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Journal of Applied Mathematics and Physics, 2013, 1, 37-42
Published Online November 2013 (http://www.scirp.org/journal/jamp)
http://dx.doi.org/10.4236/jamp.2013.16008
Open Access JAMP
Effects of Noncircular Inlet on the Flow Struc tures
in Turbulent Jets
Won Hyun Kim, Tae Seon Park
School of Mechanical Engineering, Kyungpook National University, Daegu, South Korea
Email: [email protected]
Received October 2013
ABSTRACT
Turbulent jet flows with noncircular no zzle inlet are investigated by using a Reynolds Stress Model. In order to analyze
the effects of noncircular inlet, the cross section of inlet are selected as circular, square, and equilateral trian gular shape.
The jet half-width, vorticity thickness, and developments of the secondary flow are presented. From the result, it is con-
firmed that the secondary flows of square and equilateral triangular nozzle are more vigorous than that of the circular jet.
This development of secondary flows is closely related to the variations of vortical motions in axial and azimuthal di-
rections.
Keywords: Noncircular Turbulent Jet; Jet Half-Width; Vorticity Thickness; Secondary Flows
1. Introduction
Turbulent jets are primary flow structures in many ap-
plications such as jet pumps, ejectors, jet propuls ions and
combustors etc. In such systems, the higher mixing rate
is very critical for the system performance. So, various
studies have been conducted to get the well-mixed states
for turbulent jets. Among them, non-circular jets have
been widely drawing attention as an efficient method for
mixing flows.
From a literature survey, previous studies were con-
ducted on the turbulent flow of a jet issuing from differ-
rently shaped nozzles [1-5]. From their results, it was
found that the near-field flow of the jet is strongly influ-
enced by the three-dimensional structure dependent on
the loss of axisymmetric nature. From this structure, the
mixing characteristics are improved. However, the de-
tailed flowfields were weakly studied for the change of
inlet nozzle.
Although the flow structures of non-circular jets are
basically similar to the circular jet flow, their mixing
characteristics are quite dif ferent. First of all , at the plane
perpendicular to the main streamwise flow, secondary
flows are generated by the anisotropy of the turbulent
stresses [6,7]. It can serve that the inlet flow has vortical
motions. As the jet flow develops downstream, the inlet
vortical motions are decayed and the vortical flows due
to the circumferential variation of momentum difference
grow. So, the above two factors are strongly related to
non-circular jet flows near the inj ection plane. Such flow
structure can affect the mixing characteristics and turbu-
lent structures. However, unfortunately, the studies for
examining the interrelation b etween the flow mixing and
various vortices are very rare.
In the present study, although various turbulence mod-
els are available for turbulent flows of noncircular jet, a
Reynolds stress model (RSM) is applied. To investigate
the variation of the flow structure depending on the inlet
nozzle, the nozzle cross-section is selected as circular,
square, and triangular. The results are discussed with the
flow mixing and peculiar characteristics of three jet
flows.
2. Numerical Methods
The governing equations for continuity and momentum
are as follows
( )
0
i
i
U
x
ρ
∂=
∂
(1)
( )
ij iij
i ii
UU U
Puu
xxx x
ρµρ
∂∂
∂∂

=−+ −

∂∂∂ ∂

(2)
where Ui, P, μ,
ρ
, and
ij
uu
represent the average ve-
locity, pressure, viscosity, density, and the Reynolds
stress, respectively.
The flow of noncir cular nozzle is v ery anisotropic and
the turbulence-driven flows are primary aspects. In the
present study, a Reynolds stress model is adopted to re-
produce the anisotropic quantities of noncircular jet
W. H. KIM, T. S. PARK
Open Access JAMP
38
flows. The transport equation for the Reynolds can be
written as
( )
k iji
kjij ijij
UD
xuu P
ερ φ
∂=+ ++
∂
(3)
where
ij
D
,
ij
P
,
, and
ij
ε
denote diffusion by tur-
bulent, production, pressure-strain, and dissipation term,
respectively. The RSM model of Launder et al. [8] is
adopted. For simplicity, the details of model functions
are neglected.
The cross-section of inlet nozzle are → is selected as
circular, squ are, and triangular configuration. The cross
sectional area is fixed at the area of circular jet. Figure 1
shows a computational domain according to the experi-
mental condition of Djeridane et al. [9]. The Reynolds
number is 21,000 and the working fluid is selected as air.
In the figure, the length of inlet nozzle is 60De to get a
fully-developed flow. It is longer than the minimum
length of 4.4
1/6
Re
ed
D
[10]. Inlet is prescribed by a uni-
form velocity of Red = 21,00 0. Outlet was applied to
constant pressure boundary condition. The Reynolds
stresses at the inlet is imposed by the assumption of iso-
tropic of turbulence,
23
ij
uu k=
for i = j and
0.0
ij
uu =
for I ≠ j. The turbulent kinetic energy, k, is obtained by k
= 1.5(0.04Uc)2.
The numerical procedure is based on the commercial
CFD software, ANSYS FLUENT 12.0 [11]. The SIMP-
LEC method was applied for the pressure-velocity cou-
pling and the second-order upwind scheme was used for
the convection terms in all transport equations.
Before proceeding further, the grid resolution is tested
for three different mesh sizes. Figure 2(a) shows the
reverse axial mean velocity distribution at the centerline
for three grid resolutions. Here, Uc is the mean axial ve-
locity on the exit plane of inlet nozzle and Uco represent
mean velocity of co-flow stream. The Grid 1, Grid 2, and
Grid 3 have grid points of 200,000, 400 ,00 0, and
800,000, respectively. As can be seen, the difference
between Grid 2 and Grid 3 is minor near the injection
plane. The resolution of Grid 2 is reasonable to predict
the three dimensional flow of turbulent jet. So, the grid
resolution of all cases are → is maintained at about
600,000 points.
Figure 1. Computational domain and different inlet nozzle geometries.
(a) (b)
Figure 2. (a) Comparison of grid resolution (Square jet) (b) present streamwise mean velocity and turbulent intensity distri-
bution along the jet axis (Circular jet); (a) Grid resolution; (b) Experiment and pr esent RSM.
x/D
e
( U
c
-U
co
) / (U-U
co
)
0 4 8121620
0
1
2
3
4
Grid 1(CVs=200,000)
Grid 2(CVs=400,000)
Grid 3(CVs=800,000)
Square Jet
Djeridane et al.
Present(RSM)
X/D
e
( U-U
co
) / (U
c
-U
co
)
u'/U
c
04812 16 20
0
0.2
0.4
0.6
0.8
1
0
0.04
0.08
0.12
Circular Jet
←
←
W. H. KIM, T. S. PARK
Open Access JAMP
39
To validate the present numerical method, the pre-
dicted result of circular jet is compared to the experi-
mental data of Djeridane et al. [9]. The distribution of
mean streamwise velocity and turbulent intensity along
the jet axis is shown in Figure 2(b). The results is → are
good agreement with the experimental data. As a result,
we can consider that the present method is adequate for
describing the flow structure of turbulent jet.
Results and Discussions
To examine the influence of noncircular inlet on the
near-field of jet flows, the variations of the streamwise
velocity normalized by its center value at x/De = 5, 10,
12, and 15 are plotted in Figure 3. As can be seen in the
figure, isolines of U/Uc = 0.5 for square and triangular jet
is broadly positioned at the same axial position. The lines
of triangular jet is → are enlarged far away from the
centerline. It means that the radial developments of
square and triangular jet are faster than that of the circu-
lar jet. From this result , we understand that the flowfields
of noncircular jets have the flow structures depending on
the inlet nozzle configuration. We can expect that non-
circular jets develops → develop three-dimensionally.
This trend is similar to the result of Miller et al. [5] and
Singh et al. [6].
To see the axial evolution of jet flows, normalized
mean velocity contour and the vorticity thicknesses of
three jets and velocity vectors are presented in Figure 4.
In Figure 4(a), the axial developments of square and
triangular jet are faster than that of the circular jet. In
general, the vorticity thickness characterizes the mixing
region. So, it can depict the development of the mixing
region. Here, the vorticity thickness is calculated from
( )
max
w
UdU dr
δ
= ∆
[12]. Here,
U∆
is the differ-
ence between the jet flow and the coflow. The enlarge-
ment of the mixing region for the triangular jet is higher
than those of other two jets. This feature is consistent
with the radial distributions of Figure 3.
Figure 5 shows the radial distributions of pressure at
(a) (b) (c)
Figure 3. Normalized mean velocity contour and jet half-width at the y-z plane for different location at x/De = 5, 10, 12, and 15
(red line: inlet nozzle exit); (a) Circular jet; (b) Square j et; (c) Triangular jet.
0.1
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.6
0.7
0.9
z/D
e
-2
0
2
x/D=12.0
e
0.2
0.2
0.2
0.3
0.3
0.3
0.4
0.4
0.4
0.5
0.6
0.6
0.7
0.8
0.9
x/D=12.0
e
0.2
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.6
0.7
0.8
0.9
x/D=12.0
e
0.3
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.9
y/D
e
-2 02
x/D=15.0
e
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
y/D
e
-2 02
x/D=15.0
e
0.2
0 2
0.2
0.3
0.3
0.4
0.4
0.5
0.6
0.7
0.8
y/D
e
z/D
e
-2 02
-2
0
2
x/D=15.0
e
y/D
e
-1.3 01.3
y/D
e
-1.3 01.3
y/D
e
z/D
e
-1.3 01.3
-1.3
0
1.3
x/D=15.0x/D=5.0,x/D=10.0,x/D=12.0,
ee ee
W. H. KIM, T. S. PARK
Open Access JAMP
40
(a)
(b)
Figure 4. (a) Normalized mean velocity contour (b) Velocity
vector and vorticity thickness in the shear layer at x-y plane;
(a) U/Uc contour; (b) Vorticity t hickness .
Figure 5. Pressure distribution in the radial direction at
x/De = 1, 4, and 10.
x/De = 1, 4, and 10. The flow structure can be interpreted
from the pressure difference. The fluid near the center-
line moves towards the ambient region due to the posi-
tive radial pressure gradient, while the ambient fluid is
entrained to the jet region by the negative pressure gra-
dient. When the velocity of jet stream is larger than the
magnitude of coflow, the jet flows have the roll-up vor-
tices of positive azimuthal direction. As the nozzle con-
figuration becomes noncircular severely, the radial pres-
sure gradient increases more strongly. This can explain
the variation of the jet entrainments
The evolution of jet flows is strongly related to the
variation of the roll-up vortices. The vortices have an
important role for the mixing between jet and coflow. To
see the vortex developments more clearly, streamlines of
the secondary flows at several cross-sections of x/De =
0.0 ~ 10 .0 are displayed in Figure 6. On the injection
plane, the secondary flows except for the circular jet are
observed. The square jet has counter rotating four vortex
pairs and three vortex pairs are seen in the triangular
(a) (b) (c)
Figure 6. Axial evolution of streamlines of secondary flow
for different inlet nozzle geometries (red line: nozzle exit,
blue line: U/Uc = 0.3); (a) Circular jet; (b) Square jet; (c)
Triangular jet.
x/De
y/De
04812 16 20
0
1
2
3
Circular Jet
Square Jet
Triangular jet
x/D =1.0x/D =10.0x/D =4.0
e
ee
x/D =1.0
e
x/D =0.46
e
x/D =0.04
x/D =0.0
e
x/D =0.0
e
z/D
e
-1.2
0
1.2
x/D =0.04
e
x/D =0.04
x/D =0.46
e
x/D =1.0
e
z/D
e
-1.2
0
1.2
x/D =1.0
e
z/D
e
-1.2
0
1.2
x/D =0.46
e
z/D
e
-1.2
0
1.2
x/D =0.0
e
y/D
e
-1.2 01.2
x/D =10.0
e
y/D
e
-1.2 01.2
x/D =10.0
e
x/D =5.0
e
x/D =2.12
e
x/D =2.12
e
x/D =5.0
e
z/D
e
-1.2
0
1.2
x/D =2.12
e
z/D
e
-1.2
0
1.2
x/D =5.0
e
y/D
e
z/D
e
-1.2 01.2
-1.2
0
1.2
x/D =10.0
e
W. H. KIM, T. S. PARK
Open Access JAMP
41
jet. These are driven by the anisotropy of turbulent
stresses. From these results, we can expect that the flow
evolution of the square jet is more three dimensional and
the square jet has a better mixing, because it has many
vortical structures. However, the streamwise velocity of
the triangular jet evo lves much faster. This represents the
weak dependency of the turbulence driven secondary
flows on the enhanced mixing. Also, it is supposed that
the jet mixing strongly depends on the roll-up vortices.
The vortex evolutions are coupled the nozzle configura-
tion, because the inflow has the radial and azimuthal
variati ons due to t he n on -circular cross-section.
As can be seen in the figure, the positive radial mo-
tions are observed in the center region, while the ambient
fluid moves to the center region. As a result, two motions
form a line. The line indicates the interface of secondary
flows between the central jet and ambient coflow. Ac-
cordingly, the interface can be used as a parameter
representing the evolution of jet flows. Near the injection
plane, the interface line nearly coincides with the nozzle
cross-section. As the flow develops down-stream, the
interface line becomes a circle. It is because the vortical
structures are declined gradually and the axial flow
spreads out radially.
On the other hand, the changes of the second ary flows
for the square and triangular jet are faster than that of the
circular jet. From a closer inspection of the figure, we
found that the interface lines nearly correspond to the
location of U/Uc = 0.3 regardless of the nozzle shapes. It
is very interesting to explain the development of jet
flows.
To compare quantitatively the magnitudes of second-
ary motions, the cross-sectional averaged
22
VW+
for different inlet no zzles are shown in Figure 7. Here, V
and W are the radial and azimuthal velocity, respectively.
22
(1 /)
ec
SAVW dA= +
∫
. The Sec values increase
quickly in the region of x/De < 2.0. Also, the secondary
motions of square and triangular jets are stronger than the
circular jet. As show n in Figure 6, the turbulenc e-driven
secondary flows and the roll-up vortices coexist in the
Figure 7. Axial distribution of Sec for different inlet nozzle
geometries.
region. The region has special characteristics that the
turbulence driven secondary flows are decayed and the
roll-up vortices grow up together. The turbulence-driven
secondary flows are nearly disappeared after x/De ≈ 2.0.
The Sec values are maximized at near the disappearing
position of the turbulence-driven secondary flows. Also,
it is observed that the location of maximum Sec for the
triangular jet is the closest to the inlet plane. This means
that the radial flow structure of the triangular jet is
quickly changed to an asymmetry pattern. Consequently,
the symmetrical flow structure of the noncircular jet is
destroyed more faster. So, the flows of noncircular jets
are more three dimensional that that of the circular jet.
3. Conclusions
To investigate the geometric eff ects on the turbulent flow
structures by different inlet nozzles, numerical simula-
tions were performed for the circular, square, and trian-
gular jets. For th at purpose, the variation of jet half-width,
vorticity thickness, and secondary flows for non-circular
jets were compared with the circular jet.
The jet half-width and vorticity thickness of non-cir-
cular jets developed much faster → faster. Symmetric
vortical structures of the nozzle exit as the flow devel-
oped downstream, they are decayed. And then, the sec-
ondary motion related to the difference between jet and
coflow grows up downstream. From the results, the thr ee
dimensional development of the triangular jet is more
stronger than those of other jets. Finally, it was found
that the interface lines of secondary flows between the
central jet and ambient coflow nearly correspond to the
location of U/Uc = 0.3 regardless of the nozzle shapes.
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Open Access JAMP
42
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