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The effect of large-amplitude, low-frequency disturbances on the two-dimensional region of a turbulent, planar wall jet

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Title:
The effect of large-amplitude, low-frequency disturbances on the two-dimensional region of a turbulent, planar wall jet
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Claunch, Scott David
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English
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xiv, 160 leaves : illustrations (some color) ; 29 cm

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Subjects / Keywords:
Wall jets ( lcsh )
Turbulence ( lcsh )
Turbulence ( fast )
Wall jets ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaves 157-160).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Mechanical Engineering.
General Note:
Department of Mechanical Engineering
Statement of Responsibility:
by Scott David Claunch.

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|University of Colorado Denver
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Auraria Library
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Resource Identifier:
31250684 ( OCLC )
ocm31250684

Full Text
THE EFFECT OF LARGE-AMPLITUDE, LOW-FREQUENCY DISTURBANCES
ON THE TWO-DIMENSIONAL REGION OF A TURBULENT,
PLANAR WALL JET
by
Scott David Claunch
B.S., University of Colorado at Denver, 1991
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado at Denver
in partial fulfillment
of the requirements for the degree of
Master of Science
Mechanical Engineering
rm
1994


This thesis for the Master of Science
degree by
Scott David Claunch
has been approved for the
Department of
Mechanical Engineering
by
Richard S. Passamaneck
John A. Trapp
Robert B. Farrington

Date


Claunch, Scott David (M.S., Mechanical Engineering)
The Effect of Large-Amplitude, Low-Frequency Disturbances
on the Two-Dimensional Region of a Turbulent, Planar
Wall Jet
Thesis directed by Associate Professor Richard S.
Passamaneck and Robert B. Farrington
ABSTRACT
Periodic low-frequency, large-amplitude disturbances
can increase the rate of mass entrainment and result in
greater transport of momentum and energy between the
surrounding fluid, the free mixing layer, the wall layer
and the wall surface of a turbulent, planar wall jet.
Outlet velocity fluctuations at disturbance frequencies
of 4, 8, and 16 Hz, with corresponding Strouhal numbers
of 0.028, 0.056, and 0.112, were applied to a planar jet
issuing from a slot diffuser with an aspect ratio of 55
at a Reynolds number of about 4500. The amplitudes of
the fluctuations were 25% of the mean velocity for
Str=0.028, 45% for Str=0.056, and 35% for Str=0.112.
Hotwire anemometry was used to determine the
velocity and velocity fluctuation profiles in the region
from the outlet to an axial distance of 20 nozzle widths.


Infrared imaging was used to visualize the thermal
distribution in this region of the jet. High-speed films
and photographs of smoke released into the surrounding
fluid adjacent to the nozzle outlet and also into the
wall layer were used to illustrate the effect of the
disturbances on the formation, interaction, and
dissipation of instability structures.
Low-frequency, large-amplitude disturbances generate
large-scale vortical structures adjacent to the free edge
of the nozzle exit. The result is that the velocity and
velocity fluctuation profiles become distorted. The
pulsed jet has greater spreading and accelerated decay of
maximum velocity between 5 and 10 nozzle widths. The
pulsed wall jet is a self-preserving flow at Str=0.028
and 0.112 but is not self-preserving at Str=0.056. The
disturbances cause structures to form in the wall layer
that can result in distortion of the large-scale vortices
that form in the shear layer due to the disturbances.
This abstract accurately represents the content of the
candidate's thesis. I recommend its publication.
Signec
Richard S. j?assamaneck


ACKNOWLEDGMENTS
I am pleased to thank and to acknowledge the efforts
of these groups and individuals who made this work
possible:
Dr. Robert B. Farrington for giving me the
opportunity to do research, for the many stimulating
hours discussing fluid dynamics, and for his confidence
in me,
Dr. Richard S. Passamaneck for his encouragement,
support, and irrepressible passion for teaching and
engineering,
The National Renewable Energy Laboratory for funding
this work and providing first-rate facilities,
and my sister, friend, and illimitable advocate
Paula without whose constancy and support this would not
have been possible.
v


CONTENTS
Chapter
1. Introduction....... .............0.0. ....... ......1
1.1 Description, Function, and Applications
of the Wall Jet.............................. 1
2. Literature Review............................... 7
2.1 Historical...................................... 8
2.2 Turbulence...................................... 9
2.3 Turbulent Wall Jets..............................10
2.4 Excited Turbulent Jets......................... 15
3. Experimental Apparatus and Procedure.............18
4. The Flow Field in the 2-D Region of a
Pulsed, Turbulent Wall Jet......................27
4.1 Jet Dynamics.....................................27
4.1.1 Entrainment Across a Turbulent Interface.........28
4.1.2 Geometry and Nomenclature of a 2-D,
Turbulent Wall Jet..............................29
4.2 Previous Results.................................34
4.2.1 Analytic Models of Velocity Distribution.........34
4.3 Nondimensionalizing of the Data..................45
4.4 Measurement of Wall Jet Used for Present
Study...........................................48
4.4.1 Outlet Conditions.............................. 49
4.4.2 Dimensional Transverse Velocity Profiles.........51


4.4.3 Dimensionless Transverse Velocity Profiles......51
4.4.4 Axial Velocity Decay.......................... .52
4.5 Measurement of Pulsed Wall Jet................. 53
4.5.1 Outlet Conditions................................53
4.5.2 Dimensional Velocity Profiles....................55
4.5.3 Velocity Profiles at Each Axial Distance.........60
4.5.4 Velocity Fluctuation Profiles for Each
Frequency.......................................61
4.5.5 Velocity Fluctuation Profiles at Each Axial
Position........................................64
4.5.6 Axial Velocity Decay......................... ..69
4.5.7 Jet Width........................................70
5. Flow Visualization..............................118
5.1 Characterization of the Natural Jet.............118
5.2 Visualization of the Pulsed Wall Jet............120
5.2.1 Free Mixing Layer............................. 121
5.2.2 The Wall Layer..................................124
5.4 Infrared Imaging................................126
5.5 Conclusions.....................................130
6. Discussion and Conclusions......................152
References..............................................157
vii


FIGURES
Figure
3-1 Schematic of Experimental Setup.....................24
3-2 Rotating Damper Mechanism............... ...........25
3- 3 Nozzle Approach.....................................26
4- 1 Regions of a Wall Jet...............................71
4-2 Diagram Of Shear Layer Development..................72
4-3 Outlet Transverse Velocity Profile, Natural Jet....73
4-4 Outlet Transverse Turbulence Intensity Profile,
Natural Jet....... ...............................0.74
4-5 Sample Outlet Velocities at Various Longitudinal
Positions......................................... 75
4-6 Sample Outlet Turbulence Intensities at Various
Longitudinal Positions............................ 76
4-7 Longitudinal Variation of Outlet Velocity Along
(X,Y,Z)=(0,0.5B,Z)..................................77
4-8 Longitudinal Variation of Outlet Turbulence
Intensity Along (X,Y,Z)=(0,0.5B,Z)............*.....78
4-9 Transverse Velocity Profiles, Natural Jet..........79
4-10 Transverse Velocity Profiles in the Potential
Core Region, Natural Jet............................80
4-11 Transverse Velocity Profiles in the Potential
Core Region, Viets and Sforza (1966)................81
4-12 Transverse Velocity Profiles in the
Fully-Developed Region, Natural Jet.................82


4-13 Axial Decay of Maximum Velocity, Natural Jet.......83
4-14 Outlet Transverse Velocity Profiles..............*.84
4-15 Outlet Transverse Velocity Fluctuations............85
4-16 Outlet Velocity, Natural Jet.......................86
4-17 Outlet Velocity, Str=0.028.........................87
4-18 Outlet Velocity, Str=0.056.........................88
4-19 Outlet Velocity, Str=0.112 ...... .................89
4-20 Transverse Velocity Profiles, Str=0.028.............90
4-21 Transverse Velocity Profiles, Potential Core
Region, Str=0.028 .... .................. 91
4-22 Transverse Velocity Profiles, Fully-Developed
Region, Str=0.028...................................92
4-23 Transverse Velocity Profiles, Str=0.056............93
4-24 Transverse Velocity Profiles, Potential Core
Region, Str=0.056............ ......................94
4-25 Transverse.Velocity Profiles, Fully-Developed
Region, Str=0.056...................................95
4-26 Transverse Velocity Profiles, Str=0.112 ...........96
4-27 Transverse Velocity Profiles, Potential Core
Region, Str=0.112...................................97
4-28 Transverse Velocity Profiles, Fully-Developed
Region, Str=0.112...................................98
4-29 Transverse velocity Profiles, X = 1................99
4-30 Transverse Velocity Profiles, X = 3...............100
4-31 Transverse Velocity Profiles, X = 5...............101
ix


4-32 Transverse Velocity Profiles, X = 10.............102
4-33 Transverse Velocity Profiles, X = 15.............103
4-34 Transverse Velocity Profiles, X = 20.............104
4-35 Transverse Velocity Fluctuation Profiles,
Natural Jet........................................105
4-36 Transverse Velocity Fluctuation Profiles,
Str=0.028..........................................106
4-37 Transverse Velocity Fluctuation Profiles,
Str=0.056 .........................................107
4-38 Transverse Velocity Fluctuation Profiles,
Str=0.112...................................... 108
4-39 Transverse Velocity Fluctuation Profiles,
X = 1..............................................109
4-40 Transverse Velocity Fluctuation Profiles,
X = 3..............................................110
4-41 Transverse Velocity Fluctuation Profiles,
X = 5......................................... .111
4-42 Transverse Velocity Fluctuation Profiles,
X = 10. ..................................... 112
4-43 Transverse Velocity Fluctuation Profiles,
X = 15.............................................113
4-44 Transverse Velocity Fluctuation Profiles,
X = 20.............................................114
4-45 Axial Decay of Maximum Velocity...................115
4-46 Axial Decay of Maximum Velocity...................116
4-47 Jet Half width....................................117
x


5-1 Natural Jet, Outside Smoke..........................133
5-2 Natural Jet, Outside Smoke, Regular Vortices...... 134
5-3 Natural Jet, Outside Smoke, Irregular Vortices.... 135
5-4 Str=0.028, Outside Smoke..........................136
5-5 Str=0.056, Outside Smoke..........................137
5-6 Str=0.112, Outside Smoke..........................138
5-7 Natural Jet, Wall Smoke............................139
5-8 Str=0.028, Wall Smoke............................140
5-9 Str=0.056, Wall Smoke............................141
5-10 Str=0.112, Wall Smoke............................142
5-11 Natural Jet........................................143
5-12 Str=0.028..........................................144
5-13 Str=0.056..........................................145
5-14 Str=0.112 .......................................146
5-15 Subtracted Image,Natural Jet
Minus Str=0.028.................................. 147
5-16 Subtracted Image, Natural Jet
Minus Str=0.056....................................148
5-17 Subtracted Image, Natural Jet
Minus Str=0.112....................................149
5-18 Str=0.056, Outside Smoke, Deformation of
Exterior of Vortex.................................150
5-19 Str=0.112, Outside Smoke, Deformation of
Exterior of Vortex.................................151
xi


TABLES
3-1 Hotwire Anemometry System Characteristics..........21
3- 2 Thermal Imaging System Characteristics.............23
4- 1 Strouhal Numbers for Disturbance Frequencies.......48


SYMBOLS
B
f
L
t
u
u0
um
UP
ur
U
umax(x)
x
X
y
Y
*0.5
z
z
Re
Nozzle width (mm)
Frequency (Hz)
Nozzle length (mm)
Time (sec)
Axial velocity (m/s)
Outlet velocity u(X,Y,Z)=u(0,0.5B,0.5) (m/s)
Mean component of velocity (m/s)
Periodic component of velocity (m/s)
Random component of velocity (m/s)
Nondimensional axial velocity u/uO
Nondimensional maximum axial velocity at axial
Axial axis (mm)
Nondimensional axial distance x/B
Transverse axis (mm)
Nondimensional transverse distance y/B
Jet momentum halfwidth
Longitudinal axis (mm)
Nondimensional longitudinal distance z/L
distance X
Reynolds number, uqB/v
xiii


Str
Strouhal number, fB/ug
Turbulence intensity (%)
Kinematic viscosity (m^/s)
T.I.
v
xiv


1.
Introduction
This research project is an experimental
investigation of a specific case of turbulent air flow.
The objective of this work is to determine the effect of
low-frequency, large-amplitude disturbances on the
behavior of a turbulent wall jet with a Reynolds number
of about 4500 and to describe in detail the physical
characteristics of the air flow.
1.1 Description, Function, and Applications of the Wall
Jet
The term 'wall jet', as described by Bakke (1957),
refers to the flow field created "when a jet, consisting
of a fluid similar to that of its surroundings, impinges
on a plane surface and spreads out over the surface".
Viets and Sforza (1966) state that "the wall jet is of
interest wherever one wishes to add mass, momentum, or
energy to a fluid system". This flow field that is
referred to as a wall jet occurs in many engineering
applications.
Wall jets have application in a variety of
engineering fields including aerospace, mechanical, and
civil engineering.


A method of implementing boundary layer control on
aerodynamic surfaces on aircraft is to add a pulsed air
stream tangentially to the surface in the presence of the
external stream already flowing over it. The flow field
created by this pulsed air stream has all the features of
a wall jet and is modeled as such. When a sluice
separating two different water levels is opened the flow
that develops as the water flows through the long slot at
the opening is a wall jet. Industries that dry sheets of
paper by blowing air over them are employing wall jets
and, because the objective is to efficiently remove heat
and moisture particles from the paper surface, have an
interest in their mixing and transport characteristics.
However, the most important applications of wall jets, in
both number and economic importance, are in areas of
heating, cooling, and ventilation (Launder and
Rodi, 1983). In reference to the level of technical
sophistication to which these areas have developed in
recent years they state that these are
2


...areas where traditionally design has
proceeded unfettered by any deep concern
about the turbulence structure of the flows
in question, (pg. 429)
The quality of the air in an artificially maintained
indoor environment is in part dependent on the mixing
characteristics of jets that issue from heating,
ventilation, and cooling (HVAC) outlets, as is the energy
efficiency of the system. For this reason maximizing the
performance of such systems requires some understanding
of the structure of turbulent jets such as the one
produced by the air diffuser used for the experimentation
presented here. This study is a result of the particular
needs of this application.
The objectives of air distribution in enclosed
spaces are to (lj maintain the temperature, humidity, and
velocity of the air so that it is comfortable for the
occupants and (2) to dilute and remove pollutants that
may be harmful (ASHRAE Fundamentals, 1989). When the
first objective is not met the occupants may experience
discomfort that can result in decreased productivity and
may also cause the occupants to adjust the thermostat to
3


obtain "local" comfort at increased energy consumption.
When the second objective is not met there may be zones
of air that become stagnant which can have adverse
physiological effects on the occupants. This phenomenon
is often referred to as the 'sick building syndrome'.
Efficient mixing of the jet is beneficial in meeting
both of these objectives. As a jet mixes it gains, or
entrains, mass and transfers momentum to the entrained
mass. This results in the velocity of the jet decaying
in the downstream direction as it gains mass. A certain
volume of the enclosed space to which the jet is supplied
will be occupied by the issuing jet as it entrains mass,
mixes, and diffuses momentum. This is known as the jet
mixing region. It is usually desirable for the mixing
region to constitute as small a volume fraction of the
room as possible. The air flow in the mixing region is
of an unacceptable velocity for the comfort of the
occupants and, therefore, the smaller the volume fraction
of the room taken up by the jet mixing region the greater
the volume fraction acceptable for human occupation. The
region of the room that is utilized for human activity is
called the occupied zone. In some cases, depending on
room volume and geometry, increasing the mixing
4


efficiency of the jet may reduce the number of diffusers,
and therefore reduce capital expenditure, required by the
HVAC system design.
The primary motion in the air diffusion process is
the issuing jet. However, as the jet entrains mass from
the ambient room air it induces a secondary room air
motion because the entrained mass is replaced by adjacent
air. This process occurs continuously. Therefore, the
secondary room air motion increases as the rate of
entrainment of mass by the jet is increased. The
secondary room air motion is the mechanism by which
ambient air, which carries potentially harmful
pollutants, is brought to the jet where it is diluted by
mixing and eventually removed in the return air.
Most air diffusers, which come in a variety of
outlet geometries and locations in a room, blow air along
the ceiling so that the jet is not blown directly into
the occupied zone of the room. As a result, the air that
is delivered to the occupied zone is of acceptable
velocity and temperature. Because the jets utilized in
this way flow along the ceiling, they are called wall
jets, i.e., flows attached to and spreading out over a
surface. They may flow radially or in a swirling pattern
5


from round or square outlets or they may flow somewhat
unidirectionally along the ceiling from rectangular
outlets.
The main motivation for this study is to affect the
behavior of wall jets so that they mix more efficiently,
which can be beneficial for the reasons outlined above.
6


2.
Literature Review
The body of literature regarding turbulent flows is
very large. However, the study of jets, and of turbulent
wall jets in particular, was relatively limited until
perhaps the early 1960's when advances in the modeling of
turbulent wall jets, experimental capabilities, and
applications resulted in a proliferation of research.
The research was more specific and less general in nature
than that which preceded Glauert's important work in the
late 1950's. With respect to the analytical
representations of turbulent wall jets, the literature
can be traced directly to Prandtl's work in the field of
turbulence and his mixing length hypothesis. General
observations of turbulent jets was documented as early as
the beginning of the nineteenth century.
The literature reviewed in this chapter is by no
means a complete history of the field of turbulent fluid
dynamics nor of the study of turbulent wall jets.
Instead, it is a collection of literature that briefly
summarizes the main works that produced a general
understanding of these specific turbulent flows and also


attempts to establish the uniqueness of this particular
study.
2.1 Historical
In 1800 Thomas Young published his observations on
the behavior of axisymmetric jets and other properties of
flow, as well as acoustical phenomena. His observations,
although stated in the classical language of the time,
are quite familiar to contemporary observers of turbulent
jets. He observed the spread angle of axisymmetric jets,
the Bernoulli effect on a flame near an air stream, and
the Coanda effect, i.e., the attachment of a stream of
fluid to a concave surface. He described regions of the
jet that he called the 'central particles' and the
'superficial ones', which are known today as the core and
shear layers, respectively.
In 1857 Plateau studied the behavior of liquid jets
which were exposed to acoustical vibrations. He observed
the effect of tones on the spread, decay characteristics,
and transformation of jets into droplets. This
experimental investigation anticipates much of the
research of jets that has been performed in this century,
with the flow descriptions being familiar to contemporary
8


researchers, even though the benefits of modern analysis
and instrumentation that are used today were not
available.
In 1858 LeConte, a medical doctor, observed the
flame of a coal-gas lamp that was exposed to acoustical
vibrations at a musical performance. The flame responded
to the various pitches created by the instruments and was
so striking that he was moved to publish an account of it
in a paper entitled "On the Influence of Musical Sounds
on the Flame of a Jet of Coal-Gas". He remarked in his
paper that "A deaf man might have seen the harmony".
In 1867 Tyndall published a paper describing the
effects of vibrations on gaseous and liquid jets in which
he performed experiments to reproduce the response of a
flame to musical sounds as seen by Dr. Leconte. He also
produced jets of smoke and exposed them to sound. Among
his observations were the bifurcation and trifurcation of
the flames and jets.
2.2 Turbulence
The study of turbulent fluid flow has always been
semiemperical due to the stochastic nature of the flow.
In 1925 Prandtl introduced the concepts of a "mixing
9


length" and an "eddy viscosity" in developing an
analytical understanding of turbulent fluid flow. These
concepts have enabled much of the subsequent work in
turbulence to be modeled and are essential to most
analytical models of turbulent flows.
2.3 Turbulent Wall Jets
Building on recent analytical developments by
Prandtl and others, E. Forthmann presented a paper in
1934 on turbulent jet expansion. He developed
expressions for the velocity and shear stress
distributions in a two-dimensional wall jet and compared
them to experimental results. The jet flowed through a
rectangular channel from a slot with an aspect ratio of
about 22 and was referred to as a "partially open jet".
Forthmann's nondimensional transverse velocity
profiles, taken from 20 to about 33 nozzle widths
downstream, collapsed to a single curve, thus he found
the wall jet to a be self-preserving flow. He determined
that the maximum axial velocity decayed as the inverse
square toot of the axial distance and that the velocity
in the region near the wall was proportional to the
distance from the wall to the one seventh power.
10


Glauert is credited with introducing the term 'wall
jet' in a 1956 paper entitled "The Wall Jet". This paper
is an important landmark in the literature on wall jets
and is referenced often in subsequent studies. Since the
publishing of "The Wall Jet" the class of flows created
when a jet attaches to a solid surface has been
conventionally referred to as wall jets. In this paper
Glauert obtained similarity solutions for laminar wall
jets and solutions requiring empirical constants for
turbulent wall jets that impinged both radially and
tangentially on the solid boundary.
Glauert's similarity solution for the turbulent jet,
which will be summarized in Chapter 4, was found by
employing the concept of an eddy viscosity and analyzing
the transverse velocity profiles in two regions one
region being from the wall to the point of maximum
velocity and the other region being beyond the point of
maximum axial velocity to the quiescent flow. Glauert
assumed that in the inner region of the jet the shear
stress distribution was like that in turbulent pipe flow
and that in the outer region the eddy viscosity is
constant. Glauert found that, unlike a free jet,
expressions for both the axial velocity decay and the
11


boundary layer thickness were functions of the Reynolds
number.
After Glauert's important work a number of
experimental studies were presented, verifying the
validity of his analysis. Bakke performed an
experimental study of a radial wall jet in 1957. The jet
was a radial wall jet at a Reynolds number, based on the
maximum axial velocity and the boundary layer thickness
at a given distance downstream, of 3500. Bakke
experimentally determined constants required by Glauert"s
similarity solution for the turbulent wall jets and
achieved a good comparison between the transverse axial
velocity profile predicted by Glauert and experiment.
In 1958 Sigalla produced a correlation of existing
experimental and analytical work. Findings for velocity
decay, spread rate, velocity distribution, temperature
coefficient, shear stress distribution, and heat and mass
transfer were given.
Schwarz and Cosart, in 1960, studied two-
dimensional, turbulent wall-jets at Reynolds numbers,
based on maximum velocity and boundary layer thickness,
ranging from 22,000 to 106,000. They found that "a
single velocity scale and a single length scale seem to
12


correlate all the velocity data" where the maximum
velocity decayed as x"0.555 ancj that the boundary layer
thickness varied linearly with x. In 1962, Bradshaw and
Gee presented experimental results of wall jets blowing
over both flat and curved surfaces and beneath an
external stream. They concluded that Glauert's theory
accurately predicted most of the flow characteristics of
a turbulent wall jet in still air.
In 1963 Verhoff found that for predictions of the
growth of the jet and the thickness of the boundary layer
the assumption that the Reynolds is zero at the point of
maximum velocity was a reasonable assumption. He found
that maximum velocity decayed as x0-556^ which agreed
closely with Schwarz and Cosart, and that the boundary
layer thickness increased linearly with x.
In 1966 Chun and Schwarz studied the stability of a
laminar wall jet subjected to small disturbances and
found the critical Reynolds number to be 57. Irwin
(1973) made a detailed experimental investigation of the
characteristics of the wall jet including velocity
profiles and decay, turbulent intensity, intermittence,
the production of turbulent kinetic energy, and Reynolds
stresses which showed that the turbulence and the mean
13


flow reached a self-preserving state. He also found that
the Reynolds stress was not zero at the point of maximum
velocity.
Gartshore and Newman (1969) determined a method for
calculating the growth of a turbulent wall jet by using
four integral momentum equations. This method was used
to predict what the jet-momentum coefficient would have
to be in order to prevent the separation of the boundary
layer over the trailing edge flap of an airfoil.
In 1974 Rajaratnam and Pani studied the behavior of
wall jets issuing from round, square, and elliptical
outlets having aspect ratios approaching unity. They
found that the length scale in the longitudinal
direction, parallel to the surface of the wall, grew
about four or five times faster than the length scale in
the transverse direction.
Hammond (1982) produced an analytic expression for
the complete velocity profile for the fully-developed
region of a plane, turbulent wall jet. He used a log
relation for the inner region of the jet and a sine
function for the "wake component" of the jet, making use
of the effect of skin friction.
14


Planar two-dimensional, radial, three-dimensional
wall jets, and wall jets on curved surfaces are presented
in a 1983 paper by Launder and Rodi. They give an
insightful, qualitative description of the influence of
the outer layer on the inner layer of the planar two-
dimensional jet by observing the distribution of
turbulent kinetic energy. They give a method of
calculating flow characteristics by solving descretized
forms of the momentum and continuity equations, making
use of Boussinesq Viscosity Models and Reynolds-Stress
closures and derivatives.
2.4 Excited Turbulent Jets
Rockwell and Toda (1971) studied the behavior of
turbulent jets attached to curved surfaces while being
exposed to sound. The frequency of the sound ranged from
200 to 4000 Hz with amplitudes from 100 to 140 dB. They
found that the jet was altered greatly by certain
frequencies which matched the nozzle resonance
characteristics. They also found the effect of the sound
to be dependent on the amplitude of the sound waves.
Because it was the separation angle that was of interest
15


to them, they did not investigate the mixing
characteristics of the jet.
In 1972 Williams, Ambrosiani, and Palmer studied the
mixing characteristics of a pulsed wall jet for purposes
of boundary layer control. They introduced intermittent
blowing of air into the boundary layer on a trailing edge
flap of an airfoil (essentially creating a pulsed wall
jet in an external stream) and found that the pulsed jet
mixed considerably better with the free stream thereby
re-energizing the boundary layer through the diffusion of
kinetic energy.
In a Ph.D. dissertation Farrington (1992)
investigated the effect of periodic large-amplitude, low-
frequency, internally generated disturbances on a free
plane jet at Reynolds number, based on nozzle width, of
about 7200. The amplitude of the disturbances was as
much as the mean velocity and the frequency ranged from 2
to 56 Hz. He found that at low frequencies the
disturbances generated large-scale, symmetric vortices at
the nozzle exit by enhancing the natural column mode
instability, and that the magnitude of the overall effect
of the disturbances on the jet was dependent on the
amplitude as well as the frequency of the disturbances.
16


Farrington found that when the jet was exposed to
disturbances, the axial velocity decay did not obey the
inverse square law. The rate of decay of axial velocity
was generally increased by the disturbances and
accompanied by an increased spread rate, indicating
increased mixing. However, decreased mixing was also
observed at certain frequencies the frequencies at
which suppressed mixing was observed varied with the
amplitude of the disturbances. Another significant
finding was that the transverse velocity profiles for the
pulsed jet were not similar downstream. By means of
infrared flow visualization Farrington found that the
mixing efficiency of the jet was increased by as much as
11% at 22 nozzle widths.
17


3. Experimental Apparatus and Procedure
To examine the effect of periodic, nonlinear
disturbances on a plane wall jet an apparatus was
constructed to produce such a jet and to generate the
disturbances. A laminated wall was made from a piece of
rigid insulation with a surface of hard, thin, synthetic
material similar in texture to a common cardboard surface
but smoother and harder. The wall was then mounted on an
aluminum frame and suspended adjacent to a slot outlet in
such a way that the plane jet issuing from the outlet
flowed parallel and attached to the wall. A schematic of
this setup is shown in Figure 3-1. The slot diffuser,
which had an aspect ratio of 47, was originally designed
to produce a free plane jet and the wall was designed as
an accessory to that apparatus. The final aspect ratio,
after the addition of the wall, was 55.
Air was supplied to the outlet by a squirrel cage
blower located in an adjacent room via a 23 cm galvanized
duct. For nonisothermal cases the air was chilled by a
cooling coil located on the downstream side of the blower
housing.


The disturbances were generated by rotating a disk
inside the duct perpendicular to the axis of flow. The
mechanism was a rotating damper which opened and closed
twice for each full rotation of the disk. The rotating
damper mechanism is shown in Figure 3-2. It was located
5 m upstream of the diffuser outlet. Turning vanes and 4
sets of screens were placed in the plenum between the
disturbance mechanism and the outlet to ensure a uniform
outlet velocity distribution and that the turbulent
structures created by the disk did not reach the outlet.
The motor speed could be continuously varied from 0
to about 1680 rpm with an error of less than 1% of full
scale. The rotational speed was measured by a
photoelectric tachometer with a digital readout. The
flow rate was measured by a flow nozzle with a hot-film
sensor that was located immediately downstream of the
blower and cooling coil and wais adjusted by the use of a
blast damper located about 1 m downstream of the
flowmeter.
The diffuser design was a compromise between a
research diffuser and an actual diffuser because of the
emphasis of this project on application. Thus the
approach to the outlet of the wall jet was not a channel
19


approach nor was it symmetric in the X-Y plane. A 7 inch
curved extension was inserted into the nozzle through the
outlet. It had a radius of curvature that was large
enough so that the boundary layer on the surface of the
extension did not separate from the surface, thus
avoiding a region of reverse flow that would produce a
highly nonuniform outlet velocity. The cross-section of
the approach is shown in Figure 3-3. The outlet
velocities and turbulence will be addressed in Chapter 4.
Velocity data was taken by a microprocessor-
controlled hotwire anemometry system. Single 1.5 jur
tungsten wires were used. The hotwire sensor was
attached to a 48 cm probe support and positioned in the
flow by a two-axis traversing mechanism. Data was
acquired at a rate of 1000 Hz. The length of tests at
each point in the flow was 120 seconds resulting in
120,000 data points per location. The data acquisition
rate and test length were determined by the number of
samples at the low end of the disturbance frequency range
to ensure that enough points were available for accurate
statistical analysis. Performance characteristics of the
hotwire anemometry system are given in Table 3-1.
20


Table 3-1
Hotwire Anemometry System Characteristics
Anemometer System IFA 100
Bridge Compensation Provides quantitative display of settings at optimum frequency response for various sensors.
Operating Resistance
Standard #1 Bridge 3 to 19.999 ohms, repeatability of 0.002 ohms
Standard #2 Bridge 20 to 99.99 ohms, repeatability of 0.002 ohms
High Power Bridge 3 to 19.999 ohms, repeatability of 0.002 ohms
Cable Resistance Maximum up to 1.999 ohms can be locally or remotely entered or monitored
Frequency Response Measured at 100 m/s velocity in air with a
(Typical) 4 fjm (T1.5 wire) tungsten wire probe
Standard #1 Bridge DC to 150 kHz
1:1 Bridge DC to 450 kHz
Probe Current 1.2 A maximum
Stability Typical equivalent input drift 0.35 jjV/C on 5:1 bridge, 0.6 pV/C on 1:1 bridge
Output 0 to 12 V, 50 ohms impedance
Frequency Response Built-in square wave generator variable
Check from 300 Hz to 30 kHz
Digital Display Digital LEDS, 4.5 digits
The disturbance frequencies that were chosen were
determined by observation of a preliminary set of
infrared images of a much wider range of frequencies.
The infrared images will be presented and discussed in
detail in Chapter 5.
21


Infrared images were created by placing a fiberglass
mesh screen in the flow as a target for the infrared
camera. The screen was 70% porous and had a response
time of 0.3 seconds. The supply air was chilled to a
temperature that was 10C to 20C cooler than the ambient
temperature. The exit Richardson number was about 0.001,
indicating that bouancy forces at the nozzle were
negligible when compared to the inertial forces. Image
averaging was used to produce final images that were the
average of 120 images.taken at 1 second intervals. The
images were digitally processed by the use of a FORTRAN
program to produce the data sets necessary for making
contour plots. The performance characteristics of the
infrared imaging system are given in Table 3-2.
22


Table 3-2
Thermal Imaging System Characteristics
Output Format EIA RS-170 video standard and NTSC color 30 Hz frame/60 Hz field rate/2:l interlace 256 digital samples per line, 200 lines active, 400 lines displayed 7 bits (128 intensity levels) per sample (42 dB dynamic range) 8 bits with image averaging options (256 intensity levels) per sample (48 dB dynamic range)
Scan Format Total field of view without accessory opticss 15 V x 20 H Zooms electro-optical, continuously adjustable 4 s1 range 8 kHz horizontal scan 60 Hz ramp vertical scan Spatial resolution (typical)s 2.4 mrad § 50% slit contrast (8-12 pm) Detector types HgCdTe (Mercury/Cadmium/Telluride) Detector coolings liquid nitrogen Spectral sensitivitys 8-12 pm std. (3-5 pm or 3-12 pm optional)
Measurement Specifications Temp rangess 5, 10, 20, 50, 100, and 200 C Extended temp ranges: 50, 100, 200, 500, 1000, and 2000 C Center temp adjustment ranges 0 to 400 C Extended center temp adjustment ranges 0 to 1000 C Temperature readout resolutions 3 digits Thermal sensitivity (MDT)s 0.1 C Internal temp reference sampled at 60 Hz rate, 0.5 second periodic calibration update
Computer Algorithm for Image Analysis Converts binary image data to temperature data Displays images to EGA and VGA screens in 16 colors Subtracts images Performs image enhancements Creates and displays screen shows Exports ASCII data files and .PCX image files for use by other programs
23


1
Figure 3-1. Schematic of Experimental Setup.


Figure 3-2. Rotating Damper Mechanism.
25


Figure 3-3. Nozzle Approach.
26


4. The Flow Field in the 2-D Region of a Pulsed,
Turbulent Wall Jet
This chapter will present the effects of periodic,
large-amplitude, low-frequency disturbances on the
velocity characteristics in the two-dimensional region of
a turbulent wall jet. The behavior of a natural wall jet
will be described in order to provide a background for
comparison with the pulsed jet. A qualitative
description of the entrainment and mixing processes which
occur in turbulent shear flows will also be presented in
order to establish the physics underlying jet mixing and
resulting in the effects to be demonstrated.
4.1 Jet Dynamics
The study of the flow fields of turbulent jets is
largely a study of the diffusion of the outlet momentum
of the jet. Turbulent jets are often described by global
characteristics such as the shape of the jet boundary,
the rate of decay of the velocity of the jet, and the
distribution of momentum, or velocity, within the jet.
One way to affect these global characteristics is to


manipulate the micro-mechanisms which produce them
(Farrington, 1992).
4.1.1 Entrainment Across a Turbulent Interface
Although momentum is not entirely conserved in a
wall jet, particularly in the boundary layer adjacent to
the wall where friction is significant, the concept of
momentum transport is useful in understanding the
development of the flow field. As a turbulent jet
emerges into a body of quiescent or flowing fluid an
interface develops between the jet and the irrotational
fluid across which mass is entrained, or assimilated
(Paizis and Schwarz, 1973), and across which vorticity is
transported by viscous diffusion. The transport of
vorticity into the quiescent fluid results in the spread
of turbulence into it and, therefore, the propagation of
the jet boundary into the region of ambient air.
Conservation of momentum requires that as mass is
added to the jet and the relative momentum distribution
within the jet remains unchanged, the velocity everywhere
must necessarily decrease with axial distance. This
situation is a near approximation of what happens in a
real wall jet. The velocity of the flow decreases as
28


the original momentum of the jet is distributed
throughout the continuously increasing mass of the flow
until it has been dissipated sufficiently so that
complete mixing of the jet with the quiescent fluid has
occurred.
4.1.2 Geometry and Nomenclature of a 2-D, Turbulent Wall
Jet
The natural wall jet, which belongs to the class of
self-preserving flows, forms a flow field which has a
distinctly shaped boundary and distinguishable regions
along the main axis of flow characterized by the rate of
maximum axial velocity decay in that region. Figure 4-1
shows a schematic of a cross-section of a wall jet
including regions that will be described.
4.1.2.1 Spread Rate
Sigalla found the half-width of the wall jet, the
transverse position at a given axial distance where the
velocity is one half of the maximum, to form an angle of
3.7 with the wall (Sigalla, 1958). This was determined
from a wall jet flowing at Reynolds numbers from 20,000
to 50,000.
29


4.1.2.2 Axial Regions
The flow field of a wall jet has distinguishable
regions in both the axial and transverse directions
(Sfeir, 1975; Viets and Sforza, 1966). Identification of
these regions is useful in comparing different jets or
the effects of changing some flow parameter such as the
Reynolds number or the nozzle aspect ratio.
4.1.2.2.1 Potential Core Region
As the flow emerges from the outlet a shear layer
develops at the free edge of the jet and a boundary layer
develops at the wall. Each of these layers grow and at
some point downstream they meet. The region near the
outlet where the two viscous layers have not yet
propagated all the way across the flow in the transverse
direction is the potential, or inviscid, core region
where local velocities between the free mixing layer and
the wall layer are unaffected by viscosity. The axial
length of the potential core is dependent upon the outlet
geometry (Sfeir, 1975).
30


4.1.2.2.2 Characteristic Decay Region
The second region of the jet, the characteristic
decay or 2-D region, is characterized by a maximum axial
velocity decay which is proportional to x to some
constant power. Experiments show that the maximum
velocity decay in this region is approximately
proportional to x-3*. Some results have shown this
dependence to be
In this region the effects of both the free shear
layer at the transverse jet boundary and the boundary
layer are felt throughout the transverse width of the jet
(Viets and Sforza, 1966). However, effects of the shear
layers developing at the longitudinal ends of the jet
have not yet permeated into this part of the flow.
Therefore, this region is two-dimensional. There has
been disagreement about whether the rate of decay of the
maximum velocity is dependent upon the aspect ratio of
the outlet or not. However, Swamy and Gowda found it to
be strongly affected by the aspect ratio at values from
10 to 20 and marginally affected between 20 and 40 nozzle
widths (Swamy and Gowda, 1974).
31


4.1.2.2.3 Radial Type Decay Region
At the streamwise point where the effects of the
shear layers at the ends of the jet, as well as the
effects of the free mixing layer and wall layer, are felt
throughout the entire flow the maximum velocity decays in
proportion to xl, the same as for a radial type wall
jet.
The potential core region is the developing region
and the characteristic decay region and the radial type
decay region make up the fully-developed region of the
flow.
4.1.2.3 Transverse Regions
The fully-developed regions of the flow can further
be broken down into an inner layer (Meyers, et al.,
1973), where the flow behaves like a boundary layer in
flow over a flat plate, and an outer region that behaves
like the free shear layer of a free jet (Hari, 1973).
These regions, or layers, separated by the maximum
velocity, will be referred to as the wall region and the
free mixing region, termed so by Hari.
32


4.1.3 Mixing and Momentum Diffusion
Mass and momentum transport occur simultaneously in
a turbulent wall jet. These essential features and the
mechanisms by which they occur are now described.
4.1.3.1 Free Mixing Layer
In the free mixing layer turbulent structures form
due to instabilities that result from the steep velocity
gradients and associated viscous effects. These
structures form an array of large-scale vortices which
entrain mass via re-entrant wedges that separate them
(Phillips, 1971). A representation of this is shown in
Figure 4-2. The vorticity transported to the quiescent
fluid.is then amplified by the rate of strain field.
Farther downstream the vortical structures interact
by pairing, coalescing, and tearing and are eventually
broken down by viscous diffusion until complete mixing
has occurred.
4.1.3.2 Mixing between the Inner and Outer Layers
At the location of the velocity maximum the effects
of both the free mixing layer and the wall layer
interact. Kinetic energy, or momentum, is transported
33


across the interface between the wall layer and the free
mixing layer in the same way that momentum is transported
across the turbulent interface between the free mixing
layer and the surrounding fluid. Additionally, any
turbulent structures formed in the wall layer can affect
the mixing process in the free mixing layer (Hari, 1973).
This phenomenon has generally been observed as a
consequence of the formation of vortical structures due
to roughness elements on the wall surface.
4.2 Previous Results
In order to establish conventional descriptions and
measurements of wall jets found in the literature a
review of previous findings is now given. This will
provide a set of reference characteristics that will
again be used to present the results of the pulsed wall
jet.
4.2.1 Analytic Models of Velocity Distribution
A variety of analytic expressions for the transverse
velocity distribution in a wall jet have been developed.
Glauert, Hammond, Verhoff, and Meyers, et al., among
others, have produced similarity solutions for laminar
34


and turbulent radial and tangential wall jets. As was
stated previously, the wall jet is a self-preserving
flow. In these flows the velocity distribution is a
result of a continuous balance of transport processes.
This leads to the velocity profiles in the fully-
developed region being similar and enables the transverse
velocity distribution to be expressed analytically based
upon a similarity variable.
Several similarity solutions are available which
describe the fully-developed velocity profile for the
natural wall jet. Each similarity solution is based on a
particular set of assumptions. Examples of similarity
solutions and the associated assumptions follow. Further
details of their derivations can be found in the
referenced work.
4.2.1.1 Glauert
As was mentioned previously, Glauert's work in 1956
is considered by many to be the primary analytical work
on wall jets. Glauert found a similarity solution for
the transverse velocity profile based on the assumptions
that the velocity profile near the wall was like that of
flow in a pipe, u<*=yl/7 and that Prandtl' s hypothesis,
35


which states that the eddy viscosity is constant, is
valid further out from the wall. An eddy viscosity was
proposed that was based on these two assumptions. The
similarity solutions are
for the outer layer, where f is a function of the
similarity variable, T), and the parameter a is dependent
on the Reynolds number and represents the relative
thickness of the inner layer. Solutions to these
equations are
for the inner layer where the subscript 2 indicates the
arbitrarily chosen value of a, and
(1)
for the wall layer and
(2)
^(r,) = A-1/5Z72(^5ri)
(3)
36


f = i_c-i +1(1 + a)e~2r> (1 + a)(5 + 4a)e'3r> + (l + a)(34 + 53a + 21a2)e^"-...
4 72 1728
(4)
for the outer layer. These solutions must be matched at
the velocity maximum. Because Blassius' law and
Prandtls' hypothesis are assumed over different
transverse regions of the jet, complete similarity is
unattainable. However, these solutions are in good
agreement with experimental results.
4.2.1.2 Verhoff
Verhoff (1963) found a similarity solution based on
the assumption that the entire velocity profile could be
represented by a single similarity function f(T|), which
is a solution to the momentum equation
An)+(x i)f (n)Jo" mdz+(2 x)as (n) o (s >
where X is a constant and S (Tj) is a function which
describes the similarity of the shear stress
distribution. Assuming that Blassius' law is valid for
the inner portion of the profile and that Prandtl1s
37


hypothesis is valid for the outer portion of the profile,
as did Glauert, f(Ti) is
/(n) = 1- 4794t]1/7[1 erf(0.67753ri)3.
(6)
with the similarity variable, T|, being equal to y/8,
where 8 is a characteristic thickness. Equation 6 is
calculated numerically and is in good agreement with
experimental results and with the similarity solution of
Verhoff which will be plotted later.
4.2.1.3 Hammond
Hammond assumed that the log-law was valid near the
wall and that the jet behaved like a free jet (a wake
component) outside the near-wall region. The velocity
profile for the turbulent boundary layer outside the
viscous sublayer may be represented by
(7)
where
38


(8)
C = -
^ln(A^) + iS
9
B being a log-law additive constant, and k is von
Kantian's constant. The wake function is given by
03 f = sin < D0n
U+J 1 Ik)
where and D2 are functions of the Reynolds number.
Hammond arrives at a two-part expression for the complete
velocity profile, which is;
y+eKCa(y*/b:) = f{u+),y+ c 150
y+e*c>(y'iK) = e(^-A)y >150
(10)
where y+ is the transverse coordinate, y,
nondimensionalized by a "friction velocity" and kinematic
viscosity, i.e. y+=uT/v, u+ is the local mean velocity
nondimensionalized by the friction velocity, and
39


f(u+) = u++e~A
(11)
JCH*
e
1 KU+
(k U+)2 (tcw+)3 (kw+)4
~2l 3! 4!
with A=kB. The expression of the complete velocity
profile separates the influence of the viscous sublayer
from the influence of the outer layer. This is typical
of the analytical expressions for the transverse velocity
profile because it consists of two distinct regions where
the flow is the result of different physical influences.
Hammond acknowledges that the choice of the partitioning
value y+ is somewhat arbitrary (it falls in the range
70 usual "law of the wall" behavior.
When this is expressed in terms based on the local
mean velocity rather than a friction velocity then
equation (7) can be written as
u
u
(CfT
,2,
'*J
\ 1/2 f

yy.)
vA j
+ B + C sin
in-l D-n

V1
(12)
where
40


bu = jet halfwidth
um = maximum velocity
ym = transverse location of maximum velocity
at a given axial position
Cf = skin friction coefficient
4.2.1.4 Meyers, Schauer, and Eustis
Meyers, et al. assumed that the near-wall flow
behaves similar to an ordinary boundary layer which forms
a flow over a flat plate and the flow further out behaves
like a free jet. They didn't assume that the entire
profile was similar, but that each region (inner and
outer) was similar within itself. They said that the
thickness of the wall layer is given by
115
&m = M-^VS**15
(13)
where
(14)
41


and
P = dimensionless velocity profile in
the inner layer u/um
rj = is the dimensionless coordinate y/5m
The flow in the inner and outer regions was
described by relating three unknowns and integrating the
momentum boundary layer equation
gc\ du du
+ v (15
p dx dy
over the inner region from 0 to ^ and the outer region
from 5m to the jet edge. The following three equations
were developed to solve for the three unknowns,
v
,1/4
- u. . (16)
0.0225
42


(17)
£ (22 (6 6 J] + ^ (m6 J Jp(r)) Jri = 0 ,
and
£e3(5)*S-0 (18)
where Q is the dimensionless velocity profile in the
outer layer, and k is a constant in Prandtl's mixing
length hypothesis. These equations were then solved
simultaneously by making several algebraic substitutions
to produce three differential equations which were solved
numerically to produce predictions of maximum velocity
decay, jet growth, and skin friction factor which is a
ratio of the wall shear stress and the velocity pressure.
4.2.1.5 Applicability to the Pulsed Wall Jet
It is seen that the two assumptions of Blassius'
profile near the wall and Prandtl's hypothesis away from
the wall enable the velocity profiles to be described in
a variety of similarity solutions, some of which are
quite complex. However, as will be demonstrated, the
43


pulsed wall jet may or may not have the characteristic of
self-similarity and clearly is not described by Blassius'
profile near the wall. Additionally, the mixing length
upon which the eddy viscosity and Prandtl's hypothesis
are based varies substantially in magnitude between the
natural jet and the pulsed jet. Based on this
information it is apparent that similarity solutions for
the velocity profiles of a pulsed wall jet would need to
be based on unique assumptions for each of the
disturbance frequencies that produced self-similar
velocity profiles but would be meaningless for the
disturbance frequencies that were not self-preserving.
Therefore, a general theory describing the effects of
both the amplitude and frequency of disturbances on the
flow field of a pulsed jet would not be based on the
concept of self-preservation but rather on an analysis of
the stability of each shear layer, and boundary layer,
and their interaction, for each disturbance frequency.
This general theory would need to describe the motion as
a function of space, time, and disturbance frequency
which is beyond the scope of this work.
44


4.3 Nondimensionalizing of the Data
Nondimensionalizing was used to achieve two
purposes. The first purpose is to remove bias error in
the measurement process. The second purpose, in some
cases related to the first, is to make the results more
general. For each set of velocities measured to
construct a profile at a particular axial distance a
nondimensionalizing outlet centerline mean velocity,
U(X,Y,Z)=U(0,0.5B,0.5), was first taken and recorded.
B is the nozzle width of the diffuser. Each of the mean
velocities taken for that profile was nondimensionalized
by this velocity. Therefore, if the outlet velocity
changed slightly from one test to another and the
measured absolute velocities were different, their
relative velocities would not be different as long as the
point in the flow field was still in the same region of
the jet, i.e. the characteristic decay or the radial type
decay region.
Absolute velocities are only meaningful to the
specific case determined by such factors as the outlet
Reynolds number, the outlet shape and aspect ratio, and
temperature of the fluid. For example, to report that
the velocity 10 inches downstream and 2 inches away from
45


the wall was 8 ft/sec would not communicate anything
useful unless the other parameters were also given.
Fluid flow fields are not best described by absolute
quantities but by characteristic quantities. The linear
coordinates x and y were nondimensionalized by the linear
characteristic dimension, which was chosen to be the
nozzle width, and will be notated by X and Y,
respectively. The coordinate z was nondimensionalized by
the longitudinal length of the diffuser and will be
notated Z.
With these nondimensionalizing techniques it could
be reported, for example, that the mean velocity,
relative to the outlet velocity, at a point 5 nozzle
widths downstream and 1 nozzle width from the wall was
0.8, or
_WL = 08
U(0,0.5B, 0.5)
This communicates that the velocity is decreasing in a
space of dimensions characterized by a fundamental length
scale that may or may not be similar to a conventional
length scale such as a foot or a meter.
46


Velocity profiles were presented both dimensionally
and nondimensionally. However, this refers to a
geometric nondimensionalizing only. Even for the
dimensional velocity profiles the length and velocity
data are nondimensionalized as described above. The
purpose of nondimensionalizing the velocity profiles is
to examine the relative distribution of velocity within
the jet. The reference quantities used for this purpose
are the maximum velocity, Umax(X,Y,Z), and the half-width
of the jet, Yq.5 The jet half-width is defined as the
transverse position, Y, where the local velocity is one
half of the maximum velocity at axial distance X, or,
equivalently,
TO =
(19)
Presenting velocity profiles in both ways is important in
showing the growth or decay of the jet and also the
relative balance of transport processes within the jet.
The forced disturbances are nondimensionalized by
expressing their frequency in terms of the Strouhal
number
47


fB
Str =
o
(20)
where f is the disturbance frequency, and uq is the
outlet velocity. The disturbance frequencies and their
corresponding Strouhal numbers are given in Table 4-1.
Table 4-1
Strouhal Numbers for Disturbance Frequencies
f (Hz) St
0 0.000
4 0.028
8 0.056
16 0.112
4.4 Measurement of Wall Jet Used for Present Study
The natural wall jet produced by the experimental
apparatus used here compared well with conventional
representations of turbulent wall jets found in the
literature. The most important characteristics, the
48


self-similarity or shape of the velocity profiles,
correlated very well with those found in the literature.
The wall jet was chosen because of its wide range of
commercial and industrial applications.
4.4.1 Outlet Conditions
The outlet velocity and turbulence intensity of the
nozzle used for this study were found to vary in the
transverse direction but were nearly constant in the
longitudinal direction. The outlet transverse velocity
profiles were measured at 12 cm intervals over the entire
length of the nozzle. The nondimensionalized transverse
outlet velocity profile at the longitudinal center of the
nozzle is shown in Figure 4-3. The standard deviation of
the velocities was 0.12, neglecting the data points at
the transverse extremes which were measured inside the
nozzle outlet boundary layers. The velocities at the
ends were measured inside the boundary layers of the
nozzle outlet as is confirmed by the transverse outlet
turbulence intensity profile shown in Figure 4-4. The
turbulence intensity is the ratio of the root-mean-square
of the velocity to the mean velocity and is defined as
49


where u(t) is the instantaneous velocity and um is the
mean component.
The data points at the transverse extremes are
clearly turbulent whereas the points outside the boundary
layers show a very low intensity turbulence in the
potential core.
The profiles in Figures 4-3 and 4-4 were found to be
representative of the transverse profiles taken at
different longitudinal locations. Sample velocities
taken at different longitudinal positions are shown in
Figure 4-5. The points taken inside the inviscid flow
show that the outlet velocities were nearly uniform in
the Z-direction. Sample outlet turbulence intensities,
shown in Figure 4-6, again show that the outlet
conditions are nearly uniform in the Z-direction. The
outlying curves were measured in the turbulent shear
layer developing at the ends of the jet.
The variation of outlet velocities and turbulence
intensities along (X,Y,Z)=(0,0.5B,Z) are shown in Figures
50


4-7 and 4-8, respectively, and confirm that the profiles
of Figures 4-3 and 4-4 are accurate representations of
the outlet conditions everywhere with the centerline
velocities varying along the longitudinal centerline only
by about 2 %.
4.4.2 Dimensional Transverse Velocity Profiles
The axial development of the transverse velocity
profiles from 1 to 20 nozzle widths is shown in Figure
4-9. As the flow field develops in the axial direction
the velocity gradient in the free mixing layer becomes
more shallow, the jet boundary extends further in the
transverse direction, and the transverse maximum of the
axial velocity decreases.
4.4.3 Dimensionless Transverse Velocity Profiles
The potential core region of the natural jet
extended to about 5 nozzle widths. The
nondimensionalized velocity profiles for the potential
core region are shown in Figure 4-10. The profiles in
this region develop in the same general manner as those
of Figure 4-11 which were produced by Viets and Sforza
(1966). Figure 4-12 shows the nondimensionalized
51


velocity profiles in the fully- developed region with the
curve of f(T]), the similarity solution given by Verhoff.
The similarity solution breaks down at the wall, where
71=0, and outside the jet boundary. The transverse
position y=0 was actually just adjacent to the wall
surface so that the point from the similarity solution is
actually calculated for a different physical location
than the actual data point. The profiles of Figure 4-12
show that the velocity profiles in the fully-developed
region for the natural jet have similarity to one another
and also to conventional representations of fully-
developed wall jet velocity profiles. This verifies that
the lack of outlet uniformity in the transverse direction
did not adversely affect the characteristics of the
natural jet and that the characteristic balance of
transport processes is occurring.
4.4.4 Axial Velocity Decay
In the two-dimensional region the maximum axial
velocity should decay as xl/2e Figure 4-13 shows a plot
of the maximum axial velocity decay for the jet used
here. When (Umax/Uo)2 vs. axial position is plotted the
curve will form a straight line over those velocities in
52


the region over which the maximum velocity decays as
which is the case for the fully-developed region
of this natural jet.
4.5 Measurement of Pulsed Wall Jet
The results of the measurements of the pulsed wall
jet are now given, beginning with the establishment of
the outlet conditions and then the development of the
flow field in the downstream direction. The comparisons
of the pulsed jet with the natural jet used for this
study can be regarded as good comparisons to conventional
wall jets due to the close similarity established between
the experimental jet used here and those found in the
literature.
4.5.1 Outlet Conditions
The outlet velocity distributions for the jet pulsed
at the frequencies observed were not significantly
different from the outlet velocity distribution for the
natural jet as shown in Figure 4-14. However, as seen in
Figure 4-15, the outlet velocity fluctuations for the
pulsed jet were significantly different from that of the
natural jet. The term velocity fluctuation is used here
53


because the term turbulence intensity, as it has been
presented, thus far is not meaningful when applied to the
jet when forced velocity fluctuations are included.
Turbulence intensity typically compares the random
velocity fluctuations to the mean velocity. However, the
flow field of the pulsed jet is affected by both the
random and forced periodic fluctuations that together
make up the total velocity fluctuation.
The natural jet has two velocity components, the
mean velocity um, and the random fluctuation of the
velocity ur. The pulsed jet on the other hand has three
velocity components the mean velocity um, the random
velocity fluctuation ur, and the periodic component Up,
i.e. .
(*> 0 = (*. 0 + K (x, t) + up(x, t), (22)
where x is the position vector. When periodic, forced
fluctuations are applied to the velocity, they contribute
to the value of the numerator of Equation 21, inferring a
greater value of random velocity fluctuation than is
actually occurring. Therefore, for the pulsed jet, the
term velocity fluctuation refers to the value computed by
54


Equation 2 and will represent the ratio of the
combination of the periodic and the random components of
the velocity to the mean component of the velocity.
The outlet velocity fluctuation shown in Figure 4-14
was taken from a two second sample of the velocity at the
outlet. The maximum velocity fluctuation is not at the
maximum disturbance frequency tested. Observation of the
actual outlet velocity fluctuation curves, which are
plotted in Figures 4-16 through 4-19, indicates that the
periodic component of the outlet velocity had a greater
amplitude for disturbances at Str=0.056 than for any
other frequency tested. The approximate peak-to-peak
amplitude as a percentage of the local mean velocity was
less than 2% for the natural jet, 25% at disturbances of
Str=0.028, 45% for Str=0.056, and 35% for Str=0.112.
4.5.2 Dimensional Velocity Profiles
The velocity profiles, when plotted in dimensional
form, give a good indication of the growth of the jet as
well as describe the momentum distribution within the
jet. The profiles for the jet pulsed at each of the
frequencies tested had a significant effect on the
velocity profiles. Most significantly, the profiles
55


tended to have greater relative values toward the free
shear layer. This change in shape indicated a change in
relative transport within the jet and enhanced
interaction of the jet with the surrounding fluid.
4.5.2.1 Str=0.028
The development of the velocity profiles for the jet
pulsed at Str=0.028 is shown in Figure 4-20. When
compared to the velocity profiles for the natural jet in
Figure 4-8 it is seen that as the flow develops
downstream the velocity maximum shifts slightly farther
from the wall, the jet becomes wider and the velocity
gradient in the transverse direction throughout the free
mixing layer is shallower than for the natural jet.
However, the general shape of the profiles is not
significantly skewed.
The nondimensionalized velocity profiles shown in
Figure 4-21 for the potential core region of the jet
pulsed at Str=0.028 are not significantly different than
those of the natural jet given in Figure 4-10. The
nondimensionalized velocity profiles for the fully-
i
developed region, shown in Figure 4-22, represent a
self-preserving flow and, in fact, are closely
56


represented by Verhoff's similarity solution f(ri),
Equation 6, which describes the velocity profile of the
natural jet in the fully-developed region.
4.5.2.2 Str=0.056
Disturbances at Str=0.056 had a significant effect
on the shape of the velocity profiles, particularly in
the fully-developed region. The transverse velocity
profiles are shown in Figure 4-23. In contrast to the
effect of pulses at Str=0.028, the shapes of the profiles
are skewed drastically from those of the natural jet.
The transverse location of the velocity maximum is much
greater in the fully-developed region, and its magnitude
less, than for the natural jet.
The profiles in the fully-developed region form into
transverse line segments rather than the smooth curves
that characterize the natural jet. The profiles in
Figure 4-23 develop into curves with 2 inflection points.
The first is near the wall and the second is about half
of the transverse distance of the halfwidth. Comparing
the profiles from Figure 4-23 at 10 and 15 nozzle widths,
the latter inflection point can be seen beginning to
form. The former inflection point seems to be located
57


where the wall layer interacts with the free part of the
jet. This point is where the maximum velocity is located
in the natural jet.
The disturbances result in accelerated development
of the velocity profiles in the potential core region,
which are given in nondimensional form in Figure 4-24.
This can be seen by comparing Figure 4-24 with
Figure 4-10, the natural jet. The shear layer can be
seen propagating more quickly into the inviscid part of
the flow.
The dimensionless velocity profiles in the fully-
developed region can be seen, in Figure 4-25, to lack
similarity. The profiles taken at 15 and 20 nozzle
widths are nearly similar in the outer region of the jet
but the profile taken at 10 nozzle widths is much
different in shape in both regions. This lack of
similarity means that the transport processes are being
affected by instabilities within the jet and as work is
done by the stress field to remove these instabilities
the internal transport of vorticity and momentum changes
with axial distance.
58


4.5.2.3 Str--0.112
For the jet pulsed at Str=0.112 the velocity
profiles develop in a manner similar to that of the jet
pulsed at Str=0.056. The transverse velocity profiles
are shown in Figure 4-26. The profiles in the fully-
developed region form into segmented curves of the same
shape as the profiles taken at 15 and 20 nozzle widths
shown in Figure 4-23. Again, there is an inflection
point near the wall where the boundary layer interacts
with the free stream and another at the velocity maximum
located just under half of the transverse distance of the
jet halfwidth.
When the velocity profiles in the potential core
region are plotted in dimensionless form, shown in
Figure 4-27, it can be seen that the flow develops more
quickly for the jet pulsed at Str=0.112 than for any of
the other frequencies observed. The profile taken at 3
nozzle widths in Figure 4-27 is nearly identical to that
taken at 5 nozzle widths in Figure 4-24, for the jet
pulsed at Str=0.056.
In the fully-developed region the profiles are
nearly similar when nondimensionalized. This can be seen
in Figure 4-28.
59


4.5.3 Velocity Profiles at Each Axial Distance
It is useful to directly compare the dimensionless
velocity profiles at each axial distance in order to
demonstrate the effects of the disturbances on their
streamwise development. This is plotted in Figures 4-29
through 4-34 for X=1, 3, 5, 10, 15, and 20 nozzle widths,
respectively.
At 1 nozzle width the disturbances have little
effect although for the jet pulsed at Str=0.056 and 0.112
the free mixing layer can be seen to have propagated
further into the potential core than for either the
natural jet or the jet pulsed at Str=0.028.
At 3 nozzle widths downstream this same trend
continues, with the disturbances at Str=0.112
accelerating the propagation of the shear layer
significantly, the disturbances at Str=0.056 noticeably,
and the pulses at Str=0.028 having little effect on the
flow field development.
At 5 nozzle widths the velocity profiles are more
similar in shape for all disturbance frequencies, with
disturbances of Str=0.112 having the most significant
60


effect and disturbances of Str=0.028 having almost no
effect on the shape of the profile.
At 10 nozzle widths the profile for disturbances of
Str=0.112 is skewed severely and for disturbances of
Str=0.056 the profile is significantly different. At
this downstream distance the jet pulsed at Str=0.112 has
developed the two distinct inflection points which are
just beginning to form in the profile for pulses of
Str=0.056.
At 20 nozzle widths the profiles for the natural jet
and the jet pulsed at Str=0.028 are again not
significantly different. The profiles in the free mixing
region for the jet pulsed at Strouhal numbers of 0.056
and 0.112 are approximately the same but have different
slopes in the wall region.
4.5.4 Velocity Fluctuation Profiles for Each Frequency
The fluctuation of the velocity is of great
importance to this study as the method of instability
enhancement being employed is to force velocity
fluctuations at the outlet and to propagate their effect
downstream in the shear layer. The streamwise
61


development of the velocity fluctuation profiles maps out
locations of highly turbulent activity.
4.5.4.1 Natural Jet
For the natural jet the transverse velocity
fluctuation profiles show two definite peaks, one being
near the wall and the other outside the jet halfwidth.
The shape of the profiles does not change significantly
with axial distance, as is seen in Figure 4-35. The
maximum value of velocity fluctuation is about 50% of the
local mean velocity at (X,Y)= (20,3.7).
4.5.4.2 Str=0.028
For the jet pulsed at Str=0.028 both the shape and
the magnitude of the profiles is affected. This is shown
in Figure 4-36. Near the wall the velocity fluctuations
are 50% to 90% greater than for the natural jet. The
maximum values in the free mixing layer are almost the
same for all axial distances, the overall maximum value
being at (X,Y) = (15,3). The profiles in the fully-
developed region maintain higher values past the peak in
the free mixing layer than do those of the natural jet.
62


In general, however, the shape of the profiles is
analogous to those of the natural jet.
4.5.4.3 Str=0.056
For the jet pulsed at Str=0.056 the velocity
fluctuation, as a percentage of the local mean velocity,
reaches a maximum value of 57% at the position
(X,Y) = (3,1.25), an increase of about 43% over the
fluctuation of the natural jet at that same axial
distance, as can be seen in Figure 4-37. At axial
distances of 15 and 20 nozzle widths, the profiles are
elongated in the transverse direction. At an axial
distance of 15 nozzle widths and a transverse distance of
6 nozzle widths, the velocity fluctuation is about 200%
greater than for the natural jet, and at 20 nozzle widths
downstream at that same transverse distance is about 80%
greater than for the natural jet.
4.5.4.4 Str=0.112
The elongation of the velocity fluctuation profiles
seen for the jet pulsed at Str=0.056 also occurs for the
jet pulsed at Str=0.112, which is shown in Figure 4-38,
but even more severely. The fluctuations near the wall
63


are even greater than for the jet pulsed at Str=0.028 and
are 100% to 300% greater than for the natural jet in the
region near the wall.
4.5.5 Velocity Fluctuation Profiles at Each Axial
Position
The velocity fluctuation profiles, when plotted for
all Strouhal numbers at each axial position, show a
dramatic redistribution of energy when compared to the
natural jet.
4.5.5.1 X=1
The outlet velocity fluctuations at 1 nozzle width,
shown in Figure 4-39, were similar to that of the outlet
velocity fluctuations that were shown in Figure 4-15
except that the velocity fluctuations in the developing
shear layer were much greater for the jet pulsed at
Str=0.056 and Str=0.112. At the free edge of the jet the
velocity fluctuations for the jet pulsed at Str=0.056
were greater than for the jet pulsed at Str=0.112. The
velocity fluctuations for all disturbance frequencies in
the potential core remained at approximately the same
values as those at the outlet.
64


4.5.5.2 X=3
At 3 nozzle widths the velocity fluctuations for
disturbances of Str=0.056 and Str=0.112 were
significantly higher than for the natural jet at all
transverse locations. This is shown in Figure 4-40. For
the jet pulsed at Str=0.028 the velocity fluctuations
were about twice as great as the natural jet in the
potential core region but in the free shear layer were
not much greater than the natural jet. At this axial
distance the velocity fluctuations for disturbances of
Str=0.056 were about 10% greater than for disturbances of
Str=0.112 past a transverse distance of 1 nozzle width.
This suggests greater rates of strain and structural
formation in the free mixing layer of the pulsed jet than
for the natural jet. The velocity fluctuations at the
wall surface were more than 300% greater for the jet
pulsed at Str=0.056 and Str=0.112 than for the natural
jet and nearly 100% greater for the jet pulsed at
Str=0.028 than for the natural jet.
Because instability increases with the time
derivative of the velocity and given that the formation
and dissipation of vortical structures is a result of
65


instabilities, this suggests that much greater transport
of mass and momentum are occurring across the layer
interfaces in the pulsed jet than for the natural jet at
this axial distance. Visualization of the flow field,
presented in Chapter 5, verified this.
4.5.5.3 X=5
At 5 nozzle widths the extent of the potential
core of the natural jet the velocity fluctuation curves
for the jet pulsed at Str=0.056 and Str=0.112 for the
region between the wall and the location of maximum
velocity fluctuation are the same shape and nearly of the
same magnitude. The velocity fluctuation was more than
100% greater than for the natural jet, as can be seen in
Figure 4-41.
For these two curves the location of the minimum
velocity fluctuation is at about 0.25 nozzle widths from
the wall. The curve for disturbances of Str=0.028 in
this region is approximately the same shape as for the
natural jet with the velocity fluctuations in the wall
region being about 50% higher than for the natural jet.
The velocity fluctuation curve for the jet pulsed at
Str=0.112 shows a significant change in shape when
66


compared to the natural jet. In fact the velocity
fluctuations for this disturbance frequency were less
than the natural jet between transverse locations of 1.25
and 2.25 nozzle widths.
4.5.5.4 X=10
The curves of the velocity fluctuations at 10 nozzle
widths, shown in Figure 4-42, demonstrates a
distinguishable trend with respect to disturbance
frequency. The maximum velocity fluctuation for the
natural jet occurs at about 2.25 nozzle widths from the
wall and the minimum at about 0.25 nozzle widths from the
wall, corresponding to high rates of strain in the
interfaces between the layers. When the jet is pulsed at
a disturbance frequency of Str=0.028 the maximum was
reduced slightly and moved toward the wall, the minimum
increased slightly and moved away from the wall, and,
most importantly, the velocity fluctuation in the shear
layer interfaces increased in magnitude. As the
disturbance frequency was increased these trends in the
velocity fluctuation curves continued.
The curve for the jet pulsed at Str=0.056 shows this
trend. Again the location of the maximum velocity
67


fluctuation moved toward and decreased in magnitude while
the maximum velocity fluctuation occurred farther from
the wall and was of greater magnitude than for the
natural jet. The velocity fluctuations in the free
mixing layer increased in magnitude and past 5 nozzle
widths were nearly 250% greater, as a percentage of the
mean velocity, than for the natural jet.
At a disturbance frequency of Str=0.112 the relative
magnitudes of the velocity fluctuation were inverted from
those of the natural jet. The velocity fluctuation at
the wall was more than 100% greater than for the natural
jet and in the free mixing layer was more than 250%
greater than for the natural jet. This is very
significant with respect to mass and momentum transport
within the jet.
4.5.5.5 X=15
At 15 nozzle widths the curve for the jet pulsed at
Str=0.056 is very similar in shape to that of the jet
pulsed at Str=0.112. This is shown in Figure 4-43. The
velocity fluctuations for the jet pulsed at Str=0.028
were significantly greater in the free mixing layer than
for the natural jet, indicating greater instability at
68


the interface between the jet and the surrounding fluid,
and that this interface is pushed significantly farther
out from the wall by the disturbances.
4.5.5.6 X=20
The development of the velocity fluctuation profiles
continues in the same manner between 15 and 20 nozzle
widths. The velocity fluctuation profiles at 20 nozzle
widths are shown in Figure 4-44. Again the disturbances
increased the velocity fluctuations near the wall and in
the free shear layer at the outer edge of the jet. The
curve for the jet pulsed at Str=0.056 is nearly the same
in shape and magnitude as that of disturbances of
Str=0.112 with the curve for the jet pulsed at Str=0.028
being closer in shape to that of the natural jet but with
much greater magnitude near the wall and in the shear
layer at the outer edge of the jet.
4.5.6 Axial Velocity Decay
The rate of axial velocity decay in the fully-
developed region was not significantly changed by the
disturbances. Rather, between 5 and 10 nozzle widths the
axial velocity decay curve was shifted by the inclusion
69


of disturbances, as is shown in Figure 4-45. When
plotted as the inverse square of the velocity vs. the
axial position, which is given as Figure 4-46, it is seen
that the rate of maximum velocity decay is nearly uniform
for all of the disturbance frequencies tested, as well as
for the natural jet.
4.5.7 Jet Width
The rate of propagation of the turbulent interface
into the quiescent fluid can be represented by the jet
halfwidth, Yq.5, which has already been defined as the
transverse location at an axial distance where the
velocity has decayed to half of the maximum velocity at
that same axial distance. The rate of spread, or
propagation of the turbulent interface, is shown if
Figure 4-47. For all the disturbance frequencies
observed, the pulsed jet had a greater spread rate than
the natural jet. Disturbances of Str=0.056 resulted in
the greatest spread rate. The spread rate for the
natural jet and for the jet pulsed at Str=0.112 the
spread rate was linear. It was nearly linear for the jet
pulsed at Str=0.056 but highly nonlinear for disturbances
of Str=0.028.
70


Figure 4-1. Regions of a Wall Jet.
71


Figure.4-2. Diagram of Shear Layer Development.
72


CO
Y
Figure 4-3. Outlet Transverse Velocity Profile, Natural
Jet.


-J
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Y
Figure 4-4.Outlet Transverse Turbulence Intensity Profile
Natural Jet.


) -J-' I I > I I j U.1 I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Y
Figure 4-5. Sample Outlet Velocities at Various Longitudinal
Positions.


J 1 1 1 1 -* - I I I -I I I __l
0.0 0.1 0.2. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Y
Figure 4-6. Sample Outlet Turbulence Intensities at
Various Longitudinal Positions.



LO
CD
LO"
CD
o"
3
M
CD
UD
C)
o~
1 .1
1 .0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Z
Figure 47. Longitudinal Variation of Outlet Velocity
Along (X/YfZ)=(0/0.5B,Z).


00
LO
CD
LO
CD
o'
M
OQ
LO
o'
cn
E
L_
3
J ---->--1---1---1---L--1---1---1--1---J---1---1-_j___|___ I I I
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Z
Figure 4-8. Longitudinal Variation of Outlet Turbulence
Intensity Along (X,Y,Z)=(0,0.5B,Z).


-J
VO
0 1 2 3 4 5 6 7
Y
Figure 4-9. Transverse Velocity Profiles, Natural Jet.


U(X,Y,0.5)/U(X,YUmox,0.5)
Figure 4-10. Transverse Velocity Profiles in the
Potential Core Region, Natural Jet.


Figure 4-11. Transverse Velocity Profiles in the
Potential Core Region, Viets and Sforza
(1966).


00
to
Y/Yo.5
Figure 4-12. Transverse Velocity Profiles in the
Fully-Developed Region, Natural Jet.


{U(X>Yumox,0.5)/U(0)0.5B)0.5)}-2
jiiijjij_i_i i i i i
0 2 4.6 8 10 12 14 16 18 20
X
Figure 4-13. Axial Decay of Maximum Velocity, Natural
Jet.


00
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Y
Figure 4-14. Outlet Transverse Velocity Profiles.


Figure 4-15. Outlet Transverse Velocity Fluctuations.


U(0)0.5B)0.5)/Um(0,0.5B,0.5)
1 .2
1 .1
1 .0
0.9
0.8
0.7
0.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Time (sec)
Figure 4-16. Outlet Velocity, Natural Jet.
- i 1 F 1 1 1 1 i 1 1
VyWiM |/lWl^R l/*v MW
- -
- -
. 1 _i _i 1 i . _i __u