Measurement of turbulence in an annular jet
Transcript of Measurement of turbulence in an annular jet
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Masters Theses Student Theses and Dissertations
1972
Measurement of turbulence in an annular jet Measurement of turbulence in an annular jet
George Philip
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MEASUREMENT OF TURBULENCE
IN AN ANNULAR JET
··BY
GEORGE PHILIP, 1944-
-A THESIS
Presanted to the Faculty of the Graduate School of the
' ' : , , i
UNIVERSITY OF MISSOURI-ROLLA
In Partial Fulfillment of the Requirements for the Degree
MASTER OF SCIENCE IN MECHANICAL ENGINEERING
1972
Approved by
(Advisor).
T2721 55 pages c. I
ii
ABSTRACT
An experimental investigation was conducted for an annular
jet which consisted of a circular jet and a concentric wake.
The annular air jet mixed with quiescent atmospheric air. The
jet velocity was kept constant at 137.0 feet per second which
corresponds to a Reynolds Number of 73,200. Using the technique
of hot-wire anemometry, mean velocities, turbulence intensities
and Reynolds stresses were measured in the longitudinal and
lateral directions.
Two distinct flow regimes, the free stream jet regime and
the diffusing jet regime, are observed. In the free stream
jet regime, higher turbulence intensity and shear stress occur
in the inner region where the annular jet interacts with the
wake. In the diffusing jet regime, higher turbulence intensity
and higher turbulent shear occur in the outer mixing region
where the annular jet interacts with the quiescent air. In
both regimes, high turbulence intensities and Reynolds stresses
correspond to high velocity gradients. The axial component
of turbulence is approximately twice as large as the turbulence
components in the lateral directions. The wake turbulence dissi
pates rapidly, whereas the turbulence caused by the jet mixing
is preserved to a large extent.
iii
ACKNOWLEDGMENT
The author gratefully acknowledges and sincerely appreciates
the efforts of his advisor, Dr. Shen C. Lee, in guiding this
thesis. His help and assistance during the experimentation and
preparation of the thesis were invaluable.
The author is grateful for the advice and constructive
criticism of Dr. R. A. Medrow. The a ssistance given by Mr. R. D.
Smith of the Mechanical Engineering Laboratory, during the
fabrication of the experimental equipment, is appreciated.
ABSTRACT ....
ACKNOWLEDGEMENT
LIST OF ILLUSTRATIONS.
LIST OF TABLES . .
I. INTRODUCTION
TABLE OF CONTENTS
II. EXPERIMENTAL PROGRAM
A. Turbulent Mixing Apparatus
1. Compressed Air Source.
2. The Plenum Chamber
3. The Annular Nozzle
4. The Traversing Mechanism
B. Hot-Wire Anemometry ..
C. Experimental Procedure
III. RESULTS AND DISCUSSION ..
A. Mean Velocity Characteris t ics .
iv
Page
ii
iii
vi
viii
1
4
4
4
4
7
7
7
9
11
11
1. Region of the Free Stream Annular J e t. 11
2. Region of the Diffusing Annular Jet. 13
3. General Comments . 15
B. Turbulence Intensities 15
1. Region of the Free Stream Annular Jet. 15
2. Region of the Diff using Annular J e t.
3. General Comment s
C. Reynolds Stresses ..
19
23
24
1. Region of the Free Stream Annular Jet. 24
v
Page
2. Region of the Diffusing Annular Jet. . 27
3. General Comments
IV. CONCLUSION .
V. BIBLIOGRAPHY
VITA
APPENDIX A. AXISYMMETRIC TURBULENCE EQUAT I ONS
APPENDIX B.. INSTRUMENTATION
1. Calibration ..
2. Pressure Measurement
3. Single Wire Measurement.
30
32
34
36
37
41
41
43
43
vi
LIST OF ILLUSTRATIONS
Page
Figures
1. Elevation of Experimental Equipment. 5
2. End View of Experimental Equipment 6
3. The Annular Nozzle . 8
4. Scheme of Flow of an Annular Jet 10
5. Axial Mean Velocities in the Region of the Free Stream Annular Jet . . . 12
6. Axial Mean Velocities in the Region of the Diffusing Annular Jet. . 14
7. Axial Component of Turbulence in the Region of the Free Stream Annular Jet. . . . . . . 16
8. Radial Component of Turbulence in the Region of the Free Stream Annular Jet. . . . . . . 17
9. Tangential Component of Turbulence in the Region of the Free Stream Annular Jet . . . . . . 18
10. Axial Component of Turbulence in the Region of the Diffusing Annular Jet. . . . . . . 20
11. Radial Component of Turbulence in the Region of the Diffusing Annular Jet. . . . . . . . 21
12. Tangential Component of Turbulence in the Region of the Diffusing Annular Jet . . . 22
13. Reynolds Stresses in the Radial Plane in the Region of the Free Stream Annular Jet. . 25
14. Reynolds Stresses in the Tangential Plane in the Region of the Free Stream Annular Jet. . 26
15. Reynolds Stresses in the Radial Plane in the Region of the Diffusing Annular Jet. . . 28
16. Reynolds Stresses in the Tangential Plane in the Region of the Diffusing Annular Jet. . . 29
vii
Page
17. Scheme for DISA Instrumentation with an X-Wire Probe. . ... 42
18. X-Wire Calibration 44
viii
LIST OF TABLES
Table Page
I. Comparison of Results by X-wire and Single \.Jire Measurements . . . . . • . . . . . . . . . 46
1
I. INTRODUCTION
Studies establishing the characteristics of wakes behind
bluff bodies and mixing phenomena of a jet with ambient fluid
have many engineering applications. These flow problems have
been analysed separately by many investigators. Some practical
flow problems, such as the mixing of fuel and air in a combustor
of a gas turbine engine are related more closely to the phenomenon
of the interaction of an axisymmetric wake with a concentric
diffusing jet.
Experimental investigations of mean velocity and static
pressure distributions have been conducted by Chigier and Beer (1)
for swirling air jets issuing from annular nozzles into stagnant
air surroundings. Chigier and Beer (2) also studied double
concentric jets consisting of a central round air jet surrounded
by an annular air jet issuing into ambient air. However, no
information is available on the turbulence structure of the
flow field of an annular jet which consists of an axisymmetric
wake and a concentric jet.
Study of turbulence structure is essential for understanding
the mixing processes and the noise generating mechanisms.
Bradshaw and Ferris (3) studied the primary source of jet noise
and found it to be due to a group of large eddies in the turbulent
flow field.
Experimental investigations of the structure of turbulence
have been conducted for comparatively simple flow geometries.
Turbulence intensities and Reynolds shear stresses have been
2
measured for simple jets as well as for wakes behind blunt and
semistreamlined bodies. Since the annular jet consists of a
circular jet with a concentric wake, experimental results on
flow fields of simple jets and wakes are to be reviewed.
Simple axisymmetric jets have been studied extensively
by Sami (4). He has measured mean velocity, pressure, turbulence
components and their correlations. Computations yielded the
intermittency factor, the average eddy scale and the dissipation
length of turbulence. This data \vas utilized to analyse pro
duction, convection, diffusion and dissipation of turbulence
energy. Curlet and Ricou (5) analysed energy dissipation in
ducted jets. Heskestad (6) investigated plane jets under
varying jet velocities to establish the self-preserving char
acteristics of turbulence. A simple closed form solution for
the decays of axial and swirling velocities of a turbulent
swirling jet has been obtained by Lee (7).
In the class of wakes behind blunt bodies, Naudascher (8)
studied the production, convection, diffusion and dissipation
of turbulence behind an axisymmetric self-propelled body.
Simulated by a disk in an air tunnel, these measurements were
used to verify the condition of self-propulsion and to provide
a picture of the force field and the process of energy transfor
mation. High intensity turbulence and Reynolds stress components
behind a disk were measured also by Carmody (9) to investigate
wakes behind bluff bodies.
In the class of wakes behind streamlined bodies, Pepper (10)
3
investigated the turbulent wake structure of a spherical body
suspended in a vertical wind tunnel. Using a constant temperature
hot-wire anemometer, he measured mean velocities, turbulence
intensities and turbulent shear stresses of the wake in order
to understand the turbulence characteristics induced by a moving
sphere. Similar parameters have been measured by Chevray (11)
in the wake of a semistreamlined body of revolution. Turbulence
intensities in the wake of a horizontal cylinder was measured
by Townsend (12) to determine the transport of turbulent energy.
In order to provide the necessary information for analytical
studies on annular jets, turbulence data are necessary in addition
to the mean parameters given by Chigier and Beer (1,2). The
present investigation is to obtain the turbulence intensities
and Reynolds stresses in the flow field of an annular jet and
to study the interaction between an axisymmetric wake and a
concentric jet.
4
II. EXPERIMENTAL PROGRAM
The experimental equipment consists of the turbulent mixing
apparatus and the instrumentation to measure mean velocity and
turbulence parameters. Using the technique of hot-wire anemometry,
measurements were carried out at six downstream sections, under
constant velocity conditions.
A. Turbulent Mixing Apparatus
1. Compressed Air Source
The compressed air line coming to the UMR Gas Dynamics
Laboratory was connected to the plenum chamber. The line has
two throttle valves and one air-bleed valve to control the amount
of air coming into the chamber. A 400 cfm reciprocating compressor
supplied the compressed air during the experiment. The compressor
had sufficient capacity in terms of quantity, but the pressure
was between 80 and 100 psig instead of the one psig required
at the plenum chamber. The throttle valves served the dual
purposes of reducing the pressure to one psig and of controlling
the amount of air entering the plenum chamber.
2. The Plenum Chamber
Figures 1 and 2 show in detail the construction of the plenum
chamber. A 15 cubic feet tank was utilized to allow the air
flow to become uniform in velocity at low turbulence level.
The center body which produces the wake was screwed on to the
6 inches diameter inside cylinder so as to give a smooth contour
for the air flow. A screen consisting of five layers of number
18 steel mesh was placed in between the flanges of the two halves
46" I 22" 2~rr I I
, Clearance - 11" I
The Probe
/ Nj ll ll I I~ Oi
LJ[ ~1 t;jl
t-J I/ t-'• Pl .
1(\ \
\ I \ I
\2~" Compressed Air Pipe \Screen
PLENUM CHAMBER TRAVERSE SYSTEM Vl
Figure 1. Elevation of Experimental Equipment
Tank Dia. 2011
Figure 2. End View of Experimental Equipment
Nozzle Body - ~" Dia.
The Annular Nozzle
Clearance - 11" //
Longitudinal Traverse
~Radial Traverse 0'
7
of the chamber. This was intended to break up the large
turbulent eddies in the flow. A pitot probe was brought into
the flow temporarily during the experiment to measure the jet
exit velocity.
3. The Annular Nozzle
Figure 3 shows the annular nozzle which consists of a
circular nozzle and a center body. The center body ends abruptly
at the nozzle exit to give an axisymmetric bluff body. They
were machined for a uniform surface and polished smooth to obt~tn
an annular nozzle of minimum skin friction. The nozzle part
is welded on to the inside cylinder, as shown in Figure 1. The
center body was aligned so that the eccentricity was less than
1/64 inches.
4. The Traversing Mechanism
Figures 1 and 2 also show the traversing mechanism which
was constructed from a lathe bed and a saddle. Attachments
on the saddle were designed to carry the probe holder for the
desired orientation of the probe. The error in locating the
probe at any point was not greater than 1/32 inches.
B. Hot-Wire Anemometry
The hot-wire anemometer is used for measuring the structure
of turbulence, especially in the realm of incompressible flo~.
A DISA Model 55 DOl dual channel constant temperature hot-wire
anemometer was used for this investigation. Detailed discussion
on measurement principles and operation procedures was given by
Pepper (10). An outline of the turbulent flow equations iS
I
1/2
u D
ia ...,.------_
_j
I I
.--------
6" I Dia-,a .
;--------_
j
·I
8
Q)
rl
N
N
0 z ,_. Cll rl
;::l ~
~ Q)
,..c: H
9
given in Appendix A. The required information for data reduction
and probe calibration is given in Appendix B.
C. Experimental Procedure
The experiment was conducted for a jet velocity of 137.0
feet per second. This corresponds to a Reynolds number of
73,200 for the annular jet, taking the inner diameter of the
annulus as the characteristic length. This velocity was chosen
to provi de an incompressible turbulent jet with the available
experimental facility. The X-wire probe traversed the field
of flow at six sections, Z/D = 0.125, 0.375, 1.0, 3.0, 6.0 and
10.0. At each section, radia l traverses covered the entire
field of the turbulent flow region.
The X-wire probe was oriented in the radial plane for the
first set of measurements ; and in the tangential plane for the
second set of measurements, as illustrated in Figure 4. The
mean velocities and turbulence intensities in the axial direction
were obtained separately by the two sets of measurements. The
radial components of the turbulence in t ensi ty and Reynolds stress
were obtained from measurements with the probe orientation in
the radial plane. Similarly, the tangential components of
turbulence intensity and Reynolds stress were obtained through
the t an gential orientation of the probe.
r
8
2
/ a. Mixing Region
b. The Wake
Figure 4. Scheme of Flow of an Annular Jet
/ '
8
// r
The Region of Diffusing Annular Jet
The Region of Free Stream Annular Jet
1. Radial Orientation of The X-Probe
2. Tangential Orientation of The X-Probe
1-' 0
11
III. RESULTS AND DISCUSSION
The experimental results of the annular jet issuing into
quiescent atmosphere consist of three parts: mean velocities,
turbulence intensities, and Reynolds stresses. They are non
dimensionalized with reference to the jet velocity and are
presented graphically. Distances are non-dimensionalized with
reference to the diameter of the bluff body. The region up
to Z/D = 1.0 is termed the region of the "free stream" annular
jet and the region beyond Z/D = 1.0 is termed the region of
the "diffusing" annular jet. The reasoning of this terminology
is evident from the mean velocity profiles of Figures 5 and 6.
The mixing and the wake regions of the annular jet are illustrated
in Figure 4.
A. Mean Velocity Characteristics
1. Region of the Free Stream Annular Jet
Figure 5 shows the mean velocities in the axial direction
for the region of the free stream annular jet. The maximum
velocity in this region corresponds to the free stream velocity.
The flow reduces sharply at the outer skirt of the annular jet,
where it has a boundary with stagnant atmospheric air. In the
wake, the axial velocity of the flow is about 20 percent of the
jet velocity at Z/D = 0.125 and increases to about 50 percent
of the jet velocity at Z/D = 1.0 . The flow spreads from the jet
to t he wake ve ry r apidly and causes a h ighe r ve loci ty a long
the wake centerline than elsewhere in the near wake. This
characteristic terminates befo re Z/D = 1.0 as the radial velocity
0.8
0.6
0.4
0.2
0.0
0.8
0.6
Nl 0 ::J ~
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
-3.0
Note: 0 6
Figure s.
12
l I f
I ~ I i
I Z/D = 1. 0 l
-2.0 -1.0 0.0
r/D
1.0
I I
l/D ~ 0.375
~
Z/D 0.125
2.0 3.0
Corresponds to Radial Orientation of tile Probe Corresponds to Tangential Orientation of the Probe Axial Mean Velocities in the Region of the Free Stream Annular Jet
13
of the wake becomes insignificant compared to the axial velocity.
The high velocity gradients are limited to narrow shear
zones at the inner and outer regions of the annular jet. The
velocity gradients are zero at the center of the wake and in the
free stream. The gradient due to mixing with the quiescent air
diminishes only gradually, whereas the gradient in the wake
reduces sharply for increasing Z/D.
2. The Region of the Diffusing Annular Jet
Figure 6 shows the mean velocities in the axial direction
for the region of the diffusing annular jet. The free stream
characteristic terminates between Z/D = 1.0 and 3.0, and the
flow diffuses significantly in the wake region. Entrainment
of atmospheric air also occurs in this region. The increase
of mass flow is noticeable at Z/D = 10.0 where the maximum
velocity is only 10 percent less than the jet velocity.
Further reduction of this maximum velocity is to be expected
beyond Z/D = 10.0.
The velocity defect at the center of the wake has reduced
to 20 percent at Z/D = 3.0 compared to about 50 percent at
Z/D = 1.0. The influence of the wake on the velocity profile
becomes insignificant at Z/D = 10.0.
The velocity gradients due to mixing have reduced con
siderably compared to those in the near wake and they further
decrease with increasing Z/D. The velocity gradient due to
the wake has also diminished to an extent that its magnitude
is near zero at Z/D = 10.0.
0.6
0.4
0.2
o.o
0.8
0.6
Nl 0 ::::::> ::::::>
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
-3.0
Note:
Figure 6.
0 D.
0
0 D.
-2.0 -1.0 0.0 r/D
1.0
14
Z/D = 6.0
Z/D = 3.0
2.0 3.0
Corresponds to Radial Orientation of the Probe Corresponds to Tangential Orientation of the Probe Axial Mean Velocities in the Region of the Diffusing Annular Jet
15
3. General Comments
The mean velocity measurements indicate that the annular
jet spreads into the regions of the quiescent air and the wake.
The velocity gradients decrease as Z/D increases. A backf1ow
was observed by Chigier and Beer (2) in the near wake region
for the double concentric jets with zero exit velocity at the
central jet. Much stronger backflow was observed by the same
investigators (1) for swirling jets. No effort was made to
measure the backflow in this experiment because of the difficulty
in instrumentation. The axial velocity at the center of the
wake reached 90 percent at Z/D = 2.4 for the case of the double
concentric jet with zero exit velocity at the central jet.
The axial velocity at the center of the wake reached 90 percent
at Z/D = 9.0 in the circular disk investigated by Carmody (9).
The wake center line velocity reaches 90 percent at Z/D 6.0
in the present investigation. Comparable results based on Z/D
are not expected, because Z/D is not necessarily a similarity
parameter of turbulent flow. In general, the trend of mean
velocity characteristics obtained by Chigier and Beer (1,2)
and Carmody (9) is comparable with those obtained from this
experiment.
B. Turbulence Intensities
1. The Region of the Free Stream Annular Jet
Figures 7 through 9 show the axial , radial and tangential
turbulence intensities for the regions of the free stream annular
jet.
.08
.06
.04
.02
.00
.08
.06
.04
- Nl 0 ;::l p
.02
.00
.10
.08
.06
.04
.02
.00
-3.0 -2.0
I I
I~ ~ I ! I
I I I
-1.0 0.0 r/D
16
Z/D = 1. 0
Z/D 0.375
Z/D = 0.125
1.0 2.0
Note: 0 o Corresponds to Radial Orientation of the Probe
3.0
6 \7 Corresponds to Tangential Orientation of the Probe Figure 7. Axial Component of Turbulence in the Region of
the Free Stream Annular Jet
.08
.06
.04
. 02 l._
. 06
- ~~ 0 ;:l ~
.04
.02
.00
.08
.06
.04
.02
. 00
-3.0
Figure 8.
17
l Z/D = 1.0
Z/D 0.375
Z/D = 0.125
-2.0 -1.0 0.0
r/D
1.0 2.0 3.0
Radial Component of Turbulence in the Region of the Free Stream Annular Jet
.06
- CDI 0 ;j ~
.04
.02
. 06
.04
. 02
.00
Figure 9.
-2.0 -1.0 0.0
r/D
18
Z/D 1.0
Z/D = 0.375
Z/D 0.125
Tangential Component of Turbulence in the Region of the Free Stream Annular Jet
19
The turbulence intensities which are approximately zero
in the free stream of the annular jet, increase rapidly at the
outer regions and in the near wake. The turbulence intensity
of the near wake is higher than those of the outer regions.
Approximately 30 percent dissipation of the maximum intensity
was observed between Z/D = 0.125 and Z/D = 1.0. A minimum of
turbulence intensity occurred in the center of the wake and
increased in magnitude with Z/D. At each cross-section, the
turbulence intensity increases from the center of the wake to
a maximum at the outer edge of the wake.
High turbulence intensity occurred at the outer edge of
the annular jet. The region of high turbulence intensity spread
to the quiescent air region at the same rate as the mean velocity.
The magnitudes of the turbulence intensities in the axial
direction was approximately twice as large as those of the radial
and tangential directions. This phenomenon was observed by
Sami (4), Pepper (10) and many others in the turbulence developing
region.
2. The Region of the Diffusing Annular Jet
Figures 10, 11, and 12 show the turbulence intensities in
the axial, radial, and tangential directions for the diffusing
annular jet region.
Turbulence intensities caused by the mixing of the annular
jet with quiescent air diffuse laterally at a faster rate than
in the region of the free stream annular jet. The point of
maximum intensity tends to move away from the longitudinal axis,
.02
.00
.08
.06
~ Nl 0 ::l I=)
.04
.02
.00
.08
.06
.04
.02
-2.0 -1.0 0.0 1.0 r/D
20
= 10.0
0
0
Z/D = 6.0
Z/D = 3.0
Note: o Corresponds to Radial Orientation of the Probe 6 Corresponds to Tangential Orientation of the Probe
Figure 10. Axial Component of Turbulence in the Region of the Diffusing Annular Jet
.08
.06
.04
.02
.00
.08
.06
- ~j 0 ::l :::::>
.04
.02
. 08
.06
.04
Figure 11.
21
Z/D 10.0
Z/D 6.0
r/D
Radial Component of Turbulence in the Region of the Diffusing Annular Jet
.06
.04
.02
.00
.06
- CDI 0 ;:l ::::>
.04
.06
.04
.02
.00
-3.0
Figure 12.
22
Z/D = 10.0 j
-2.0 -1.0 0.0
r/D
1.0
0
Z/D =
2.0 3.0
Tangential Component of Turbulence in the Region of the Diffusing Annular Jet
I
23
for increasing Z/D. The turbulence in the mixing region is
sustained by the shear flmv between the jet stream and the
entraining air. The intensities reduce by about 20 percent at
Z/D = 10.0 compared to those at Z/D = 1.0. However, the maximum
turbulence intensity in the wake has dissipated by about 80
percent at Z/D = 3.0. Further downstream, the intensities reduce
only marginally. They also become uniform everywhere in the
wake unlike the behavior noted in the near wake region.
The magnitude of the turbulence intensity in the axial
direction was still approximately twice as much as those in the
radial and tangential directions. Comparing the mean velocity
profiles of Figure 6 with the turbulence intensity profiles of
Figures 10, 11, and 12, it can be seen that the maximum velocit i es
are converging along the longitudinal axis while the maximum
turbulence intensities are confined to the mixing region.
3. General Comments
The turbulence i ntensity data indicates that the max imum
inte ns i t i es a re a s s ociated with steep velocity g r a dient s a t
each cross-section. The turbulence intensities in the longi
tudinal direc tion are approx i mately twice a s large a s those i n
the l a tera l d irect ion s . The magn i tudes o f the max imum i nte ns i t y
decreased even i n the region where the averaged jet velocity
remained const ant .
Th e tur bulen ce ch aracteris t i c s i n the mix ing region a re
similar to those obtained by Sami (4) f o r a circular jet. The
turbulence intensities in the wake compa re well with the
24
characteristics observed by Carmody (9) behind a disk. The
cumulative rate of turbulence production approaches a constant
value almost within an axial distance of Z/D ~ 10.0 according
to Naudascher (8); and this investigation concludes that the
same occurs around Z/D = 6.0.
C. Reynolds Stresses
The Reynolds shear or the one-point double correlation
of the fluctuating velocity components has been obtained for
the radial and tangential planes in the regions of the free
stream and the diffusing annular jet.
The Reynolds stresses which are directly related to the
velocity gradients have a magnitude proportional to the velocity
gradient. The turbulent shear stresses in the radial and in the
tangential planes show two maximum positive values and two
minimum negative values. These correspond to the maximum gradients
of the velocity profile and are found both in the region of the
free stream and in the region of the diffusing jet.
1. The Region of the Free Stream Annular Jet
Reynolds stresses or the turbulent shear stresses in the
radial and tangential planes are presented in Figure s 13 and 14
respect i vely. The gene ral cha r act e ri s t i cs shown by the Reyno l ds
stresses in the two planes are similar. The large magnitudes
correspond to the high shear regions of the wake and of mixing .
Mean veloc ity charac t e r i st i cs show l a r ge gradi ents at the s e
locations. Reynolds stresses in the radial and tangential planes
diminish just as the velocity gradients reduce downstream of the
flow.
+.0075
+.0050
+.0025
-.0025
-.0050
-.0075
+.0075
+.0050
+.0025
.0000
-.0025
-.0050
-.0075
-3.0
Figure 13.
-2.0 -1.0
I I
1 0.0
r/D
1.0
i' ,, ,, " " .
25
+.0075
+.0050
+.0025
Z/D = .375
-.0025
-.0050
-.0075
Reynolds Stresses in the Radial Plane in the Region of the Free Stream Annular Jet
o.
-3.0
Figure 14.
-2.0 -1.0 0.0
r/D
26
1.0 2.0
Reynolds Stresses in the Tangential ]?lane in the Region of the Free Stream Annular Jet
3.0
27
In the regions of r/D < 0.5, the profiles of the free
stream and diffusing regions shows two maxima of very small order
and of opposite sign. This is in agreement with the gradients
of the mean velocities in this region. This characteristic
terminates at Z/D = 1.0, as the high magnitude Reynolds stresses
of the outer skirt of the wake diffuse into the center of the
wake.
Reynolds stresses in the free stream region are very small,
because of the small turbulences in t h e region. Turbulent shear
stresses in the outer regions of the wake are higher than the
turbulent shear stresses due to mixing until Z/D = 0.375, but
become more or less equal at Z/D = 1.0. The maxima of the Reynolds
stresses due to turbulent mixing shift slightly outward radially ,
whereas in the wake, the same shift inward. Turbulent shear
magni tudes due to mixing show a small radial spread as do the
turbulent intensities and the mean velocity characteristics.
2. The Region of the Diffusing Annular Jet
Reynolds stresses in the r adial and in the tangential planes,
just as the mea n velocity and turbulence characteristics, diffuse
into the mixing r egion and i nto the wake. The pattern of
Reynolds stresses shown in the radial and in the tangential
planes is similar with one positive and one negative maximum
in both the mixing and the wake regions. These magnit udes
have reduced significantly in the diffusing region with the
result that the Reynolds stresses due to mixing and the wake
have reduced to 15 percent and 10 percent, respectively, at
Z/D = 10 .0 in comparison with these intensities at Z/D = 0.125.
28
Scale 2/10 ths. the Scale of the Free Stream Graphs
-.0010
- 1-l ::l N 0
- N ::;J ::l
+.0015
+.0010
+.0005
.0000
-.0005
--.0010
-.0015
-3.0
Figure 15.
= 10.0
= 3.0
-2.0 -1.0 o.o r/D
0
1.0
+.0015
+.0010
+. 0005
Z/D :: 6.0
-.0005
-.0010
-.0015
2.0 3.0
Reynolds Stresses in the Radial Plane in the Region of Diffusing Annular Jet
29
+.0015
Scale 2/10 ths the Scale of the Free Stream Graphs
-.0015
~ <D ::l N 0
~ N 0 ::l
+.0015
+.0010
+.0005
.0000
-.0005
-.0010
-.0015
-3.0
Figure 16.
-2 .0 -1. 0
' ' ,o \ 0
' I \ 0 \
0
0
o.o r/D
\
I
o' D\
1.0
+.0015
+.0010
+.0005
Z/D = 6.0
-.0005
-.0010
-.0015
2 .0 3 .0
Reynolds Stresses in the Tangential Plane in the Region of the Dif f using Annular Jet
30
Reynolds stresses due to mixing are higher than the Reynolds
stresses due to the wake at Z/D = 3.0 and 6.0, but become nearly
equal at Z/D = 10.0.
The Reynolds stresses due to mixing relates well with the
velocity gradients in this region. The influence of the wake
has reduced greatly and the velocity gradients and the Reynolds
stresses in the wake region lead to the conclusion that the
turbulence in the wake has not completely dissipated even at
Z/D = 10.0.
3. General Comments
The analysis of the Reynolds stresses and the velocity
gradients shows that the Reynolds stress is a measure of the
velocity gradient. Corresponding to a zero velocity gradient, the
Reynolds stress profile passes through a zero magnitude.
As the mean flow and the turbulence characteristics diffuse,
the Reynolds stress intensities also spread radially into the
region of mixing and the region of the wake, showing similar
characteristics in the radial and tangential planes. Reynolds
stresses in the tangential plane are higher in the region of
the free stream annular jet, whereas the Reynolds stresses of
the radial plane are higher in the region of the diffusing
annular jet. Shear stresses of the wake show more reduction
in intensity downstream of the flow than the shear stresses
due to mixing, suggesting more dissipation of turbulence in
the wake.
The Reynolds stresses in the mixing region reduce in magnitude
and spread radially as have been observed by Sami (4) for jet
31
mixing. For the wake behind a disk, the peak value of the
Reynolds stresses increases till Z/D = 2.0 and then decreases.
This phenomenon and the inward spreading of Reynolds stress
intensities downstream of the flow observed by Carmody (9)
are not seen in the results of this investigation. This is
attributed to the fact that the wake studied by Carmody (9)
is submerged in the flow in a tube, unlike the free jet under
investigation here.
32
IV. CONCLUSIONS
Based on the experimental data obtained from measurements
in the annular jet, the following conclusions can be reached.
1. High turbulence intensities and Reynolds stresses are
associated with large velocity gradients.
2. The axial component of turbulence is approximately
twice as large as the turbulence components in the
radial and tangential directions. Turbulence intensities
in the radial and tangential directions are of the
same order of magnitude.
3. Positive turbulent shear stress corresponds to a positive
velocity gradient.
4. Two distinct flow regimes can be observed:
i. The free stream jet regime where the maximum jet
velocity remains constant in magnitude.
ii. The diffusing jet regime where the jet velocity
is decreasing.
5. In the free stream jet regime, higher turbulence intensity
and higher shear stress occur in the inner region where
the annular jet interacts with the wake, in comparison
with those in the outer region where the annular jet
interacts with the quiescent air.
6. In the diffusing jet regime, higher turbulence intensity
and higher turbulent shear occur in the outer mixing
region in comparison with the inner wake region.
33
7. The turbulence due to the interaction of the annular
jet with the wake dissipates rapidly, whereas the
turbulence due to the mixing of the annular jet with
the atmospheric air sustains itself to a greater extent.
34
V. BIBLIOGRAPHY
1. Chigier, N. A. and Beer, J. M. (1964), "Velocity and StaticPressure Distributions in Swirling Air Jets Issuing from Annular and Divergent Nozzles," Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, No. 4, December, p. 788-796.
2. Chigier, N. A. and Beer, J. M. (1964), "The Flow Region Near the Nozzle in Double Concentric Jets," Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, No. 4, December, p. 797-804.
3. Bradshaw, P., Ferris, D. H. and Johnson, R. F. (1964), "Turbulence in the Noise-Producing Regions of a Circular Jet," Journal of Fluid Mechanics, Vol. 19, August, p. 591-624.
4. Sami, S. (1966), ''Velocity and Pressure Fields of a Diffusing Jet," Ph.D. Dissertation, University of Iowa, 99 p. (with 50 figures).
5. Curlet, R. and Ricou, F. P . (1964), "On the Tendency of SelfPreservation in Axisymmetric Ducted Jets," Journal of Basic Engineering, Vol. 86, December, p. 765-776.
6. Heskestad, G. (1965), "Hot-Wire Measurements in a Plane Turbulent Jet," Journal of Applied Mechanics, December, p. 721-734.
7. Lee , S. (1965), "Axisymmetrical Turbulent Swirling Jet," Journal of Applied Mechanics, June, p. 258-262.
8. Naudascher, E. (1965), "Flow in the Wake of Self-Propelled Bodies and Related Sources of Turbulence," Journal of Fluid Mechanics, Vol. 22, Part 4, p. 625-656.
9. Carmody, T. (1964), "Establishment of the Wake Behind a Disk, "Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, No. 4, December, p. 869-882.
10. Pepper, D. w. (1970), "Turbulent Structure in the Wake of a Sphere," M. S. Thesis, Universit y of Missouri-Rolla.
11. Chevray, R. (1968), "Turbulent Wake of a Body of Revolution," Journal of Basic Engineering, June , p. 257-284.
12. Townsend, A. A. (1947), "Measurement in the Turbulent Wake of a Cylinder ," Proceedings of the Royal Society, London, Series A, Vol. 190, p. 551-561.
13. Cooper, R. D. and Tulin, M.P. (1955), ·~urbulence Measurements with the Hot-Wire Anemometer," North Atlantic Treaty Organization Advisory Group for Aeronautical Re search and Development.
35
14. DISA (1969), "Instruction and Service Manual for type SSDOl Anemometer Unit."
15. Gibson, M. M. (1962), "Spectra of Turbulence in a Round Jet," Journal of Fluid Mechanics, Vol. 15, February, p. 161-173.
16. Hinze, J. 0. (1959), Turbulence, McGraw-Hill.
17. Lee, S. C. and Harsha, P. T. (1970), "Use of Turbulent Kinetic Energy in Free Mixing Studies," AIAA Journal, Vol. 8, No. 6, June, p. 1026-1032.
18. Keffer, J. F. (1965), "The Uniform Distortion of a Turbulent Wake," Journal of Fluid Mechanics, Vol. 22, Part 1, p. 135-159.
19. Schlichting, H., (1968), Boundary Layer Theory, 6th Edition, McGraw-Hill.
36
VITA
The author, George Philip, was born on January 29, 1944
in Kottayam, Kerala, India. He graduated from the C.M.S. High
School, Kottayam, India in Harch 1960. He entered the College
of Engineering, Trivandrum, India in June 1961. He received
the degree of Bachelor of Science in Hechanical Engineering
in 1966.
He enrolled in the Graduate School of the University of
Hissouri - Rolla in June 1970, for the degree of Master of
Science in Hechanical Engineering.
37
APPENDIX A: AXISYMMETRIC TURBULENCE EQUATIONS
Since the experiment deals with an axisymmetric flow
problem, which can be described most conveniently in terms
of cylindrical co-ordinates, it is important to consider the
conservation of momentum and energy equations in cylindrical
co-ordinates.
Let Ur' u8 , and U2 be the velocity components in the
directions of the three cylindrical co-ordinates r, 8 , and z.
The equation for the conservation of mass is
~ + a t +
u r
p r + 1 + r
0
The equations of motion in the three co-ordinate directions
for constant viscosity are
r - direction:
cu U~2) aP Pd/ = + ar
)..1 ('iu8 u8
+ 2 r
8 - direction:
+ +
1 - )..I 3
2 2
r
2 2
r
a-r a;
au8) + F ae r
au ) a8r +
z - direction:
where,
dU z
p dt =
d dt
T =
=
a at
au r
ar
+
ap az
+
+
u r
r
1 aT -)J 3 dZ
r
1 d + -;a;
+
d ae +
au z
az
+ F z
The Reynolds equations of motion for turbulent flow
may be obtained by substituting for p , P, Ur, u8 , U2
p = p + p
p = p + p
u u + u r r r
ue = ue + ue
u = u + u z z z
38
An important assumption is made here, before carryi ng out
the averaging procedure. The flow under examination is well
below the sonic speed and hence may be considered incompressible.
The resulting simplified equations are:
r - direction:
P(d~r _ u82) = dt r
(Jp
Clr
- rP ~r (r urz) - _p_ L -u u 0 r ae r 8
e - direction:
p (J 2 --- u r ae e
z - direction:
ap 2-+ fl lj u
dZ Z
The shear components are:
rr8 :J ('us ar +
r = u eur zr · a z
rez (' u
fl rCl ~
(J p-;;,- u u
o r z z
au r -a 8
+ d uz) j r
+ a u8 ) 3 z
ur _ ~ au8 ) - 2 2 a8
r r
+ F r
2p -- + - u u r 8 r
QE_ r ar
~s) p uru8
p u u r z
- p u8uz
39
40
p u u8 , p u u and p u8u are known as Reynolds stresses. r r z z
The energy equation for axisymmetric incompressible flow
is derived by Sami (4) and Naudascher (8); and is not attempted
here.
41
APPENDIX B: INSTRUMENTATION
Figure 17 shm.rs the scheme of instrumentation for the
measurements with the X-wire probe. The following equations
were used to calculate the turbulence components.
w~ere,
u z
--= u
u r
u
u u and, z r
uz
.707 2S
.707 2S ~("A- eB/
RAB GA GB
4S 2
are the turbulences
U - the axial mean velocity
-1 u
u -1
u -2
eA, e8 are the bridge output voltages
of channels A and B
R - the reading on the correlator AB
GA, G8 - the attenuator settings
and the sensitivity, s v 4U
Vo and V are the D.C. output voltages corresponding to the
zero and the axial mean velocities. The equations correspond
for the tangential plane.
1. Calibration
To normalize the turbulences and the Reynolds stresses
~obe a::=;-
Flow
3, 1, ~. ' 2' 3. I I I l
eB ~ .. •- 4. I
eA r-
1. SSDOl Anemometer
2. SSD25 Auxiliary Unit 5 ls eA + eB eA - eB
3. 55D30 Digital Voltmeter
4. 55D70 Correlator
5. 55D35 IU,.!S Voltmeter
Figure 17. Scheme for DISA Instrumentation with an X-Wire Probe.
"'-Read RAB
~ N
43
I I I I I 2 I I 2 to u /Uo, u /Uo, u8 /Uo, u u /Uo , u2 u8 /Uo , the mean axial z r z r
velocity U at each measuring point had to be known. The
teclmique employed is to calibrate the D.C. output voltage to
the axial velocity. ru is plotted against the bridge voltage
as shown in Figure 18 and the points lie approximately on a
straight line. The equation to this line was found by the
least square technique and was used in the computer program
for the calculation of mean velocities, turbulences and
Reynolds stresses.
2. Pressure Measurement
The stagnation pressure had to be measured for the purpose
of calibrating the X-wire probe. A pitot probe and a manometer
were employed to find the stagnation pressure of the jet. The
velocity was calculated, knowing the difference in heights of
water columns in the manometer. A pressure gauge connected
to the plenum chamber gave this pressure approximately.
The jet velocity Uo, was calculated from the relation,
where,
Uo U*
= M 61 ) 12 X 32.2
r-1 r
M = the Mach number
U* = sonic velocity of air
r = ratio of specific heats
~L manometer reading in inches
3. Single Wire Measurement
- 1] • 2 r-1
Measurements using single wire probe and DISA 55D01
anemometer and instrumentation, served the purpose of checking
44
~ 0 . 0
I r-1
:>
I
J aJ b
!)
"' 0
.u
I
r-1
0 0
' 0 :> Q
) tJj)
"'J ......
i 0
)...< ;tl
0 i co
~~ c:: 0
•rl .u
ell )...<
..n ...... r-1 ell
0 u
\0
aJ )...< ...... :3:: I X
__
j ____ __
j_ __ l ___ _L
_
0 If'\
0 0
0 0
0 0
0 0
0 0
0 0
::0 r-1
0 0
'\ ·"Xl
r-.. \0
lf'\
-s ('"')
N
r-1 0
.~
r-1 r-1
Cl)
~
)...<
;:l t>O
...... ~
45
the results obtained by the X-wire measurement scheme. Ti1e mean
velocities and turbulence intensities in the axial direction
are obtained from one traverse of the single wire probe at Z/D 1. 0.
Table I shows the comparison of these results with the corres
ponding results from the main experiment.
46
TABLE 1.
Comparison of Results by X-wire and Single wire Measurements
r/D ~1ean Velocity Axial Component of Turbulence
a. b. c. a. b. c .
0.000 . 5242 .4884 . 5456 . 0377 5 .03651 . 04097
0.125 .5654 . 5405 .6436 .04720 .04646 . 05128
0.250 . 71 7~ .7655 .8221 . 05238 .05647 . 06110
0.375 .9140 .9903 . 9502 .03842 . 03778 .04279
0.500 1. 0015 1.0184 .9950 .00841 .00756 • 00925
0.625 1. 024 0 1. 0240 1.0132 . 00404 .00258 . 00467
0.750 1. 0015 1. 0240 1. 0041 .00258 .00161 .00233
0.875 .9737 1. 0184 .9860 .00155 .00013 .00058
1. 000 .9792 1. 0184 .9770 .00312 . 00241 .00286
1.125 .9682 1. 0184 . 9680 . 01314 .01480 . 01594
1. 250 .5041 .7655 . 6582 . 02833 . 03464 . 03554
1. 375 . 2971 .2880 .3153 . 02113 .02030 .02338
1. 500 .1221 .1445 .1478 . 00676 .00879 .00707
1. 625 .0690 .1201 .1089 .00210 .00373 .00399
1. 7 50 . 0619 .1182 .0889 .00109 .00184 . 0014 9
2 .000 .0551 .1069 .1059 .00065 .00096 . 00098
2 . 500 .0184 .0797 . 0550 . 00014 .00047 . 00050
3.000 .0144 . 0633 .0316 .00009 .00029 . 00039
(Cant inued)
Note : a . Radial Orientat i on of the X-wire Probe b. Tangential Orientation of the X-'>-l ire Probe c. Single Wire
47
-r/D Mean Velocity Axial Component of Turbulence
a. b. c. a. b. c .
0.125 . 5446 . 5242 .6148 .04480 .0424 7 .04907
0.250 .6986 .7895 .6986 .04829 .04889 . 05969
0.375 .9247 .9518 . 9680 . 03654 .03815 • 04098
0.500 .9848 .9903 1. 0014 • 007 52 . 01180 . 00930
0.625 . 9959 1. 0127 .9950 . 00427 .00304 .00428
0.750 1.0127 1. 0240 .9950 . 00144 .00242 . 00220
0.875 .9848 1. 0212 .9905 .00078 .00161 .00092
1.000 1.0071 1.0184 .9842 .00175 . 00321 • 00529
1.125 9518 1.0015 .9680 . 01144 . 01366 .01252
1. 250 .4845 .7655 . 6805 . 0279 5 .03978 . 02972
1. 375 .1877 . 3646 . 2855 . 01415 .02512 .01871
1.500 .0750 .1466 .1089 .00446 .01193 . 00598
1. 625 . 0647 .0813 .0916 .00182 . 00281 . 0021 2
1.750 .0463 .0633 .0709 .00080 .00149 . 00132
2.000 .0227 .0633 .0685 .00027 .00089 .00067
2.500 . 0118 . 0487 .0341 .00009 .00036 .00044
J .OOO . 0101 .0320 .0120 .00005 .00059 .00026