AN ABSTRACT OF THE THESIS OF
Arjan Stander for the degree of Master of Science in Mechanical Engineering
presented on October 29, 2002.
Title: The Effects of Pulsing and Blowing Ratio on a 45° Inclined Jet in Cross
Flow.
Abstract approved:
Redacted for privacy
urdy
De orah V. Pence
The effect of jet flow pulsing and blowing ratio on a jet in cross flow has
been investigated. Preliminary jet flow studies were performed without cross flow
and an extensive study of jet with cross flow was done for a total of nine test
cases. The effect of velocities ratios of 0.85 and 3.4, as well as pulsing the jet flow
at 20Hz, was investigated in the near and far field of the jet. A comparison
between the jet in cross flow and an inclined cylinder in cross flow was also
performed.
Hot film measurements were taken within a grid of the flow field in the jet
symmetry plane and out of the symmetry plane. Instantaneous velocities were
generated at each location and mean velocity, RMS values, Reynolds stresses and
mean vorticity were calculated and compared for each case.
The higher velocity ratio case (VR = 3.4) caused the jet flow to lift up
from the wall penetrating into the cross flow compared to the lower velocity ratio
case (VR = 0.85) where the jet fluid remained attached to the wall and no lift off
was observed. The higher velocity ratio case resulted in increased mean
velocities, RMS values, Reynolds stresses and mean vorticity throughout the flow
field compared to the low velocity ratio case. Secondary turbulent structures were
discovered in the wake region of the inclined cylinder. Similar structures were
absent in the downstream flow region during the jet in cross flow experiments.
There was no significant effect on the jet trajectory as a result of jet
pulsing. For both velocity ratio cases the jet trajectory remained similar to the
steady cases. Jet pulsing increased the instantaneous velocity RMS levels and
Reynolds stresses in the near field of the jet, but did not seem to affect the RMS
levels and Reynolds stresses beyond x/d =4.
Jet pulsing had a significant effect on the distribution of spectral energy.
Distinct energy peaks are generated at the pulsing frequency and its harmonics.
The distinct spectral peaks were largest close to the jet exit and within the jet
flow, but were detectable throughout the entire flow field.
The Effects of Pulsing and Blowing Ratio on a 45°
Inclined Jet in Cross Flow
by
Arjan Stander
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Presented October 29, 2002
Commencement June 2003
Master of Science thesis of Arian Stander presented on October 29. 2002.
APPROVED:
Redacted for privacy
Co-Mi or Professor, representing
Redacted for privacy
Co-Major Professor, representing Mechanical Engineering
Redacted for privacy
Head of the Department of Mechanical Engineering
Redacted for privacy
Dean of the Qthduate School
I understand that my thesis will become part of the permanent collection of
Oregon State University libraries. My signature below authorizes release of my
thesis to any reader upon request.
Redacted for privacy
Arjan Stander, Author
ACKNOWLEDGEMENTS
T would like to take this opportunity to thank some of the many people that
made possible not only this thesis, but also my stay here in the US. First of all, not
enough words can describe the gratitude that I have for my parents. For their
guidance, the constant love and their support during my life and my time away
from home, here in the US. For letting me fulfill my drive to seek adventure so far
away from home.
I remember the advice that was given at the start of graduate school. Most
relationships do not survive graduate school. I created one. Thanks Stephanie for
all your love and support during these years. We made it.
I would like to thank both of my advisors. Dr. Liburdy, for bringing so
much 'comedy' to my work. Thanks for your support, guidance and reassurance
throughout my studies. It was Dr. Pence who made it possible for me to come
over and attend Oregon State University in the first place. Thanks for giving me
this opportunity, for your advising and support.
Although my thesis work was done in cooperation with Dr. Pence and Dr.
Liburdy, I was able to spend a great deal of time with Dr. Peterson who made it
possible for me to work with him in his lab and made it possible for me to
financially 'survive' during my stay here. Thank you for your continuous support
and interesting conversations in the lab.
In addition to the faculty that supported me I have to thank the many
friends I have here as well as back home. A combination of faculty and a good
group of friends make life away from home especially rewarding and sustainable.
Friends came and went and there are many I would like to thank and I will try to
name a few. From the start there were the diehards in Rogers Hall that have
remained good friends over the years. I would like to thank Bertrand for his
support and work on the many projects at the Aerolab wind tunnel as well as
being a good friend, along with his wife Renellys. Brian thanks for sharing your
support during the years. I have enjoyed talking to you and discussing a broad
range of topics.
Kiersten, Ali and Ron who were someof the first people I grew close to
and are still good friends and will certainly be in the future. Su Young,
Younghoon, Lukito, Ryan and Aristotel, Li Na and more whom I all enjoyed very
much.
It was amazing to get to know so many people from so many different
backgrounds and different origins. These were all friendships that I enjoy very
much and which made my time in Oregon a very rewarding experience.
Finally I would like to especially thank my entire family and all my
friends back in Holland and France. Oma's, opa, ooms, tantes, nichten and neven.
I am looking forward to being with you again. Thanks for the visits, cards, letters,
phone-calls and support.
TABLE OF CONTENTS
1 INTRODUCTION
1
2 LITERATURE REVIEW
2
2.1 YAWED CYLINDER IN A CROSS FLOW
2
2.2 STEADY JETS IN CROSS FLOW
4
2.3 PULSED JETS IN CROSS FLOW
9
3 PROBLEM STATEMENT
12
3.1 GENERAL PROBLEM STATEMENT
12
3.2 SPECIFIC EXPERIMENTAL OBJECTIVES
13
3.2.1 Fully modulated inclined pulsed jet without
cross flow
3.2.2 A 45 degree inclined solid cylinder in cross flow
3.2.3 A 45 degree inclined steady jet in cross flow
3.2.4 A fully modulated inclined pulsed jet in cross flow
4 EXPERIMENTAL SETUP
13
14
14
15
16
4.1 WIND-TUNNEL FACILITIES
16
4.2 CROSS FLOW SETUP
20
4.3 JET PULSING
23
4.4 AIR SUPPLY SYSTEM
25
4.5 HOT WIRE SYSTEM
26
TABLE OF CONTENTS (Continued)
Page
5 TEST PLAN
28
5.1 CROSS FLOW QUALITY ASSESSMENT
30
5.2 JET CHARACTERISTICS
31
5.3 PiTCHED CYLINDER IN CROSS FLOW
32
5.4 STEADY JET iN CROSS FLOW
34
5.5 PULSED JET IN CROSS FLOW
34
6 DATA ANALYSIS METHODS AND REDUCTION
35
6.1 CONVERTING BRIDGE VOLTAGE TO
VELOCITY DATA
35
6.2 ANALYZING INSTANTANEOUS VELOCITY DATA
37
7 RESULTS AND DISCUSSION
41
7.1 CROSS FLOW CHARACTERISTICS
41
7.2 PiTCHED JET CHARACTERISTICS, NO CROSS FLOW
46
7.2.1 Mean jet velocity profile
7.2.2 Jet averaged velocity versus frequency
7.2.3 Pulsed jet time trace
7.2.4 Jet trajectory
7.2.5 Jet turbulence characteristics in the near field
of the jet
7.2.6 Jet turbulence characteristics at the jet exit
7.3 CASE I: PITCHED CYLINDER IN CROSS FLOW
47
48
50
56
59
62
64
TABLE OF CONTENTS (Continued)
Pag
7.4 CASE II: STEADY JET iN CROSS FLOW
7.4.1 Velocity ratio of 0.85, at centerline at z/d = 0
7.4.2 Velocity ratio of 3.4, at centerline at zld = 0
7.4.3 Velocity ratio of 0.85, off-center at z/d = 0.8
7.4.4 Velocity ratio of 3.4, off-center at z/d = 0.8
7.5 CASE III, PULSED JET iN CROSS FLOW
7.5.1 Velocity ratio of 0.85, at centerline at zld = 0
7.5.2 Velocity ratio of 3.4, at centerline at z/d = 0
7.5.3 Velocity ratio of 0.85, off-center at z/d = 0.8
7.5.4 Velocity ratio of 3.4, off-center at z/d = 0.8
8 CASE COMPARISONS
67
67
71
73
76
80
80
83
86
89
92
8.1 INFLUENCE OF VELOCITY RATIO AND PULSING
FREQUENCY ON X-DIRECTION MEAN VELOCITY
92
8.2 INFLUENCE OF VELOCITY RATIO AND PULSING
FREQUENCY ON RMS OF U VELOCITY COMPONENT
97
8.3 INFLUENCE OF VELOCITY RATIO AND PULSING
FREQUENCY ON REYNOLDS STRESSES
100
8.4 INFLUENCE OF VELOCITY RATIO AND PULSING
FREQUENCY ON MEAN VORTICITY
105
9 SPECTRAL AND VELOCITY CHARACTERISTICS
109
9.1 INCLINED CYLINDER
110
9.2 STEADY JET
117
9.3 JET PULSING
123
TABLE OF CONTENTS (Continued)
Pe
10 DISCUSSION
130
11 CONCLUSIONS AND RECOMMENDATIONS
135
BIBLIOGRAPHY
137
APPENDICES
140
LIST OF FIGURES
Figure
1g
4.1
Test section of closed loop wind tunnel photograph
17
4.2
3-bladed variable pitch propeller photograph
17
4.3
2Ohp AC motor with drive belts photograph
18
4.4
Motorized traversing system photograph
19
4.5
Schematic of wind tunnel facility
20
4.6
Plate assembly photograph
22
4.7
Jet plate photograph
22
4.8
Machined diffuser section photograph
24
4.9
Schematic of pulsing setup
24
4.10
Schematic of the air supply system
26
4.11
TSI model 1246-20 probe photograph
27
5.1
Schematic of cross flow plate/jet assembly with coordinate system 28
5.2
GridA
32
5.3
GridB
33
7.1
Plate's leading edge velocity profile, main stream velocity 4 mIs
42
7.2
Velocity profile at 10 jet diameters upstream of jet leading edge
43
(U =4 mIs)
7.3
Velocity profile 3 mm upstream of the leading edge of the jet
(U =4 mIs)
44
LIST OF FIGURES (Continued)
Figure
Page
7.4
Turbulence intensity at 10 diameters upstream of the jet exit
45
7.5
Turbulence intensity immediately upstream of jet exit
46
7.6
Fractional change in velocity distribution relative to
steady jet conditions for two velocity ratios
48
7.7
Mean velocity magnitude as a function of pulsing frequency
for the low jet flow case
= 3.4 mIs)
49
7.8
Mean velocity magnitude as a function of pulsing frequency
for the high jet flow case (Vjet = 13.6 mIs)
49
7.9
Time trace at low flow setting for 0 Hz pulsing frequency
52
7.10
Time trace at low flow setting for 2 Hz pulsing frequency
52
7.11
Time trace at low flow setting for 20 Hz pulsing frequency
53
7.12
Time trace at low flow setting for 40 Hz pulsing frequency
53
7.13
Time trace at high flow setting for 0 Hz pulsing frequency
54
7.14
Time trace at high flow setting for 2 Hz pulsing frequency
54
7.15
Time trace at high flow setting for 20 liz pulsing frequency
55
7.16
Time trace at high flow setting for 40 Hz pulsing frequency
55
7.17
U-velocity profiles for the low flow, non-pulsed case
57
7.18
U- velocity profiles for the low flow, pulsed case
57
7.19
U-velocity profiles for the high flow, non-pulsed case
58
(Vjet
LIST OF FIGURES (Continued)
Figure
Page
7.20
U-velocity profiles for the high flow, pulsed case
7.21
RMS (mis) of instantaneous velocity magnitude, Vjet = 3.4
no pulsing
7.22
RMS (mis) of instantaneous velocity magnitude, Vjet = 3.4
20 Hz pulsing
7.23
RMS (mis) of instantaneous velocity magnitude,
Vjet = 13.6 mIs, no pulsing
61
7.24
RMS (mis) of instantaneous velocity magnitude,
= 13. 6 mIs, 20 Hz pulsing
61
7.25
U-component RMS at variable frequencies, low jet flow rate
63
7.26
U-component RMS at variable frequencies, high jet flow rate
63
7.27
Pitched cylinder in a cross flow
65
7.28
Steady jet in a cross flow, VRO.85, zld = 0
68
7.29
Steady jet in a cross flow, VR=3.4, zld = 0
72
7.30
Steady jet in a cross flow, VRO.85, z/d
74
7.31
Steady jet in a cross flow, VR3.4, zld = 0.8
77
7.32
Pulsed jet in a cross flow, VR0.85, z/d = 0
81
7.33
Pulsed jet in a cross flow, VR3.4, zld =0
84
7.34
Pulsed jet in a cross flow, VRO.85, zld
7.35
Pulsed jet in a cross flow, VR3.4, z/d = 0.8
58
ITflIS,
60
flTIIS,
60
Vjet
0.8
0.8
88
90
LIST OF FIGURES (Continued)
Figure
Page
8.1
Mean velocity profiles at zld = 0
93
8.2
Mean velocity profiles at z/d = 0.8
95
8.3
RMS values at z/d = 0
98
8.4
RMS values at z/d = 0.8
99
8.5
Reynolds stresses at zld = 0
101
8.6
Reynolds stresses at z/d = 0.8
103
8.7
Mean vorticities at zld = 0
106
8.8
Mean vorticities at zld = 0.8
108
9.1
RMS-u, inclined cylinder at z/d = 0.8
111
9.2
RMS-v, inclined cylinder at z/d = 0.8
111
9.3
Power spectra at x/d = 2.5
112
9.4
Power spectra at x/d = 4.5
113
9.5
Power spectra at x/d7.5
114
9.6
Histogram at x/d = 2.5 and y/d = 2
115
9.7
Timetraceatx/d2.5andy/d2
116
9.8
RMS values, x-direction, VR = 3.4, z/d = 0
118
9.9
Steady jet spectral power density plot
118
9.10
Velocity Trace xld = 2.5, y/d = 1, VR = 0.85, steady
120
LIST OF FIGURES (Continued)
Figure
Page
9.11
Velocity trace x/d = 2.5, yld = 4, YR = 3.4, steady
120
9.12
Histogram, x/d = 2.5, y/d = 0.5, YR = 3.4, steady
122
9.13
Histogram, x/d = 2.5, y/d = 4, YR = 3.4, steady
122
9.14
Jet spectral power density plot
123
9.15
Power Spectral Density for YR = 0.85, x/d = 2.5, y/d = 0.2,
126
z/d =0
9.16
Power Spectral Density for YR = 0.85, x/d = 7.5, y/d = 1, z/d = 0
126
9.17
Power Spectral Density for VR = 3.4, x/d = 2.5, y/d = 1, z/d = 0
127
9.18
Power Spectral Density for YR = 3.4, x/d = 7.5, y/d = 2.5, z/d = 0 127
9.19
Power Spectral Density for YR = 0.85, x/d = 2.5, y/d = 0.2,
128
Power Spectral Density for YR = 0.85, x/d = 7.5, y/d = 0.2,
128
zId0.8
9.20
z/d0.8
9.21
Power Spectral Density for YR = 3.4, xld = 2.5, y/d = 1, z/d = 0.8 129
9.22
Power Spectral Density for YR = 3.4, x/d = 7.5, y/d = 2.5,
z/d0.8
129
LIST OF TABLES
Table
Page
5.1
Test plan
29
9.1
Location of power spectral density plots
124
LIST OF APPENDICES
Appendix
ige
A DIIFERENTIAL PRESSURE MAP
141
B CROSS FLOW PLATE ASSEMBLY
TECHNICAL DRAWINGS
148
C UNCERTAINTY ANALYSIS
156
CI JET AVERAGED VELOCITY
156
C.2 X,Y AND Z LOCATIONS
158
C.3 iNSTANTANEOUS VELOCITIES
159
D HOT FILM CALIBRATION
160
E POWER SPECTRA, TIME TRACES
163
AND HTSTOGRAMS
LIST OF APPENDIX FIGURES
Figure
A.1
Test section locations
142
A.2
Pressure distribution at location A
144
A.3
Pressure distribution at location B
146
B.i
Technical drawing of jet in cross flow assembly
149
B.2
Technical drawing of cross flow plate
150
B.3
Technical drawing of jet plate
151
B.4
Technical drawing of strut block
152
B.5
Technical drawing of plate strut
153
B.6
Technical drawing of stringer A
154
B.7
Technical drawing of stringer B
155
D.1
Calibration curve sensor 1
161
D.2
Calibration curve sensor 2
161
E.1
Power spectral density at x/d = 2.5, y/d = 0.2
inclined cylinder
4.0,
164
E2
Power spectral density at x/d = 7.5, y/d = 0.2
inclined cylinder
4.0,
165
E.3
Power spectral density for VR = 0.85, at x/d = 2.5,
y/d = 0.2 4.0, z/d =0, steady jet
166
E.4
Power spectral density for VR = 0.85, at x/d = 7.5,
y/d = 0.2 4.0, z/d =0, steady jet
167
LIST OF APPENDIX FIGURES (Continued)
Figure
E.5
Power spectral density for VR = 0.85, at x/d = 2.5,
168
y/d = 0.2-4.0, z/d =0, pulsed jet
E.6
Power spectral density for VR = 0.85, at x/d = 7.5,
y/d = 0.2 4.0, zld =0, pulsed jet
169
E.7
Power spectral density for VR = 3.4, at xld = 2.5,
170
y/d = 0.2 4.0, zld = 0, steady jet
E.8
Power spectral density for VR = 3.4, at xld
7.5,
171
E.9
Power spectral density for YR = 3.4, at x/d = 2.5,
y/d = 0.2 4.0, z/d =0, pulsed jet
172
E.10
Power spectral density for YR = 3.4, at x/d = 7.5,
y/d = 0.2 4.0, z/d =0, pulsed jet
173
E.1l
Power spectral density for YR = 0.85, at xld = 2.5,
174
y/d = 0.2-4.0, z/d = 0, steady jet
y/d = 0.2 4.0, zld = 0.8, steady jet
E.12
Power spectral density for YR = 0.85, at xld = 7.5,
175
y/d = 0.2 4.0, z/d = 0.8, steady jet
E.13
Power spectral density for YR = 0.85, at x/d = 2.5,
176
y/d = 0.2-4.0, z/d = 0.8, pulsed jet
E. 14
Power spectral density for YR = 0.85, at x/d = 7.5,
177
y/d = 0.2-4.0, z/d = 0.8, pulsed jet
E.15
Power spectral density for YR = 3.4, at x/d = 2.5,
178
y/d = 0.2 4.0, zld = 0.8, steady jet
E.16
Power spectral density for YR = 3.4, at x/d = 7.5,
y/d = 0.2 4.0, zld = 0.8, steady jet
179
LIST OF APPENDIX FIGURES (Continued)
Figure
E.17
Power spectral density for VR = 3.4, at xld = 2.5,
180
y/d = 0.2 4.0, z/d = 0.8, pulsed jet
E.18
Power spectral density for VR = 3.4, at x/d = 7.5,
y/d = 0.2 4.0, z/d 0.8, pulsed jet
181
E.19
Velocity time traces at x/d = 2.5, y/d = 0.2-4.0,
inclined cylinder
182
E.20
Velocity time traces at x/d = 7.5, y/d = 0.2 - 4.0,
inclined cylinder
183
E.21
Velocity time traces for VR = 0.85, at x/d = 2.5,
y/d = 0.2 40, z/d =0, steady jet
184
E.22
Velocity time traces for VR = 0.85, at x/d = 7.5,
185
y/d = 0.2-4.0, z/d = 0, steady jet
E.23
Velocity time traces for VR = 0.85, at x/d
2.5,
186
Velocity time traces for VR = 0.85, at xld = 7.5,
187
yld = 0.2-4.0, z/d =0, pulsed jet
E.24
y/d = 0.2 4.0, z/d =0, pulsed jet
E.25
Velocity time traces for VR = 3.4, at x/d = 2.5,
188
y/d = 0.2 4.0, zld =0, steady jet
E.26
Velocity time traces for VR = 3.4, at x/d = 7.5,
189
y/d = 0.2 4.0, zld =0, steady jet
E.27
Velocity time traces for VR = 3.4, at xld = 2.5,
y/d = 0.2 - 4.0, z/d =0, pulsed jet
190
E.28
Velocity time traces for VR = 3.4, at x/d = 7.5,
y/d = 0.2 - 4.0, z/d =0, pulsed jet
191
LIST OF APPENDIX FIGURES (Continued)
Figure
E.29
Velocity time traces for VR = 0.85, at x/d = 2.5,
yld 0.2 4.0, z/d 0.8, steady jet
192
E.30
Velocity time traces for VR = 0.85, at x/d = 7.5,
y/d 0.2-4.0, z/d = 0.8, steady jet
193
E.31
Velocity time traces for VR = 0.85, at xld = 2.5,
194
y/d = 0.2-4.0, z/d = 0.8, pulsed jet
E.32
Velocity time traces for VR = 0.85, at x/d = 7.5,
y/d = 0.2 4.0, z/d = 0.8, pulsed jet
195
E.33
Velocity time traces for VR 3.4, at xld = 2.5,
y/d 0.2-4.0, z/d = 0.8, steady jet
196
E.34
Velocity time traces for VR = 3.4, at x/d = 7.5,
y/d 0.2 4.0, z/d = 0.8, steady jet
197
E.35
Velocity time traces for VR = 3.4, at xld = 2.5,
197
y/d = 0.2-4.0, z/d = 0.8, pulsed jet
E.36
Velocity time traces for VR = 3.4, at xld = 7.5,
199
y/d = 0.2-4.0, z/d = 0.8, pulsed jet
E.37
Histogram at xld = 2.5, y/d = 0.2
inclined cylinder
4.0,
200
E.38
Histogram at xld = 7.5, y/d = 0.2
inclined cylinder
4.0,
201
E.39
Histogram for VR = 0.85, at x/d = 2.5,
y/d = 0.2 4.0, z/d =0, steady jet
202
E.40
Histogram for VR = 0.85, at x/d = 7.5,
y/d = 0.2 4.0, z/d =0, steady jet
203
LIST OF APPENDIX FIGURES (Continued)
Figure
E.53
Histogram for VR = 3.4, at x/d = 2.5,
y/d = 0.2 4.0, z/d = 0.8, pulsed jet
216
E.54
Histogram for VR = 3.4, at xld = 7.5,
217
y/d = 0.2-4.0, zld = 0.8, pulsed jet
LIST OF APPENDIX TABLES
Table
A. 1
Differential pressure measurements at A
143
A.2
Differential pressure measurements at B
145
A.3
Statistical data at A
147
A.4
Statistical data at B
147
NOMENCLATURE
dU
X direction velocity differential, UsteadyUpulsed, (m/s)
dV
Y direction velocity differential, VsteadyUpu1sed, (mis)
D
Jet diameter, 10mm
Qiiowmeter
Volume flow rate through flow meter
Re
Reynolds number, UD/v
Rejet
Jet Reynolds number, VjetDjet/V
RMS(U)
RMS of fluctuating velocity component (u'), (m/s)
TI
Turbulence Intensity, (%)
u, v
Instantaneous velocities in x and
u', v'
Fluctuating velocity in x and
U,V
Time average velocities in x and y direction, (mis)
U
Free stream velocity, (m/s)
Umax
Maximum velocity along u-component velocity profile
y direction,
y direction,
(mis)
(m/s)
Normalized velocity, U/U
Usteady/Upulsed
U-component velocity at particular x/d location along
jet exit, in steady and pulsed operation, respectively
VR
Velocity ratio, Vjet/Uco
vt
Instantaneous vector velocity, (mis)
V
Time average mean velocity vector,
U2 + V2 , (m/s)
NOMENCLATURE (Continued)
Vjet
Average jet exit velocity based on flow meter,
Qflowmeter / Ajet,, (mis)
Vmax
Maximum velocity along v-component velocity profile
VN
Velocity component normal to sensor wire
Vsteady/Vpulsed
U-component velocity at particular x/d location along
jet exit, in steady and pulsed operation, respectively
VT
Velocity component tangent to sensor wire
Mean vorticity,
(us)
x, y, z
Locations from origin, (mm)
x/d, y/d, zld
Non dimensional locations, d = 10 mm
The Effects of Pulsing and Blowing Ratio on a 45°
Inclined Jet in Cross Flow
CHAPTER 1
INTRODUCTION
Jets in a cross flow are found in a wide range of applications from
chimney plumes and waste water exhaust to combustor fuel injection, turbine
blade cooling and boundary layer control. In some applications mixing and
stirring are the primary indicators of an effective system, while in others the jet
penetration is more important. The use of a jet in cross
requires an understanding of the relation between the
flow
flow
in any application
variables and the effect
they have on the flow structure. Because of the many applications of jets in cross
flow
and the academic interest in this particular flow, research in the area of jets
in cross flow was initiated.
The particular type of investigation that is described herein is meant to
complement past research to better understand the effect of velocity ratio and jet
pulsing on the jet/cross flow in the near and mid/far region of the jet. In particular,
the effect of a relatively high pulsing frequency on the
momentum within a cross
flow,
flow
at low and high jet
as well as a comparison with the effect on the
wake of a solid inclined cylinder in cross flow,
will
be presented.
2
CHAPTER 2
LITERATURE REVIEW
Literature from different topics is included in this chapter. The main focus
of the current research is on pulsed jets in cross flow, but other topics like
cylinders and inclined cylinders in a cross flow will also be shortly discussed. The
main part of the literature review will concern some past investigations of jets in
cross flow. Steady jets in cross flow will be reviewed, followed by a review of
pulsed jets in particular.
2.1 - YAWED CYLINDER IN A CROSS FLOW
One of the many studies on cylinders in cross flow was performed by
Roshko1
in 1954. He presented a detailed quantitative description on the
development of wakes behind solid cylinders over a large Reynolds number
range, where the Reynolds number was based on the freestream velocity and the
cylinder diameter. He identifies three ranges of shedding. A lower range, starting
at a Reynolds number of 40 up to 150, where a pair of standing vortices behind
the cylinder become unstable and start shedding alternatively, resulting in a von
Karman vortex Street. A transition range is identified between Re = 150 to 300,
where laminar to turbulence transition occurs and a third, upper, range is
identified between Re = 300 to 10,000+. In this last range the vortices contain
turbulence and these turbulent vortices tend to diffuse faster and become fully
turbulent at about 40 to 50 diameters downstream. The distinct shedding
frequency components tend to be more buried in the high levels of turbulent
energy in the third range, or high Reynolds number region.
In addition to normally mounted cylinders perpendicular to a cross flow,
studies like the one by A.R.
Hanson2
involve a yawed cylinder in a cross flow.
Low Reynolds number studies were carried out and it was shown that the
Reynolds number at which shedding occurs is postponed as yaw angle is
increased away from the normal. The frequency of shedding is also affected by
yaw, however in the low Re range tested, it is still in linear relation to the
Reynolds number.
Kawamura et
al.4
in 1994 carried out a computational study on the
interaction of an inclined cylinder in a cross flow with Reynolds number of about
2000. More specifically they were interested in the wake region behind the
cylinder. They studied the case of an infinitely long cylinder and one that was
located between two end plates. Among other results they showed that 'strong
three-dimensionality' was observed in the case of a finite cylinder between two
end plates. The wake region tended to grow wider further away from the upstream
end plate, which was consistent with the results indicating an increasingly earlier
separation along the cylinder while traveling downstream along the cylinder.
The wake of a 60 degree inclined cylinder in a cross
flow
was
experimentally investigated by Hara et al.5. It is interesting to note that in
preliminary experiments that were carried out, von Karman vortex shedding was
seen in both cases of inclination of 0 and 30 degrees from the normal. It is also
reported that such shedding was absent in the cases of larger yaw angles. The
main study was focused on a 60 degree inclined jet, since the
flow
pattern was
'steady and highly three-dimensional'. A combination of trailing vortices along
the plate and a pair of wake vortices were found in the wake of the cylinder,
'nearly parallel' to the cylinder. It was again observed that the wake size increases
dramatically over the first few diameters along the downstream direction of the
cylinder. This section summarized a small number of studies done on cylinders
and inclined cylinders in cross
flow
and introduces the interesting behavior
inherent to this particular setup.
2.2 - STEADY JETS IN CROSS FLOW
Steady jets in cross flow have been investigated for over 50 years. There is
a wide range of applications that are relevant to the jet in a cross
flow
configuration and applications range from jet exhaust into a free stream, turbine
blade cooling, Vertical and Short Take Off and Landing aircraft applications
(VSTOL), fuel injection, boundary layer control, reaction control for missiles and
5
aircraft, and more. Each application requires a different approach to the jet/cross
flow interaction.
There are four types of structures that are inherent to a jet in cross flow.
One of the two steady structures is the so-called horseshoe vortex. It is generated
at the leading edge of the jet close to the wall, where the cross flow boundary
layer experiences an adverse pressure gradient and is forced to roll up. A second
steady phenomenon is the counter rotating vortex pair, or kidney shaped vortex.
The interaction between the jet boundary layer and the cross flow results in a
shear layer, inducing vorticity aligned in the cross flow streamwise direction. This
vorticity is convected downstream resulting in a counter rotating vortex pair.
Occasionally vortices at the leading edge of the jet separate and form a third
distinct feature, namely the jet shear layer vortices that travel along the upper side
of the jet surface. The fourth structure, wake vortices, can be found in the wake of
the jet between the bottom of the jet column and the cross flow wall.
A summary of jet in cross flow work over the last 50 years is given in
Margoson6. He describes early research up to 1970, where some of the first
investigations were applied to chimney plumes, followed by applications such as
combustor injection and early research on VSTOL applications. From a military
perspective, research in the 1980's was primarily driven from missile reaction
control and VSTOL aircraft development, which yielded research in the area of
impinging jets in a cross flow. The development of the turbojet engine has
increased the research of inclined jets within a cross flow for the application of
turbine blade cooling.
One of the experiments that reported on the similarity between vortex
shedding behind a cylinder and that behind a jet in a cross flow was that
conducted by McMahon
et al.7
in 1971. At a cross flow Reynolds number of
about 52,000, hot wire measurements were made in the downstream side of the
jet. Wake shedding frequencies were normalized and resulted in Strouhal numbers
between 0.083 and 0.093 for momentum flux ratios of 8 and 12, respectively.
Experiments were also made with a splitter plate installed in the wake region,
which resulted in a reduction of the discrete energy within the wake. It is argued
that the "vortices behind the jet are similar to the ones behind a bluff body in a
sense that the shedding phenomena is suppressed by a splitter plate". There is a
clear difference between the calculated Strouha] numbers and the cylinder
shedding Strouhal number of 0.21. However, it is also stated that using a jet
spread diameter instead of the physical jet diameter results in a Strouhal number
of about 0.205, which more closely resembles the cylinder shedding Strouhal
number.
A comparison between a pipe jet and a flush mounted jet in a cross flow
was performed by Moussa
et a18.
(1977). Experiments where the jet was flush
mounted on a rectangular metal plate showed agreement with earlier experiments
like those made by McMahon
et al.
However, in the case were the pipe itself
protruded into the cross flow, the shedding was found to be dominated by the
V1
shedding from the pipe itself. Identical shedding frequencies were measured
behind the pipe and in the jet wake. At velocity ratios higher than 5.5 this
dependency seemed to alter slightly and the influence of the jet on the wake
became significant.
The behavior of the wake behind a jet in cross flow is often set analogous
to the famous vortex shedding behind a solid cylinder. Fnc and
Roshko9
argue
that this analogy does not hold and that the source of vorticity that feeds the
vortices is not found within the jet/cross flow interface, but instead in the cross
flow boundary layer. They attribute the generation of vorticity to a 'separation
event' occurring within the cross flow boundary layer as it flows around the
cylinder into an adverse pressure gradient. The separation of the boundary layer
allows spanwise vorticity to bend and stretch into upright vortices. The wake
vortices seem to be most prominent at velocity ratios around 4, where the velocity
ratio is defined as U/U. At velocity ratio 4 the jet column is close enough to the
boundary layer to 'pull the separated fluid away from the cross flow wall', but far
enough from the wall to 'induce significant amount of turning'. It seems that too
large and too small of velocity ratios degrade the generation of wake vortices. It is
also mentioned that the vorticity stretching and pulling by the jet could explain
the results of Mousa et al. (1977), who found a better match between the wake
Strouhal numbers for a protruding jet within a cross flow compared with that of a
flush mounted jet in a cross flow. Fnc and Roshko argue that this closer
agreement could be because of the extension of the wake vortices that are shed
from the cylinder into the jet wake, just as the wake vortices are extensions of
vorticity at the cross flow boundary layer in flush mounted jets.
Studies by Kelso
et a!10.
indicated, among other things, that at high
Reynolds numbers the wake structures change intermittently from one
configuration to another. One configuration is similar to the von Karman pattern
with vortices alternating in circulation, whereas the second configuration consists
of mushroom like vortices and are grouped in pairs of opposite circulation.
One important aspect of film cooling for turbine blades is the attachment
of the jet flow to the wall. The generated counter rotating vortex pair (kidney
vortices) both entrains surrounding fluid and promotes jet lift off. Haven and
Kurosaka11
performed an extensive study on the effect of hole geometry on the jet
lift off. Using a constant area jet, various hole shapes and aspect ratios were
tested. It was clear that a low aspect ratio jet, which results in a close distance
between the sidewall vortices increases 'mutual induction', resulting in an
increase in jet lift off. It was also shown that the leading edge and trailing edge
vortices also contribute to the jet lift off.
Large-eddy simulations of jets in cross flow have been performed by Yuan
et
a!12. Experimental measurements have been reproduced numerically and large
scale structures were apparent in the simulation. Among other things, the wake of
the jet was studied and upright vortices were identified and attributed to the
reorientation of streamwise vortices directly behind the jet.
The flow characteristics of a 35 degree inclined jet were compared to a
normal injection case by Lee
et
a113. They concluded that the jet flow was
predominately dominated by turbulence at small velocity ratios, but influenced by
inviscid vorticity dynamics at larger velocity ratios. The wake region consisted
mostly of jet fluid at the lower velocity ratios, but jet lift off was evident at larger
velocity ratios (VR=2). Cross flow entrainment for the inclined jet was also less
than for the normal injected case.
Many applications of inclined jets in cross flow can be found in film
cooling applications where, among others, research has been performed by
Brittingham and Leylek'4 and Isaac and Jakubowski15. The effect of variable hole
geometries and its effect on film cooling was investigated by Thole
Berger and
et al.16
and
Liburdy17.
2.3 - PULSED JETS IN CROSS FLOW
The importance of mixing in gas turbine combustors has resulted in
research of the acoustically pulsed jet interacting with a confined crossflow.
Vermeulen
et al.'8
in 1990 showed that acoustically pulsing the jet flow
significantly increased mixing, jet spread and penetration. The jet response in
terms of jet turbulence and penetration was found to be optimal at a Strouhal
number of 0.22.
Further research by Vermeulen et
al.'9
in 1992 used a hot crossflow and
temperature profile measurements to more directly assess the jet/crossflow
mixing. Results again showed a significant increase in mixing zone size,
penetration (at least 100% increase), and mixing. Jet penetration and mixing was
determined to be at an optimum at a Strouhal number of 0.27.
Water tunnel flow visualizations, laser induced fluorescence and hot film
anemometry were used by Chang and
Vakili2°
to study the vortex ring formation
of a fully modulated pulsed jet in a cross flow at velocity ratios of 1.5 to 6.7.
Previous research indicated that the penetration and lift off of the jet was
increased at lower pulsing frequencies. This increase in penetration was attributed
to the generation of vortex rings which at lower frequencies penetrate far higher
into the cross flow than when pulsed at higher frequencies and for a steady jet. At
lower frequencies (below 3 Hz), vortex rings do not interact with each other and
tend to penetrate further into the flow. Interaction among vortex rings was found
at higher pulsing frequencies and at lower velocity ratios.
McManus and
Magill21
in 1996 used transverse pulsed jet vortex
generators embedded in the leading edge of a wing profile to control boundary
layer separation by enhancing cross stream mixing. It was found that at low mach
numbers the pulsed jet actuator resulted in a 50% increase in lift. Increasing free
stream Mach number, in general, had a degrading effect on the effectiveness of
the pulsed vortex generator, but small lift increases were still observed. Maximum
lift enhancements were generated at a pulsing Strouhal number of about 0.6.
11
Other studies by Magill and
McManus22
in 1998 found that pulsed vortex
generators could be used in the control of dynamic stall.
Planar laser induced fluorescence techniques were used by Johari et al.23
to study the effect of duty cycle and pulsing frequency on the dilution and
structural features of a pulsed transverse jet. A variety of duty cycles over a
pulsing frequency range of 0.5 to 5 Hz were tested. Long injection times resulted
in only small improvements in jet penetration, while short injection times resulted
in the generation of vortex rings and increased penetration of up to 5 times
compared to the steady jet. The effect of longer duty cycle and thus the decreased
separation between the generated vortex rings decreased the penetration.
Separation time between successive pulses seemed to be the major determinant in
jet penetration and mixing.
The effect of periodic pulsing on the structure and mixing of a transverse
jet have also been investigated by Eroglu and Breidental24. For a given velocity
ratio an optimum pulsing frequency could be selected that increased the
penetration and mixing of the jet. Experiments done at Reynolds number of 6200
showed an increase of jet penetration as much a 70%.
12
CHAPTER 3
PROBLEM STATEMENT
3.1 - GENERAL PROBLEM STATEMENT
The goal of this research is to investigate the near and mid to far field
characteristics of a 45 degrees inclined, pulsed jet in a cross flow during low and
high Velocity Ratios (VR). The mean velocity and turbulent quantities and
trajectories will be studied throughout the field.
To fully understand how the various cases contribute to the overall flow
structure it was necessary subdivide the general test objective into a number of
sub-problems. More specifically, the following cases were studied and compared:
1.
fully modulated 45 degrees inclined pulsed jet without cross flow,
2. 45 degrees inclined solid cylinder in a cross flow,
3. 45 degrees inclined steady jet in a cross flow,
4. 45 degrees fully modulated inclined pulsed jet in a cross flow.
13
3.2 - SPECIFIC EXPERIMENTAL OBJECTIVES
3.2.1
Fully modulated inclined pulsed jet without cross flow
To better understand the behavior of the jet without a cross
flow
it was
decided to study the jet characteristics in both pulsed and non-pulsed cases
without the cross
flow present
for a low and high jet flow rate.
In order to investigate the effect of jet pulsing on the quality of the jet flow
it is necessary to study the following aspects. First, a comparison of the mean jet
velocity profiles for a pulsed and non-pulsed case will show if the pulsing will
alter the velocity profile at the jet exit. The effect of pulsing on the velocity
profiles will be studied at low and high velocity ratios. Secondly, the performance
of the valve in terms of its operating frequency was for a great deal unknown. It
was necessary to test the valve pulsing operating range and study its effect on
both the instantaneous and mean velocity at the jet exit at low and high velocity
settings. Thirdly, turbulence data was obtained for the non-pulsed and the pulsed
case for both jet exit velocities for comparison purposes. Fourthly, the penetration
and trajectory of the inclined, fully modulated jet is also of interest and a
comparison will be made with the unforced case at both low and high jet
velocities.
14
3.2.2 A 45 degrees inclined solid cylinder in cross flow
The 45 degrees inclined cylinder in a cross flow forms a reference case for
the steady/pulsed jet in cross flow experiments and will be used to study and
compare the influence of a rigid obstacle on the cross flow and that of a jet on the
cross flow. Special attention will be given to the wake characteristics behind both
the cylinder and the jet. Of particular interest is the known analogy between the
shedding around a cylinder and the wake vortices present in particular jet cross
flow experiments.
The spectral behavior of the shedding behind the cylinder is of interest and
is compared to that of the potential wake vortices in the jet in cross flow setup.
Hot film measurements were taken throughout the wake along the cylinders side
(outside of the axis of symmetry) and instantaneous velocity datasets were
converted into mean velocity quantities, turbulence related quantities and wake
energy spectra.
3.2.3 - A 45 degrees inclined steady jet in cross flow
A steady jet within a cross flow was tested such that a comparison can be
made between it and both the cylinder case and the case where pulsing is applied
to the jet. Two velocity ratios are studied to alter the jet penetration and lift off
15
which are expected to result in different wake structures. One jet flow at
approximately the cross flow velocity and one high jet flow were selected.
Hot film data was obtained inside and outside of the jet symmetry plane.
Mean velocity quantities, turbulence data and energy spectra will be generated to
study the effect of blowing ratio on the near and mid/near field.
3.2.4 A fully modulated inclined pulsed jet in cross flow
Jet pulsing is the last variable that is introduced. The influence of pulsing
in combination with low and high velocity ratios on the near and mid/near field
will be the main focus for this test. Hot film data were gathered for a pulsing jet at
two blowing ratios and data converted to evaluate mean velocities, turbulence
data and power spectra.
16
CHAPTER 4
EXPERIMENTAL SETUP
The experimental setup involved in the cross flow experiments is
described in this chapter. An experimental apparatus was designed, fabricated and
installed in a wind tunnel to perform the jet in cross flow experiments. Various
instrumentation equipment and support systems were also needed, and are
described.
The chapter will explain in detail the low speed closed ioop wind tunnel,
the instrumentation that was used, the jet in cross flow setup that was specifically
designed for this research and the hot wire system that was used to collect the
data.
4.1 - WIND-TUNNEL FACILITIES
All jet in cross flow experiments were conducted in a closed loop, low
speed wind tunnel at Oregon State University's Aerolab. The wind tunnel's
contraction region is followed by a 30 ft long, 4 by 5 feet cross-section test
section, a photograph is included in Figure 4.1. The wind tunnel is powered by a
2Ohp AC drive and motor, which drives a 3-bladed variable pitch propeller
17
through a set of drive belts. A photograph of the propeller and motor are
presented in Figures 4.2 and 4.3, respectively.
Figure 4.1 Test section of closed ioop wind tunnel photograph
Figure 4.2: 3-bladed variable pitch propeller photograph
Figure 4.3: 2Ohp AC motor with drive belts photograph
During jet in cross flow tests the blade pitch was maintained at a low angle
of attack resulting in a high motor rpm setting. With a low angle of attack setting
on the propeller and a motor speed of 1175 rpm, the wind tunnel is capable of
maintaining speeds up to 10 mIs. Higher operating speeds are readily available
through higher pitch settings and faster motor rotation, but were not necessary for
this particular research. The cross flow velocity within the test section for the jet
in cross flow experiments was maintained at a comfortable 4 m/s throughout all
experiments. The turbulence intensity within the test section measured away from
the test plate was on the order of 1 %. Initial velocity fluctuation measurements
indicated a favorable test location about half way through the test section (see
location B in Figure A. 1, Appendix A). To minimize the levels of turbulence and
to 'straighten' the flow, one course grid and a pair of fine grids were mounted
upstream of the contraction area.
19
Plexiglas panel doors along the entire length of the test section allowed for
a visual inspection of the test setup, while a motorized traversing system allowed
for measurement probes to be positioned at various locations in the test section. A
photograph of the traversing system is shown in Figure 4.4.
Motorized traversing is available in the vertical and lateral directions,
while a manual translation is required in the streamwise direction. A schematic of
the wind-tunnel facility can be found in Figure 4.5.
Figure 4.4: Motorized traversing system photograph
20
AC
drive
Motor
Screens
Test section
*
I
testplate
I
transverser
Figure 4.5: Schematic of wind tunnel facility
4.2 - CROSS FLOW SETUP
A 24" x 48" x 3/8" Plexiglas® flat plate was installed 14 feet downstream
from the test section entrance. Since the test section floor boundary layer develops
along the wind tunnel floor test section and a uniform velocity profile was
required at the leading edge of the flat plate, the flat plate was positioned 14
inches away from the test section floor, well outside the wind-tunnel floor
21
boundary layer. A set of 10 aluminum support struts mounted between the flat
plate and four aluminum flat stringers located on the wind tunnel floor created a
sturdy plate assembly. These same support struts also allowed for easy leveling of
the flat plate. A 30 degrees bevel was machined at the leading edge of the plate to
create a sharp edge minimizing the obstruction for the oncoming flow. A
photograph of the plate assembly is shown in Figure 4.6.
Current
jet in cross flow
measurements were confined to a 10 mm
diameter cylindrical jet hole, pitched streamwise at a 45 degrees angle. The
pitched circular jet results in an ellipse shaped jet exit with a minor diameter of 10
nm-i and a major diameter of 14 mm. To allow for future configurations the jet
was made separately from the plate. The separate jet assembly was machined out
of an aluminum disk (male), which can be fitted inside a slot machined in the
plexiglas flat plate (female). This design allows for one particular jet assembly to
be yawed in steps of 45 degrees, and can be easily interchanged with other jet
plates. A photograph of the jet plate is included in Figure 4.7.
Since the cross flow velocity throughout the tests was maintained at 4 mIs,
the local Reynolds number at the leading edge of the jet was 8.47x 10g. To ensure
a turbulent developing boundary layer along the surface of the plate, a 1.8 mm trip
wire was mounted 50 mm downstream of the plate's leading edge. The jet
Reynolds numbers for the test case velocity ratios of 0.84 and 3.4 are 2260 and
8930, respectively. All technical drawings for the cross flow plate assembly are
included in Appendix B.
22
Figure 4.6: Plate assembly photograph
Figure 4.7: Jet plate photograph
23
4.3 - JET PULSING
Jet pulsing was achieved by installing a miniature solenoid valve upstream
of the jet opening. To achieve a relatively high pulsing frequency a small solenoid
valve with an orifice opening of 2.5 mm diameter was used. To ensure a smooth
flow readjustment from the 2.5 mm diameter solenoid orifice to the 10 mm jet
opening a 30 mm long diffuser section was custom made. The diffuser was flush
mounted and threaded into the jet opening as well as screwed into the solenoid
valve opening. The diffuser was fitted with a 6 degrees diffuser angle to allow for
flow re-adjustments while preventing flow separation within the nozzle. A
photograph of the machined diffuser is seen in Figure 4.8.
The solenoid pulsing frequency was controlled by an amplified function
generator output from a Tektronix FG503 3 MHz function generator. A 40-Watt
amplifier boosted the function generator output signal (square wave) to an
amplitude of 24 VDC. A Tektronix TDS 3054 oscilloscope was used to verify the
input signal to the amplifier as well as the amplified signal to the solenoid. The
input to the solenoid was set to the specified voltage of 24 VDC at low
frequencies, but required slight adjustments to be able to operate at higher
frequencies. Frequency and voltage offset adjustments where made using the
function generator, while signal amplitude was controlled using the amplifier. A
schematic of the pulsing setup can be seen in Figure 4.9.
24
Figure 4.8: Machined diffuser section photograph
Bleed air
during pulsing
air supply
Function
Generator
Amplifier
Oscil
OOflflf1J
Figure 4.9: Schematic of pulsing setup
25
4.4 - AIR SUPPLY SYSTEM
Compressed air for the jet was supplied from a compressor and pressure
vessel system. The compressor was set such that the system's pressure vessel was
pressurized up to 90 psig, after which the compressor automatically shut off until
the pressure dropped below 60 psig when the compressor automatically engaged
again. Pressure lines were used to supply the necessary compressed air to
underneath the wind tunnel test section. Underneath the wind tunnel a pressure
regulator was installed in the pressure line and set to 32 psig, which allowed for
enough pressure to obtain the desired jet flow rates. A flow meter was installed
just downstream of the pressure regulator. The valve on the flow meter was used
to regulate the flow resulting in a downstream line pressure between 3 and 15
psig. The flow rate, measured by the flow meter, which was calibrated at
atmospheric conditions, was corrected for pressure and temperature to calculate
actual flow rate through the flow meter. The correction method is included in the
uncertainty analysis and is included as Appendix C. During pulsing operations the
mass flow rate through the flow meter was unaltered with half of the flow exiting
into the atmosphere during the closed portion of the cycle and the other half
through the jet during the open portion of the cycle. The current setup was
capable of averaged jet exit velocities up to 20 mIs in the steady case. Figure 4.10
shows a schematic of the air supply system.
26
Wind Tunnel!
Fluidized bed wall
boundary
JetNatve assembly inside
wind tunnel
ump
Motor
Pressure
Vessel
!eTank
Flowmeter
Filter
Pressure
Regulator
L____
Pressure
Transducer
Thermocouple
Figure 4.10: Schematic of the air supply system
4.5 - HOT WIRE SYSTEM
A constant-temperature-thermal-anemometer system, including a dual hot
film x-probe was used to gather instantaneous velocity data. The sensors were
part of a 90 degrees elbow support interconnected with a 18" long probe support.
The probe/probe-support assembly was fixed to the traversing system inside the
wind tunnel test section. A plastic clamping arrangement was designed to hold the
probe support at two different locations. Each hot film was connected to a bridge
circuit located within a cabinet outside the test section. The bridge circuitry was
interfaced with a desktop computer, used for data collection, conversion and
storage. To maximize the input range of the analog to digital converter the voltage
27
signals from the bridge circuits were conditioned. Gain and offset values were
selected for each individual channel such that the bridge output voltage would fill
most of the 5 VDC to +5 VDC range on the analog to digital converter. A
photographs of the TSI model 1246-20 hot film is seen in Figure 4.11.
A hotwire calibration was performed over a velocity range from 0 to 40
mis and the exact procedure and calibration files can be found in Appendix D.
Figure 4.11: TSI model 1246-20 probe photograph
CHAPTER 5
TEST PLAN
The following test plan was created and adhered to throughout the
research. All tests are listed in Table 5.1 and are consistent with the problems
stated in Chapter 3. Each test mentioned within the test matrix will be shortly
described.
A schematic of the flat plate and its coordinate system is included in
Figure 5.1. Initial data locations presented in Chapter 7 are identified along the x,
y and z axes, while most of the data are presented as non-dimensional locations:
x/d, y/d and z/d, where d = 10 nmi is the jet exit diameter. References will be
made to the near field, which is defined as the area from the jet to x/d = 4 and the
far field, defined as x/d =4 to xld = 10.5
U
Figure 5.1: Schematic of cross flow plate/jet assembly with coordinate system
Table 5.1: Test plan
Hot film location
Test name
1
x (mm) Jameters
y (mm)
Case
ros,bwqualityassessrnenf
LP1ate leading edge (LE) profile
Boundary layer velocity/TI profile 100 upstream of jet
ndary layer velocity/TI profile at LE of jet
2-25, dy = 1
2-17, dy = 0.5
2-19, dy = 0.5
j
at LE
U
100
U,TI
-
U,Tl
-
Vjet High/Low
Jtcharate1istLcs
Mean jet velocity profile, non-pulsed
2
0 20
U
Mean jet velocity profile, pulsed
2
0 20
U
Jet trajectory non-pulsed
Grid A
U
Jet trajectory pulsed
Grid A
U
Average jet velocity at various frequencies
2
7
V1
Jet pulse time trace
2
7
Vt
Jet turbulence characteristics near jet exit
2
7
RMS
f=2OHz
Viet High/Low
V0t High/Low
f=2OHz
Viet High/Low
V1
let turbulence characteristics in near field
Grid A
RMS
High/Low
f=1-4OHz
V1
High/Low
f=1-4OHz
,
let __
steady & 20Hz
V1 Hiqh/Low
P itchecl Cylinder in a cross flow
Mean velocities in the cylinder wake
Grid B
U,V,V1
Turbulence characteristics in the wake
Grid B
RMS,Re
Spectral content within the wake
Grid B
Spectra
Mean velocities and jet trajectory
Grid B
U,V,Vt
2 yR's
ITurbulence characteristics in the wake of the jet
Grid B
RMS,Re
2 VR's
Spectral content within the wake of the jet
Grid B
Spectra
2 VR's
Mean velocities and pulsed jet trajectory
Grid B
U,V,V1
Turbulence characteristics in the wake of the pulsed jet
Grid B
RMS,Re
Spectral content witin the wake of a pulsed jet
Grid B
Spectra
* Grids A and B can be found in Figures 5.2 and 5.3
'::'.j
2VR's
Pulse/no-pulse
puIse/-ulse
2VR's
Pulse/no-pulse
30
Throughout all experiments the sampling frequency was held at 2000 Hz
and a total of 8192 data points were gathered per dataset. This resulted in a
sample time of 4.096 seconds. A low pass filter was automatically set at 1000 Hz.
5.1 - CROSS FLOW QUALITY ASSESSMENT
To assess the cross flow quality, the mean velocity profile near the leading
edge of the plate was obtained. Hot film data were gathered starting 2 mm above
the plate up to 25 mm above the plate, with a 1 mm interval. Mean velocities were
obtained by analyzing the instantaneous velocity samples at each location.
The thickness of the boundary layer at the leading edge of the jet exit was
predicted to be on the order of the jet diameter25. Boundary layer velocity profiles
were obtained at two locations along the flat plate by traversing the hot film probe
from 2 mm above the flat plate up to 17 mm at 1OD upstream of, and up to 19 mm
at, the jet leading edge. Instantaneous velocities were gathered and mean
velocities, as well as turbulence related profiles, were generated.
31
5.2 - JET CHARACTERISTICS
For a comparison between the steady and pulsed mean jet velocity
profiles, hot film measurements were made along the jet opening. The hot film
was placed 1 mm upstream of the leading edge of the jet and data samples were
taken at 1mm intervals along the x-direction past the trailing edge of the jet (x =
20 mm). During this traverse, the hot film was positioned at a constant height of 2
mm above the cross
flow
plate. At each x-location two data sets were collected;
one for the steady case and one for the pulsed case (20 Hz). This test was repeated
for a low
(Vjet
= 3.4 mIs) and a high
(Vjet
= 13.5 mIs) jet velocity based on
flow
meter settings. Mean velocity quantities were generated and used for comparison.
The effect of jet pulsing on the mean velocity and instantaneous velocities
was evaluated by positioning the hot film probe at the center of the jet (x = 7
mm), while collecting data over a frequency range from 0 to 40 Hz for low and
high jet
flow
settings. The jet pulse time trace was evaluated by presenting the
instantaneous velocity magnitude vt, while the influence of pulsing frequency on
the mean
flow
was studied by calculating mean velocities for every time trace. It
was of interest to study the level of turbulence right at the jet exit with various
pulsing frequencies and jet
flow
settings; therefore, RMS values were calculated
from the instantaneous velocities. Based on the pulsed jet response an operating
frequency was selected that could be used in the
pulsed jet in cross flow
case. The
vertical height above the plate was 2 mm throughout these tests. The turbulent
32
layout of the jet was also studied starting with a 7 by 4 grid (grid A) as indicated
in Figure 5.2.
35
3Ol
0
2O
0.
0
15
.0
0
)10
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
0
0
10
20
30
40
50
Distance from leading edge of jet, x (mm)
Figure 5.2: Grid A
5.3 - PITCHED CYLINDER IN CROSS FLOW
For increased resolution in the cross flow cases a new grid was generated
and can be seen in Figure 5.3. It shows a predominantly 5 mm vertical staggered
and 10 mm horizontally staggered points, combining to a total of 117 points. The
row closest to the cross flow wall is set at y = 2 mm, followed by a row at y =
5mm and further staggered each 5 mm until y =40 mm. Shedding from a cylinder
is expected to originate from either side of the cylinder at z = 5 mm or z = 5 mm.
33
The z = 8 mm plane was selected for study and throughout that plane hot film data
were gathered according to grid B. Mean velocities, turbulence related quantities
and spectral data were generated and compared to the steady and pulsed jet cases.
The cross flow velocity setting was 4 mIs and was held constant throughout the
experiments.
[- Cylinder
80
E60
-
- -
20--
-
-/
-
-
Grid points
/
/
/
/ //
/ /
/
/ //
/
70
c5O
-
-/--/A
-/
'I-/--/-/ -
-
-/- /
/ -/-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-/-
-
-
-
-
-
-
-
25
35
45
55
65
75
85
95
0
.5
5
15
Distance from leading edge of jet, x (mm)
Figure 5.3: Grid B
105
115
34
5.4
- STEADY JET IN CROSS FLOW
For the steady jet case, grid B was also used, but data was gathered in the
symmetry plane of the jet at z = 0 mm in addition to z = 8 mm plane. Hot film
data was gathered for velocity ratios: 0.85 and 3.4. A total of 234 data sets were
collected and converted into mean velocity, turbulence and spectral data.
5.5
- PULSED JET IN CROSS FLOW
A similar test setup was used for the pulsed case, with the exception that at
each velocity ratio the hot film data were collected with the valve pulsing at the
preferred frequency. This test and the previous test were actually done in one and
the same run, since the pulsing is relatively easy to activate and deactivate. At
each point along grid B one data set for the non-pulsed case and another for the
pulsed case were collected. A total of 234 data sets were gathered in the pulsed jet
in cross flow case.
35
CHAPTER 6
DATA ANALYSIS METHODS AND REDUCTION
This chapter describes the various analysis methods that were used to
convert the raw bridge voltage data into velocity, turbulent and spectral data. The
first section addresses the very basics of hot wire data interpretation, while the
other sections further discuss data post processing.
6.1 - CONVERTING BRIDGE VOLTAGE TO VELOCITY DATA
During each test raw bridge voltages from the hot wire system were
collected and stored for post processing. The relationship between bridge voltage
and the 'effective velocity' of the hot film determined during calibration was used
to calculate the effective velocities for each wire. Below is described how the
instantaneous velocity components u, v and the instantaneous velocity vector
magnitude
Vt
are calculated from the effective velocity.
Assuming that a single wire probe was used, the cooling velocity that was
obtained from the calibration data cannot be taken as the actual velocity crossing
the wire. The effective cooling velocity for a one-wire probe with a finite length
can be defined as a combination of cooling from flow perpendicular to the wire
36
and flow parallel to the wire. The resulting equation for cooling velocity can be
defined as:
Veff
=vtVcos2a+k2sin2a
Veff = Jv
+ kv
,or
6-1
6-2
,
where a is the angle between the main flow and the normal of the sensor and
k is
an empirically determined constant that takes into account cooling parallel to the
hot wire. v is defined as the instantaneous velocity vector magnitude,
tangential component of instantaneous velocity and
VN
VT
the
the normal component of
instantaneous velocity.
For an X-probe oriented such that a = 45°, where two wires are oriented at
a 90 degree angle to each other, it can be stated that
UN! = UT2
and
UT! = UN2.
Equation 6-2 can then be written for each wire as:
V1
UJ?
+ k!2Ul
Ve2 = U,2 + kU2 - U1 + kU,!
6-3
6-4
Solving for the normal and tangential velocities gives:
2
UN!
v2 k2V2
effl
eff2
1
1_1.212
!
6-5
2
and
2
UT!
v2
eff2
k2V2
2
eff!
11.212
K,
!
6-6
37
Knowing the individual cooling velocities from the calibration curve and the
constants
k1
and k2, the tangential and normal velocities can be calculated. Using
simple trigonometry, both of the velocity components u and v and the
instantaneous vector velocity magnitude can be calculated:
UT! +UN1
v= UT!
UN!
v=V(u2+v2)
6-7
6-8
6-9
6.2 - ANALYZING INSTANTANEOUS VELOCITY DATA
After instantaneous velocity information has been obtained, a number of
other useful quantities can be generated. Although the hot wire software is
capable of generating various quantities for assessment, most of the processing
was accomplished using MATLAB.
The first assessment of the instantaneous velocity is the mean velocity.
Mean velocities were calculated for the u and v components, while the total mean
velocity magnitude was calculated from those directional quantities. Mean
velocities were calculated by time averaging an instantaneous velocity signal. In
our case, the velocity signal was sampled at 2000 Hz and discretized into 8192
points over a period of 4.096 seconds. The mean is then calculated by summing
over all data-points and dividing by the total number of points within the velocity
file according to the following equations:
U!uJ
6-10
V!vJ
6-11
V=VU2+V2
6-12
The normal stress, or variance, for each individual velocity component
was used throughout to indicate regions of high turbulence. For the u component
of velocity, the normal stress is defined as the mean squared value of the
fluctuating quantity u', where the fluctuating quantity is the difference between
the instantaneous velocity u and the mean velocity U. Throughout the results the
terms RMSU and RMSV will be used. The RMS is basically the square root of
the variance, which is also the standard deviation:
RMSU =
6-13
and similarly for RMSV. The standard deviation gives insight into the amount and
spread of fluctuations around the mean velocity.
The RMS is normalized with the freestream velocity U to calculate the
turbulence intensity and is defined as:
TI(%)=
U
100%
The quantity u' was also calculated. These values represent the amount
of stress exerted on the flow due to turbulence. Reynolds stresses can be
computed, using the following relationship, which is the actual Reynolds stress
per density:
Re
6-15
stress
Positive values of Reynolds stress indicate negative values of u'v' and, within a
boundary layer, indicate an increase of momentum towards the wall. Positive
values of u'v' on the other hand represent a deficit in momentum and tend to
transport momentum away from the wall. Fluctuating velocities for u and v
throughout the data set are multiplied and averaged to calculate u'v', after which
they are plotted as Reynolds stresses throughout the grid.
Mean vorticity was calculated and defined as follows:
au
U) i(av
=I---
2ax
iy
6-16
The vorticity in the z-direction was calculated at grid locations xld = 0.5 through
x/d = 9.5 and from y/d = 0.2 until y/d = 3.5. A backward finite difference routine
was used to calculate the velocity gradients at each point, using average velocities
throughout the grid. Vorticity could therefore not be calculated for all y locations
along x/d = 9.5 and for all x locations along y/d =4.
Vorticity calculations give insight into the velocity gradients within the
flow and in particular it is useful to identify jet shear layers and therefore establish
a jet trajectory. Mean vorticity throughout the field are plotted and presented in
Chapter 7.
41
CHAPTER 7
RESULTS AN!) DISCUSSION
7.1 - CROSS FLOW CHARACTERISTICS
Prior to performing the jet in cross flow experiments, it was necessary to
study the general cross flow characteristics. A uniform velocity profile was
preferred at the leading edge of the cross flow plate. For this reason the plate was
positioned 0.3 meter above the wind tunnel test section floor and the leading edge
of the flat plate was machined into a sharp edge. The leading edge velocity profile
measured with the hot film probe for a mainstream velocity of 4 mIs is shown in
Figure 7.1. The normalized velocity U is defined as U/U.
An acceleration of about 12% from the mainstream was apparent near the
tip of the plate. This was attributed to a slight positive angle of attack of the flat
plate with the mainstream and the slight bluntness of the plate tip, causing an
increased curvature of the streamlines near the leading edge, resulting in more
acceleration than with a zero angle of attack. Leading edge and boundary layer
velocity profiles were then obtained for other than 'normal' angles of attack. It
was concluded from these tests that the alteration of the angle of attack and a
lesser acceleration near the tip did not affect the downstream boundary velocity
profile. Hence, it was decided to keep the plate at its original level avoiding
further complications in other areas like hot wire traversing and test grid
alterations.
25
E
E
15
.1
0
>
0
.0
10
-c
C)
0
I
15
Normalized velocity, U (mis)
Figure 7.1: Plate's leading edge velocity profile, main
stream velocity 4 mIs
Boundary layer velocity profiles were obtained at two locations
downstream of the leading edge. A trip wire was then installed about 50 mm
downstream from the plate's leading edge of the plate to ensure a turbulent
boundary layer. The location of the trip wire was picked such that the boundary
layer thickness would be on the order of the jet diameter at the jet exit. With the
43
type of hot film probe that was used, it was not possible to get closer than 2 mm
from the wall. Figure 7.2 shows the velocity profile approximately 10 jet
diameters upstream of the leading edge of the jet. The velocity gradually increases
from about 2.87 mIs at 2 mm to 4.12 mIs at the edge of the boundary layer.
40
1
E
E1
ti)
ci)
>
0
C)
ci)
I
0.5
1
1.5
Normalized velocity, U (mis)
Figure 7.2: Velocity profile at 10 jet diameters upstream
of jet leading edge (U =4 mIs)
The profile adheres closely to the 117th power curve, which is apparent in
turbulent boundary layers. The thickness of the boundary layer is estimated at
about 15 mm.
Figure 7.3 shows the velocity profile near the leading edge of the jet. The
hot film was positioned in such a way that the tips of the wire were located 3 mm
upstream of the jet leading edge. Again the
117th
order power fit is added as
reference. The velocity 2 mm from the plate in this case is 2.71 mIs and increases
to a free stream velocity of 4.12 mIs at the edge of the boundary layer. Using this
velocity profile a boundary layer of about 17 mm was estimated at the leading
edge of the jet.
E
E
>'
Wi
0.
WI
>
0
-a
0)
0
I
U L__
0
I
0.5
I
1
1.5
Normalized velocity, U (mis)
Figure 7.3: Velocity profile 3 mm upstream of the leading edge
of the jet (U = 4 mIs)
45
18
16
14
E
12
a)
a.
a)
08
>
-D
(
1)
I
ru
2
0
2
4
6
8
10
Turbulence Instensity Profile TI(%)
12
14
Figure 7.4: Turbulence intensity at 10 diameters
upstream of the jet exit
In addition to the velocity profiles, turbulence intensity profiles within the
boundary layer were also generated. Figure 7.4 shows the turbulence intensity at
10 diameters upstream of the jet exit.
As can be seen, the turbulence intensity varies from 9.7% near the wall to
0.8% at the edge of the boundary layer at y = 15 mm. Figure 7.5 shows the
turbulence intensity just upstream of the jet exit.
nfl
1
1
E
>'
0
'p1
>
0
.0
-C
0)
1)
2
4
6
8
10
Turbulence Instensity Profile Tl(%)
12
14
Figure 7.5: Turbulence intensity immediately upstream of jet exit
The turbulence intensity at the jet exit varies from 10.6% at the wall to 0.96%
near the edge of the boundary layer.
7.2 - PITCHED JET CHARACTERISTICS, NO CROSS FLOW
The following results are specific to the 45 degrees pitched, fully
modulated jet, which was used in all further jet in cross flow experiments. Both
47
low and high jet
flow
cases as well as pulsed and non-pulsed operations without
the presence of a cross flow were tested.
7.2.1 Mean jet velocity profile
Mean jet velocity profiles along the jet centerline were generated at low
and high
flow
settings. Hot film data were gathered at x = 2 mm through x = 20
mm in 1 mm intervals. The fractional change in mean velocity profiles for both U
and V are presented in Figure 7.6 and represent the amount of deviation from the
velocity profile in the steady case, where dU and dV are defined as
and Vsteady -
Vpulsed,
Usteady
Upuiseij
respectively
The effect of pulsing clearly affects the magnitude of the mean velocity as
only half of the mass
flow is
now exiting through the jet compared to the steady
case. A comparison between mean velocity profiles in terms of U
and
Vmax
can
be made between the steady and pulsed case. The drop of mean velocity for both
velocity ratios is on the order of 50% for the V component of velocity. The drop
in U is on the order of 45% for Vjet = 13.6 mIs and on the order of 40% for
3.4 mIs.
Vjet =
Vjet
= 3.4
Vjet = 13.6
0.6
0.6
0.5
0.5
0.4
0.4
D
J
0
0.3
-o
0.2
0.3
0.1
0.1
0
)
5
10
15
20
3
5
)
5
x(mm)
1
15
20
15
20
1
0.5
>
>
10
x (mm)
0.5
>
>
0
0
-0.5
-0.5
3
5
10
15
20
x(mm)
10
x(mm)
Figure 7.6: Fractional change in velocity distribution
relative to steady jet conditions for two velocity ratios
7.2.2 Jet averaged velocity versus frequency
Figures 7.7 and 7.8 indicate the change in mean velocity (Vi) with
frequency for low and high flow cases as measured at the center of the jet exit (x
= 7 mm). The mean flow rate through the flow meter was held constant, while the
pulsing frequency was changed in increments from steady up to 40 Hz. At each
frequency, instantaneous velocity data were collected and the mean velocity
calculated.
5
4.5
4
>
3.5
3
2.5
0
I
5
10
I
I
20
15
25
I
30
35
I
40
f(Hz)
Figure 7.7: Mean velocity magnitude as a function of pulsing
frequency for the low jet flow case (Vjet= 3.4 mIs)
13
12
>:
.7
0
5
10
20
15
25
30
35
40
f(Hz)
Figure 7.8: Mean velocity as a function of pulsing frequency
for the high jet flow case
= 13.6 mIs)
(Vjet
50
From these results it is clear that the mean velocity is nearly independent
of frequency in the range of 3-25 Hz, but that an increase in total mean velocity
magnitude is apparent as pulsing frequency increases beyond 25 Hz. The spike
near f = 0 Hz is of course the mean velocity when no pulsing is present and when
100% of the supplied air exits through the jet opening, instead of the 50% as in
the pulsed case. More discussion about this frequency dependency at higher
pulsing frequencies is discussed in the next section.
7.2.3
Pulsed jet time trace
A pulsed jet time trace was generated from data gathered at the center of
the jet exit (x = 7mm). Pulsed and non-pulsed traces are compared for low and
high jet flow settings and presented in Figures 7.9 through 7.16. Data for the
pulsed cases are plotted with variable time scales, such that for each pulsing
frequency the same number of pulse periods are shown.
Figures 7.9 through 7.12 represent time traces at a low jet flow setting for
pulsing frequencies of 0, 2, 20 and 40 Hz, respectively. For the pulsed case, the
square-wave like velocity trace are most distinct at low pulsing frequency and
become increasingly disordered as pulsing frequency is increased. Moving up in
pulsing frequencies to 20 Hz and 40 Hz, see Figures 7.11 and 7.12, the pulse
becomes less defined and is influenced by the jet turbulence as the pulse time
51
scale approaches the jet turbulence time scales. Comparing the 40 Hz case, Figure
7.12, with a similar scale but steady case, Figure 7.9, reveals identical small-scale
fluctuations. Similar trends are seen at the higher velocity setting and results are
presented in Figures 7.13 through 7.16.
Another interesting observation can be made that is apparent both at low
and high jet flow settings. Theoretically, the valve shuts completely during the
'off' cycle and no flow is expected to exit the jet, which should result in a zero
velocity. However, one can see in the figures that as jet pulsing frequency
increases, the velocity does not return back to 0 rn/s completely. This effect is
more noticeable at higher pulsing frequencies and is attributed to the inertia of the
valve. Simply stated, the valve does not have enough time to fully close, before
the next 'on' period is initiated. The increase in mean velocity at higher pulsing
frequencies as was indicated in Figures 7.7 and 7.8 is a result of this phenomenon.
52
12
10
V (m/s)
8
6
4
0.12
0.11
0.1
0.13
0.15
0.14
0.16
0.17
0.18
0.19
Time (sec)
Figure 7.9: Time trace at low flow setting for 0 Hz
pulsing frequency
Vt (mis)
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Time (sec)
Figure 7.10: Time trace at low flow setting for 2 Hz
pulsing frequency
0.2
53
12
10
8
Vt (mis)
6
4
2
0.1
0.12
0.14
0.16
0.18
0.22
0.2
0.24
0.26
0.28
0.3
Time (sec)
Figure 7.11: Time trace at low flow setting for 20 Hz
pulsing frequency
8
6
V (m/s)
4
2
0
0.1
U.11
U.1
U.1j
0.14
0Th
0Th
0.11
0.1
0.1w
O.
Time (sec)
Figure 7.12: Time trace at low flow setting for 40 Hz
pulsing frequency
54
25
20
Vt (m/s)
15
10
5
0.1
I_i. I
V.0
1.1. IL
I
V. I'+
V.0
V. IV
V.
U. IU
ti. Ii
Time (sec)
Figure 7.13: Time trace at high flow setting for 0 Hz
pulsing frequency
30
25
20
V (mis)
15
10
5
0
U.4
O.I
U.
1
12
1.4
1.0
1.0
Time (sec)
Figure 7.14: Time trace at high flow setting for 2 Hz
pulsing frequency
'.i..
55
25
20
V (m/s) 15
10
5'
0
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
0.3
Time (sec)
Figure 7.15: Time trace at high flow setting for 20 Hz
pulsing frequency
20
15
V (mis)
10
5
0 L_L_
0.09
0.1
I
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
Time (sec)
Figure 7.16: Time trace at high flow setting for 40 Hz
pulsing frequency
7.2.4 Jet trajectory
Mean velocity profiles in the x-direction for low and high jet flow settings,
as well as pulsed versus non-pulsed operation, are presented in Figures 7.17
through 7.20. Instantaneous velocity data were collected at each grid point
according to the pattern given for grid A, see Figure 5.2. Comparing velocity
profile maxima for all four figures it appears that the jet trajectory is not
significantly altered by the varying jet flow rate, nor does jet pulsing seem to have
an effect on the trajectory. The exit angle remains roughly 35 degrees with the flat
plate.
The effect of pulsing on the velocity profile is most noticeable near the
profile's maximum. As can be seen by comparing Figures 7.18 and 7.20 to
Figures 7.17 and 7.19, respectively, pulsing the jet results in a sharp decrease in
the velocity maximum, while the remainder of the velocity profile remains
relatively unchanged.
57
x=l5mm
x35mm
x=25mm
301
x=45mm
30
25
25
25L-.
25
20
20
20
20
/
\
/
I
15
15
10
10
-
15I----
15
10
10
H
/
/
5
5
5
/
/
00
2
4
00
U (mis)
I
2
00
U (m/s)
2
4
00
2
U (m/s)
4
U (m/s)
Figure 7.17: U-velocity profiles for the low flow, non-pulsed case
xl5mm
x25mm
x45mm
x=35mm
30
30
30
30
25
25
25
25
20H
20
20
20
15
l5
15
10
10
5
5
5i
10
-4
I
0
0
/
__ J
2
U (m/s)
/
5
40
0
2
U (m/s)
40
0
2
U (m/s)
40
0
2
4
U (m/s)
Figure 7.18: U-velocity profiles for the low flow, pulsed case
x25mm
x=l5mm
x45mm
x=35mm
30f
30
30
30
25
25
25
25
20
20
20
15
15
H
__I
15
/
\
10
-
/
10
10
/
/
5
5
/
5
/
5
1
/
0__
00
U (mis)
i
00
ib
U (m/s)
00
U (m/s)
5
10
U (m/s)
Figure 7.19: U-velocity profiles for the high flow, non-pulsed case
x15mm
>.
x25mm
x=35mm
x=45mm
30
30
3Q.
30
25
25
25
25.
20
20
20
20
15
15
15
15
10
10
10
10
I
\
5
00
--
5
10
U (m/s)
-
5
00
.
5
5
10
U (m/s)
00
5
10
5
U (m/s)
00
5
10
U (m/s)
Figure 7.20: U-velocity profiles for the high flow, pulsed case
59
7.2.5 Jet turbulence characteristics in the near field of the jet
The effect of jet pulsing and changes in the jet velocity on the RMS values
(mis) in the downstream region of the jet are presented in Figures 7.21 through
7.24 for the x-direction velocity magnitude. In both jet velocity cases jet pulsing
increases the overall turbulence throughout the near field. At
Vjet
= 3.4 mIs,
pulsing increases the RMS values near the jet exit at x/d = 1.5 and yld = 0.5 by
53%. For the
Vjet
= 13.6 mIs this increase at the same location is 81%. The higher
velocity jet, in general, generates more turbulence than the lower velocity jet. The
turbulence levels in terms of RMS for the
Vjet
= 13.6 mIs case at x/d = 1.5 and y/d
= 0.5 are 120% higher than that in the Vjet = 3.4 mIs case. As can be seen from all
four figures, the RMS values tend to diminish gradually as the jet flow moves in
the downstream direction, with the highest values close to the jet exit. In addition
the majority of the turbulence tends to be concentrated near the centerline of the
jet and seems to decay towards the jet boundary.
E
E
/.
15
20
25
30
35
40
45
x (mm)
Figure 7.21: RMS (mis) of instantaneous velocity magnitude,
Vjet = 3.4 mIs, no pulsing
-
25
E
E
//
/
5
15
1.
20
25
30
35
40
4
x(mm)
Figure 7.22: RMS (mis) of instantaneous velocity magnitude,
Vjet = 3.4 mis, 20 Hz pulsing
E
E
>.
20
25
30
x (mm)
35
40
45
Figure 7.23: RMS (mis) of instantaneous velocity magnitude,
= 13.6 mIs, no pulsing
Vjet
2
E
E
N
5
LI
15
20
25
30
35
40
45
x (mm)
Figure 7.24: RMS (mis) of instantaneous velocity magnitude,
= 13.6 mIs, 20 Hz pulsing
Vjet
62
7.2.6 Jet turbulence characteristics at the jet exit
The effect of pulsing frequency on the turbulence levels was also
investigated. From Figures 7.21 through 7.24 presented in the previous section it
is obvious that pulsing increased the RMS values throughout the flow field, but it
is
unclear what the frequency dependency of the turbulence levels is.
Measurements were taken close to the jet exit at x = 7 mm and y = 2 mm, while
the pulsing frequency was adjusted from 0 to 40 Hz. The results in terms of RMS
values in the x-direction are presented in Figures 7.25 and 7.26. For both jet
velocity cases an increase in pulsing frequency has a negative effect on the
generation of turbulence near the jet exit. The RMS values in both cases were
highest at the lowest pulsing frequency of 2 Hz. As pulsing frequency was
increased the lower jet velocity case showed a sharper decrease in RMS values
than the high jet velocity case.
63
2.6
2.6
2.4
2.2
0)
1.8
1.6
14
5
10
15
20
25
30
35
40
f(Hz)
Figure 7.25: U-component RMS at variable frequencies, low jet flow rate
7r
6.5
6
C))
4.5
4/
3.5
f(Hz)
Figure 7.26: U-component RMS at variable frequencies, high jet flow rate
7.3 - CASE I, PITCHED CYLINDER IN CROSS FLOW
Results of the pitched cylinder in a 4 mIs cross flow are presented in this
section. Hot film data were gathered, using grid B, at a z/d location of 0.8. Data
presented include velocity profiles, root mean squared value of the velocity
fluctuations in both x and y-directions, Reynolds stresses and the mean vorticity.
The cross flow velocity was maintained at 4 m/s and the Reynolds number based
on the cross flow velocity and cylinder diameter was Re = 2650.
The general flow characteristics can be easily identified by the mean
velocity plots presented in Figures 7.27a and 7.27b. Figure 7.27a combines the
velocity magnitude in the x-direction with velocity vector plots. A significant
acceleration in the x-direction can be seen around the perimeter of the cylinder.
For easy reference, the location of the cylinder's front and back side are indicated
by white dotted lines and, in combination with the velocity data, clearly show a
maximum in velocity half way around the cylinder circumference. This
acceleration is most obvious far from the flat plate and tends to be damped by the
boundary layer close to the flat plate. Streaks of high u-component velocity are
also apparent in the wake and can be seen at y/d locations of 1.0 and 3.0 and
might be caused by accelerations within the cylinder's wake.
The velocity vectors in the same figure indicate a downward motion of the
flow as it is accelerated around the cylinder. This is attributed to the decrease in
pressure behind the cylinder as a result of the cylinder's wake.
a) Mean velocity, U-component (mIs)
I- -. -* -
0
0
5
10
b) Mean velocity, V-component (mIs)
4
-0.2
35
0L__________________
0
2.5
10
5
xld
-04
-0.8
x/d
RMS, U-component (mIs)
C)
0.2
0
:
0.8
d)
RMS, V-component (m/s)
0.8
0.6
e)
Reynolds stresses.
0
0
f)
(m2/s2)
Mean vorticity (1/sec)
-
5
10
0
0
xld
5
10
-015
x/d
Figure 7.27: Pitched cylinder in a cross flow
U,
The downward motion can also be seen in Figure 7.27b, where the velocity
magnitude in the y-direction is plotted on a separate scale.
The root-mean-squared values of the fluctuating velocities are presented in
Figures 7.27c and 7.27d. They give interesting insight into the amount and
location of turbulence present in the wake of the cylinder. Figure 7.27c shows a
turbulent spot, in terms of the RMS value in the x-direction velocity component,
downstream of the cylinder and extending parallel behind the cylinder from y/d =
1 to y/d = 4, with a peak value at x/d = 4.5 and y/d = 1.5. Figure 7.27d shows a
similar spot, however the location is not identical to the one for the x-direction
velocity component and instead is skewed relative to the cylinder. The maximum
in RMS value in the y-direction velocity component is found at x/d = 6.5 and y/d
= 3.0. It is interesting to note that the maximum magnitude of the RMS value is
greater in the y-direction than in the x-direction velocity component, while the
mean velocity in the y-direction is only a fraction of the mean in the x-direction.
Figure 7.27e shows the Reynolds stresses that were calculated from the
instantaneous velocity data obtained with the hot film. A region of high positive
Reynolds stress is present in the wake of the cylinder at the same location as the
turbulent spots identified in Figure 7.27c. These positive stresses redistribute
momentum from the outer flow towards the wall boundary layer.
The mean vorticity throughout the flow field remains relatively unchanged
as can be seen in Figure 7.27f. A band of negative vorticity occurs close to the flat
67
plate, where the fluid experiences a positive velocity gradient within the wall
boundary layer.
The turbulent area that was identified behind the cylinder is further
analyzed in Chapter 9, where additional spectral information, time traces and
histograms are used to quantify the flow in more detail.
7.4 - CASE II, STEADY JET IN CROSS FLOW
In this section results from the steady jet in a cross flow are presented. The
cross flow velocity throughout these experiments was maintained at 4 mIs, while
the jet velocity ratio was set to 0.85 and 3.4. The Reynolds numbers for both jet
velocity cases were 2260 and 8930, respectively. Data for both velocity ratios
were collected using grid B, see Figure 5.3, for z/d locations of 0 and 0.8.
7.4.1 Velocity ratio of 0.85, at centerline at zld = 0
Figures 7.28a and 7.28b show the mean velocity profiles generated from
data taken through the jet symmetry plane (z/d = 0) for a velocity ratio of 0.85.
a)
4---- -,.
b)
Mean velocity, U-component (mIs)
--i- --
-- .-. -,..
- -. --p- ---
,-
,_. -- ---
>. 2
-
-.--
1
_-_
--. - - ---.
-- -
->
3.5
o
> 2
RMS, U-component (mis)
1.4
1.2
--- ---k,
0.5
.__ _
o'
2.5
c)
Mean velocity. V-component (mis)
4
-.
.-
d)
RMS. V-component (m/s)
1
1
0.8
0.6
0.8
0.6
468
I
xid
Reynolds stresses, (m21s2)
1.4
1.2
10.2
Mean vorticity (1/sec)
0
u
-0.5
0
8.
I
0
2
4
x/d
6
2
0
0
-0 1
0
2
4
x/d
Figure 7.28: Steady jet in a cross flow, VRO.85, z/d = 0
6
8
The jet column can be seen penetrating through the cross flow boundary layer into
the mainstream were the jet momentum is quickly distributed and the jet can
hardly be identified. The jet column width within the first few diameters of
exiting is about one diameter, after which it spreads into the cross flow and is
difficult to distinguish. Both the jet spread and the jet penetration are hard to
identify using the mean velocity plots.
The vector plot in Figure 7.28a also shows an interesting downward
velocity component at the jet leading edge. This negative velocity can be
attributed to a combination of induced downward velocity by the horseshoe
vortex and a roll up of jet leading edge vorticity as described in Haven et a111
RMS fluctuations in both x and y-direction velocity components are
presented in Figures 7.28c and 7.28d, respectively. The RMS value near the jet
exit in the x-direction velocity component plot is 1.4 mIs, and are of the same
order of magnitude as the no-cross flow results presented in section 7.2.6, where
the RMS value of the fluctuating velocity magnitude in the x-direction at similar
jet flow settings was approximately 2.1 mIs. The decay of the turbulence in term
of the RMS values seems to be influenced by the cross flow, resulting in a
'smearing' of the RMS values in the streamwise direction as observed in Figures
7.28c and 7.28d. Also, higher RMS values are present near the wall as, in the
presence of the cross flow, the jet flow is 'pushed' down towards the cross flow
wall.
70
The RMS values in both x and y-direction tend to gradually decay as the
turbulence within the jet column decreases in scale and merges with the cross
flow turbulence levels. There is no indication of secondary turbulent structures
like those described in the solid cylinder case.
Reynolds stress profiles are plotted in Figure 7.28e, where the largest
negative Reynolds stresses appear close to the jet exit. Reynolds stresses seem to
decay quite rapidly and decay to 25% of its original value within the first diameter
or so. The Reynolds stresses are negative in sign and seem to align
with the
general direction of the jet flow.
Two counter rotating vorticity regions can be identified in Figure 7.28f.
Negative values of vorticity behind the jet represent a clockwise rotation, while
positive values inside the jet represent counter clockwise rotation. As the shear
layer in the jet exits into the boundary layer it slowly decays into the cross flow.
The shear is most noticeable at the trailing and leading edges of the jet exit where
the velocity gradients are greatest. As velocity decays in the jet and the jet
velocity profile is smeared out, the vorticity decays in the downstream direction.
If the shear layer on each side of the jet is taken as a representation of the jet
boundary, then it can be seen that the jet hardly lifts off from the wall. The lower
side of the jet column tends to lift no further than 1 jet diameter away from the
wall.
71
7.4.2 Velocity ratio of 3.4, at centerline at zid = 0
Mean velocity magnitudes are again plotted in combination with a total
velocity vector plot for a velocity ratio of 3.4. Figure 7.29a shows the mean u-
component velocity, and here it is easier to establish a jet trajectory and
penetration compared to the VR = 0.85 case. The same trend is clear from the v-
component velocity magnitudes plotted in Figure 7.29b. Note that a different
scale is used.
RMS fluctuations for both u and v velocity components are presented in
Figures 7.29c and 7.29d, respectively. The RMS values of both components have
increased in the near region of the jet up to 100% compared to the values at VR =
0.85. The RMS values in the YR = 0.85 case near the cross flow wall for x/d = 0,
0.5 and 1.5 were 0.45, 1.01 and 0.58 mIs respectively, while the case YR = 3.4
produced RMS values of 0.42, 3.61 and 2.45 mIs, respectively.
It is interesting to note that the RMS values near the center of the jet exit
are quite similar for both the no-cross flow and the cross flow cases. As
mentioned before the RMS value of the u-component of velocity at xld = 0.5 and
0.2 was 3.61 mIs, while the no cross flow case at similar jet flow settings was on
the order of 3.5 mIs.
a) Mean velocity. U-component (mis)
10
8
6
o
0
5
10
4
xld
c)
RMS. U-component (mis)
e)
Reynolds stresses, (m2/s2)
0
d)
RMS, V-component (mis)
f)
Mean vorticity (1/see)
08
10
02
xd
Figure 7.29: Steady jet in a cross flow, VR3.4, z/d = 0
-I
73
Reynolds stresses are presented in Figure 7.29e and show a considerably
larger negative stress near the jet exit than for the low velocity ratio case.
Reynolds stresses at x/d = 0.5, y/d = 0.2 for VR = 3.4 have decreased in
magnitude are 5.43
m2/s2
compared to 0.82 m2/s2 for VR = 0.85.
Comparing the mean vorticity for both velocity ratio cases, Figures 7.28f
and 7.29f shows an increase in vorticity throughout the near field for the VR = 3.4
case. The increase is most obvious near the jet leading and trailing edges where
the increase in jet exit velocity generates greater shear resulting in higher
vorticity. It is obvious that the jet penetration and lift off based on the mean
vorticity is greater than the VR = 0.85 case, however the lower boundary of the jet
is less defined. The negative vorticity at the lower side of the jet appeares to have
been smeared out over the entire near field region, and no real jet shear layer can
be identified.
7.4.3
Velocity ratio of 0.85, off-center at zld = 0.8
The hot film measurements presented in this section were made at z/d =
0.8, which is 8 mm away from the symmetry plane and similar to the location
used in the inclined cylinder test.
Figure 7.30a shows the velocity magnitudes of the u velocity component,
while the v velocity component is plotted using a different scale in Figure 7.30b.
a) Mean velocity, U-component (mIs)
4
b) Mean velocity. V-component (mIs)
0
4
_____________________________
-.
3.5
-0.2
0
0
5
0
10
-0.3
0
5
xfd
x/d
RMS, U-component (m/s)
C)
0.4
4
0
d)
RMS, V-component (m/s)
0.3
0.3
0.2
0.2
01
0
5
Reynolds stresses,
-04
0.4
4
--
-
01
10
0
5
xld
a)
10
1
01
10
x/d
1)
(m21s2)
Mean vorticity (1/sec)
0
0.04
'Figure 7.30: Steady jet in a cross flow, VRO.85, z/d = 0.8
-0.05
75
Figure 7.30a looks similar to a normal wall boundary layer flow, apart
from the flow interruption near the jet exit at x/d = 1 to 4, where an acceleration
of flow is apparent. This high velocity region might be caused by acceleration of
fluid around the jet column similar to the pitched rod case, or might be partially
due to the entrainment of the cross flow into the jet flow. A downward flow is
also apparent from the plots in Figure 7.30b, where the velocity magnitude in the
y-direction is plotted using a separate scale. The region of negative velocity is
located at x/d = 2.0 and y/d = 0.2. The downward flow may be caused by a realignment of entrained cross flow fluid sweeping around the perimeter of the jet
and bending over as the jet fluid is pushed down towards the wall by the cross
flow. A slight positive y-direction velocity is also apparent at xld = 0.5 and y/d =
1.
Figures 7.30c and 7.30d show the RMS fluctuations in the x and ydirection velocity components, respectively, and are plotted using the same scale.
Although the highest values of RMS are concentrated near the wall for the xdirection velocity, in Figure 7.30c, an extension of this wall turbulence away from
the wall is found at xld = 2.5 and y/d = 1. The highest value of RMS occurs at the
jet exit, at x/d = 0, y/d = 0.2 where the values of RMS are 0.44 m/s. A similar
region of high turbulence is seen in the v-component RMS plot, see Figure 7.30d,
where the maximum value of RMS is located at x/d = 2.5 and y/d = 0.5.
Reynolds stresses are plotted in Figure 7.30e and show that most of the
Reynolds stresses are located within 1 jet diameter of the wall boundary. The peak
76
Reynolds stress can be found at xld = 1.5 and y/d = 0.2 where it reaches 0.0542
m2/s2. The positive stress again tends to drive momentum down into the near wall
region, which might be an explanation for the slight negative down flow observed
in Figure 7.30b.
The mean vorticity is plotted in Figure 7.30f and is similar to the vorticity
plots in the pitched cylinder case (Figure 7.271). Vorticity is located close to the
wall within the wall boundary layer where the shear is greatest. The vorticity at
x/d = 1.5 and y/d = 0.2 almost reaches values of that in the free stream and might
be due to the acceleration near the wall, as noted in Figures 7.30a and 7.30b, at
that particular location.
7.4.4 Velocity ratio of 3.4, off-center at zld = 0.8
Figure 7.31a presents the velocity magnitude in the x-direction as well as
the velocity vectors throughout the grid. This higher velocity ratio case shows
quite a different velocity distribution compared to the VR = 0.85 case at z/d = 0.8.
a) Mean velocity, U-component (mIs)
0
0
c)
5
x/d
b) Mean velocity. V-component (mis)
0-
10
0
5
xfd
1.2
RMS, U-component (mis)
d)
10 O.6
1.2
RMS, V-component (m/s)
0.8
2
06
2
06
0
0.4
0.2
0
0.4
0.2
0
5
10
x/d
e)
Reynolds stresses,
0
5
10
x/d
f)
(m2/s2)
Mean vorticity (1/sec)
:
Figure 7.31: Steady jet in across flow, VR3.4, z/dO.8
-1
An acceleration of cross flow fluid is seen throughout the region and is
most apparent near the jet column, where the jet column was identified in Figure
7.29 for the same velocity ratio, but at z/d = 0. This acceleration is again
attributed to two potential phenomena. The first being the entrainment of the cross
flow fluid in the jet fluid and the second being the acceleration of the cross flow
fluid around the jet column which is better defined in this case, at VR = 3.4, than
for VR = 0.85.
The acceleration in the u component of velocity is accompanied by a
strong negative velocity in the y-direction as is apparent from the v-velocity
magnitude plot in Figure 7.31b. Note that Figure 7.31b has a different scale than
Figure 7.31a. A region of negative v velocity can be identified again around xld =
1 to 2 and y/d
0.2 to 0.5, but is stronger than the VR 0.85 case. The maximum
negative y-direction velocity in this case is 0.7339 mIs compared to 0.4288 mIs
for the YR = 0.85 case. Unlike the YR = 0.85 case, no positive velocity in the v
velocity component can be seen in the upstream area, but instead a positive v
velocity component can be found further downstream between x/d = 4.5 and 10.5
and y/d = 1.5 and 3.5.
Figures 7.31c and 7.3 Id clearly show the influence of the jet turbulence at
zld = 0.8. RMS fluctuations in both x and y-direction velocities look similar in
topology, but the magnitudes of RMS reach higher values in the x-direction than
in the y-direction. The highest RMS value found for the u-component is 1.23 mIs,
while the highest value for the v-component is 0.91 mIs. Both are located at about
79
x/d = 2.5 and y/d = 1. The general distribution of the RMS values tends to be in
agreement with the distribution of the velocity magnitudes seen in Figure 7.31a.
Large Reynolds stresses in the VR = 3.4 case, noted in Figure 7.31e, can
be identified further downstream in the jet flow compared to the YR = 0.85 case.
The maximum is now found at x/d = 3.5 and y/d = 1.5 and reaches a value of
0.5196 m2/s2. It is interesting to note that the Reynolds stresses have increased
by about ten times and are negative in sign, transporting momentum up from the
boundary layer into the cross flow. The magnitude of Reynolds stresses close to
the jet exit are in fact very similar to the YR = 0.85 case, but appear nullified
because of the increased Reynolds stresses downstream. In fact the Reynolds
stresses close to the jet are still positive and equal in magnitude and comparable to
the values at VR = 0.85.
In contrast with the steady YR = 0.85 case a streak of positive vorticity, as
depicted in Figure 7.3 if, can be found for the pulsed case with the same order of
magnitude as the vorticity in the wall boundary layer, but opposite in sign. The
vorticity upstream of the jet from x/d = 0.5 to 0.5 remains relatively unchanged
compared to the YR = 0.85 case, while the vorticity downstream of x/d
0.5 is
significantly different, where an acceleration of the fluid near the wall can cause
shear, and thus vorticity, to increase significantly. This increase in near wall
vorticity peaks at x/d = 3.5. The influence of the jet has an equal but opposite
effect on the cross flow above the jet column as can be seen by the streak of
positive vorticity.
7.5 - CASE III, PULSED JET IN CROSS FLOW
Pulsed jet experiments within a cross flow will be presented in this
section. The cross flow velocity throughout these experiments was again
maintained at 4 mIs, while the jet velocity ratio was set to 0.85 and 3.4. The
pulsing frequency was maintained at 20 Hz, which resulted in forced Strouhal
numbers of 0.058 and 0.015 for the low and high velocity ratios, respectively.
Data collected in the symmetry plane will be presented first, followed by the data
collected at z/d
0.8. For each location data are presented for both velocity ratio
cases.
7.5.1
Velocity ratio of 0.85, at centerline at z/d = 0
The velocity magnitudes in both x and y-directions are plotted in Figures
7.32a and 7.32b, respectively. It is clear that the distribution of velocity does not
change very much but the magnitudes are clearly different from the steady case
presented in Figure 7.28. The velocity magnitude near the jet exit at x/d = 0.5 and
y/d = 0.2 is 3.85 mIs compared to 4.45 m/s in the non-pulsed case. This is due to
the fact that during pulsing half of the mass flow is vented into the atmosphere
and thus causing the average jet flow rate through the jet to be twice as small.
a)
b)
Mean velocity, U-component (mis)
4
Mean velocity, V-component (mIs)
4
35
0
c)
e)
2
4
6
8
o10
125
d)
RMS, U-component (mis)
06
1 0.4
0.2
- __
2
4
6
8
0
I
RMS, V-component (mis)
I
p
io.
jO.5
1)
Reynolds stresses, (m2/s2)
0
I
-0.5
Mean vorticity (1/sec)
4
2
xid
Figure 7.32: Pulsed jet in a cross flow, VRO.85, z/d = 0
o1
0
It is worth mentioning that although the mass flow through the jet is
theoretically half that of a steady jet, the average velocity at the jet exit only
changes from 4.45 to 3.85 mIs, which is only a decrease of 13.5%. It is believed
that this slight variation is caused by the presence of the cross flow during the jet
off cycle as jet without cross flow experiments indicated that the mean velocity
magnitude in the x-direction for the pulsed case at
Vjet
= 3.4 mIs decreased about
40% compared to the non-pulsed case. This effect of the cross flow should be less
apparent in the y-direction as the cross flow in predominantly in the x-direction.
Figure 7.32b shows that the y direction velocity component in the pulsed case at
x/d =1.5, y/d
0.2 indeed settles to about 45% of the mean velocity during steady
operating, which is closer to the 50% reduction seen in no cross flow experiments.
RMS quantities are again plotted in Figures 7.32c and 7.32d for both u and
v velocity component, respectively, using the same scales. RMS values of the u
component are slightly higher in the pulsed case than in the non-pulsed case,
which is consistent with the results without cross flow described in section 7.2.6.
The turbulence generated at the jet exit at x/d = 0.5 and y/d
0.2 changes from
1.43 mIs in the steady case to 1.60 mIs in the pulsed case, which is an increase of
11.6%. The distribution of turbulence seems to be similar to the steady case and is
deflected quickly and distributed over the cross flow wall as the jet exits into the
cross flow.
Unlike the larger RMS values of velocity in the x-direction due to pulsing,
the y-direction velocity component RMS at the jet exit is 3% smaller in the pulsed
case compared with the steady case presented in Figure 7.28. The RMS value at
the jet exit at x/d = 0.5 and y/d = 0.2 for the pulsed case is 0.97 mIs while for the
unforced case the RMS values reach no higher than 0.94 mIs. The decay of
turbulence on the other hand is quite different and both figures show that for the
unforced case the y-direction velocity RMS decays less rapidly with x/d than the
forced case.
A 20% increase in negative Reynolds stress over that in the non pulsed
case is seen near the jet exit, but the decay is as rapid as in the unforced case. Free
stream Reynolds stress levels are attained within one jet diameter (see Figure
7. 32e).
Figure 7.32f shows the mean vorticity for the forced case, where it seems
that the decrease in average jet velocity in the pulsed case results in a near 50%
decrease in mean vorticity near the jet's leading edge compared with the non
pulsed case.
7.5.2 Velocity ratio of 3.4, at centerline at z/d = 0
As was the case for the pulse/no-pulse comparison for VR = 0.85, the
difference between pulsing and non-pulsing for VR = 3.4 is apparent from the
velocity magnitudes and not the jet trajectory, see Figures 7.33a and 7.33b. The
jet in the pulsed case lifts off similarly to the un-forced case (Figure 7.29) and
a)
b) Mean velocity, V-component (mis)
Mean velocity, U-component (m/s)
U
o
5
JO.5
10
0
x/d
c)
d)
RMS, U-component (mIs)
2
,2
10
Reynolds stresses, (m21s2)
2
0
x/d
e)
RMS, V-component (m/s)
4
3
5
10
x/d
4
0
5
5
10
xId
0
f)
Mean vorticity (1/sec)
0xd10
Figure 7.33: Pulsed jet in a cross flow, VR3.4, z/d = 0
0.4
reaches a height of 20 mm at an xld value of 5.5. The height of the jet is based on
the maximum u velocity.
The mean velocity in the x-direction at the jet exit, where x/d = 1.5, was
measured to be 10.34 mIs in the non-pulsed case and dropped 38%, to a velocity
of 6.42 mIs, in the pulsed case. Compared with the no-cross flow pulsed jet case
in Figure 7.20 a drop of 46% was apparent.
As seen in Figure 7.33b, compared with Figure 7.29b, the drop in ydirection mean velocity is more significant and decreased roughly 45% from 4.00
mis to 1.82 m/s at x/d = 1.5, y/d = 0.2 in the pulsed case.
The effect of pulsing on turbulence levels is larger than for the VR = 0.85
case. The RMS values of velocity for pulsing at VR = 3.4 near the jet exit at x/d =
1.5 are 3.68 m/s compared to 2.52 rn/s in the non-pulsed case, which is an
increase of 46%. The increase, however, is largest near the jet exit and less
apparent in the near field. If it is assumed that the highest turbulence intensity,
represented by RMS values, is located along the centerline of the jet, than it is
apparent again from Figure 7.33c that the jet clearly lifts off the surface and high
levels of turbulence stay well clear of the wall in the far field.
Studying the v component RMS values in Figure 7.33d more closely, it is
clear that the location for maximum RMS is shifted from x/d = 0.5 in the nonpulsed case to xld = 1.5 in the pulsed case. Both maximums are, however, located
close to the wall at y/d = 0.2. Similar to the comparison of the pulsed and non
pulsed cases for VR = 0.85, the pulsed case at VR = 3.4 results in a more rapid
decay of RMS values while Figure 7.33d also shows a concentration of higher
RMS values within the first diameter of the jet as compared to the non pulsed
case.
Reynolds stresses are again plotted in Figure 7.33e and show a significant
increase in negative stress near the jet exit. Not only did the maximum Reynolds
stress increase from a value of 6.63
m2/s2
in the non pulsed case to 7.01
m2/s2
in the pulsed case, the distribution of stresses also shifted in the x direction and
are more strongly concentrated over the trailing edge of the jet. The increase in
Reynolds stress is attributed to the increase in turbulence generated by the valve
pulsing.
Finally, the mean vorticity is plotted for the pulsed case in Figure 7.33f
and shows similarities with the comparison made in the VR = 0.85 case. The
vorticity at the leading edge is less strongly defined and has decreased more than
50% compared to the non-pulsing case. Again this is attributed to the decrease in
average jet velocity, resulting is less average shear between the jet fluid and the
cross flow, resulting in a lower mean vorticity.
7.5.3 Velocity ratio of 0.85, off-center at z/d = 0.8
The influence of pulsing is much less apparent out away from the
symmetry plane of the jet where z/d = 0.8. The change in u-direction velocity
magnitude in Figure 7.34a is noticeable close to the jet at x/d = 1.5 where the
acceleration of the fluid does not extend down to the wall as much as in the Unpulsed case. The down flow that was identified in the un-pulsed case is also much
less intense and decreased from 0.43 m/s in the un-pulsed case, see Figure 7.30,
at x/d = 1.5 and y/d = 0.2 to 0.20 rn/s in the pulsed case, as can be seen from the
velocity vector plot in Figure 7.34a and from the v velocity plot in Figure 7.34b.
The RMS velocity fluctuations in both x and y directions are plotted with
similar scales in Figures 7.34c and 7.34d. Comparing the pulsed case with the
steady case in Figure 7.30, a small decrease in RMS values for the x-direction of
velocity is apparent near the jet exit. A decrease is also found in the y-direction
component of velocity where the maximum RMS value decreases by 17%
compared to the steady case, from 0.31 rn/s to 0.26 mIs.
Reynolds stresses provided in Figure 7.34e, on the other hand, are
increased as pulsing is applied. An increase of Reynolds stress of as much as 39%
is found at x/d = 1.5 and y/d = 0.2. Apart from the increase near the trailing edge
of the jet the general topology, in terms of the Reynolds stress distribution,
remains unchanged. The least change, between pulsed and non pulsed cases, is
observed in the mean vorticity plot provided in Figure 7.34f.
The cross flow vorticity that was found protruding close to the wall in the
un-pulsed case at x/d = 1.5, y/d = 0.2 is absent in the pulsed case.
a) Mean velocity, U-component (mis)
4
b) Mean velocity, V-component (mis)
-0.1
o
C)
RMS, U-component (mis)
0.4
4
e)
4
Reynolds stresses,
d)
RMS, V-component (m/s)
f)
(m2/s2)
0.06
0.4
4
0
Mean vorticity (1/sec)
4
0.04
0
002
0
5
xid
10
0
-0.05
0
0
5
xid
Figure 7.34: Pulsed jet in a cross flow, VRO.85, z/d = 0.8
10
-0.1
7.5.4 Velocity ratio of 3.4, off-center at z/d
0.8
While the differences in terms of magnitudes are greater between non
pulsing and pulsing cases at a velocity ratio VR = 3.4, overall trends remain
similar to the VR = 0.85 no-pulsed/pulsed cases. Figure 7.35a shows a decrease in
u-direction mean velocity relative to the steady case, which could be attributed to
a combination of less cross flow being entrained by the jet and a lesser defined jet
column which results in less cross flow fluid being accelerated around the jets
perimeter. Velocity vectors in Figure 7.35a and velocity magnitudes Figure 7.3 Sb
show a weaker downward motion of fluid near the trailing edge of the jet and the
absence of the positive velocity that was apparent in the un-pulsed case between
x/d = 5.5 and 10.5 at y/d = 2.5.
Figures 7.35c and 7.35d show the RMS of velocity quantities in both the x
and y directions using the same scale. Comparing the pulsed case with the steady
case, the general topology of the turbulence in the pulsed case remains unchanged
in terms of its trajectory; however, the maximum RMS values in both u and v
velocity components have decreased significantly. Maximum RMS values in the
x-direction velocity have decreased 20% from 1.23 mIs to 0.99 mIs, while the
maximum RMS value in the y-direction velocity decreased 31% from 0.91 mIs to
0.63 mIs with the onset of pulsing.
The Reynolds stresses plotted in Figure 7.35e show an interesting change
in the two structures that were described earlier at xld = 1.5, yld = 0.2 and x/d
45
a) Mean velocity, U-component (mis)
b) Mean velocity, V-component (mis)
0
I
C)
d)
RMS, U-component (mis)
0.8
r
a)
RMS, V-component (m/s)
0.8
ti;
f)
Reynolds stresses, (m2/s2)
Mean vorticity (1/sec)
J
Figure 7.35: Pulsed jet in a cross flow, VR3.4, zid = 0.8
91
2.5-5.5, yld = 0.5-2.5 in Figure 7.31c. The spot with high positive Reynolds
stresses in the pulsed case has further decreased in magnitude and spread over a
larger area compared with the steady VR = 3.4, z/d = 0 case, while the area with
large negative Reynolds stress has decreased in intensity and spread.
The mean vorticity plot in Figure 7.35f shows a similar trend as the VR =
0.85 case, where the jet shear layer is less defined during pulsing compared to the
non pulsed case.
92
CHAPTER 8
CASE COMPARISON
All of the previously addressed cases are studied more closely in this
chapter. Mean velocity profiles, RMS fluctuations, Reynolds stresses and mean
vorticity profiles for all cases are plotted at x/d locations of 0, 1.5, 4.5 and 8.5
such that an accurate determination can be made as to how the different types of
jet flow influence the characteristics of the mean flow. The two different velocity
ratios as well as the non-pulsed/pulsed cases are compared with each other and to
the inclined cylinder case for a z/d location of 0.8. The cylinder case is omitted
from comparisons made at z/d = 0, simply because no inclined cylinder data could
be collected at that particular location. Mean velocity profiles are compared first,
followed by the RMS fluctuations, Reynolds stresses and finally mean vorticity.
8.1 - INFLUENCE OF VELOCITY RATIO AND PULSING FREQUENCY
ON X-DIRECTION MEAN VELOCITY
Mean velocity profiles at z/d = 0 are plotted for all cases in Figure 8.1 a
through 8.ld for various x/d values. Except for Figure 8.lb, which is plotted using
a velocity scale from 0 to 11 mIs, all scales are similar and range from 0 to 6 m/s.
4... 4.
a)
b)
x/d=O
xfdl.5
c)
4n
d)
x/d=4,5
4
x/d8.5
o VR=O.85i2OHz
-u--- VR=3.4/2OHz
VRO.85
-v- VR3.4
3.5
3.5
3.
2.5
3.5
3...
,> .................
3
3
2.5-
2.5
2.5
7
21.5
1.5
1.5
T
ITT
,'
1
1
1
o.:j/
0.:
a
Mean velocity, (mis)
...
1.5
o.:)
a
Mean velocity, (mis)
Mean velocity, (mis)
Figure 8.1: U velocity profiles at z/d = 0
a
'a
Mean velocity, (mis)
Figure 8.la shows the mean u component velocity profile at x/d = 0,
which coincides with the leading edge of the jet. Plots for the velocity ratio 0.85
are quite similar to the ones obtained within the boundary layer without jet flow
present see Figure 7.3. In Figure 8.la an increase of 20% in the u component of
velocity is apparent at y/d = 0.2, between VR = 0.85 and VR = 3.4. This
acceleration close to the wall may be attributed to the entrainment of the
surrounding fluid into the exiting jet.
Figures 8.lb through 8.ld all indicate that the VR = 3.4 non-pulsed case
yields the highest x-direction velocity, peaking at y/d = 0.5, 2 and 2.5 at locations
x/d = 1.5, 4.5 and 8.5, respectively. The next largest peak velocity is observed for
the pulsed jet at VR = 3.4 followed by both non-pulsed and pulsed cases of VR =
0.85. The mean velocity profiles at x/d = 4.5 and 8.5 for VR = 0.85 pulsed and
steady cases closely resemble the velocity profile found upstream of the jet at x/d
= 0 and make it difficult to establish a jet trajectory. The peak velocity of the YR
= 3.4 steady jet case, however, is defined up to x/d = 8.5 and seems to penetrate to
a height of y/d = 2.5. Pulsing does not seem to increase or decrease this
penetration and the peak velocity for the pulsed case at x/d = 8.5 remains at y/d =
2.5.
Similar velocity profiles are generated for the off-symmetry measurements
at zld = 0.8, and are shown in Figures 8.2a through 8.2d. The plots for z/d = 0.8
include the data gathered in the pitched cylinder case as a reference.
a)
---4
0
35
b)
xIdO
1?
L11
Cylinder
VRO.85120Hz
x/d1.5
i-
1
a-- VR3.4/2OHz
VRO.85
3.5
-v VR3.4
....,...
2.:
2.:-
2.:
1.5
1.5
2
1:
1:
I................. 4-............
0.5
0.5-
0.5
+7
3
0.:
-7/
0
I
0
I
4
5
Mean velocity, (mis)
I
4
5
Mean velocity, (m/s)
3
1
+
0
I
4
5
Mean velocity, (m/s)
3
Figure 8.2: U velocity profiles at zid = 0.8
0
3
4
5
Mean velocity, (m/s)
The mean velocity profiles are very similar to the ones at z/d = 0 in a sense
that velocity profiles for the VR = 0.85 case decrease to about 2.5 mIs near the
wall. The slight acceleration for the VR = 3.4 pulsed and steady cases is also
similar, but extends further into the cross flow where it starts deviating from the
VR = 0.85 case at y/d = 1.5. The results from the pitched cylinder indicate a
slightly lower mean velocity throughout the region and are probably caused by
slight wind tunnel speed variations between experiments.
Figure 8.2b indicates the same pattern of acceleration as described for
Figure 8.lb and is strongest for the VR = 3.4, non-pulsed case. This acceleration
is again attributed mainly to the jet column that spreads out into the cross flow
increasing the u component of velocity, and in a lesser sense, to the acceleration
of cross flow fluid around the jet perimeter. The velocity profile for the pitched
cylinder case indicates a quite different distribution. Here the peak in u-direction
velocity is attributed purely to the acceleration of fluid around the solid cylinder.
Figures 8.2c and 8.2d again show similar trends to the ones described in
the symmetry plane. The steady VR = 3.4 case results in the highest velocity
magnitude within the profile, followed by the pulsed VR = 3.4 case and the VR =
0.85 cases.
The u velocity profiles for the cylinder case do not seem to follow the
trends seen for the jet in cross flow cases.
97
8.2 - INFLUENCE OF VELOCITY RATIO AND PULSING FREQUENCY
ON RMS OF U VELOCITY COMPONENT
RMS values of the u velocity component are plotted in Figures 8.3a
through 8.3d for data collected in the z/d = 0 plane on a scale from 0 to 2 mIs,
with the exception of Figure 8.3b where a scale from 0 to 4 mIs is used. RMS
values at the leading edge of the jet, see Figure 8.3a, all coincide and no
significant difference is seen between test cases. At x/d
1.5, however, the RMS
values close to the wall in Figure 8.3b have increased by more than 100% for both
YR = 0.85 cases, more than 400% for the non-pulsed VR = 3.4 case and more
than 700% for the pulsed VR = 3.4 case when compared with xld = 0 RMS
values, shown in Figure 8.3a. Applying pulsing to the high velocity jet seems to
cause the most observable increase in RMS values within the first few diameters
of the jet exit.
According to the RMS maxima in Figure 8.3c and 8.3d, the YR = 3.4 case
causes a higher penetration of turbulence into the cross flow than the YR = 0.85
case at x/d = 4.5 and xld = 8.5, while there is no apparent difference in penetration
between non pulsed and pulsed cases for both velocity ratios.
The influence of the different test cases on the RMS values at z/d = 0.8 is
presented in Figures 8.4a through 8.4d. Similar scales are used for easy
comparison. The upstream u component RMS values at x/d = 0 are similar to the
zld = 0 case and are all smaller than 0.5 m/s near the wall.
a)
b)
x/d=O
c)
xIdl.5
4
4
d)
x/d4.5
4 r
xd=8.5
4
r
VR=3.4I2OHz
VRO.85
3.5
3.5
35
35
3
3
3
3
25
2.5
2.5
2.5
'v-- VR=3.4
2r ....................................
2r ...................................
1.5
..
1.5
................................
............................
s.::..............................
':.......
RMS magnitude, (mis)
2
RMS magnitude, (m/s)
RMS magnitude, (m/s)
Figure 8.3: RMSU values at z/d = 0
................................
2c ..............................
1.5 ."
': ....
RMS magnitude, (m/s)
a)
b)
4
4
Hinde
o VRO.85/2OHz
I
3.5
c)
x/d1.5
x/d=O
VR3.4/2OHz
VRO.05
L-v- VR3.4
x1d4.5
d)
4
x1d8.5
....... +
35
3
3
3
2.5
2
2.5
2.5k ............................
1.5
1:c
2
0.:
°:;
1
RMS magnitude, (mis)
O5i
RMS magnitude, (m/s)
RMS magnitude, (m/s)
Figure 8.4: RMSU values at zid = 0.8
RMS magnitude, (mis)
IDI&
The effect of higher velocity ratio on the RMS values is again larger, but not as
pronounced as in Figure 8.3b. The increase in RMS, at yld = 0.5, for the steady
VR = 3.4 case is 200%, while the increase for the pulsed case has only increased
150% compared to the upstream values at x/d =0.
The effect of the inclined cylinder on the RMS values is similar to the
lower velocity ratio cases at xld = 0 and 1.5, but agrees more with the higher
velocity ratio case of YR = 3.4 for x/d location of 4.5 and 8.5.
8.3 - INFLUENCE OF VELOCITY RATIO AND PULSING FREQUENCY
ON REYNOLDS STRESSES
Reynolds stresses at zld = 0 for all cases are plotted in Figures 8.5a
through 8.5d. Data for x/d = 1.5 are plotted using a scale from 8 to +2
m2/s2,
while the data for the three other x/d locations are plotted on a scale from ito
+0.35 m2/s2. The Reynolds stresses upstream of the jet at x/d = 0, see Figure 8.5a,
show no significant difference between cases. Small positive Reynolds stress
values exist close to the wall in the turbulent boundary layer and are close to zero
throughout the rest of the cross flow.
Figure 8.5b indicates about a 0.5
m2/s2
increase in Reynolds stress for both
YR = 0.85 cases, but the greatest increase in Reynolds stress occurs in the high
velocity ratio case. Close to the cross flow wall a 3.75 m2/s2 decrease is noticed
a)
b)
xfd=O
4
4.......
x/d=1.5
.,........
0 VRO.85/2OHz
-e- VR=3.4/2OHz
VR=O.85
35
....
-v--
VR=3.4
3
3
Z.b
2.5k
2.5L ..................... o ........
//
/
1.5
1.5
1.5
1.5
I
/
I
1
N
I
//
0:
//
__
X
__ __
0:
o:
05
Reynolds stress, (m2/s2) Reynolds stress, (m21s2) Reynolds stress, (m21s2) Reynolds stress, (m21s2
Figure 8.5: Reynolds stresses at z/d = 0
102
for the steady VR = 3.4 case, while a decrease of up to 7.10 m2/s2 can be seen for
the pulsed case at YR = 3.4. Although the highest stress reduction at x/d = 1.5 is
seen near the wall, a significant decreases in Reynolds stress is still seen as far up
as y/d = 1. It is again pulsing at the high velocity ratio that causes the greatest
decrease in Reynolds stress magnitude, as was the case for the increased RMS
values seen in Figure 8.3b.
Although the Reynolds stresses decay rapidly in the downstream region a
significant stress difference between the cases YR = 0.85 and YR = 3.4 is still
noticeable at x/d = 4.5 and 8.5. The largest differences in Reynolds stress due to
pulsing occur at xld = 1.5 between y/d = 0.2 and y/d = 1.5, but are far less
apparent at the downstream locations x/d = 4.5 and 8.5. Some difference between
Reynolds stress profiles is still seen at locations x/d = 4.5 between y/d = 1 and y/d
= 2 and is presented in Figure 8.5c.
The Reynolds stresses throughout the grid yield negative peaks near the
same vertical position as the RMS maxima described earlier. The negative peak
values are found at y/d = 0.2, 2 and 3 for x/d values of 1.5, 4.5 and 8.5
respectively. Although the y/d location of the peak stress value at x/d = 4.5
between the pulsed and non-pulsed high velocity ratio case is identical, it seems
that the distribution of stress are skewed towards the plate.
Reynolds stress profiles at zld = 0.8 are plotted on a scale from 1 to
+0.35 m2/s2 in Figures 8.6a through 8.6d.
4.. 4..
a)
b)
xfd=O
c)
x/d1.5
d)
x/d=4.5
4-
4
-±-- Cylinder
o VR=O.85/2OHz
35
VR=3.4I2OHz
VR=O.85
-v- VR=3.4
3
1:
35 - .......................
3 ............................
'15
3.5
3.5
3
3
2.5
2.5
is
//
x/d=8 .5
....................
7
/'
I:
4
0.:
0.5
5:
0.:;
Reynolds stress, (m2/s2) Reynolds stress, (m2/s2) Reynolds stress, (m21s2) Reynolds stress, (m2/s2
Figure 8.6: Reynolds stresses at z/d = 0.8
104
As was the case at z/d =0, there is only a small influence on the Reynolds stresses
at the leading edge of the jet, see Figure 8.6a, and it is impossible to distinguish
between the cases.
Reynolds stresses at location x/d = 1.5 and zld = 0.8 are shown in Figure
8.6b and are quite different from the ones described at z/d = 0 and shown in
Figure 8.5b. Again, it is the pulsed VR = 3.4 case which causes the largest change
in Reynolds stress from x/d = 0 to x/d = 1.5, but unlike at the centerline, the sign
is positive which drives momentum down closer to the wall instead of up from the
wall, as is the case with a negative Reynolds stress. The YR = 3.4, non-pulsed
case has a lesser effect on the change in Reynolds stress, followed by the pulsed
VR = 0.85 case and the steady YR = 0.85, which has the least effect, causing a
only a small change compared to the stress at x/d = 0. There is no observable
change in Reynolds stress for the inclined cylinder between x/d = 0 and 1.5.
The jet in cross flow Reynolds stresses further downstream at x/d = 4.5,
see Figure 8.6c, have opposite signs from the inclined cylinder Reynolds stresses.
The inclined cylinder case indicates a positive Reynolds stress away from the
wall, with a maximum positive stress located at y/d = 2.5. The Reynolds stress
decays back to the cross flow value by y/d = 3. Both the decreases in Reynolds
stress for VR = 3.4 and the positive Reynolds stress for the inclined cylinder
experiments are damped out at x/d = 8.5, as observed from Figure 8.6d, with only
slight variations among each case between y/d = 1.5 and 4.
105
8.4 - INFLUENCE OF VEOCITY RATIO AND PULSING FREQUENCY
ON MEAN VORTICITY
The mean vorticity throughout the symmetry plane is plotted in Figures
8.7a through 8.7d. All Figures except Figure 8.7b are plotted using the same scale
of 0.3 to 0.3 s_i. Figure 8.7b is plotted using a scale of 0.4 to 0.4 s. Figure
8.7a shows an increase in mean vorticity near the wall with increasing velocity
ratios, whereas the pulsing has an overall decreasing effect on the mean vorticity.
Note that whenever pulsing is applied, the instantaneous velocity during the 'on'
cycle of the pulse is equal in magnitude to that of the steady case, but the time
averaged velocity is half that of the steady case. It is this reduction in average jet
velocity that creates a lower average shear as the jet exits into the cross flow and
thus producing less mean vorticity at the leading edge of the jet.
At xld = 1.5 the mean vorticity is still dominant in the positive direction,
but a generation of opposite and equal amount of vorticy can be seen in locations
x/d = 4.5 and 8.5. The minimum and maximum locations at y/d = I and y/d = 2,
respectively, at x/d = 4.5 represent the location of two shear layers in the jet. As
the jet issues from the flat plate, shear is created between the jet colunm and the
cross flow on the top side of the jet as well as between the lower side of the jet
and the wake. A similar phenomena occurs at location x/d = 8.5, where the
maximum is located at y/d = 3, while the minimum is somewhere between y/d = 1
and 2.
a)
b)
xld=O
0
4-
L
1
VR=O.85
VR=3.4
3-
d)
x/d4.5
4-
4-
1
x/d8.5
I
j 3.5
3.5
3-
2.5
2.5
2-
2-
°
2
c)
VRO.85/2OHz
s-- VR3.4/2OHz
I
xjd=1.5
Mean vorticity, (1/sec)
3.
3
2.5
2.5
2
2
0
0'2
3.5
L
0
Mean vorticity, (1/sec)
0
Mean vorticity, (1/sec)
Figure 8.7: Mean vorticities at z/d = 0
002_
Mean vorticity, (1/sec)
107
Mean vorticity for the cases of YR = 0.85 are not plotted in Figure 8.7d,
because data for these conditions was only collected up to x/d = 8.5 and the
vorticity calculations are based on a forward finite differencing scheme.
Off symmetry plane (z/d = 0.8) results of mean vorticity are plotted in
Figures 8.8a through 8.8d. Because the vorticity at the off symmetry location, at
x/d = 0, is apparently not strongly influenced by the jet flow, as was the case for
the vorticity in the symmetry plane, presented in Figure 8.7a, the vorticity is
opposite in sign, as is the case in the upstream boundary layer..
Comparing Figures 8.8b through 8.8d with Figures 8.7b through 8.7d
shows similar trends of increasing mean vorticity near the wall at xld = 1.5. There
is also both positive and negative mean vorticity values at x/d = 4.5 and 8.5,
respectively, with negative values near the wall and positive values further out
away from the flat plate. Noting the scale difference between Figures 8.7 and 8.8,
the maxima in mean vorticity at x/d = 1.5 are much smaller in magnitude for the
measurements at the cross section z/d = 0.8, than in the symmetry plane zld = 0.
Also shown in Figure 8.8 is that the inclined cylinder has little effect on
the mean vorticity as compared with the jet cases. The decrease in mean vorticity
at x/d = 1.5 between y/d = 1.5 and 3 is attributed to a combination of acceleration
and downward motion of the fluid around the perimeter of the solid cylinder.
a)
4
b)
x/d0
4
-±- Cylinder
0 VRO.85I2CHz
35
-8---x-
1
c)
4-
x/d=4.5
d)
4.
x/d=8.5
I
I
VR=3.4/20Hz
VRO.85
-v- VR=3.4
3
xld=1.5
D
J
3.5
1
2.5
1.5-
1.5-
35
3-
3-.
2.5
3.5
1
3
2.5
2.5
1.5
1.5
I
Mean vorticity, (1/sec)
Mean vorticity, (1/sec)
I
Mean vorticity, (1/sec)
Figure 8.8: Mean vorticities at z/d = 0.8
Mean vorticity, (1/sec)
109
CHAPTER 9
SPECTRAL AND VELOCITY CHARACTERISTICS
Similar to the case comparisons in Chapter 8, a set of vertical slices
through the flow field were selected to perform a more in-depth analysis of the
flow behavior in terms of its spectral content and fluctuating velocities. Power
density spectra, time traces and histograms were generated for two locations; one
location in the near field of the jet (xld = 2.5, y/d = 0.2 to 4.0) and one in the far
field of the jet (x/d = 7.5, y/d = 0.2 to 4.0) both along the symmetry plane and off
symmetry at z/d = 0 and zld = 0.8, respectively. Due to the shear volume of the
data that were generated, all plots are included in Appendix E, but only selected
ones are referred to throughout the text.
The spectral density plots are, among other things, used for a more indepth comparison between the inclined solid cylinder, and the steady and pulsed
jet cases. It is also used to study the jet more carefully and to comment on the
effect of pulsing on the flow in terms of the spectral changes that are seen.
Velocity time traces and histograms are, in some instances, discussed and referred
to for clarification purposes.
110
9.1 - INCLINED CYLINDER
Figures 9.1 and 9.2 show a region of high RMS values that occurs just
downstream in the wake of the cylinder. Spectral density plots, see Figures 9.3
through 9.5, at the near field and the far field show the most spectral energy over
the frequency range, at x/d and y/d locations that coincide with the maxima in
RMS values seen in Figure 9.1. The highest increase in energy in the power
spectra is seen at xld = 7.5 and y/d = 3 where a maximum in RMS fluctuations in
the v component was pointed out earlier in Section 7.3, seen Figure 9.2.
A potential turbulent structure might be present near the wall at x/d = 2.5
and xld = 4.5, that has a limited extent into the flow and increases the local
spectral energy content. It is separated from the high spectral energies further
away from the flat plate by a region of low spectral energy, between y/d = 0.2 and
y/d = 1 at x/d = 2.5, as is evident from Figure 9.3. A similar decrease in energy
occurs at x/d = 4.5 between y/d = 0.5 and y/d = 1.5, see Figure 9.4.
111
0.7
0.6
0.5
4
3
0.4
V
0.3
1
0
0
2
4
6
8
10
0.2
x/d
0.1
Figure 9.1: RMS-u, inclined cylinder at z/d = 0.8
S.
0.7
4
0.6
3
0.5
V
>,
0.4
I
0.3
0
0
2
6
4
8
10
x/d
0.2
0.1
Figure 9.2: RMS-v inclined cylinder at z/d = 0.8
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2Is)
O.O2
0.O1
0.02
0
0.02
0.02
o.o1
>.
0
40.01
O.O2
0.02
>'
o.oiL___________
0
O.O2
"001
c-i
0
0
0.02
e-i0.02
ooiLj
0,01
0
O.O2
11
0.02
o.o
II
>'
0.02
0.o1
0
>' 0.01
0
0.02
0.O2F
(0.01
0.01
0
.
0.02F
4, 0.01 h-.--,
01
0
0.02
-I
--' V V
100
102
4!, 0.01
0 ----100
f(Hz)
102
f(Hz)
Figure 9.3: Power spectra at xld = 2.5
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2Is)
0.05
0.05
0
I1)
0.05
I',
0
0.05
II
0
0 ----.L_.----
0.05
c)
0.051
0
0
0.05
-.
---
-C
05
c'1
C.,'
t---,r,.'.',&
0
0.05
00
c'1
0L
I',
C','
0
0.05
I')
05
I'
0
0.05
0.05
-
0
0.05
ci
-
0
,0.05
0.05
0
,'0.05
II
100
102
>'
0
100
f(Hz)
102
f(Hz)
Figure 9.4: Power spectra at x/d = 4.5
U-component, Power I frequency (m2Is)
,
0.1
V-component, Power I frequency (m2Is)
, 0.1
?0.o5
III
o.o5L
0
III
0.1
0.1
o:5L.
4O.O5-
0:5
o.osL
-
0
0.1
0.1
o.o5LA
-
I'0.1
0.1
o.o5L
1
0.1
c'lj
0.05
0.1
o.osL
0
100
102
102
10°
f(Hz)
f(Hz)
Figure 9.5: Power spectra at xld = 7.5
e
115
The power spectra in Figures 9.3 through 9.5 seem to have discrete
spectral peaks at low frequencies. A strong bimodal behavior can be seen in both
histograms and velocity time traces at locations x/d = 2.5 and x/d = 7.5. A typical
histogram and time trace of this bimodal behavior at x/d = 2.5 are presented in
Figure 9.6 and Figure 9.7, respectively.
80
70
60
50
U)
0
0
o 40
4,
.0
E
30
20
10
01
4.2
ii
III
4.4
4.6
4.8
5
Um mean veociti, (mis>
Figure 9.6: Histogram at x/d = 2.5 and y/d = 2
5.2
5.4
116
O3
O
O5
O7
oa
Time (sec)
Figure 9.7: Time trace at x/d = 2.5 and y/d = 2
The time trace shows fluctuating behavior with a number of burst within a
one second period. The fluctuating, or bi-modal, behavior increases the
periodicity of the fluctuations which is seen in the power density spectrum for the
same location (Figure 9.3), where a peak in energy is seen around 3.5 Hz. This
oscillation is seen throughout the field, but is most noticeable in the near field
region. More examples on this behavior can be found in the spectra, time-traces
and histograms in Appendix E.
117
9.2 - STEADY JET
As was described in Chapter 7, the use of mean velocity profiles is
sometimes inadequate to accurately describe the jet trajectory. This is especially
true in the lower velocity ratio case, where a distinction between the cross flow
and the jet flow is hard to make in terms of mean velocity. A combination of
RMS and mean vorticity plots give a better indication of the jet trajectory.
Spectral density information can be used in addition as a means of identifying the
jet. RMS values of the x-direction component of velocity for VR = 3.4 and z/d
0
are again plotted in Figure 9.8. The region of high RMS values, show that the jet
is much more turbulent than the cross flow. This distinction can also be made
using spectral density, time trace and histogram plots. Typical jet spectral power
density plots can be seen in Figure 9.9, where the spectral distribution of the high
velocity ratio jet is plotted in red, the low velocity ratio jet in blue and the
spectrum of a point in the cross flow in black.
118
fl:
4
12.5
3
>,
1.5
1
00
4
2
6
8
10
xld
05
Figure 9.8: RMS values, x-direction, VR = 3.4, z/d = 0
1
02
C
6
(N
E
0)
l0
1010
Blue: Steady jet, yR = 3.4, x/d = 2.5, yld 1.5
Red: Steady jet, VR = 0.85, x/d = 2.5, y/d = 0.2
Black: Cross flow, x/d = -0.5, yld = 4.0
1O14
101
io°
1o1
Frequency, (Hz)
Figure 9.9: Steady jet spectral power density plot
io3
119
Comparing the two jet flow power spectra shows somewhat larger energy
levels throughout the frequency range for the higher velocity ratio jet (YR = 3.4).
Comparing both jet spectra to a spectra taken at x/d = 2.5 and y/d = 4, which is
well outside the jet flow, reveals a different distribution of spectral energy. The
amount of energy decay is similar in magnitude, but becomes saturated at f = 300
Hz, after which the energy levels remain constant. No saturation is seen in the jet
cases, where small scale turbulence, corresponding to high frequency content, is
more dominant in terms of its energy compared with the cross flow.
Velocity time traces were studied and a typical velocity time trace from
inside a steady jet at YR = 3.4, y/d = 1, is compared to a typical velocity time
trace from outside the jet, y/d = 4, and are presented in Figures 9.10 and 9.11,
respectively. Note that the same scales are used in both figures.
120
16
14
12
_1 0
E
6
4
2k0
I
0.2
0.4
0.6
0.8
1
Time(sec)
Figure 9.10: Velocity trace xld = 2.5, y/d = 1, VR = 3.4, steady
16
14
12
1 0
E
6
4
2
0.2
0.4
0.6
0.8
Time(sec)
Figure 9.11: Velocity trace x/d = 2.5, y/d = 4, VR = 3.4, steady
121
A comparison between the steady jet flow and the cross flow is presented
using histograms in Figures 9.12 and 9.13, respectively. Velocity fluctuations in
the cross flow at x/d = 2.5 and yld = 4, presented in Figure 9.13, show a narrow
distribution around the mean, while those in the steady jet flow, presented in
Figure 9.12, show a large spread around the mean.
For the low velocity ratio case, all steady jet spectral plots reveal that in
the symmetry plane (zid = 0) the majority of the jet is concentrated within 2.5
diameters above the flat plate. Spectral plots similar to jet spectra presented in
Figure 9.9 are seen within the first diameter above the flat plate at x/d = 2.5 and
within the first 2 to 2.5 diameters above the wall at xld = 7.5 (see Appendix E).
For the higher velocity ratio (VR = 3.4) the majority of the jet fluid lifts
off from the surface, as is apparent from the shift away from the wall in typical jet
spectral distributions. Spectral distributions, with high spectral energy, similar to
the steady jet cases seen in Figure 9.9, are seen between y/d = 1.5 and y/d = 3.5 at
x/d=7.5.
122
40
35
30
25
0
0.
20
0
E
.0
15
10
4
6
8
10
12
u (mis)
Figure 9.12: Histogram, jet flow at xld = 2.5, y/d = 0.5, VR = 3.4, steady
100
90
80
70
1:
40
20
10
0
2
4
6
I
I
8
10
12
u (m/s)
Figure 9.13: Histogram, cross flow at xld = 2.5, y/d =4, YR = 3.4, steady
124
Figure 9.14 shows distinct energy peaks in both cases, located at 20 Hz,
which coincides with the pulsing frequency of the jet. Second, third and higher
harmonics are seen at f = 40, 60 and 100 Hz. The peak amplitude in the pulsed
case for VR = 0.85 is about one order of magnitude larger than the peak energy
magnitude in the un-pulsed case, while the peak amplitude for the pulsed VR =
3.4 case is about 2 to 3 orders of magnitude larger than the non-pulsed case.
The distinct peak at 20 Hz, and its sub-harmonics, tends to decrease in
relative magnitude in both the downstream direction and away from the jet The
peak is best defined within the jet flow and closest to the jet exit.
The effect of pulsing on the spectral distribution at a number of points
along the jet flow can be noted from Figures 9.15 through 9.22. Non-pulsed and
pulsed results are plotted for the locations shown in Table 9.1.
Table 9.1: Location of power spectral density plots
z/d=O
VR = 0.85
x/d=2.5 x/d=7.5
yld=0.2 y/d=1
VR = 3.4
xld=2.5 x/d=7.5
y/d=1
yld=2.5
z/d=O.8
VR = 0.85
VR = 3.4
x/d=2.5 x/d=7.5 xld=2.5 xld=7.5
y/d=0.2 yld=O.2 y/d=1
yld=2.5
125
At the jet centerline, z/d
0, the highest spectral energy content occurs
close to the jet exit and at VR = 3.4, see Figure 9.17. The pulsing frequency and
its sub-harmonics are seen in the near field, while the energy within the subharmonics decreases and merges with the rest of the spectra in the far field, see
Figure 9.18. The decay in energy at higher frequencies at higher velocity ratio jet
(VR = 3.4) is smaller than the lower velocity ratio case and is independent of
pulsing, see Figures 9.15 and 9.17. Off center (zid = 0.8) power spectra are
plotted in Figure 9.19 to 9.22 and show similar energy levels with the exception
that the energy peak caused by pulsing is significantly reduced in magnitude
throughout the flowfield.
130
CHAPTER 10
DISCUSSION
A total of 10 cases were studied and results are presented in Chapters 7, 8
and 9. Instantaneous velocity measurements and subsequent analysis of a steady
and pulsed jet without a cross flow show that jet pulsing alters the flow
significantly. The high flow rate jet in general creates as much as 120% more
RMS at the jet exit than the low flow case. Pulsing, as expected, reduces the mean
velocity at the jet exit between 40 and 60%, while it increases the RIVIS levels at
the jet exit by as much as 53% for the low jet flow case and as much as 81% for
the high jet flow case. Neither low jet flow, high jet flow, nor pulsing seem to
influence the jet's trajectory in the no-cross flow case.
The inclined cylinder in cross flow results in strong accelerations and
mean flow deflection near the cylinder's perimeter, while regions of high
turbulence and shear stress are created in its wake. Turbulence is seen in both u
and v velocity components with the v component turbulence increasing in the far
field The velocity in the y-direction is only a small fraction of that in the xdirection. Mean vorticity distributions remain relatively unchanged compared to
normal boundary layer flow.
Steady jet experiments show that the low velocity ratio jet is deflected
towards the wall very close to the jet exit and adheres to the wall as indicated by
131
the velocity in the x-direction and from RMS plots. Maxima in turbulence, similar
to the levels in the no-cross flow case, were generated at the jet exit and decayed
in the x-direction. No significant acceleration was seen in the off symmetry plane
(z/d = 0.8) where maxima in turbulence and Reynolds stresses are located close to
the jet exit. No secondary turbulent structures, like the ones seen in the inclined
cylinder with cross
flow,
seemed to be present. Higher velocity ratio experiments
on the other hand show a lift off of the steady jet further into the cross
flow.
Mean
velocity, RMS values, Reynolds stresses and mean vorticity indicate a separation
of the
flow
from the wall. RMS values for the high VR case compared to the low
VR case increased as much as 100% in the near region, being consistent with the
no-cross flow results. Reynolds stresses are six times higher in the near field than
for the low VR case. The high VR jet also has a greater effect on the off
symmetry plane where increases in all assessed values are seen. Increases in
RMS, Reynolds stresses and mean vorticity seem to have their origin from the jet
fluid and are not a result of strong secondary structures in the wake of the jet, as is
the case with the inclined cylinder in cross flow.
The effect of pulsing on the jet has a lesser effect when in the cross flow
than for the no-cross flow case. The velocity deficit, throughout the jet flow, due
to pulsing is greatest in the high velocity ratio case where the jet momentum is
much larger than the cross flow. The effect of pulsing on the turbulence levels is
more apparent at the higher velocity ratio where increases in RMS in the near
field are 45% compared with the steady case. At the lower velocity ratio increases
132
were measured to be up to 20%. The increase in RMS levels are concentrated
close to the jet exit and along the centerline of the jet. RMS levels further
downstream are lower for the pulsed case than for the steady case. Reynolds
stresses only increase slightly for both pulsed cases compared to the steady cases.
Mean vorticity in both pulsed cases is drastically reduced due to the reduced
average jet momentum during pulsing compared with the steady cases. In the off
symmetry plane the result of pulsing is a decrease in RMS fluctuations throughout
the field. Although the average flow rate through the jet, and therefore the average
jet momentum, has been significantly reduced, the jet trajectory does not seem to
be influence by the jet pulsing. The same penetration into the cross flow occurs
with only half the average fluid flow rate.
The effects of pulsing and velocity ratio on the velocity, RMS, Reynolds
stresses and mean vorticity profiles were studied at all y/d locations at x/d
locations of 0, 1.5, 4.5 and 8.5. Results show that the influence of both velocity
ratio and pulsing is most noticeable close to the jet exit. Velocity deficits for
pulsed cases occur both in and out of the symmetry plane.
The effect of pulsing on the turbulence levels is greatest for the high
velocity ratio case and close to the jet exit. RMS profiles for the low velocity ratio
case shows hardly any difference between non-pulsed and the pulsed cases, while
RMS levels further away from the jet seem to be similar between pulsed and non-
pulsed for the high velocity ratio case. The differences in RIvIS between nonpulsed and pulsed are less in the off symmetry plane.
133
Differences in Reynolds stress is small between the low velocity ratio non-
pulsed and pulsed cases. The pulsing has the most effect for the high velocity
ratio case, and an increase in Reynolds stress is seen up to x/d =
4.5.
At x/d = 4.5
the distribution of the stress are skewed toward the flat plate more in the pulsed
case than the non-pulsed case. These stresses are all positive. In the off symmetry
plane the stresses are greater for the non-pulsed case compared to the pulsed case.
The inclined cylinder stress profiles show negative stresses in the wake of the
cylinder.
Mean vorticity profiles are as expected with pulsed cases showing less
vorticity due to a decrease in shear generated at the jet cross flow interface as a
result of loss of jet momentum.
Spectral plots, time traces and histograms were used to study the different
cases more thoroughly. Analyses of these data show a strong bimodal behavior
around 3.5 Hz. The strongest spectral energy was found in the y-direction velocity
component at 6 Hz, which is located in the mid/far field (xld = 7.5). The
frequencies at which the bimodal behavior occur do not agree with the shedding
that was expected from an inclined cylinder according to the literature. Shedding
was expected at a frequency of about 60 Hz, or 30 Hz per side1.
Spectral analyses show that the cross flow, steady jet flow and the pulsed
jet all have distinct characteristics. The high velocity ratio, steady and pulsed jet,
consist of more energetic small scale turbulence compared to the low velocity
134
ratio jets. The cross flow has less energy throughout the spectrum and seems to
have much smaller energies at the smaller scales.
Using spectra to identify the jet trajectory, it was found that the low
velocity ratio jet does not separate from the wall, while the higher velocity ratio
jet does. No spectral high energy was located underneath the jet core as a result of
secondary structures like that in the inclined cylinder case.
Pulsing causes large discrete spectral energy at I = 20, 40, 60 and 100 Hz,
with the largest amount of energy concentrated in the 20 Hz peak. Peak energy at
20 Hz is largest near the jet exit and along the jet and tends to decay in the
downstream direction as well as away from the jet and into the cross flow.
135
CHAPTER 11
CONCLUSIONS AND RECOMMENDATIONS
The effect of pulsing at low and high velocity ratio was investigated for a
45 degrees inclined jet in cross flow. A comparison was made among the different
cases and also to flow around an inclined cylinder. Initial jet tests were carried out
without cross flow, followed by a thorough near to far field analysis of low and
high velocity ratio jets in both non-pulsed and pulsed cases.
It is concluded that at the high velocity ratio of 3.4 the jet penetrates
further into the cross flow and separates from the wall allowing cross flow fluid to
flow between the detached jet column and the wall, The lower velocity ratio jet
(VR = 0.84) remains attached to the wall as the flow moves downstream.
Turbulence RMS levels, Reynolds stresses and mean vorticity are all greatly
influenced near the jet exit velocity and are, in general, all larger for the higher
velocity ratio jet. No secondary flow structures were found downstream for jets in
cross flow like those seen with the inclined cylinder. All maxima in turbulent
RMS levels were attributed to jet flow and not to secondary structures formed by
the wake of the cross flow fluid.
Jet pulsing resulted in the jet trajectory being similar to the non-pulsed
case, even though the average mass flow through the jet was reduced by roughly
50%. Jet pulsing increased turbulent RMS levels and Reynolds stresses in the near
136
field of the jet, but did not have a great effect beyond x/d of 4. Increases in the
pulsed case, of up to 45% were recorded for the high velocity ratio case at the jet
exit compared with the steady case. Spectral energy distributions within the flow
changed significantly in magnitude and distribution as a result of jet pulsing. A
strong singular spectral peak was detected at the pulsing frequency, which is the
main energy contributor to the flow. The strong spectral peak is strongest in
magnitude at the jet exit and along the jet flow and seems to decay in the
downstream direction of the jet flow. Spectral energy distributions provided a
good method to track the jet fluid within the cross flow.
Recommendations for future research include jet pulsing at lower
frequency ranges where much larger turbulence levels are expected. A trade off
may be made between the turbulence generation due to lower pulsing and the
decreased jet momentum which carries the turbulence into the downstream
direction.
Even higher velocity ratio jets could be tested, which should result in the
jet lifting off even further from the wall. A better comparison could be made
between shedding behind an inclined cylinder and the turbulence in the wake of
the jet. Current jet lift off was apparent, but might not have been enough for
secondary structures to form between the wall and the jet column.
An endless range of jet geometries are also possible with the current jet in
cross flow setup, but would be better suited for a separate research effort.
137
BIBLIOGRAPHY
1.
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streets", NACA Report. 1191, pp. 1-25
2. Kawamura, T. and Hayashi, T., "Computation of flow around a yawed
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229-236.
3. Hara, Y., Higuchi, H. and Hayashi, T., 1999, "Flow visualization on the
leeward side of the upstream juncture of a yawed circular cylinder", Journal
of Flow Visualization & Image Processing, vol. 6, pp. 205-2 19.
4. Hanson, A.R., 1966, "Vortex shedding from yawed cylinders", AL4A Journal,
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5. Ramberg, S.E., 1983, "The effect of yaw and finite length upon the vortex
wakes of stationary and vibrating circular cylinders", Journal of Fluid
Mechanics, vol. 128, pp. 81-107
6. Margason, R.J., "Fifty years ofjet in cross flow research",
72ND
AGARD
Fluid Dynamics Panel Meeting and Symposium.
7. Mcmahon, H.M., Hester, D.D. and Palfery, J.G.,1971, "Vortex shedding from
a turbulent jet in a cross-wind", Journal of Fluid Mechanics, vol. 48, part 1,
pp. 73-80
8. Moussa, Z.M., Trischka, J.W. and Eskinazi, S., 1977, "Mixing of a round jet
with a cross stream Journal of Fluid Mechanics, vol. 80, part 1, pp. 49-80
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transverse jet", Journal ofFluid Mechanics, vol 279, pp. 1-47.
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round jets in a cross-flow", Journal ofFluid Mechanics, vol. 306, pp. 111144.
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138
12. Yan, L.L, Street, R.L. and Ferziger, J.H.,1999, "Large-eddy simulations of a
round jet in crossflow' Journal of Fluid Mechanics, vol. 379, pp. 71-104.
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characteristics of streamwise inclined jets in crosfiow on flat plate", Journal
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14. Brittingham, R.A. and Leylek, J.H., 1997, "A Detaile Analysis of Film
Cooling Physics: Part IV, Compound-Angle Injection With Shaped Holes",
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15. Isaac, K.M. and Jakubowski, A.K., 1985, "Experimental Study of the
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"pp. 1679-1683
16. Thole, K., Gritsch, M., Schulz, A., and Wittig, S., 1996, "Flowfield
Measurements for Film-Cooling Holes with Expanded Exits", ASME 96-GT
174, IGTI, 10-13 June, Birmingham, UK.
17. Berger, P.A. and Liburdy, J.A, 1998, "A near-field investigation into the
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18. Vermeulen, P.J., Chin, C. and Yu, W., 1990, "Mixing of an acoustically
pulsed air jet with a confined crossflow", AIAA Journal, vol. 6, No. 6, pp.
777-783
19. Vermeulen, P.J., Grabinski, P. and Ramesh, V., 1992, "Mixing of an
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IM!]
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company, New York
APPENDICES
141
APPENDIX A
DIFFERENTIAL PRESSURE MAP
Pressure field measurements were conducted at two locations along the
wind-tunnel test section. Location A is 0.3 m downstream of the test section
entrance, while location B is half way along the test section (see Figure A. 1).
Differential pressure data (inches of H20) were measured within a 25
point grid. It was found that the differential pressure and thus velocity at the
bottom row at location B was considerably less than the rest of the field,
indicating the presence of a boundary layer. Variations in the mean flow were
calculated omitting these 5 data points. Raw data (25 points) is still presented, but
graphical plots and statistical analysis were based on the 20 remaining data points.
The test location was selected based on the standard deviation of pressure
measurements throughout the grid. Section B showed the lowest deviation from
the mean and was therefore selected for testing.
142
Flow direction
JSectioJ
Figure A. 1: Test section 'ocations
143
Table A. 1: Differential Pressure measurements at A
5mIs / 0.062"H20
5
4
3
2
1
0.0620 0.0640 0.0600 0.0600
0.0650 0.0650 0.0620 0.0630
0.0650 0.0650 0.0640 0.0650
0.0630 0.0620 0.0620 0.0620
0.0620 0.0620 0.0600 0.0620
1
2
3
4
0.0590
0.0600
0.0620
0.0620
0.0620
Downstream
5
7.5m/s I 0.139"H20
5
4
3
2
1
lOm/s
5
4
3
2
1
0.1430 0.1490 0.1390 0.1400 0.1390
0.1520 0.1490 0.1440 0.1480 0.1400
0.1480 0.1460 0.1450 0.1470 0.1430
0.1420 0.1400 0.1390 0.1380 0.1380
0.1390 0.1390 0.1350 0.1370 0.1370
1
2
3
4
5
/
Downstream
0.246"H20
0.2390
0.2520
0.2500
0.2430
0.2440
1
0.2480 0.2340
0.2480 0.2430
0.2460 0.2430
0.2380 0.2380
0.2410 0.2340
2
3
0.2380 0.2330
0.2500 0.2390
0.2470 0.2430
0.2380 0.2380
0.2380 0.2380
4
5
EBDownstream
144
Relative pressure (inch (-(20) from mean at 5.7.5 and 10 rn/s
-.
-..-
10
20
x iO3
0
..
30r''
-2
WITlocr
x103
:
WITfIoor
wtr floor
Figure A.2: Pressure distribution at location A
x10
j:
145
Table A.2: Differential Pressure measurements at B
5m/s / 0.062"H20
5
4
3
2
1
0.0630
0.0660
0.0650
0.0640
0.0480
0.0630
0.0660
0.0640
0.0630
0.0430
0.0620
0.0640
0.0630
0.0630
0.0380
1
2
3
0.0600
0.0630
0.0650
0.0630
0.0470
4
0.0600
0.0620
0.0640
0.0640
0.0380
Downstream
5
7.5m/s / 0.139"H20
0.1390 0.1400 0.1380 0.1380 0.1350
0.1470 0.1450 0.1450 0.1420 0.1370
3
0.1440 0.1420 0.1390 0.1450 0.1430
2
0.1440 0.1410 0.1410 0.1410 0.1400
1
0.1020 0.1010 0.0870 0.1060 0.0950*
1
2
3
4
5
lOmIs / 0.2460"H20
5
4
5
4
3
2
1
0.2490
0.2630
0.2550
0.2560
0.1850*
1
0.25 10
0.2580
0.2540
0.2520
0.1870
2
0.2460
0.2570
0.2500
0.2500
0.1660
3
0.2460
0.2590
0.2570
0.2510
0.1950
4
Note: * indicates slightly fluctuating values.
0.2430
0.2490
0.2570
0.2510
0.1760*
5
Downstream
Downstream
146
Relative pressure Inch H20) from mean at 5 7 5 and 10 rn/s
10
-5
2
0
20
25
5
10
15
20
25
30
W/Tfloor
xlO
_______________
5t
10
5
1ftJPJfL I
10
Wltfloor
15
20
25
x103
30
W/T floor
Figure A.3: Pressure distribution at location B
147
Table A.3: Statistical data at A
Flow velocity
5mIs
7.5 mIs
lOmIs
Set Pressure
0.062
0.139
0.246
Mean
0.0624
0.1422
0.2417
Standard Deviation
0.0018
0.0046
0.0054
0.0626
0.1435
0.2424
0.00 19
Omitting lower 5 points
5mIs
7.5m/s
lOmIs
0.062
0.139
0.246
[
J
0.0043
0.0055
Table A.4: Statistical data at B
Flow velocity
Sm/s
7.5m/s
lOm/s
Set Pressure
0.062
0.139
0.246
Mean
0.0633
0.1413
0.2527
Standard Deviation
0.00 16
0.0031
0.0050
APPENDIX B
CROSS FLOW PLATE ASSEMBLY TECHNICAL DRAWINGS
p
---
Figure B.1: Technical drawing of jet in cross flow assembly
nil
>
L638
4800
24.00
100 mm
l50 mm
State Unver iy
Cross flow plate
002
App
Figure B.2: Technical drawing of cross flow plate
:
o-
Figure B.3: Technical drawing of jet plate
00
/
62I
H5O
0.63
327
Figure B.4: Technical drawing of strut block
U'
63
\
00
L
Oregon State Unreeror ty
Plate Strut
005
:
Figure B.5: Technical drawing of plate strut
2.00
400
H00
7
00
3.00
20.00
egon Stffe Un i ver sity
Stringer_A
Unknown
Approv&k
St Ondw
Figure B.6: Technical drawing of stringer A
006
feg NO.
SEn
None
fine.
fleck:
I
of
I
r°85
1.50
15.00
,TT
.25
HO
900
25.00
38.00
H
44.00
Oregon State Uni Vera i ty
Stringer 5
o.
Appoeis
S end r
Figure B.7: Technical drawing of stringer B
Si
001
.
None
SV.i
I
156
APPENDIX C
UNCERTAINTY ANALYSIS
This appendix describes the uncertainty analysis performed on the
following parameters: Jet averaged velocity, x,y and z location and instantaneous
velocities.
C.1 JET AVERAGED VELOCITY
Flow meter readings were corrected for pressure and temperature to calculate the
actual volumetric flow rate using the following relation:
QActual = QRe
x CF
(C-i)
Where the correction factor CF is defined as:
530
cF.7(Psjg)
xI
14.7
46OT(°F)
I
(C-2)
Pressure and temperature were measured using an electronic pressure transducer
and a thermocouple located just downstream of the flow meter.
Mass flowrate was then calculated using the relationship:
Al
'Line
QActual
RTLine
(C-3)
157
Because of a constant mass flowrate from the flow meter to the jet opening, the
average jet exit velocity was calculated knowing the jet exit area:
Vjet
- RTLne M
(C-4)
lAmbAjet
The uncertainty associated with the jet exit velocity can be given as:
2,
2
[
(
auje,
Uujet
UPflO.aneter)
aPflo,,e,er
Ur
UQread
aQrea,
J
The uncertainty within the flowmeter
2
(aUi,
aUje,
(C-5)
Ucf
J
J
was estimated at 4.4% at the
lowest reading, while the uncertainty of the pressure reading downstream of the
flowmeter was estimated at 0.9 psid. The thermocouple uncertainty was estimated
at 2.6 degrees Celsius, which included instrument and datalogger uncertainty. The
uncertainty in the correction factor (CF) attributed to pressure sensor and
thermocouple uncertainties was estimated at 9.2%. The uncertainty associated
with the jet exit diameter was estimated at 0.005 inch. The total uncertainty in the
jet exit velocity was estimated to be on the order of 11.6% for the VR=0.85 cases
and on the order of 8.6% for the VR=3.4 cases.
158
C.2 X,Y AND Z LOCATIONS
The uncertainty in locations that are specified throughout the thesis are
now presented. Uncertainties in x and z locations are easily determined, since
these locations were al determined by direct readings of off metric rulers. The
associated uncertainty in reading is estimated at ± 0.5 mm. The locations in the y
direction however were determined using potentiometers and a voltage readout
attached to the traversing system. The uncertainty in these locations can be
written as.
+ UadOUf
=
where
umech
(C-6)
is the uncertainty due to the mechanical slop within the motor and
gearing of the traverser and was estimated after repeated measurements to be on
the order of 0.31 mm. The uncertainty due to resolution error in the readout,
ureadout,
was estimated at ±0.05 mm. This adds up to an uncertainty per traverse, ut,
of ±0.32 mm.
For each traverse the y location would be zeroed and this added an
uncertainty of ± 0.5 mm between traverses.
159
C.3 INSTANTANEOUS VELOCITIES
The uncertainty in the instantaneous velocities are calculated using
=
pressure
+ Ui cue +
(C-7)
Uncertainties are determined by the hot film probe are attributed by errors during
calibration, the truncation errors within the analog to digital conversion and the
resolution of the de-conditioned voltage signal. The uncertainty within the analog
to digital conversion was extremely low since a l2bit converter was used. This
contributed to an error of O.3226x103 rn/s in u-velocity and
0.3104x103
rn/s in v-
velocity. The output voltage signals resolution introduces an even smaller error,
such that the total errors due to truncation and voltage resolution become
O.4562x103
rn/s for the u-velocity and 0.4390x103 rn/s for v-velocity.
Errors in pressure measurements during micro manometer reading were
estimated to be ±0.0255 m/s.
The error introduced when the calibration points are fit can be estimated
by the standard error of the fit. The precision interval in bridge voltage associated
with sensor 1 and 2 were ±0.0353 Volts and ±0.0201 Volts, respectively. The
associated error in terms of u direction velocity varies throughout the calibration
curve and is largest at higher velocities (10.4% or 0.21 mIs) and lowest at small
velocities (6.7% or 1.1 mIs).
The total uncertainty of velocity measurements in the u direction varies
from 10.4% to 6.7% and is mainly caused by the standard error of the fit.
160
APPENDIX D
HOT FILM CALIBRATION
A main stream calibration was performed using TSI model 1 125C
calibrator, a micro manometer, pitot tube and a model 1246 x-probe. The TSI
calibrator was used to calibrate the hot film over a velocity range from 0 to 40 mIs.
A low velocity range calibration (0
5 mIs) was done using the calibrator's mid-
size nozzle. An external pitot tube was used for accurate velocity measurements
in this range. For the higher velocity range ( 7.6
40 mIs ) the external nozzle
plate was installed on the calibrator and the calibrator's plenum pressure port was
used to determine the exit velocity at the nozzle exit.
A slight offset in the initial main stream calibration was detected, which
lead to skewed velocity vectors in terms of the angle of attack throughout the field.
A correction was applied to the mainstream calibration data and new calibration
curves were generated which resulted in data that better agreed with flow
visualization experiments done within the flow field.
The new calibration curves are presented in Figures D.1 and D.2.
161
2.
w
1.5
IL
0
5
10
15
20
30
25
Veff 1, (m/s)
Figure D. 1: Calibration curve sensor 1
2.
0
w
cfl 1.5
1'
0
5
10
15
20
25
Veff2, (mis)
Figure D.2: Calibration curve sensor 2
30
35
162
Bridge voltages stored by TSI' s thermaipro software had to be corrected before
effective velocities could be calculated. The voltages are designated as *.E000l,
* .E0002,
etc. These voltages are corrected for temperature using the following
relations:
ET =E
T and
T1
/(25o_i)
(D-1)
(250-1)
are the temperatures during calibration and during the test respectively.
T can be found in the calibration file *.CL, while Tt can be found in the *T0001
files and are stored at the same time as the * .E000 1 files.
The effective velocity could then be found using the two calibration curves for
sensor 1 and 2:
Veff I
= 4.43592 + 9.74868E1
Veff 2
= 41.59791+114.04084E2 111.797O8E +43.82417E 4.52267E
5.26423E
2.18 132E + 2.O7459E
The effective velocity was then corrected for density as follows:
Veffl
17eff1[J
(D-2)
P is the pressure during calibration and P1 the pressure during test. P can again
be found in the calibration file and P1 in the *.T* files.
These effective velocities were used to calculate u and v using the equations
described in Chapter 6.
163
APPENDIX E
POWER SPECTRA, TIME TRACES AND HISTOGRAMS
U-component, Power / frequency (m2/s)
0O2
V-component, Power / frequency (m2Is)
HH
OO2E
LI)
002
¶D.02
NH
I'
Hh1
002
o
o
002
11002
,
HH
H
-
o________________________
002-
-
o
ill
10°
102
10'
1(1-f z)
HUH
t°:LLLLU1LJILiJIi
io°
102
10'
1(Hz)
Figure E.1: Power spectral density at xld = 2.5, y/d = 0.2 - 4.0, inclined cylinder
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2/s)
L0oL
-
0
4
01
0o5
0 05
.:'!AALLJ jj:_.:
ii
A
I01 TI i
rn
4
0
,
----- - -
]
1
o-----'----
__A
.A
0
o05
- ___
o
iuiiii
1
CT,,,,,
11111,1
1
T
01
I
-
i?
:',;:::::
ous F
1O
lot
:
:
102
:'
iO
z
005
:',;:;:::
:::'.::
100
:1::
lOt
102
f(Hz)
f(f-fz)
Figure E.2: Power spectral density at xld = 7.5, y/d = 0.2 - 4.0, inclined cylinder
io3
0.
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2/s)
0.02
0.02
0.01
0.02
i00_
0.02
u,,,u,,,
rr
0.02
en
001
0 01
o
0
0.02
0.02
1::::::
001
¶jl 001
0
0
0.02
0.02
IN
-t
o.oi
oo
0
0.02
,,,,,,,,
,,,,,,,
-i--
III
o.oi::::
0.02
JLI I
,,,,,,,,,
.,,,,
0.01
0
''.:; L. _i..Li'
002 ,,,,,,,,
0
'''''""
0.02
,,.,,,,,
lull,,,,
u,,,,,,
1-r-l-nr,
- 'j'''-'
_______________________
1-
001
0hHJLLi
-
lOD
io
1(1-I z)
io
100
_'J
...'
101
!L(',hJ.,
102
f(Hz)
Figure E.3: Power spectral density for VR = 0.85, at x/d = 2.5, y/d = 0.2-4.0, zld = 0, steady jet
U-component, Power / frequency (m2/s)
V-component, Power I frequency (m2/s)
*
10
0
H
0
10
iii
I' 10
5
rr-i--rr1,
0
S
i--i-
0L
L
010
5
x10
r- ,,,,,,,,,,,,,,,,,.,,,,
0 1O
5 i-
(N
0
_-_I
--'
-' __________
0*10_
(I 10
5 r-
: L
0 10
-
J
0 1O
xl0
r-
-r-r
rrr--
r
i
0J jj
IN
100
1&
fQ-fz)
10
iü
[T
100
102
f(Hz)
Figure E4: Power spectral density for VR = 0.85, at xld = 7.5, y/d = 0.2 4.0, zld = 0, steady jet
1o3
U-component, Power / frequency
V-component, Power / frequency (m2/s)
(m2/s)
-r
rn-
1T1 rrr-
1
02
:::
0:
::::
jj
In
0.2
'01
::::;
o
'::::
':::
III,,.
H .
02
0
'
H:'':
In
I
I::::::
...............
::::::
I
0
0.2
I:::::
_J ______________________
H':::
I,,,,,,
021-
01
-
:1::::::
: _ '
0
2.
0
:1::::
-.
................
O.2
I::
0
:
:
II::::::
:
:::::
:
:
H'i
-
:
0
I
A
100
:
:
:
: ::::
:
01
10'
f(Hz)
:::::
111111
1
'I'ffl H 1H'1I
______________________
102
o3
100
102
10'
f(Hz)
Figure E.5: Power spectral density for VR = 0.85, at xld = 2.5, y/d = 0.2-4.0, z/d =0, pulsed jet
io2
U-component, Power / frequency (m2/s)
:::::::
004
if::::::
:::::::
if
.
V-component, Power! frequency (m2/s)
t][4
::'
if
:::if:::
:
41s oo1
I]
I
002
::'.
0
[
04
'...'.
!!
I
4,002
...:..
0
Il
I
004
*002
C'D
*0.02
0'':if'ifif;
'if:::';
::::'''
:'''
if
,0.U4ififif,,ififif
(N
.J,,
002
1
if
if!!!,,,
if
'''':::;
:::::if:::
)0.04ififififif
(N
:
:
:
:
: ::
:
:
:
:
: :
:
:
:
:
:
: :::
:
:
:
:
:
:
:
4,, 002
:
: if::::
:
:
:
:
: : ::
:
:
:
if:::
:
:
:
:
:
0if::
0.04
if
if
if if
J)0.04!!if!!if!!
_LJ, 0.02
:
0.04
:
if
::
:
:
:
if
:
*0U2ififififififif
:
0
::
004H!if:!
::::::j_
0
0.02I-
: :
if
if
if
if
if
if:
::ifif!!!!:
:::
if
if
if
if::::
if
if
if
if
if
if
if
if
if
i..
A '
:' : ;::
.
1..
if if:::,':
if
!!if!!if!if
()0.04ififif!ifif!
if
if
::,
'
''
0.02
:
:
::
:
!::!::if,
:
:
::
:
:
:':::I
o 04
if
:
if
:::
:ififj
if::::
if
if
,(004!if!!!if!!
:::
:
:
: :::j
if
:
:
:
:
:
:
:
:
:
if
if
:1:,
if
if
if
if
if if
if
if
if
:::
if!ififif!ififif
:
:
:::::
:
..
L.'''
U..
'.'',
:
''''''
'''''
0
10'
f(Hz)
if
if
10n
ic?
:
.if:ifiififif;
0tJ2
j
.'-
if
0
!!!!
if
if!H:H!!
:::
Lif._2,_i-._.L__---.-"..:
if
:
:,if:if::
:
if
!!!:!!!!!
!!ifif!!!!
004
:9
if
if
0
0
if
,
if
if
if
102
f(Hz)
Figure E.6: Power spectral density for VR = 0.85, at x/d = 7.5, y/d = 0.2 4.0, z/d =0, pulsed jet
if
ic?
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2/s)
0.05
................
0
TTT
0.05
-
0.05
.
LU
en
.
oo:
I
0.05
0
0,05
0.05
-
0.05
................
................
(N
.-
1-rn
en
I
.
(N
.
$
00:
0.05
MW
4!,
0
0.05
0
0.05
:::
10°
- -
:
_j_____,
0 ------- . -',
lOt
100
io
f(Hz)
Figure E.7:
.
:
0
Power spectral density for VR
flLJL
..,
..A.:_, 1.i..
...
101
,.
..
102
f(Hz)
= 3.4,
at x/d = 2.5, y/d = 0.2 4.0, z/d = 0, steady jet
10
U-component, Power / frequency
V-component, Power / frequency (rn2/s)
(m2/s)
LI IL
JJILHiL i
11Th
0.02
0.02
i0o1____
ooiL.L_
0
T
0.02
'
i....Li
002
-
001
ft:: ::àjj,:::
11.02,,,,,,,
LLI ttILL
0
0.02
i _ 1Li. HI
0.02
AL
('4
-J,00i
o
:::::::
:1::::::
I:::
:
__
1:::::::
jj
.1
0.02,,,,,,
0.01
_
0.02
0.011:::::::
'' .
: :1
.1. ' .
0.02
ooiLU L.t'_/\J
0.02
0.01
: I:::;:, :
1
:
0.02
'Ii'
_ -.
0.02
111111111
0
1:::::::
: ::
:
0
I
100
l&
f(Hz)
'
-----
,
-
11111111
'-'-"
1.02
::::::::
::
-'''"
io2
o_oi
:1::::::
0
:::::::
__.J_'
100
..'..
'I
10'
.._!
"I
io2
I(Hz)
Figure E.8: Power spectral density for VR = 3.4, at x/d = 7.5, y/d = 0.2 4.0, z/d = 0, steady jet
io
tJcomponent, Power I frequency (m2Is)
V-component Power / frequency (m2/s)
HH
:::;:::::;:
2
100
101
102
HH
HH
2
o
100
f(Hz)
Figure E.9: Power spectral density for VR = 3.4, at x/d = 2.5, y/d = 0.2
101
io
((I-f z)
4.0, z/d =0, pulsed jet
iü
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2/s)
Di____________________________________________
II,uuII
111111111
o1
lI!uII,utII(tI,ICTII4(II
11111111
_ 0.1
0. i::::::::
:
I
1
I
*02
HH
Oil
', 0.1
: ::
:
**O.2
I
1
1111111
I
1.11111
I
:
02
Ii
uJIIIflIuI)IIflhtluIItt
:
r
t
I
I
:11:11
:1:1::
1:1111
1
1
:1:1.1
Il)
0
0.1
0
:1
:
IlIli
0l
:l:I
o
o.i
1
O2
0l
0
01
111111
IIIIII
IIIII
'I
11111111
II
100
I
I
I
E.10:
:._:_._.I
:I.j
I
.L..l..__
101
102
iO3
II:::
111111
1
111111
I
0
01
1111
t(Hz)
Figure
,oi
01
Il.
I
111111
I
1I
0
102
I
II
I
1111', II
III
II
I,
10'
102
f(Hz)
Power spectral density for VR = 3.4, at x/d = 7.5, y/d = 0.2 4.0, z/d =0, pulsed jet
U-component, Power/frequency (m°Is)
V-component, Power! frequency (m2/s
11
iO3
:FI
x 10
x 10
:FI
1110
22 10
r
HFJh7
HiiJ
10
0
dO
o
11
I
hull
11111
x 10
L
1
x 10
.Ii.IIi
)c 10°
ci
11
x 10
A
I.
10
22 10
2
xlO
x 10
-1
Il
11r
I:
21
22 10
1-I
2JJIF
10°
101
102
ftl-iz)
Figure E.11: Power spectral density for
10°
UIILHI JJJIIJIL
iO2
iO'
f(Hz)
VR = 0.85, at xld = 2.5, yld = 0.2-4.0, zld = 0.8,
steady jet
10
U-component, Power / frequency (m2Is)
V-component, Power / frequency (m2/s)
0.01
0.01
0'
_________________
0.01
0.01
.0.005
o.00s
_________________
0
__________________
0
O.0lp---,1
____________________
0.01
C',
40.00s
0 005
0 ''-"
____________________
0
-,-.,
0.01
0.01
0 005
,,,,,,,,,,,,,,,,,,,
0
0.01
4
-
0.01
0.005
0.01
000:L
-
r,-r---
L0
0.01
,,,,,,,,,,,,,,,,,,
0
'.:
L4)
o.oas
.a___
0
0.01
-.-,--
o.00s
0
0.01 i-,
',
,------
LL.__ 'H'''
'''''','''''''','''''
'i-
_______
0.01
- -
r m
LID
,,,I,I,
0,01
o.006
o'
'ii
'-----
0
0.01
0,01
0
io2
f(Hz)
1o3
p
r r-,-,-,-,--------'r'--
'H
,,,,,,,,,,,,,,,,,,,,
H
'
HH
i000s
lo°
_,
'
,-rr-----
__________
,H'''.H
'
10°
Figure E.12: Power spectral density for VR = 0.85, at x/d = 7.5, y/d = 0.2
-.
'
_______
,'
'''H
102
10'
f(Hz)
4.0, z/d = 0.8, steady jet
U-component, Power / frequency (m2/s)
-0.05
V-component, Power / frequency (m2/s)
0.05
0
00
0.O5j;
0
41,
0
0
'.''''I:''.:1!I
o.cs
0o6L
I
100
io
io
fI-tz)
100
1&
102
f(t-fz)
Figure E.13: Power spectral density for VR = 0.85, at x/d = 2.5, y/d = 0.2 4.0, z/d = 0.8, pulsed jet
io
U-component, Power / frequency (m2/s)
V-component, Power / frequency (m2/s)
0o05L._
tEl
00Q5H
0.01
HHW
o
I
0
001
0 005
o
0
_________
II
tEl
o.oi
0 005
I
0
001
0.005
0
0.0
HH
rI
o.uos
_!LII.
0
HH !!I
.
1
0005L
000G
0
000sL
100
io
f(I-tz)
io3
100
102
1o3
f(Hz)
Figure E.14: Power spectral density for VR = 0.85, at xld = 7.5, y/d = 0.2-4.0, z/d = 0.8, pulsed jet
1
U-component, Power / frequency (m2Is)
:ffh1:
i[ 1ftffiiiI1
0.2
'ii
V-component, Power / frequency (m2/s)
II
H
[1
111
01
o-
LLLL._
j,.
r rTrr- -r r
0i
-
L:_:_i______
-,-l-rrT
- -
rrr-
- 1
02
H
0
r-rr
-r-r
TT
TTfl
r--1--T- r-T-,
02
----
o-'---------'-02IT
0.2
h'
,
o1L
::::j
''--a
a
H1T1
02
H
ai
--
'H
rrrr
-'r r ti-rn
rTr-
1
02I-
r'rrT rTrIHH-I
:
I
0.2
I
TTh,,u,uu
Ill,,,,,
III
H
:______
01
O1
0.1
,
0
1
10°
10'
1(1-f z)
l0
0.1
0
IO
10°
10'
10
l0
f(Hz)
Figure E.15: Power spectral density for VR = 3.4, at x/d = 2.5, y/d = 0.2 4.0, z/d = 0.8, steady jet
00
U-component, Power I frequency (m2Is)
V-component, Power I frequency (m2/s)
0.01
001
000F
.
'--
111
0.01
001
LI)
.
0 005
L___
..-\
0.01
LLUJ
/& T L
II::
0
001
. ..
(N0005
HI
LI)
0.01
5000:
0.01
:
:
HI
H
0.01
LI)
JLI
Lii L_L-1
0.01
.t
o.00s
LL L
0.01
I::
:
:
:
:
:
:
::
-
0
0.01
.
-
0,01
J.LLi
0
0,01
0005
11
100
102
10
f(Hz)
io3
0
100
1&
-.
102
f(Hz)
Figure E.16: Power spectral density for VR = 3.4, at x/d = 7.5, y/d = 0.2 4.0, zld = 0.8, steady jet
U-component, Power / frequency (m2/s)
0,5
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
0
0.5
0
0.5
,.,,,,
r
"-,--rr
0.5
,,,,,
r
r-rr 1-1-n-
0
V-component, Power / frequency (m2/s)
_
,,-,-,-
r ,r,
0.5
i,
r-,r r-rrr- r r--r
0.5
11 1
--,-rr r,-n-
I1E _
---'-------
0
''
I
100
io'
1o2
io3
100
f(Hz)
Figure E.17: Power spectral density for VR = 3.4, at x/d = 2.5, y/d = 0.2
102
10'
f(Hz)
4.0, z/d = 0.8, pulsed jet
li-component, Power I frequency (m2/s)
V-component, Power / frequency (m2/s)
01
0.1
4!,aos
HH
0
0.1
0.1
LI)
0
0
0.1
0.1
en
en
005
0.05
0 ''!'".i
0
0.1
.L)
I-
I
0
.
005
0
0.1
N
0.05
0.1
O
0.1
0'
0.05
13
0,1
o
:''i
'
0.1
oo
oosL0
_,-..,:
100
:::
::::::
101
f(Hz)
0
io
/0'
f(Hz)
Figure E.18: Power spectral density for VR = 3.4, at x/d = 7.5, y/d = 0.2-4.0, z/d = 0.8, pulsed jet
00
v-component (nVs)
u-component (rrVs)
°40T°81
20
02
0.4
0.6
0.8
1
20.40.60.81
02
0.4
0.6
0.0
I
02
0.4
0.6
0.8
1
62O406O81
2O.40.6O.81
2O.4O.6O.01
:20401
:20001
0.4O.6O.01
Figure E.19: Velocity time traces at x/d = 2.5, y/d = 0.2-4.0, inclined cylinder
00
u-component (mis)
io40081
io4001
ic81
ic401
io406081
v-component (m/s)
H-HHH
52Q4O6O61
52O4O.6O81
2204O6O81
62040.6081
46O81
Figure E.20: Velocity time traces at x/d = 7.5, y/d = 0.2
4.0, inclined cylinder
00
u-component (ni's)
v-component (mis)
040601
L441
0.0L081
0.2
0.4
0.6
0.8
1
0.2
0.4
0;6
0;8
1
0.2
0;4
0.6
0.8
c
0
io40,60
C
F
-E
Figure E.21: Velocity time traces for VR = 0.85, at x/d = 2.5, yld = 0.2-4.0, zld = 0, steady jet
u-component (m's)
v-component (m's)
4
HHHHHH
60
02
0.4
0.6
0.8
CA
0.6
08
E:HHH
Figure E22: Velocity time traces for VR = 0.85, at xld = 7.5, yld = 0.2-4.0, z/d = 0, steady jet
u-component (rn(s)
2O4O6O.81
I4o
v-component (rn's)
:
0a2040606
0.4
0.6
0.6
O4O6O8i
Figure E.23: Velocity time traces for VR = 0.85, at x/d = 2.5, y/d = 0.2-4.0, z/d = 0, pulsed jet
u-component (rn's)
v-component (rn's)
&51
4
5m40.60.oi
2
:406081
:
0.
620406081
-2
0.40.60.81
-2
20
20
02
U;4
0;6
08
0.2
0.4
08
08
1
0
60
02
0.4
0.6
0 8
Figure E.24: Velocity time traces for VR = 0.85, at xld = 7.5, yld
O.40.608l
0.2 4.0, z/d = 0, pulsed jet
rJ?o
u-component (m's)
v-component (m's)
:
2H.01
0.2
0.4
0.6
0.8
1
0.2
0.4
0.6
0.8
ft2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
1
:
2c:2:.::1
100
200020406081
0
-5
0
Figure E.25: Velocity time traces for VR
3.4, at xld = 2.5, yld = 0.2 4.0, z/d 0, steady jet
1
u-component (ni's)
10
o.
v-component (ni's)
5o
0
0
0,2
0.4
02
0.4
fl.B
0.8
-E
0.8
0,8
-C
m;0i81
Figure E.26: Velocity time traces for VR = 3.4, at x/d = 7.5, y/d = 0.2 4.0, z/d = 0, steady jet
u-component (m's)
v-component (m/s)
:
.4O.60.81
O.4O.6O.61
2O4O.6O.8i
iO.406081
O4O.61
0
0.2
0.4
0.6
0.8
1
Figure E.27: Velocity time traces for VR = 3.4, at x/d = 2.5, y/d = 0.2 4.0, z/d = 0, pulsed jet
"C
u-component (m/s)
v-component (mis)
5
100
0.2
14
0.6
0.8
1o:4008
0L
1c01
-5
C0
-5
t12
0;6
0.8
JJLuW
0.2
o
0.4
0;4
0.6
0.8
6Q8
.5
0.40.60.8
60020406081
Figure E.28: Velocity time traces for VR = 3.4, at x/d = 7.5, y/d = 0.2-4.0, zld =0, pulsed jet
u-component (rn's)
v-component (mis)
o2O4O.6O81
2O.4O.6O.51
2O4a6O.B1
c.
O.4O.6O.8i
Figure E.29: Velocity time traces for VR = 0.85, at xld = 2.5, y/d = 0.2 4.0, z/d = 0.8, steady jet
u-Component (n-Vs)
v-Component (rn's)
O0a204o6081
O
04
0.8
00
0.2
0.4
0.6
0,0
04
0.6
08
0j
02
-2
0.4
0.6
0.8
0.4
0.6
0.8
Figure E.30: Velocity time traces for VR = 0.85, at x/d = 7.5, y/d = 0.2-4.0, z/d = 0.8, steady jet
'.0
u-component (ni's)
v-component (ni's)
::60H
60
c2
E2
0.4
0.6
0.6
04
06
0.8
c]
20.48
Figure E.31: Velocity time traces for VR = 0.85, at x/d = 2.5, yld = 0.2 - 4.0, zld = 0.8, pulsed jet
'0
u-component (mis)
v-component (m's)
PH*HHH
2a4O.6O81
O.4O.6O.81
20406081
:400;81
io,001
a2O.4o.6o.o1
Figure E.32: Velocity time traces for VR = 0.85, at xld = 7.5, yld = 0.2 4.0, z/d = 0.8, pulsed jet
LI,
u-component (rWs)
v-component (nVs)
2O4O60.81
2040608
:H-H
C0.2
io20.8
C
200
0.2
0,4
0.6
0.8
0.4
0.6
0.8
O
-s
!40;608,
0.2
0.4
06
08
-10
Figure E.33: Velocity time traces for VR = 3.4, at xld = 2.5, yld = 0.2 4.0, zld = 0.8, steady jet
1
u-component (rn's)
v-component (rn's)
¶ih2040H
C
S
0.2
1:406081
C
0.4
0,8
1
2:0:040:0:1
0.4
62O406081
0.6
0.6
0.8
1
H2040.60.H
Figure E.34: Velocity time traces for VR = 3.4, at xld = 7.5, yld = 0.2
4.0, zld = 0.8, steady jet
'0
u-component (rTVs)
3e
v-component (rn's)
81
40400.81
:6081
o 5°
02
0.4
0.6
0.8
02
0.4
0 .6
06
0.4
0.6
0.8
0.4
0.6
0.8
20
1
I
5
C
1401
a20.4a6oal
£
-5
0
0.2
Figure E.35: Velocity time traces for VR = 3.4, at x/d = 2.5, y/d = 0.2-4.0, zld = 0.8, pulsed jet
1
u-component (ni's)
ic
v-component (ni's)
02
0.4
0.6
08
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
E2040.6081
Figure E.36: Velocity time traces for VR = 3.4, at x/d = 7.5, y/d = 0.2 4.0, z/d = 0.8, pulsed jet
u-component (rn's)
v-component (rn's)
150
150
100L
100
50
2
4
6
8
10
12
100
0
-3
-2
-1
0
1
2
3
-3
-2
-1
0
1
2
3
:
:
i
:
:
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
100
50
50
C
0
150
2
4
6
6
10
12
100
C
-4
150
100
50
0
0
150
2
4
6
8
10
12
2
4
6
8
10
12
100
50
0
0
150
i
100
2
4
6
8
10
12
150
100
60
0
2
4
6
8
10
12
o
-4
150
100
T
0
2
4
6
6
10
12
160
100
'0
50
50
2
4
6
0
10
12
100
100
too
0
0
-4
150
50
0
2
4
6
8
10
12
0
-4
Figure E.37: Velocity histograms at xld = 2.5, yfd = 0.2
4.0, inclined cylinder
u-component (m/s)
vcompOflSnt (m/s)
O4
i012
Q12
1012
i2
1:
0i
Figure E.38: Velocity histograms at x/d = 7.5, y/d = 0.2 - 4.0, inclined cylinder
u-component (rrVs)
v-component (m/s)
1512
150
100
10
12
150
4
100
50
C
___
0
150
100
50
0
2
4
6
8
10
C
12
-4
1512
100
-3
-2
-1
1
2
3
4
-r
100
60
0
2
150
4
5
6
10
C
12
isd4
100
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
100
50
60
0
150
-3
0
2
2
150
4
4
6
8
10
12
6
8
10
12
0
-4
150
-
160
100
100
10
12
4
150
1110
100
,
50
0
150
0
2
4
6
8
10
12
150
100
50
0
2
4
6
8
10
0
-4
150
12
100
;
4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
1110
50
0
-;
50
0
150
;
100
50
0
2
4
6
8
10
Figure E.39: Velocity histograms for VR
0
-4
12
0.85, at xld
2.5, y/d = 0.2
4.0, zld = 0, steady jet
u-component (mis)
v-component (mis)
150
150
100
iooL
50
2
4
12
100
a
-4
-3
-2
-1
-3
-2
-1
-3
-2
-1
mc
0
1
2
3
4
1
2
3
4
1
2
3
4
100
50
10
150
C
12
100
-4
mc
100
50
60
0
1500
2
4
6
8
10
12
100
c
-4
150
0
100
0
150
-
-;
-
-;
0
4
100
150
100
10
150
t
4
100
12
100
150
-
-
-
-3
-2
-1
4
100
50
50
C
8
mc
10
12
100
0
-4
150
0
1
2
3
4
100
50
.IlIiII_
C-
2
mc
4
6
6
10
12
100
150
-
-
4
-
4
100
tso
C
0
2
4
6
8
10
12
Figure E40: Velocity histograms for VR = 0.85, at x/d = 7.5, y/d = 0.2
4.0, zld = 0, steady jet
u-component (rn's)
v-component (rn's)
150
150
100
100
'- 50
50
0
1600
10
0
12
4
P
mo
100
50
60
0
1500
2
4
6
8
10
12
, 100
0
isd4
P
100
5°
5
C
2
4
6
8
10
12
iscr4
1
9
100
tso
50
1500
2
4
6
6
10
12
0
15O
100
P
100
C
isc°
'
10
12
100
JAIL
2
4
6
8
10
12
2
4
6
6
10
12
2
4
6
8
10
12
- 100
15Cc
'' 100
isc°
5.,
:
:
:
:
i
P
100
100
tso
C
0
2
4
6
8
10
12
-4
-3
-2
-1
0
1
2
3
Figure E.41: Velocity histograms for VR = 0.85, at x/d = 2.5, yld = 0.2 4.0, zld = 0, pulsed jet
4
u-component (rn's)
v-component (rn's)
150
150
100
50
10
12
100
0
i5C
0
-
4
100
50
0
6
150
8
10
12
C
-2
'100
100
50
50
0
6
8
10
12
-1
0
1
2
3
4
:
:
i
0
:1::
150
:
:
:
I
i
100
100
6
iso,
8
10
12
150
4
-
-
-
-
4
-
100
via0
50
4lI__
C
6
iso
8
10
12
1ao
150
4
100
50
C
6
15C
8
10
12
100
150
-
ilk.
;
;
4
100
50
C
0
2
4
6
8
ID
12
1"-
4
Figure E.42: Velocity histograms for VR = 0.85, at x/d = 7.5, y/d = 0.2 4.0, zld =0, pulsed jet
L/t
u-component (ni's)
v-component (ni's)
150
1
12
100
-;
-;
4
100
L
°0
11
12
', 100
150
4
;
;
:
:
4
100
50
0
0L.8102
" 100
:
:
-
-:t
-
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
0
1
2
3
4
:
:
:
14
150
100
50
lIt
150
12
C
-4
iso
- 100
100
50
50
C
10
15Cc
C
12
100
-4
150
100
50
C
isc°
2
4
6
8
10
-T
12
iso
100
100
50
50
C
0
2
4
6
0
10
C
12
-4
-3
-2
Figure E.43: Velocity histograms for VR = 3.4, at x/d = 2.5, y/d = 0.2
-1
4.0, z/d
0, steady jet
u-component (m's)
v-component (mis)
AL..
:
:
!I
100
2
4
6
6
10
12
100
4
100
50
50
C
1500
:
100
2
4
6
10
12
100
0
-:
4
-
100
50
1500
'
2
4
8
8
10
12
100
4
-
50
C
2
4
6
10
12
100
'--S
0
100
60
50
C
10
iso?
icoj-
5L
isc°
-:
100
50
1600
0
2
-.
4
12
C
4
t
15C
IOU
6
8
10
12
100
-
-
-
-2
-1
4
100
50
0
0
2
4
6
8
10
12
-4
-3
0
I
2
3
4
Figure E.44: Velocity histograms for VR = 3.4, at x/d = 7.5, y/d = 0.2 4.0, z/d =0, steady jet
C
u-component (m's)
v-component (m/s)
150
150
100
100
50
0
50
0
2
4
5
6
10
12
0
-4
150
-3
-2
-1
:
:
:
0
1
2
3
:
:
4
100
,
2
4
6
2
4
6
2
4
6
S
10
12
10
12
10
12
100
IOU
c
JIIIIIL.
6
-
I
I
2
4
10
it
100
!If
100
2
4
6
5
10
12
2
4
6
8
10
12
100
50
C
0
:
:
:-
:
:
Figure E.45: Velocity histograms for YR = 3.4, at x/d = 2.5, y/d = 0.2 4.0, z/d =0, pulsed jet
i
u-component (rn's)
v-component (m's)
rTiT7T[TTI1
:_
iitii
t
°LIII
.,
I,
Figure E.46: Velocity histograms for YR
3.4, at x/d
7.5, y/d
0.2 4.0, z/d = 0, pulsed jet
u-component (rrVs)
v-component (rrVs)
O
10
12
°10
1234
if
4
!
I
:
£
2
Ii
71
:
12
100
12
'It100
18J
-3
-2
-1
0
-3
-2
-1
0
-3
-2
-1
-3
-2
-1
2
3
4
1
2
3
4
0
1
2
3
4
0
1
2
3
4
1
i°0
5O
4
12
1O0
loop
m GO
5O
isc
6
8
it)
12
6
8
10
12
l00
GO
0
0
2
4
-4
Figure E.47: Velocity histograms for VR = 0.85, at xld = 2.5, y/d = 0.2-4.0, zfd = 0.8, steady jet
u-corTponent (rrvs)
v-component (m's)
150
150
100
160
50
50
C
150
8
16
12
0
150
100
100
50
50
0
,
6
4
2
6
4
8
10
12
100
6
-4
156
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
:
:
:
:
:
100
a
1500
2
4
6
8
10
12
2
4
6
6
10
12
100
50
0
150
0
!II
1
L
1J
1500
2
4
6
8
10
12
2
4
6
8
10
12
0
150
4
-
-
4
-
-i---
150
;
4
IOU
0
100
-
100
100
150
-;
100
100
150
-
150
1a0
2
4
24
6
8
10
12
.j__
0
4
150
100
6
8
10
12
0
4
-;
Figure E.48: Velocity histograms for VR = 0.85, at x/d = 7.5, y/d = 0.2
4.0, zld = 0.8, steady jet
u-component (rn's)
v-component (rn's)
150
150
100
50
U
1b
12
-4
160
-3
-2
-1
0
1
2
3
4
-3
-2
-i
0
1
2
3
4
-3
-2
-i
0
1
2
3
-3
-2
-1
0
1
2
3
:
:
:
:
:
100
tso
50
0
-4
150
IOU
50
C
-4
150
'
100
100
tso
50
C
10
1500
12
100
100
sg
50
1500
10
12
10
12
10
12
0
100
1500
- 100
0
;
4
6
150
-
-
-3
-2
-3
-2
H
-
100
2
4
6
6
10
12
100
04
150
-10
1
2
3
4
2
3
4
100
0
2
4
6
6
10
12
-1
0
1
Figure E.49: Velocity histograms for VR = 0.85, at x/d = 2.5, y/d = 0.2 4.0, zld = 0.8, pulsed jet
u-component (m's)
v-component (rrils)
150
150
100
50
0
-4
10
160
15c
'' 100
50
0
150
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
-3
-2
-1
0
1
2
3
4
:
:
:
:
:
-
-;
-
-;
100
50
0
2
4
6
8
10
12
0
-4
150
100
100
-50
50
0
0
150
2
4
6
8
10
12
100
0
-4
160
100
50
1500
2
4
6
8
10
12
2
4
6
8
10
12
0
100
1500
'
100
i
150
100
1500
2
4
6
8
1L.
10
12
100
160
4
4
100
2
150
4
6
10
12
100
160
4
-
100
50
0
150
0
2
4
6
8
10
12
100
;
160
;
4
100
50
0
0
2
4
6
8
10
12
-;
-
Figure E.50: Velocity histograms for VR = 0.85, at x/d = 7.5, yld = 0.2 4.0, zld = 0.8, pulsed jet
4
u-component (ni's)
v-component (rrVs)
150
150
100
1110
50
50
0
B
1500
10
12
0
-4
150
100
100
tso
50
0
1500
2
4
6
8
10
-3
-2
-1
0
-3
-2
-1
0
:
:
1
2
3
4
2
3
4
:
:
U
12
e' 100
-4
150
1
100
50
0
00
100
tso
2
4
6
8
10
12
150
100
80
ALL.
150
-
150
- 100
2
46
_y
100
50
B
10
12
0
-4
150
-3
----2
-1
0
1
2
3
4
-2
-1
0
1
2
3
4
100
50
50
C
0
2
4
6
6
10
12
0
-4
150
-3
IOU
0
2
4
6
B
10
12
-
Figure E.51: Velocity histograms for VR = 3.4, at x/d = 2.5, yld = 0.2 4.0, z/d = 0.8, steady jet
4
u-component (rrils)
v-component (rrVs)
150
100
tso
4
150
12
I
' 100
150
2
0
160
2
4
U
12
10
12
-4
15c
100
3
-4
60
13
4
6
5
10
12
6
3
10
12
100
is°
2
4
100
-2
-1
0
-3
-2
-1
0
-3
-2
-1
0
C
-4
160
100
C
100
150
-3
-;
160
----'
100
2
4
24
1
2
3
1
2
3
4
1
2
3
4
O
iso
50
2
:
50
6
100
0
-
:
1
1613
' 100
150
: :
50
10
JiII.
0
:
100
46
r' 100
150
100
6
6
10
12
iso
-
-;
100
6
8
10
12
-;
-
-
--
i
4
4
AL
4
Figure E.52: Velocity histograms for YR = 3.4, at xld = 7.5, yld = 0.2 4.0, z/d = 0.8, steady jet
U'
u-component (tms)
v-component (tm's)
15C
150
100
50
90
2
4
6
8
10
12
100
0
-3
-2
-1
:
:
:
0
1
2
3
:
:
4
100
C
0
2
4
6
8
10
12
2
4
6
8
10
12
'2 100
50
C
156°
IOU
tso
0
:r
4
:
:
:
ilL
:
1
101234
i54
't 100
1I
0
6
10
12
10
12
-
100
50
0
0
2
4
6
8
-3
-2
-i
0
I
2
3
Figure E.53: Ve'ocity histograms for VR = 3.4, at x/d = 2.5, y/d = 0.2 4.0, z/d = 0.8, pulsed jet
4
u-component (Tm's)
v-component (m's)
15C
4
100
:
:
:
:
1
I
:
15C
:
100
50
o
2
4
t3
CO
2
4
6
150
B
10
12
10
12
:
:
:
:
100
150
'
I
100
O
150
----4..----.
100
0
2
4
6
8
10
12
100
150
4
-
150
100
2
4
6
8
10
12
-
160
4.--
4
4'..
4
100
i1iI
150
!-
2
4
6
8
10
C
12
150
100
2
4
6
8
10
12
-:
-
-
Figure E.54: Velocity histograms for VR = 3.4, at x/d = 7.5, yld = 0.2-4.0, zld = 0.8, pulsed jet
4