatially Averaged Streamwise Vorticity Results.............:81
6. SUMMARY AND CONCLUSIONSI45
6.1 Analysis of the Changes for the Flow Field of the Modified Tab Geometry...: 145
6.2 Conclusronsl46
APPENDIX A: Determination of [3150

vi

LIST OF FIGURES
Figure 1.1: Inferred flow directions from action of the streamwise vorticity ........................ :13
Figure 1.3 Schematic ofa typical boundary layer13
Figure 1.2: Cross section of the centerline of the tabbed jet .................................................. :13
Figure 1.4: Geometry definitions a) untabbed, b)simple, c)modified....................................:14
Figure 2.1: Schematic ofexperimental facrlrty20
Figure 2.2: Schematic ofthe modified flow facrlrty21
Figure 2.3: Velocity calibration curve for flow facrlrty21
Figure 2.4: Schematic ofthe tunnel extensron22
Figure 2.5: Schematic ofthe probe traverse system23
Figure 2.6: Schematic ofsingle sensor hot-wire probe24
Figure 3.1: Hot-wire calibration data with changing n values ................................................ :38
Figure 3.2: Schematic ofx-array hot-wire probe39
Figure 3.3: E versus Q from a typical x-array calibration......................................................:39
Figure 3.4: 7 versus 11 data for x-array calrbratron40
Figure 3.5: Comparison of streamwise velocity contours for the single sensor

and x-array hot-wire probes .................................................................................. :40
Figure 3.6: Definition of the "very near field" ........................................................................ :41
Figure 3.7: Schematic ofcross-vane vorticity probe41
Figure 3.8: Data acquisition grid spacing: a) static pressure, b) hot-wire at x/b=0.7, c)

hot-wire at x/b=l .2 and 2042
Figure 4.1: Error bar estimate for pressure surveys47
Figure 4.2: Error bar estimates for velocity measurements, a) average, b) rms48
Figure 4.3: Statistical convergence for $17 Uup z 0.6 in the plume region, a) average, b)rms:49
Figure 4.4: Statistical convergence for U/ Uup z 0.3 in the plume region, a) average, b)rms:50 '
Figure 4.5: Statistical convergence for U/ Uup z 0.3 in the side wall shear layer,

a) average, b)rrns .................................................................................................. :51
Figure 4.6: Shear stress convergence, a) W/ ng, b) W/ U3p52
Figure 5.1: Exit boundary layer survey for untabbed jet ........................................................ :85
Figure 5.2: Upstream static pressure survey, (p(x,y)—Paun)/0.5pUup2, for the untabbed

geometry85
Figure 5.3: Velocity survey for untabbed geometry at x/b=0.7: a) U/ Uup, b) E/ Uup. .......... :86
Figure 5.4: Velocity survey for untabbed geometry at x/b=l.2: a) U/ Uup, b) E/ Uup..........:87
Figure 5.5: Velocity survey for untabbed geometry at x/b=2.0: a) ii/ Uup, b) ii/ Uup..........:88
Figure 5.6: Upstream static pressure survey, (p(X,Y)-PaUn)/O.5pUup2, for the simple

geometry89
Figure 5.7: Surface streaking results for the primary tab geometry ........................................ :90
Figure 5.8: Singular points upstream ofthe primary tab9l
Figure 5.9: Top view topological analysis for the primary tab geometry...............................:92
Figure 5.10: Alternate signular point pattern93
Figure 5.11: Side view, center plane topological analysis of the primary tab geometry ........ :94

Figure 5.12: Streamwise velocity survey for the primary tab geometry at x/b=0.7:

vii

Figure 5.13: Streamwise velocity survey for the primary tab geometry at x/b=l.2:

Figure 5.14: Streamwise velocity survey for the primary tab geometry at x/b=2.0:

a) fi/ Uup, b) 17/ Uup97
Figure 5.15: Static pressure at x/b=-0.05 versus angle of secondary tabs98
Figure 5.16: Upstream static pressure survey, (p(x,y)-Paun)/0.5pUup2,

for the modified tab geometry99
Figure 5.17: Surface streaking results for the modified tab geometry..................................:100
Figure 5.18: Streamwise velocity survey for modified tab geometry at x/b=0.7:

a) U/ Uup, D) U/ Uup ............................................................................................ 2101
Figure 5.20: Streamwise velocity survey for modified geometry at x/b=l.2:

a) U/ Uup, b) ii/ Uup102
Figure 5.20: Streamwise velocity survey for modified geometry at x/b=2.0:
Figure 5.21: Schematic representation of streamlines for the primary tab geometry at

y/bz-l.0 ............................................................................................................... :104
Figure 5.22: Schematic representation of streamlines for the modified tab geometry at
Figure 5.23: Pressure distribution for x=-0.05b: a)P*(x=-0.05,y), b)0P*/ 6% 106
Figure 5.24: Pressure distribution for y=0: a)P*(x,y=0), b)6P'/ 6%107
Figure 5.25: Definition ofpenetration measure3108
Figure 5.26: Penetration ofthe shear layer into the core region...........................................:109
Figure 5.27: Penetration ofthe shear layer into the ambient region.....................................:110
Figure 5.28: Penetration of high speed fluid into the ambient region ................................... :111
Figure 5.29: Location of shear layer momentum thickness measurements..........................:l12
Figure 5.30: Shear layer momentum thickness,0, for the plum113
Figure 5.31: Shear layer momentum thickness,9, for the side and tip shear layers .............. :113
Figure 5.32: Average lateral velocity, V/ Uup, for the primary tab geometry:

a)l.2, b)20114
Figure 5.33: Average lateral velocity, V/ Uup, for the modified tab geometry:

a)l.2, b)20115
Figure 5.34: Average transverse velocity, 67/ Uup, for the primary tab geometry:

a)l.2, b)20116
Figure 5.35: Average transverse velocity, W/ Uup, for the modified tab geometry:

a)l.2, b)20117
Figure 5.36: Fluctuating lateral velocity, 37/ Uup, for the primary tab geometry:

a)l.2, b)2.0 .......................................................................................................... :118
Figure 5.37: Fluctuating lateral velocity, 37/ Uup, for the modified tab geometry:

a)l.2, b)20119
Figure 5.38: Fluctuating lateral velocity, 51/ Uup, for the primary tab geometry:

a)l.2, b)20120

viii

Figure 5.39: Fluctuating transverse velocity, V'V/ Uup, for the modified tab geometry:

a)l.2, b)20121
Figure 5.40: vw vector plot for the primary tab geometry at x/b=l .2:

a) sealed, b) unsealed, e) V = 0 and W = 0 intercepts, d) singular points.............:122
Figure 5.40: (continued) ........................................................................................................ :123
Figure 5.41: vw vector plot for the primary tab geometry at x/b=2.0:

a) sealed, b) unsealed, e) V = 0 and W = 0 intercepts, d) singular points.............: 124
Figure 5.41: (contrnued)125
Figure 5.42: vw vector plot for the modified tab geometry at x/b=1.2:

a) sealed, b) unsealed, e) V = 0 and VI = O intercepts, d) singular points............:126
Figure 5.42: (continued) ....................................................................................................... :127
Figure 5.43: vw vector plot for the modified tab geometry at x/b=2.0:

a) sealed, b) unsealed, e) V = 0 and Vi = 0 intercepts, d) singular points.............: 128
Figure 5.43: (contrnued)129
Figure 5.44: W/ Uup 2 for the primary tab geometry at x/b=l.2 ...................................... :130
Figure 5.45: E’V/ Uup 2 for the primary tab geometry at x/b==20130
Figure 5.46: E’VV Uup 2 for the modified tab geometry at x/b=1213l
Figure 5.47: W/ Uup 2 for the modified tab geometry at x/b=2.0 .................................... :131
Figure 5.48: W/ EV for the primary tab geometry at x/b=12132
Figure 5.49: W/ EV for the primary tab geometry at x/b=20132
Figure 5.50: W/ EV for the modified tab geometry at x/b=12133
Figure 5.51: E’V/ EVfor the modified tab geometry at x/b=20133
Figure 5.52: W/ Uup 2 for the primary tab geometry at x/b=12134
Figure 5.53: W/ uup 2 for the primary tab geometry at x/b=2.0 ...................................... :134
Figure 5.54: EW/ Uup 2 for the modified tab geometry at x/b=12135
Figure 5.55: W/ Uup 2 for the modified tab geometry at x/b=20135
Figure 5.56: E’WV EV! for the primary tab geometry at x/b=l.2 ......................................... :136
Figure 5.57: W/ EV? for the primary tab geometry at x/b=2.0 ......................................... : 136
Figure 5.59: W/ EV»? for the modified tab geometry at x/b=20137
Figure 5.58: W/ EV; for the modified tab geometry at x/b=1.2 ....................................... :137
Figure 5.60: Cross-vane results for the primary tab geometry at x/b=:

a) 0.1 b) 0.2 e) 0.3 (1) 04138
Figure 5.60: (contrnued)139
Figure 5.61: Cross-vane results for the modified tab geometry at x/b=:

a) 0.1 b) 0.2 e) 0.3 d) 0.4 .................................................................................... :140
Figure 5.61: (continued) ........................................................................................................ :141
Figure 5.62: (9*); for the primary tab geometry: 3) x/b=1.2, b)x/b=2.0.................................:142
Figure 5.63: w‘x for the modified tab geometry: a) x/b=l.2, b)x/b=2.0...............................:143
Figure 5.64: Overlay of vw vectors and co'x contours for the modified tab geometry at

x/b=l.2 ................................................................................................................ :144
Figure 5.65: Inferred upstream vorticity connections ........................................................... :145

NOMENCLATURE

English

{PP-‘7?

zza

U
0

"6'0
9, ..
B

cawwwo
5. " "

fifif

Greek

or:
B:

Xsurfacei

5:
5ambient3
Dcorcl

6d:

5lrigh speed:
‘YI

11:

OZ

Coefficient in Collis and Williams relationship. Sec (3.1).
Base length of the primary tab, 200mm.

Coefficient in Collis and Williams relationship. See (3.1).
Length of active region of hot-wire sensor.

Coefficient in Collis and Williams relationship. See (3.1).
Node. See (5.1) and (5.2).

Half node. See (5.2).

Static pressure.

Atmospheric pressure.

Magnitude of the velocity measured by a hot-wire.

Radius of curvature. See (5.3).

Saddle. See (5.1) and (5.2).

Half saddle. See (5.2).

Velocity in the streamwise (x) direction.

Upstream reference velocity, calculated from the pressure
differential in the tunnel contraction upstream of the tunnel exit.
Velocity in the spanwise (y) direction, lateral velocity.
Velocity magnitude.

Velocity in the vertical (2) direction, transverse velocity.

Angle of secondary tab to the horizontal plane, generic length
measure.

Angle between a slant wire and the probe axis, generic velocity
measure.

Euler characteristic for a surface. Sec (5.1) and (5.2).

Boundary layer thickness.

Maximum penetration of the shear layer into the ambient region.
Maximum penetration of the shear layer into the core region.
Displacement thickness.

Maximum penetration of high speed fluid into the ambient region.
In-plane flow angle.

Ratio of voltage of a hot—wire at an angle divided by the voltage of
the same wire at y=0. See equation (4.3).

Angle of the secondary tabs with respect to the x-z plane.

6: Shear layer momentum thickness. See (5.4).
03x: Stream wise vorticity. See equation (4.10).

Symbols

-: Average value; Velocities are time averaged, Stream wise vorticity
is spatially and temporally averaged. See equation (4.13).

~: Root mean square value. See equation (4.14).
*: Non dimensional value. See section 4.7 for definitions.
Definitions

ambient region:
core region:
modified geometry:
primary tab:
secondary tab:

primary geometry:

un-tabbed geometry:

Area in the flow field outside of the projected tunnel walls.
Area in the flow field inside of the projected tunnel walls.
Tab configuration that consists of one primary tab with one
secondary tabs on each side of the primary tab.

The single large (200mm) tab that protrudes into the

core region. Used in both the simple and modified geometries.
The smaller (100mm) tab that protrudes into the ambient
region. Used in pairs.

Tab geometry that consists of a single primary tab.
Tunnel configuration without any tabs. Reference case.

xi

1. INTRODUCTION

1.1 Previous Work

The restrictions on noise emissions from jet engines have led to the development of
strategies to combat noise in jet flows. There are two sources of j et noise that can be
targeted by the rapid mixing of the heated jet core with the cooler co-axial fan flow. The
first of these two sources is termed "screech". This noise source is related to the growth
rate of feedback waves between the coherent structures shed from the jet and the pressure
field at the exit of the jet. The second noise type is a "broad band" noise that occurs over
a range of low frequencies. The thermal energy in the jet core and the resulting density
gradients are the dominant source for this noise (Ahuja and Brown (1989)).

The development of the High Speed Civil Transport has centered on two passive
mixing strategies previously investigated. The first of these strategies is the use of lobed
nozzles. A study of the effects of lobes in mixing two streams of fluid was conducted by
Koch am Brink (1991) and also reported by Koch am Brink and Foss (1993). This study
demonstrated that the lobe geometry creates strong streamwise vortieal motions which
substantially increase the mixing between the two layers. It was shown that the shape of
the lobes creates pressure gradients which re-orient the boundary layer vorticity from
each lobe into the streamwise direction. The areas of streamwise vorticity were found to
have a length scale on the order of the lobe height. The lobed geometry was shown to
have superior mixing characteristics over a simple two stream mixing layer.

An alternate strategy, pursued by the NASA Lewis Research Center, has been to use

passive mixing tabs in the exit plane of the jet. An obstruction is placed in the exit plane

of the high speed jet core. The obstructions (i.e. "passive mixing tabs") promote rapid
exchange of the core fluid with the surrounding fluid.

Early research into the physics of tabbed flows was reported in Bradbury and
Khadem (1975). In that work the authors studied the effect of changing boundary
conditions on the entrainment rate of free jets. They found that boundary layer thickness,
turbulence levels in the approach boundary layer and nozzle convergence did not have
any significant effect on the entrainment rate of the jet flow. Rather they determined that
by placing an object perpendicular to the streamwise direction into the core flow they
could create large scale distortions in the flow field. It was shown in this work that the
core splits into two high speed regions for a round jet with two tabs placed 180 degrees
apart in the jet exit plane. Entrainment for a tabbed jet was shown to increase by
nominally 400% over the untabbed jet.

Bradbury and Khadem (1975) proposed that two possible reasons for the distortion in
the jet flow. They reported that either: 1) trailing vortex motions shed by the tab "stirred"
the fluid or 2) the simple deflection of the core flow by the object created the distortions.

Ahuja and Brown (1989) expanded on many of Bradbury and Khadem’s (1975)
results. They showed that a jet with two opposing tabs had a nondimensional centerline
velocity decay that was much faster than that for the untabbed jet. However, they also
showed that the rate of decay of the nondimensional centeriine velocity was much higher
for a tabbed jet with two tabs rather than three or four. Finally the authors showed that
the same effeetcan be seen in both heated and unheated cores and that the two tab
configuration showed a significant drop in the average core temperature downstream of

the exit.

This work (Ahuja and Brown (1989)) was important in that the authors reported two
results that were important to later studies. First, the tab placed into the flow must have a
certain length dimension in order to have an effect on the flow field. Second, it was
reported that the flow distortion was not restricted to compressible flows. This second
result was critical in that the analytical as well as experimental analysis of the flow field
could be performed on an incompressible fluid.

In an attempt to infer the physics of a tabbed jet Ahuja and Brown (1989) noted that
the high level of mass entrainment in a round jet is caused by the large scale motions
shed by the jet. It was shown (by the elimination of the screech tones) that for a tabbed
jet these motions were altered. The conjecture was that other large scale motions, created
by the tab, were responsible for the rapid mixing in the tabbed jet. Ahuja and Brown
concluded by stating that the simplicity (i.e. the lack of moving parts) in the tabbed jet
concept made it attractive for use in gas turbine engines.

Much of the current work in the use of tabbed jets has been conducted jointly by
NASA Lewis Research Center (Dr. K. Zaman) and the Ohio State University (Dr. M.
Reeder and Dr. M. Samimy). A series of studies were performed over several years
which resulted in several conference papers and journal publications. Their results are
summarized here and provide the basis for the present study.

Zaman et. al. (1994) reported that tabs, which were perpendicular to the streamwise
direction and extend into the core flow, produce an area of counter rotating streamwise
vorticity, (ox, on either side of the tab. The sign of this vorticity was of opposite sign from
what one would expect from the re-ori entation of the boundary layer vorticity around the

tab. These regions, shown schematically in Figure 1.1, create the large scale distortion in

the flow field shown in previous works (Ahuj a and Brown ( 1989) , Bradbury and
Khadem (1975)). In their discussion the authors stated that fluid from the core region
would be ejected as a result of the streamwise vorticity as shown in Figure 1.1. Ambient
fluid was entrained into the core region downstream of the tab also as a result of the
vortical motion shown in Figure 1.1. This large scale exchange of fluid between the core
and ambient regions provided the rapid mixing produced by the tabbed jet (Zaman et. al.
(1994)).

These studies also confirmed many of the results of Ahuja and Brown(l989) in that

they showed:

1) the results were similar for both supersonic and subsonic flows. This result was
demonstrated through flow visualizations results which clearly showed qualitatively
similar results for both flows (Zaman et. al.( 1991)).

2) the tab height (i.e. the height of the tab projected into the exit plane of the jet) must

be on the order of the approach boundary layer thickness or larger in order to have a

significant effect on the flow. A tab which does not exceed this height will not generate

structures larger than the boundary layer and will not effect the global flow field (Zaman

et. al. (1994)).

3) more than four tabs resulted in a decreased effectiveness of the tabs. Specifically
the lobes of core fluid that were created by the tabs interacted and combined when
four or more tabs were used to reduce the number of effective lobes. For example, a

jet with six tabs created a similar distortion of the flow field as a tabbed jet with three

tabs (Zaman et. al. (1992).

4) a two tab configuration experienced more rapid centerline decay than a three or
four tab configuration. It was clearly shown by the authors that for a tabbed round jet
with two opposing tabs the core flow split into two high speed regions. With four or
more tabs the flow field formed four lobes of high speed fluid connected at the center of
the jet (Zaman et. al. (1994)). Note that this observation illustrated that using the
centerline average velocity decay to determine the "effectiveness" of a tab is incomplete
and could be deceptive.
5) the screech tones in the jet were completely eliminated. Additionally, the broad
band noise was also reduce in the tabbed jet flow (Zaman et. al. (1992)).
In addition to items 1-5 above other important features of the flow field were also
detailed. A series of results were reported in which the orientation of the tab was
changed and the differences in the flow field were observed (Zaman et. al. (1994)). The
authors showed that by orienting the tabs so that they pointed upstream it was possible to
create an ejection of fluid from the region behind the tab. (Note that this was opposite of
the effect seen when the tab was placed perpendicular to the streamwise direction as
described above.) The reason for this difference was believed to be a change in sign of
the streamwise vorticity introduced into the flow. When the orientation of the tab was
changed so that the tab point downstream in the flow, the distortion of the flow field (i.e.
the ejection of core fluid) increased when compared to the perpendicular orientation. In
addition the pressure penalty decreased for the same size tab. Thnrst loss for the

downstream orientation was estimated to be nominally 1.5% per tab. This "penalty" was

computed by comparing the actual thrust to the thrust calculated for a uniform flow from
the isentropic relationship (Zaman et. al. (1994)).

Steffen et. al. (1996) reported results from a computational study in a 3:1 aspect ratio
rectangular jet which mimicked an experimental jet to which the computational results
were compared. These results showed that when two tabs were placed at the midpoint of
the short sides, the jet experienced a switch in the major axis at x/d=3, where d is the
hydraulic diameter of the rectangular nozzle. For the same jet without tabs, axis
switching was not reported at the farthest measurement location x/d=14, although the
data did indicate that the flow would experience an "axis switch" at a farther downstream
location.

Foss and Zaman (1996) studied the effects of a tab on a two stream mixing layer. In
this experimental study the velocity ratio between the free streams was 2:1 with the tab
pointing into the high speed stream. Using the "Peak-Valley-Counting" technique (Ho
and Zohar (1994)) the authors were able to show that the peak in the dissipation spectra
in the tabbed flow shifted to higher wave numbers. This indicated that the turbulent
cascade increased in length (i.e. the wave number distance between the largest and
smallest scales increased) for the tabbed flow. In addition to having smaller scales when
compared to the untabbed shear layer the small scales in the tabbed shear layer contained
more energy. It was noted that the location in the flow field with the highest peak in the
dissipation spectra did not coincide with the location of the peak in the fluctuating

streamwise velocity values.

7

1.2 Analytical Considerations of the Flow Field

The effect of placing tabs into the exit plane of a jet is to produce large scale
streamwise vortical motions into the flow field. The orientation of the tabs is responsible
for determining the sign of the vorticity introduced into the flow. The tab is assumed to
be oriented downstream, see Figure 1.2, in the following analysis.

In past studies (Reeder (1994), Zaman (1993)), analysis of the sources of vorticity in
the flow has concentrated on the streamwise vorticity created by the tabs. This analysis,
while important, serves to analyze only part of the streamwise vorticity seen in the flow
field afier the jet exit. There is also a significant region of streamwise vorticity present
due to the re-orientation of the approach boundary layer vorticity.

In a two dimensional laminar boundary layer the vorticity is aligned with the
y-direction using the coordinate system shown in Figure 1.3. Note that all three
components of vorticity in a turbulent boundary layer there can exist instantaneously;
however, the time averaged vorticity in a turbulent boundary layer only involves the

y-direction component. This vorticity was introduced into the flow by the creation of a
velocity gradient in the z-direction, i.e. 6 u/ 6 2. To understand possible additional
sources of vorticity in a boundary layer consider the x-component linear momentum

equation:

 

 

-a—u+u§—u+v@+w—a—9= __1_Q+v(___62u+62u+62u
at 6x 8y 62 gx pax 62x 62y 622

). (1 . 1)
At a wall u,v,w as well as the derivatives parallel to the wall (i.e. a O/ 6 x and a ()/ 6 y)

will be equal to zero if there is no blowing/suction applied. If, in addition, the body

forces are equal to zero and the time derivatives are neglected, (1.1) simplifies to

_ 1213. 52"

Vorticity in the y-direction, toy, is defined as

6 u 6 w
= __ _ _. 1.3
my 6 z 6 x ( )
Equation (1.3) can be simplified in a two dimensional boundary layer to
6 u
-—. 1.4
my “‘ 6z ( )
Which is then substituted into (1.2) to yield
6
vfilzflzlfllw (1.5)
6 z p 6 x
Equation (1.5) can be generalized for a flow parallel to a surface by
6 l 6P
cDb|n=0______|“=0 (1.6)
6 n u 3

Where n is the direction normal to the surface, s is the direction of the velocity vector
parallel and near to the surface, and b is the direction perpendicular to the same velocity
vector. This general result indicates that a static pressure gradient at a surface provides a
flux of vorticity into the flow with a direction parallel to the plane of the surface.
Equation (1.5) specifically shows that if there is a pressure gradient in the x-direction
there will be y-component vorticity, 0),, added into the flow at z=0. It has been shown in
past studies (Reeder (1994), Zaman (1993)) as well as in the present study (section 5.3.1
and 5.5. 1) that the presence of a passive mixing tab creates a strong positive pressure

gradient upstream of the jet exit. The adverse pressure gradient serves as a source of

vorticity into the flow. In the analysis of a boundary layer it is instructive to note that
separation occurs when the vorticity becomes zero at the wall.

The vorticity upstream of the tab is re-oriented and stretched by the velocity gradients
in the flow. The x-direction vorticity transport equation is given by (Whitham (1963),
equation (17)):

_)
Dar
_:5)->,

Dt Vv—>+ vvzo? (1.7)

Equation (1.7) can be decomposed into the x-direction transport equation as

6201,. 62(1),. 6203,.

93 + +
62x 62y 622

62

 

 

 

+v( ) (1.8)

Dt x6x y6y 2

Where the first term of the right hand side is the stretching term, the second and third
terms are re—orientation terms, and the fourth term is the viscous diffusion term. It is
possible to re-orient the boundary layer vorticity, (0,, into streamwise vorticity in the
presence of a velocity gradient 6 u/ 6 y via (1.8). The -coy from the boundary layer will
become +mx for y<0 for the tabbed jet. Note that for a tabbed jet 6 u/ 6 y < 0 for y<0.
The vorticity from the re-oriented boundary layer is of opposite sign to what was found
to dominate the tabbed jet flow (Zaman (1993)). It was this observation which led to the
further analysis (Reeder (1994), Zaman (1993)) of the sources of the negative sense
streamwise vorticity seen in the flow field. (Note, it will be shown in this study that the
re-oriented boundary layer vorticity plays a significant role in the large scale transport of
fluid from the core region to the ambient region.)

It is possible to show, using (1.6), that a pressure gradient in the y-direction will also

serve as a source of streamwise vorticity in the flow by

10

60)x 16P
Z— ~-——~Z . 1.9
V 62 I4) pay|=o ( )

 

Equation (1.9) is derived from the general expression (1.6) where n is the z-direction, b is
the x-direction and sis the y-direction. The tabs, in addition to creating a pressure
gradient in the x-direction, also create a pressure gradient in the y-direction (Zaman
et. al. (1993), section 5.3.1 and 5.5.1). Since 6 P/ 6y was greater than zero for y<0 this
pressure gradient will act as a source of negative cox in the flow field.

Zaman (1993) first discussed the two regions where pressure gradients were found
that would provide a flux of negative sense streamwise vorticity into the flowl. These
regions (labeled 1 and 2 on Figure 1.2) were found directly upstream of the jet exit along
the jet wall and on the face of the tab itself. The upstream pressure distribution, dubbed
the "pressure hill", was found to be the dominate source of vorticity for the flow field.
This was determined by displacing the tab downstream from the jet exit (creating a gap
between the tab and the jet exit) which reduced the pressure distribution upstream of the
tab. This was shown greatly reduce the overall effect of the tabbed jet (Zaman et. al.
(1994)).

The observation that the effects of tabs are independent of compressibility (Ahuja and
Brown (1989) and Zaman et. al. (1991)) is important in the analysis sources of
streamwise vorticity in that there are other sources of vorticity in a compressible flow
which have been neglected in the above analysis.
lZaman credits Dr. J. Foss of Michigan State University with proposing the idea of the

two possible regions of pressure gradients which provide a flux of streamwise vorticity
into the flow.

11

1.3 Present Study

The present study was performed to provide further details about the flow field of the
tabbed jet. The experimental apparatus, with exit dimensions of 610 mm x 610 mm and a
tab length of 200 mm was of a very large scale when compared to those used in the
works of K. Zaman, M. Reeder, and M. Samimy. This permitted measurements to be
readily made very close to the exit plane of the jet; the present data are the first to be
reported in this near region. These measurements included cross-vane vorticity
visualizations as close as x/b=0.1. The scale of the experimental apparatus also reduced
the spatial resolution problems of x-array hot-wire probes that were experienced by
Zaman eta]. (1994).

Four experimental procedures were used in this work to interrogate the flow field.
First, static pressure measurements were made upstream of the tunnel exit. This gave
insight into the vorticity sources of the flow field and how geometry changes could be
utilized to enhance the tab’s effect. Second, a cross-vane vorticity probe was used to
determine the nominal borders of the streamwise vorticity in the very near field of the
tabbed jet, i.e. x/b=0.l to 0.4. Third, a single sensor probe was used to determine the
streamwise velocity field for the untabbed jet at x/b=0.7,1.2, and 2.0, as well as for the
simple and modified jets at x/b=0.7. Finally x-array hot-wire probes were used to provide
u,v, and w measurements at x/b=l .2 and 2.0 for the primary tab jet and modified tab jet.

Note that at x/b=0.7 the flow angle fluctuations were found to be too large (i.e. greater
than i36 degrees) to allow the use of x-array hot-wire probes. These data were then

processed to provide the spatially averaged streamwise vorticity, cox, at those locations.

12

Three geometries were investigated, see Figure 1.4. The untabbed jet, Figure 1.4a,
provided the reference case for the basic flow field. The primary tab geometry, Figure
1.4b, has one primary tab. This geometry (an equilateral triangle oriented 45 degrees
downstream) served as a connection to the past work of K. Zaman, M. Reeder and M.
Samimy. Note that the percentage of the exit area to the projected tab in the y-z plane
was nominally 3 times greater in this study. A primary goal of this study was to provide a
basis for enhancing effects of the tabs in jet flows. The modified tab geometry was
created by the addition of two secondary tabs, one on each side of the primary tab, see
Figure 1.4c. A rationale for the changes in the flow field for the modified tab geometry
when compared to the primary tab geometry will be given and further insights into the

physics of tabs will be discussed.

13

ENTRAINMEN'I‘ OF
AMBIENT FLUID

EJEC'I‘ION 0F EJEC‘I‘ION 0P
CORE FLUID CORE FLUID

so 3

Figure 1.1: Inferred flow directions from action of the streamwise vorticity.

JET EXIT
\\\\\\\\\\:\\\\\\\1\\\\\
now 9

Figure 1.2: Cross section of the centerline of the tabbed jet.

 

 

 

Figure 1.3 Schematic of atypical boundary layer.

14

Z? X Z? y a)

'l/I/I/I/I/ III/III]; ’I/I/I/I/I/I/I/I/I/I l/I/I/I/I/I/I/I/Il -

 

 

 

FLDW>

Z? x z? y b)

% r////////////<////////////// //////////, -
O

 

 

 

Z? A Zr 0)

‘i A E ,A y,
‘WR X 'I/I/I 'I/I/Il/I/Il // VII/z

w ”b“ LA

 

 

I-‘LDW>

Figure 1.4: Geometry definitions a) untabbed, b)simple, c)modified.

2. EXPERIMENTAL APPARATUS

2.1 Flow System

An Engineering Laboratory Design closed loop wind tunnel, shown in Figure 2.1,
was used as the flow system for this study. The unmodified tunnel has a clear plastic test
section of 61cm x 61cm x 244cm (2’x2’x8’). The flow is driven by a JOY 50 hp AC
motor with a constant speed of 1770 rpm. Adjustments to the flow speed are made via a
manual controller which varies the angle of attack on the fan blades. Tunnel cooling is
accomplished using a fin/tube heat exchanger with building water as the cooling
medium. The plenum-test section contraction ratio is 6.25. Static taps upstream and
downstream of the contraction provided the reference velocity Uup. The calibration curve
for this tunnel was found using a single sensor hot-wire probe located at the exit of the
tunnel extension, see Figure 2.2. The calibration curve is shown in Figure 2.3.

The tunnel was modified by removing the test section creating a Goettingen style
wind tunnel as shown in Figure 2.2. A 24 cm long tunnel extension, shown in Figure 2.4,
was placed at the tunnel "exit". Two rows of static pressure taps in the x-direction were
placed on the top surface of the extension. That the top surface was machined to allow
the position of the top surface (and hence the static pressure taps) to be variable in the
y-direction. This permitted P(x,y)-Pm to be measured upstream of the tab. The exit plane
was machined to allow the attachment of the tabs. The entrance to the tunnel was fitted
with half round flow conditioners. Cheese cloth with a wire mesh backing was placed

over the inlet to prevent airborne particles from entering the modified tunnel.

15

16

A four degree of freedom traverse system, shown in Figure 2.5, was in place in the
wind tunnel test section. The system allows for x,y,z and 6 (about the z-axis). The probe
support, seated on linear bearing blocks, was driven by high precision lead screws. An
IBM/XT clone was used in conjunction with an OMNITECH ROBOTICS MC-3000 and
MC-1000 controller board to provide the motion control. Five YASKAW 100 watt DC
servo motors with optical encoders drive the lead screws. The servo motors have a
resolution of 36000 counts per revolution. The accuracy of the traverse in the x,y,z
directions was found to be 0.1mm. Probes were located by sighting the probe location
with respect to the center top surface of the tunnel extension. Extensions for the probe

holder were machined to allow measurements to be made above the top of the tunnel.

2.2 Experimental Configuration Definitions

Figure 1.4 defines the geometries used in this study. The "untabbed" flow was used
as the reference flow field. This flow field can be characterized as a square free jet. The
”primary tab geometry" was created by the addition of one "primary” tab to the top
surface of the untabbed jet. The primary tab was placed on the top surface of the tunnel
and was oriented 45 degrees downstream of the exit plane as shown. The primary tab
(machined from 3.14mm (1/8") thick stock) was an equilateral triangle with a base
length, b, of 200 mm. The modified tab geometry consisted of the primary tab with two
secondary tabs placed symmetrically about the center line of the primary tab. The
secondary tabs had a base length of 100mm or 0.5b; they were also machined from 3.14
mm (1/8") thick stock. The location of the secondary tabs as well as the angle at which

they were positioned was variable. For both tabbed geometries the percent blockage of

17

the jet exit was calculated to be 6.6% and was determined from the projected area of the

primary tab in the y-z plane in thejet core.

2.3 Data Acquisition and Processing Systems

Data acquisition was performed using an Analogie Fast-16 A/D card with an IBM
486-66 PC clone. The MD card had a resolution of 16 bits with a range of 21:10 volts.
This allows an A/D resolution of 0.31 millivolts. The inherent noise of the A/D board
was found to be i1 bit. The maximum sample rate of the system was 1 MHz. An eight
channel sample and hold card was used in conjunction with the A/D card to provide eight
channels of true simultaneous sampling.

The data were processed on the indicated PC as well as on a DEC ALPHA AXP-150

computer system.

2.4 Pressure Transducers

Two pressure transducers were used to take the reference and static pressure
measurements for this study. A 1 Torr MKS Baratron pressure transducer was used to
provide the reference pressures for the normalization of all hot-wire data as well as for
the calibrating the hot-wire sensors. Additionally the Baratron was used to measure the
static pressure, P(x,y)-Pm, upstream of the tunnel exit. A Validyne DP15-20 pressure

transducer was used to provide the reference pressure during the static pressure surveys.

18

2.5 Hot-Wire Anemometers Anemometers

Hot-wire data were taken using several constant temperature anemometers. The
single sensor surveys, as well as some of the x-array probe surveys, were accomplished

using DISA 55M10 anemometers. The noise on these anemometers was found to be on

the order of :20 millivolts peak to peak. The typical frequency response was found to be
48 KHz at 10.5 m/s flow speed. The remainder of the data were taken using T81 1750
anemometers. The noise level on these anemometers was found to be $1.5 millivolts with
a frequency response of 16 KHz at 10.5 m/s.

All hot-wire probes used in this study were fabricated (in-house) at the Michigan
State University Turbulent Shear Flows Laboratory. Individual hot-wire sensors were
constructed from Sum diameter tungsten wire. A schematic of a typical single sensor
probe is found in Figure 2.6. The wire spanned a length of 3mm with a 1mm active
sensing region centered between two 1mm regions of nominally 50pm diameter copper
plated tungsten. The active region of the sensor had a length to diameter ratio of 200.
Hot-wire sensors were operated with an overheat value of 1.7. Nominal cold resistances
of the wires were found to range from 3.5 to 4.5 ohms.

The sensors of the x-array hot-wi re probes were the same as those for the single
sensor probes described above. Two x-arrays were used simultaneously to provide u,v
and u,w measurements at each location. The u values from the two arrays were averaged
to provide the measurement of u.

All hot wire data were temperature compensated to reduce errors caused by a change
in flow temperatures between the calibration and the measurements. Temperature

measurements were conducted using a thermistor with a sensitivity of 2.03 K/Kohm at

19

293 K. At 293K the thermistor had an accuracy of i0.2K and a frequency response of
10Hz. All temperature changes were assumed to be long term (on the order of hours) and

therefore the response time of the thermistor was considered sufficient.

24 INCH RECIRCULATING WIND TUNNEL

20

 

Figure 2.1: Schematic of experimental facility.

21

 

 

 

 

 

 

 

 

 

 

reference vetocsty neosurenent location

re Ference pressure tops

Figure 2.2: Schematic of the modified flow facility.

 

YT7'IYYTrIYTrerrYTITTVV'IY'VV'Y'YY'VY'

T
1

a)
\ I- -I
E 10
V T U =21228*AP°'5°° 1
a. > “P '
3
D .
5 ~ _

JALILLLLILAAAAIILLLIllAlLllllllLJlllAl

0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
AP (in H20)

 

 

 

contraction

Figure 2.3: Velocity calibration curve for flow facility.

22

 

 

 

 

  

 

 

 

 

 

A: Primary Idle
3 Secondary Tob

 

Figure 2.4: Schematic of the tunnel extension.

23

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

VHS: :1 ”is?"

not to scale

 

 

Figure 2.5: Schematic of the probe traverse system.

24

 

 

 

 

 

 

 

 

 

Figure 2.6: Schematic of single sensor hot-wire probe.

3. DATA PROCESSING METHODS AND CONSIDERATIONS

3.1 Introduction

The information presented in sections 3.2-3.4 describes the protocols for the use and
calibration of the hot-wire probes in this study. The first two sections deal with the
processing algorithms and calibration methods for the probes. The rationale for the use of
each probe in different measurement locations in this study are presented in section 3.4 .
Sections 3.5-3.7 deal with the cross-vane vorticity probe and further data reduction

methods for all data in this study.

3.2 Single Sensor Calibration and Processing Algorithms

Data from the single sensor probes were processed using the modified Collis and
Williams (1959) relationship:

E2=A+BQ“ (3.1)
The measured hot-wire voltages were converted into velocities by solving (3.1) for the
flow velocity Q.

A probe was calibrated by exposing the sensor to a steady flow and sampling the
resulting anemometer output voltage and a reference pressure voltage. A MKS Baratron
pressure transducer was used to measure the pressure differential in the calibration
facility which provided the measured reference speed Qm. Six flow speeds, ranging from

1.5 m/s to 13 m/s, were used in each calibration. Note, 1.5m/s represented the minimum

25

26

measurable speed in the calibration unit, while 13 m/s represented a velocity that
exceeded the highest expected velocity in the flow field.

The calibration data were then transformed into E21,“, and Q"... where the subscripts
"hw" and "m" represent "hot-wire" and "measured" respectively. A least squares linear fit
was performed on the transformed data to calculate the constants A and B used in (3.1).

The standard deviation of the calibration data was calculated by

N
sd = “1112‘ Q ..........d — Q... )2)”2 (3.2)
I

where Qcaleulated was the velocity calculated from the measured anemometer voltage using
the fit A and B for the given 11 and (3.1). The coefficient n was varied from 0.2 to 0.7 to
determine the calibration coefficients that minimized the standard deviation. Figure 3.1
shows the affects of changing it for a given set of calibration data. The calibration data
became most linear as the "best" 11 was approached . Typical "best" values of n ranged

from 0.4 to 0.5.

3.3 X-Array Calibration and Processing Algorithms

An x-array was used to provide two components of velocity in the "plane" of the
probe. Note that the "plane" of the probe refers to the plane parallel to the two wires of
the probe, see Figure 3.2. The processing of an x-array hot-wire probe required the two
voltages from the wires in the probe to be known at the same instant. These two voltages

were processed simultaneously to provide measurements of the flow speed, Q(t), and

angle, y(t) in the plane of the probe.

27

The simplest x-array processing algorithm, termed the "cosine law", was based on the
concept of the effective cooling velocity (Bradshaw (1975)). It was assumed that a
hot-wire sensor was cooled only by the velocity component perpendicular to the wire,
Qcm The effective cooling velocity, chf, for a hot-wire was determined by the relation

Qen=Qcos(B-r). (3.3)
The angle 7 , termed the "flow angle", was defined as the angle between the probe axis
and the in-plane velocity vector as shown in Figure 3.2. The angle B was the angle
described by a line drawn perpendicular to the wire and probe axis. The effective [3 was
determined using the calibration data as described in Appendix A.

Expansion of (3.3) using a two angle formula yielded

Qea=Qlc08(B)COS(r)+sin(B)sin(r)]. (3.4)
Substituting the values

u=Qcos(y) (3.5)

v=Qsin(y) (3.6)
into (3.4) yielded

Q¢n=ucos(B)+vsin(B). (3.7)
Equation (3.7) yielded one equation with two unknowns, u and v, for each sensor. The
two sensors in the x-array were used simultaneously to solve for u and v by

Q“; = ucos( [3+ ) + vsin( (3+) (3.8)
and

Qent. = ucos( B- ) + vsin( B- ). (3.9)

The terms Qeff+ and chr. in (3.8) and (3.9) were defined from the calibration data and

28

measured hot-wire voltage as

i—A+(y=0)

 

 

 

 

Qcm=[ E ](n.(l=0)) (310)
B+(Y=0)/COS(B+)n’ ’ '
and
2 _
chf-=[ E'_A‘(Y_O) ](rL(yl=O)). (3.11)

B- (r = 0)/ cos( B- ) "'
Where - and + indicate the voltages and coefficients associated with the -B and + B
sensors. Note that in (3.10) and (3.11) A, B and n values were only required for y=0.
Calibration of an x-array for use with the cosine law could therefore be accomplished
using the same protocol as described for a single wire if B were known. The in-plane
flow velocity and flow angle were defined from u and v from as

Q-“-(uz+v2)“2 (3.12)
and

y=tan'l(v/u). (3.13)
This routine has been shown to be accurate for flow angles up to i 12 degrees (Foss et.
al.(1986)).

The "modified" cosine law was introduced as an attempt to increase the effective
range of an x-array. In the cosine law it was assumed that the wire responded only to the
flow which was perpendicular to the wire. This assumption became less valid as the flow
angle was increased for a finite length wire. The modified cosine law accounted for this
affect by adding a term to the effective velocity as:

Q.a=Q(cos’(B-v)+k’sin’w-y». (3.14)

Note that the kzsin2(B-y) term was included to account for the transverse cooling velocity

29

and that the term k2 could be determined using calibration data for the probe. This routine
has been used extensively, however it also has some disadvantages. Specifically, the
processing algorithm assumed A, B and n values were constant for all flow angles. This
assumption has been to shown to be incompatible with experimental calibration data
(Foss et.al. (1986)). Note this same limitation was also present for the cosine law
algorithm. In addition, the values for k2 determined from the calibration data have often
been determined to be negative from the calibration data.

An alternate processing algorithm, described in Foss et. al.(1995), was used in this
work. In this algorithm it was assumed that the wire which was more perpendicular to the
flow direction was more responsive to the flow speed; therefore, that wire was designated
the "speed wire". Conversely, the wire which was more tangent to the flow angle was
more responsive to angle variations, and this wire was designated as the "angle wire".
Wire 1 was the speed wire and wire 2 was the angle wire for the velocity vector shown in
Figure 3.2.

This processing algorithm required extended calibration data. Specifically, the angle
of the probe with respect to the flow was varied at a given speed. This provided speed
and angle calibration data (i.e. E(Q,y)). These data were fit at each calibration angle to
the modified Collis and Williams form by

Ez(Q,r)=A(v)+B(r)Q"‘”. (3.15)
The best fit 11 was determined for the calibration data at each angle as described in
section 3.2. A typical set of calibration data, plotted as E versus Q, is shown in Figure

3.3. These data clearly illustrate the probe dependence on both angle and speed.

30

A relationship for the wire voltage versus flow angle for a constant speed was

developed for this processing algorithm. Namely the function n(y) at a fixed Q was

defined as
112.11
= —1. 3.16
7‘ E(Q.0) ( )

Using the curves described by (3.15) 11(7) was defined for any arbitrary speed at all
calibration angles. In this work, 51 curves of flow angle, 7, versus 1] were defined for
even speed increments from 0.25 m/s to the highest calibration speed, nominally 13 m/s.
This allowed for the rational interpolation of the calibration data between the calibration
speeds. Figure 3.4 shows a typical y versus 11 curve for an arbitrary speed. A fifth order
polynomial was used to describe the curve.

The enhanced sensitivity of the "angle wire" to the pitch angle (7), in contrast to the
insensitivity of the "speed wire" is clearly illustrated in Figure 3.4. Specifically, for flow
angles greater than zero the calibration data were spaced over a range of n from -0.09 to
0. For negative flow angles these data ranged from n=0 to 0.045. This clearly illustrated
that there was a greater resolution of flow angle for a positive angles with this wire.
Conversely, a change in flow angle did not create as great a change in the hot-wire
voltage indicating it was more sensitive to the flow speed for negative flow angles.

The following processing algorithm was developed to use the speed wire/ angle wire
concept described above. The speed wire and angle wire were determined using an initial
estimate of the flow angle, you. In this work the initial estimate of the flow angle for the
speed wire/angle wire algorithm was provided by first using the cosine law to process the

data pairs. A new estimate for the speed, Qnew, was made using the speed wire with the

31

A,B, and n values for the calibration angle closest to you. The variable 11 was determined
for the angle wire using its voltage, E, and (3.16). Two estimates for the new flow angle
were made using the two 1 versus 11 curves closest to the new flow speed Qmw. The new
flow angle, yaw, was found by linear interpolation between the two angles based on the
flow speed.

This processing algorithm was iterative. At the end the algorithm the new estimates
for the flow speed and angle became Qord and you for the next iteration pass. In this work
the solution was iterated 5 times to achieve the final values for Q and y. The speed wire/
angle wire processing algorithm has been shown to increase the effective range of an
x-array to 3:36 degrees for sufficiently high flow speeds (Foss et. al. (1995)).

Calibration of the x-array probe was accomplished using six speeds, ranging from
1.5m/s to 13m/s, and thirteen angles, ranging from -36 to +36 degrees. Note that the
calibration angle range was larger than the effective angle range to permit full resolution
of the angles within the effective range.

It is important to note that an x-array probe will also respond to a velocity component
which is perpendicular to the measurement plane. The effect of this component, typically
referred to as the "bi-normal" component, is present in the x-array data contained within

this work.

3.4 Determination of the Use of the Single Sensor and X-Array Probes

The decision to use a particular type of hot-wire probe was based upon the flow

conditions, the data to be acquired, and the limitations of the probe.

32

In this study, the single sensor hot-wire probe was used to measure the streamwise
velocity component for the untabbed geometry at x/b=0.7,1.2 and 2.0. Note that a single
sensor probe was assumed to respond to two components of velocity which were
perpendicular to the sensor wire. Specifically in this work, the sensor will respond to a
streamwise velocity component, u, and to the transverse velocity component, w, because
the sensor was parallel to the z-axis. The magnitude of the velocity measured at an
instant by this probe will be

Q(t)=(U(t)2+W(t)2)'/2. (3.21)
The average value as well as the fluctuating value will therefore be a result of the two
velocity components. If either E or \V were equal to zero than the average value of (3.21),
Q, will be identically 'vV or E respectively. The untabbed jet flow field had nominally one
mean velocity component, E, which allowed accurate average streamwise velocity
measurements to be made with the single sensor probe. The fluctuating values, which
showed w’ s u’, allowed a reliable estimation of E to be made using the single sensor
probe.

The flow pitch angle fluctuations were too large (i.e. greater than 30 degrees) at
x/b=0.7 to allow the use of x-arrays for the primary tab and modified tab geometries.
Single sensor measurements were made at this location for these geometries so that
qualities of the flow field could be inferred. This inferential process was limited by the
non-zero W in both tabbed jet geometries. Specifically, these data will contain the

combined effects of u(t) and w(t) in both the mean and fluctuating values as indicated by

(3.21).

33

The flow pitch angles were found to be less severe at x/b=l .2 and 2.0 for the primary
tab and modified tab geometries; this permitted the use of x-array probes in these
locations. At these locations it was possible to measure u(t), v(t), and w(t). Note that in
order to resolve u,v, and w, two x-arrays, with their measurement planes horizontal and
vertical, were used in the flow field simultaneously. The two x-arrays were separated by
a distance of nominally 2.12mm from the center of the sensing arrays. The average
streamwise velocity value, E, was computed by averaging the streamwise velocity data
from both x-arrays. The x-array hot-wire probe allowed the computation of the average
velocity values, correlations, cross-correlations, two normal stresses, and one shear
stress, to be made for each x-array. Note that the sensors on the x-array hot-wire probe
will respond to the velocity component perpendicular to the plane of the x—array (the
"bi-normal" velocity). In this study no attempt was made to correct for this velocity
component.

Figure 3.5 was included to provide a comparison of the streamwise velocity
measurements of the two probes. Note that single sensor hot-wi re probe was held such
that the sensor was parallel to the z-axis for all data in this work and therefore responded
to the u(t) and w(t) velocity components. Figure 3.5, taken from the data of the modified
geometry at x/b=l.2, showed that the single sensor and x-array hot-wire probe measure
the same average streamwise velocity along the side wall of the tunnel where the
transverse velocity was small, i.e. Vv’ < < E. However, in the region above the tunnel exit
(i.e. +z) the single sensor hot-wi re probe over estimated the magnitude of the streamwise

velocity. This was expected since the magnitude of W was significant in this region (i.e.

W z 0.15 m and therefore E < Q.

34

3.5 Streamwise Vorticity Calculations

The spatially averaged streamwise vorticity, (ox, was defined as:

6 W 6 V

6 y 6 z ( )
Thus, the spatially averaged streamwise vorticity was calculated from the appropriate
partial derivatives of the V and W velocity fields which were computed using a second

order finite difference method. The interior points were central differenced using (3.28)

of Anderson (1984) by:

ai+l — ai-l

6a
__ i: 3.23
6h) 2Ah ( )

while boundary points were either forward or backward differenced depending on the

boundary using (3-29) of Anderson (1984) by:

2 A h I

 

6 a _
a h) ' "
and (3-30) of Anderson (1984) by:

as - 4211—1 + am
2 A h

 

6a 3
i.__ 3.25
ah) ( )

Note, h was the spatial distance between data grid points. This method was found to give

comparable results to fitting the data and taking a derivative of the fit curve.

3.6 Cross-Vane Vorticity Probe

The very near field of the jet was defined as the area from the physical exit of the

tunnel, x/b=0, to the downstream plane which was described by the tip of the primary

35

tab, see Figure 3.6. The tip was nominally located at x=0.61b. In this region the angle
range of the flow pitch angles was greater than :30 degrees. A cross-vane vorticity probe
was used in this region to provide qualitative information about the streamwise vorticity.
Figure 3.7 is a schematic of the cross vane vorticity probe. This probe was placed into the
flow such that the probe axis was in the streamwise direction. The blades on the probe
rotated in the presence of nonzero streamwise vorticity, cox, (with a sufficient magnitude
to overcome the friction of the device) as described by (3.22). In this study the probe was
used in a qualitative manor. Specifically, it was noted which direction the probe spun
and if the probe spun "fast" or "slow" at each measurement location. The data presented
in section 5.3.13 represented the nominal boundaries of the regions of streamwise
vorticity from x/b=0.l to 0.4. The friction in the probe did not allow observations to be

made for streamwise distances greater than about x/b=0.4.

3.7 Statistical Calculations

The data presented within this study were a result of single point measurements. Each
time series was processed to provide average and fluctuating values at one measurement

location. The mean and mean square values were defined for a time series of data as

N
_ 1
g = E20: g (3.26)

and

N
E": fiZew-oz (3.27)
0

36

Finally the nns fluctuating value was defined as

sets—2% (3.28)

Data for both the single sensor and x-array hot-wire measurements were acquired at a
variety of sampling rates for 30 seconds. The sample time corresponded to 1575 tab base
lengths units passing the tunnel exit with a nominal approach velocity of 10.5 m/s.
Pressure data were taken at a sample frequency of 200Hz for 30 seconds.

These data were primarily represented in contour form to allow global features of the
flow field to be represented. Three plots of data acquisition grids are presented in Figure
3.8 to provide a frame of reference as to the data point spacing used to form the contour
plots. The first of these plots, Figure 3.8a, shows the data acquisition grid for the
upstream pressure surveys. Data were acquired with increments of Ax=Ay=0. 1b. Figure
3.8b shows the grid spacing for the hot-wire surveys conducted at x/b=0.7. These data
were acquired with Ay=Az=0.05b. Finally, Figure 3.8e represents the data acquisition
spacing for hot-wire surveys conducted at x/b=1.2 and 2.0. These surveys were

conducted with a spacing of Ay=Az=0.075b.

3.8 Normalization of Data

All quantitative data are presented in non-dimensional form. The lengths were
non-dimensionalized by the base length of the tab, b, as

K‘=K/b (3.29)
where K represents any length measure in the flow field. Average and fluctuating

velocity values were normalized with the approach velocity, Uup, by

37

o‘=<r>/U..p (3.30)
where (I) is a velocity statistic in the flow field. The streamwise vorticity values were
normalized with the approach velocity and the base length of the tab by, b/Uup as

m‘x=ZoI(b/ Uup). (3.31)
Finally the pressure values were made non-dimensional by the dynamic head of the
approach flow as

PEP/0.513112... (3.32)

38

I W I I

 

    
  

5 I- I 002
- . 00.4
.. ‘ 00.7 A
’ curve fit
c I
O 4 I—
E A
3 r-
: . E2=7.116+5.164Q°"

  

71' I T I I

 
 

I
lLlllllAkngLl+llll l lllJlllllLllllllJllLJ

14 15 16 17

 

Figure 3.1: Hot-wire calibration data with changing n values.

39

 

 

  
 

 

 

 

 

 

 

 

 

 

O O
_ 33.993-524.13.-. -
0 <5
Z
I B /
B (a,
Figure 3.2: Schematic of x-array hot-wire probe.
5.4j_'1fi 1“ r1 tr 1 "Yr ' l .Wagm"
'- D -30
r ‘ '24
_ a A 49
I- v "2
5.2 ’- 3 V -o
. D o
t D V D o
* A ’ 4 12
t A p 0 re
5.0 r 5 ‘ O 24
I. D ' 0 so
I A Q C so
.. V D
I v 4 O
4.8 ~ v <1
. D O .
. g ‘ ’ o
,
. 3 0 .
E E o .
O a
4'6 g g c .
I o
J
4.4% l l 1 L41 1 l l l I l l J J l L L A l l L l 1 1 L 1 l A
2 4 6 8 10 12

Figure 3.3: E versus Q from a typical x-array calibration.

 

IIITT‘IYYYTIT‘I’jT

  

Y
o
.1”

    
 

O nitration
5" order potynominel

 

[VII

'1‘

lllllAllllLlLJJAilLJJLlLJALLAALJAJAL

IIIIVITTI

 

 

 

Figure 3.4: 7 versus 7} data for x-array calibration.

1.0-

-------- single sensor
x-array sensor

   

0.5 *-

Y I V T T V Y
cup-um--

__ a
Q-‘
I

0.950up

I
d
O
v I 1

 

 

;1 L L l 1 L L l l l L j l 1 I l l l l A L A 1 L4

«05 0.0 0.5

 

Figure 3.5: Comparison of streamwise velocity contours for the single sensor
and x-array hot-wire probes.

41

tunnel exit XIO
Z f
X

________.>

 

 

_. _— very near Field, O<><<O.61lo

note: meow Field —1.95b<x<8.0b

Figure 3.6: Definition of the "very near field".

 

 

 

 

 

 

 

 

 

—~— -—~19.1 mm
=$= l H: e
4.7mm +

Figure 3.7: Schematic of cross-vane vorticity probe.

42

(a)

(b)

 

-2.0 -1.5 -1.0 -0.5 0.0 0.5

y/b

 

-2.0 -1.5 -1.0 -O.5 0.0 0.5

y/b

Figure 3.8: Data acquisition grid spacing: a) static pressure, b)
hot-wire at x/b=0.7, c) hot-wire at x/b=1.2 and 2.0.

4. UNCERTAINTY CONSIDERATIONS

4.1 Pressure Measurements

Data taken with the 1 Torr MKS Baratron had an associated uncertainty of i0.08% of
the measured value( MKS Instruments (1994)). The i0.08% level of uncertainty
corresponded to an uncertainty of 004ch (0.004% of U...) in the measurement of the
approach velocity Uup. Note, this level of uncertainty was based on a nominal 4.8 volt
measurement for an approach velocity of 10.5 m/s. For the measurement of the static
pressure field the uncertainty for the Baratron can be taken to be i0.08% directly. The
reference pressures for the static pressure surveys were taken using a Validyne DPISTL
pressure transducer. This device had an uncertainty of 105% of the measured value
(Validyne Engineering (1978)) which corresponds to a velocity uncertainty of 02ch
(0.02% of Uup).

The static pressure measurements on the top surface of the tunnel extension without
tabs present provide details about the how well the static taps perform in a flow field.
Specifically, any physical defects in the taps will provide a greater error in the pressure
measurements than will the errors associated with the pressure readings. The pressure
data upstream of the tunnel exit for the untabbed geometry (shown in Figure 5.2 ) show
static pressures bounded by the magnitudes Cp=0 $0.02. The farther upstream data show
a back pressure which is made rational given the boundary layer growth in the tunnel
extension. The pressure measurements also show a value of Cp z —0.02 along the wall.
Note that the same pressure tap is used to measure all of the pressures for x=constant

locations, therefore the pressure measurements in this region are due to imperfections in

43

44

the apparatus (i.e. the side wall/top wall interface) and not these local tap. The pressure
measurements at the exit of the tunnel should be equal to zero. The nonzero
measurements in this region indicate the uncertainty in the pressure to be $0.006 as a
conservative estimation of the uncertainty due to the tap imperfections. Figure 4.1 shows

a typical pressure distribution for a fixed x location with uncertainty bars.

4.2 Hot-Wire Measurements

All hot-wire probes were pre and post calibrated to ensure that the wires did not
experience significant drift during usage. Drift values were limited to a maximum of 0.05
m/s for a single sensor probe and 0.15 m/s for the x-array probes. These estimates of dn'ft
were calculated by combining the pre and post calibration data to provide calibration
constants from the combined data and checking the standard deviations of the combined
calibration data.

Single sensor hot-wire calibrations show a typical standard deviation of 0.03 m/s
between the measured velocity and the analytical form E2=A+BQ" , as described in
section 3.1. Note that at 10.5 m/s, nominally the approach velocity Uup, this level of
deviation represents 0.3% uncertainty in the velocity measurements.

The x-array calibrations show a typical deviation of 0.08 m/s, i.e. 0.8% of Uup, and an
angle variation of 0.1 degree except at the lowest calibration speed (nominally 1.5 m/s)
and at the largest angles (i 36 degrees). In these extreme conditions the velocity was
recovered to nominally 0.2 m/s and the angle to within 3 degrees. This estimation of the

uncertainty in the x-array data was made by taking the calibration data, i.e. voltage at an

45

known angle and speed, and using the processing routine to calculate the speed and
angle. The processed data are then compared to the measured data.

Figure 4.2a shows a typical average velocity traverse with error bars included for
illustration. Note the error bars included in this figure were derived from the uncertainty
in the calibration data. Figure 4.2b shows the ii/ Uup survey for the same traverse. The
error bars included with Figure 4.2b were determined by processing the same data set
with the pre and post calibration coefficients separated. The difference between the
measurements was found to be A ( U/ Uup) = 0.003.

Figures 4.3 and 4.4 show the convergence of the mean and fluctuating statistical
properties as a function of sample size in the plume region of the flow (i.e. at y=-b and
+2) for two data sets with U z 0.6Uup and U z 0.3Uup respectively. Note that the total
number of samples n=60,000 was fixed by the sample rate (200Hz) and the total sample
time (30 seconds). The data for ii z 0.6Uup, Figure 4.3a, suggest that the "infinite sample
size” mean value can be estimated to be 5/ Uup z 0.62 i 0.005 by the convergence
pattern. Figure 4.4a also shows G as a function of the number of samples for E 2: 0.3Uup.
The convergence of the data at this location is less pronounced. The mean value of
0.32, obtained from 60,000 samples clearly does not represent a "converged statistic".
From the variation of the "mean values" with increasing sample size, it is also difficult to
estimate the true mean value at this point in the flow field: x=2.0b, y=-1.05b, z=0.825. It
is instructive that this location is near the peak of the out-flow "plume" to be described
below. In contrast, data taken from the outer edge of the jet flow (away from the tab) at

x=2.0b, y=-1.8b and z=-1.05b and also for U z 0.3Uup exhibit convergence for as few as

46

10,000 samples; see Figure 4.5a. This clearly illustrates that different integral scales, and
hence strong difference in the number of independent samples for the 30 second period,
are present in the distorted and undistorted shear layer.

The convergence of the standard deviation values has also been assessed; these data
are shown in Figures 4.3b, 4.4b and 4.5b. It is apparent that fewer samples (30000,
40000, and 10000 respectively) are required for the evaluation of this statistical measure.

The data from the x-arrays was used to provide calculations of the shear stresses in

the flow field. Figure 4.5 shows the collapse of 6’7/ U34, and W/ U39 as a function of
the number of samples. (Note these data were calculated from the same measurements
used in Figure 4.3.) These plots show the data tending to convergence, although these
calculations appear to be oscillating. An estimation of the uncertainty in these data was
determined to be i0.002 for both quantities.

In this study there are large regions of low velocity with magnitudes that are not
within the calibration range. Specifically, the minimum possible calibration speed given
the experimental facilities was nominally 1.5 m/s. Measurements of velocities smaller
than those of the the calibration data require extrapolation of the calibration data and
exhibit a larger uncertainty than do measurements that fall within the calibration velocity
range. To minimize the effect of this uncertainty on the results the velocity data are
presented in contour form with a minimum streamwise velocity contour of 0. 15*Uup.
This represents a dimensional value of nominally 1.6 m/s which was within the

calibration velocity range.

47

 

11f]IIIIIIIIU'IYTYfiTIIIIUIIlTIVI

IIIUIYII

 

IUYTIIII

  

lllllllllLLJlLlll

   

llllLllLllllllLlllll

llllllll

 

 

Figure 4.1: Error bar estimate for pressure surveys.

 

 

 

 

 

1 .2 ,_ T j ‘r 1 I f T v T I r 1 v v I f r v r I f r r 7 d
C 1
1 o b i
_ "i
i a) .
i a
i I
0.8 - ~
i' a
Q i-

:3” ‘
\ 0.6 — _
i3 - «
0.4 - J
~ 4
0.2 *- -
: nominal minimum calibration speed 1

o o 1 1 r L l L 1 l 1 l 1 1 1 r l 1 L 1 L l 1 J L L

-2.0 -1 .5 -1 .0 -0.5 0.0 0.5

y/b

 

0.15 r —
. b)

g. .. -<
2 0.10 r —
23 L

0.05 - _

 

 

 

000 i 1 1 4 i . . l 1 i i i l i . . I
-1.5 -1.0 -0.5 0.0

y/b

Figure 4.2: Error bar estimates for velocity measurements, 3) average, b) rms.

 

 

 

 

 

s : 4
D 0.4 ' _
:3 g 1

0.3 - _
0.2 _- _
0.1 _— _‘

' i

b ‘i
0.0 ’- 1 1 1 1 1 l 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 L4 1

0 100 00 20000 30000 40000 50000 60000

number of points

b)

 

0.30 Y r I T Y Y T T T I’ V T ‘T T Y T T Y Y ‘7’ T I Y T
I I I I T
q

 

 

 

 

0.00.“‘lltllll1111lL111l11111L11
0 1 00 00 20000 30000 40000 50000 60000

number of points

Figure 4.3: Statistical convergence for U/ Uup~ 0.6 in the plume region,
a) average, b) rms.

50

 

I I V I I I I I V I I V Y I I Y 1 V V I I Tfi' Y I Y Y Y T

0.7

 

 

 

 

 

 

 

 

 

I
J
o 1
.6 ) 1
0.5 _.
.1
Q .1
3 1
3 ,
\ 1
l 3
0.3 - q
r 1
' 4
: 1
0.2 - _.
’ 4
’ 4
' 4
h 1
0.1 - ..
00 F 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 1 1 1 l L 1 1 1 i 1 1 1 1 ‘
0 10000 20000 30000 40000 50000 60000
number of pornts
030 ' T Tfi j r Tfi T T T Y Y r I t r fiY T 1 v v v I r f r r
L cl
p 1
0.20 — b) _
,- '1
5‘ L ,
3 MM ‘
\
I :3 ' 1
0.10 - .1
O_m 1 1 1 1 1 1 1 1 1 l 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1 1 1 1 1

 

 

 

0 10000 20000 30000 40000 50000 60000

number of points

Figure 4.4: Statistical collapse for U/ Uup~ 0.3 in the plume region,
a) average, b) rms.

51

 

I II T I I I r I frI 1' I I Ifi 1 I T I' I Ifi I I I

 

0.7 - -
p
b )
()6 r ‘
P '4
; I
F Ii
(15 F ‘
I '1
b -l
E 4
o. b -
3041’
D 7 'n“.v‘-‘I'...~..‘-ahow'..oooou*—‘ ............................ ~— --------
\ ' q
u: r 1
(l3 - ‘
’ ‘1
(l2 — 1
i -l
i q
p
0.1 — d
. I
0 0 1 1 I 1 1 1 l 1 1 Lg l 1 1 1 1 l 1 1 1 l 1 1 1

 

 

 

' 0 ‘10000 20000 30000 .40000‘ 50000 60000
ruunberofpouus

b)

 

 

 

 

 

0.30 p IiT I r I I r I I I I I I I I I I I I T I I I I I I I I I d
P 4
L -4
’ i
30.20 - g
D ' 1
F d
\ W‘M‘g-
33 0.10 [- ~
I
h
0.00 L A J_]_ l A A A L J. L#L A l J L L A l L A g

0 10000 20000 30000 .40000 50000 60000
runnberofpouns

Figure 4.5: Statistical collapse for U/ Uup ~ 0.3 in the side wall shearlayer,
a) average, b) rms.

52

 

(1008

 

.1--.
l

(1002

(1000

 

 

A L J l I A 1‘. l .L L L J J J. L L L I L A J l A I A

10000 20000 3000? 40000 50000 60000
number 0 pornts

 

p
p
_
F

0

 

 

(1002

I
1 l 1 1 1 1

fi'--

(L000

 

 

1
11.1.11.1111111.111....l.111
0 10000 20000 3000? 40000 50000 60000

numbero pornts

 

Figure 4.6: Shear stress calculation convergence, a) u’ v’/ Uup, b) u’ w’/ Uup.

5. RESULTS AND DISCUSSION

5.1 Introduction

The results of this study are divided into two parts. The first part, section 5.2, details
the untabbed jet results. These data were used to provide a reference case for the tabbed
jet results. The results for the tabbed jets are presented and discussed in sections
5.3-5.6. The initial results (static pressure, streamwise velocity and surface streak
patterns) for the primary tab geometry are first presented (section 5.3). These data
provided the details which served as a basis for the modification of the tabbed jet. This
section is followed by a discussion on the orientation of the secondary tabs for the
modified tab geometry (section 5.4). The initial results for the modified geometry are
then presented (section 5.5). Finally the remaining results for tabbed jet geometries are

compared and discussed (section 5.6).

5.2 Untabbed Jet

5.2.1 Exit Boundary Layer Survey

A velocity survey using a single sensor hot-wire probe was conducted at the exit of
the tunnel extension to provide detailed information about the approach boundary layer
for the untabbed jet. The results, shown in Figure 5.], indicated the approach boundary
layer had: a boundary layer thickness, 5, of 3mm (0.015b), a displacement thickness, 5.1,
of 1.27mm (0.0064b) and a momentum thickness, 9, of 0.52mm (0.0026b). The approach
boundary layer remained laminar up to the exit as indicated by the shape factor H, which

was found to be 2.47. (H for the Blasius solution is 2.59.) The peak fluctuating velocity

53

54

value was Emu = 0.014Uup at y/ 0 = 3. The fluctuating values were seen to decrease to
nominally 0.006Uup as the core flow was approached. This turbulence level indicated that
the tunnel flow conditioners were able to quiet any disturbances created by removing the
test section and opening the tunnel to the laboratory flow. Note also the fluctuating
velocity profile shown in Figure 5.1 was consistent with that made rational by Foss
(1977) for a laminar boundary layer. That is, the peak in the fluctuation intensity and the
shape of the U/ Uup distribution could be explained by a modulation in the height of the
boundary layer and a proportionate variation (by/y=constant) for y values less than

8. There was a local maximum in the velocity profile (U = 1.02 Uup) at y/ 9 z 7. This
maximum in the velocity profile was an artifact of the contraction in the tunnel upstream
of the measurement location. The velocity profile appeared to be relaxing to E = Uup for

y/B greater than 10.

5.2.2 Upstream Pressure Distribution

The upstream static pressure survey, Figure 5.2, showed that the untabbed tunnel had
a static pressure upstream of the tunnel exit nominally equal to the atmospheric value.
This result was expected given the small percentage (0.1%) change in area of the tunnel
calculated from the momentum thickness. The peak values of these data were P'=i0.02.

Note that these results indicated that the pressure taps were functioning properly.

5.2.3 Velocity Magnitude Profiles

55

Figures 5.3a-5.5a show the average streamwise velocity field downstream of the
tunnel exit for the untabbed jet. The results from these data indicated the development of
the untabbed jet to be as expected. Specifically, the shear layer, as described by the
isotach lines, remained strongly aligned with the tunnel top and side walls as the
downstream distance was increased. The shear layer grew into both the core and ambient
regions with slightly more penetration of the shear layer into the ambient region. This
was expected given the higher momentum of the core flow and the entrainment of
ambient fluid.

Turbulence intensity values are presented in Figures 5.3b-5.5b. The maximum
turbulence intensity for the three measurement planes was located at x/b=0.7 (nominally
Emu z 0.18Uup). This value was located near the center of the shear layer. The values
indicated that the velocity field was highly turbulent in the sheared region of the free jet.

Note that these maxima are characteristic of single stream shear layers (Wygnanski and

Fiedler (1970) and Bruns et. al. (1991)).

5.3 Primary Tab Jet: Preliminary Results

5.3.1 Upstream Pressure Distribution Results

Figure 5.6 shows the upstream static pressure distribution for the primary tab
geometry. A static pressure distribution, P(x,y), was indicated upstream of the tab. This
pressure distribution was created as a result of placing the primary tab into the core flow
and changing the streamline patterns upstream of the tab. The observed peak static
pressure was found to be P.=0.7 at x/b=-0.05 and y/b=0. (Larger pressures could exist

closer to the tab/nozzle wall junction as suggested by Figure 5.6.) A significant drop in

56

static pressure occurred along the centerline of the tunnel from x/b=-0.05 to x/b=-1. That
is, the static pressure decreased from P‘=0.7 to P'z0.2 for these values. From x/b=-1 to
x/b=-1.95 (the farthest upstream measurement location ) the static pressure decreased
from 0.2 to 0.15. A pressure distribution, in the y-direction, was also indicated by Figure
5.6. These pressure values ranged from a maximum value of 0.7 at x/b=-0.05 and y/b=0,
to nominally atmospheric at x/b=-0.05 and y/b=-l.4. Note that this static pressure
distribution was qualitatively similar to that reported by Zaman et. al. (1994) for a round

tabbed jet.

5.3.2 Surface Streak Results: Primary Tab Geometry

Surface streaking experiments were performed upstream of the tab face to further
clarify the flow characteristics. The streaks were acquired by taping mylar sheets to the
tunnel surfaces upstream of the exit and to the tab faces. The tab faces were then cut out
of the mylar sheet such that the mylar sheet covered only existing surfaces. A red
pigment (Day-Glo Red AX-l3) was mixed with kerosene and was painted onto the mylar
sheet. The tunnel was then turned on with an approach velocity of nominally 10.5 m/s
and the streaking was allowed to progress until the mixture dried. The pigment was
affixed to the mylar sheet with a clear spray fixative. The streak patterns were
photo-reduced and scanned into electronic format.

Figure 5.7 shows the surface streaking results for the primary tab geometry. Note that
the tab orientation was the same for these data as for the other data presented in this
report (Figure 2.4) although the results for the tunnel and tab surfaces are presented as

though they existed on the same x-y plane. These traces show the complex surface

57

pattern created by the primary tab geometry. Four singular points can be identified along
the centerline of the flow field. Specifically (from left to right) a saddle, node, saddle,
node pattern was observed as shown in Figure 5.8. Two topological arguments were
made to show that this pattern was allowable. Viewing the geometry from the top, a
sphere with two holes was drawn as shown in Figure 5.9. Note that a sphere with two
holes has an Euler characteristic, 13mm, of zero. This value, xsurfm, was found by
identifying the Euler characteristic for the present surface as that for a sphere (+2) with
the with the addition of two holes (-1 each). Hence, for the present case, Xxurface =0. The
sum of the indices of the singular points on the subject surface is equal to the Euler

characteristic for that surface by:

ZN“Z S=Xsurrace (51)
where N and S are the number of nodes and saddles respectively. There had to be an
equal number of nodes and saddles in this case for the nodal pattern to be allowed; thus
the pattern shown in Figure 5.9 was allowed, but not unique.

This limitation (i.e. the lack of a unique solution) of a topological analysis is made
clear if the node on the primary tab face (N2) is examined. In Figures 5.7 this node
appeared to be a line of singular points. An alternate topological argument could be made
if one considered the node (N2) to be part of the following pattern: node, saddle, node,
saddle, node as shown in Figure 5.10. This configuration of singular points had one net
node and therefore had the same implications topologically as one node used in the

previous analysis. Any combination of nodes and saddles which had one net node was

58

therefore an allowable pattern. Figure 5.8 shows the simplest topological argument that
was permitted.

A second topological inferrence was made by viewing the flow in the x-z plane as, as
shown in Figure 5.11. In this view there was also a sphere with two holes(x,u,fm=0).
Note that, the sphere, in this case, was flattened. Equation (5.1) is modified to

accommodate the flattened sphere by:

221x1+21x1’-2ZS—-ZS’zxsmf,cc (5.2)

where N’ and S’ are nodes and saddles that lie on the "crease" of the flattened sphere
(note these singular points are dubbed "half nodes" and "half saddles"). The indicated
surface singular points were four "half saddles" in this case. These singular points gave
-4 which was not equal to xsurrace. Note that two half saddles, 82’ and 84’, were shown in
Figure 5.9 as nodes N1 and N2. This change in "type" from node to saddle is due to the
change in orientation of the analysis. The sum of the singular points on the surface points
indicated that more singular points in the flow field were required. These were inferred to
be located above the surface as shown in Figure 5.11. (Note also that the following
inferences are made rational by the streamwise vorticity data presented in sections 5.6.6
and 5.6.7.) The value of xsmfm was zero with these full nodes and saddles added in. The
most upstream node (N 1) represented the approach boundary layer vorticity which
separates from the surface. This vorticity is related to the organized motion that has been
referred to as the "necklace vortex" by various authors; see, e.g., Zaman et.al. (1991).
The second half saddle point (82’) was an attachment point for the flow (N 1 in the top

view, Figure 9). It was inferred that the second node (N2) was characterized by vorticity

59

with the opposite sign as compared with the approach boundary layer. In particular, the
sign of the vorticity in N2 is compatible with the dominant streamwise vorticity
downstream of the exit. As shown below, this inferred sign of the vorticity in N2 is
required to account for the "solenoidal condition" (V - (7)): 0) of this dominant motion.
(These dominant motions correspond to the vorticity created by the upstream pressure
distribution.) The final full node (N3) denotes vorticity with the same sign as the
approach boundary layer and corresponds to the second attachment point. Note that the
full saddle (SS) was required to create a smooth vector field in the indicated plane and to
bring the sum of the singular points to zero.

The streak lines presented in Figure 5.8 were used to describe the s— and b- directions
at the wall used in (1 .6) to determine the flux of vorticity into the flow from the pressure
gradient. Recall that the s-direction was parallel to the direction of the flow, and was
therefore described by the direction of the streaks. The b.direction was perpendicular to
the streaks such that 3 x 6 2 ii. In Figure 5.8 the s-direction would be the x-direction and
the b-direction would be the y-direction well upstream of the tab. This implied a flux of
to, into the flow because of the pressure gradient. As the separating streamline was
approached along the centerline (i.e. for y=0) the s-direction shified to become aligned
with the y-directi on. In the separated region directly upstream of the tab, the s-direction
was strongly in the y-direction indicating a flux (0,, from the pressure gradient into the
flow.

Note that it was not possible to determine, from the streak pattems alone, what

happened to the vorticity once it was introduced into the flow. The streak results

60

indicated some of the boundary conditions for the flow field. The streamwise vorticity
results (presented in sections 5.6.6 and 5.6.7) also represent part of the solution of the
flow field. Flow mechanics (specifically what the vorticity did once it was in the flow)
may be inferred by using these data in combination. These inferences will be made once

the streamwise vorticity data are presented.

5.3.3 Streamwise Velocity Results

Figures 5. 12a-5. 14a show the average streamwise velocity magnitudes plotted for
primary tab geometry. These data showed the effect that the passive mixing tabs had on
the average streamwise velocity field. The shear layer became aligned with the side of
the tab and the tunnel side wall. Near the top of the tunnel a "plume" of fluid, ejected
from the core region into the ambient region, was shown. A significant region of high
speed fluid was found above the projected tunnel exit in the plume region unlike the
distributions for the untabbed geometry. This area of high speed fluid appeared to be
increasing in size for the downstream locations investigated. A large region of low speed
flow was seen directly aft of the tab. This low speed region grew in size as the
downstream distance was increased. In addition, these data also suggested that the flow
was displaced laterally as the downstream distance was increased. This was shown by the
increased distance of the isotach lines from the tab and tunnel side wall. These
observations illustrated the strong tendency of the tabbed jet core fluid to expand rapidly
into the ambient region.

The turbulence intensity values, Figures 5.12b-5. 14b, also revealed an important

aspect of this flow. The maximum turbulence intensity was found to be nominally

61

fi=0.18Uup. This value was found in the region of the shear layer where the jet fluid was
penetrating into the ambient region, i.e. in the plume. It was instructive to note that the
peak turbulence intensity showed no increase when compared to that for the untabbed
geometry. This suggested that the large scale exchange of fluid was not associated with
an increase in the turbulence levels, but rather it was a result of the streamwise vorticity
that was present at the jet exit plane created by the upstream ”pressure hill". Note
however that the use of a tab has also been shown to increase the small scale mixing and
dissipation in the shear layer (Foss and Zaman, (1996)) which suggests the passive

mixing tabs could be used to enhance both large scale and small scaling mixing.

5.4 Addition of the Secondary Tabs

5.4.1 Motivation for Modification of the Primary Tab Geometry

One of the goals of the present study was to determine methods for increasing the
large scale exchange of fluid between the core and ambient regions using the tabbed jet
concepts. The modified tab geometry was conceived using the results from section 5.3. It
was noted while performing the experiments on the primary tab geometry that the flow
had a naturally "upward" (+z direction ) trajectory along side of the primary tab, i.e. for
y/b<-O.5. Using a woolen tuft this trajectory was estimated to be nominally 10 degrees at
the tunnel exit. It was surmised that the expansion of the core fluid into the ambient
region could be increase if attachment surfaces were provided. It was found that when
the secondary tabs were added, the flow could achieve an upward trajectory of nominally

45 degrees before separation from the secondary tabs was detected.

62

5.4.1 Determination of the Secondary Tab Orientation

The final orientation for the secondary tabs was found by varying the angle of the
secondary tabs and measuring the static pressure just upstream of the exit for each of
these angles. Figure 5.15 shows the results of this survey. This survey was conducted by
setting the angular position of the secondary tabs and surveying the static pressure for
y-locations from y/b=-O.5 to -1.2 for x/b=-0.05 (the taps closest to the exit plane of the
jet). The angular position of the secondary tabs was then varied from 0 degrees, i.e.
horizontal, to 50 degrees up from horizontal. These data indicated that there were two
distinct angular positions of the secondary tabs that created locally minimum pressure
regions in the upstream pressure field. From 6:10 to o=15 degrees a small region of
negative pressure was found upstream of the secondary tab. The second region was from
o=20 degrees to 0:50 degrees. The selected position of 0:40 degrees was chosen
because it contained the largest negative static pressure region in the survey. Note that as
of the time of this report no additional data have been acquired for other angular

positions of the secondary tabs. All further data presented within this report were for

<b=40 degrees.

5.5 Modified Tab Geometry: Preliminary Results

5.5.1 Upstream Static Pressure Results: Modified Tab Geometry

The results of the upstream static pressure distribution are shown in Figure 5.16.
These data show that the upstream static pressure distribution for the modified geometry
was qualitatively similar to the primary tab geometry shown in Figure 5.6. However,

there were two significant differences in the pressure fields. First, the observed peak

63

value of the pressure coefficient increased from 0.70 for the primary tab geometry to 0.72
for the modified tab geometry. Second, a region of subatmospheric pressure was

measured at the exit of the tunnel, i.e. for x/b=-0.05 and y/b from -1.1 to 08.

5.3.2 Surface Streaking Results: Modified Tab Geometry

The results of the surface streaking for the modified tab geometry are presented in
Figure 5.17. These data showed the same trends upstream of the primary tab as were
discussed in section 5.3.3.

An interesting pattern was seen on the surfaces of the secondary tabs. The streak
patterns in these regions showed a bifurcation line (i.e. a line which divides two regions
of fluid) which followed along the face of the secondary tab. The flow separated from the
outer portion of the secondary tab as indicated in Figure 5.17 while remaining attached to
the inner portion. This indicated that only a portion of the secondary tab may be needed
for the same effect to be achieved. This was significant in that it may be possible to
optimize the shape of the secondary tabs to reduce the projected area of the secondary
tabs in the ambient flow. Note, in a typical gas turbine engine this outer region is
composed of cool co-flowing fluid. It will be desirable to minimize the projections of
tabs into this flow in order to maximize the fan flow.

The direction re-oriented boundary layer vorticity was tracked upstream of the tunnel
exit using a wool tuft. Its trajectory was very similar to the streak pattern of Figure 5.17.
Specifically, the re-oriented boundary layer followed a path similar to the bifurcation line
on the tunnel wall and proceeded along this side of the secondary tab nominally with the

same path as the bifurcation line shown in Figure 5.17. The re-oriented boundary layer

64

vorticity separated from the tab face at nominally half way up the outer edge. The
orientation of this vorticity upon leaving the surface was such that there were significant
non-streamwise components of vorticity (my and 0);). This was shown by the direction of
the tuft which was not directly in the streamwise direction at the point of separation. This
was rational since the inferred velocity gradient in the re-orientation term on, 6 u/ 6 y
from (1.7) was small in this region. This was in direct contrast to the inner edge of the
secondary tab, y/b=-O.5, and at the tunnel surface where the vorticity induced by the
pressure hill was strongly streamwise due to the large inferred 6 u/ 6 y in that region.
Note that in a jet flow with both a core flow and a co-flow this velocity gradient should
be larger which will re-orient the boundary layer vorticity more into the x-direction. This

in turn should increase the effectiveness of the modified tab geometry even further.

5.5.3 Streamwise Velocity Results: Modified Tab Geometry

The results for the streamwise velocity surveys for the modified tab geometry are
shown in Figures 5.18-5.20. The average velocity and turbulence intensity results
showed similar trends as were seen in Figures 512-5. 14 for the primary tab geometry. A

comparison of the results for all three geometries will be made in section 5.6.3.

5.6 Comparison of Jet Geometries

5.6.1 Discussion of the Static Pressure Fields

Tufl observations showed that the flow had approximately 10 degree upward (+z)
trajectory in the plume region at the exit plane of the jet for the primary tab geometry.

This upward trajectory was increased to approximately 45 degrees for the modified tab

65

geometry. These observations can be used to describe the differences in the static
pressure fields of the two tabbed geometries.

Figures 5.21 and 5.22 are schematic representations of the streamlines at some y
location near a secondary tab (y/ b z —1). The flow had a slight upward trajectory with
only the primary tab, as shown in Figure 5.21. The associated streamline curvature
created a pressure gradient perpendicular to the streamlines. Given the Euler-n equation

evaluated for a steady flow:

V2

S’I-Qu’

the pressure will increase on a curve drawn in the outward normal direction and
perpendicular to the streamlines. Equation (5.3) indicated that the pressure at locations
along the exit of the tunnel, where there was an upward trajectory of fluid present, must
have been subatmospheric. Note in the case of the primary tab geometry this effect did
not extend into the tunnel far enough to be detected by the pressure taps closest to the
exit (i.e. for x/b=-0.05).The streamlines had more curvature because the flow remained
attached to the secondary tabs for the modified tab geometry. This is shown
schematically in Figure 5.22. The change in the streamline curvature resulted in the
changed upstream static pressure field shown in Figure 5.16. Specifically, because the
curvature of the streamlines was more compact (i.e. smaller R) for the modified tab jet,
the magnitude of the pressure gradient normal to the streamlines increased and the
subatmospheric region increased in size and magnitude.

Figure 5.23a shows the pressure distribution as a function of y for x=-0.05b (the most

downstream pressure tap). These data support the above analysis of the flow field using

66

the inferred streamlines. Specifically, the region of negative pressure was clearly shown
for the modified tab geometry. Note that a negative streamwise pressure gradient is
favorable to the boundary layer. Note also that the modified tab geometry also showed an
increased peak pressure at x=-0.05b and y=0 when compared to the primary tab
geometry. Equation (1.8) indicated that a pressure gradient in the y-direction will flux 0),,

into the flow field. This quantity was calculated and plotted in Figure 5.23b. These data

show that the peak in the pressure gradient (6P7 6( yA) )) occurred at y=-0.5b (the edge
of the primary tab) and that there was a slightly higher peak in the positive gradient for
the modified tab geometry.

An interesting feature on Figure 5.23b was the local minimum value for the modified
tab geometry at y=-O.9b. The pressure gradient changes sign for the modified tab
geometry from y=-O.8b to y=-1.2b. This indicated that a flux of +0)x ,which served to
reinforce the reoriented boundary layer vorticity, was introduced into the flow in that
region. This change in the pressure distribution represented a significant change in the
flow fields for the two tabbed geometries.

A plot of P.(x,y=0) was also created and is presented in Figure 5.24a. These data
again show the slightly higher peak P. value for the modified tab geometry at x=-0.05b
and y=O. Note that the pressure distributions become nearly identical for x<-0.85b.
Equation (1.5) indicated that a pressure gradient in the x-direction (shown in Figure

5.24b) will flux my into the flow field. These data indicated that a slightly higher flux of

my will occur for the modified tab geometry. It was instructive to note in Figure 5.23a the

67

slight back pressure shown for the untabbed jet which indicated that the flow continued

to accelerate slightly in the tunnel extension.

5.6.2 Comparison of the Streamwise Velocity Fields

Several parameters were created in order better quantify the changes in the distortion
of the average streamwise velocity field for the three geometries. These parameters,
evaluated from the average streamwise velocity fields, were developed to aid in the
interpretation of the available data. Figure 5.25 shows the definition three penetration
measures overlaid on the modified tab geometry streamwise velocity data at x/b=2.0.

The maximum penetration of the shear layer into the core region, as defined by the
minimum z-location along the 0.95 contour line at y=0, was described by 5cm. Figure
5.26 shows this measure plotted versus the downstream distance. It was clear that the tab
created a large low speed region downstream of the primary tab. It was also clear that this
wake region did not display typical characteristics. Specifically, the velocity deficit (Uup -
Q remained constant rather than decreasing and the area of high velocity deficit (i.e. low
5) increased in size. These data implied that the penetration of the wake into the core
region continued well past x/b=2.0 for the tabbed jets. This observation was supported by
the results of Zaman et. al. (1992) which showed that the jet bifurcated into two distinct
regions of core fluid at a downstream distance of x/D=4.0 for a round jet with two
primary tabs. (D was used to designate the diameter of the round jet.) For this measure
the degree of penetration did not appear to be significantly different between the primary

tab and modified tab geometries.

68

A second measure of the distortion in the flow field was described by fimbrem. This
measure, shown in Figure 5.27, was defined by the maximum z-location that the shear
layer penetrated into the ambient region along the 0.15Uup contour line; see Figure 5.25.
This measure clearly detailed both the distortion in the flow field by the primary tab
alone and the enhanced distortion created by the addition of the secondary tabs. The
primary tab geometry showed a nominally 250% increase in the depth of penetration of
the shear layer into the ambient region over than seen for the untabbed geometry. The
addition of the secondary tabs increased the penetration to nominally 400% over the
untabbed geometry.

Finally, in a typical jet flow the shear layer grows into both the core region and the
ambient region. The average streamwise velocity results for both tabbed geometries
showed that there was a significant region of high speed fluid above the projected exit
plane of the jet. Figure 5.28 shows Shgghspwd versus the downstream distance. 5113311 speed
was defined by the maximum z—location of the 0.95 contour line; see Figure 5.25. These
data showed that early in the tabbed jet development, the high speed fluid (i.e. fluid with
U greater than 0.95Uup ) extended well into the ambient region. It was expected that this
penetration of the high speed fluid from the core flow would decrease as the jet
continued to develop downstream. Specifically, as the jet becomes fully developed the
region described by the 0.95Uup contour will decrease in size; hence Enigma; will first
decrease to zero, then become negative. Note that the untabbed geometry showed a
negative penetration of high speed fluid indicating that the high speed fluid was , as

expected, contained within the core region.

69

An alternate measure of the growth in the shear layer was represented by the shear

layer momentum thickness, 9, defined by

8 =Iu'(1-—u')ds (5.4)
where
u‘=(u-um...)/(um.,.-um.n) (5.5)

and s is the direction of the velocity survey in the y-z plane. This direction was different
for the three surveys performed. See Figure 5.29. Note that in (5.8) umin was the
minimum velocity (nominally 0.1Uup) measured in each traverse. Equation (5.8), typical
of a two stream mixing layer, was adopted to normalize the velocity traverses for this
section of the results because of the difficulty in accurately measuring flow speeds below
the minimum calibration speed (section 4.2). Three regions of the shear layer were
investigated to provide a measure of the shear layer characteristics. Note that (5.7) was
first evaluated using data from the velocity surveys already presented. These data were
found to have too few data points in the shear layer for an accurate calculation of the
momentum thickness. Therefore, additional single sensor hot wire data were taken to
allow better calculation of 8. Figure 5.29 shows the locations where the shear layer
thickness was evaluated for the primary tab geometry at x/b=2.0.

The plume, where the penetration of the shear layer into the ambient region was a
maximum, was the first region investigated. The shear layer thickness was found to have
a maximum value in this region. The location of this survey was determined by viewing
the average velocity profiles and determining the y location where 5mg}. speed was a

maximum. At this location the shear layer thickness was a maximum and a line drawn

70

perpendicular to the isotachs was oriented nominally in the z-direction. If a traverse were
conducted at another location then the shear layer momentum thickness would have been
artificially inflated. This can be clearly seen for the traverse indicated by the dashed line
in Figure 5.29. To guard against this two checks of the results were made. First, if a
velocity survey were not perpendicular to the shear layer there would be a region in the
traverse data where the velocity profile was distorted. For example, in the limiting case
where a velocity survey was parallel to an isotach the velocity would be constant and the
velocity profile would not have been as expected for a shear layer. All surveys were
plotted and visually checked to avoid this condition. Any surveys that showed this effect
were re-acquired after the y-location was adjusted. The second check was a self
consistency check. A zero pressure gradient shear layer will have a growth rate that
becomes constant in the self preserving region. The data were checked against this trend.
Results which did not fit this trend were retaken.

The second interrogated region was the shear layer that was aligned with the side of
the tab. In this survey, a traverse was performed perpendicular to the edge of the tab and
at the midpoint of the edge of the tab. The third survey was conducted in the z—direction
off the tip of the tab. Both of these surveys were also checked through the plotting of the
surveys and by checking for linear growth.

The shear layer momentum thickness in the plume was plotted versus the
downstream distance for all three geometries in Figure 5.30. Data for the untabbed jet
were taken at the top center line of the tunnel. The data for the untabbed jet showed the
expected characteristics. Specifically, the shear layer growth quickly became linear.

Although it was not shown here, the first three measurement locations in the downstream

71

survey displayed laminar/transition shear layer characteristics. The growth rate, dG/dx,
found by fitting the points in the survey from x=0.4b to x=2.0b, had a value of 0.035.
This was consistent with experimental values from other single stream shear layers (see
Bruns et. al. (1991)).

The results from the plume region illustrated the increased distortion of the modified
tab geometry. The momentum thickness for the primary tab geometry was slightly larger
than that for the untabbed jet due to the distortion in the shear layer in this region.
However, the primary tab geometry had the same growth rate (d8/dx=0.035) as was
found the untabbed jet. The modified tab geometry results indicated that the momentum
thickness was nominally twice those for both the untabbed jet and the primary tab
geometry. In addition the growth rate had increased from 0.035 to 0.050. These data
implied that the primary tab geometry deformed the shear layer in the plume region. The
modified tab geometry therefore represented a more significant change in the flow field
because of these changes in some of the shear layer characteristics.

The side and bottom momentum thickness surveys, Figure 5.31, showed that the
primary tab and modified tab geometries had similar effects on the flow field. The
bottom momentum thickness, Obonom, was the smallest of all of regions investigated. This
was not surprising since this shear layer originated at the location where the tip of the tab
ended in the flow field, at a downstream distance of x/b=0.61. The growth rate, 0.024,
was much smaller than the untabbed jet’s growth, 0.035. This result was supported by the
observation that the shear layer in this area grew almost exclusively into the high speed,

high momentum region. The high momentum of the core flow retarded the growth rate of

72

the shear layer in this region. Along the side of the tab the momentum thickness, Operp,

and the associated growth rate, 0.027, were between those reported for 9m", and Gprumc.
These data indicated that the shear layer thickness and growth rate increased as the top of
the tunnel was approached from the core region.

It was also made clear from these data that the effect of the secondary tabs localized
to the top portion of the flow field. Specifically, both the penetration measures and the
momentum thickness measures below the tunnel top (for z<0) showed identical values
for both geometries. These same measures above the tunnel were substantially increased
for the modified geometry.

Figures 5.18a-5.20a, when viewed in sequence, showed the flow field for the
modified tab geometry to have experienced a large scale rotation in the plume. For these
data at x/b=0.7 a line drawn perpendicular to the plume contour lines pointed in the -y
and + z direction. At x/b=l .2 this same line appeared to be directed in the +2 direction.
And finally at x/b=2.0 the line pointed in the +y and +2 direction. Note that the apparent
center of the rotation was displacing laterally (i.e. in the -y direction) with the shear layer
as the downstream distance was increased. This apparent large scale rotation in the plume
was less evident in the primary tab geometry data but it was apparent given close
inspection. It should be noted that the turbulence intensity plots, Figure 5.18b- 5.20b,
also showed this same large scale rotation in the flow field.

A significant difference between the average streamwi se velocity data presented for
the primary and modified tab geometries was most clearly seen at x/b=2.0. In Figure
5.20a there was a large region of fluid with a significant streamwise velocity in the wake

region of the tab. During the data acquisition at x/b=2.0, and to a lesser extent at

73

x/b=l.2, for the modified geometry it was noted noted that in the low speed region of the
flow field downstream of the tab the flow was highly intermittent. Oscilloscope traces
revealed that highly turbulent/active fluid periodically passed by the probe. These times
of "active" fluid passage were separated by what appeared to be times of nominally
quiescent low velocity fluid.

A comparison of the peak value of the turbulence intensity for the three geometries
revealed a slight increase for the modified tab geometry. The peak values were found to
be 0.18Uup for the untabbed and primary tab geometries and 0.21Uup for the modified tab
geometry. These results further support the conclusion that the characteristics as well as

the shape of the shear layer were changed for the modified tab geometry.

5.6.3 Lateral and Normal Velocity Results

The in-plane velocity results at x/b=1.2 and 2.0 indicated the source of the strong
outflow of the core fluid into the ambient region. Figures 5.32 and 5.33 show the average
lateral, V, velocity contours for the primary tab and modified tab geometries respectively.
These data show a significant lateral velocity (V z —0.2Uup) away from the tab in the core
region. Note that the modified tab geometry showed a significantly larger lateral velocity
(Vmax = -0.24Uup) when compared to that of the primary tab geometry (me = -0.21U..p)
indicating an increased expansion rate for the flow field. Additionally, there was a
significant lateral velocity above the projected top surface of the tunnel for both
geometries, although this region extended farther into the ambient region for the

modified tab geometry.

74

At x/b=2.0 the V velocities decreased in magnitude for both geometries. The primary
tab geometry, Figure 5.32b, showed a small decrease in magnitude of the maximum in
lateral velocity along side of the tab (from me = —0.21Uup at x/b=1.2 to V...“ = —0.20Uup
at x/b=2.0). There continued to be a significant lateral velocity above the top of the
tunnel. The results for the modified tab geometry, Figure 5.33b, showed a more
significant decrease in magnitude of V (from nominally -O.24Uup to -O.18Uup), however
the lateral velocity in the plume region continued to be significant showing very little
decrease in magnitude.

The W profiles, shown in figures 5.34 and 5.35, confirmed the upward (+z-direction)
flow trajectory for yz-b and no as well as the downward (-z-direction) trajectory for yst
and z<-0.8b. The velocity in the second region resulted from the re—direction of the
upstream core fluid by the physical surface of the tab. The re-direction of the core flow
has been shown to bifurcate a jet into two distinct regions of high speed fluid for a round
jet with two opposing tabs (Zaman et. al.(1992)).

These data for the modified tab geometry data at x/b=1.2, shown in Figure 5.34a,
showed that the up-wash, i.e. expansion into the ambient region, effect was enhanced
with the addition of the secondary tabs when compared to the primary tab geometry; see
Figure 5.33a. Specifically, in the plume region the VV magnitudes were seen to be
significantly larger than those seen for the primary tab geometry (0.21Uup compared to
0.16Uup). It was instructive to note the downward flow below the projected tip of the tab
(for the modified tab geometry) had nominally the same value as was seen for the

primary tab geometry at the same location. This observation was in agreement with the

75

earlier results which showed that the effects of the secondary tabs were limited to the
portion of the flow above the projected tunnel top wall.

Figures 5.34b and 5.35b show the W velocity contours at x/b=2.0 for the primary tab
and modified tab geometries respectively. These data indicated that the plume region
continued to have a strong +VV velocity component although the magnitudes had
decreased. The downward penetration of the shearlayer also appeared to be slowing as
expected since the high x-momentum of the core fluid will overcome the downward
momentum of the fluid redirected by the tab.

The turbulence intensity data for the y-z plane velocity components are presented in
Figures 536-539. The shear layer was aligned with the side walls and tab surfaces and
the peak values occurred in the plume region of the flow. Note that the location of the
high fluctuations did not coincide with the peak values in the average velocity
components, but rather corresponded to the location of the largest gradient in the average
streamwise velocity. The peak values for the lateral and normal velocity fluctuations
were nominally 0.16Uup. This was in contrast to the streamwise velocity component
which showed a peak fluctuating value of nominally 0.18Uup for the primary tab
geometry and 0.21Uup for the modified tab geometry. The fluctuating results were similar

when the primary tab and modified tab geometry results were compared.

5.6.4 y-z plane Vector Results
Vector fields made up of the V and 'VV values were plotted to better allow the y-z
plane features of the flow field to be determined. Each data set is presented with both

scaled and unscaled vectors, see Figure 5.40-5.43.

76

The scaled y-z plane vector plots are presented in Figures 5.403 -5.43a. All four
figures showed similar trends with varying magnitudes. The region behind the tab (in the
wake of the tab) had a very small in-plane velocity with respect to the free stream value.
This was expected in that the fluid flow in this region will be a result of either
recirculation of core fluid or entrainment of ambient fluid. Both sources were expected to
provide velocity magnitudes that were small compared to the approach velocity. Note
that the vectors in this region were directed in the -z-direction which indicated there was
an entrainment of ambient fluid into the core flow. A strong in-plane velocity was
encountered primarily in the -z direction for z/b<-0.65 and y/b=0. This result was
expected since the flow should be symmetric about the centerline of the tab. The y-z
plane velocity vector in this region was found to be the strongest in the flow ( nominally
0.27Uup for the modified tab geometry and 0.26 for the primary tab geometry at x/b=1.2).
For y<-0.5b and z<0 (within the projection of the tunnel) there was a very strong
outward velocity as shown by the vectors which pointed in the -y-direction (away from
the primary tab). The y-z plane velocity vector was dominated by V in this region.

An interesting feature of these vector plots was found in the plume region above the
projected top of the tunnel wall. There was a strong ejection of fluid from y=-0.7b to
-1.1b for z greater than 0. This ejection penetrated up to z=0.5b in the ambient region for
the modified tab geometry. The velocity magnitudes in this region were near, but slightly
less than, the velocity magnitudes seen below the tab in the core region (i.e. 0.24Uup
compared to 0.27Uup for the modified tab geometry at x/b=l .2). This observation
indicated that the ejection of fluid from the core region was a strong feature of the flow

field. Note that the velocities in the plume represented the most significant difference in

77

the velocity field of the two geometries. Specifically, the y-z plane velocities were
noticeably smaller in the plume region for the primary tab geometry at the same
downstream location when compared to the modified tab geometries at the same location
(i.e. 0.21Uup compared to 0.23Uup at x/b=1.2).

Unscaled vectors, i.e. vectors with constant length, are also presented with y-z plane
streamlines in Figures 5.40b-5.43b. Simplified plots with streamlines and the indicated
singular points are presented in Figures S.40c—5.43c. These data indicated four singular
points in the flow fields (2 nodes and 2 saddles) for all but the primary tab geometry at
x=1.2b which showed two singular points (a node and a saddle). (Note the node at
z/b=0.3 and y/b=-0.9 in Figure 5.43c does not show a spiral to the node. This is a results
of the data grid spacing.) At the singular points the in-plane velocity directions were
indeterminate (V and 'w' were both zero; see Figures 5.40c-5.43c) and a singularity
resulted. In this flow field there were two saddle points and two nodal points. The two
nodal points for these data indicated a flux of mass out of the y-z plane by the
streamlines which pointed into both nodes. Figures 5.40d-5.43d also show schematic
outlines of the domains for which an even number of nodes and saddles must be present.
The surface was made up of a sphere with 2 holes (xsurfacEO) which was balanced by the

even number of nodes and saddles shown for all of the data.

5.6.5 Shear Stress Results
The turbulent shear stresses were calculated using the x-array data at x/b=1.2 and 2.0.
There were two regions of peak negative values in the W/Ufip data; see Figures

544-547. These local minimums occurred along the side wall and in the plume region.

78

The stress values along the side walls were nominally the same with a peak value of

W/ U3,,=-1 .25x10’2 for both geometries. The results from the plume region showed that

the modified tab geometry experienced an increased stress level when compared to the
primary tab geometry. Specifically, peak values were nominally {1"V/U3p=-1.25x10'2 for

the primary tab geometry and G’VVUE‘F-l .50x10'2 for the modified tab geometry. This
was consistent with the the results in section 5.6.2 which showed an increased growth
rate in the momentum thickness of the modified tab geometry in the plume region. It was
instructive to note that the peak value for the primary tab geometry (-1.25x10'2)
corresponded to that measured for the shear layer on the side wall of the tunnel indicating
that the shear stresses experienced in each region were comparable. This further
reinforced the observation that the shear layer in the plume region for the primary tab
geometry was not significantly different from the shear layer for the untabbed jet,
although it was significantly displaced into the ambient region.

Both geometries also showed a region of positive stress in the shear layer aligned
with the side of the tab. This corresponded to the change in sign of 6 U/ 6 y in the
average streamwise velocity field. Note also that the peak positive stress values were
significantly increased for the modified tab geometry. In the core region, where 6 fi/ 6 y
was equal to zero the corresponding stress values were also nominally equal to zero.

Renormalizing these data as TVV i V provided information on the cross-correlation
coefficients of the fluctuations in the data. These results, presented in Figures 548-551,
showed that the peak correlations occurred in the regions where the peak stress values

were noted.

VG

C0

n0

sht
mo
”in

bem

T9810.

b0Una

79

The u’w’/ Ufip stress values are presented in Figures 552-555. These data showed

positive values in the plume region as expected ( 6 U/ 6 2 decreased in the entire region).
The peak values again showed a significant increase from 1.25x10'2 for the primary tab
geometry to 1.50x10'2 for the modified tab geometry. This again supported the previous
observation of the increased growth rate in the plume region shear layer for the modified
tab geometry. Note that along the wall, where the shear layer was oriented nominally
vertically, the stress values were nominally zero.

The cross-correlation data, Figures 5.56-5.59, show that the peak positive
correlations occurred in the region of the peak stress values. Again values were

nominally the same for both geometries as was seen in the lateral results.

5.6.6 Qualitative Vorticity Results

The flow pitch angles were too severe near the exit of the jet for the use of x-arrays;
therefore, quantitative measurements were not made near the exit, as was noted in
chapter 3. A cross-vane vorticity probe was used to determine some characteristics of
the streamwise vorticity field very near to the exit of the tunnel . Figures 5.60 and 5.61
show the results for the downstream locations from 0.1 to 0.4 for the primary tab and
modified tab geometries respectively. These data were instructive in that they clearly
illustrated the effect of passive mixing tabs on on a jet flow as well as the differences
between the geometries.

There were two regions of streamwise vorticity shown for both geometries . The
region of positive sense vorticity (a result of the re-orientation of the vorticity in the

boundary layer) had a sign that was as expected for a "necklace" vortex about a

80

protrusion into the flow. The negative region of streamwise vorticity was a result of the
vorticity fluxed into the flow by the upstream static pressure distribution (i.e. the
"pressure hill").

A significant portion the streamwise vorticity was seen above the projected exit plane
of the tunnel for both geometries at all locations. It was interesting to note that both
geometries showed a significant portion of streamwise vorticity in the ambient region at
the closest location x/b=0. 1. These observations indicated the strong upward expansion
of the flow occurs at the exit of the jet. Both geometries also showed the negative regions
to be several times larger in area than the positive sense regions.

The qualitative use of the cross-vane vorticity probe did not provide quantitative
results to be presented in this section. However, it was instructive to note that the rate at
which the cross-vane probe rotated did vary visibly as the downstream distance was
increased. It was observed that, at the more upstream locations, the cross vane probe
spun "faster". More over, the delineation between "spin" and "no spin"was more clearly
defined at the farther upstream locations. As the downstream distance was increased the
probe spun slower and the boundaries become more difficult to discern. Additionally, the
area describing the regions of streamwise vorticity also increased as the downstream
distance was increased. Note the one exception to this trend was observed for the positive
region in the primary geometry. These two observations implied that the negative sense
streamwise vorticity in the flow was introduced very near to or upstream of the tunnel
exit, and that the increased area was a result of the diffusion of this vorticity. This
observation was supported by prior results that showed that it was the upstream pressure

distribution, not the pressure distribution on the tab face that provided the major flux of

81

the streamwise vorticity in the flow (Zaman et. al. (1994)). The one exception to this
evolution was the region of positive sense vorticity in the primary tab geometry case
which did not increase in area with increasing downstream distance. This was probably a
result of interaction with the larger and stronger negative sense vorticity.

The cross-vane observations also illustrated the differences between the two
geometries. Specifically, the negative sense regions were slightly larger in area for the
modified tab geometry than for the primary tab geometry at the same x-locations. This
suggested a slightly larger total circulation for the modified tab geometry. The positive
sense region was significantly larger in area for the modified tab geometry. This implied

a significant increase in the total circulation for this region of vorticity.

5.6.7 Quantitative, Spatially and Temporally Averaged Streamwise Vorticity Results

The V and W data were processed using (3.22) to provide the spatially averaged

streamwise vorticity, co—x'. Figures 5.62 and 5.63 show the streamwise vorticity results.
These data clearly showed two counter rotating regions of streamwise vorticity. The
larger region was the negative sense vorticity created as a result of the upstream static

pressure gradient on the top wall of the tunnel. This region had a peak value of
{0:34.60 for the primary tab geometry at x/b=1.2, Figure 5.62a. The smaller region, a
result of the re-ori entati on of the approach boundary layer vorticity, showed a peak

positive vorticity value of nominally 5:31.22.
These data for the modified tab geometry at x/b=l.2 are presented in Figure 5.63a.

These data showed the same two regions of counter rotating vorticity as were seen in the

82

primary tab geometry data, however the effects of the secondary tabs were again
illustrated in the differences between the data. The positive sense vorticity was nominally

the same size and magnitude as was seen for the corresponding region for the primary tab

geometry, although the peak value increased slightly to Err-{=4 .74 for the modified tab
geometry. This indicated that the total circulation in the negative sense region was
slightly higher for the modified tab geometries.

The primary difference between the two geometries was seen in the positive sense

vorticity. This region increased significantly in both area and magnitude for the modified
tab geometry. The peak value increased from co_x'=1.22 for the primary tab geometry to

co_x’=1.67 for the modified tab geometry. Given the increased magnitudes and area of this
region the total circulation must therefore have increased significantly in this region for
the modified tab geometry.

The downstream evolution of the streamwise vorticity is shown in Figures 5.62b and
5.63b. These data show that the streamwise vorticity magnitudes decreased as the

downstream distance was increased. Note that the peak values were nominally the same

for both geometries at this location (LEE-1.3 and ctr—{=1 .0). This implied that the
increased mixing of the modified tab geometry may be localized to the near field of the
jet flow. Additionally the increased spacing between the vorticity contours indicated the
vorticity was diffusing into the flow field. The vorticity contours also indicated that the
presence of the large scale rotation in the plume region described in section 5.6.2.

These data also further clarify and explain the vector patterns shown in section 5.6.4.

The two areas of counter rotating vorticity act as a "pump" to eject fluid from the core

83

region into the ambient region. A "current" was created in between the two regions of
vorticity because of the counter rotation. A fluid element caught in this "current" was
ejected from the core region. The exchange of fluid seen in the tabbed jet was a result of
this pumping action. Note that this explanation of governing phenomena is inherently
different from that which would be inferred from enhanced turbulence intensity. Figure
5.64 shows a combined plot of the streamwise vorticity and the y-z plane vectors for the
modified geometry at x/b=1.2. These data show that the ejection of fluid from the core
occurred between the two regions of vorticity in the flow. Note that the y-z plane
velocities seen in the plume between the two regions of streamwi se vorticity had
magnitudes near the maximum y-z plane velocity values. The flow accelerated between
the regions and quickly decelerated after exiting the fluid "pump".

The streamwise vorticity results, in conjunction with the upstream static pressure
results, were also used to infer some of the upstream flow mechanics. It was shown that
there existed an adverse pressure gradient on the surface of the tunnel upstream of the
tab. However near the exit of the tunnel the pressure gradient became favorable for the
modified tab geometry in the region of y=-l . lb to y=-0.8b for x=-0.05b. In this region
the sign of 6P/ 6y changed. Note that the sign of 6P/ 6x also changed for y constant over
the same range of y values. It was clearly illustrated that the additional flux of vorticity
from the pressure gradient in this region significantly increased the the streamwise
vorticity in the re-oriented boundary layer vorticity (i.e. the positive region for y<0).

A schematic representation of the vorticity connections upstream of the tunnel exit
can be inferred using a combination of the downstream streamwise vorticity observations

and the surface streaking data. Figure 5.65 shows the inferred connections from these

84

data. Specifically, the solenoidal condition requires that a vorticity filament: 1) end at a
wall (as a singular point for a viscous fluid), 2) end at infinity, or 3) forms a closed loop.
The regions of streamwise vorticity must, therefore, connect from one side of the tab to
the other since there is no indication of a swirl pattern on the iy sides of the region
upstream from the tabs. The pattern shown is also compatible with the inferred pattern
from the topological analysis. It is instructive to note that the vorticity which corresponds
to N3 in Figure 5.11 did not appear in the downstream measurements. It is inferred that

this region of vorticity must be weak when compared to the other regions.

85

 

 

u/uup

 

 

 

 

 

 

 

anabuawoo>moommoz’hxf’

 

0.020
0.016
0.016
0.01 4
0.012
0.010
0.”
01!”
OM
0.002
0.000
-0.(X12
0.004
-0.WB
-o.ooe
-0.01 0
-0.01 2
-0.01 4
-0.01 6
-0.01 6
0.020

1] ll lllll‘llljllll

11

 

0.014

0.012

0.010

0.008

/Uup

0.006 2 3

0.004
‘ 0.002

‘ 0.000

Figure 5.2: Upstream static pressure survey, (p(X,y)-Parm)/O.5pUupz, for the untabbed

geometry.

86

 

 

 

 

 

 

 

 

 

 

1.0rvvrrffirrrrrrrr‘ 90.95
* a 0.05
4 7 0.75
. s 0.05
_ . . .... (a)
4 0.45
0.5 . ‘ a 0.35
2 0.25
‘ r 0.15
$0.0 _
p-
b
-0.5 r ‘
l
l-
-1.0 - -
I L L l l l 1 1 l l l l l L l l L 1 A;
-2.0 -1.5 -‘l .0 -0.5 0.0
1.0 I I I I I I I I r I I I I I I I I 6 02‘
' 5 0.10
4 0.15
- a 0.11
» 2 0.00
r

_ _: 0.05
0.5 + . (b)

 

 

 

 

 

 

 

 

-0.5 — ~
-1.0 — ~
1 1 1 1 l 4 1 . 1 l 1 I 1 1 l 1 1 I 1
-20 -1.5 -1.0 -05 0.0

y/b

Figure 5.3: Velocity survey for untabbed geometry at x/b=0.7: a) 11/ Uup, b) E/ Uup

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 I I fit I I I r I I fiT V f] 9 0.95
t 0 0.05
b 4 7 0.75
4 8 0.65
_ . . .... (a)
4 0.45
0‘5 a 0.35
2 025
r 0.15
P ' I—\———
.0 gm
hoo- _: n —T
P [f v v e W:
. l l? .
» 4
-005 _ ‘
P
-1.0~ q
l 1 L 414 A 1 L 1 1 1 1 LI 1 L I l
-2.0 -1.5 -1.0 -0.5 0.0
1,0 I I. I I I I f I I 1 I I I I I I I I I 8 02‘
. l 5 0.10
- 4 4 0.15
- - a 0.11
r . 2 0.00
.. g r

0-5. . (b)

 

 

 

 

 

 

 

 

 

r 1/ ft)
-0.5 - -
~ 1
-1.0 - —
.4 4 1 1 l 1 1 1 1 I r I . 1 l I L L 1 d
-2.0 -1.5 -1.0 -0.5 0.0

y/b

Figure 5.4: Velocity survey for untabbed geometry at x/b=1.2: a) H/ Uup, b) 6/ Uup.

88

1.0 I T I I I I I 7 I I I I U T T I Y Y I

 

 

 

 

 

 

 

 

9 0.95
r 1 a 0.05
. . 7 0.75
. a 0.05
. . .... (a)
_ 4 0.45
0.5 r 3 0:15
' 2 025
t ’__/\/11 1 0.15
.D .
NOD ’
-0.5 ‘-
t
-1.0 - -
h . . r . 1 . . . . L . . . . r r . . .
-2.0 -1.5 -1.0 -0.5 0.0
y/b
1.0 r r I r 5 0.21
’ 5 0.15
4 0.15
. 1 3 0.11
. . 2 0.00
0.5 _ _ 1 0.05 (b)

 

 

 

 

 

 

 

-0.5 -— -
-1.0 - 5
h g L 1 l 1 1 1 I l 1 1 1 1 | 1 1 I
-2.0 -1.5 -1.0 -0.5 0.0

y/b

Figure 5.5: Velocity survey for untabbed geometry at x/b=2.0: a) U/ Uup, b) E/ Uup.

89

 

0.700
0.650
0.600
0.550
0.500
0.450
0.400
0.350
0.330
0.250
0.200
0.150
0.100
0.050
0.000

d~w&MONOO)WODm-n

 

 

 

 

Figure 5.6: Upstream static pressure survey, (p(x,y)-Paun)/0.5pUup2, for the simple
geometry.

90

: Tip of primary tab not scanned

Note

        

tab geometry

rimary

lts for the p

rng resu

0

Surface streak

Figure 5.7

91

f primary tab not scanned

ipo

T

Note

 

tab

lar points upstream of the primary

Singu

Figure 5.8

92

tab not scanned

Tip of prrmary

Note

: HOLE
: SPHERE SURFACE

 

tab geometry

rimary

for the p

IS

logical analys

Top View topo

9

Figure 5

93

 

Not Scanned

ip Region

T

Note

        

t pattern.

rn

lar p0

rngu

Alternate s'

Figure 5.10

94

 

 

 

ll. \i'bj G/ \ 84’

l __. ‘_ N8
I: 35\ N3@/ \
ll

 

Figure 5.11: Side view, center plane topological analysis of the primary tab geometry.

95

 

 

 

 

 

 

 

 

 

1.0 . . . 1 r . 1 rr ' r 0 0.05
” 1 0 0.55
. ~ 7 0.75
. 5 0.55
_ . ... (a)
_ _ 4 0.45
0'5 _ 3 0.35
2 0.25
‘ 1 0.15
.D P 4
ROC-
-0.5 - -
p-
-1.0- -
1 l 1 l l l 1 l 111 1 1 L L 1 l l I
-2.0 -1.5 -1.0 -0.5 0.0
1.0 I I I I I I I I I I 7 0'23
[ 5 0.20
5 0.17
. 4 0.14
- . 3 0.11
_ _4 2 0.00
0.5+ . 1 0.05 (b)
p
.0 '
N00—
r- -r
1- Il
-0.5 - 3
-1.0— —
r .41 r

 

 

 

-2.0 -1.5 -1.0 -0.5 0.0
y/b
Figure 5.12: Streamwise velocity survey for the primary tab geometry at x/b=0.7: a)
0/ Uup, b) 0/ Uup-

96
1.0 I I I I I I IfI l I I I I l I I I I

 

 

 

  

 

 

 

 

9 0.95
P 4 a 0.85
l J 7 0.75
_ 6 0.65
_ , 5 0.55 (a)
_ 4 0.45
05 b 0 _i 3 0.35
2 0.25
1 0.15
Q _
No.0 _
-0.5 -
-1.0 — l l
l'
A , , , 1 r r r
-2.0 -1 5
1.0 f V I I I I I I r l I I I I I I 7 0.23
_ 6 0.20
5 0.17
F 4 0.14
’- 3 0.11
0.5 — ‘ 2 0.0..
_ F‘A , t 015 b
_ . <>

\5’

N ' _ y
-o_5_ l 1 ._
r . \
l

-1.0:- \ j

l 1 I L4 1 1 1 1 l 1 1 1 L

-2.0 -1.5 -1.0 -0.5 0.0
V/b

 

 

 

Figure 5.13: Streamwise velocity survey for the primary tab geometry at x/b=1.2: a)
U/ Uup, b) 11/ Uup.

97
140 fifi Y I I I I I I I I I I I I I I I r
.1

 

0.95
0.65
0.75

if? (a)

0.3
0.25
0.15

dflthUIQVO‘D

 

 

 

 

 

 

 

 

 

0.23
0.20
0.17
0.14
0.11
0.06

(b)

HMQbUIGN

 

 

 

 

 

 

 

-2.0 - .5 -1.0 -0.5 0.0
V/b

Figure 5.14: Streamwise velocity survey for the primary tab geometry at x/b=2.0: a)
U/ Uup, b) 0/ Uup-

 

98

b
O
I I I I

(3)
O
‘l I I I

 

 

 

 

N
O
l I

secondary tab angle,or (degrees)

 

I J 1 l 1 1 1

O 1
-1.2 -1 .1

 

Figure 5.15: Static pressure at x/b=-0.05 versus angle of secondary tabs.

 

99

 

 

 

 

 

Figure 5.16: Upstream static pressure survey, (p(x,y)-Parm)/0.5pUup2, for the modified
tab geometry.

dNQbU‘QVOO)UODM'fl

0.700
0.650
0.600
0.550
0.500
0.450
0.400
0.350
0.30
0.250
0.200
0.150
0.100
0.050
0.000

 

I

100

  

Note: Tip of primary tab not scanned

attached flow

Figure 5.17: Surface streaking results for the modified tab geometry.

101

 

1.0 r I I I‘r I I I I I I I I

 

 

 

 

 

 

 

 

1.0 I I I I I I I I I I I I I

0.5 _

 

 

 

11111.1

 

 

 

 

 

-2.0 -1.5 -1.0

y/b

-0.5

0.0

dMQbUIQVOD

anubmmw

0.95
0.85
0.75
0.65
0.55
0.45
0.35
0.25
0.1 5

0.23
0.20
0.1 7
0. 1 4
0.1 1
0.08
0.05

(a)

(b)

Figure 5.18: Streamwise velocity survey for modified tab geometry at x/b=0.7: a)

0/ Uup, b) 0/ Uup-

 

 

 

 

 

 

 

 

 

 

 

 

1-0 ' ' . . T ' ' ' ' 1 ' ' ' ' l ' ' ' ' 9 0.95
r ‘ a 0.05
4 7 0.75
. 5 0.55
_ 5 0.55 (a)
0.5- 2 21;:
’ 2 0.25
r 0.15
go...
-0.5-
-1.0- -
b 1 1 1 41L 1 I l 1 1 1 1|. . . .
-2.0 -1.5 -1.0 -0.5 0.0
v/b
1-0 ""'1 ' ' ' r ' r . . 1 'I ' ' 7 0.23
. 5 0.20
5 0.17
4 0.14
. f2 1 3 0.11
0'55. 4&0 ) d I 5:: (b)
:z—g‘\\\
$0.0: . .
-0.5-
-1.0- q
" I 1 1 1 [1 1 1 .11 1 1 1 l 1 1 1 g‘
-2.0 -1.5 -1.0 -0.5 0.0

V/b

Figure 5.20: Streamwise velocity survey for modified geometry at x/b=1.2: a) U/ Uup,
b) 0/ Uup—

 

 

 

 

 

 

 

 

1.0 I I 1 1 l T Y T T I Y T Y1 I I I 1' V I 9 0'”
L 4 a 0.05
D- 1 7 0.75
6 0m
_ 5 0.55 (a)
4 0.45
0.5 3 0.35
2 0.25
r 1 0.15
$0.0 '-
r-
-005 —
r
-1.0 '-
-2.0
1.0 7 0.23
- s 0.20
s 0.17
4 0.14
_ 3 0.11
2 0.00
0.5 ‘

(b)

 

~0.5 ~

"'0; Iii

1 l

-2.0 -1.5

 

 

 

 

l

14.01 A A
V/b

 

 

Figure 5.20: Streamwise velocity survey for modified geometry at x/b=2.0: a) U/ Uup,
b) ii/ Uup.

 

104

 

 

 

 

ZI IZ
——;~X W1.
\ 45'
<
\ '0‘
FLD®
/
”////////////////. «VII/lllllllllllh

'//////////////J /

,/ /’ ##0##! %/
\‘ g \ /I i
/ /

\ \
/ /

 

 

Figure 5.21: Schematic representation of streamlines for the primary tab geometry at
y/bz-l .0.

105

 

 

 

 

 

—- --0.5Io
Z Z
Y /<o< 1
___l_)< W W/ i...
45'
<
\ b‘”
FLDW>
/
”I/I/I/I/I/I/I/I/A WI,

 

\/

Figure 5.22: Schematic representation of streamlines for the modified tab geometry at
y/bs-1.0.

106

 

 

  

 

 

 

. + primary tab geometry
- + untabbed geometry

 

 

: ' '
0.7 _-
N O- .
3 : + modifiadtabgeometry (a)
a 0'6 :- + primarytab geometry
Lo " + untabbedgeometry
g 0.5
.5.
(U
or 04
>: 0 3
.0
lo
q 0.2
C?
II ,
5 01
$M~_~—~ ____,
4.0 -0 5 0.0
y/b
2.5 . I l r .
I :
20 -__ + modified tab geometry _1

I L 1

(b)

 

 

-O.5 A 1 I I 0.0
y/b

Figure 5.23: Pressure distribution for x=-0.05b: a)P*(x=-0.05,y), b)6P*/ 8%.

107

 

 

 

 

 

" l I I
0.7 _-

: + modified tab geometry :1 (a)
N go’s :- + primarytabgeometry :1
D : + umabbedgeometry i
O. o
l!) ‘
Q .2
A ..
g ‘
a: I
m. ‘
A I
O 1
—+
4
{2:1 I I I
. l l . . P J ‘

-2 0 -1 5 -1 0 -0 5 0 0

 

  

1 .0 I I I I I I I I f I I I t I I T tj I
.1
l' + modified tab geometry ‘
0.8 " + primarytabgeometry ‘
P + uriabbed geometry . (
I ‘ b)
l 'l
A r .
g 0.6 — -
V " d
CD ~ 4
«\ - 4
0. 0.4 ~ -*
CD

 

 

 

 

 

Figure 5.24: Pressure distribution for y=O: a)P*(x,y=O), b)6P*/ 6%.

Z/b

1.0

108

 

 

ambient
0.5
" 6high speed
0.0
-0.5
6core

-1.0

 

 

 

1

Note: contours shown are Q/Uup

l l l l l l l l l l 1 l L l l L l l l l l I

 

-1.5 -1.0 -O.5 0.0 0.5
y/b

Figure 5.25: Definition of penetration measures.

 

0.0

-1.0

109

V I

+ untabbed geometry

—0— primary tab geometry
—9— modified tab geometry

1 T I I I l I I

    

Y T I Tfij I [1 I

 

LLIILALJ+1111LLLLi1llllklIllllLLl

0.8 1.0 1.2 1 .4 1 .6 1.8 2.0

X/b

 

Figure 5.26: Penetration of the shear layer into the core region.

 

110

0.9 ~

: untabbed geometry
primary tab geometry

—I— modified tab geometry

[W111

0.8

0.7

lWUfiIUUII

 

aambient/b
o
01

OOrllllquLllLllllllllll[111111111]
.

0.8 1.0 1.2 1.4 1.6 1.8 2.0

Figure 5.27: Penetration of the shear layer into the ambient region.

6high speed/b

0.5 _

0.4 ;

0.3 j

 

 

111

+ untabbed geometry

+ primary tab geometry
+ modified tab geometry

 

 

 

l 1 l L 1 1 1 L L 1 l 1 l l 1 l 1 1 1 l l l l l l l L l A l I

0.8 1.0 1.2 1.4

X/b

Figure 5.28: Penetration of high speed fluid into the ambient region.

 

112

1.0~

plume

0.5 -

 

 

 

 

-1.0 -

 

 

 

 

Figure 5.29: Location of shear layer momentum thickness measurements.

0.12

0.10

0.08 "

B/b

0.06
0.04

0.02 _

0.00

113

+ m... d6/dx=0.050

+ primery ten geometry. pume
—C}— moaned teb geometry. pume

  
  
  

FYIIIVTI‘I

d9/dx=0.035

 

1 l . A A A l A . . A
0.5 X/b 1.0 1.5 2.0

Figure 5.30: Shear layer momentum thickness,6, for the plume.

0.12

0.10

0.08

G/b

0.06 '

0.04 ,

M‘

prmery no geometry. me no
+ pnmery too geometry. bottom
—0— mama no geometry. and tab
—-0— modmd teb geometry. bottom

I I Y Y Y

d0/dx-0.035

   

VT

d0/dx=0 .027

dflldx=0.024

 

1 l . . A . l A A .
0.5 X/b 1.0 1.5 2.0

Figure 5.31: Shear layer momentum thickness,8, for the side and tip shear

layers.

1.0

0.5

N r . B of \
-0.5 b \>
-10 .. l
I l 1 1 1 l 1 ‘
-2.0 -1.5 -1.0 -0.5 0.0
v/b
1-0 I I I I I I I I I
0.5 — g -
r- O ..
" 5 4 ..
£0 0 _ /R i
N e
- / K / \
-0.5 —
Z .
I l
-1.0 —
F 1 1 L 1 1 l 1 1 1 1 1 1
-2.0 -1.5 -1.0 -0.5 0.0

114

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V/b

dNULUlm

dMG‘MG

01!)
0.05
-0.10
-0.15
0.20
0.25

0.00
-0.05
-0. 10
-0.15
0.20
0.25

 

(b)

Figure 5.32: Average lateral velocity, V/ Uup, for the primary tab geometry: a)l.2,

b)2.0.

115
1.0 r I I I rfi I I r I I I I

 

.1
q

QC!)
.005
0.10

: ' -0.15
P . 0.20 (a)

-0.5 -

dNG-‘Dbulm

 

K
(7/

 

 

 

 

 

-2.0 -1.5 -1.0 -0.5 0.0

 

0.00
-O.(5
-O. 10
-0. 15
0.20

05 _ _ -O.25

I ~ . : (b)

1.0 I I I I I I I I I I I I I I I I I I r
b

dMObUIO

 

 

 

 

 

 

v/b

Figure 5.33: Average lateral velocity, V/ Uup, for the modified tab geometry: a)l.2,
b)2.0.

 

116
1.0 T V I T l I Ifi I I I I v I

 

1
.l

0.25
0.20
0.15

E (a)

«0&5
«0. 10
-O. 15
-0.20
43.25

dNUbU‘OVOD)m

 

 

 

 

 

   

 

1.0 I I I I I I I I fi' l I I I I I I I I I

0.5
0.20
0.15
0.10
0.15
0.00

if}? (b)

-0.20
-O.25

I fiI’

l I

0.5

I Wfir

dMUbMONOD)G

 

 

 

 

 

#-
-1.0- f’
4 A 4 A l 1 114 l

-1.0

v/b

 

Figure 5.34: Average transverse velocity, W/ Uup, for the primary tab geometry: a)l.2,
b)2.0.

 

117
1.0 r I I I l I I I I I I I I I I I I I I

 

 

 

 

 

 

 

 

e 0.25
' I A 0.20
1 . 9 0.15
. v . a 0.10
l- 4 7 0.05 (a)
_ _ e 0.00
0'5 _ <> 1 s -0.05
E 3 4 -0.10
0 ‘ 3 0.15
. 2 0.20
1 .025
l
~0.5 ~
I l
-1.0 - .
. 1 L1 1 1 1 1 1+ 1
-2 0 -1 5 -1.0 -0 5 0 0
V/b
1.0 I I I I l . 8 0.25
v > A 0.20
9 0.15
a 0.10
. 7 0.05
_. s 0.00
0.5 _ a (> s .0... (b)
V 9 v 4 0.10
3 .015
Q 2 .020
1 .025

 

 

 

-05; f\_/)
.l.

 

 

-2.0 -1.5

 

Figure 5.35: Average transverse velocity, '07 Uup, for the modified tab geometry: a)l.2,
b)2.0.

 

118

 

 

 

 

 

 

 

 

1.0 r w r r I 7 0.23

. e 0.20

< 5 an

1 4 0.14

P. 0 1 a 0.11 (a)

_ _ 2 0.00

0'5 _ 1 0.05
goo -
p
-005 b
l-
-1.0 -
r

L l l l J l A L
-2 0 -1 5 -1.0 -0 5 0 0

1.0 I I I F I I I I I r I I I I 1 I I I I 7 023

1 6 0.20

L 5 m7

. 4 0.14

a 0.11

0.5 f m

(b)

I I I I I

 

fiO-Or ‘j/ “J
-05“- W \
L
: 1
l.
L 11 1 1 1 #1 1 1 1 L 1 1 1 1

-2.0 -1.5 -1.0 -0.5 0.0

v/b

 

 

 

 

 

Figure 5.36: Fluctuating lateral velocity, V/ Uup, for the primary tab geometry: a)l.2,
b)2.0.

 

 

 

 

 

 

 

 

 

 

 

 

1-0""T“"l""l" 7023

- s 1120

5 (117

4 0.14

_ 3 0.11 (a)

2 nos

0.5 r 1 0.05
l.
gen -
-0.5 *-
-‘l.0 -
-2.0

1.0 r . . 1 0.23

. s 0.20

s 0.17

4 0.14

1 3 0.11

_ 2 0.00

0'5 _ 1 0.05 (b)
No.0 :'
l-
-0.5 -
-1.0 P
l

-2.0

 

Figure 5.37: Fluctuating lateral velocity, V/ Uup, for the modified tab geometry: a)l.2,
b)2.0.

 

 

 

 

 

 

 

1.0 I I T I l T 1 1 I I T ’T T—Y I I I *Y 1 7 0.23
* s 0.20
1 5 0.17
. 4 0.14
. c: 3 0.11 (a)
2 0.03
0'5 y 1 0.05
.— 1 1
>/\/\ - 1
Q l /‘ %\
N040 _ l
-005 b
-1.0 -
1
2.0
1.0 I I V I I I I I T l I 1’le I I I 7 0.23
6 0.20
s 0.17
4 0.14
3 0.11
2 0.03
0.5 1

(b)

 

 

 

 

 

 

N
-0.5 -
-10- l
1 i 1 1 1 . m1 1 1 1 1 1 1 1\.
-2.0 -1.5 -1.0 -0.5 0.0

V/b

Figure 5.38: Fluctuating lateral velocity, {17/ Uup, for the primary tab geometry: a)l.2,
b)2.0.

121

 

 

 

 

 

 

 

 

 

 

 

1.0 T—I I I I I I I I I I I I I I I I I 7 on
. s 0.20
- 5 0.17
. 4 0.14
_ - J 3 (111 (a)
_l 2 0.03
0.5 1 0.05
1- -1
Q 4
No.0 '-
-0.5 -
l.
l.
-1.0 — .1
1- q
l 1 L L l 1 l 1 1 l 1 I l l l l k l l
-2.0 -1.5 -1.0 -0.5 0.0
7 0.23
a 0.20
s 0.17
4 0.14
3 0.11
2 0.05
1

(b)

 

 

 

 

 

 

-2.0 -1.5 -1.0 -o.5 0.0
V/b

Figure 5.39: Fluctuating transverse velocity, W/ Uup, for the modified tab geometry:
a)l.2, b)2.0.

122

 

1.0 I I I I I I f I I l I I I I T f I I I I I I I I I I

0.5>_ .......... .,,

 

\

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\\\

 

 

 

A 1 1 L l l 1 1 L l 1 1 l 1 l l

 

 

 

  

  

 

 

1.0.,,.,....,....,....,....,..
III lll/
' :11 III! ‘
0.5~ iii xiii — (b)
’ I I 1111 ‘
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-0.5— l -
. I .
- 11 1
\1 1
l\ ‘
' ll
-1.0— H _
1 ll
1 ll 1 1114

 

 

 

 

Figure 5.40: vw vector plot for the primary tab geometry at x/b=l.2: a) scaled, b)
unsealed, e) V = 0, W = 0 intercepts d) singular points.

123

 

1.0 I I I I I fiI I I I T I I I I

 

 

-0.5 _ ~

L as {-1
\‘\ 4
h F
'
-1.0 - ;'-i
L 4

 

 

 

 

 

 

------ hole

sphere _ (d)

 

 

 

 

 

1 l L j l l L 1 l l l L 1 1 J l 1 l 1 I

-2.0 -1.5 -1.0 -0.5 0.0 0.5
v/b

 

Figure 5.40: (continued)

 

 

flM

 

0.5

  

 

 

 

 

 

 

 

 

 

 

 

 

 

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5. o. 5 o. o. o. 5 o. 5. o.

2.0: a) scaled, b)

unscaled, c) V - 0, W - 0 intercepts d) singular points.

0.0

-o.5
Y/ b

-LO

~15

2.0
Figure 5.41: vw vector plot for the primary tab geometry at x/b

125

 

1.0 fl ' I V I f I t I I v I T I 1' I I v I

 

 

 

 

 

 

 

 

 

 

 

 

 

l
l
sphere; ()
------ hole r d
r
-1.0- ~
1111111111.111111111111111.
-2.0 -1.5 -1.0 -0.5 0.0 0.5

v/b

Figure 5.41: (continued)

 

1.0

0.5

No.0

-0.5

1.0

0.5

No.0

-O.5

 

 

      
  

'.'.\\\\\\\ \

--n\\\

I ‘Tfi’ I fIfi

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I

 

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I

    

 

 

     
   

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1 1 l 1 1__1 1 l 1 1 1 1 l 1 1 l 1 l L ‘ l 4

 

 

 

 

 

 

 

-o.5
Y/ b

(b)

Figure 5.42: vw vector plot for the modified tab geometry at x/b=1.2: a) scaled, b)

unscaled, c) V - 0, W - 0 intercepts d) singular points.

127

 

1.0

 

 

 

 

 

 

-1.o - . -
I l 1 4 l 1
-2o -15 -1o -05 oo

 

 

 

 

 

 

 

 

I l
.4
sphere; ( )
...... hole . d
.J
-0.5— —
-1.0- -
#111l1111111..111111.1..111
-2.0 -1.5 -1.0 -0.5 0.0 0.5

V/b

Figure 5.42: (continued)

 

 

      
    
  

 

  
  

 
 

 

 

 

 

 

 

1.0 v I.r.t.[.v.v.1.t.l.|.I-T-I-[.'-'-"'°| ‘ ' ‘firf‘
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. ....... \OIII-~\\“‘ 2Um _J (a)
...... \ e o i I I I - . . . . . . _l‘
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1.0 I V UFI'Y I T Y I T W
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1 (b)

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-_.-.—.—1 ~—.-.—.—.—\§
MK
0’ “...—“T“...— “9..
1 1 l 1 l l

 

 

 

 

l
H
II!
HI _
H H .
ll \\
H x \\ ~
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// tt\\
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llllii .
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5

-2.0 -1.5 -1.0 -O.

.0
o
o
01

Figure 5.43: vw vector plot for the modified tab geometry at x/b=2.0: a) scaled, b)
unsealed, e) V = 0, Vv' - O intercepts d) singular points.

1.0 .

129

 

0.5

I Y

I

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-O.5 -
-1.o - ‘
1 l 1 L
-2.0 -1.0 -0.5 0.0
v/b
1.0 W, ,1
L .......... /<(( l
I 1
0.5 r- sphereu
. O ...... hole 1
_Q ----- A”- /
No.0 -
r 4
-O.5 - ‘ ‘ d
-1.0 - -
1 l 1 1 1 1 L 1 1 1 1 1 l 1
-2.0 -1.0 -0.5 0.0 0.5

V/b

Figure 5.43: (continued)

((1)

130

1.0 T V Y V l V V T I I j’ Y Y Y I Y Y V V

 

 

 

 

 

 

a ace-3
' 7 ace-3
1 0 106-3
1. 4 5 ~3.$'3
1 . 4 ace-a
3 ace-3
0'5 h - 2 4.2a-2
' 1 1 4.56-2
. @ 1
n b
no.0 r ”‘2
L
-0.5 -
-1.0 - -
4g 1 1 1 1 1 1 1 1 1 1 1
-2.0 -1 .0 -0.5 0.0

 

V/b

Figure 5.44: W/ Uup 2 for the primary tab geometry at x/b=1.2.

 

1.0 r T r V T V U V T I f r Y T I Y V f Y

. 96:?
05%

lid
ti-S
3.5-3
-3.E-3
-6.$-3
4.5-3
-1 .252
-1 .SE-2

0.5

I

z/b
O
O
fi'IjV—I
41114
dNUbMONO

 

 

 

 

 

1 1
-1.0 — -
' 1 L 4 1 1 l 1 1 1 1 l 1 1 1 1
-2.0 -1.5 .1.0 -o.5 0.0

v/b

Figure 5.45: W/ Uup 2 for the primary tab geometry at x/b=2.0.

131

 

 

 

 

 

 

1.0 V V Y V l V V V V l V V V I I fi" T Y . O'm
" 7 ace-3
-' O 1&4
r -1 5 ‘3."3
i. .1 4 ace-3
3 {CE-3
0'5 :- 2 4252
D 1 4.552
.1
.D ‘
\OOO ... v
N _ .
i. .1
- 1
r- 4
-0.5 ~ '1
1.
-1 o _ i _
L 1 l l l #1 1 L l 1 1 1 L J l l g 1
-2.0 -1.5 -1.0 -0.5 0.0

V/b

Figure 5 .46: W/ Uup 2 for the modified tab geometry at x/b=1.2.

 

 

 

 

 

 

 

a ace-3
" 7 ace-3
1 0 106-3
1. 5 ~3.¢£-3
_ 4 406-3
— 3 ace-a
0’5 2 425-2
’ 1 4.582
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-0.5 -
1
-1.0 - \ q
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 d
—2.0 -1.5 -1.0 -0.5 0.0

v/b

Figure 5.47: W/ Uup 2 for the modified tab geometry at x/b=2.0.

132

 

 

   

0 0.00
t * 7 0.50
1 1 0 0.40
. v 1 s 0.30
1 1 4 030
a -0.00
O'SL d9? 1 2 -0.so
1 0.00
' i
.Q ’ ‘
EDD r-
-O.5 P
1 ' O
i- . a d
h ‘ I1
#- q
'1-0 ' 1 A ‘
4 L l l l 14 1 l l L 11 L l 1 1L 1

 

 

 

 

-2.0 -1.5 -1.0 -05 0.0
V/b

Figure 5.48: W/ UV for the primary tab geometry at x/b=1.2.

 

1.0 V'r v I l v v v v r v v v v r T’fi 1 v

 

 

 

 

 

O 0.”
" 7 0.50
L 0 0.40
.. 5 0.30
_ 4 0.30
0-5 r 2 222
P 1 0.60
1
Q
No.0 i:
t
-0.5 -
-1 .0 1. ? _
1 1 1 1 1 1 1 1 1 1 1 1 1 J 1 1 4 1 d
-2.0 -1.5 -1.0 -0.5 0.0

V/ b

Figure 5.49: W/ UV for the primary tab geometry at x/b=2.0.

 

133

 

.1
1

0.”
0.50
0.40
0.”
0.3)
-0.40
0.50
0.”

1.0 Y Y Y I I I Y 7 I I r T V V
b

4
i

 

 

 

 

.o ,
N - 1» ' 1;
11" ‘
’05 " i Q ‘
if \ 1
) 65—..— '—‘~ 9
-1 o - y 9
-2.0L1 1 11.51 l L 11.01 1 I L-o.5l I 140.0
V/b

Figure 5.50: W/ W for the modified tab geometry at x/b=1.2.

 

0.00
0.50
0.40
0.30
030
-0.40
-0.50
-0.60

111‘;
‘NULU‘ONO

 

 

.4
Ck.

 

 

 

 

 

/
1 I S
-0.5 — g]
-1.0 - -1
1. A )1 ‘
1 1 1 1 l L 1 1 4 J 1 1 1 1 l #1 1 1
-2.0 -1.5 -1.0 -0.5 0.0

V/b

Figure 5.51: W/ ii? for the modified tab geometry at x/b=2.0.

 

134

 

 

 

 

 

 

 

1.0r..-,....,111111111 cue-2
’ 1 s LEE-2
" 4 125-2
4 3 9.064
, .. 2 &m
0.5 +_ _‘ 1 3.5-3
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F 1
£00 Q1” 1
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> 0
05 i
r d
.1 4
-'| .0 - -
F 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1
-2.0 -1 .5 -1 .0 -0.5 0.0

V/b

Figure 5.52: u'w'/ Uup 2 for the primary tab geometry at x/b=1.2.

1.0 V V V V I V V V U I V V V V l V Y r V

 

 

 

0 1.5-2

1 ‘* 5 1.584

b i ‘ ‘.£‘2

y- -1 3 0.5-3

1. .1 2 fififi

0.5 _ .1 1 1&4
~ ' r \v .
r -1
1- . 1
~0.5 - “'4

F
-1.0 P C
b- .1
i L l l L L l l A 4 J 4 1 + A L

 

 

 

 

-2.0 -1.5 -1.0 -05 0.0
V/b

Figure 5.53: u 'w'/ uup 2 for the primary tab geometry at x/b=2.0.

135

 

 

 

 

 

 

 

1 10 j T ' ' I ' ' r ' I 7 fi Y ‘ I v 1 T T . ‘.£°2
5 1.55-2
p 4 1.2E-2
1 3 1&4
r- 2 0.(£-3
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0.5 - “5
r
.0 '
\1 .—
N000
r
-0.5 -
y-
y.
-1.0 1 —
p-
1 l 1 l 1 1 1 1 l gL 1 1 l 1 1 1
-2.0 -1.5 -1.0 -0.5 0.0

V/b

Figure 5.54: u’w'/ Uup 2 for the modified tab geometry at x/b=1.2.

 

 

 

 

 

 

 

1.0 t v v V [ V I Viv l’ 1 Y T v I v v—v f o ‘.£.2
r t 5 1.552
1 < 4 1.22.2
. 1 3 006-3
1 . 2 6.063
1 3.063
0.5 r- —
t
.D ’
pap 1
p
-O.5 —
i‘
~1.0 _
1
A 14411 1 1 1 l 1 1
-2.0 -1.5 -1.0

 

V/ b

Figure 5.55: u 'w’/ uup 2 for the modified tab geometry at x/b=2.0.

136

 

 

 

 

 

 

O
-0.5
. Q o y 7 .
'110 '- A / -i
1 1 1 1 1 1 L L l L 1 L #1 1 1 1 1
-2.0 -1 .5 -1 .0 ~05 0.0

V/b

Figure 5.56: u 'w’/ G»? for the primary tab geometry at x/b=1.2.

 

 

L L l L l I A A A l

 

 

 

L L l 1 A L l

 

 

-2.0 -1 .5 -1.0L
V/b

Figure 5.57: u"w'/ SW for the primary tab geometry at x/b=2.0.

-0.5

0.0

‘NUbMONO

dNUbUON.

0.”
0.50
0.40
0.30
0.3
-0.40
0.50
‘0.”

0%
0.50
0.40
0.”
0.30
-0.40
0.50
0.60

 

 

 

 

 

 

 

 

137
1-0 1 ' ‘ ' a 0.00
1 7 0.50
~ 0 0.40
1 s 0.30
_ 4 41.30
0-5 r 2 2:22
' t -o.ao
Q
No.0;—
1.
-0.5 -
-1.0 -
P 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
-2.0 -1.5 -1.0 -0.5 0.0

 

V/ b

Figure 5.58: u 'w’/ UK! for the modified tab geometry at x/b=1.2.

 

1.0 I ‘ I I I I r I—fj I I I T I T I W Y

.1
' (D

0.5 _ '17
» A e

0.”
0.50
0.40
0.3)
~o.3o
-0.40
-0.50
«0.60

dMUbMONO

 

-11; m g

l L 1 L l 1 l A L l

 

 

 

 

-2.0 -1.5 .1.0 -o.5
V/b

Figure 5.59: u'w’/ SW for the modified tab geometry at x/b=2.0.

0.3

0.2

0.1

-0.1

0.3

0.2

0.1

Figure 5.60: Cross-vane results for the primary tab geometry at x/b=: a)0.1, b)0.2,
c)0.3, d)0.4.

 

 

 

 

 

 

 

 

 

 

I j I I I I I Yfi I I I f I I I 1 I I I
1- o q
_ ----- negative .
1- .
1- .1
1— —1
i- '4
p- .1
p d
r- d
p- d
i” A "
r ’ ‘ q
1 1 ‘ ‘ x ‘ (a) .
,. "' \ \ .1
\ \ ¥
" \
1 . j
I- II
p q
— .
P 'i
r 1
1- II
p- ..
r -
i' ..
p u
r- d
b -
_ Iii
'- q
p c:
P
y- a
1 1 J 1 4 l 1 1 1 1 l L L 1 4 1 1 1 L J
-1.0 -0.8 y/b -0.6 -0.4 -0.2
fl r I I I I I I I I I I l l I I T f U l
> a d
_ ----- negative .
- posntive -
p .4
P -
i- q
p q
p- d
I— '- - — — d
r- \ \ \ \ ..
\

i. \ \ d
P \ \ \ (b) I:
\

i' I \ \ \ \ x \ d

M“ < \ j

_ \ 4
P \ q
r- ‘ '4
L _
p d
u- -4
P -1
r 1
- A
P d
i' '1
1- -1
1- cl
i. —.
~ 1
- 1
,-

il 1

1 1 l 1 1 1 1 1 1 1 J 1 1 1 l L 1 1 1

 

 

-0.8 y/b -0.6

-0.2

139

 

 

 

 

-0.2
-0.2

 

 

 

 

 

 

 

 

 

1! d d 4 d1 1 u d d — u q d d .44. d d1 d 1414 d I 1 d d - q d d J 4+d1qd d q 4 — 1 1- . d 10‘ d1- 4 d d d — 4 14 ‘1- d d
T ) 1 I \ I 4
( (
I e 1 I e 1
v w v e
“0| 0" v
I t l I I. L
8.1. a“
Wm 4 fix 4
.I ll 0 TI! 1 o
n p 0. n p O.
I u 1 I o 1
. .
' . l I - 1
. .
I - l I - 1
I \ 1 I \ J
\
1_\ \ 6 \\ x 6
I \ l I \ 1
1 1 0 11 1 O
\ u \ a
I \ \ 1 I \\ \ 1
\ \ \ \
. . x . b . . . . b
\ 1 / \ \\ /
I \ \\ l y I \ V 1 y
\\ \ \ \
I- \ ‘ l I. \ \ 1
\ \ \ \
. x O x 0
x . s .
I P I _l \ \ 1
le \
~ \
I J I \\ \\ 11
\
w 1 .1 [Ix 1
I 1 I 1
0 O
T 1 1|. 1| 1 4|.
- c
I 1 fi 1
I J I 14
b P F b — I V P P _ b b b b bib D b p I P P h - P b P P — h P PL F b h b 1— h n P h _ F b P b p h h D — P h D P — n b b b _ D I P h
3 2 4| 4| 2 3 3 2 4| 1 2 3

4
O. 0. O. . . O. O O. mu.

A . .
O 0 O mu 0 0 O

O. O
0 n u g 0 -
QM QM

Figure 5.60: (continued)

0.3 1

 

     
   

I I I I I I I

 

’ ----- negative 1
0 2 *- positive _‘
. 1 J
i 2
0.1 *-
L.
.0 ~

 

c':
IIIrIIIIrTIIIIIIII

 

 

 

 

0.3 1

 

----- negative
positive

 

0.2

0.1

IIITIrfTIlUIII

 

ITIIIIIIIIIITITIjII

 

 

 

41411111111111.1111111111
-1.0 -0.8 -0.6 -O.4 -0.2

y/b

Figure 5.61: Cross-vane results for the modified tab geometry at x/b= a)0.], b)0.2,
c)0.3, d)0.4.

0.3

 

   

----- negative
positive

 

0.2

0.1

IfiIIlIIIIIIIII-J

 

h 0.0

-0.1

 

 

II1I IIrI T—IWI IIWI
_ l T l

 

 

0.3 .

 

----- negative
positive _j

 

0.2

0.1

IIITIrfIITrTTI

 

O
.0 .

- N
ITIUIIIIIIIIIIIIIII

 

 

 

_0.4Jr1.1111111111.r11.1.1
-1.0 -0.8 -0.6 -0.4 -0.2

y/b

Figure 5.61: Cross-vane results for the modified tab geometry at x/b= a)0.1, b)0.2,
c)0.3, d)0.4.

0.3

0.2

0.1

0.3

0.2

0.1

 

 

 

 

 

 

 

 

 

 

 

 
   

 

 

 

 

I I
,_ I I v I I J
u- d
.
- - - - - - negative «
_ posntive _
I- I
~ 4
I- It
I- d
I—Iv _
I- I1
. C .
y- at
. .
P s ‘ \ ‘
I- ‘ \ ‘ \ u
.. \ ‘ ..
\ \
-— \ ‘ .1
I- \ d
\

u- \ q
u- ‘ It
- 4
— --t
n d
l- d
I- It
- d
l— —t
b 1
I- II
p

r- u

1 l l 1 l l 1 l l 1 l l I l J l l l l A 1 l
-o 4 -o.2
If I I I I I I

.

. . .J
. ----- negative 1
P I I

_ posuttve _
F d
r- 4
P I
I- It
I— —t
. .
. .
I- d d
. .
I- I
n It
P It
_. _
b d
b d
I. a
n d
— d
P d
. .
i- d
- -
D d
b q
.

 

 

 

y/b

Figure 5.61: (continued)

142

 

 

 

 

 

 

 

 

 

 

 

 

 

l l r I
0.5 - -
1
. @ \
$0.0 " \
-05 - k o
l i t l 4 L 1 L q
-1 5 -1.0 -0.5 0.0
y/b
l r T I fl l
0.5 — _
Q ©
4) .1
no 0 — W . '
-0.5 -
F 4
I L L L ¥ L L 1 1
-1 5 4.0 -O.5 0.0

y/b

anuamauuo)

dMGOMOVOO)

1.50
1.25
LN
0.75
0.50
41m
-O.75
4 .oo
-1 .25
-1 .50

1.50
1 .25
LN
0.75
0.50
0.8)
-0.75
-1 .oo
4 .25
-1 .50

(a)

(b)

Figure 5.62: of} for the primary tab geometry: 3) x/b=1.2, b) x/b=2.0.

 

143

 

1 .50
1 .25
1 .oo
0.75

-0.50
-0.75
4.00
4.25
4.50

dNUbMOVOO)
o
8
A
83
v

 

 

 

 

 

 

 

1 .50
1 .25
1 .oo
0.75
0.50
-0.50

3?: (b)

4.50

dNGéO‘IOVOQ)

 

 

 

 

 

 

-1.5 -1.0 -O.5 0.0

Figure 5.63: w*x for the modified tab geometry: 3) x/b=1.2, b) x/b=2.0.

 

1.0 fi' I I I l I I I Ifi I I I I I I I I I

  
    
 

 

 

 

 

_ '1
: c 1 0 I | | I I I l I I I 'J
I 1 U 0 l I I I I I l I I I
_ . . . . . . - 0 - 1 \ a l l i l l l I l l 1
0.5_ :....-\ iiiillllll-t
L . . . - . - | l l I I I I I 1 ’1
. . . . . I I I I I 1 I I I l
. IIIIIIIII'J
,_ . . . ‘. ; ‘- ‘ I I I I I I I I i
’ . . . I I I I I I I
'00 ..\\\\\\\\‘ IIIIIIi
WO' P . . _-s\\\\\\ ' I I I I4
- -<p~\\\\\ I I I A
l' .-....c-N“ I I I J
,. n-gb——.- I I I ’ 1
. ~¢-cu-c— ’ I ’ I 4
--.pvo—W ’ ’ I I
-005 — Oc—‘w'v’o—W/ I I I l %
p - 0'01 P””W//”/ ’ ’ ' ’
P . d’o’”””’”/// / I ’ I J
. - ah///////////// / I ’ 1
“’AP//////////// ‘
. -.—.»/////////// /¢fj l
-10— -«fl,,,//////// /////
_ -'D.l'//////////// //// I
1 1 1 1 l 1 1 1 l l i ‘ 1 L l l A A l
-2.o -1.5 -1.0 . -0.5 0-0

v/b

Figure 5.64: Overlay of vw vectors and w—x" contours for the modified tab geometry at
x/b=1.2.

 

 

 

 

 

\u

Figure 5.65: Inferred upstream vorticity connections.

 

 

 

6. SUMMARY AND CONCLUSIONS

6.1 Analysis of the Changes for the Flow Field of the Modified Tab Geometry

The expansion of a jet into the surrounding or ambient region can be greatly
increased by using secondary tabs in addition to primary tabs which have previously
been investigated. The addition of secondary tabs is herein designated as the modified tab
geometry. The secondary tabs provide attachment surfaces for the naturally occurring I
expansion of the core flow into the ambient region. The resulting change in the trajectory

of the jet flow causes a tighter curvature in the streamlines at the exit which changes the

 

static pressure field near the exit.

The resulting changes in the static pressure field serves two purposes. First, the flux
of (ox into the flow upstream of the tab increases which enhanced the negative sense
streamwise vorticity downstream of the exit. Second, the changes in the pressure field
results in a favorable pressure gradient in some regions near the exit of the jet which
significantly increases the positive 0),. downstream of the exit. The large scale distortion
in the flow field is increased through the combined "pumping action" of the two regions
of streamwise vorticity for the modified tab geometry.

In the case of the primary tab geometry the region of negative sense streamwise
vorticity dominates the flow and creates the distortion demonstrated in the present study
as well as in the past studies (Bradbury and Kahdeme (1975), Ahuja and Brown (1989),

and Zaman et. al. (1994)) .

145

146

6.2 Conclusions

The following conclusions were supported through the use of several experimental

techniques:

0 Although the shear layer in the plume region of the primary tab geometry was
severely distorted in shape compared to the untabbed geometry, it had similar
characteristics. Specifically, the growth rate of the momentum thickness, dG/dx,

was the same and the Reynolds shear stresses were similar for both geometries.

o The shear layer in the plume region for the modified tab geometry showed
increased distortion in shape as well as a significant increase in both the growth
rate of the momentum thickness and the Reynolds shear stresses compared to

the primary tab geometry and the untabbed geometry.

0 The flow field of the primary tab geometry and the modified tab geometry were

 

nominally the same below the projected top wall of the tunnel. This indicated
that the effect of the secondary tabs was primarily felt in the upper portion of
the flow field.

0 A favorable pressure gradient was created along side the primary tab and near
the jet exit by the addition of the secondary tabs. This change in the pressure
field increased the magnitude of the streamwise vorticity associated with the
re-orientation of the boundary layer vorticity downstream of the exit for the

modified tab geometry when compared to the primary tab geometry.

0 The magnitude of the streamwise vorticity due to the upstream pressure hill
was slightly increased downstream of the exit plane for the modified tab

geometry when compared to the primary tab geometry for y<O.

- The two counter rotating regions of streamwise vorticity acted like a "pump" to
eject fluid from the core region in the near field. The modified tab geometry
showed a greater expansion of the core flow into the ambient region due to the

increase in both regions of streamwise vorticity.

 

7. REFERENCES

Ahuja, KK, and Brown, W.H., "Shear Flow Control by Mechanical Tabs", AIAA Paper
89-0994, 1989.

Anderson, Dale, Tannehill, John, and Pletcher, Richanrd, ComputationaLEluid
Mechanimndfleatlmnsfer, Hemisphere Publishing Corp., New York, 1984.

Bradbury, L.J.S, and Khadem, A.H., "The Distortion of a Jet By Tabs”, lQumaLniEluid
Wigs, v01. 70, 1975.

BradshaW, P., AnlnnoductionJQIurhulenmnditsMeasuLemems, Pergamon. New
York, 1975. l

 

Bruns, J.M., Haw, R.C., Foss, J .F., "The Velocity and Transverse Vorticity Field in a

Single Stream Shear Layer", EighLSxansiumonjltrbulmLShearflm Paper 3-1,
1991.

Collis, DC, and Williams, M.J., "Two-Dimensional Convection from Heated Wires at
Low Reynolds Number", Journal of Fluid Mechanics, 6:3 57-84, 1959.

Foss, J .F., "The Effects of the Laminar/Turbulent Boundary Layer States on the

Development of a Plane Mixing Layer", WW, Paper
ll-D, 1977.

Foss, J .F., Wallace, J ., Wark, C., "Vorticity Measurements", InsjmmgntationIQLELujd
Dynamics, Joseph Schetz and Allen Fuhs ed., Wiley and Sons, Inc., pp. 1066-1067, 1995.

Foss, J .F., Klewicki, C.L., and Disimile, P.J., "Transverse Vorticity Measurements Using

an Array of Four Hot-Wire Probes", NASA Contractor Report 178098, Appendix A,
1986.

147

148

Foss, J.I(., and Zaman, K.B.M.Q., "Effect of a Delta Tab on Fine Scale Mixing in a
Turbulent Two-Stream Shear Layer", AIAA Paper 96-0546, 1996.

Kock am Brink, B., and Foss, J .F., "Enhanced Mixing via Geometric Manipulation of a
Splitter Plate", AIAA Paper 93-3244, 1993.

Kock am Brink, 3., WW and
W, MSU-ENG-9l-OO9, 1991.

MKS Instruments, Inc, Bulletin 120/510-2/94, 1994.

Reeder,M.F.,° EXO' '1‘ 1,1 0. 0 ix"1._1'1' '1‘ 1' 01‘
W115, PhD. Dissertation, Ohio State University, 1994.

Steffen, OJ, and Zaman, K.B.M.Q., "Analysis of Flow Field From a Rectangular Nozzle
With Delta Tabs", AIAA Paper 95-2146, 1995.

Validyne Engineering Corporation, Bulletin DP15TL-2/78F, 1978.

Whitham, G.B., W, L. Rosehead ed., Clarendon Press, Oxford,
pp. 114-133,1963.

Wygnanski, 1., and Fiedler, HE, ”The Two-Dimensional Mixing Region", loumalgf
WWII} pp.327-361, 1970.

Zaman, K.B.M.Q, Samimy, M., Reeder, M.F., "Control of an Axisymetric Jet Using
Vortex Generators", BMW, pp.778-793, 1994.

Zaman, K.B.M.Q, Samimy, M., Reeder, M.F., "Effect of Tabs on the Evolution of an
Axisymetric Jet", EighLSxmesiummlumulemfiheaLflms, Paper 25-5, 1991.

 

 

 

149

Zaman, K.B.M.Q, Samimy, M., Reeder, M.F., "Streamwise Vorticity Generation and
Mixing Enhancement in Free Jets by ’Delta-Tabs’", AIAA Paper 93-3253, 1993.

Zaman, K.B.M.Q, Samimy, M., Reeder, M.F., "Supersonic Jet Mixing Enhancement by
’Delta-Tabs’", AIAA Paper 92-3548.

 

APPENDIX A: Determination of B

The angle 13 was defined by a line drawn perpendicular to the sensor and the probe

axis. This angle was nominally :45 degrees for the sensors of as x-array, and zero for a

single sensor probe. Note that while the angle B, was a physical property of the probe

defined by the assembly of the sensors it was determined by the calibration data. The

following analysis therefore determined the effective [3, not the physical [3 for use in the

processing algorithm. Equation (3.3) was rewritten with the dependence on y removed

from the AB and n values by

Ez(Q,1)=A+BQ“cos(B-v)"-
Equation (Al) was then differentiated with respect to y to produce

d—E—z=O+BQ"ncos(B--Y)"-l sin(B-1).

Solving equation (A2) for the quantity BQ" yielded
BQ"=(E2-A)/cos(B-y)".
Equation (A3) was substituted into equation (A2) and solved to give

dE2=(E2-A)n
dv 90803-7)"

 

cos(B—v)""sin(B-v)

which simplified to

dE’

tan(B)=d—y(y=0)/(E’(v=0)~A(v=0))n-

(A1)

(A2)

(A3)

(A4)

(A5)

The calibration data were used to form a second order fit of E2 versus 7, see Figure A. 1.

150

 

 

151

The curve was differentiated once and evaluated at y=0. The angle [3 was then determined

using equation (A4).

 

"1111111111111“