AN ABSTRACT OF THE THESIS OF
Bertrand P.E. Dano for the degree of Master of Science in Mechanical Engineering
presented on October 12, 2000. Title: Flow Characteristics of Semi-confined Impinging
Jet Arrays
Abstract approved:
Redacted for Privacy
James A. Liburdy
The present study proposes to investigate the flow structure of different arrays of
jets impinging on a flat surface enclosed by three walls, creating a channel that forces the
air to leave in one preferential direction, generating a self sustain crossflow. Details of
both the mean and some turbulence quantities for two 7x7 jet arrays are presented. The
first array was a circular orifice array while the second was a "cusped" ellipse array. The
non-symmetry of the cusped ellipse shape allowed two alignments with the crossflow,
one where the crossflow was along the major axis (0°) and one where the crossflow was
along the minor axis (90°). The Reynolds number ranged from 8,500 to 15,900.
Surface flow visualization, jet orifice flow coefficient measurements and PIV
measurements of the entire flow field were used to interpret the complex flow
characteristics. The mean velocity, turbulent kinetic energy, mean vorticity and mean
squared vorticity fields were calculated from the PIV data at three different locations
along the downstream flow direction: close to the back, at the center of the jet array and
close to the exit.
The visual observation of the impinging flow pattern shows similar results for all
of the different geometries and configurations. The jets generated cells defined by
detachment-reattachment zones with a characteristic horseshoe shape around each jet.
The cells become increasingly more oblong in shape with increasing crossflow due to an
uneven shifting of the upstream and downstream cell boundaries, in the downstream
direction. The flow coefficient of each jet decreases monotonically and quasi-linearly
along the crossflow direction while the average value increases only a few percent for
increasing Re. PIV measurements of the entire flow field in the vicinity of the jet exits
reveals complex flow structures. A large rotating vortex created by the merging of the
crossflow and the jet column return-flow, moves towards the jet column as the crossflow
increases in strength. This interaction appears to generate multiple turbulent flow patterns
that may have consequences in improved surface cooling. For the lower values of Re, the
cusped ellipse jet array, placed in the
(00)
position, appears to generate significantly more
turbulence than the circular jet array. For higher values of Re, both configurations show
similar results. But when placed in the (90°) position, there is a considerably smaller
increase in the levels of turbulence when compared to the circular jets. Evidence of axis
switching in the jet column for the cusped ellipse jets tends to prove that a transport in the
lateral direction could be a secondary factor to take into account for surface cooling
efficiency.
Flow Characteristics of Semi-confined Impinging Jet Arrays
by
Bertrand P.E Dano
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirement for the
degree of
Master of Science
Presented October 12, 2000
Commencement June 2001
Master of Science thesis of Bertrand Dano presented on October 12, 2000
APPROVED:
Redacted for Privacy
Majr)ofessor, representing Mechanical
Redacted for Privacy
Head of Department of Mechanical Engineering
Redacted for Privacy
Dean of Gra1ika-gchool
I understand that my thesis will become part of the pennanent collection of Oregon
State University libraries. My signature below authorizes release of my thesis to any
reader upon request.
Redacted for Privacy
ACKNOWLEDGEMENT
I would like to thank my parents (Raymond and Nicole) and the rest of my
family members for their endless support, patience and love.
I would like to offer my deepest thanks to all the teachers I ever had, past
and present, east and west, scientific and non-scientific, and in particular to Dr
Liburdy who brought my interest in science and in life together. Thanks to all the
members of my committee: Dr Pence, Dr Kanury and Dr. Skyllingstad.
I would like to thank all my colleagues and especially Brian Daniels for his
help and suggestions throughout the entire experimental process.
My warmest appreciation I also express to "Stevy" Adams, who did much
more than help with the experimental setup. His comments and suggestions were
invaluable and were matched only by his patience for my antics.
Finally, I extend my grateful thanks to all my friends who in any way,
helped, supported and encouraged me.
TABLE OF CONTENTS
I. INTRODUCTION
1
Background ............................................................
Objectives ...............................................................
1
2
II. LITERATURE REViEW ................................................
3
Jet Array without Impingement or Crossflow .....................
3
Jet Array with Crossflow .............................................
6
Jet Array with Impingement ..........................................
7
........................
8
Jet Array with Crossflow and Impingement
Ill. EXPERIMENTAL SETUP ............................................
14
Air Delivery System ..................................................
14
Impingement Surface .................................................
18
Pressure Drop Measuring Apparatus ...............................
19
Flow Visualization Apparatus .......................................
22
Velocity Measurements ........................................
P.I.V. Acquisition and Software ..............................
Impingement Surface Streamline Apparatus ................
22
24
25
IV. EXPERIMENTAL DATA ANALYSIS ..............................
28
Velocity Ratio ..........................................................
28
Pressure Data ..........................................................
29
Velocity and Mean Velocity Field ..................................
30
TABLE OF CONTENTS (Continued)
Mean Vorticity..
32
Turbulent Kinetic Energy ............................................
33
Mean Squared Vorticity ..............................................
34
Data Reduction ........................................................
34
Surface Flow Visualization ...........................................
36
V. RESULTS AND DISCUSSIONS .....................................
37
Flow Structure along Downstream Position .......................
39
Effect of Reynolds Number ..........................................
56
Effect of Impingement Distance .....................................
69
Effect of Geometry/Alignment of Cusped Ellipse Jet Array.
81
Side Wall Effects ......................................................
95
Discussion ..............................................................
100
VI. CONCLUSION AND RECOMMENDATIONS ....................
105
BIBLIOGRAPHY .....................................................................
107
APPENDICES .........................................................................
109
A. Uncertainty Analysis ...................................................
110
B. Flow Visualization Software Analysis and Methods ...............
115
C. Raw Data Tables ........................................................
117
LIST OF FIGURES
Figure
2.1
Impinging jet topology
11
3.1
Schematic of the air delivery system
16
3.2
Jet array geometry (top: circular jet array, bottom: cusped
ellipse jet array
17
3.3
Impingement plate setup
21
3.4
Pressure tap location
21
3.5
Visualization apparatus
23
3.6
Laser sheet location
23
3.7
Impingement layer location
27
3.8
Impingement layer visualization
27
4.1
Crossflow-to-jet velocity ratio, versus jet number
measured from the most upstream jet
28
4.2
Computation area for property levels
35
5.1
Definition of jet regions with four points of interests
identified
38
5.2
Flow coefficient, H/DH=4, Flow rate QR=14CFM,
Circular jet: Re=9,740, Cusped ellipse (00) jet: Re=8,570
40
5.3
Close-up of the flow visualization by surface deposition
illustrating the surface vortex and stagnation point relative
dimensions
40
Surface Flow Visualization, Circular Jet, HIDH=4,
QR=14CFM, Re=9,740
42
5.4
V1
LIST OF FIGURES (Continued)
Figure
5.5
Surface Flow Visualization, Cusped Ellipse (0°), I-lID=4,
QR= 14CFM, Re=8,570
5.6
Surface vortex and Stagnation point relative location,
HJDH=4, QR=14CFM, Circular: Re=9,740, Cusped ellipse
(0°): Re=8,570
43
Surface vortex deposit size, HJDH=4,QR=14CFM,
Circular jet: Re=9,740, Cusped ellipse (0°) jet: Re=8,570
43
5.8
PIV, Circular jet, H/DH=4, Vr=0.032, Re=9,740
45
5.9
PIV, Cusped ellipse (0°), Vr=0.032, HfD=4, Re=8,570
45
5.10
Flow characteristics, Circular jet, HfD=4, Vr=0.032,
Re=9,740
46
Flow characteristics, Cusped ellipse (0°), Vr=0.032, H/D=4,
Re=8,570
47
5.12
PIV, Circular jet, HJDH=4, Vr=0.095, Re=9,740
49
5.13
PIV, Cusped ellipse (0°), H/DH=4, Vr=0.095, Re=8,570
49
5.14
Flow characteristics, Circular jet, H/DH=4, Vr=0.095,
Re=9,740
50
Flow characteristics, Cusped ellipse (0°), HJDH=4, Vr=0.095,
Re=8,570
50
5.16
PlY, Circular jet, H/D=4, Vr=0.159, Re=9,740
53
5.17
PlY, Cusped ellipse (0°), HIDH=4, Vr=0.159, Re=8,570
53
5.18
Flow characteristics, Circular jet, I-I/DH=4, Vr=0.159,
Re=9,740
54
5.7
5.11
5.15
42
LIST OF FIGURES (Continued)
Figure
5.19
Flow characteristics, Cusped ellipse
Re=8,570
(00),
HIDH=4, Vr=0.159,
55
5.20
Flow coefficient, Circular jet, HJDH=4
57
5.21
Flow coefficient, Cusped ellipse (0°) jet, 1-IJD=4
57
5.22
Surface flow visualization, Circular jet, HIDH=4,
QR=2OCFM, Re=15,800
59
5.23.
Surface flow visualization, Cusped ellipse (0°), HJDH=4,
QR=2OCFM, Re= 13,500
59
Surface vortex and stagnation point relative location,
H/DH=4, QR=2OCFM, Circular: Re= 15,800, Cusped ellipse
(0°): Re=13,500
60
Surface vortex deposit size, HJDH=4,
QR=2OCFM, Circular: Re= 15,800, Cusped ellipse (0°):
Re=13,500
60
5.26
PIV, Circular jet, 1-IJDH=4, Vr=0.032, Re= 15,800
61
5.27
PIV, Cusped ellipse (0°), HJDH=4, Vr=0.0.32, Re= 13,500
61
5.28
Flow characteristics, Circular jet, H/DH=4, Vr=0.0.32,
Re=15,800
62
Flow characteristics, Cusped ellipse (0°), HJDH=4,
Vr=0.0.32, Re= 13,500
63
5.30
P[V, Circular jet, Fi/DH=4, Vr=0.159, Re= 15,800
65
5.31
PIV, Cusped ellipse (0°), HJDH=4, Vr0.l59, Re=13,500
65
5.32
Flow characteristics, Circular jet, I-TJDH=4, Vr=0.159,
Re= 15,800
66
5.24
5.25
5.29
LIST OF FIGURES (Continued)
Figure
5.33
Flow characteristics, Cusped ellipse
(00),
Re= 13,500
H/DH=4, Vr=0.l59,
67
5.34
Flow coefficient, Circular jet, H/DH=2
70
5.35
Flow coefficient, Circular jet, HJDH=1
70
5.36
Surface flow visualization, Circular jet, HIDH=2, Re=9740
71
5.37
Surface flow visualization, Circular jet, HJDH=2, Re= 15,830
71
5.38
Surface vortex and stagnation point relative location,
Circular jet, H/DH=2, Re 1=9740 and Re2= 15,830
72
Surface vortex deposit size, Circular jet, HIDH=2, Rel=9740
and Re2=15,830
72
5.40
PlY, Circular jet, H/DH=2, Vr=0.048, Re=9740
74
5.41
PlY, Circular jet, HJDH=2, Vr=0.048, Re= 15,830
74
5.42
Flow characteristics, Circular jet, H!DH=2, Vr=0.048,
Re=9740
75
Flow characteristics, Circular jet, HIDH=2, Vr=0.048,
Re=15,830
76
5.44
PIV, Circular jet, HJDH=2, Vr=0.095, Re=9740
78
5.45
PlY, Circular jet, HJDH=2, Vr=0.095, Re= 15,830
78
5.46
Flow characteristics, Circular jet, H/DH=2, Vr=0.095,
Re=9740
79
Flow characteristics, Circular jet, HJDH=2, Vr=0.095,
Re=15,830
80
5.39
5.43
5.47
LIST OF FIGURES (Continued)
Figure
5.48
5.49
Flow coefficient, Cusped ellipse
Re=8,530
(00)
and (90°), H/DH=4
82
Average flow coefficient, Cusped ellipse (90°), HIDH=4
Re=8,530
82
5.50
Flow coefficient, Cusped ellipse (0°) HJDH=l, Re=l3,500
83
5.51
Flow coefficient, Cusped ellipse (90°), }UDH=1 Re=l3,460
83
5.52
Surface flow visualization, Cusped ellipse (90°), H/DH=4,
Re=8,530
85
Surface flow visualization, Cusped ellipse (90°), H/DH=4,
Re=13,460
85
Surface vortex and stagnation point relative location, Cusped
ellipse (90°), HJDH=4 and H/DH=2
86
5.53
5.54
5.55
Surface vortex deposit size, Cusped ellipse (90°), HIDH=4
and HJDH=2
86
5.56
PIV, Cusped ellipse (90°), H/D4, Vr=0.032, Re=8,530
88
5.57
PlY, Cusped ellipse (90°), HJD11=4, Vr=0.032, Re= 13460
88
5.58
Flow characteristics, Cusped ellipse (90°), HIDH=4,
Vr=0.032, Re=8,530
89
Flow characteristics, Cusped ellipse (90°), H/DH=4,
Vr=0.032, Re= 13460
90
5.60
PIV, Cusped ellipse (90°), H/DH=4, Vr=0.095, Re=8,530
92
5.61
PlY, Cusped ellipse (90°), HIDH=4, Vr=0.095, Re= 13460
92
5.62
Flow characteristics, Cusped ellipse (90°), HJDH=4,
Vr=0.095, Re=8,530
93
5.59
LIST OF FIGURES (Continued)
Figure
5.63
Flow characteristics, Cusped ellipse (90°), I-I/DH=4,
VrO.O95, Re= 13460
94
5.64
PlY, Cusped ellipse (90°), H/DH=4, Vr=0.l59, Re=8,530
96
5.65
PlY, Cusped ellipse (90°), FI/DH=4, Vr=0.159, Re=13460
96
5.66
Flow characteristics, Cusped ellipse (90°), HJDH=4,
Vr=0.159, Re=8,530
97
5.67
Flow characteristics, Cusped ellipse (90°), H/DH=4,
Vr=O.159, Rel3460
98
5.68
Side-wall flow visualization
99
5.69
Comparison of <W2>
102
5.70
Comparison of <TKE>
104
5.71
Comparison of <Wms>
104
LIST OF TABLES
Table
3.1
Pressure tests and conditions
20
3.2
PIV tests and conditions
26
3.3
Streamline visualization tests and conditions.
26
4.1
Velocity Filter weight-coefficient
30
4.2
PIV scaling factor
31
5.1
Jet array flow conditions
102
NOMENCLATURE
A3
Jet exit area, m2
A1
Total jet exit surface area, m2
DH
Hydraulic orifice diameter, m
H
Height of jet array above surface, m
M
Mass flow rate, kg/s
N3
Number of jets
QR
Volume flow rate readout from flowmeter, m3/s
QA
Actual volume Flow Rate, m3/s
Re
Reynolds number, M DH/AJJI
S
Spacing from jet center to center, m
Sc
Stagnation Point Size
Svs
Surface vortex stagnation to stagnation point distance
Ss
Surface vortex separation distance
T3
Jet air temperature, °C
Ta
Ambient temperature, °C
X
Distance along the streamwise direction, m
Z
Height of jet array above impingement surface, m
Viscosity,
p
Density, kg/rn2
Flow Characteristics of Semi-confined Impinging Jet Arrays
CHAPTER I
INTRODUCTION
Background
Many engineering applications currently use jet impingement to improve the
cooling of micro- and macro-systems. The use of impinging jets of air in industrial
applications evolved rapidly from a single jet to arrays of jets, providing better
mixing andlor a more uniform cooling.
Numerous combustion systems, such as airplane jet engines, are
substantially improved using jet arrays mixers" due to their superior mixing and
their lower noise levels. The glass uniformity and transparency is an example of
this uniform cooling capability where an array of air jets is used to quench the glass
still hot from the foundry. Gas turbine industries often use rows of jets to cool large
turbine blades with operating temperature above 1,000°F. Inside the blades, a
core/tubing system supplies air to multiple orifices disposed along the inner surface.
Each hole generates a jet that impinges on the inside surface of the turbine blade,
reducing the temperature and the temperature gradient of the blade. In this specific
case, the impinging air carries away the heat but also generates a cross flow that
2
influence the cooling effect of the other jets. Special military applications also use
air jet arrays. The V.S.T.O.L (Vertical/Short Take Off and Landing) system used on
various tactical military fighters found air jet arrays to help the planes take off
quasi-vertically. The uniformity of the jet creates a more stable base to sustain the
military airplane above the ground.
Specific Objectives
The present study proposes to investigate the flow structure of different
arrays of jets impinging on a flat surface in the presence of a crossflow. The surface
is enclosed by three walls, creating a channel that forces the air to leave in one
preferential direction, generating a crossflow. Two jet nozzle geometries are
studied: a circular cross section and a cusped ellipse cross-section. The cusped
ellipse nozzle offers a non-axisymmetric shape and suggests two different
orientations: aligned parallel to the crossflow and normal to the crossflow.
The goal of this study is to achieve two main objectives. The first focuses
on understanding the crossflow-to-jet interaction along the flow and the
corresponding effect of the impingement distance and the flow rate (or Reynolds
number). The second objective is to identify any specific behavior for a jet array
with a non-axisymmetric geometry (cusped ellipse).
3
CHAPTER II
LITERATURE REVIEW
This literature surveys four principal area of interest: free stream jet arrays,
jet arrays with a crossflow, jet array with impingement and finally, jet arrays with
crossflow and impingement. In the free stream jet arrays literature review, the
co-
flowing jet interaction and mixing distance will be emphasized along with the role
of the flow structure in the mixing process. Different experiments on the use of jet
arrays for cooling purposes will be discussed, emphasizing the flow characteristics
rather than the cooling efficiency. Then, the use of jet arrays in presence of a
crossflow or an impingement surface will be presented. Finally, the effect of an
impingement plate and a self-induced crossflow will be presented with special
attention being given to the experimental methods used.
Jet Arrays without Impingement or Crossflow
Raghunathan and Reid (1) investigated the noise level and flow structure of
multiple air jets. The number of nozzles was varied from 5 to 9 and arranged in a
circle around a central jet. The total nozzle area for each configuration was kept
constant at 9.75mm2. Using a Pitot tube, they measured the velocity profiles at
different distances along the central axis. For the multiple jet configurations, the
peak velocity of the outside jets appears to shift closer to the center axis until they
merge into a single unique jet. The downstream merging distance is about Z/D0=14
for the 5-jet configuration. For the single jet the axial velocity stay constant until
ZJD0=5 where it starts to decrease asymptotically until ZJD0=20 where it remains
constant. This axial velocity decay starts to drop earlier at Z/D0=2 for the 9-jet
configuration, and reach its asymptotic value at about Z/D0=lO. The rate of decay
appears to increase with the number of jets. After a distance of ZID0=50, the axial
velocity is less than 2% than the exit velocity and the differences between the
multiple-jet configurations are not significant. Concerning the noise level, a
significant reduction of noise is observed compared to a single jet but the noise
reduction difference between 5 and 9-jets is very small.
Moustafa et
al. (2) studied
the
modified behavior of a twin-jets
configuration in addition of a third jet, creating a triple air jets configuration. The
nozzles were arranged in an equilateral triangular configuration for different jet-to-
jet spacing (12, 16, 18 and 22 mm). Velocity profiles were measured along the
central axis using a three-hole Pitot tube. Three different planes were studied:
across the flow of the twin-jets, across the center line between the twin-jets and the
third jets, and across the flow of the third jet. Results shows that the velocity decay
of the third jet is more rapid than for a single jet and strongly dependent of the jet-
to-jet spacing. The base twin-jets merge together to form a unique jet further
downstream and this merging distance increases with nozzle spacing while the
potential core length decreases with bigger nozzle spacing. At the exit, the
spreading rate of the twin-jets appears to be larger than for the third jet. Along the
symmetry axis, the spreading rate of the twin-jets increases, but much slower that of
the third jet. At an intermediate location of approximatly Z/D0=20, the spreading
rate of the three jets crossover. The entrainment of the three jets generates a low
pressure in the interior region between the jets. Due to this low pressure and the
difference in velocity profiles, the jets attract each other and an axis switching
occurs. This phenomenon is found to enhance the entrainment as well as the mixing
of the jets.
Moustafa, and Rathakrishnan (3) took the preceding results one step further
and studied the behavior of four jets in a square formation with the same flow
conditions. This configuration shows the same behavior as the three jet array,
except for the spreading rate: starting with a larger value, the spreading rate of the
4-jet array increases slightly faster than that of the 3-jet configuration. Therefore,
the crossover takes places much further downstream at about ZID0=50.
Villermaux and Hopfinger (4) investigated the interaction of circular jets set
in a large network. Perforated plates with two different configurations were studied:
a square network with 1mm diameter holes with a mesh size of S=2.54mm and a
triangular network of 0.8mm diameter holes with a mesh size of S=2.73mm. The
perforated plates were placed into an 80x80 mm2 cross-section wind tunnel
designed for low residual turbulence. Measurement of the velocity fluctuations
were performed with one or two independent hot-wire probes, while the mean
velocity measurement was made with a Pitot tube attached to a differential pressure
6
sensor. Flow visualization was performed using a continuous laser and a 25 fps
digital camera. The laser beam was directed on an oscillating mirror, generating a
1mm laser-sheet, which was aligned with a row of jets, inside the wind tunnel test
section. A smoke generator injected dense white smoke at a distance of lOxS
(where S is the mesh size) upstream of the network and with an injection velocity
equal to the mean wind-tunnel velocity. A large-amplitude quasi-periodic
oscillation was observed at the jet merging distance for 300<Re<3-4x 10. This
instability appears to be part of a feedback process. A weak positive pressure
gradient eases the creation of a recirculation flow in the cavity formed by coflowing jets. The authors implemented a new model (non-linear delay saturation)
that proved to be in close agreement with the experiment results.
Jet Arrays with Crossflow
Kim and Benson (5) proposed a computer simulation of a row of jets in a
confined crossflow without impingement. Using a finite volume method to solve
the Reynolds-averaged Navier-Stokes equations, they successfully reproduced the
complex flowfield in the vicinity of the jet exit for low Re (-500). A primary vortex
is observed immediately downstream of the jet. Due to the blockage of the
crossflow, a recirculation flow is formed in the wake of the jet. A strong adverse
pressure gradient is formed, creating a reverse flow, upstream of the jet. This
7
reverse flow and crossflow interaction leads to the formation of a secondary vortex,
formed upstream of the jet, in the streamwise plane of symmetry. In the spanwise
direction, the secondary vortex is deflected along the jet column, creating a helical
vortex shaped like a horseshoe.
Jet Arrays with Impingement
Arjocu and Liburdy (6) investigated the effect of non-axisymmetric orifice
jets using a 3x3 array of elliptic jets on an impingement surface. The jet orifice
aspect ratio was set to the values r=2 and 3. The jet hydraulic diameter was
DH=9mm, the Reynolds number ranged in 300<Re<l,500 and the impinging
distance was varied between HJDH=l and 5. The authors used flow visualizations in
three planes: two were placed along the central row of jets along the major and
minor axis of the ellipse while the third one was placed parallel to the surface, at a
distance of ZIDH=1/9, from the impingement surface. Using a 1mm thin argon-ion
laser sheet to illuminate the flow, 60 jim size glass micro-particles were introduced
as tracers while a CCD camera recorded the images. Particle Image Velocimetry,
(PIV) measurements were also obtained using 27p.m fluorescent micro-beads and
illuminating the planes with a pulsed Nd:YAG laser.
Finally,
velocity
measurements at different locations were obtained using a hot-film anemometer.
Based on the velocity measurements, the vorticity field was also computed. The
8
results show that at the higher impingement distances, the jet streamlines converge
in the major axis planes while they spread in the minor axis plane. This behavior is
typical of non-symmetric jet orifices and is known as "axis switching". The axis
switching superimposed on the jet column instability, swaying motion, and
presence of small-scale shear layer structures leads to a high level of turbulence and
entrainment in the impingement region.
Jet Arrays with Crossflow and Impingement
Barata et al (7) examined the crossflow effects on twin-water-jets impinging
on a surface in two different configurations: a uniform crossflow normal to the jets,
and a crossflow with a third jet placed upstream of the twin-jets. The twin-jets
separation distance was 5D and the distance to the third jet is 15D (where D is the
diameter of the jet). For all the experiments, the impingement distance was kept at
HJD=5, the Reynolds number was kept constant (Re= 105,000) as well as the jet-to-
crossflow velocity ratio at V/V=3O. Several flow visualizations were performed
using a continuous argon-ion laser while air bubbles were injected in the crossflow.
The beam was expanded through a cylindrical lens to produce a 2mm thick laser
sheet, which was aligned with the downstream flow with the plane of symmetry
between the twin-jets. Mean and turbulent velocities were measured with a dual-
beam, forward-scatter laser Doppler anemometer. For both configurations, an
upwash fountain flow was observed in the symmetry plane, and upstream of the
twin-jets position. They noted that while impinging, the twin-jets form a wall jet
that interacts with the crossflow, creating a complex vortical structure, referred to
as a horseshoe vortex, wrapped like a scarf around then twin-jets. For the three-jet
configuration, the recirculation zone appears to be extended upstream and confined
between the singular jet and the twin-jets.
Later, Barata (8) proposed a numerical study to correlate these results. Based
on time averaged Navier-stokes equations and the k-E turbulence model, the
numerical results show a very good agreement with the previous experiments. The
model adequately represents the fountain upwash flow and reveals a large lowpressure zone, resulting from the acceleration of the crossflow around the twin-jets.
Florschuetz and Isoda (9) studied the flow distribution of circular air jets
impinging on a surface. The jets were arranged into arrays of ten spanwise parallel
rows with the number of jets in the streamwise direction varying between 9 and 36,
depending on the jet-to-jet spacing. The impingement distance was varied with
values of 1D, 2D, and 3D, with D being the jet exit diameter. The impinging flow
was constrained to exit in a single direction by an independent crossflow, with jet
flow rate ratio values of 0.2, 0.5, and 1.0. The pressure measurement was achieved
by introducing a static pressure probe at a determined position along the
downstream direction, at the bottom surface of the channel. The jet plate flow
coefficient CD was obtain as the ratio of the actual to the ideal flow rate:
lvi Actual
CD=.
where M
Isentropic
is the actual mass flow rate measured with an orifice meter upstream
of the jet plate and Misentrope was computed assuming one-dimensional isentropic
ideal gas flow. The results show that the average value of CD can be considered a
constant for crossflow-to-jet velocity ratios smaller than one and decreases
asymptotically from 0.85 to 0.50 for a crossflow-to-jet velocity ratio between 1.0
and 3.0, respectively. CD was not found to be very sensitive to ReD variations
(0<ReD<40,000), with deviations from the mean value no larger than a few percent.
The authors also presented a theoretical and a numerical model based on a onedimension assumption, which numerical results are in excellent agreement with the
experimental results. It is also observed that for the smaller impingement distance.
Z/D= 1, CD strongly decreases, thought to be due principally to wall shear effects.
Most recently, Bernard et
al.
(10) extended Barata's results on the
"horseshoe vortex" in the specific case of an array of round jets within their own
crossflow. The impingement surface is enclosed between three walls, leaving a
unique direction for the flow to exit. The array was made of 5x3 orifices with a
diameter of D=lOmm. The separation distance was set at 4D and the impingement
distance was kept constant at FI/D=2. The Reynolds number was chosen to be
Re= 12,600. Various experimental techniques were used: surface flow visualization,
laser sheet visualization, and laser-Doppler velocity measurement. The surface flow
visualization has been achieved by spreading a mixture of calcium carbonate
particle suspended in oil, over the impingement surface. The results reveal the
cellular aspect of the flow near the impingement surface and the detachment zone
separating each jet impingement area to the others. Laser sheet visualizations were
performed using an argon-ion laser (- 1mm laser sheet) illuminating sections of the
flow. A glycerin and water mixture was sprayed into the flow while a S-VHS
camera (50 fps) was used to record images. A similar rotating structure as Barata's
"ground vortex" was observed upstream of the impinging jets. The fountain flow
was also observed between co-flowing jets. Finally, velocity measurements were
performed using a LDA system, providing the three velocity components in the test
section. Combining these different techniques, the authors proposed a topology of
the flow structure including the ground vortex structure and the fluid behavior in
the vicinity of the plane wall. This topology is shown in figure 2.1.
L1
L
J
Figure 2.1 Impinging jet topology
12
Many authors investigated the heat transfer distribution from impinging jets
and jet arrays. Iii these studies, the cooling efficiency was emphasized rather than
the flow mechanism. Meanwhile, the effect of some parameters such as the jet
spacing, the impingement distance, and the Reynolds number was analyzed,
providing a comparative database to be linked with the associate flow analysis.
Metzger et al. (11) investigated the cooling effects of circular jet arrays on a
impinging surface enclosed between three walls. The impinging air is forced to exit
in one direction, creating a crossflow. The crossflow-to-jet velocity ratio ranged
from 0 to 0.8. The jet spacing was varied from 4D to 8D, with D being the jet
diameter. The Reynolds number ranged from 2,500 to 70,000 and the impingement
distance was varied between HID= 1 and 3. The authors found that for the larger jet
spacing and smaller channel height, the crossflow provided an increased heat
transfer distribution. They explained that for the smaller jet spacing, the crossflow
becomes canalized between adjacent rows, creating non-uniformity in the jet
distribution. For the larger channel height, the authors concluded that the cooling
effectiveness is reduced by the crossflow diffusive action on the jets.
A similar study was achieved recently by Koonlaya Kanokjaruvijit (12). The
effect of the orifice geometry and the surface boundary condition on the heat
transfer distribution of an impinging jet array are investigated for two 7x7 jet
arrays. The first one is composed of circular jet nozzles while the second one is
13
composed of cusped-ellipse nozzles with the long axis perpendicular to the
crossflow. In a similar setup as Metzger et al. (11), the impinging air is forced to
exit in one direction, creating a crossflow with a crossflow-to-jet velocity ratio
increasing from 0 to 0.194. The Reynolds number ranged from 5,000 to 11,000 and
the impingement distance was varied between H/DH= 1 and 4. The local heat
transfer was mapped using thermochromic liquid crystals for two boundary
conditions: isothermal surface and uniform heat flux. The experimental results
show that the cusped ellipse jet array provides a better cooling compared to the
circular jet array for both boundary conditions. In addition, the results show that the
cusped ellipse performance is more sensitive to Reynolds number variation.
14
CHAPTER III
EXPERIMENTAL SETUP
The test facility is described in the following two sections. The first section
describes the compressed air delivery system which supplies air to the jet arrays,
and the second section describes the impingement surface setup, including the
pressure measurement apparatus, the flow visualization, and the PIV system to
obtain the jet characteristics and the method used to obtain the impingement surface
streamline pattern.
Air Delivery System
A 110-psi dried air compressor provides the air for of all the impingement
experiments. A schematic of the air delivery system is presented in Figure 3.1. The
air is passed through a filter to remove any potential impurities present in the
supplied air. Then, a pressure regulator is used to damp the pressure fluctuations
due to the cycling of the compressor. A persistent pressure fluctuation was still
measurable and the use of a surge tank would have been a possible solution.
Instead, it was decided to open another line from the air supply and vent it to the
atmosphere through a needle valve. Since the compressor was designed to supply a
unique maximum flow rate, the second line was set to "complete" our flow rate at
15
this maximum. The compressor did not cycle under these conditions and tests
proved that this method reduced the fluctuations to below 0.5%. In order to turn
on/off the air without changing the settings, a gate valve was installed followed by a
flowmeter equipped with a needle valve for fine adjustment. A pressure gage was
placed at the flowmeter outlet. This pressure was used to correct the flowmeter
readout (see Appendix A). A thermocouple was also placed downstream of the
flowmeter in order to measure the air temperature needed for the calculations in
Appendix A.
Further downstream of the flowmeter, the air flowed into the plenum
chamber through a 3.6-meter section of 25.7 mm inside diameter PVC pipe,
followed by a 1.5-meter section of 35-mm inside diameter flexible tube. The
plenum chamber was made of five 300x300x3.5 mm steel plates welded together.
The 6th plate was tightened with 16 screws providing a quick and easy access for
set-up and maintenance. A diffuser plate was placed inside the plenum chamber 11
centimeters from the top. Breaking down any turbulence of the incoming jet from
the air supply, the diffuser plate generated a volume of high pressure, low velocity
air above the jet array. At the center of the bottom plate was attached a mounting
frame that held the jet array plate in place. The jet array plates were square pieces of
steel 3.6 mm thick containing 7x7 circular holes or cusped ellipse holes. Figure 3.2
shows the different geometries and jet array spacing.
I (
Figure 3.1. Schematic of the air delivery system
17
25
103
/
25
4 ROLES
0
o
0
0
0
0
0
0
o
o
a
a
o
o
o
o
0
0
0
0
0
0
o
o
o
o
o
o
o
o
o
0
0
0
0
0
o
0
0
0
0
0
0
2.815
°
050
313
49 HOLE5
EOUAE
SPACES
.I?5
03
25
/
a
.438
I
438
4 HOLES
o
a
a
0
a
a
a
0
0031N
0
33
r
0 .-
a
a
0
a
0.031
.027-4.---
o
a
a
e
a
a
a
a
a
o
a
a
0
a
a
a
2815
? 875
Figure 3.2. Jet arrays geometry (top: circular jet array,
bottom: cusped ellipse jet array)
18
Impingement Surface
The impingement surface was built with 5.8 mm thick Plexiglas plates,
mounted together to form a "U-shaped" channel and closed on one side (the "back
wall") such that the jets generate a crossflow in the "forward" direction (Figure 3.3
shows the general setup). To provide a better viewing medium for the PIV studies,
a glass window was inserted in one of the Plexiglas side walls. Two Plexiglas
blocks were mounted on either side of the channel, providing a stable base to be
attached to the plenum chamber's mounting frame. A thin layer of foam, with a
film of silicon paste covered the tops of the walls to prevent leaks. The
impingement plate was mounted in between the sidewalls, using 90° brackets
fastened to the walls. A groove was machined along the impingement plate where
an 0-ring was placed to prevent leaks. Four pairs of metallic rods were machined at
specific diameters. Each pair was used as a spacer to measure the distance in
between the jet array and the impingement plate. The impingement distance to jet
hydraulic diameter ratio (H!DH) ranged from 1 to 4 (HJDH=l, 2, 3 & 4). Once the
impingement plate was fastened at the desired impingement distance, the spacers
are removed and the experimental system is ready.
Since the cusped-ellipse is not an axisymmetric shape, three different cases
were studied: (i) the circular jet (abbreviated CJ), (ii) the cusped ellipse with the
19
major axis aligned parallel the crossflow (abbreviated CEO), and (iii) the cusped
ellipse with the major axis normal to the crossflow (abbreviated CE9O).
Pressure Drop Measuring Apparatus
In order to obtain the pressure drop and the orifice flow coefficient, a
special pressure measurement impingement plate was prepared: seven 1mm
diameter holes were drilled on the impingement plate at specific locations (see
Figure 3.4). Five pressure taps were placed along the central streamwise flow-line
to measure the crossflow effect on the pressure drop. Two additional taps were
placed on either side of the centerline on the central spanwise axis and were used to
obtain the average pressure on the impingement plate, and also served as a
guideline to center the impingement plate under the jet array. Each pressure tap was
located halfway between two adjacent jets along the symmetry axes of the jet array.
(See Figure 3.4 for more details). A needle pressure tap was inserted into each hole
and connected to a pressure manifold with 4mm inside diameter flexible tube. The
manifold consisted of a series of on/off valves connecting each pressure tap to a
common pressure transducer. The pressure measurements were taken one at a time,
which reinforced the necessity of a steady flow rate between the measurements.
Two pressure-taps were also placed in the plenum chamber, on each side of the
20
diffuser plate, in order to measure the generating pressure and the pressure drop
through the diffuser plate.
Once the desired air flow rate is set with the needle valve, the adjustment
valve was set to achieve the maximum flow rate that the compressor could sustain.
The needle and the adjustment valves were readjusted again until the desired flow
rate was obtained and the pressure in the plenum was stabilized. Then, the pressure
at the different pressure taps was acquired, switching the corresponding valves on
the manifold. The pressure transducer used was a Kulite-K190, providing a
resolution of 0.75 psi for a working pressure of 25 psi. The pressure transducer
output was connected to a Fluke data logger that was programmed to transform the
voltage directly into pressure units (psi), according to the manufacturer's calibration
curve. Table 3.1 shows the different test conditions used during the pressure
measurements, and then used to determine the flow coefficient.
Table 3.1. Pressure tests and conditions
Jet Array
H/PH
1
Circular jet
(CJ)
2
3
4
Cusped Ellipse 0°
2
1
(CEO)
3
CuspedEllipse9o°
2
(CE9O)
4
1
3
4
Re
9,860- 11,880- 13,920- 16,760
9,740- 11,680- 13,660- 15,980
9,740- 11,550- 13,590- 15,830
9,740- 11,550- 13,590- 15,830
8,730-10,420- 12,260- 14,200
8,560-10,200- 11,830- 13,580
8,560-10,160- 11,770- 13,520
8,560- 10,160- 11,770- 13,520
8,730 10,420
12,260
14,200
8,560- 10,200- 11,830- 13,580
8,560- 10,160- 11,770- 13,520
8,560-10,160- 11,770- 13,520
21
Back Wall
Jet Array
Side Wall
o"o 00000
00
o 0000
00000
C) C) C) C) C) C) C) /
C) C) C) C) C) C) C) /
C) C) C) C) C) C) C) /
C) C) C) C) C) C) C) /
/
Mounting Blocks
Impingement Plate /
Figure 3.3. Impingement Plate Setup
Pressure Taps
Spanwise
Axis
I
I
Projection of
Jet Orifice
on the
R
Direcflon
Streamwise
Axis
17
V
Figure 3.4. Pressure Tap Locations
22
Flow Visualization Apparatus
Velocity Field Measurements
Particle Image Velocimetry, PIV, provides an improved method to obtain
the entire velocity field across a well define flow region. Compared to the classic
single point hot-wire anemometry measurement or laser Doppler anemometry, PJV
offers a nonintrusive measuring method which covers a larger field of view for
instantaneous measurement. The flow is seeded with micron-size particles and a
laser is pulsed through the flow-field. The seed particles scatter the laser light,
which is formed into a planar sheet. By pulsing the light, two images of this field
are taken at a known time delay between the two laser pulses. One can then analyze
the two pictures and estimate the local velocity field within the light sheet plane.
Using a modified sand blaster as a seed-injector, the seeds were injected
into the plenum chamber at mid-height, providing good mixing. Titanium Dioxide
(T102)
particles were used with an average particle size of 2 to 3 jim. These seeds
proved to be an excellent "tracer" for PJV but also for the streamline pattern
visualization. The laser, a double Nd:YAG laser, was able to perform a double
pulse with a ijis time interval at a frequency of 15 Hz. After a series of lenses, the
round beam is converted into a laser sheet (<1mm thick) and directed vertically into
the space between the jet array and the impingement plate (see Fig 3.5).
Figure 3.5. Visualization Apparatus
rojection of
Fet Orifice
Jet
on the
ripingement
Plate
Jet
Jet
Las
Figure 3.6. Laser Sheet Location
24
The laser sheet is lined up with a designated row of jets, as shown in Fig.
3.6, lighting it up at the appropriate frequency while a digital camera (placed
perpendicular to the laser sheet) was capturing the images. The camera used was a
Princeton Instruments, Inc. MicroMAX 5MHZ, with a CCD array resolution of
1,300x 1,030 pixels. The camera and the laser were synchronized such that pairs of
pictures could be taken with a time separation lower than 2ts.
P.I.V Acquisition and Software
In order to analyze the images of the seed particles to obtain the velocity
field, VISIFLOWTM was used.
VISIFLOWTM is software package that directly
computes the velocity vector fields. For more information on the software and the
parameters used for throughout the experiments, refer to Appendix B. PlY analyses
have been performed for 3 jets along the adjacent row to the center streamwise
row/axis (see Figure 3.6), for two volumetric flow rates (QR=i4 and 20 CFM), and
for two impingement distances (HJDH=2 and HJDH=4). The list of PlY tests and the
corresponding Reynolds number for each geometry are shown in Table 3.2.
25
Impingement Surface Streamline Apparatus
Visualizations of the streamline patterns on the impingement surface were
realized by seeding the flow with the same
Ti02
seeding system as used for PlY
seeding. A set of exchangeable impingement surfaces was designed to suit the
different tests and investigate the streamlines on the impingement surface and the
sidewall surface. Made of 0.2 mm thick propylene, they offer a smooth and robust
impingement layer that can be inserted in between the actual impingement surface
and the jet arrays. The list of tests is given in Table 3.3. Once the flow is set to the
desired flow rate,
Ti02
seeds are injected in the plenum and flow toward the
impingement surface, leaving a deposit at the stagnation points and the locations of
near zero velocity. Then, the air is cute-off and the impingement layer is removed.
A Sony Digital Color Camera provided the 640x480 pixels pictures of the surfaces
and the side walls. See Figure 3.7 and 3.8 for the surface and viewing orientations.
26
Table 3.2. PIV tests and conditions
Jet Array
JET
H/DH
Re
4
9740- 15,800
9740- 15,800
9740-15,800
2
4
6
4
8,570- 13,500
8,570- 13,500
8,570 13,500
2
4
4
#
2
Circular jet
Cusped Ellipse
00
Cusped Ellipse
90°
&4
2&4
2
6
4
4
4
4
6
8,570- 13,500
8,570- 13,500
8,570- 13,500
Table 3.3. Streamline Visualization tests and conditions
Jet Array
H/DH
Circular jet
2
Cusped Ellipse
0°
Cusped Ellipse
90°
4
2
4
2
4
Re
9740-15,800
9740-15,800
8,570- 13,500
8,570- 13,500
8,570- 13,500
8,570
13,500
27
Air Flow
+ Ti02 seeds
ingement
Layer
Figure 3.7. Impingement Layer Location
Still Color
Digital Camera
Still Color
Digital Camera
Viewing of
Impingement
Surface
Streamlines
Viewing of
Side Wall
Surface
Streamlines
Figure 3.8. Impingement Layer Visualization
28
CHAPTER IV
EXPERIMENTAL DATA ANALYSIS
Velocity Ratio
The downstream location along the flow can be defined either as the jet
number or the distance from the back-wall. However, the crossflow-to-jet velocity
ratio, V, is a convenient variable used to define this location. It is defined as
follows:
Vr = --,
where V is the velocity of the flow coming from the upstream
jets, and V is the exit velocity of the jet. As can be seen in Figure 4.1,
Vr
is a linear
function of the jet position with a larger slope for larger impingement distance
H/DH.
0.900
0.800
0.700
0 600
0.500
>
0,400
0.300
0.200
808=1
0 100
808=2
4/08=3
4/08=4
0.000
2
3
4
5
6
7
Jet I
Figure 4.1 Crossflow-to-jet velocity ratio, Vr versus jet number
measured from the most upstream jet.
29
Pressure Data
Pressure data are used to determine the flow coefficient of the jets and how
it varies along the downstream flow. The flow coefficient,
CD,
for an individual jet
is defined as follows:
N'1 actual
Cd
isentropic
where
Mactual
Misentropic
is the actual mass flow rate measured from the flowmeter, and
is the ideal mass flow rate (isentropic). Using the isentropic gas dynamics
laws for flow through an orifice, Florschuetz and Isoda (9) expressed CD in the
following form:
actual
A
CD=
P
PO[]
where
A1
2'
R.T0(ilY[
= Total area of jets = 49 x jet orifice area
P = Impingement surface pressure,
Po = Plenum chamber pressure,
T0
= Plenum chamber temperature.
This definition assumes that the total mass flow rate is evenly divided among
the 49 jets. Prior tests were performed to verify the uniformity of the flow by using
30
a Pitot tube under each jet to detect any variation in the dynamic pressure and were
found uniform within 2%. For each jet-array configuration, impingement distance
and Re, graphs of CD are plotted versus crossflow-to-jet velocity ratio along the
center streamline and the average flow coefficient, <CD>, versus Reynolds number.
Velocity and Mean Velocity Field
The field of view for the pictures is 6DHX4DH for the higher impingement
distance. Each instantaneous PTV velocity field is composed of 37x25 vectors.
Therefore, the spacing between adjacent vectors is typically less than 200j.im.
In order to highlight the properties and specific behavior of each jet and the
interaction with the crossflow, a large number of instantaneous fields were obtained
(approx. 50). All PlY realizations for each jet were filtered to show the intrinsic
interaction of the jet and the crossflow. In order to smooth the data, a 5x5smoothing filter was applied using VISIFLOWTM to each of the instantaneous flow-
fields. The filter weight-coefficient table is presented in Table 4.1.
Table 4.1 Filter Weight-Coefficients
0.05917
0.10687
0.13533
0.10687fb5917
0.10687
0.24311
0.36787
0.13533
0.36787
1
0.24311 10.10687
0.36787 1 0.13533
0.10687
0.24311
0.36787
0.05917
0.10687
0.13533
0.24311 10.10687
0.10687 Lp.05917
31
VISIFLOWTM provides velocity vector flow field plots, but uses an
automatic scaling function (based on the maximum velocity) to make convenient
flow fields without vectors crossing each other. Therefore, each smoothed flow
field was exported into a data file composed of the position, magnitude and angle of
each vector of the flow field. Then, all these data files were imported into
MATLABTM and processed to provide the following results. The use of a unique
scale factor for all jets and all configurations provides unreadable results for very
low or very high velocities. MATLAB's auto-scale feature was de-activated and the
scale factor adjusted manually for each flow field for the same jet, with the same
configuration, but different Re. This scaling coefficient was applied to the flow
field for both Re, dividing each velocity component by the scaling factor. The
scaling factor used for the different configurations is given in Table 4.2.
Table 4.2 PJV scaling factor
Configuration Case
HID11=4
Round Jet:
H/D=2
Cusped Ellipse (0°)
Cusped Ellipse (90°)
H/D11=4
HJD-4
Jet #
Scaling coefficient
2
45
4
90
6
180
4
90
6
90
2
110
4
130
6
150
2
45
4
80
6
100
32
The larger the velocity is, the larger the scaling factor needs to be to reduce
the vector length in order avoid the overlap of the adjacent vectors. Meanwhile, the
mean velocity field was also displayed. Its purpose is to provide details on the
velocity range and the local spot of maximum velocity.
Mean Vorticity
The mean vorticity fields are used to identify the locations of various eddies
and concentrated vorticity resulting from the interaction of the crossflow and jets.
Using a cell-centered finite difference scheme, the mean vorticity was computed
using two different methods. First, the vorticity field based on the mean velocity
field was computed, second, the vorticity field for each instant flow-field was
computed, summed up and averaged to obtain an average vorticity field. Both of
these methods yield the same results. The finite difference approximation used was
of the form
(av au
(0=-I--1
2
)x
Y)
=
1
(v1 V
(0.. =-I
2
Ax
U11
U
Ay
33
Turbulent Kinetic Energy
The TKE field provides a good overview of the location of large scale
turbulent eddy production. Using the Reynolds decomposition of the Navier-Stokes
equation the turbulent kinetic energy is represented by:
TKE=i+V),
where
and
V2=Vms=i(Vn_VY.
First, the average velocity fields, U and V (x axis and z axis, respectively) are
computed by averaging the local velocity components over all the instantaneous
flow field. The number of instantaneous flow field used was approximately N=50
for each configuration. Then, the mean squared
Urns
and
Vms
are computed by
subtracting the local values of U and V to the average U and V for each
instantaneous flow field, respectively, then squaring the results. The TKE flow field
is then obtained by averaging the local values of the two mean squared
Vms, at
each position throughout the entire flow field.
Urns
and
34
Mean Squared Vorticity
For any turbulence production, there is always an associated dissipation.
Using the Reynolds decomposition of the Navier-Stokes equation the dissipation
due to turbulent motion is proportional to the mean of the fluctuating vorticity
squared. Therefore, taking the mean squared vorticity gives information on the
location where the dissipation of TKE is concentrated. The means squared vorticity,
was calculated as:
°ms
The mean squared
COrns
is computed, subtracting the local values of W on each
instantaneous flow field to the average
,
squaring the results and finally
averaging the local values over the N=50 instantaneous flow fields.
Data Reduction
In order to compare the flow characteristics for each of the cases, average
levels of vorticity, TKE and mean squared vorticity were computed. The
information of interest is near the impingement surface. A section of the flow has
35
been defined by excluding the top part of the flow and the borders. A schematic of
this section is shown in Figure 4. 2.
Discarded
Tn frrrn ti en
Figure
4.2
Computation area for property levels.
In the case of HJDH=4, the computation area is reduced to 3.7x3.2 DH. For
HIDH=2,
a larger stripe of data is discarded. In that case, the area has is reduced to
3.7x2.6 DH.
The justification for this reduced computation region is provided in
Chapter V. in the discussion of the side wall effect section.
36
Surface Flow Visualization
For each combination of jet-array geometry, impingement distance, and Re,
pictures of the
Ti02
deposits have been acquired and analyzed. Direct observation
of the general impingement surface provides interesting information on the
impingement surface flow patterns and the locations of surface vortices. For each
row aligned with the downstream flow, the dimensions and locations of the
stagnation points and the accumulation rings were measured directly from the
pictures, in units of pixels. With the assumption of a quasi-uniform flow, from one
row to the over, in the downstream direction, averaged values have been calculated
and converted into millimeters, and finally into proportions of DH.
37
CHAPTER V
RESULTS AND DISCUSSIONS
This chapter discusses the results of the experiments and is subdivided into
five sections: (i) flow structure versus downstream positions, (ii) effect of the
Reynolds number, Re, on the flow structure, (iii) effect of impingement distance,
I-IIDH, on the flow structure, (iv) effect of geometry/alignment of the cusped ellipse
jet array, and (v) side-wall effects. In the first section, the flow structure is
described and the influence of the crossflow on the jets is discussed. The second
section analyzes the effects of Re on the flow structure. The third section discusses
the effects of the impingement distance, HIDH, on the flow structure. The fourth
section discusses the effects of the alignment of the cusped ellipse jet array on the
flow structure. The cusped ellipse, being a non-axisymmetric shape, two
configurations arises with either the major axis aligned with or normal to the
crossflow direction or not. Finally, the fifth section analyzes the effects, direct and
indirect, of the side walls on the flow and its visualization.
For each section, sample plots of the flow coefficient is shown for the
different parameters, HIDH and Re. Graphs of PIV plots, mean velocity, vorticity,
turbulent kinetic energy and mean squared vorticity flow fields and
flow visualization are also provided.
Ti02
surface
38
In order to highlight the different properties of the impinging jet, a
schematic of the different jet areas of interests are defined. These are listed below,
and illustrated in Figure 5.1.
Region 1:
Jet Column Development
Region 2:
Jet Column Impingement
Region 3:
Upper Crossflow
Region 4:
Upstream Surface Vortex Flow
Region 5:
Downstream Flow
Figure 5.1 Definition of jet regions with four points of interests identified
Four points of interest are defined below and labeled in Figure 5.1:
A:
Jet Exit
39
B:
Stagnation Point
C:
Surface Vortex Detachment Point
D:
Upstream Flow Detachment Point
The stagnation point, B, will also be referred to as the stagnation area due to the
relatively large size of the stagnation flow around B. Therefore, B is defined as the
geometric center of the stagnation region. The near-stagnant flow region, close to
the surface between C and D, will be referred to as the "surface vortex stagnation"
region.
Flow Structure versus Downstream Position
In this section, the flow structure and the influence of the crossflow on the
jets are described for both the circular and the cusped ellipse
(00)
jet array for the
following conditions: higher impingement distance (HIDH=4) and the same low
flow rate QR=14CFM. The corresponding Reynolds number are Re=9,740 for the
circular jet array and Re=8,570 for the cusped ellipse (0°) jet array. The cusped
ellipse (90°) jet array is described separately due to its unique flow-field, in the
forth section of this chapter.
In Figure 5.2, the variation of the flow coefficient,
CD,
is plotted as a
function of downstream distance labeled with the corresponding crossflow-to-jet
40
0.9
0.85
0.8
e 0.75
0.7
0.65
0.6
0
0.04
0.02
0.06
0.08
0.1
0.12
0.14
0.16
0.18
yr
Figure 5.2. Flow coefficient, HIDH=4, Flow rate QR=14CFM,
Circular jet: Re=9,740, Cusped ellipse (00) jet: Re=8,570
Sc
Stagnation
Downstream
surface vortex
stagnation
Side roll-up
Upstream
surface
vortex
stagnation
S
Figure 5.3. Close-up of the flow visualization by surface deposition illustrating
the relative dimensions of the surface vortex and stagnation point.
41
velocity ratio, Vr, which was determined to be the best variable to describe the
downstream distance. Moving downstream along the impingement surface, the flow
coefficient,
CD,
decreases slightly and monotonically. The average value, <CD>, is
0.70 for the circular jet array and 0.80 for the cusped ellipse
(00)
jet array. For
Vr>
0.16, Ci appears to reach a constant value.
The surface flow visualization provides details of what the flow pattern is at
the impingement surface. All the jets spread over the surface, creating an array of
cells defined by four detachment-reattachment zones with a characteristic
'horseshoe shape around each jet. A close-up of a cell is shown in Figure 5.3. The
first zone is due to the upstream collision of the crossflow and the return-flow
(upstream surface vortex stagnation). The bands on each side of the jet are due to
the roll-up of the jet flow with the two adjacent jets. The downstream zone is
caused by the surface vortex detachment, which is a result of the impingement of
the flow with the downstream jet. Along the lateral direction (across the flow), the
results show a quasi-periodic aspect proving that each row can be considered as a
partial symmetry plane. Results shown in Figures
5.4
and
5.5
show the typical
patterns for the circular and the cusped ellipse (0°) jet array, respectively.
Moving downstream from the back to the exit where the crossflow ratio is
increasing, it can be observed that the "horseshoe" shapes of the cells become
increasingly more oblong in shape. For jets closer to the back wall, the
impingement point is located at the center of the cell, but further downstream, this
center appears to shift slightly upstream of the center of the cell. Figure
5.6
shows
42
Eli
El
El
EE.
Figure 5.4. Surface Flow Visualization, Circular jet,
HIDH=4, QR=14CFM, Re=9,740
Figure 5.5. Surface Flow Visualization, Cusped ellipse
H/DH=4, QR=14CFM, Re=8,568
(00)
jet,
43
8,
7]
6
I
I
r
I
-t--CEO-Svs
U
-0- CEO S
1
ZZ1
.......-
-
0
0
0.02
0.04
006
008
0.1
012
0.14
016
018
0.2
yr
Figure 5.6. Surface vortex and Stagnation point relative location, HIDH=4,
QRl4CFM, Circular jet: Re=9,740, Cusped ellipse (0°) jet: Re=8,570
2
1.8
1.6
1.4
1.2
I.,
08
0.6
00
002
0.04
0,06
008
0.1
012
0.14
0.16
0,18
02
Vr
Figure 5.7. Surface vortex deposit size, HIDH=4, QR=14CFM,
Circular jet: Re=9,740, Cusped ellipse (0°) jet: Re=8,570
44
the evolution of Svs and Ss (which are defined in Figure 5.3) along the flow for the
circular and the cusped ellipse
(00)
jet array. Both configurations show similar
results: a very small increase (<5%) in the surface vortex separation distance, Ss,
indicates that the cell size is not changing significantly along the downstream
direction while a 50% decrease in Svs is observed. Because the cell size is
relatively unchanged, it is concluded that it is not the center that is shifting, but the
upstream and downstream cell boundaries. As the crossflow-to-jet ratio increase,
the boundaries are progressively shifted downstream. This indicates that Svs
decreases along the flow direction such that the distance from the upstream
boundary to the stagnation point decreases due to the downstream movement of the
surface vortex stagnation region. Figure 5.7 shows the evolution of the surface
vortex stagnation size, Sc, along the downstream flow. For the cusped ellipse (0°)
jet array, Sc doesnt appear to be very sensitive to the crossflow except near the exit,
where there is a 27% drop. However, for the circular jet array, there is a greater
sensitivity in the region closer to the exit (25% increase followed by an equivalent
drop), as the crossflow velocity ratio increases.
For jet 2, close to the back wall, the impingement point is localized at the
center of the cell. At this location, the crossflow-to-jet velocity ratio, Vr,
5
0.032.
The mean velocity vector field plot for both the circular and the cusped ellipse (0°)
jet 2, are shown in Figures 5.8 and
5.9,
respectively. From these P[V plots, the
upper part of the flow [region 3] appears nearly stationary. The jet column [region
1] breaks into a downstream flow [region
5]
and a relatively weak return-flow
45
-
II-,,-
445\\
\'-
5.0
44
-444
'44
'14
\
\
'4
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4
4
4
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's
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41
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-------
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1
0.5
0
-0.5
-1
-1.5
-2
-2.5
01D
Re=9,740
Vr=O.032,
2,
Jet
HIDH=4,
jet,
Circular
PIV,
5.8.
Figure
-Os
-1
4444
4''
............
44444
444144'
.........
44444144
4445
4544544545
44
44454454554544444
'\\\\\144441444
\\5 \\\
44444
''''4''4
l444444\\444444441444\4444
'''4'''''
-1.5
5545555554
55555
5
5
4
55
'4
'4
444'
4
4
4
55444
55554
'4
'4
\\\\\\
5,
4454444444''
4
4
44
4
4
4
0
I.
4
4
4
4
4
4
4
4
4
4
444
4 44
4
4
4
555
\\\\\\\\\
'
'455
'4
'4
4
4 4 '4
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5555444444545
5 '4\\'4
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-2.5
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-
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4'44444441144444'''4SII//I4
-3
-
5
4
4
S
-
'
4
4
/1
1
//
1
4
4
4
'
'
4
1
4
-----
'44111//1114
14'
'41
----:zi''
-
41"'
-3.0
2
15
1
0.5
0
-0.5
-,
-1.5
-2
05044
Re=8,570
Vr=0.032,
HJDH=4,
jet,
(0°)
ellipse
Cusped
PlY,
5.9.
Figure
46
Mean Vorticity
Mean Velocity Magnitude
x
4
10
8
6
C
N
a
0
N
4
-2
2
-4
-4
X/DH
1400
1200
1000
800
a
N
600
0
N
400
200
X/DH
X/DH
Figure 5.10. Flow characteristics, Circular jet,
H/DH=4, Vr=O.032, Re=9,740
47
Mean Vorticity
Mean Velocity Magnitude
0
4
15
10
a
N
I
2
0
a
-2
5
-4
-6
-2
-1
0
1
2
XJDH
X/DH
Mean Squared Vorticity Fluctuations
2000
-1
1500
I
N
1000
-3
500
-4
-2
-1
0
XIDH
1
2
0J
35
-2
-1
0
1
X/DH
Figure 5.11. Flow characteristics, Cusped ellipse (00) jet,
Vr=0.032, H/DH=4, Re=8,570
2
10
I
48
[region 4] at 1DH from the impingement surface. This return-flow and the flow
coming from the upstream jets appear to generate a large scale rolling structure with
its center of rotation outside of the field of view (X/DH>2). This structure is more
pronounced and therefore stronger for the cusped ellipse
(00)
jet 2. This rolling
structure is defined as a "surface vortex". The stagnation point region, B, is very
well defined for the cusped ellipse (0°) jet 2 but very scattered for the circular jet 2.
The flow downstream of the jet column [region 5] is vertically entrained flow,
progressively turning into a parallel flow along the impingement surface. For both
geometries, this parallel flow region is about
1 DH
thick. The flow characteristics for
this jet location are shown in Figures 5.10 and 5.11. The jet is particularly well
defined for the circular jet 2 with a high-speed core generating pairs of counterrotating vorticity by shear with the air present in the channel. The cusped ellipse
(0°) jet 2 has a slightly faster jet with a better-diffused vorticity field. The turbulent
core and the dissipation seem concentrated in the jet column but the average over
the flow field shows a 43% increase in both properties, compared to the circular jet.
Further downstream, near the jet array center, at jet 4, the crossflow-to-jet
velocity ratio is V=0.095. Figures 5.12 and 5.13 show the mean velocity vector
field plot for the circular and the cusped ellipse (0°) jet 4. For both configurations,
the jet column [region 1] separates into a downstream flow and a return flow at 1DH
from the impingement surface [region 2]. The return flow collides with the
upstream jet flow and creates a surface vortex in region 4 that is stronger than at the
upstream location, jet 2. For the circular jet, the center of rotation of the surface
49
-
'''''''
''I
''
''S
S'''''
444 4''
-
44444
'''44444''''''
4''''''
-I_s
N
N N
'S
4
\
'S
'S 'S
'S
'S
4
N N
N.NN.N.NN\
'
-
II''' I
N N \ 4 4''''
N. N5 "S S I''
2
N NN.\'S
'S 'S
-
N \ \ \ \ 'S N N 'S
NNNNN\\\ 44
.N N \ \
NNN'N\ 5
'NN'N.'.'--..'--.N\ 4
-25
----5---.
4
I
4
4
4
1
'SN
'S
1
4
4
4
-
'S"'1I''"'
1 11 / / / ' - -
'
1
4
N N S
1
4
'SN\'S S
1
4
4
4
'
4
4
4
'S
4 4
4
4
1
I
'5' 4
N
-
S S S
t
-
/ / / / / /
- -
25
-2
.- .-
-
.-
-1.6
-
I
I
4
'S
'S
\
'S
N
-
'
-
-06
-1
4
I
-
- -
-
-
1
'
/
T
- / / / / / / / / / / - - ' / / / / / / - -
-35
S
'
'
-
4
-3
S
1
4
I
4 I'''
4'
4
4
'S
'
-
-
05
0
50
N
1 5
1
Figure 5.12. PIV, Circular jet, HIDH=4, Vr=0.095, Re=9,740
-16
N.N.NN.'\\ \ \ 54 4
44
4
1
4
4
4
4
4
4
Q
4.
-3
4 44 4
4.
4.
4441
4444444.
44
1
-2.5
4
44.4.
4.
4
4
4.41
1
4
4
4
4.
1
4
I
4.
4.
4.
4
4.
222 2l 4j/ -
-2
-16
-1
-
'
-05
-
0
45
4.4.4.4.
'S
4.45' 'SN
445554 414\\'''S'S
4444445454
'''4544
------5''''
- --
S
-
1
'4 4 4
4.4.4.445 5
441444 /55 '4
-3-5
'4
\\\\\444
544
4.
\\\\\\\\\\\ 4421121 4 5444.4
44454545 54.4441'-5
/44
4. \ '1
-
'
/
0.5
1
1.5
2
0403
Figure 5.13. PIV, Cusped ellipse (0°) jet, HIDH=4, Vr=0.095, Re=8,570
50
Mean Velocity Magnitude
Mean Vorticity
20
0
x
6
4
4
a
j::
N
1
2
L2.1o12 IC
X/DH
XJDH
Turbulent Kinetic Energy
Mean Squared Vorticity Fluctuations
1
r2II
a
N
1
0
XIDH
1
l
i
X/DR
Figure 5.14. Flow characteristics, Circular jet,
H/DH=4, Vr=O.095, Re=9,740
Mean Vorticity
Mean Velocity Magnitude
0
10
0
16
25
14
a
N
-2
-1
0
1
2
1
2
XIDH
-1
-3
-4
-2
-1
0
X/DH
0
1
X/DH
Figure 5.15. Flow characteristics, Cusped ellipse (0°) jet,
HIDH=4, Vr=O.095, Re=8,570
2
52
vortex comes into the field of view and is at l.8DH from the impingement point.
For the cusped ellipse
(00)
jet, the center of rotation is still outside of the field of
view but the rotation speed is faster than for the circular jet. The flow downstream
of the jet column [region 5] shows a vertically entrained flow, progressively turning
into a parallel flow along the surface. It is important to note that for the circular jet,
the downstream flow is slightly disturbed by some independent structures in the
flow. Also, not that for the cusped ellipse (0°) jet , the top part of the flow field is
very weak. This phenomenon will be explained by the side wall effect discussed in
last section of this chapter. The flow characteristics for this jet are shown in Figures
5.14 and 5.15. For the circular jet, the shearing within the jet increases in intensity
while spreading over the impingement surface. The turbulent kinetic energy and the
dissipation spread over a larger portion of the channel increasing the average
vorticity by 160% compared to jet 2. Similar results are obtained for the cusped
ellipse (0°) jet but the increase is smaller, only 16% higher than jet 2.
Further downstream, at jet 6, the crossflow-to-jet velocity ratio is V=0.l59.
The mean velocity vector field plot for the circular jet and the cusped ellipse (0°) jet
are shown in Figures 5.16 and 5.17. For both configurations, a surface vortex is
created by the return flow from the impinging jet and the flow coming from the
upstream jet in region 4. The center of rotation appears to be at height Z=IDH from
the impingement surface and at distance X=1DH, upstream of the stagnation point.
For the circular jet, the surface vortex appears to lean strongly against the jet
column, entraining a large mass of flow [region 3] into the jet column. The flow
-
Re=8,570 Vr=0.159,
HJDH=4, jet, (0°) ellipse Cusped PIV, 5.17. Figure
15
I
114
0.5
OlD
0
''''"'/'
'05
-1
-1.5
''lI4
4U S54UUS\44jj
4555 414
4
4
4
4
1
-25
Ill
-'''I
-3-5
-
I
''U\\4\
-3
4
-
14,1
-2.5
------
/
-
'U
4
4
-2
/44
444
U
5''S_
US--
UI''''''
\\\\1
411'
1/1%
14
1114
/1J11144
'U
//1/
t 4
111/'''
41
44//
44.
111' \\414
4.
1
4
1
--'--"' --'---.--------..--.--
1
'U
4,
4
4,
'U
S
-
-'
-
\ I \
-1.5
14
44U
4444'U4\ 4114
S'
I/U 1./U
U''''
U
I
-0,5
Re=9,740 Vr=0.159, HJDH4, jet, Circular PIV, 5.16. Figure
2
2.1
1.5
5
0.5
1
-
I
'U
/
'
-1.5
-1
__.___/
-
-
-
.
-
S
11
44
4
lI11
U4IIJ4
'UU4
4lII
-3,5
S\'U4
-3
-25
I
'U
\ \ \ \ \
'U
'U
4
I
Q
I
.
1
I
1
4
4
Il,.,
I',...
4
it?
f
'U
4
'U
4
4444
/U''''
-
-05
I
--
4''
4''
4/U
44/55555
lUUl\\\\\
//
4411
44444
4144
445\\'U\\\\
\\\\\
4
44
14
I I I
.
I I I
\ " \ \ \ \ I
\\
S S
4
4
U'''
I
F-
1
4
1
4
4
S
S
\
-1.5
\
\
\44
\\\4
444
SU--
l
t
S\/S4
4
/
U
53
54
0
Mean Velocity Magnitude
0
35
x
5
30
-1
Mean Vorticity
-1
25
I
20
N
15
-3
10
N
-5
-3
5
-4
-2
I
0-2
-10
-1
X/DH
0
1400
1200
1000
a
N
800
600
400
200
-4
-2
-1
X/DH
X/DH
Figure 5.18. Flow characteristics, Circular jet,
H/DH=4, Vr=O.159, Re=9,740
55
Mean Vorticity
Mean Velocity Magnitude
35
0.01
30
0.005
25
20
0
N
II
15
0
N
-0.005
10
-0.01
5
-0.015
X/DH
3500
U
3000
2500
2000
a
N
a:i
1500
1000
500
X/DH
XJDH
Figure 5. 19. Flow characteristics, Cusped ellipse (0°) jet,
H/DH=4, Vr=0.159, Re=8,570
56
characteristics for this jet location are shown in Figures 5.18 and 5.19. The pair of
counter-rotating vorticity appears to be broken and is biased in the downstream
direction. The TKE appears to be concentrated in the jet column and spread
relatively uniformly over the impingement surface creating
concentrated TKE. For the cusped ellipse
(00)
'pockets' of
jet, the surface vortex appears to be
slightly larger in size. Multiple vorticity pockets appears all over the flow while the
jet shearing layers appears locally reduced. Both TKE creation and dissipation
occurs all over the channel with levels of TKE 2 times greater than for the circular
jet and mean squared vorticity levels 5 times greater than for the circular jet.
Effect of the Reynolds Number
In this section, the influence of Re on the flow is described at two locations:
close to the back of the jet array and close to the exit, at jet 2 and jet 6 locations,
respectively. The flow structures for the circular jet array and the cusped ellipse jet
array
(00)
are analyzed for the following conditions: the higher impingement
distance (I-IJDH=4) and with the flow rate ranging from 14 to 20 CFM, resulting in a
wide range of Reynolds number values. For the circular jet, the Re range is
9,740<Re<l5,830 while for the cusped ellipse
(00)
jet, the Re range is
8,570<Re<13,530. For each jet along the flow, the crossflow-to-jet velocity ratio is
unchanged with Re variations, since it is solely a function of the geometry.
57
085
1
i
T
PT1
P12
£PT3
OP14
08-
---
-------
--
4
Average
075
1.)
N
07
0.65
0.6
9000
I
10000
11000
I
12000
13000
14000
15000
16000
17000
Re
Figure 5.20. Flow coefficient, Circular jet, HIDH=4
PT1
--
a PT2
U
0.95
I
I
I
I
PT3
I
I
I
0 PT4
Z PT5
Average
0.9
0.85
0.8
I
.
I
I
0.75
I
I
10000
11000
I
I
I
I
I
I
I
I
I
I
0.7
8000
9000
12000
13000
14000
Re
Figure 5.21. Flow coefficient, Cusped ellipse (0°) jet, HJDH=4
15000
58
Figures 5.20 and 5.21 show the evolution of the flow coefficient versus
increasing Re. On these graphs, the flow coefficient values are plotted for the
different pressure taps as a function of Re and the corresponding average values,
<CD>.
For the lower Re, <CD> is about 0.70 for the circular jet and 0.80 for the
cusped ellipse
(00)
jet. For the circular jet, <CD> fluctuations of ±4% are observed
over the range of Re, but no clear pattern is detected. For the cusped ellipse (0°) jet,
<CD> first decreases by 3.5%, then continues to increase until the maximum Re is
reached. For this maximum value of Re, <CD> is only 1% higher than for the
lowest Re and still decreases monotonically along the crossflow with the same
slope as in Figure 5.2.
Figures 5.22 and 5.23 show the surface flow visualization for the maximum
Re condition. Compared to the lower Re (see Figures 5.4 and 5.5), no major
difference in the flow pattern are perceptible. Figure 5.24 shows the change of Svs
and Ss along the flow for the circular and the cusped ellipse (0°) jet arrays.
Compared to Figure 5.6, the surface vortex to stagnation point distance, Svs,
decreases along the downstream flow with equivalent values and corresponding
slope for both lower and higher Re. The surface vortex separation distance, S,
increases slightly along the downstream direction, but by less than 6%. Figure 5.25
shows the change of the surface vortex stagnation size, Sc, along the flow. For both
configurations, Sc doesn't appear to be very sensitive to the crossflow up to the jet
array center. Further downstream (near jet 4), Sc appears to increase by nearly 20%,
until the exit location where a significant drop is observed.
59
4
Figure 5.22. Surface flow visualization, Circular jet,
HIDH=4, QR=2OCFM, Re= 15,800
A
n
Figure 5.23. Flow coefficient, Cusped Ellipse (0°) jet,
H/DH=4, QR=2OCFM, Re= 13,500
60
8
I
+--CJ-Svs
F
-------,
5
_____-o-cJ-s
-p---
--CE0-Sv
0CEO-So
0
002
004
006
008
01
012
014
0.16
018
02
Figure 5.24. Surface vortex and stagnation point relative location, HIDH=4,
QR=2OCFM, Circular jet: Re=15,800, Cusped ellipse (00) jet: Re=13,500
18
1.6
14
12
08
0.6
H,
04
02
I
002
0.04
I
006
I
008
I
01
I
012
I
014
I
016
CEO-Sc
018
02
v
Figure 5.25. Surface vortex deposit size, HJDH=4,
QR=2OCFM, Circular jet: Re=15,800, Cusped ellipse (0°) jet: Re= 13,500
Re=13,500 Vr=0.032, HIDH=4, jet, (0°) ellipse Cusped PIV, 5.27. Figure
0100,
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61
62
Mean Vorticity
Mean Velocity Magnitude
x
6
10
4
8
6
a
-r
N
2
a
N
4
0
2
-2
z1
XIDH
X/DH
0
0
Mean Squared Vorticity Fluctuations
1
3.5
1500
2.5
j
a
11
N
2
2
L1
1:111.
1.5
3
1
0.5
-4
4
XIDN
X/DH
Figure 5.28. Flow characteristics, Circular jet, HIDH=4, Vr=O.O.32, Re=15,800
63
a
N
Mean Squared Vorticity
rgy
N31i:I
a
N
1
X/DH
2
XIDH
Figure 5.29. Flow characteristics, Cusped ellipse (00) jet,
HJDH=4, Vr=0.0.32, Re=13,500
1
i
64
The mean velocity vector field plot for the circular jet and the cusped ellipse
(00)
jet are shown in Figures 5.26 and 5.27. Closer to the back of the array, at the jet
2 location where VFO.O32, the jet structure of the circular jet strengthens slightly
for the higher Re. The breakdown of the jet column [region 2] into a parallel flow
and a return flow is better defined than for the lower Re. For the circular jet 2, the
surface vortex center of rotation location appears to be at Z=1DH from the
impingement surface and its distance to the impingement point is X=1.7DH. The
flow characteristics for the circular jet array at this location are shown in Figure
5.28. The vorticity plot indicates that the jet column [region 1] is disturbed about
half way down the height of the channel with similar vorticity levels, as for lower
Re. The TKE and mean squared vorticity seems to spread further downstream, but
also a 54% increase in TKE levels and 61% in mean squared vorticity can be
observed compared to the lower Re. As can be seen in Figure 5.27, no major
change occurs for the cusped ellipse (0°) jet. The flow characteristics for the cusped
ellipse (0°) jet array at this location are shown in Figure 5.29. The surface vortex
appears to strengthen slightly but its location and size remain unchanged. The
entrainment of the downstream flow appears stronger. The vorticity plots show a
better definition of the jet shearing layers and the vorticity levels stay the same. The
TKE and mean squared vorticity locations are localized along the jet column and
along the impingement surface. Their levels increase slightly by 6% and 9%
respectively, when compared to the lower Re (see Figure 5.11).
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Mean Vorticity
x
4
25
2
20
0
N
15
0
N
-2
10
-4
5
-6
-4
_____________________
-2
-2
0
Turbulent Kinetic Energy
1600
1400
1200
1000
d-2
N
800
0
-3
-4
-1
3
25
a -2
2
200
0
XJDH
1
10
4
400
-1
-8
2
Mean Squared Vorticity Fluctuations
600
-2
1
X/DH
XIDF
0
-1
2
XJDH
Figure 5.32. Flow characteristics, Circular jet,
HIDH=4, Vr=O.159, Re=15,800
(i7
Mean Velocity Magnitude
0
Mean Vorticity
x
20
5
-1
15
a
N
10
0
I
a-2
-5
-3
5
-4
2
2
XIDH
0
3000
2500
2000
a
N
1500
Q
N
1000
500
2
X/DH
X/DH
Figure 5.33. Flow characteristics, Cusped ellipse (00) jet,
H/DH=4, Vr=0.159, Re= 13,500
-10
68
Further downstream, at jet 6, singular changes occur. Figures 5.30 and 5.31
show the mean velocity vector field plot for the circular and the cusped ellipse
(00)
jet 6. For the circular jet, the surface vortex [region 4] seems to strangely collide
with the jet column [region 1], deflecting the column significantly downstream. The
surface vortex size appears to expand in the streamwise direction while it shrinks in
height. The jet column velocity reaches a minimum just at the interface with the
surface vortex, before accelerating in the downstream direction. Consequently, the
entrainment of the downstream flow increased. The different flow characteristics
for the circular jet are shown in Figure 5.32. The vorticity plot shows that the jet
column is not disturbed until reaching the ground vortex interface and the shearing
effect strength drops by 57%. The TKE and mean squared vorticity repartition
appear to stay essentially the same but with a 36% increase in TKE levels and 43%
increase in mean squared vorticity.
A major change is observed for the cusped ellipse (0°) jet, shown in Figure
5.31. As the jet breaks down into a downstream and return-flow a contraction of the
jet column is observed at 1DH from the impingement surface. This appears to create
a slight "return-curve" of the downstream flow creating a larger and more diffuse
impingement zone. This is speculated to be due to the axis switching effect, typical
for non-axisymmetric jets where the major and minor axis interchange some
distance downstream. This also explains the reduction of the jet column velocity,
resulting from a flow transfer in the transversal direction. The surface vortex
location appears unchanged with its center of rotation at X=1DH from the
69
stagnation point and at Z=1DH from the impingement surface. The different flow
characteristics for the cusped ellipse (00) jet are shown in Figure 5.33. Significant
decreases are observed for all the flow properties. The average over the flow field
shows a 39% decrease in TKE and a 65% decrease in dissipation.
Effects of the Impingement Distance
In this section, the influence of the impingement distance, H/DH, on the
flow structure of the circular jet array is investigated. The impingement distance is
varied from 2 to 4. Results for the lower Reynolds number, Re=9,740, are
investigated in details, but the Reynolds number influence is also discussed.
Recall from Figure 5.2, for HJDH=4, the local
flow
coefficient,
CD,
decreases slightly and monotonically from the back wall to the exit, with an average
of 0.70. The change of CD with Re are shown in Figure 5.34. For HJDH=2, it is
observed that the decrease along the downstream direction is more pronounced. CD
increases by 6% close to the back-wall (PTI) and simultaneously decreases by less
than 2% at the exit (PT5), resulting in an average
flow
coefficient, <CD>, close to
0.73. When the height of the channel is reduced to HJDH=l (Figure 5.35), CD
increases by 13% close to the back wall and decrease by 8% close to the exit, with
the average
flow
coefficient at 0.74. Therefore, the use of the average
flow
coefficient, <CD>, has to be interpreted with care, since a very low impingement
70
o 85
08
0.75
Q
U
0.7
0.65
0.6'
9000
10000
11000
12000
13000
14000
15000
16000
17000
Re
Figure
5.34
Flow coefficient, Circular jet, FIJDH=2
0 85
I
I
I
I
I
APT3
* ------- * ------- H ----------------- 4 ------- F
I
0.8
PT2
I
.
I
I
I
U
.1
0.75
I
I
I
I
i
I
I
I
0 PT4
I PT5
Average
I
I
I
------T--I
_I..
__.I..
..__ ....l ------- 1......
:
0
U
I
I
I
I
I
----
I
I
I
I
I
I
DI
0.7
I
I
0
I
XI
0.65
-
I
I
4
I
I
I
I
I
I
I
---Al
I
--
I
I
I
I
--
-:
A
I
--
-
0
x
I
I
0.6 L
9000
10000
11000
12000
13000
I
14000
I
15000
Re
Figure
5.35
Flow coefficient, Circular jet, I-I/DH=1
I
16000
71
Figure 5.36 Surface flow visualization, Circular jet,
H/DH=2, Re=9,740
Figure 5.37 Surface flow visualization, Circular jet,
HJDH=2, Re=15,830
72
8
i
I
F
I
H
:
CJ-Ss Rel
____
(04
0.01
0
O--CJ-SsRe2
L.
aCJ-Svs Rel
àCJ-Scs-Re2
0.02
0.03
0.04
0.05
0.06
0.07
yr
0.08
0.09
0.1
Figure 5.38 Surface vortex and stagnation point relative location, Circular jet,
H/DH=2, Re 1=9,740 and Re2= 15,830
2
I
I
I
I
I
I
I
1.8
I
I
I
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I
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1.6
1.4
1.2
I
(I)
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I
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I
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I
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1
1
I
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003
0.04
0
0
I
0.02
I
1
0 05
0.06
0.07
0.08
0.09
yr
Figure 5.39 Surface vortex deposit size, Circular jet, HJD11=2,
Re 1=9,740 and Re2=15,830
0.1
73
distance results in large variations over the surface. Large impingement distances
have fairly uniform values for the average flow coefficient <CD>.
Figures 5.36 and 5.37 show the surface flow visualization for HIDH=2 and
for both low and high Re. Figure 5.38 shows the change of Svs and Ss along the
flow. The surface vortex-to-stagnation point distance decreases along the
downstream flow with equivalent values and slope for both lower and higher Re.
Svs decreases linearly and reaches a minimum of 1DH at the channel exit indicating
that the surface vortex is close to the stagnation point or that its size decreases
greatly. The surface vortex separation distance, Ss, grows slightly along the
downstream direction but by less than 6%. The surface vortex stagnation size, Sc,
appears to decrease along the downstream direction as shown in Figure 5.39.
At the center of the jet array, at jet 4, the crossflow-to-jet velocity ratio is
Vr=0.048. The mean velocity vector field plot for the circular jet is shown in Figure
5.40. A relatively weak surface vortex is visible, impinging against the jet column
and deflecting it downstream. Its center of rotation appears is approximately from
Z=O.2DH to the impingement surface, but extends to X= 1 .2DH in the streamwise
direction. The flow appears to accelerate in a similar way, as the case for the flow
from jet 6, with H/DH=4 and high Re (Figure 5.30). The jet column appears to
entirely feed the downstream flow, creating a O.2DH thick parallel flow along the
impingement surface. The vorticity plots in Figure 5.42 show that several spots of
counter-rotating vorticity appears along the impingement surface accompanied by a
40% decrease in vorticity level, when compared to HIDH=4. The TKE and mean
Re=15,830 Vr=0.048, HfD=2, jet, Circular PIV, 5.41 Figure
OlD"
2
2
-.
\
\
\
\
.5
-
.5
.
-
.
15
-
-_---5
-_
I
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-.5
-'
5
5
\
-
.
OS
0
5
5
/
25
-1
I
8
S
6
S
I!.-
2
5 S
\\\\\S
\\'\
\ \
55
\
\ \
s
\
\
\
\
S \
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-
16
4
\ \ \ \
55522255
\
1
5
\
'
5
12
\ \
\ \
e
-1
22255555
..........
...
S
06
S
2.4
T
Re=9,740 Vr=0.048, HJDH=2, jet, Circular PIV, 5.40 Figure
2
25
-. -. -.
SD5
05
2
_a_.2_aa>_*.è,e,.>*,._5
0
.05
-1
-
-.
S.
/
...S
/
...
S
-.
S.
.
\ \
\
S \ S
-15
..
T
i
-
S
'
-
\SSSSSS
'I
/
/
-
-
r
-.
/
1,,i
.-.
-.
B
7,,
2 -1
S
-
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-
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\\\\\\'
-o
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-.-.-.--.
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-
-.
-o
74
75
Mean Velocity Magnitude
Mean Vorticity
x
20
4
-c
15
a
N
10
-1
-c
aI
0
-1
-2
5
-4
-2
-1
0
1
2
XIDH
XJDH
Mean Squared Vorticity Fluctuations
1200
0
1000
-C
I
a
N
-1
-2
XIDH
-1
0
XIDH
Figure 5.42 Flow characteristics, Circular jet,
H/DH=2, Vr=O.048, Re=9,740
1
2
io
76
Mean VeIocty Magnitude
Mean Vorticity
14
6
12
4
10
8
a.
N
6
-1
4
.2
a
I
0
N
-2
-1
-4
2
-1
0
1
2
X/DH
X/DH
2000
-(
1500
aI
1000
N
500
X/DH
x 10
0
Mean Squared Vorticity Fluctuations
1
3
2.5
-0.5
-1
1.5
-1.:
05
X/DH
Figure 5.43 Flow characteristics, Circular jet,
H/DH=2, Vr=0.048, Re= 15,830
77
squared vorticity plots in Figure 5.42 show a more localized creation and
dissipation of turbulence along the impingement surface. The levels of TKE and
dissipation drop by 47% and 51%, respectively, compared to H/DH=4 and same low
Re. The mean velocity vector field for the same jet but for a higher Re is shown in
Figure 5.41 with the associated flow characteristics in Figure 5.43. Increasing Re
seems to strengthen the surface vortex both in speed and size, creating a stronger
acceleration of the jet column with a smaller deflection of the jet. The vorticity plot
in Figure 5.43 shows a slightly better defined jet column with the classic pair of
counter-rotating vorticity pockets defining the jet shearing with the crossflow. The
TKE and mean squared vorticity fields don't appear to be different than the
precedent case (Figure 5.42), with H/D1-=2 and a lower Re.
Further downstream, at jet 6, remarkable changes occur. The crossflow-tojet velocity ratio at jet 6 is V=O.O95. These changes are shown in the mean velocity
vector field, Figure 5.44. For low Re, the surface vortex appears to merge and
accelerate with the jet column, resulting in a strong downstream parallel flow. The
surface vortex size increases to approximately one half of the channel height. The
center of rotation appears to move downstream, at X=O.6DH from the stagnation
point. The vorticity plots show a well defined jet column with a symmetry breakup
half way down the height of the channel. Compared to H/DH=4, a 11% decrease in
TKE and a 1% decrease in mean squared vorticity can be observed from Figure
5.46. The mean velocity vector field for the same jet and conditions but with a
higher Re is shown in Figure 5.45, and the corresponding flow characteristics in
78
-02
.04
.06
\\
.08
,,
Q
/
I.,
/
I
I
-I 8
-2
444
\
\ \ \ 44 44
.
_,, ll'l\\\...
-I 6
\\\\\\
/
,
.12
-1 $
-I
.. .-.''
-.
0
-0.5
0_s
i
2
I 5
0/05
Figure 5.44 PIV, Circular jet, HIDH=2, Vr=O.095, Re=9,740
-02
.5
'Ill
-0.4
-'IS.5'
'\\\1 I
-06
-
.
-0.8
.....
'''1111111'''' --'5-,
''1/ / lI4' ''/444 \ \\//
Q
-12
.5-
.1.4
.5.-,, f/Il\'....1.._.,,,
.1.6
..,/F/I
/
-1.8
/
..
.
1\'-...._...........'
.
I
1
.
-
- -'--.5 -.-.-.-'--.-.--. -.
- -'
, .5,----- -''-'-''' III'5
I 1////..........
-2
2
-1.0
-1
-0.5
05
0
1
1.5
2
0/05
Figure 5.45 PlY, Circular jet, HJDH=2, Vr=O.095, Rel5,83O
79
Mean Velocity Magnitude
1°_j
Mean Vorticity
25
4
20
-C
2
15
0
N
10
I
C
N
0
-2
5
-4
-2
-1
0
1
2
X/DH
XIDH
0
4
2000
-c
35
-0.5
3
1500
2.5
I-
I
C
N
2
1000
-1
500
1.5
-1.5
1
0.5
-2
XJDH
io
Mean Squared Vorticity Fluctuations
X/DH
Figure 5.46 Flow characteristics, Circular jet,
H/DH=2, Vr=O.095, Re=9,740
80
Mean Vorticity
Mean Velocity Magnitude
x1
6
14
12
4
-C
10
a
I
.
N
8
6
-1
2
I
a
N
0
-2
4
2
-2
-1
0
1
-4
2
XIDH
XJDH
Mean Squared Vorticity Fluctuations
-C
aI
N
-1
-2
-1
0
XIDH
1
2
-2
-1
0
XIDH
Figure 5.47 Flow characteristics, Circular jet,
H/DH=2, Vr=0.095, Re= 15,830
1
2
< 1
o4
81
Figure 5.47. Increasing the Reynolds number seems to increase the feedback
process: the jet column appears to merge completely with the surface vortex,
feeding directly into the downstream jet location. The vorticity plot shows a larger
shearing layer at the jet-surface vortex interface, accompanied by a 78% drop in
intensity. There is no downstream deflection is apparent, and a similar downstream
flow can be observed, but weaker in magnitude than the lower Re case. Compared
to HJDH=4, for higher Re, the level of TKE unexpectedly decreased by 30% while
the mean squared vorticity decreased by 23%.
Effects of the Geometry Alignment of the Cusped Ellipse Jet Array
The cusped ellipse shape is a non-axisymmetric shape. Therefore, the jet
array can be set into two configurations: the first one with the major axis aligned
parallel to the crossflow, and the second one with the major axis aligned normal to
the crossflow. This section discusses the effect of these two configurations on the
flow structure. The cusped ellipse (0°) and the cusped ellipse (90°) jet arrays are
presented for the following conditions: high impingement distance (HJDH=4) and
Reynolds number values ranging from 8,500 to 13,500.
The evolution of the flow coefficient versus increasing values of Re are
shown in Figure 5.48. Moving downstream from the back to the exit of the array,
the flow coefficient, CD,
decreases slightly and monotonically for both
82
09
0 85
0.8
075
0.7
0.65
0.6
0
0.02
004
006
0.08
0.1
0.12
0.14
016
0.18
yr
Figure 5.48 Flow coefficient, Cusped ellipse (0°) and (90°) jet arrays,
H/DH=4, Re=8,530
0.805
0.8
0.795
0.79
0.785
A
0 78
a
C,
0.775
0.77
0.765
0.76
0.755
0.75
8000
9000
10000
11000
12000
13000
14000
Re
Figure 5.49 Average flow coefficient, Cusped ellipse (90°) jet array,
HIDH=4, Re=8,530
15000
83
--r------------
1
0.95
F
l
+
0.9
*
0.85
I
A
I
I
j..
I
P11
r
P12
A PT3
o P14
x PT5
0.8
075
0.7
0
I
I
0
Average
I
o
xi
-ix
0.65
I
-
J.
----------
.
-
0.6
8000
9000
10000
11000
12000
13000
14000
15000
Re
Figure 5.50 Flow coefficient, Cusped ellipse (0°) jet, H/DH=1
'"r-------1-
1
0.95
I
0.9
I
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0.85
I
I
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I
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0
H
8000
9000
10000
11000
12000
13000
14000
15000
Re
Figure 5.51 Flow coefficient, Cusped ellipse (90°) jet, H/DH
84
configurations. Shown on Figure 5.49, are the variations of the controversial'
average flow coefficient, <CD>, versus Re and the impingement distance, for the
cusped ellipse
(90°)
jet array. For the lower Re, <CD> is approximately 0.80 for the
cusped ellipse (0°) jet array and 0.79 for the cusped ellipse
(900)
jet array. Recall
from Figure 5.21, for the cusped ellipse (0°) jet array, no clear pattern could be
identified concerning the dependence on Re. A similar behavior is observed for the
cusped ellipse
(90°)
jet array jet with slightly lower values for
CD.
When HJDH is
decreased, the flow coefficient increases closer to the back wall and decreases at the
channel exit, increasing the slope of the curves. The flow coefficient results of the
cusped ellipse (0°) and
(90°)
jet arrays for HIDH=1 are shown in Figures 5.50 and
5.51. For this extreme case, the flow coefficient for the cusped ellipse (0°) jet array
reaches values close to CD0.97 at the back wall, and a 27% drop is observed along
the downstream direction. For the cusped ellipse
(90°) jet
array the maximum value
reaches CD0.87 at the back wall and drops only 20% along the downstream
direction. From the surface flow visualization for the cusped ellipse
(90°)
jet array
at lower and higher Re, shown in Figures 5.52 and 5.53, no major difference is
discernable between the two flow pattern. Figures 5.54 shows the evolution of Svs
and Ss along the flow direction. For HIDH=4, the surface vortex-to-stagnation point
distance appears slightly lower for the cusped ellipse
(90°)
jet array. The difference
increases for lower impingement distance values: for HJDH=2, the surface vortex is
30% closer for the cusped ellipse
(90°)
jet than for the cusped ellipse (0°) jet. For
HIDH the surface vortex size, S, is 14% smaller than for the cusped ellipse (0°) and
85
Figure 5.52 Surface flow visualization, Cusped ellipse (900) jet,
H/DH=4, Re=8,530
Figure 5.53 Surface flow visualization, Cusped ellipse (90°) jet,
H/DH=4, Re= 13,460
86
8
F
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7
6
5
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016
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02
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Figure
Surface vortex and stagnation point relative location,
Cusped ellipse (90°) jet, HIDH=4 and H/DH=2
5.54
1.8
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1.6
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I
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0.8
IIIII
06
04
02
0
0
002
004
0.06
0.06
01
012
014
016
018
Yr
Figure 5.55 Surface vortex deposit size, Cusped ellipse (90°) jet,
HIDH=4 and H/DH=2
02
87
the circular jet. A 37% drop is observed at the exit (Figure 5.55). For H/DH=2, these
result increase to 22% and 60%, respectively.
The mean velocity vector field plot for the cusped ellipse (900) jet is shown
in Figure 5.56. Close to the back wall, at jet 6, the crossflow-to-jet velocity ratio is
V1-=0.032. No surface vortex is visible for both of the flow configurations. For the
cusped ellipse (0°) jet, the jet column breaks down into a return and downstream
flow (Figure 5.9). The return-flow, interacting with the upstream flow, appears to
create a large rotating structure localized outside of the field of view. The cusped
ellipse (90°) jet doesn't show any organized return-flow (Figure 5.56). The jet
column appears to contract at 1DH from the impingement surface and breakdown
into relatively weak and multidirectional flows. The same behavior is observed for
the larger Re, shown in Figure 5.57. The flow characteristics for the lower and
higher Re are shown in Figures 5.58 and 5.59, respectively. The vorticity plots
confirm the jet column disturbance [region 2 in the lower part of the channel,
while multiple "pockets" of vorticity can be found all along the channel but with
significant weakness. Compared to the cusped ellipse (0°) jet, the vorticity level is
60% smaller. For the TKE and mean squared vorticity, dramatic changes occur due
to cusped ellipse alignment. The cusped ellipse (0°) jet shows a wide mixing of the
flow all along the channel, particularly close to the impingement wall. The cusped
ellipse (90°) jet shows no evidence of turbulence mixing except in the jet column
and the TKE and mean squared vorticity levels drop by 76% and 75%, respectively.
Re=l3,460 Vr=0.032, HIDH=4, jet, (90°) ellipse Cusped PIV, 5.57 Figure
0I0,
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88
89
Mean Velocity Magnitude
x
3
10
2
8
1
6
0
N
4
0
0
N
-1
-2
2
-3
-4
-2
-1
0
-41
-2
2
XJDH
-1
0
1
400
300
200
Mean Squared Vorticity Fluctuations
8
0
Ri
-4
-2
-1
X/DH
10
12
10
-1
100
-2
2
XIDH
0
0
N
F
XIDH
Figure 5.58 Flow characteristics, Cusped ellipse (900) jet,
H/DH=4, Vr=0.032, Re=8,530
90
Mean Velocity Magnitude
2
d
N
XJDH
Figure 5.59 Flow characteristics, Cusped ellipse (900) jet,
HIDH=4, Vr=0.032, Re= 13,460
91
Increasing Re appears to strengthen slightly the jet column and its shearing layers,
but no other significant changes can be observed.
Further downstream, at jet 4, the crossflow-to-jet velocity ratio is V-=0.095.
The flow structure, shown in Figure 5.60, is very similar to the upstream jet 2 flow
structure. While the cusped ellipse
(00)
jet shows a surface vortex close to the jet
column, there is no evidence of surface vortex formation for the cusped ellipse
(90°) jet (Figure 5.60). The jet column appears to contract at l.2DH from the
impingement surface, then re-expand and breakdown into relatively weak,
multidirectional flows. The downstream flow appears to strengthen slightly when
Re is increased (Figure 5.61). The flow characteristics for the cusped ellipse (90°)
jet array at this location are shown in Figure 5.62. The jet shearing layers are well
defined in the lower part of the flow, with a symmetry break at ZIDH=3 which
appears to be due to the axis switching effect. The vorticity level is still rather weak
as for jet 2. The TKE and mean squared vorticity spread over a larger part of the
channel than jet 2, but stay relatively localized in the jet column area. The TKE
level drops by 45%, while the mean squared vorticity level drops by 49% when
compared to the cusped ellipse (0°) jet.
Figures 5.61 and 5.63 show the flow structure and the associated
characteristics when Re is increased. Surprisingly, no significant change can be
observed. Figures 5.64 and 5.65 show the mean velocity vector field plot for the
cusped ellipse (90°) jet 6. The crossflow-to-jet velocity ratio is Vr=0. 159. The flow
structure of the cusped ellipse (90°) jet appears to turn into a wall jet (Figure 5.64).
O9I=°1 'c600=A ''=11uIn '°i(o6) sdiij pdsn 'AId 19c
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93
Mean Vorticity
U
x
4
14
12
2
10
0
N
8
6
0
N
0
-2
4
2
-4
2
X/DH
XJDH
Mean Squared Vorticity Fluctuations
700
600
0
N
400
300
200
100
-4
2
XJDH
X/DH
Figure 5.62 Flow characteristics, Cusped ellipse (90°) jet,
H/DH=4, Vr=0.095, Re=8,530
i
94
Mean Vorticity
Mean Velocity Magnitude
x 10
4
16
14
2
12
10
Li
N
8
0
Li
N
-2
6
4
2
-2
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0
1
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2
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Li
N
X!DH
X/DH
Figure 5.63 Flow characteristics, Cusped ellipse (90°) jet,
HJDH=4, Vr=0.095, Re=13,460
-4
95
The jet column is progressively deflected by the crossflow until it is completely
aligned parallel with the impingement surface. The flow seems to grow in speed in
the lower half of the channel, creating a large entrainment of the upper flow, but
there is no surface vortex visible. Increasing the Reynolds number augments the
flow entrainment and shows an increase in flow velocity, but the general flow
structure remains the same (Figure 5.65). The flow characteristics for this jet and
for the two different Re are shown in Figures 5.66 and 5.67. The jet shearing layers
appear very scattered, and multiple pockets of vorticity can by found all over the jet
column and the impingement point area. The TKE and mean squared vorticity
spread over a larger area of the channel, but without matching the cusped ellipse
(00)
jet mixing. No dramatic change in TKE and mean squared vorticity levels are
observed when compared to those of jet 4. But when compared to the cusped ellipse
(0°) jet, there is a drop of 57% for the TKE and a 76% drop for the mean squared
vorticity.
Side-Wall Effects
During the PlY measurements, some configurations were less willing to
show what they had to offer. The images obtained from the digital camera showed a
zone of "blur" in the upper part of the flow, which introduced error into the
analysis. This problem occurred mainly for the cusped ellipse configurations, but
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96
97
Mean Vorticity
Mean Velocity Magnitude
0
x
4
16
14
2
12
0
N
8
0
0
6
-2
4
2
-2
-1
0
1
2
2
XIDH
0
1400
1200
-1
1000
I
8OO
N
600
-3
400
200
XIDH
XJDH
Figure 5.66 Flow characteristics, Cusped ellipse (900) jet
H/DH=4, Vr=0.159, Re=8,530
-4
98
Mean Vorticity
Mean Velocity Magnitude
x 10
4
16
14
2
12
10
N
8
a
0
N
-2
6
4
-4
2
-2
-1
0
1
2
X/OH
XJDH
Mean Squared Vorticity Fluctuations
i
1400
1200
1000
800
N
600
400
200
-4
XIDH
'!!I i
XJDH
Figure 5.67 Flow characteristics, Cusped ellipse (900) jet,
H/DH=4, Vr=0.159, Re=13,460
o
99
also occurred for all of the jets when the impingement distance was low, HIDH=2.
The reason for this can be seen in Figure
5.68.
The insert-layer used to identify the
surface flow conditions was folded to fit the wall of the channel. This insert-layer
provides information on the side-wall effects. As the surface vortex develops
downstream around the edge jets, outside the PIV laser sheet, it also grows in
height along the side-wall. A detachment zone is formed, resulting in a deposit of
particles on the channel's sides. The camera is focused on the laser sheet's plane and
the pictures are captured directly through the glass side-wall. The deposit on the
wall explains the "blur" effect and the resulting error in velocity calculation. It was
also observed that the size of the side-wall "band" of deposit decreases slowly into
a "bow" curve as the horseshoe vortex increase in size.
Undesired
it
/
Si
Fig. 5.68
Side-wall flow visualization
Discussion
Surface
flow
visualization, jet orifice
flow
coefficient measurements, and
Ply measurements of the entire flow field were used to interpret the complex flow
features. Based on these measurements, specific conclusions can be drawn about
this
flow
and the impact of the flow parameters on the flow structure.
The surface
flow
visualization provides details of the flow pattern at the
impingement surface. For all the jet configurations, the jets spread over the surface
creating cells defined by multiple detachment-reattachment zones with a
characteristic "horseshoe" shape around each jet. The cell size appears to expand
slightly along the downstream flow direction (less than 4%). The impingement
point distance to the upstream detachment zone was measured and was found to be
linearly decreasing function of the downstream position, with a 50% drop for
H/DH=4 and 70% drop for HIDH=2. On the other hand, the results show little
change over the range of Re studied. Therefore, decreasing the impingement
distance affects the cells distribution with increased sensitivity to changes along the
flow direction.
The flow coefficient,
CD,
was found to decrease along the downstream
crossflow direction. The average is 0.70 for the round jet and 0.80 for the cusped
ellipse (0°) jet. As Re is increased, CD drops slightly (less than 5% over the range of
Reynolds numbers studied) for all of the configurations. However when the
impingement distance HJDH is decreased, CD is much more sensitive to the
crossflow effect. Locally, CD is largest close to the back of the channel and
decreases at the exit, therefore the overall average value
<CD>,
increases slightly
(<5 %). It must be kept in mind that these results assume uniform mass flow rate
from all of the jets in the array.
The PIV results provide a large amount of information about the twodimensional flow structure. Each jet appears to split near the impingement surface,
into downstream flow and return-flow. This return flow and the flow coming from
the upstream jets collide and create a large recirculation region identified as a
"surface vortex" that can be observed upstream of the jet column. Close to the back
of the channel, this vortex appears large and relatively slow. Further downstream,
the surface vortex location moves downstream relative to the jet column. Its size
appears to decrease while its strength increases. Its proximity with the jet creates a
large flow entrainment that leads to a relatively large acceleration and a slight
deviation of the jet column in the impingement area. This phenomenon appears to
be sensitive to Re. The higher the value of Re, the closer the surface vortex is to the
Jet.
The vorticity field provides details of the various large-scale vortex
locations resulting from the interaction of the crossflow and the jets. Shown in
Figure
5.69
are the overall averaged mean vorticity squared,
<02>,
and for each jet
array configuration. The corresponding flow conditions are shown in Table
5.1.
Pairs of counter-rotating vorticity are visible, delimiting the jet shearing layers. For
lower Re, the jet is mostly well defined. For increasing Re, the symmetry breaks-up
102
Table 5.1 Jet array flow conditions
Reynolds Number
Jet Array
Configuration
Low
Re!
High
Re2
Circular jet
9740
15,800
Cusped ellipse (0°)
8,570
13,500
Cusped ellipse (900)
8,570
13,500
1.2E-05
DRel DRe2
1.OE-05
8.OE-06
A
6.OE-06
4.OE-06
2.OE-06
O.OE+OO
CEO
CE9O
Figure 5.69 Comparison of <02> levels
cJ
103
and pockets of vorticity can be found throughout the flow field. The "cusped"
ellipse shows a much better spreading of these pockets all over the channel
associate with a greater level of intensity. Compared to the circular jet, a 16%
increase in averaged vorticity,
<c2>,
while in the (90°) orientation, the
is observed for the cusped ellipse
<w2>
(00)
jet array
level is 4 times smaller. Therefore,
significant changes to the mean vorticity level can be made by changes in the jet
orifice geometry.
The TKE field shows wide variations from one configuration to the other.
Figure 5.70 shows the spatially averaged levels of <TKE> for each jet array. One
can clearly see that the cusped ellipse in the (0°) position generates more turbulence
than in the (90°) position. Compared to the circular jet, a 36% increase in TKE is
observed throughout the overall surface.
The Mean squared Vorticity (Wms) fields also show wide variations from
one jet array to the other. In Figure 5.71, the overall spatially averaged dissipation
for each jet configuration is shown. Again, one can see that cusped ellipse (0°)
generates 97% more dissipation than the circular jet while the (90°) configuration
shows its relative weakness.
For a Re, the above results seem to change notably. The circular jet and the
cusped ellipse in the (0°) configuration show similar intensity of TKE and
dissipation with the circular jet results only a few percent larger than the cusped
104
ellipse (00) jet array. The cusped ellipse (90°) jet array improves slightly, but the
results stay well below the values for the two other configurations.
1000
900
800
700
A
w
I-
V
600
500
400
300
200
100
0
CEO
CE9O
CJ
Figure 5.70 Comparison of <TKE> levels
3.5E-04
3.OE-04
2.5E-04
E
2.OE-04
1.5E-04
1 .OE-04
5.OE-05
O.OEOO
CEO
CE9O
Figure 5.71 Comparison of <Wms> levels
CJ
CHAPTER VI
CONCLUSION AND RECOMMENDATIONS
The experimental investigation presented in this study was focused on an
array of jets impinging on a surface, enclosed by three walls. The air, leaving in one
preferential direction, generates a crossflow that interacts with the jet structure of
the other jets. Two main objectives guided the study. The first focused on
understanding this crossflow-to-jet interaction along the flow and its dependence on
various parameters such as the impingement distance and the flow rate. The second
objective was to identify any specific behavior for a particular jet array with a nonaxisymmetric geometry.
The study of two 7x7 array of impinging air jets was based on three
experimental methods used to define the jet structure within the channel and in the
vicinity of the impingement surface. The first array was a circular orifice array
while the second was a "cusped' ellipse array. The non-symmetry of the cusped
ellipse shape allowed two alignments with the crossflow. For all case, the flow area
for each configuration was held constant.
Surface flow visualization, jet orifice flow coefficient measurements, and
Ply measurements of the entire flow field were used to interpret the complex flow
features. The visual observation of the impinging pattern shows similar results for
all the different configurations. The jets generated cells that progressively expand in
size with increasing crossflow. The flow coefficient of each jet decreases
106
monotonically and quasi-linearly along the crossflow direction, while the average
value increases only a few percent for increasing Re. The most variation along the
flow was found for the lowest impingement distance, H/D=l. PIV measurements
of the entire flow field in the vicinity of the jet exits reveals complex flow
structures: a large rotating vortex created by the merging of the crossflow and the
jet column return-flow, moves towards the jet column as the crossflow increases in
strength. This proximity generates multiple turbulent flow patterns. This may have
consequences for improved surface cooling applications.
For low Re, the cusped ellipse jet array placed in the
(00)
position, major
axis aligned parallel to the crossflow, appears to generate significantly more
turbulence than the circular jet array, while for higher Re, both configurations show
similar results. However, in the (90°) position, major axis normal to the crossflow,
the results show considerably smaller increases in the levels of turbulence when
compared with the circular jets. Meanwhile, evidence of axis switching in the jet
column development tends to prove that a transport in the lateral direction could be
a secondary factor to take into account for surface cooling efficiency.
Recommendations for further studies are to find a different 'tracer" for the
Ply measurements that would combine a good reflectivity for flow visualization
with a smaller tendency to agglomerate and to use a faster digital camera to capture
PIV fields at a higher data rate to better measure the turbulence. Recommendations
for future studies involve 3D flow visualization methods in order to obtain the full
channel flow structure and the lateral flow structure development.
107
BIBLIOGRAPHY
1.
Raghunathan S. and Reidl.M, 1981, "A study of multiple jets', AIAA Journal,
Vol. 19, No. 1, pp. 124-126.
2.
Moustafa G.H., Sundararajan T. and Rathakrishnan E., 1993, "Mean streamwise
velocity measurement of a triple jet of equilateral triangular configuration,
Transactions of the ASME, Vol. 115, pp. 534-536.
3. Moustafa G.H. and Rathakrishnan E., 1993, "Studies of the flowfield of multijet
with square configuration", AIAA Journal, vol. 37, No. 7, pp. 1189-1190.
4. Villermaux, E. and Hopfinger, E. J., 1994, "Periodically Arranged Co-flowing
Jets", Journal of Fluid Mechanics, Vol. 263, pp. 63-92.
5. Kim S.-W. and Benson T.J., 1993, "Fluid flow of a row of jets in crossflow a
numerical study", AMA Journal, Vol. 31, No. 5, pp. 806-811.
6.
Arjocu S. C. and Liburdy J. A., 1999, "Near surface characterization of an
impinging elliptic jet array", Transactions oftheASME, vol. 121. Pp. 384-390
7. Barata J.M.M., Durao D.F.G. and Heitor M.V., 1992, "Velocity Characteristics
of Multiple Impinging Jets Through a Crossflow', Journal of Fluids
Engineering, Vol. 114, pp. 23 1-239.
8. Barata J.M.M., 1996, "Fountain Flows Produced by Multiple Impinging Jets in
a Crossflow", AIM Journal, Vol. 34, No. 12, pp. 2523-2530.
9. Florschuetz L.W. and Isoda Y., 1983, "Flow distributions and discharge
coefficient effects for jet array impingement with initial crossflow",
Transactions of the ASME, Vol. 105, pp. 296-304.
10. Bernard A., Brizzi L.-E. and Bousgarbies J.-L., 1999, "Study of Several Jets
Impinging on a Plane Wall: Visualizations and Laser Velocimetry
Investigation", Transactions of the ASME, Vol. 121, pp. 808-812.
11. Metzger, D.E., "Heat Transfer in Gas Turbine Engines," Winter Annual
Meeting of The American Society of Mechanical Engineers, Boston,
Massachusettes, Vol. 87, December 13-18, 1987.
I 08
12. Kanokjaruvijit, K., 'Effects of orifice geometry and surface boundary condition
on heat transfer of impinging jet array", MS Thesis, Oregon State University,
February 2000.
109
APPENDICES
APPENDIX A
Uncertainty Analysis
This appendix is presented to determine the uncertainty of the following
dependent and independent variables: volumetric flow rate, mass flow rate,
Reynolds number, and the flow coefficient.
Volume Flow Rate
According to the gas correction formula provided by the manufacturer, the
readout volumetric flow rate needs to be corrected according to the downstream
pressure and temperature immediately downstream of the flowmeter.
QActuaFQReadout X
CF
14.7 + P(psig)
CF is the correction factor: CF
530
460+T(°F)
14.7
The uncertainty for the volume flow rate is estimated from the Kline-McClintock
relation:
2
UQ
QActua1
Readout
U
QRekm
2
+
(aQActual
aQCF
U CF
+ Uanu + uat
The readout uncertainty was
uQreadout= 0.5
CFM. The temperature was measured
using a calibrated thermocouple (J type) connected to a Fluke data logger,
introducing an error of
UT= 0.04°C.
The pressure was measured using a pressure
gauge that introduced an uncertainty of Up=l PSI. Since the flowmeter used was
only 4% full-scale accurate, it has been re-calibrated using a more accurate
flowmeter (2% full-scale accurate) reducing the manufacturer uncertainty to
Umanu0.4 CFM. This re-calibration induced a bias of
CFM. The final
Ucai=O.5
uncertainty for the actual flowrate ranged from 4.47 to 6.98%.
Mass flow rate
The mass flow rate, M, was computed based on the density, p, and the
previously obtained actual flow rate, QActual. It is calculated from the expression:
M = PQActuaI
P0
RT0
QActual
The uncertainty for the mass flow rate is estimated from the Kline-McClintock
(
relation:
=
!1j%/
J
2
,-
.
+QActua
2
UQ
112
The plenum pressure, Po, was measured with a pressure transducer, introducing an
error of u,
=0.75
psi. The temperature was measured using a calibrated J-type
thermocouple connected to a Fluke data logger, introducing an error of
0.04°C. The uncertainty in mass flow rate was computed to be 4.5 to
uTo=
7.0%.
Reynolds number
The Reynolds number is calculated as follows:
Re=M,
where M is the mass flow rate, DH is the jet hydraulic diameter, and AT is the total
orifice surface area. The total surface area being AT= 49xA. The uncertainty for the
mass flow rate is estimated from the Kline-McClintock relation:
Re
2
Re
URC[UMJ +D
2
UDJ +
(
Re
UAJ
The instrument to measure DH and A introduced an uncertainty of UD =3.tm and
UA
=0.007pm2, respectively. Finally, the uncertainty for the Reynolds number
ranged from 4.51 to 7.01%.
113
Flow coefficient
The flow coefficient is calculated from the expression:
M
A
Po-_I.[
2y
o)
i
where M is the mass flow rate, AT is the total orifice surface area, Po is the plenum
chamber pressure, P is the impingement surface pressure, and
T0
is the plenum
chamber temperature.
The secondary part under the square root in the denominator is a second order term
for the error definition. Therefore, it is discarded for the final error computation.
The uncertainty for the flow coefficient is estimated from the Kline-McClintock
relation:
2
UC
2
±
ap0
J
±
P
J
±
T0
'°
The pressure transducer used for the measurement of the plenum and impingement
surface pressure introduced an uncertainty of u, = u=O.75psi. The temperature
was measured using a calibrated J-type thermocouple connected to a Fluke data
logger, introducing an error of uT0= 0.04°C. Finally, the uncertainty for the flow
coefficient ranged from 4.11% to 7.16%.
114
Impingement Flow Pattern Characteristics
The size of the surface vortex stagnation, S, the distances between the
surface vortex stagnation and the stagnation point, Svs, and the relative distance
between two respective surface vortex stagnation, S, have been measured directly
from the images of the flow pattern in pixels, then re-scaled in mm. The uncertainty
on the edge location, u,, was 1 pixel.
Sc is expressed as Sc= X2-X1, where Xs2 and
are the stagnation point edges
Xs1
location. The uncertainty in Sc can be expressed as:
2
u
=/[-_u2
2
+[!-c-u
J
=JiJu,
J
Separation distances, such as Svs and Ss, are expressed as S (Xv2+Xv1- Xs2-Xsi)/2,
where XV2 and Xv1 are the vortex stagnation edges location. The uncertainty in Svs
and Ss can be expressed as:
2
4[_uxJ
usijlaS
=ux
Finally, the uncertainty for Sc was 0. 1OxDH, and the uncertainty for Svs and Ss was
0.O7xDH.
115
APPENDIX B
Flow Visualization Software analysis and methods
The Ply analyses have been obtained using VISIFLOWTM, a
software package that computed the velocity vector fields of the flow. The method
used to compute the PIV flow-fields for this dissertation were obtained by crosscorrelation of pairs of images, taken at a known time delay.
First, the general parameters of the flow are entered: (1) the pulse
separation, which is the time between the multiple laser pulses, (2) the image scale,
obtained from the channel size on the images (in pixels), and (3) the real size of the
channel (in m). The software support both square and non-square image pixels. The
software divides the two pictures into cells, which are comparedlcorrelated against
the corresponding cell of the second picture. For each cell, a cross correlation
function is yielded where one (or more) more peaks appears, distributed nonsymmetrically. These secondary peaks are due to correlation with other particles
rather than themselves. These peaks, which are usually of lower amplitude can be
thought of as noise, and can occasionally give bad results. The spatial position of
the main peak within the cross-correlation image of the region gives the average
frequency of the multiple particle image separation in the P[V image. This
information is then combined with the time separation to give the average velocity
vector of the particles in the cell. Various parameters are applicable for this
analysis. The analysis resolution determines the precision used to compute the cross
correlation function of the images. It can be adjusted from (16xl6) to (256x256)
pixels. Higher values give greater accuracy of velocity determination. The degree of
overlap of the correlation area can be varied from 0% (areas are bordering, but not
overlapping), to 50%, to 75% (areas are overlapping by 75%). Finally, a choice
between two algorithms is given: Gaussian fit or center of gravity. The Gaussian
option uses a two-dimensional Gaussian function, which is adjusted to fit around
the highest point of the peak. The center of gravity option thresholds the pixels
around the peak maximum, and then computes a center of gravity for the threshold
shape. This center of gravity is taken as the new maximum. The Gaussian option is
potentially more accurate, but the center of gravity option may give better results
when the correlation peaks have a distorted shape.
All of the PlY analyses in this dissertation have been obtained using the
Gaussian algorithm with the following parameters: (1) the pulse separation was set
to 2is, (2) the image scale was 1 l8imIpixel p.mlpixel, and (3) the analysis
resolution was 256x256 pixels, with a 75% overlap.
117
APPENDIX C
Raw Data Tables
Table C.1 Jet arrays orifice geometry
Perimeter
(m)
Hydraulic Diameter
(m)
Orifice
Area (m2)
Total Area (m2)
Circular
0.003989832
0.001270
1.26687E-06
6.207E-05
Cusped
Ellipse
(% difference)
0.004453 128
0.001138
1.26697E-06
6.208E-05
(11.612%)
(10.38%)
(0.0079%)
(0.015%)
118
Table C.2 Flow coefficient, Circular Jet
WDHl
Re
CD(PTI) CD(pT2) CD(pT3) CD(pT4) CD(pT4) CD(p'5) CD(pr6) <CD>
0.810
0.782
0.743
0.699
0.660
0.758
0.758
0.744
Qactuat
14
9,863
16
11,884
0.713
0.675
0.639
0.727
0.727
0.715
13,922
0.776
0.744
0.750
18
0.721
0.686
0.651
0.622
20
0.699
0.699
0.689
16,767
0.742
0.717
0.683
0.642
0.619
0.695
0.695
0.685
WDH=2
Qactuai
Re
14
9,736
16
11,683
18
20
HJD=3
Qactua1
CD(prl) CD(p12) CD(pl'3) CD(p1.4) CD(pT4) CD(p1's) C0(p'ro) <CD>
0.758
0.744
0.728
0.7 17
0.711
0.737
0.737
0.733
0.705
0.678
0.699
0.701
0.692
0.689
0.683
13,661
0.717
0.711
0.677
0.695
0.696
0.693
15,984
0.698
0.689
0.680
0.682
0.674
0.699
0.695
0.670
0.684
0.684
0.683
Re
CD(pT1) CD(PT2) CD(pT3) CD(pT4) CD(p'r4) CD(pTs) CD(pl'6) <CD>
14
9.736
0.729
0.718
0.710
0.705
0.703
0.719
0.719
0.715
16
11,539
0.699
0.690
0.683
0.678
0.677
0.690
0.690
0.687
18
13,582
0.711
0.702
0.696
0.692
0.691
20
0.703
0.703
0.700
15,818
0.693
0.687
0.682
0.679
0.678
0.687
0.687
0.685
H/D14=4
Re
CD(p'rI) CD(pT2) CD(p'r3) CD(p'r4) CD(p1'4) CD(pl'5) CD(p1'6) <CD>
Qactuat
14
9,740
0.717
0.707
0.702
0.699
0.700
0.712
0.712
0.707
16
11,545
0.689
0.681
0.677
0.675
0.675
0.685
0.685
0.68!
18
13,592
0.703
0.695
0.691
0.689
0.690
0.699
20
0.699
0.695
15,829
0.687
0.68!
0.679
0.677
0.677
0.684
0.684
0.681
Table C.3 Flow coefficient, Cusped ellipse (00)
H/DH=l
Qactual
Re
14
8,736
0.949
0.901
0.836
0.758
0.698
0.867
0.867
16
10,42!
0.943
0.893
0.826
0.747
0.691
0.856
0.856
0.830
18
12,260
0.969
0.915
0.845
0.763
0.708
0.877
0.877
0.851
20
14,198
0.973
0.915
0.842
0.760
0.706
0.877
0.877
0.850
H/D H=2
CD(pTI) CD(p12)
CD(p-1-3)
CD(pT4) CD(PT4) CD(PT5) CD(pT6)
<CD>
0.839
Qactuai
Re
14
8,559
0.845
0.824
0.812
0.792
0.777
0.817
0.817
0.812
16
10,224
0.817
0.797
0.786
0.771
0.755
0.790
0.790
0.787
18
11,829
0.836
0.818
0.807
0.792
0.776
0.810
0.810
0.807
20
13,584
0.852
0.835
0.824
0.809
0.794
0.826
0.826
0.824
HJDH=3
CD(pTI) CD(pT2) CD(p13) CD(pr4) CD(pT4) CD(PT5) CD(pT6)
<CD>
Qactuai
Re
14
8,562
0.829
0.814
0.806
0.800
0.789
0.815
0.815
0.810
16
10,162
0.811
0.798
0.791
0.785
0.775
0.801
0.801
0.794
18
11,767
0.822
0.810
0.803
0.797
0.788
0.813
0.813
0.807
20
13,517
0.823
0.813
0.806
0.801
0.792
0.814
0.814
0.809
H/DH=4
CD(pTl) CD(pT2) CD(pT3 CD(pT4) CD(pT4) CD(pT5) CD(PT61
<CD>
Qactuai
Re
14
8,568
0.813
0.804
0.797
0.793
0.789
0.808
0.808
16
10,169
0.784
0.776
0.770
0.765
0.762
0.782
0.782J0.774
18
11,777
0.803
0.796
0.791
0.786
0.783
0.803
0.803
0.795
20
13,530
0.819
0.813
0.807
0.803
0.801
0.819
0.819
J 0.812
CD(p'rI) CD(p'r2) CD(pT3
CD(p-I'4)
CD(pr4 CD(pT5) CD(PT6J
<CD>
0.802
120
Table C.4 Flow coefficient, Cusped ellipse (900)
HIDH=1
Qactuai
Re
14
8,543
0.830
0.810
0.763
0.708
0.663
0.780
0.780
0.762
16
10,469
0.848
0.828
0.779
0.723
0.678
0.795
0.795
0.778
18
12,318
0.865
0.844
0.794
0.737
0.691
0.809
0.809
0.793
20
14,182
0.874
0.852
0.800
0.741
0.696
0.816
0.816
0.799
CD (PTI) CD±PT2) CD (PT3) CD (PT4) CD (PT4) CD (PT5) CD (PT6)
<CD>
HJDH=2
Qactuai
Re
14
8,545
0.8 18
0.8 15
0.803
0.786
0.774
0.792
0.792
0.797
16
10,470
0.781
0.780
0.768
0.754
0.749
0.759
0.759
0.764
18
11,886
0.797
0.795
0.783
0.769
0.758
0.776
0.776
0.779
20
13,565
0.810
0.812
0.800
0.787
0.776
0.793
0.793
0.796
Qactuai
Re
14
8,540
0.800
0.793
0.786
0.776
0.769
0.792
0.792
0.787
16
10,136
0.803
0.796
0.789
0.779
0.773
0.795
0.795
0.790
18
11,809
0.795
0.791
0.784
0.775
0.769
0.788
0.788
0.785
20
13,561
0.800
0.795
0.790
0.782
0.776
0.789
0.789
0.789
CD(pTI)CD(pT2)CD(pT3)CD(pr4)CD(pT4)CD(pT5)CDçpT6)
CD(PTI)CD(PT2) CD(pT3)CD(pT4)CD(p14)CD(pTs)CDçpT6)
<CD>
<CD>
HJDH=4
Qactuai
Re
14
8,526
0.801
0.790
0.785
0.780
0.779
0.801
0.801
0.791
16
10,054
0.791
0.780
0.776
0.771
0.770
0.792
0.792
0.782
18
11,789
0.785
0.775
0.772
0.767
0.766
0.784
0.784
0.776
20
13,460
0.811
0.802
0.798
0.794
0.792
0.808
0.808
0.802
CD (Th CD
(P12) CD (fl3) CD (1Y14) CD (PT4) CD (PT5) CD (PT6)
<CD>