- Email: [email protected]
The effect of aspect ratio on the near-field turbulent structure of elliptic jets
The effect of aspect ratio on the near-field turbulent structure of elliptic jets Sang-Joon Lee and Seung-Jo Baek Department of Mechanical Engineering and Advanced Fluids Engineering Research Center, Pohang University of Science and Technology, Pohang, 790600, Korea Revised 20 January 1994 The near-field turbulent structures of elliptic jets issuing from sharp-edged elliptic slot nozzles were experimentally investigated using a 3D LDV system. To examine the effect of the slot aspect ratio on the flow characteristics of the elliptic turbulent jet, we have used elliptic slot nozzles with aspect ratio AR -= a/b = 1, 2, 4, 8 having the same equivalent diameter (D e = 2 (ab) ~n) of 60 mm; the Reynolds number, based on De, is 4 x 104. An elliptic jet issuing from a sharp-edged nozzle had higher mean streamwise velocity decay rates than a contoured nozzle jet due to the effect of the extremely slender elliptic vortical structure. Also, there was a remarkable difference in the jet spreading rates along the major and minor axes. The effects of aspect ratio on the turbulence characteristics of the elliptic jet were apparent, and in particular the elliptic jet of AR = 2 showed vigorous turbulence characteristics in the near flow fields.
Keywords: aspect ratio; near-field turbulence; elliptic jets
Nomenclature a
b AR By, Bz De q2
Major axis radius of the elliptic nozzle Minor axis radius of the elliptic nozzle Aspect ratio of the nozzle (~ a/b) Jet half-widths on the minor and major planes, respectively Equivalent diameter of elliptic nozzle (=- 2 (ab)1/2) Turbulent kinetic energy (=_ ~(u '2 + v'2 + w'2)lU~)
Ruv Ruw Rvw ReDe &,re,g, U',V',W' ! UC
uL Uc Ue UM U,V,W 170
Reynolds shear stress (~- U'v'/Uie) Reynolds shear stress (-= U'w'/U2e) Reynolds shear stress (~- v'w'/Ug) Reynolds number based o n D e (=-- UeDe/p) Instantaneous velocity components in the X, Y,Z-directions, respectively Fluctuating velocities in the X,Y,Zdirections, respectively Streamwise turbulence intensity on the jet centreline (-= (U'2)l/2/Ue) Local turbulence intensity on the jet centreline (~ (u'2)ln/Uc) Mean streamwise velocity on the jet centreline Nozzle exit velocity in the X-direction Maximum mean streamwise velocity due to the vena contracta effect Mean velocity components in the X,Y,Zdirections, respectively Flow Meas. Instrum., 1994 Volume 5 Number 3
U,V,W VB
v~ Vxy
X Xc XZ, MIN
Y Z
/3 or
Mean velocity components in the X,Y,Zdirections normalized by UM Velocity measured by blue beam Velocity measured by green beam Velocity measured by violet beam Instantaneous velocity projected to XYplane Coordinate in the jet axial direction Axial location of cross-over point Axial location of minimum jet half-width in major plane Coordinate in the jet minor axis plane Coordinate in the jet major axis plane Beam separation angle between violet and green optical axis Standard deviation of velocity
Introduction Due to the enhanced mixing and engulfment of ambient fluid, jet flows have been used in industry as mixing augmentation, fuel injection, heat exchanger, drag and aerodynamic noise reduction devices. For the purpose of understanding the jet flow, a wide variety of turbulent jets (especially two-dimensional or axisymmetric jets) have been experimentally studied. In particular, the evolution and mutual interaction of the large-scale structures in the free shear flow play a key role in the shear layer turbulence, entrainment and mixing 0955-5986/94/030170-11
© 1994 Butterworth-Heinemann Ltd
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
processes. Experimental evidence reveals that the evolution of large coherent structures plays a key role in mass entrainment and turbulence characteristics in the flow. In recent years, three-dimensional jets, such as elliptic, rectangular, square and cruciform jets, have been used as an effective passive technique to control mixing and entrainment. Among these, elliptic jets have wide engineering applications and have general features between those of axisymmetric (round) and plane jets. Since several kinds of characteristic length scales, including the curvature variation along the nozzle perimeter, are imposed on the initial elliptic nozzle geometry, the flow characteristics of elliptic jets are quite different from those of two-dimensional or axisymmetric jets. The entrainment rate of elliptic jets is several times greater than that of circular or plane jets. The jet spread in the plane of the minor axis is much greater than along the major plane. The jet crosssection eventually switches its orientation at some distance downstream from the nozzle due to the difference in the spreading rate along the two symmetric axis planes. ~ Gutmark and Ho 1,5,Ghave investigated the coherent structure of elliptic jets having a contraction nozzle of aspect ratio AR = 2. They observed flow phenomena such as necking, bending and merging of the elliptic vortex ring. They also found that the elliptic jet had a higher entrainment rate than that of a round jet. This was due to the self-induction caused by the vorticity distributed on an asymmetric contour and by the azimuthal deformation and interference of elliptic vortex ring pairs. Quinn 7 has found that an elliptic jet (orifice type nozzle) with AR = 5 has a greater entrainment rate than that of a round jet and axis switching occurs twice within the measurement range. In general, the flow characteristics of free shear flows depend strongly on the nozzle geometry and initial flow conditions. 8,9 Hussain and Husain ~ have investigated the effects of initial conditions, nonuniformity of momentum thickness along the nozzle exit perimeter, aspect ratio and excitation on the development of elliptic jets (and coherent structure) having contoured elliptic nozzles of AR = 2 and 4. In order to investigate the effect of aspect ratio on the development of the elliptic jet, they have also studied an orifice-type nozzle jet in which the initial shear layer has virtually zero momentum and thickness and no noticeable azimuthal variations. However, they measured the turbulence intensities only along the jet centreline and jet spreading rates along the major and minor axes by using hot-wire anemometry. Among the non-linear interactions of coherent structures, pairing plays an important role in the dynamics of coherent structure and in the large-scale engulfment. Husain and Hussain ~° have studied the mechanism of pairing events occurring in the excited elliptic jet (contoured-type nozzle with AR = 2) by using the phase-locked measurement technique. Using appropriate control of the coherent structure one could increase the mixing and engulfment of ambient fluids. The control of the coherent structure may be divided into active and passive control. While the former uses an external energy, such as excitation,
the latter controls a flow by using the variation of nozzle initial conditions or nozzle geometry, and so on.
To improve the jet efficiencies with passive control, the flow characteristics of jets with respect to the geometry of the jet slot nozzle should be understood. It was known that the sharp-edged slot nozzle increases the entrainment and mixing more effectively by controlling the coherent structure of the elliptic jet in the near fields compared with the contoured-type one. The use of sharp-edged slots has the additional merits of rapid manufacturing and easy installation. In the present study, the turbulence characteristics of elliptic jets from sharp-edged elliptic slot nozzles were investigated experimentally using a three-component LDV system. We put an emphasis on the effect of the nozzle aspect ratio on the flow characteristics of the elliptic jet in the near field.
Experimental apparatus and procedure A blow-down type wind tunnel, which had a 9:1 contraction ratio, 0.1% uniformity of longitudinal velocity and 0.6% maximum turbulence intensity, was used in this experiment. The sharp-edged elliptic slot nozzle was attached at the downstream end of the contraction. Four slot nozzles of different aspect ratios AR ~ b/a = 1, 2, 4 and 8 were used in this study, where a and b are the radii of the major and minor axes of the elliptic nozzle, respectively. They have the same equivalent diameter (De ~- 2 (ab) lj2) of 60 mm and are manufactured from brass plate (4 mm thickness) by a CNC machine. Schematic diagrams of a typical sharp-edged elliptic slot nozzle and its coordinate system are shown in Figure 1. Throughout the experiments the exit velocity Ue was maintained at 10 m s-1, giving a Reynolds number, based on the equivalent diameter, of 4 x 104 . To ¥{V}
Z{W} •
t
[Unit : mm] AR
a
1
30.0
30.0
2 4 8
42.4 60.0 84.9
21.2 15.0 10.6
b
t
4.0
Figure I Schematic of the sharp-edged elliptic nozzle and coordinate system Flow Meas. Instrum., 1994 Volume 5 Number 3
171
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
check the nozzle exit conditions, we have used a pitot tube and a hot-wire anemometer. Figure 2 shows the mean velocity and turbulence intensities along the major and minor planes measured at the jet nozzle exit. The exit velocity profile had a nearly top-hat shape and the streamwise turbulence intensities were within a limit of 1% over the nozzle exit plane (X/De = 0). The mean temperature of the working fluid was 18 °C and was maintained within a range of ---1 °C. The effect of temperature variation on the flow structure was assumed to be negligible. The velocity components of the elliptic jet were measured using a three cotour, three-component laser Doppler velocimeter (3D LDV) system (TSI 9100-12), in which scattered light was collected through the offaxis, backscattering beam collection method (Figure 3). The light source was a 4 W Ar ion laser which was carried into the multi-line mode. Each colour (green, blue and violet) was used to measure a velocity component by the dual beam method. Each colour optical train was equipped with its own light polarization unit, Bragg cell (40 M H z frequency shift) and photomultiplier tube. The beam separation angle (fl) between the green and blue optical paths and the violet one was 30 ° . The effective measurement volume of the LDV system used in this study was approximately 0.08 x 0.08 x 0.17 mm. Originally, the LDV system measured three non-orthogonal velocity components
1.2
I0
20
30
40
50
60
70
80
I
i
l
I
l
I
i
I
[ ~ Frequency , Transmittin~0~ tics [ 4WAr-lonLaser ] I s h i n e~ r t L L Green-BlueO~ticline F~Tq Violei~ -,' Optic \ / \ L~L~ZJ"
& collecting \
mbly ~
\ i
I I/y
I System (X, Y, Z con~ol)
X
iolet : 476.5 nm
Figure 3 Schematic of the 3D LDV measurement system
simultaneously. These non-orthogonal components (VG,Vv, VB) could be resolved into the three orthogonal velocity components (0,~2,@) through a coordinate transformation shown in Figure 4. The transformed orthogonal velocity components are D -
90
0 12
1,0~,
Vv + VG 2 cos(fl/2)
5 r
(1)
10 ~
15 I
20 ,
25
30
1i5
210
215
30
1.0:
0.8
0.8
(D ~0.6
~0.6
0.4
~ A R
= 1
CmmCC AR =
0.4
2
,agnn ,~, AR = 4 ~'~-~-~ AR = 8
0.2
0.2
Major 0.0
i
Plane L
,
v De=60
,
L
mm
i
~ A R
= 1
-----AR
= 8
n n n , ~ n AR = 2 ,',-'-,~-~,,', AR = 4
Minor
Plane
Minor
Plane
0.0
14 1.2
1.2
1.0
1.0
0.8
0.8
1~
0.6
0.6 0.4
0.4 0.2
Major 0,0 0
I~0'
210
Plane JO
0.2
,~ De=60 m m t 410
5i0
60
710
8i0
90
Z(mm)
Figure 2 Flow conditions at jet nozzle exit
172
Flow Meas. Instrum., 1994 Volume 5 Number 3
0.0
5[
10I
Y(mm)
S.-J. Lee and S.-l. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
z
• Viole~ o p t i•c a_l \
Y i'
[]
q
/
/Green / t o p t. i c a l
Ell!pt!c(AR=2,Contoured) Ho & G u t m a r k ( 1 9 8 7 ) Elllptlc(AR=5,0mflce) ] ~uinn[1989 | Round (Contoured) ] ~t ~ .,
l --
50 ~
l o o o o o AR =
l(Round)
| ~
4
AR
=
o
s,t
7
flow
~
a
[] u o
~ ~
[] ~
~ n ~/~
: 2 1 / /. . @ I_' - / i A~ ~ S ~w
.~
: X
/
3
2
4
6
8
10
12
!4
]0
X/De
Figure 5 Mean streamwise velocity decay on the jet centreline
Figure 4 Coordinate transformation of non-orthogonal velocity components (2)
2 sin(fl/2)
(3)
~/= V~
Following the ASME uncertainty analysis, the precision error can be calculated as follows: (50 =
6Vv
;
+
0(16 V ]z
[O& +
\211/2
J
= {0.268 [(6Vv) ~ + (SVG) z] + 0.01 7902(~fl)2} ~/2 (4) 8~
6¢' =
6Vv
error limit: -+0.01 mm) to any desired position by a computer-controlled three-axis traverse. With the high resolution of the traversing system and the small effective measurement volume, the turbulence quantities of the elliptic jet could be measured accurately. LDV measurements were carried out in the XY (minor axis) plane and XZ (major axis) plane at various downstream locations (X/Do = 2,3,5,7), and along the jet centreline up to X/De = 16. At each measurement point, the mean velocities, the turbulent intensities of the three orthogonal velocity components, the Reynolds stress tensors and higher order statistics were obtained.
2
+
Results and discussion = {3.732 [(6Vv) z + (6Vc)~l + 3 . 4 8 2 ~ ( ~ f l ) ~ } ]/~
6¢v = 6VB
(5) (6)
Here 8(VG,Vv, Va) are associated with the uncertainty of each signal processor. In our experimental system, 6(VG,Vv, Va) = -+0.01 m s-~ and 6/3 = -+0.5°; thus, 60/0 --~ 0.2% and 6Q/~ = 1.7% at 0 = ~ = 7 m s-~. At a given spatial location, 3072-9216 velocity data were sampled repeatedly and ensemble-averaged four times. By ensuring that seeding particles accurately follow the flow, the instantaneous velocity of the fluid is measured. The seeding particles used in this study were paraffin oil, which was fed in just upstream of the wind tunnel contraction. To obtain the velocity variance and covariance components, the coincidence time window of the bursttype counter processor (TSI 1990C), which has a clock resolution of -+1 ns, was set to 20/~s. To correct the velocity bias of LDV data, we adopted a method of McLaughlin and Tiederman. ~ LDV data which were out of a preset range (---3~r) were rejected during the statistical processing using an IBM PC-386. Because turbulent shear flows such as the elliptic jet studied in this experiment have highly intermittent regions where large instantaneous velocities are occurring, values above the velocity rejection criterion would result in suspicious data in those regions. However, the bias error attributed to this statistical criterion is relatively small, less than 2%. The 3D LDV system, mounted on a rigid breadboard, was traversed accurately (precision
The decay of the mean streamwise velocity along the jet centreline is shown in Figure 5. The jet axial distance X was non-dimensionalized by the equivalent diameter Do. Here, UM is the maximum value of the mean streamwise velocity on the jet centreline, which results from the vena contracta effect that commonly occurs in orifices and sharp-edged nozzle jets, and Uc is the mean streamwise velocity on the jet centreline. Thus UM = max(Uc(X)) on the jet centreline and the
,%~
U~
[]
° o
o ~ ~
g
~s ooooo
AR =
1
~ z~zzz
AR = AR =
4 8
10
x/b
100
Figure 6 Mean streamwise velocity decay Uc/UM VS. X/b Flow Meas. Instrum., 1994 Volume 5 Number 3
173
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
0.3
UL;U
AAAAA AR = 4 ] ~ AR = 8 l
[Tgf]Z]~ c' ~ : s ~ x
0.2 ~A
2
oo o
~Oo
:'
(a) S t r e a m w i s e [
turbulence
4
6
8
X/De
8
10
i
r--
12
14
i
i
ooooo AR
7
sD~oo
[Z~E I
[]
6
AR AR AR
A ~ ~ m
[]
A~
[]
~
[] ~o o
O
'
o ±
rJar~O "4I~I~I[~I~1~p~~A
A
16
i
=
1
----
2 4
= =
8
OOI.
o
o
1 (b) T u r b u l e n c e (3
4
(
'
S
'
I r,
= =
i 2
AR
=
t
~
AR
'
8
I-:
L ~]
L
2
I
4
,
I
6
, .... I
kinetic ,
8
I
10
,
energy I
12
,
I I
i4
(!
X/De Figure 7 Variation of the streamwise turbulence quantities along the jet centreline: (a) turbulence intensity; (b) turbulence kinetic energy nozzle exit velocity is represented by U e = Uc(X)lx/De=o. In this figure, the results of Ho and Gutmark 1 (contoured elliptic nozzle of AR = 2) and Quinn 7 (orifice type elliptic nozzle of AR = 5), which were fitted using linear regression based on the farfield data, are included for comparison. It can be seen that orifice type or sharp-edged elliptic jets have a larger mean streamwise velocity decay than contoured nozzle jets. The orifice type or
Figure 8 Variation of the local turbulence intensity along the jet centreline sharp-edged nozzle has an extremely thin initial boundary layer, which produces strong azimuthal variations in the induced velocity and large entrainment before the vortical structure is diffused by viscosity 3. The decay of the centreline velocity for round jets is smaller than for elliptic jets in the near field. This implies that the elliptic jets have larger mixing and entrainment effects than round nozzle jets. At the initial stage of the jet development, the centreline velocity decay for AR = 8 is the highest. Since the vortical structure for AR = 8 is very slender near the jet exit plane, the rolled-up vortical structure exerts a great influence on the jet's centre region. In addition to this, ambient fluids are entrained to the jet centre region due to the high self-induced velocity, attributed to the large curvature on the major axis side of the elliptic vortical structure. As a result, in the case of high aspect ratio elliptic jets, the momentum in the jet's centre region decreases at a higher rate in the initial development stage. For X / D e > 6, the mean streamwise velocity decay in the elliptic jet of AR = 2 is much greater than that of round jets and other elliptic jets. In the far field ( X / D e > 14), the mean streamwise velocity for AR = 2,4 decays at a still higher rate than for round jets, but the velocity decay for AR = 8 approaches the value for round jets as X / D e increases. To see the effect of the aspect ratio on the size of the potential core region, the characteristic decay region and the axisymmetric decay region, the jet centreline velocity decay data scaled to the minimum length scale (i.e. minor axis length b) of the nozzle exit are shown
Table 1 Comparison of far-field local turbulence intensities 3
Heskestad (1965) 14 Bradbury (1965) is Gutmark and Wygnanski (1976) 16 Husain (1982) 17 Corrsin and Uberoi (1950) 18 Wygnanski and Fiedler (1969) 19 Husain (1982) 17 Present result
174
i
X/De
4
o
2
intensity
• ' ' . . AR sG~ncJAR AA~±~
I
2
5
,
[]
%o
0.0
~
°~°°°°
A
0.1
X
.....
_
q
[]
U
Type of nozzle
u~
X/Do, X/h
Plane Plane Plane Plane Round Round Round Round, elliptic
0.264 0.209 0.27 0.24 0.22 0.28 0.25 0.223
160 60 120 300 26 40 200 16
Flow Meas. Instrum., 1994 Volume 5 Number 3
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
2
2.2
4
,
.....
2.0
,
10
r
i
,
12
14
i
,
16
I
T
11
,
10
A R = I ~
GDaGoAR=2 I1~ nt A,^,,^,,^,,", AR=4 rrese
/
II
//~//
\~''~''~AR=8 J
fi~///~.~
1.4
\\
1.2
b,
b~
//
/•
,
9
8
-8
7-
- 7 ~::~
6
6 z
4
s~ 4
3-
3
G~
~
, \
/"
//
//
/ /
/
~
0.8 0.6
9
. // •
~1.0
12
12
q
~
l Hussain Husain(1989)
AR=4 AR=8
1.8
8
i
AR~2=
_ _
1.6
6
i
2
",,
1
2 Fitted
line
: Xc/De
=
0.78
AR + 0 . 3 4
0
0.4
L
0.0
L
I
I
I
2
2.2
i
I
I
J
L
I
4 i
I
i
I
L
I
I
l
8
I
I
10 ~
I
12 i
I
AR=2 ] .... _ _ AR=4AR=8
Hussain & Husain(1989)
Du[]na AR=2 /',,^,,^,,~,~ AR=4
Prese
2.0
Figure 10 Location of the crossover point (Xc) and minimum jet half-width (XzM~N)- Solid symbols represent Xc and open symbols represent XzM~N. 0 : present results; I : rectangular (orifice); ~3 ,~¢: rectangular (contoured); 4 • : elliptic (orifice); z ~ : elliptic (contoured); 3 ~ . elliptic (contoured) I
l
6
14 i
0
A s p e c t Ratio(AR)
Major P l a n e
0.2
1
I
1.8 1.6 1.4 1.2
//
"~-~ 1.0 0.8 0.6 04
0.2 0.0
:-~-? ,
0
Minor P l a n e I
2
i
[
4
i
[
6
,
I
,
8
I
10
~
I
12
,
[
,
14
X/De Figure 9 Development of the jet half-width: (a) major plane; (b) minor plane
in Figure 6. From this figure, one can see that the potential core length is about six times the minor axis length, regardless of the nozzle aspect ratio. However, the size of the characteristic decay region increases and the kinematic virtual origin shifts downstream with increasing aspect ratio. The streamwise turbulence intensity (u~ = (U'~)u2/Ue) and the turbulent kinetic energy (q2 _:_ 12 (u '2 + v '2 + W'2)/U2e) along the jet centreline are shown in Figure 7. For AR = 1, 2 and 4, the turbulence intensity distribution shows a gradual initial increase due to the shear layer development resulting from the initial instability wave mode with increasing X/De. On moving downstream, the momentum in the jet core region is transferred to the surrounding shear layers and the instability wave evolves to the toroidal vortical structure. At X / D e ~ 6, due to the breakdown process of the vortical structure (see section 4.5 in ref. 12) vigorous turbulence activity occurs, and thus turbulence
intensity and kinetic energy reach a maximum value. Far downstream, turbulence fluctuations gradually decrease and attain the state of isotropic turbulence due to vorticity diffusion by viscosity. For an AR = 8 elliptic jet, the location of peak turbulence intensity moves t o w a r d ( X / D e ~- 2.2) the jet exit plane due to the minor axis side of the vortical structure located close to the jet centre in the initial development region. Note that the locations having peak turbulence intensity and kinetic energy are found where the mean streamwise velocity has the maximum decay rate. Elliptic jets with AR = 2 show the largest turbulence intensity and kinetic energy value n e a r X / D e ~ 6. From this and the centreline velocity decay, it is considered that elliptic jets of aspect ratio 2 have vigorous turbulence characteristics and strong mixing and entrainment effects compared with the other jets in the near field. It would be expected that there may be a transition process from Iow-AR elliptic jets to high-AR elliptic jets. The local turbulence intensity profiles along the jet centreline, which have been used to confirm a selfsimilarity in the far field, are shown in Figure 8. Far d o w n s t r e a m , X/D e > 14, the turbulence intensities of all elliptic jets studied approach the value (22.3 - 1.4% at X/De = 16) of round jets, and this is consistent with previous results 3 which have been measured in the self-similar region (Table 1). These results indicate that the far field of jet flow is nearly independent of the nozzle aspect ratio. The spreading rates of elliptic jets in the two planes of symmetry (major and minor axes) are shown in Figure 9. The half velocity widths By and Bz are the distances from the jet centreline to the point where the mean velocity in each plane is equal to half of the centreline velocity. The difference in the spread of the elliptic jets between the present study and Hussain and Husain 3 may be due to the different nozzle geometries (i.e. sharp-edged nozzle vs. orifice-type nozzle) and different measurement techniques (i.e. hot-wire and Flow Meas. Instrum., 1994 Volume 5 Number 3
175
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
10
0.0
0.2
0.4
0.6
~ MX ~7
1.0
1.2
1.4
.6
a or Plane AR -- ~
%~ o.a
0.8
ooooo x / D ~
= e
t~Dnt~DX~De = _ _ ~De =
&
0.6
10=% 0.0
0,8
3
0.2
0.2
-
~
-
'
'
'
'
'
1.0
1.2
1.4
1.6
~ I
(~},&
ooooo X / D e
e/
--
qE]GUEJX~De = 3t
\\k
10
0.8
06
06
04
0,4
0,2
0.2
'
'
1.0
'
'
i
i
AR
-
0.0
10
AR =
8
0.8
08
0.6
0.6
0.4
04
0.2
02
°°00
0.8
0.0
08
0.0
0.6
0,6
0.4
1 .o
0.4
nor Plane AR = 2
I-
0.4
O0
0.2
012
o4
o6
os
I
~0
I
~2
I
~4
~6
Z/De
oo
0.0
0.2
0.4
0.6
0 8
1 0
Y/D+
1.2
8
14
Figure 11 Mean streamwise velocity profiles LDV measurement). Because of the asymmetric azimuthal deformation of vortical structures in the elliptic jet, spreading in the minor plane is much greater than in the major plane. The cross-section of the jet eventually switches its orientation at some distance downstream from the nozzle. The jet width in the major plane initially decreases slightly until X / D e = 4 for AR = 2, X/De = 5 for AR = 4 and X / D e = 7 for A R - - 8 , respectively; then it starts to increase. The decrease in the jet width is attributed to the combined effects of vena contracta and the deformation of elliptic vortical structures. It is shown that the elliptic jet with AR = 2 has a larger spreading rate compared with 176
Flow Meas. Instrum., 1994 Volume 5 Number 3
round jets or other elliptic jets. Axis switching occurs twice for AR = 2, but only one axis switch is observed for AR = 4 and 8 in the measurement range of X/De <- 16. The locations of the first cross-over point (Xc) and the minimum jet half-width in the major plane (Xz.M~N) are shown in Figure 10. It is known that the jet spreading rate is a function of the initial conditions, excitation level and nozzle aspect ratio. However, in this study there exists neither excitation nor variation of the initial conditions, and therefore, Xc and XZ,MI N are functions only of the aspect ratio. Therefore Xc and XZ,M~N are linear functions of the nozzle aspect ratio.
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.04 I I l [ l I I
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 014 ~ ~ ~ ~ f i i
Minor Plane AR = 2 ococo X/De = 2
0.10
0.00
u n n o u X/(De A.*,~.*,AXXDe
7" ~ -0.04
= =
3 5
0.06
Plane AR -0.08 [
=
2
oooo o X / D e = 2 DUDDD XZDe 3 ~ *****
0.12 0.04
i
XZDe X/De i
i
0.02
5 7 -002 t
i
i
i
i
i
i
i
0.14 I =
4 0.10
0.04
0.06
-0.08
0.02
-0.12 0.04
0.02 O. 14
.
0.0 02
0
0
~
0.4 0.6 0.8 1.0 12
Z/De
AR
I
0,00
0
~
=
4
0.10
1.4 1.6
002
I
I
I
I
0.0 0 2 0.4 0.6 0.8
I
I
I 0 1.2 1
Y/D
14 6
Figure 12 Mean transverse velocity arofiles
For a given aspect ratio, the ax~s switching for a contraction nozzle occurs further downstream than the sharp-edged elliptic nozzle and this effect is considerable for a rectangular jet issuing from a contoured nozzle. Note that the first crossover point for the orifice-type nozzle jet is consistent with the least squares fitted line of the present study, regardless of the nozzle geometry (elliptic or rectangular). The mean streamwise velocity profiles in the major and minor planes at cross-sections of X/De = 2, 3, 5 and 7 are given in Figure 11. In the major plane, the shear layer shrinks into the jet centre, while along the minor plane the shear layer spreads out widely into
the ambient fluid. In the case of AR = 8, the velocity profile along the major plane at X/De = 2 shows a nearly flat hump shape. This may be caused by the breakdown process through which the slender elliptic vortical structure is divided into sub-structures. It should be noted that in the present study there is no off-axis velocity peak, which has been observed by others. <13 Figure 12 shows the mean transverse velocities, and W, in the minor and major planes, respectively. A negative value of W in the major plane implies that the shear layer tends to shrink towards the jet centre, and the jet half-width initially decreases. Further downstream, W shifts from a negative value to a Flow Meas. Instrum., 1994 Volume 5 Number 3
177
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
8
Major Plane X/De = 2
61
yyP
~,~\
X/De = 2
6 --:--=-c ~ c ~ , ~
AR AR AR
=
1
=
2
=
4
2 0
h
O0 8
J
04
08
,
~
12
,
i
,
i
16
,
_
20
X/De
01 O0 8r
24
=
i 0.4
i 08
i 12
~ , 18
J 20
X/De
3
, 24
= 3 !
6
i6 o
o x
f
i
0 8
i
i
0.4
0.0
08
i
1.2
i
i
1.6
20
24
0 I
i
O0
0.4
i 08
] 2
1.6
= 5
2 0
X/De
24
= 5
6P
s° -
o
x
i
2
1 {3 00
i 0.4
i 08
i 12
i 16
i 2.0
24
81
~
~
~
X/De
=
7
-
X/De = 7
o %
21 O0
04
08
12
16
20
24
Z/Bz
O0
-~1~ 04
08
12
16
! i 20
24
Y/By
Figure 13 Turbulence kinetic energy profiles
positive one. When W becomes nearly zero, the jet half-width in the major plane has a mi_nimum value (see Figures 9 and 10). As expected, V has positive values in the minor plane, which means outward spreading of the elliptic jet. Turbulent kinetic energy distributions in the major and minor plane at each cross-section are shown in Figure 13. At X / D e = 2 , the turbulent kinetic energy q2 of an elliptic jet with AR = 8 has distinct values compared with other elliptic jets because the elliptic vortical structure of AR = 8 is undergoing large azimuthal deformation in this streamwise location. Due to the engulfment of the elliptic jet in the ambient fluid 178
Flow Meas. Instrum., 1994 Volume 5 Number 3
in the minor plane, qZ in the minor plane has a higher value than in the major plane. Note that q2 in the major plane has a wavy distribution; it may be attributed to the breakdown process 12 of the elliptic vortical structure in the neighbouring locations. For small aspect ratio elliptic jets, q2 in the jet centre region has a small value at X / D e = 2 , which is attributed to the presence of a potential core. The turbulent kinetic energy in the centre region of the shear layer (i.e. Z/Bz-~ | and Y/By ~- 1) increases rapidly due to the influence of the rolled-up structures. On moving downstream, q2 for AR = 8 decreases globally, but in the case of elliptic jets with AR = 2 and 4 the turbulent structure still has
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
25!
2.5
Major Plane X/De = 2
20
Minor
~ o x
1.5
~
05
0.5
0.01
00,
= 2
----'-~-2 AR =
1.5
x
Plane
X/De
20
1
L_=:_~ AR : 4
I
05 OO 2.5
,
0
L 0.4
O.8
1.2
16
2.0
5
- - '
I
O0
24
i
I
0.4
I
0.8
~
1.2
a
1.6
I
20
24
25
= 3
X/De
2.0 o~ 1.5
= 3
X/De
20 ~ 15 x ¢:~ 1 0
~o 0.5
0.5
O0
o.o I
-0.5 O0 25
,
~ 0,4
,
i 0,8
,
h 1.2
,
i 1.6
,
L 2.0
24
-0.5 O0 2.5
,
L
0.4
,
J
0,8
,
~
1.2
I
I
16
2.0
X/De
2.0
20
,
2 4'
=
5
"6" o
1.5
0.5
0.5
O0
0.0
0.5 O0 2.5
-(35 0.4
0.8
12
1 6
0.0 2.5
24
20
0.8
1.2
1.6
2.0
X/De = 7
2.0
0.4
2.0
24
X/De = 7
G" o
1.5
x
1.5
0.5
0.0
@.0'
-Off
O0
04
08
1.2
i
i
16
20
24
Z/B~
O0
04
08
12
16
2.0
24
Y/By
Figure 14 Reynolds shear stress profiles a dominant influence. In particular, the turbulent kinetic energy has large values at X/D~ = 5 for AR = 2 and at X/D e = 7 for AR = 4. The location of the peak value of q2 moves from the centre of the shear layer to the jet centre. The Reynolds shear stress profiles, Ruw in the major plane, and Ruv in the minor plane, are shown in Figure 14. The non-dimensionalized Reynolds shear stress Ruw and Ruv are defined by u'w'/Ug and U'v'/U~e, respectively. The other terms, such as Ruv and Rvw in the major plane and Ruw and Rvw in the minor plane are very small compared with Ruw and Ruv in the major and minor planes, respectively. Therefore it is reasonable to suggest that a large portion of the turbulent kinetic energy may be produced via the latter terms. For an elliptic jet of AR = 8, Ruw has
a peak value near Z/Bz ~- 1, where the mean shear strain is maximum, while Ruv has a peak value at Y~ By < 1. At X/D~ = 2, Ruw is nearly zero in the range Z/Bz < 0.8; on the other hand, the turbulent kinetic energy in the major plane is high at the jet centre region. This implies that most of the turbulent kinetic energy is produced by the non-organized random motion in that region. For round and elliptic jets of AR = 2 and 4 the Reynolds stresses Ruw and Ruv have peak values in the regions Z/Bz < 1 and Y/Bv < 1, respectively. This means that most of the transverse momentum transfer in the major and minor planes occurs inside the elliptic jet. For elliptic jets of AR = 2 and 4, Ruw along the major plane has higher values than Ruv. From this, we can see that the energy production of turbulence is more vigorous in the major
Flow Meas. Instrum., 1994 Volume 5 Number 3
179
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
plane compared with the minor plane for elliptic jets with AR = 2 and 4.
The support of the Advanced Fluids Engineering Research Center (AFERC) sponsored by KOSEF is gratefully acknowledged.
Conclusions The near-field flow characteristics of turbulent elliptic jets with four different aspect ratios were studied using a 3D LDV system. The elliptic jets had quite different flow characteristics compared with a round jet. The elliptic nozzle introduced azimuthal variations of the initial vortical structure into the flow, and the emerging elliptic vortical structure was distorted in different ways along the major and minor axis planes. The jet halfwidth along the major plane decreased initially and reached its minimum at a certain distance, before increasing again downstream; however, along the minor plane it increased monotonically. The major and minor axes of the cross-section switched their orientation at X/D e ~ 2, 3.2 and 6.5 forAR = 2, 4 and 8, respectively, due to the self-induction caused by the azimuthal deformation and interference of the elliptic vortex ring pairs. The locations of the axis-switching and the minimum jet half-width in the major plane appeared in the form of linear functions of the nozzle aspect ratio. In the near field, the elliptic jets showed higher entrainment and mixing than round jets. In particular, elliptic jets of AR = 2 had a higher mean velocity decay, turbulence intensity and Reynolds shear stress. Thus, elliptic jets with a small aspect ratio of 2 can be used effectively as a passive control device in engineering applications which need strong mixing and thrust augmentation. In addition, the use of a sharp-edged slot nozzle results in rigorous turbulence activity and strong mixing by producing an intense vortical structure whose core is very slender in the initial nozzle exit plane. Although the present study provides detailed experimental results using a 3D LDV system (it should be noted that most previous studies have used hotwire anemometry, which induces a relatively large uncertainty in highly sheared flow), it is still not complete enough to enable a satisfactory understanding of elliptic jets. Further detailed investigations, such as flow-field survey measurements other than in the major and minor axis planes, are needed to characterize and elucidate the three-dimensional flow structure.
180
Flow Meas. Instrum.,
Acknowledgement
1994 V o l u m e 5 N u m b e r 3
References
1 Ho, C. M. and Gutmark, E. Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet, J. Fluid Mech., 179 (1987) 383-405 2 Husain, H. S. and Hussain, A. K. M. F. Controlled excitation of elliptic jet, Phys. Fluids, 26 (1983)2763-2766 3 Hussain, A. K. M. F. and Husain, H. S. Elliptic jets. Part 1. Characteristics of unexcited and excited jets, J. Fluid Mech., 208 (1989) 257-320 4 Krothapalli, A., Baganoff, D. and Kararncheti, K. On the mixing of a rectangular jet, J. Fluid Mech., 107 (1981) 201-220 5 Gulmark, E. and Ho, C. M. Near-field pressure fluctuations of an elliptic jet, AIAA J., 23 (1985) 354-358 6 Ho, C. M. and Gutmark, E. Visualization of a forced elliptic jet, AIAA J., 24 (1986) 684-685 7 Quinn, w. R. On mixing in elliptic turbulent free jets, Phys. Fluids A, 1 (1989) 1716-1722 8 Hussain, A. K. M. F. and Zedan, M. F. Effects of the initial condition on the axisymmetric free shear layer: effects of the initial momentum thickness, Phys. Fluids, 21 (1978) 1100-1112 9 Hussain, A. K. M. F. and Zedan, M. F. Effects of the initial condition on the axisymmetric free shear layer: effect of the initial fluctuation level, Phys. Fluids, 21 (1978) 1475-1481 10 Husain, H. S. and Hussain, A. K. M. F. Elliptic jets. Part 2. Dynamics of coherent structures: pairing, J. Fluid Mech., 233 (1991 ) 439~,82 11 McLaughlin, D. K. and Tiederman, W. G. Biasing correlation for individual realization of laser anemometer measurement in turbulent flows, Phys. Fluids, 16 (1973)2082-2088 12 Hussain, A. K. M. F. Coherent structures and turbulence, J. Fluid Mech. 173 (1986) 303-356 13 Quinn, w. R. Turbulent free jet flows issuing from sharp-edged rectangular slots: the influence of slot aspect ratio, Exp. Thermal Fluid Sci., 5 (1992) 203-215 14 Heskeslad, G. Hot-wire measurements in plane turbulent jets, Trans. ASME E: J. Appl. Mech., 32 (1965) 721-734 15 Bradbury, L. J. S. The structure of self-preserving turbulent plane jets, J. Fluid Mech., 23 (1965) 31~4 16 Gutmark, E. and Wygnanski, I. The planar turbulent jets, J. Fluid Mech., 73 (1976) 465-495 17 Husain, Z. D. An experimental study of effects of initial and boundary conditions on near and far fields of jet flows, Ph.D. Thesis, University of Houston (1982) 18 Corrsin, S. and Uberoi, M. S. Further experiments on the flow and heat transfer in a heated turbulent air jet, NACA Report 988 (1950) 19 Wygnanski, I. and Fiedler, H. E. Some measurements in the self-preserving jet, J. Fluid Mech., 38 (1969) 557~612
Keywords: aspect ratio; near-field turbulence; elliptic jets
Nomenclature a
b AR By, Bz De q2
Major axis radius of the elliptic nozzle Minor axis radius of the elliptic nozzle Aspect ratio of the nozzle (~ a/b) Jet half-widths on the minor and major planes, respectively Equivalent diameter of elliptic nozzle (=- 2 (ab)1/2) Turbulent kinetic energy (=_ ~(u '2 + v'2 + w'2)lU~)
Ruv Ruw Rvw ReDe &,re,g, U',V',W' ! UC
uL Uc Ue UM U,V,W 170
Reynolds shear stress (~- U'v'/Uie) Reynolds shear stress (-= U'w'/U2e) Reynolds shear stress (~- v'w'/Ug) Reynolds number based o n D e (=-- UeDe/p) Instantaneous velocity components in the X, Y,Z-directions, respectively Fluctuating velocities in the X,Y,Zdirections, respectively Streamwise turbulence intensity on the jet centreline (-= (U'2)l/2/Ue) Local turbulence intensity on the jet centreline (~ (u'2)ln/Uc) Mean streamwise velocity on the jet centreline Nozzle exit velocity in the X-direction Maximum mean streamwise velocity due to the vena contracta effect Mean velocity components in the X,Y,Zdirections, respectively Flow Meas. Instrum., 1994 Volume 5 Number 3
U,V,W VB
v~ Vxy
X Xc XZ, MIN
Y Z
/3 or
Mean velocity components in the X,Y,Zdirections normalized by UM Velocity measured by blue beam Velocity measured by green beam Velocity measured by violet beam Instantaneous velocity projected to XYplane Coordinate in the jet axial direction Axial location of cross-over point Axial location of minimum jet half-width in major plane Coordinate in the jet minor axis plane Coordinate in the jet major axis plane Beam separation angle between violet and green optical axis Standard deviation of velocity
Introduction Due to the enhanced mixing and engulfment of ambient fluid, jet flows have been used in industry as mixing augmentation, fuel injection, heat exchanger, drag and aerodynamic noise reduction devices. For the purpose of understanding the jet flow, a wide variety of turbulent jets (especially two-dimensional or axisymmetric jets) have been experimentally studied. In particular, the evolution and mutual interaction of the large-scale structures in the free shear flow play a key role in the shear layer turbulence, entrainment and mixing 0955-5986/94/030170-11
© 1994 Butterworth-Heinemann Ltd
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
processes. Experimental evidence reveals that the evolution of large coherent structures plays a key role in mass entrainment and turbulence characteristics in the flow. In recent years, three-dimensional jets, such as elliptic, rectangular, square and cruciform jets, have been used as an effective passive technique to control mixing and entrainment. Among these, elliptic jets have wide engineering applications and have general features between those of axisymmetric (round) and plane jets. Since several kinds of characteristic length scales, including the curvature variation along the nozzle perimeter, are imposed on the initial elliptic nozzle geometry, the flow characteristics of elliptic jets are quite different from those of two-dimensional or axisymmetric jets. The entrainment rate of elliptic jets is several times greater than that of circular or plane jets. The jet spread in the plane of the minor axis is much greater than along the major plane. The jet crosssection eventually switches its orientation at some distance downstream from the nozzle due to the difference in the spreading rate along the two symmetric axis planes. ~ Gutmark and Ho 1,5,Ghave investigated the coherent structure of elliptic jets having a contraction nozzle of aspect ratio AR = 2. They observed flow phenomena such as necking, bending and merging of the elliptic vortex ring. They also found that the elliptic jet had a higher entrainment rate than that of a round jet. This was due to the self-induction caused by the vorticity distributed on an asymmetric contour and by the azimuthal deformation and interference of elliptic vortex ring pairs. Quinn 7 has found that an elliptic jet (orifice type nozzle) with AR = 5 has a greater entrainment rate than that of a round jet and axis switching occurs twice within the measurement range. In general, the flow characteristics of free shear flows depend strongly on the nozzle geometry and initial flow conditions. 8,9 Hussain and Husain ~ have investigated the effects of initial conditions, nonuniformity of momentum thickness along the nozzle exit perimeter, aspect ratio and excitation on the development of elliptic jets (and coherent structure) having contoured elliptic nozzles of AR = 2 and 4. In order to investigate the effect of aspect ratio on the development of the elliptic jet, they have also studied an orifice-type nozzle jet in which the initial shear layer has virtually zero momentum and thickness and no noticeable azimuthal variations. However, they measured the turbulence intensities only along the jet centreline and jet spreading rates along the major and minor axes by using hot-wire anemometry. Among the non-linear interactions of coherent structures, pairing plays an important role in the dynamics of coherent structure and in the large-scale engulfment. Husain and Hussain ~° have studied the mechanism of pairing events occurring in the excited elliptic jet (contoured-type nozzle with AR = 2) by using the phase-locked measurement technique. Using appropriate control of the coherent structure one could increase the mixing and engulfment of ambient fluids. The control of the coherent structure may be divided into active and passive control. While the former uses an external energy, such as excitation,
the latter controls a flow by using the variation of nozzle initial conditions or nozzle geometry, and so on.
To improve the jet efficiencies with passive control, the flow characteristics of jets with respect to the geometry of the jet slot nozzle should be understood. It was known that the sharp-edged slot nozzle increases the entrainment and mixing more effectively by controlling the coherent structure of the elliptic jet in the near fields compared with the contoured-type one. The use of sharp-edged slots has the additional merits of rapid manufacturing and easy installation. In the present study, the turbulence characteristics of elliptic jets from sharp-edged elliptic slot nozzles were investigated experimentally using a three-component LDV system. We put an emphasis on the effect of the nozzle aspect ratio on the flow characteristics of the elliptic jet in the near field.
Experimental apparatus and procedure A blow-down type wind tunnel, which had a 9:1 contraction ratio, 0.1% uniformity of longitudinal velocity and 0.6% maximum turbulence intensity, was used in this experiment. The sharp-edged elliptic slot nozzle was attached at the downstream end of the contraction. Four slot nozzles of different aspect ratios AR ~ b/a = 1, 2, 4 and 8 were used in this study, where a and b are the radii of the major and minor axes of the elliptic nozzle, respectively. They have the same equivalent diameter (De ~- 2 (ab) lj2) of 60 mm and are manufactured from brass plate (4 mm thickness) by a CNC machine. Schematic diagrams of a typical sharp-edged elliptic slot nozzle and its coordinate system are shown in Figure 1. Throughout the experiments the exit velocity Ue was maintained at 10 m s-1, giving a Reynolds number, based on the equivalent diameter, of 4 x 104 . To ¥{V}
Z{W} •
t
[Unit : mm] AR
a
1
30.0
30.0
2 4 8
42.4 60.0 84.9
21.2 15.0 10.6
b
t
4.0
Figure I Schematic of the sharp-edged elliptic nozzle and coordinate system Flow Meas. Instrum., 1994 Volume 5 Number 3
171
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
check the nozzle exit conditions, we have used a pitot tube and a hot-wire anemometer. Figure 2 shows the mean velocity and turbulence intensities along the major and minor planes measured at the jet nozzle exit. The exit velocity profile had a nearly top-hat shape and the streamwise turbulence intensities were within a limit of 1% over the nozzle exit plane (X/De = 0). The mean temperature of the working fluid was 18 °C and was maintained within a range of ---1 °C. The effect of temperature variation on the flow structure was assumed to be negligible. The velocity components of the elliptic jet were measured using a three cotour, three-component laser Doppler velocimeter (3D LDV) system (TSI 9100-12), in which scattered light was collected through the offaxis, backscattering beam collection method (Figure 3). The light source was a 4 W Ar ion laser which was carried into the multi-line mode. Each colour (green, blue and violet) was used to measure a velocity component by the dual beam method. Each colour optical train was equipped with its own light polarization unit, Bragg cell (40 M H z frequency shift) and photomultiplier tube. The beam separation angle (fl) between the green and blue optical paths and the violet one was 30 ° . The effective measurement volume of the LDV system used in this study was approximately 0.08 x 0.08 x 0.17 mm. Originally, the LDV system measured three non-orthogonal velocity components
1.2
I0
20
30
40
50
60
70
80
I
i
l
I
l
I
i
I
[ ~ Frequency , Transmittin~0~ tics [ 4WAr-lonLaser ] I s h i n e~ r t L L Green-BlueO~ticline F~Tq Violei~ -,' Optic \ / \ L~L~ZJ"
& collecting \
mbly ~
\ i
I I/y
I System (X, Y, Z con~ol)
X
iolet : 476.5 nm
Figure 3 Schematic of the 3D LDV measurement system
simultaneously. These non-orthogonal components (VG,Vv, VB) could be resolved into the three orthogonal velocity components (0,~2,@) through a coordinate transformation shown in Figure 4. The transformed orthogonal velocity components are D -
90
0 12
1,0~,
Vv + VG 2 cos(fl/2)
5 r
(1)
10 ~
15 I
20 ,
25
30
1i5
210
215
30
1.0:
0.8
0.8
(D ~0.6
~0.6
0.4
~ A R
= 1
CmmCC AR =
0.4
2
,agnn ,~, AR = 4 ~'~-~-~ AR = 8
0.2
0.2
Major 0.0
i
Plane L
,
v De=60
,
L
mm
i
~ A R
= 1
-----AR
= 8
n n n , ~ n AR = 2 ,',-'-,~-~,,', AR = 4
Minor
Plane
Minor
Plane
0.0
14 1.2
1.2
1.0
1.0
0.8
0.8
1~
0.6
0.6 0.4
0.4 0.2
Major 0,0 0
I~0'
210
Plane JO
0.2
,~ De=60 m m t 410
5i0
60
710
8i0
90
Z(mm)
Figure 2 Flow conditions at jet nozzle exit
172
Flow Meas. Instrum., 1994 Volume 5 Number 3
0.0
5[
10I
Y(mm)
S.-J. Lee and S.-l. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
z
• Viole~ o p t i•c a_l \
Y i'
[]
q
/
/Green / t o p t. i c a l
Ell!pt!c(AR=2,Contoured) Ho & G u t m a r k ( 1 9 8 7 ) Elllptlc(AR=5,0mflce) ] ~uinn[1989 | Round (Contoured) ] ~t ~ .,
l --
50 ~
l o o o o o AR =
l(Round)
| ~
4
AR
=
o
s,t
7
flow
~
a
[] u o
~ ~
[] ~
~ n ~/~
: 2 1 / /. . @ I_' - / i A~ ~ S ~w
.~
: X
/
3
2
4
6
8
10
12
!4
]0
X/De
Figure 5 Mean streamwise velocity decay on the jet centreline
Figure 4 Coordinate transformation of non-orthogonal velocity components (2)
2 sin(fl/2)
(3)
~/= V~
Following the ASME uncertainty analysis, the precision error can be calculated as follows: (50 =
6Vv
;
+
0(16 V ]z
[O& +
\211/2
J
= {0.268 [(6Vv) ~ + (SVG) z] + 0.01 7902(~fl)2} ~/2 (4) 8~
6¢' =
6Vv
error limit: -+0.01 mm) to any desired position by a computer-controlled three-axis traverse. With the high resolution of the traversing system and the small effective measurement volume, the turbulence quantities of the elliptic jet could be measured accurately. LDV measurements were carried out in the XY (minor axis) plane and XZ (major axis) plane at various downstream locations (X/Do = 2,3,5,7), and along the jet centreline up to X/De = 16. At each measurement point, the mean velocities, the turbulent intensities of the three orthogonal velocity components, the Reynolds stress tensors and higher order statistics were obtained.
2
+
Results and discussion = {3.732 [(6Vv) z + (6Vc)~l + 3 . 4 8 2 ~ ( ~ f l ) ~ } ]/~
6¢v = 6VB
(5) (6)
Here 8(VG,Vv, Va) are associated with the uncertainty of each signal processor. In our experimental system, 6(VG,Vv, Va) = -+0.01 m s-~ and 6/3 = -+0.5°; thus, 60/0 --~ 0.2% and 6Q/~ = 1.7% at 0 = ~ = 7 m s-~. At a given spatial location, 3072-9216 velocity data were sampled repeatedly and ensemble-averaged four times. By ensuring that seeding particles accurately follow the flow, the instantaneous velocity of the fluid is measured. The seeding particles used in this study were paraffin oil, which was fed in just upstream of the wind tunnel contraction. To obtain the velocity variance and covariance components, the coincidence time window of the bursttype counter processor (TSI 1990C), which has a clock resolution of -+1 ns, was set to 20/~s. To correct the velocity bias of LDV data, we adopted a method of McLaughlin and Tiederman. ~ LDV data which were out of a preset range (---3~r) were rejected during the statistical processing using an IBM PC-386. Because turbulent shear flows such as the elliptic jet studied in this experiment have highly intermittent regions where large instantaneous velocities are occurring, values above the velocity rejection criterion would result in suspicious data in those regions. However, the bias error attributed to this statistical criterion is relatively small, less than 2%. The 3D LDV system, mounted on a rigid breadboard, was traversed accurately (precision
The decay of the mean streamwise velocity along the jet centreline is shown in Figure 5. The jet axial distance X was non-dimensionalized by the equivalent diameter Do. Here, UM is the maximum value of the mean streamwise velocity on the jet centreline, which results from the vena contracta effect that commonly occurs in orifices and sharp-edged nozzle jets, and Uc is the mean streamwise velocity on the jet centreline. Thus UM = max(Uc(X)) on the jet centreline and the
,%~
U~
[]
° o
o ~ ~
g
~s ooooo
AR =
1
~ z~zzz
AR = AR =
4 8
10
x/b
100
Figure 6 Mean streamwise velocity decay Uc/UM VS. X/b Flow Meas. Instrum., 1994 Volume 5 Number 3
173
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
0.3
UL;U
AAAAA AR = 4 ] ~ AR = 8 l
[Tgf]Z]~ c' ~ : s ~ x
0.2 ~A
2
oo o
~Oo
:'
(a) S t r e a m w i s e [
turbulence
4
6
8
X/De
8
10
i
r--
12
14
i
i
ooooo AR
7
sD~oo
[Z~E I
[]
6
AR AR AR
A ~ ~ m
[]
A~
[]
~
[] ~o o
O
'
o ±
rJar~O "4I~I~I[~I~1~p~~A
A
16
i
=
1
----
2 4
= =
8
OOI.
o
o
1 (b) T u r b u l e n c e (3
4
(
'
S
'
I r,
= =
i 2
AR
=
t
~
AR
'
8
I-:
L ~]
L
2
I
4
,
I
6
, .... I
kinetic ,
8
I
10
,
energy I
12
,
I I
i4
(!
X/De Figure 7 Variation of the streamwise turbulence quantities along the jet centreline: (a) turbulence intensity; (b) turbulence kinetic energy nozzle exit velocity is represented by U e = Uc(X)lx/De=o. In this figure, the results of Ho and Gutmark 1 (contoured elliptic nozzle of AR = 2) and Quinn 7 (orifice type elliptic nozzle of AR = 5), which were fitted using linear regression based on the farfield data, are included for comparison. It can be seen that orifice type or sharp-edged elliptic jets have a larger mean streamwise velocity decay than contoured nozzle jets. The orifice type or
Figure 8 Variation of the local turbulence intensity along the jet centreline sharp-edged nozzle has an extremely thin initial boundary layer, which produces strong azimuthal variations in the induced velocity and large entrainment before the vortical structure is diffused by viscosity 3. The decay of the centreline velocity for round jets is smaller than for elliptic jets in the near field. This implies that the elliptic jets have larger mixing and entrainment effects than round nozzle jets. At the initial stage of the jet development, the centreline velocity decay for AR = 8 is the highest. Since the vortical structure for AR = 8 is very slender near the jet exit plane, the rolled-up vortical structure exerts a great influence on the jet's centre region. In addition to this, ambient fluids are entrained to the jet centre region due to the high self-induced velocity, attributed to the large curvature on the major axis side of the elliptic vortical structure. As a result, in the case of high aspect ratio elliptic jets, the momentum in the jet's centre region decreases at a higher rate in the initial development stage. For X / D e > 6, the mean streamwise velocity decay in the elliptic jet of AR = 2 is much greater than that of round jets and other elliptic jets. In the far field ( X / D e > 14), the mean streamwise velocity for AR = 2,4 decays at a still higher rate than for round jets, but the velocity decay for AR = 8 approaches the value for round jets as X / D e increases. To see the effect of the aspect ratio on the size of the potential core region, the characteristic decay region and the axisymmetric decay region, the jet centreline velocity decay data scaled to the minimum length scale (i.e. minor axis length b) of the nozzle exit are shown
Table 1 Comparison of far-field local turbulence intensities 3
Heskestad (1965) 14 Bradbury (1965) is Gutmark and Wygnanski (1976) 16 Husain (1982) 17 Corrsin and Uberoi (1950) 18 Wygnanski and Fiedler (1969) 19 Husain (1982) 17 Present result
174
i
X/De
4
o
2
intensity
• ' ' . . AR sG~ncJAR AA~±~
I
2
5
,
[]
%o
0.0
~
°~°°°°
A
0.1
X
.....
_
q
[]
U
Type of nozzle
u~
X/Do, X/h
Plane Plane Plane Plane Round Round Round Round, elliptic
0.264 0.209 0.27 0.24 0.22 0.28 0.25 0.223
160 60 120 300 26 40 200 16
Flow Meas. Instrum., 1994 Volume 5 Number 3
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
2
2.2
4
,
.....
2.0
,
10
r
i
,
12
14
i
,
16
I
T
11
,
10
A R = I ~
GDaGoAR=2 I1~ nt A,^,,^,,^,,", AR=4 rrese
/
II
//~//
\~''~''~AR=8 J
fi~///~.~
1.4
\\
1.2
b,
b~
//
/•
,
9
8
-8
7-
- 7 ~::~
6
6 z
4
s~ 4
3-
3
G~
~
, \
/"
//
//
/ /
/
~
0.8 0.6
9
. // •
~1.0
12
12
q
~
l Hussain Husain(1989)
AR=4 AR=8
1.8
8
i
AR~2=
_ _
1.6
6
i
2
",,
1
2 Fitted
line
: Xc/De
=
0.78
AR + 0 . 3 4
0
0.4
L
0.0
L
I
I
I
2
2.2
i
I
I
J
L
I
4 i
I
i
I
L
I
I
l
8
I
I
10 ~
I
12 i
I
AR=2 ] .... _ _ AR=4AR=8
Hussain & Husain(1989)
Du[]na AR=2 /',,^,,^,,~,~ AR=4
Prese
2.0
Figure 10 Location of the crossover point (Xc) and minimum jet half-width (XzM~N)- Solid symbols represent Xc and open symbols represent XzM~N. 0 : present results; I : rectangular (orifice); ~3 ,~¢: rectangular (contoured); 4 • : elliptic (orifice); z ~ : elliptic (contoured); 3 ~ . elliptic (contoured) I
l
6
14 i
0
A s p e c t Ratio(AR)
Major P l a n e
0.2
1
I
1.8 1.6 1.4 1.2
//
"~-~ 1.0 0.8 0.6 04
0.2 0.0
:-~-? ,
0
Minor P l a n e I
2
i
[
4
i
[
6
,
I
,
8
I
10
~
I
12
,
[
,
14
X/De Figure 9 Development of the jet half-width: (a) major plane; (b) minor plane
in Figure 6. From this figure, one can see that the potential core length is about six times the minor axis length, regardless of the nozzle aspect ratio. However, the size of the characteristic decay region increases and the kinematic virtual origin shifts downstream with increasing aspect ratio. The streamwise turbulence intensity (u~ = (U'~)u2/Ue) and the turbulent kinetic energy (q2 _:_ 12 (u '2 + v '2 + W'2)/U2e) along the jet centreline are shown in Figure 7. For AR = 1, 2 and 4, the turbulence intensity distribution shows a gradual initial increase due to the shear layer development resulting from the initial instability wave mode with increasing X/De. On moving downstream, the momentum in the jet core region is transferred to the surrounding shear layers and the instability wave evolves to the toroidal vortical structure. At X / D e ~ 6, due to the breakdown process of the vortical structure (see section 4.5 in ref. 12) vigorous turbulence activity occurs, and thus turbulence
intensity and kinetic energy reach a maximum value. Far downstream, turbulence fluctuations gradually decrease and attain the state of isotropic turbulence due to vorticity diffusion by viscosity. For an AR = 8 elliptic jet, the location of peak turbulence intensity moves t o w a r d ( X / D e ~- 2.2) the jet exit plane due to the minor axis side of the vortical structure located close to the jet centre in the initial development region. Note that the locations having peak turbulence intensity and kinetic energy are found where the mean streamwise velocity has the maximum decay rate. Elliptic jets with AR = 2 show the largest turbulence intensity and kinetic energy value n e a r X / D e ~ 6. From this and the centreline velocity decay, it is considered that elliptic jets of aspect ratio 2 have vigorous turbulence characteristics and strong mixing and entrainment effects compared with the other jets in the near field. It would be expected that there may be a transition process from Iow-AR elliptic jets to high-AR elliptic jets. The local turbulence intensity profiles along the jet centreline, which have been used to confirm a selfsimilarity in the far field, are shown in Figure 8. Far d o w n s t r e a m , X/D e > 14, the turbulence intensities of all elliptic jets studied approach the value (22.3 - 1.4% at X/De = 16) of round jets, and this is consistent with previous results 3 which have been measured in the self-similar region (Table 1). These results indicate that the far field of jet flow is nearly independent of the nozzle aspect ratio. The spreading rates of elliptic jets in the two planes of symmetry (major and minor axes) are shown in Figure 9. The half velocity widths By and Bz are the distances from the jet centreline to the point where the mean velocity in each plane is equal to half of the centreline velocity. The difference in the spread of the elliptic jets between the present study and Hussain and Husain 3 may be due to the different nozzle geometries (i.e. sharp-edged nozzle vs. orifice-type nozzle) and different measurement techniques (i.e. hot-wire and Flow Meas. Instrum., 1994 Volume 5 Number 3
175
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
10
0.0
0.2
0.4
0.6
~ MX ~7
1.0
1.2
1.4
.6
a or Plane AR -- ~
%~ o.a
0.8
ooooo x / D ~
= e
t~Dnt~DX~De = _ _ ~De =
&
0.6
10=% 0.0
0,8
3
0.2
0.2
-
~
-
'
'
'
'
'
1.0
1.2
1.4
1.6
~ I
(~},&
ooooo X / D e
e/
--
qE]GUEJX~De = 3t
\\k
10
0.8
06
06
04
0,4
0,2
0.2
'
'
1.0
'
'
i
i
AR
-
0.0
10
AR =
8
0.8
08
0.6
0.6
0.4
04
0.2
02
°°00
0.8
0.0
08
0.0
0.6
0,6
0.4
1 .o
0.4
nor Plane AR = 2
I-
0.4
O0
0.2
012
o4
o6
os
I
~0
I
~2
I
~4
~6
Z/De
oo
0.0
0.2
0.4
0.6
0 8
1 0
Y/D+
1.2
8
14
Figure 11 Mean streamwise velocity profiles LDV measurement). Because of the asymmetric azimuthal deformation of vortical structures in the elliptic jet, spreading in the minor plane is much greater than in the major plane. The cross-section of the jet eventually switches its orientation at some distance downstream from the nozzle. The jet width in the major plane initially decreases slightly until X / D e = 4 for AR = 2, X/De = 5 for AR = 4 and X / D e = 7 for A R - - 8 , respectively; then it starts to increase. The decrease in the jet width is attributed to the combined effects of vena contracta and the deformation of elliptic vortical structures. It is shown that the elliptic jet with AR = 2 has a larger spreading rate compared with 176
Flow Meas. Instrum., 1994 Volume 5 Number 3
round jets or other elliptic jets. Axis switching occurs twice for AR = 2, but only one axis switch is observed for AR = 4 and 8 in the measurement range of X/De <- 16. The locations of the first cross-over point (Xc) and the minimum jet half-width in the major plane (Xz.M~N) are shown in Figure 10. It is known that the jet spreading rate is a function of the initial conditions, excitation level and nozzle aspect ratio. However, in this study there exists neither excitation nor variation of the initial conditions, and therefore, Xc and XZ,MI N are functions only of the aspect ratio. Therefore Xc and XZ,M~N are linear functions of the nozzle aspect ratio.
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.04 I I l [ l I I
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 014 ~ ~ ~ ~ f i i
Minor Plane AR = 2 ococo X/De = 2
0.10
0.00
u n n o u X/(De A.*,~.*,AXXDe
7" ~ -0.04
= =
3 5
0.06
Plane AR -0.08 [
=
2
oooo o X / D e = 2 DUDDD XZDe 3 ~ *****
0.12 0.04
i
XZDe X/De i
i
0.02
5 7 -002 t
i
i
i
i
i
i
i
0.14 I =
4 0.10
0.04
0.06
-0.08
0.02
-0.12 0.04
0.02 O. 14
.
0.0 02
0
0
~
0.4 0.6 0.8 1.0 12
Z/De
AR
I
0,00
0
~
=
4
0.10
1.4 1.6
002
I
I
I
I
0.0 0 2 0.4 0.6 0.8
I
I
I 0 1.2 1
Y/D
14 6
Figure 12 Mean transverse velocity arofiles
For a given aspect ratio, the ax~s switching for a contraction nozzle occurs further downstream than the sharp-edged elliptic nozzle and this effect is considerable for a rectangular jet issuing from a contoured nozzle. Note that the first crossover point for the orifice-type nozzle jet is consistent with the least squares fitted line of the present study, regardless of the nozzle geometry (elliptic or rectangular). The mean streamwise velocity profiles in the major and minor planes at cross-sections of X/De = 2, 3, 5 and 7 are given in Figure 11. In the major plane, the shear layer shrinks into the jet centre, while along the minor plane the shear layer spreads out widely into
the ambient fluid. In the case of AR = 8, the velocity profile along the major plane at X/De = 2 shows a nearly flat hump shape. This may be caused by the breakdown process through which the slender elliptic vortical structure is divided into sub-structures. It should be noted that in the present study there is no off-axis velocity peak, which has been observed by others. <13 Figure 12 shows the mean transverse velocities, and W, in the minor and major planes, respectively. A negative value of W in the major plane implies that the shear layer tends to shrink towards the jet centre, and the jet half-width initially decreases. Further downstream, W shifts from a negative value to a Flow Meas. Instrum., 1994 Volume 5 Number 3
177
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
8
Major Plane X/De = 2
61
yyP
~,~\
X/De = 2
6 --:--=-c ~ c ~ , ~
AR AR AR
=
1
=
2
=
4
2 0
h
O0 8
J
04
08
,
~
12
,
i
,
i
16
,
_
20
X/De
01 O0 8r
24
=
i 0.4
i 08
i 12
~ , 18
J 20
X/De
3
, 24
= 3 !
6
i6 o
o x
f
i
0 8
i
i
0.4
0.0
08
i
1.2
i
i
1.6
20
24
0 I
i
O0
0.4
i 08
] 2
1.6
= 5
2 0
X/De
24
= 5
6P
s° -
o
x
i
2
1 {3 00
i 0.4
i 08
i 12
i 16
i 2.0
24
81
~
~
~
X/De
=
7
-
X/De = 7
o %
21 O0
04
08
12
16
20
24
Z/Bz
O0
-~1~ 04
08
12
16
! i 20
24
Y/By
Figure 13 Turbulence kinetic energy profiles
positive one. When W becomes nearly zero, the jet half-width in the major plane has a mi_nimum value (see Figures 9 and 10). As expected, V has positive values in the minor plane, which means outward spreading of the elliptic jet. Turbulent kinetic energy distributions in the major and minor plane at each cross-section are shown in Figure 13. At X / D e = 2 , the turbulent kinetic energy q2 of an elliptic jet with AR = 8 has distinct values compared with other elliptic jets because the elliptic vortical structure of AR = 8 is undergoing large azimuthal deformation in this streamwise location. Due to the engulfment of the elliptic jet in the ambient fluid 178
Flow Meas. Instrum., 1994 Volume 5 Number 3
in the minor plane, qZ in the minor plane has a higher value than in the major plane. Note that q2 in the major plane has a wavy distribution; it may be attributed to the breakdown process 12 of the elliptic vortical structure in the neighbouring locations. For small aspect ratio elliptic jets, q2 in the jet centre region has a small value at X / D e = 2 , which is attributed to the presence of a potential core. The turbulent kinetic energy in the centre region of the shear layer (i.e. Z/Bz-~ | and Y/By ~- 1) increases rapidly due to the influence of the rolled-up structures. On moving downstream, q2 for AR = 8 decreases globally, but in the case of elliptic jets with AR = 2 and 4 the turbulent structure still has
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
25!
2.5
Major Plane X/De = 2
20
Minor
~ o x
1.5
~
05
0.5
0.01
00,
= 2
----'-~-2 AR =
1.5
x
Plane
X/De
20
1
L_=:_~ AR : 4
I
05 OO 2.5
,
0
L 0.4
O.8
1.2
16
2.0
5
- - '
I
O0
24
i
I
0.4
I
0.8
~
1.2
a
1.6
I
20
24
25
= 3
X/De
2.0 o~ 1.5
= 3
X/De
20 ~ 15 x ¢:~ 1 0
~o 0.5
0.5
O0
o.o I
-0.5 O0 25
,
~ 0,4
,
i 0,8
,
h 1.2
,
i 1.6
,
L 2.0
24
-0.5 O0 2.5
,
L
0.4
,
J
0,8
,
~
1.2
I
I
16
2.0
X/De
2.0
20
,
2 4'
=
5
"6" o
1.5
0.5
0.5
O0
0.0
0.5 O0 2.5
-(35 0.4
0.8
12
1 6
0.0 2.5
24
20
0.8
1.2
1.6
2.0
X/De = 7
2.0
0.4
2.0
24
X/De = 7
G" o
1.5
x
1.5
0.5
0.0
@.0'
-Off
O0
04
08
1.2
i
i
16
20
24
Z/B~
O0
04
08
12
16
2.0
24
Y/By
Figure 14 Reynolds shear stress profiles a dominant influence. In particular, the turbulent kinetic energy has large values at X/D~ = 5 for AR = 2 and at X/D e = 7 for AR = 4. The location of the peak value of q2 moves from the centre of the shear layer to the jet centre. The Reynolds shear stress profiles, Ruw in the major plane, and Ruv in the minor plane, are shown in Figure 14. The non-dimensionalized Reynolds shear stress Ruw and Ruv are defined by u'w'/Ug and U'v'/U~e, respectively. The other terms, such as Ruv and Rvw in the major plane and Ruw and Rvw in the minor plane are very small compared with Ruw and Ruv in the major and minor planes, respectively. Therefore it is reasonable to suggest that a large portion of the turbulent kinetic energy may be produced via the latter terms. For an elliptic jet of AR = 8, Ruw has
a peak value near Z/Bz ~- 1, where the mean shear strain is maximum, while Ruv has a peak value at Y~ By < 1. At X/D~ = 2, Ruw is nearly zero in the range Z/Bz < 0.8; on the other hand, the turbulent kinetic energy in the major plane is high at the jet centre region. This implies that most of the turbulent kinetic energy is produced by the non-organized random motion in that region. For round and elliptic jets of AR = 2 and 4 the Reynolds stresses Ruw and Ruv have peak values in the regions Z/Bz < 1 and Y/Bv < 1, respectively. This means that most of the transverse momentum transfer in the major and minor planes occurs inside the elliptic jet. For elliptic jets of AR = 2 and 4, Ruw along the major plane has higher values than Ruv. From this, we can see that the energy production of turbulence is more vigorous in the major
Flow Meas. Instrum., 1994 Volume 5 Number 3
179
S.-J. Lee and S.-J. Baek - Effect of aspect ratio on turbulence structure of elliptic jets
plane compared with the minor plane for elliptic jets with AR = 2 and 4.
The support of the Advanced Fluids Engineering Research Center (AFERC) sponsored by KOSEF is gratefully acknowledged.
Conclusions The near-field flow characteristics of turbulent elliptic jets with four different aspect ratios were studied using a 3D LDV system. The elliptic jets had quite different flow characteristics compared with a round jet. The elliptic nozzle introduced azimuthal variations of the initial vortical structure into the flow, and the emerging elliptic vortical structure was distorted in different ways along the major and minor axis planes. The jet halfwidth along the major plane decreased initially and reached its minimum at a certain distance, before increasing again downstream; however, along the minor plane it increased monotonically. The major and minor axes of the cross-section switched their orientation at X/D e ~ 2, 3.2 and 6.5 forAR = 2, 4 and 8, respectively, due to the self-induction caused by the azimuthal deformation and interference of the elliptic vortex ring pairs. The locations of the axis-switching and the minimum jet half-width in the major plane appeared in the form of linear functions of the nozzle aspect ratio. In the near field, the elliptic jets showed higher entrainment and mixing than round jets. In particular, elliptic jets of AR = 2 had a higher mean velocity decay, turbulence intensity and Reynolds shear stress. Thus, elliptic jets with a small aspect ratio of 2 can be used effectively as a passive control device in engineering applications which need strong mixing and thrust augmentation. In addition, the use of a sharp-edged slot nozzle results in rigorous turbulence activity and strong mixing by producing an intense vortical structure whose core is very slender in the initial nozzle exit plane. Although the present study provides detailed experimental results using a 3D LDV system (it should be noted that most previous studies have used hotwire anemometry, which induces a relatively large uncertainty in highly sheared flow), it is still not complete enough to enable a satisfactory understanding of elliptic jets. Further detailed investigations, such as flow-field survey measurements other than in the major and minor axis planes, are needed to characterize and elucidate the three-dimensional flow structure.
180
Flow Meas. Instrum.,
Acknowledgement
1994 V o l u m e 5 N u m b e r 3
References
1 Ho, C. M. and Gutmark, E. Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet, J. Fluid Mech., 179 (1987) 383-405 2 Husain, H. S. and Hussain, A. K. M. F. Controlled excitation of elliptic jet, Phys. Fluids, 26 (1983)2763-2766 3 Hussain, A. K. M. F. and Husain, H. S. Elliptic jets. Part 1. Characteristics of unexcited and excited jets, J. Fluid Mech., 208 (1989) 257-320 4 Krothapalli, A., Baganoff, D. and Kararncheti, K. On the mixing of a rectangular jet, J. Fluid Mech., 107 (1981) 201-220 5 Gulmark, E. and Ho, C. M. Near-field pressure fluctuations of an elliptic jet, AIAA J., 23 (1985) 354-358 6 Ho, C. M. and Gutmark, E. Visualization of a forced elliptic jet, AIAA J., 24 (1986) 684-685 7 Quinn, w. R. On mixing in elliptic turbulent free jets, Phys. Fluids A, 1 (1989) 1716-1722 8 Hussain, A. K. M. F. and Zedan, M. F. Effects of the initial condition on the axisymmetric free shear layer: effects of the initial momentum thickness, Phys. Fluids, 21 (1978) 1100-1112 9 Hussain, A. K. M. F. and Zedan, M. F. Effects of the initial condition on the axisymmetric free shear layer: effect of the initial fluctuation level, Phys. Fluids, 21 (1978) 1475-1481 10 Husain, H. S. and Hussain, A. K. M. F. Elliptic jets. Part 2. Dynamics of coherent structures: pairing, J. Fluid Mech., 233 (1991 ) 439~,82 11 McLaughlin, D. K. and Tiederman, W. G. Biasing correlation for individual realization of laser anemometer measurement in turbulent flows, Phys. Fluids, 16 (1973)2082-2088 12 Hussain, A. K. M. F. Coherent structures and turbulence, J. Fluid Mech. 173 (1986) 303-356 13 Quinn, w. R. Turbulent free jet flows issuing from sharp-edged rectangular slots: the influence of slot aspect ratio, Exp. Thermal Fluid Sci., 5 (1992) 203-215 14 Heskeslad, G. Hot-wire measurements in plane turbulent jets, Trans. ASME E: J. Appl. Mech., 32 (1965) 721-734 15 Bradbury, L. J. S. The structure of self-preserving turbulent plane jets, J. Fluid Mech., 23 (1965) 31~4 16 Gutmark, E. and Wygnanski, I. The planar turbulent jets, J. Fluid Mech., 73 (1976) 465-495 17 Husain, Z. D. An experimental study of effects of initial and boundary conditions on near and far fields of jet flows, Ph.D. Thesis, University of Houston (1982) 18 Corrsin, S. and Uberoi, M. S. Further experiments on the flow and heat transfer in a heated turbulent air jet, NACA Report 988 (1950) 19 Wygnanski, I. and Fiedler, H. E. Some measurements in the self-preserving jet, J. Fluid Mech., 38 (1969) 557~612