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SUPPRESSION OF VORTEX SHEDDING AROUND A
SQUARE CYLINDER USING BLOWING
Ankit Shrivastava
Dept. of Mechanical Engineering
Indian Institute of Technology, Kanpur
Kanpur, Uttar Pradesh, India
[email protected]
Abstract
in the past. For a square cylinder kept in a
uniform flow at very low Reynolds number till
1.16, the flow remains laminar, two-dimensional,
and steady and does not separate [1]. As the
Reynolds number is further increased, the flow
starts to separate and but remains steady but twodimensional till a Reynolds number of 47 [2]. The
flow loses its stability and becomes unsteady beyond this Reynolds number. With an increase of
Reynolds number beyond 161, the flow starts to
exhibit three-dimensionality though the shedding
still remains periodic. Thus, the vortex shedding
is a complex phenomenon which depends both on
the type of body and the Reynolds number. Because of unsteady nature of the flow at a relatively
higher Reynolds number, significant drag and lift
fluctuations, acoustic noise and large structural vibrations are encountered. If the natural frequency
of the structure and flow induced oscillation frequency matches, it can lead to catastrophic structural failure. This calls for an in-depth study to
control the wake dynamics so that such structural
damage can be avoided.
Direct numerical simulation (DNS) of flow past
a square cylinder at a Reynolds number of 100
have been used to explore the effect of blowing in
the form of jet(s) on vortex shedding around the
cylinder. Higher order spatial as well as temporal
discretization has been used. The varying number
of jets and different blowing velocities are studied to explore the suppression of vortex shedding.
The parabolic velocity profile has been found to
be more effective in suppressing the vortex shedding as compared to the uniform velocity. Complete suppression of vortex shedding along-with
remarkable reduction in drag has been achieved.
The study also reveals that there is considerable
effect of the number of jets on the vortex shedding
phenomena.
KEYWORDS: Square Cylinder, Vortex Shedding, Jets, Blowing, Suppression
1
Introduction
The bluff bodies like circular cylinders, rectangular prisms, etc. are the most common engineering structural configurations resembling buildings,
bridges, chimneys, cooling towers etc. Engineers
quite often face various flow-induced problems,
in dealing with flow around these bodies, most
common of which include the flow-induced vibrations. The flow induced vibrations arise due to
a very complex phenomenon called Vortex Shedding which has been addressed quite extensively
Zdravkovich [3] primarily classified the methods of flow control into 3 categories as (i) surface protrusions affecting separated shear layers,
(ii) shrouds affecting entrainment layers and (iii)
near wake stabilizers preventing shear layer interaction, on the basis of the mechanism they utilize for flow control. Flow control methods have
also been classified as active and passive methods [4]. The methods that require expenditure
of energy from external sources for flow control
1
are classified under active methods and those that
manage to modify the flow without the expenditure of energy are referred to as passive methods. A variety of passive methods such as surface
modifications with roughness, dimples [5], helical
strakes [6], longitudinal grooves, splitter plate [7],
small secondary control cylinders [8] and dampers
have been devised. Raghavan et al. [9] provided
a very comprehensive overview of all the passive
methods used to control especially vortex-induced
vibrations. Equivalently, there are enormous numbers of active method found to cater to the needs
of flow control such as streamwise or transverse
oscillations of bluff body [10] [11], wall heating
of the cylinder, modifying the local fluid properties [4], steady blowing or suction [12], electromagnetic forcing [13], periodic blowing or suction [14]
and external excitation through actuators. Choi
et al. [15] provides a condensed overview of all the
flow control methods for the suppression of vortex
shedding.
perimental work of Wood [18] in understanding
the effect on wakes due to base bleed gave deep
insights into the subject of control of vortex shedding. He used a two-dimensional brass aerofoil
model with elliptic nose and a parallel rear section
with open rear end. He inferred from the visualizations on a two-dimensional brass aerofoil model
that base bleed leads to increased formation region and elongated shear layers as a result of which
large magnitude of vorticity carried by them is dissipated even before it gets transferred to the growing vortices. This leads to formation of vortices of
strength which is insufficient to cause vortex shedding, which is well in concurrence with the basic
principles of Vortex shedding of Gerrard [16].Also,
Cohen [19] through the use of scaling arguments
put forward an analytical model for predicting
Strouhal frequency in flow around porous circular
cylinders undergoing uniform blowing or suction.
2
o
1 (Reo
His important findings include that Re
Re∞
denotes the Reynolds number in terms of blowing/suction velocity, Re∞ denotes the Reynolds
number of flow at far field) otherwise in-spite of
blowing/suction the cylinder behaves as an impervious body. He predicted a uniform increase
in Strouhal number with suction velocity but it
was later contradicted by several other numerical and experimental studies where it has been
demonstrated that the increase is possible only for
suction velocity below a critical value [25].
Dong et al. [20] addressed the issue of effectiveness of blowing or suction on suppression of
shedding around a circular cylinder at Re = 500
and 1000 using the three-dimensional unsteady
Navier-Stokes equations and came up with a novel
method which they called the WSLB-Windward
Suction and Leeward Blowing method. Their findings suggest that ’suction-only’ is effective in reducing only if it is operated at very high velocities
while low velocities tend to have the opposite effect.
Most of the work evidences focus upon analyzing the effect of uniform blowing or suction on
vortex shedding around porous circular cylinders.
There are very few evidences in literature which
investigate vortex shedding control by blowing or
suction on square cylinders. Fransson et al. [12]
experimentally studied the flow around a porous
In-spite of the large number of passive methods
devised, the use of active methods has received
less emphasis whatsoever because of the limitations like high position specificity of control rods,
trade-off with the aesthetics in case of surface
modifications and high costs involved in streamlining. Furthermore, among all the active methods, considerable research work has been concentrated on using the methods of blowing and suction due to the simplicity in its working mechanism and flexibility in its implementation. All
methods using suction or blowing utilize the two
fundamental concepts in controlling of vortex formation and its subsequent shedding as explained
by Gerrard [16].He explained that (i) shear layers
should roll up to form vortex of sufficient strength
(ii) the two shear layers must interact with each
other within a critical streamwise distance to become unstable. Blowing or suction disrupt either
of the above necessary conditions and suppress
vortex shedding.
Mathelin et al. [17]used a numerical approach
to study the effect of blowing on heat transfer
and flow around a porous circular cylinder for
Reynolds number range of 10 and 7000 and could
show a consistent decrease in the Strouhal Number with blowing velocities. The pioneering ex2
square cylinder subject to uniform blowing and
suction at a Reynolds number of 104 and concluded that suction delayed separation leading to
a narrower wake width while blowing exhibited an
opposite behavior altogether. They found that the
Strouhal number increases by 50% in case of suction and decreases by 25% for blowing. His investigations on drag showed that the drag increases
linearly with blowing rate but decreases steeply
(almost 70% reduction) at a particular suction velocity.
Arcas and Redekopp [21] performed numerical simulations to study the effect of base blowing or suction on vortex shedding from a plane
fore-body with rectangular base kept in a channel. Two symmetrically placed blowing slots of
varying size were used with different velocities.
They found that the required bleed flux (= vw B
where vw is blowing/suction velocity and B is
slot thickness) becomes asymptotic with increasing Reynolds number. Furthermore, they showed
that suction seemed to be quite sensitive to the
flux distribution and magnitude of the flux both.
Akansu et al. [22] studied experimentally the effect of uniform injection through one perforated
surface of a square cylinder on pressure and drag
coefficient in turbulent regime (Re=104, 1.6×104,
2.4×104). Their results pointed out that drag coefficient increases with injection rate for front or
top face injection but decreases modestly when injection is done from rear face.
Kim et al. [?] carried out a parametric study in
order to investigate the effect of base jet on vortex
shedding in both laminar (Re=200) and turbulent
(Re=8520) flow around a square cylinder placed
inside a channel flow. They could find out the optimum Injection Ratio at which the lift coefficient
fluctuations was minimum with drastic changes in
vortex formation. A complete disappearance of
main vortices has also been observed at certain
injection rate.
Akansu and Firat [24] investigated experimentally the flow around a square prism having injection from its base into the vortex formation region at a Reynolds number of 8000. The injection ratios at which experiment was carried out
were 1.12, 1.68, 2.24 and 2.8. They observed
two regimes in the wake of the cylinder. In first
case at low injection ratio, the vortex are displaced a bit downstream decreasing the shedding
frequency while in other case at very high injection ratio, jet penetrates into the vortices, shifting
formation region remarkably downstream. Consequently, weaker separated shear layers are formed
resulting in a thinner wake width thus causing the
shedding frequency to increase.
Mei [25] in her extensive work on Strouhal frequencies for flow around square cylinders with uniform surface suction or blowing through all four
sides found that for suction velocity between 0.025
and 0.1 lies the limiting value for which Strouhal
frequency rises. She also showed complete suppression if suction velocity falls between 0.40 and
0.45. A total suppression could also be achieved
for blowing velocities ranging between 0.15 and
0.20.
As quite evident from the studies cited above,
most of the work that concentrates on square
cylinders is focused on uniform blowing/suction on
porous/perforated cylinders and has no mention of
the effect of number of jets and their positions on
wake behind the cylinder. Also most of them illustrated the suppression of vortex shedding without
any mention of complete suppression.
The present study along with achieving complete suppression with single jet at rear face of the
cylinder also elucidates the effect of number of jets
and effect of the velocity profile of the blowing jet
on vortex shedding. In addition, the present study
also discusses the effect of blowing on the integral
parameters.
2
Problem Statement
A square cylinder of side D is kept in an infinite
medium having a cross flow. A single Reynolds
number (based on the cylinder dimension and the
average velocity at inlet) of 100 is considered in the
present numerical study. The two-dimensional geometrical model of the problem has been depicted
in Fig. 1. The origin of the coordinate system coincides with the center of the main cylinder. The
geometry considered for analysis is schematically
shown in Fig. 1. The dimensions related to the geometry are H=20.0 thus giving a blockage of 5%,
3
Lu = 7.0D; Ld = 20D.
unsteady, Navier Stokes equations for incompressTo achieve the overall objective, the analysis ible fluids. The governing equations of continuity
has been carried out by addressing the problem and momentum in x- and y-directions are repreas three small sub-problems:
sented as follows in Eq.1, Eq. 2, and Eq.3. respectively:
(a) Problem I:The effect of blowing through a single jet at the rear face on the vortex shedding
∂u
=0
(1)
phenomena has been studied. The velocity
∂x
profile at the jet exit is chosen to be uniform ∂u ∂(uu) ∂(uv)
∂p
1 ∂ 2u ∂ 2u
+
+
=−
+
+
for the analysis.
∂t
∂x
∂y
∂x Re ∂x2 ∂y 2
(2)
(b) Problem II:The second problem addresses the
∂v ∂(uv) ∂(vv)
∂p
1 ∂ 2v ∂ 2v
effect of velocity profile at jet exit on the vor+
+
=−
+
+
∂x
∂y
∂x Re ∂x2 ∂y 2
tex shedding. Two different types of velocity ∂t
(3)
profile namely, uniform and parabolic velocity
The
above
equations
are
non-dimensionalized
profile is chosen.
using with the average velocity u∞ at the inlet, all
(c) Problem III:Finally, the effect of number of lengths with the obstacle height D and the presjets on the vortex shedding has been ad- sure by ρu2∞ .
dressed. The geometrical models for various
arrangements are shown in Fig.1
3.2 Boundary Conditions
The boundary conditions employed for the present
investigations are as mentioned below:
1. Inlet: a uniform velocity has been prescribed;
u = 1.0,v = 0
2. Outflow: To this end, the convective boundary conditions proposed by Orlanski [?] have
been used, which does not affect the flow in
the upstream.
Figure 1: Computational domain for numerical
analysis
∂φ
∂φ
+ uc
= 0, where φ = u, v
∂t
∂x
3. The confining boundaries (top and bottom
boundaries) are modeled as the free slip
boundaries for example, at the transverse
confining surfaces, y = ± H2 , ∂u
= 0, v = 0
∂y
4. Obstacle: No-slip (u = v = 0) boundary conditions are used for the velocities on the main
cylinder as well as on the control cylinder surface.
Figure 2: Model of Cylinder with 1 jet, 2 jets, 3
jets used for analysis in Problem III
3
3.1
Mathematical Formulation 4
4.1
Governing Equations
Solution Methodology
MAC Method
The computation of flow field around the square The equations as mentioned from Eq. 1-3 are discylinder is carried out by solving two-dimensional cretized using finite difference method on a non4
uniform staggered grid. The technique employed
is an improved version by Harlow and Welch called
the MAC (Marker and Cell) method. When the
flow is incompressible pressure and velocity are to
be solved simultaneously such that the pressure
field is compatible with the continuity equation
as well. This is taken care of by using two steps
procedure.
In the first step, provisional values of velocity
components are explicitly calculated using previous time step values. However, these values thus
obtained need not necessarily satisfy the continuity equation. So, in the second step the pressure
and velocity components are corrected through
the pressure correction equations such that continuity equation is also satisfied simultaneously. An
explicit, second order Adams-Bashforth scheme is
used for time advancement of convection and diffusion terms.
Mathematically, the method can be expressed as
follows:
The momentum equation is written using a space
operator g, which contains the convection as well
as the diffusion terms as
study. Furthermore, the convection and diffusion
terms have both been approximated by secondorder central differencing scheme.
4.2
Stability Considerations
According to the Courant-Freidrichs-Lewy (CFL)
condition the fluid is bound to move through one
cell at a time because the difference equation assumes flux between the adjacent cells, hence the
time increment should satisfy
∆t < min{
∆x ∆y
,
}
|u| |v|
(9)
where the minimum is with respect to every cell
in the mesh and as a factor of safety ?t is chosen
between one-fourth to one-third of minimum cell
transit time.
When the viscous terms are more important,
the condition for stability in non-dimensional form
is determined by the restriction on grid Fourier
numbers and is as follows:
∆t <
Re (∆x)2 (∆y)2
{
}
2 (∆x)2 + (∆y)2
(10)
∂ui
∂p
= g(ui , uj ) −
(4)
∂t
∂xi
4.3 Grid System
The predictor step for the time advancement takes
For, computation the flow domain is divided into
the form
numerous rectangular cells. The grid is non∗
n
n
ui − ui
1
∂p
uniform in both the directions and such that it
= [3g(ui , uj )n −g(ui , uj )n−1 ]−
(5)
is clustered near the walls of the obstacle because
∆t
2
∂xi
the velocity gradients are larger near the wall and
This gets followed by the corrector step
in order to capture the separating shear layer to a
∂u∗i
greater degree in our simulations. The minimum
r◦ ∂xi
,
p =−
(6) grid size used is 0.005 In addition to being clus1
1
[2(∆t) (∆x)
2 + (∆y)2 ]
tered near the walls of the obstacle the grid is also
clustered over the width of the jets. The grid size
The final solution for velocity and pressure are
used for the baseline case without any jets was
given as Eq.7 and Eq. 8 respectively
355×264. The typical grid size used for one-Jet,
pn+1 ← pn + p,
(7) two-jets, three-jets and four-jets cases are respectively 346×294, 346×304, 346×309 and 346×316
respectively. A typical grid is shown in Fig. 3.
∆t ,
In order to prove the grid independent nature
un+1
← u∗i +
p
(8)
i
∆xi
of the code used for numerical computations, a
The corrector steps Eq. 6-8 is solved by Gauss- coarser grid (279×232) roughly 1.5 times less than
Sidel iterations with ro as the over relaxation the original grid (346×294) was used in the case
factor to accelerate the pressure correction pro- of a single jet. With both grids, a complete supcess. The value of ro used is 1.8 in the present pression was achieved. The drag coefficient is also
5
found match for both the grids. Therefore, the results with 346×294 grid points or scaled grids for
other cases are grid independent.
(a) Instantaneous Vorticity contours
(b) Time-averaged streamtrace
Figure 4: Baseline case results
helps in suppressing the vortex shedding by preFigure 3: Grid System used for the case of a single
venting the interaction of the two opposite sign
jet (Grid size: 346×294)
vortices. For this study, a uniform velocity of the
jet has been used.
Figure 5 - 7 shows the time-averaged streamlines at different blowing/jet velocities. It is quite
5 Results and Discussions
evident from the plots that as the blowing velocity
increases, the shear layer becomes elongated. At a
As mentioned earlier, the study has been divided
blowing velocity of 0.87, the flow becomes steady.
into three major cases. The following sections will
At lower blowing velocities, the jet does not
discuss the results for each case separately. Since
possess enough momentum to affect the separated
all the cases require comparison with the baseline
shear layers. The interaction of the two separated
case, the flow past a square cylinder without the
shear layers is delayed because of presence of jet
presence of any jets has been computed and is preat the center. The jet velocity affects the length
sented in Fig.4. The instantaneous vorticity conbeyond which the interaction happens by allowtours (Fig.4a) shows clear formation of wake also
ing more momentum along the centre of the wake.
called K´arm´an Vortex Street. The correspondTwin vortices are observed at the rear face of the
ing time-averaged streamlines shown in Fig.4b ilcylinder because of the jet. Because of the inlustrates common flow behavior observed in low
duced flow, one additional pair of small bubbles
Reynolds number steady flow where a pair of bubon either side of the twin larger bubbles is also
bles remains attached to the rear face of the cylinseen. As the blowing velocity is increased, the jet
der.
gradually gains enough momentum not to allow
the interaction for larger streamwise length. Be5.1 Flow Structure and Effect of yond a critical distance the shear layers lose their
strength through viscous diffusion and cannot inBlowing on Vortex Shedding
teract to gain sufficient circulation and cause tearOne may expect that high velocity blowing ing of the shear layers and their subsequent shedthrough a single jet at rear would work similar ding becomes impossible.
to that of a case where a splitter plate is attached
at the rear face of the cylinder. The splitter plate
6
(a)
(b)
(c)
Figure 5: Blowing Velocity 0.50
(a)
(b)
(c)
Figure 6: Blowing Velocity 0.70
(a)
(b)
(c)
Figure 7: Blowing Velocity 0.87
Figure : (a) Time averaged stream trace (b)Instantaneous Vorticity contours (c) Instantaneous
streamline plots at different blowing velocities for single jet at rear
7
Thus, essentially blowing works on the following
principal mechanism for the suppression of vortex
shedding. At lower range it simply shifts the recirculation region away from the cylinder giving
rise to partial reduction in fluctuations while at
high velocities it also increases the entrainment
length [18] to a great extent. This fact is testified
by Fig. 5 - 7 in which as the velocity approaches
the critical velocity at which complete suppression
is attained (here 0.87) the variation becomes flatter resulting in an increase in entrainment length.
This is caused due to lengthening of the shear layers before rolling up to form vortices. This leads to Figure 8: Streamwise velocity v/s X plot for blowdiffusion of vorticity from the shear layers and thus ing through single jet at rear
the main vortices formed are of low strength [?]
and are unable to undergo shedding.
5.2
Effect of jet exit velocity profile
Both the parabolic and uniform velocity profiles
are employed for this analysis. The results mentioned in Table ?? indicate quite clearly that the
case with parabolic velocity profile at the jet exit
requires considerably lower volume flux for almost
similar percentage reduction in Strouhal Number
when compared with the uniform profile case. The
percentage reduction in Strouhal number at a volume flux of 0.14 is 22.82% at which the parabolic
jet shows complete suppression (CS) of vortex
shedding.
A parabolic jet provides the advantage of a
higher local velocity (1.5 times the average velocity) at the center of the jet resulting in a
higher penetration in the wake. Thus, with the
same volume flux as in the uniform distribution,
a parabolic velocity profile displaces the recirculation region farther away and thus delaying the
interaction of separated shear layers more effectively.
A graph shown in Fig.9 for parabolic profile also
validates the mechanism of suppression by blowing
as explained earlier in Section 5.
Apart from the effect of velocity profiles on
shedding phenomena, CD,M EAN and CD,RM S have
also been calculated for both the jet profiles. The
results obtained are mentioned in Table ??. The
results demonstrate that if the effect of momentum of the jet is neglected in calculating CD,M EAN
Figure 9: Streamwise velocity v/s X plot for blowing through single jet at rear
there is a consistent increase in the drag with the
increase in blowing velocity, which is also in tandem with the findings of [23]. Nevertheless, there
is a drastic reduction in the drag values when the
effect of momentum of jet is taken into consideration. It can also be observed quite clearly that
the reduction in drag at complete suppression is
more in case of uniform velocity profile than the
parabolic case because of the larger mass flux and
velocity required for complete suppression in the
case of uniform velocity profile.
8
SNo.
1
2
3
4
5
6
7
8
9
Blowing
Velocity
0.00
0.50
0.55
0.57
0.60
0.70
0.75
0.85
0.87
Strouhal Number
Uniform
Parabolic
Velocity Profile Velocity Profile
0.1630
0.1630
x
0.1279
x
0.1214
x
0.1170
x
CS
0.1258
x
0.1226
x
0.1181
x
CS
x
% reduction in Strouhal Number
Volume
Uniform
Parabolic
Flux
Velocity Profile Velocity Profile
0.00
0.00
0.00
0.100
x
21.53
0.110
x
25.52
0.116
x
28.82
0.120
x
100.0
0.140
22.82
x
0.150
24.79
x
0.170
27.5
x
0.174
100.0
x
Table 1: Comparison of Blowing Velocity v/s Strouhal number for single jet having different velocity
profiles
CD,M EAN Uniform
SNo. Blowing Neglecting
Including
Velocity Effect of jet Effect of jet
1
0.00
1.524
1.524
2
0.50
x
x
3
0.55
x
x
4
0.57
x
x
5
0.60
x
x
6
0.70
1.554
0.574
7
0.75
1.561
0.436
8
0.85
1.592
0.147
9
0.87
1.599
0.086
CD,M EAN Parabolic
Neglecting
Including
Effect of jet Effect of jet
1.524
1.524
1.502
11.000
1.501
0.896
1.510
0.860
1.523
0.803
x
x
x
x
x
x
x
x
CD,RM S
5.68×10−3
9,52×10−5
7.13×10−5
2.21×10−5
6.94×10−8
8.90×10−5
6.28×10−5
4.62×10−5
2.21×10−6
Table 2: Drag Coefficients v/s Blowing Velocity for blowing with single jet at rear
9
SNo.
1
2
3
4
5
6
7
8
9
Blowing Velocity
0.00
0.50
0.55
0.57
0.60
0.70
0.75
0.85
0.87
Volume Flux
0.00
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.21
Strouhal Number
2 jets 3 jets 4 jets
0.163 0.163 0.163
0.126 0.128 0.129
0.123
0.122 0.123
0.000
0.120
0.118
0.000
0.114
0.000
% reduction in Strouhal Number
2 jets 3 jets
4 jets
0.00
0.00
0.00
22.76 21.60
20.53
24.36
25.46 24.66
100.0
26.14
27.61
29.48
100.0
Table 3: Comparison of Blowing Velocity v/s Strouhal number for blowing with different number of
jets
10
5.3
Effect of number of Jets
Numerous simulations were performed for three
more cases beyond the case of single jet with an
objective to understand the outcome of change
in the number of jets on the shedding phenomena. The total area of the jets at the rear face
is kept constant at 20% and jets are distributed
symmetrically about the wake centerline. As evident from previously obtained results, since the
parabolic profile is more effective than uniform
profile in suppressing vortex shedding, the two[1
jet, three-jet and four-jet cases are simulated with
Jet]
a parabolic profile at the jet exit.
(a)
Complete suppression was attained at a blowing
[2 Jets]
velocity of 0.75 in 2 jets case, 0.80 in 3 jets case and
1.05 in 4 jets case, all of which are greater than the
velocity (0.60) at which suppression was attained
with a single jet. The Strouhal number variation
with different blowing velocities for all the three
cases is illustrated in Table ??. A comparison of
the flow obtained in the three cases at a constant
(b)
volume flux of 0.120 is depicted in Fig.10
[3 Jets]
Increasing number of jets may weaken the
strength of jet as the peak velocity might have
been affected by the lateral interaction between
adjacent jets. This may be probable reason for an
increase in the critical blowing velocity with an
increase in number of jets. It may so happen that
the jets placed symmetrically help in diffusing the
(c)
vorticity in the separating shear layers. Never[4 Jets]
theless, this claim stands falsified by the observed
variation of vorticity v/s Y at 1.5D in Fig.11 at a
constant volume flux of 0.120 (at which single jet
exhibits complete suppression).
Fig.11 shows that there is negligible variation in
the length over which the vorticity is diffused in
the lateral direction in all the cases studied. More(d)
over, there is very less deviation from the diffusion
length for the baseline case as well which indicates Figure 10: Time averaged streamline plots at a
that increasing the number of jets does not af- volume flux of 0.120
fect the lateral diffusion of vorticity and the wake
width remains almost the same in all cases.
Figure 12 shows the variation of streamwise velocity with X at the center wake line in all 3 cases
at a constant volume flux of 0.120. It can be observed from Fig. 12 that the interaction distance
of the separated shear layers is delayed less as the
11
parabolic jet exit velocity profile is more effective
than the uniform jet exit velocity profile because
of higher local velocity at the center of jet which
provides greater wake penetration. Finally, a comparative study of the effect of number of jets on
shedding reveals that increasing the number of jets
from 1 jet to 4 jets does not add to additional diffusion of vorticity in the lateral direction. Rather,
increase in the number of jets probably reduces
the strength of the jet due to lateral interaction
between adjacent jets leading to an increase in the
Figure 11: Vorticity versus Y at 1.5D from rear required critical velocity for complete suppression.
face for 1-jet, 2-jet, 3-jet and 4-jet with parabolic This is testified by the fact that complete suppresprofile at jet exit and constant volume flux 0.120. sion with single jet having parabolic jet exit velocity profile was achieved at a mass flux of 0.120 at a
blowing velocity of 0.60. While complete suppression with 2 jets occurs at a volume flux of 0.150,
with 3 jets occurs at volume flux of 0.170 and with
4 jets at a volume flux of 0.210. In addition to
suppression of vortex shedding, a remarkable reduction in drag when the effect of jet momentum
is taken into consideration is also observed.
References
[1]
Figure 12: Streamwise velocity versus X at centerwake line for 1jet, 2jets, 3 jets and 4 jets with
parabolic profile at jet exit and constant volume
flux 0.120
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