Experimental Investigation of the Effect of Single and Twin Bluff
Bodies on the Turbulent Flow in an Asymmetric Rectangular Diffuser
SOMNATH BHATTACHARJEE1, ARINDAM MANDAL2, RABIN DEBNATH3
SNEHAMOY MAJUMDER4
1Department of Computer Science and Engineering, Jadavpur University, 188, Raja S.C.Mullick
Road, Kolkata- 700 032, West Bengal, INDIA
2Department of Mechanical Engineering, Heritage Institute of Technology, Chowbaga Road,
Anandapur, P.O.: East Kolkata Township, Kolkata-700107, INDIA
3 Directorate of Industrial Training, Government of West Bengal, Karigori Bhavan, Pin-700 160, West
Bengal, INDIA
4Department of Mechanical Engineering, Jadavpur University, 188, Raja S.C. Mullick Road, Kolkata-
700032, INDIA
Abstract: - Experimental investigation of the effect of bluff bodies on the turbulent flow through an asymmetric
diffuser has been carried out. The rectangular diffuser is designed and made keeping similarity to that used by
Buice and Eaton, [1], having an inclination angle of 10°. Three geometrical configurations have been selected
for the experimentation. (I) At first the experiment has been carried out for the validation of the present results
with Buice and Eaton, [1], placing no bluff body at all. (II) Thereafter measurements have been carried out by
placing a single bluff body on the horizontal floor of the diffuser to estimate the effect of the bluff body on the
downstream flow. (III) Finally, two identical bluff bodies are placed on the horizontal floor of the diffuser and
experimental work has been carried out in order to investigate the effect of the existence of two bluff bodies on
the downstream flow through the diffuser. The present results agree well with the results of Buice and Eaton,
[1], to show that the recirculation zone appears just adjacent to the inclined plane when there is no bluff body in
a diffuser. Also, the detailed investigation for velocity of flow field, distribution of skin friction factor along
with uncertainty analysis as well as the correlation between friction factor and Reynolds Number have been
carried out in the research paper.
Key-Words: - Bluff body, Diffuser, Recirculation, Reynolds number, Skin friction Coefficient, Bulk Average
Velocity.
Received: March 28, 2022. Revised: October 25, 2022. Accepted: November 26, 2022. Published: December 31, 2022.
1 Introduction
The axi-symmetric rectangular flow has gotten
attention of researchers long ago.The characteristics
of air flow in a rectangular two dimensional diffuser
with fully developed inlet flow condition have been
measured by Obi, Aoki and Masuda, [2]. The
authors in [2], have experimentally investigated the
flow separation and recirculation region generated
in the diffuser of high aspect ratio. Obi, Ohizumi,
Aoki and Masuda, [3] have also examined two-
dimensional separated flow in an asymmetric
diffuser having fully developed inflow conditions
with diffuser inclination angle 10o and an expansion
ratio of 4.7. The authors have measured the mean
velocities, turbulent quantities and observed the
separation occurred at halfway downstream.
Gullman-Strand, Tӧrnblom, Lindgren, Amberg and
Johansson, [4], have considered the divergent angle
of the diffuser as 8.5o for reducing the size of the
separated region and accordingly, a high aspect ratio
of the diffuser results achieving a high degree of
two-dimensionality of the average flow. They have
also made comments that fully attached flow can
occur for the angle around 7o. Buice and Eaton, [1],
have experimentally examined asymmetric plane
diffuser flow and estimated the recirculation zones.
Present authors have been motivated by their very
unique and high quality experimental results and
give effort to validate their experimental results
considering the same aspect ratio and flow
conditions through the diffuser. Earlier,
experimental research works had been performed on
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
Rabin Debnath, Snehamoy Majumder
E-ISSN: 2945-0489
48
Volume 1, 2022
turbulent flows by Okwuobi and Azad, [5] and Azad
and Kassab, [6]. According to their investigation,
sudden change of adverse pressure gradient at the
diffuser throat causes the downstream as mean and
turbulent flow fields. Bhattacharjee, Debnath, Roy
and Majumder, [7], have experimentally studied the
turbulent air flow through a two dimensional
asymmetric rectangular diffuser. Majumder, Roy,
Bhattacharjee and Debnath, [8], have investigated
experimentally the turbulent flow behaviour of air
inside a diffuser with an inclination angle of 15°.
Coller, [9], has defined the diffuser as an expanding
section of a flow-carrying duct used to slow the
mean flow. It gives effect in the conversion of
kinetic energy to potential energy causing the rise of
pressure in the downstream region. Analytical
research work on turbulent separated flows in an
axi-symmetric diffuser has also been carried out by
Sagar, Paul and Jain, [10]. In [10] the authors have
narrated that the pressure-induced separation begins
in a diffuser with the increase of its half-angle.
Mandal, Bhattacharjee, Debnath, Majumder and
Roy, [11], have explained that the turbulent flow
and boundary layer separation are observed in many
industrial applications. Hwang, Chow and Peng,
[12], have investigated numerically that the
recirculation length decreases with the increase of
the length of the bluff body whereas Antoniou and
Bergeles, [13], have experimentally studied that by
the enhancement of the aspect ratio, the flow
reattaches at the downstream with the reduction of
turbulence scale and recirculation length. Hwang,
Chow and Chiang, [14], have analyzed numerically
the turbulent flow around a surface-mounted two-
dimensional bluff body of varying length. They
have observed that the length of the re-circulating
zone remains unchanged with the variation of the
length of bluff body in the upstream of flow. In the
downstream of flow, the length of the re-circulating
region depends on the length of the bluff body.
Reattachment on the upper side of the bluff body
influences the velocity boundary layer developed at
the downstream region. This is valid as the length of
bluff body increases. According to [12] the authors
have remarked that the length of re-circulating
zones depends on the ratio of the boundary layer
thickness to the bluff body’s height and on the
geometry of the bluff body. Bergeles and
Athanassiisdis, [15], have experimentally evaluated
the lengths of the re-circulating regions in front of
and behind the bluff body. Benodekar, [16], has
mentioned that Reynolds number has negligible
effect on separation in the case of turbulent flow.
Baetke, Werner and Wengle, [17], have remarked
that wall boundary conditions at sharp corners
strongly control separation of flow. Das, Ghosh and
Singh, [18], have asserted in their literature that the
flow field around the building or structure situated
on the surface boundary layer is fully turbulent and
complex with separations at each surface of the
building. Bhattacharjee, Debnath, Mandal,
Majumder and Roy, [19], have observed through the
experimental work using two bluff bodies of
different sizes in a rectangular diffuser and
recirculation zones are distinctly pointed out. Mehdi
and Mushatet, [20], have pronounced that the
separation of boundary layer and recirculation zones
behind the bluff bodies mainly depend on the
spacing between the bluff bodies. Liu, [21], has
analyzed the numerically simulated flow around the
cylinders of different shapes changing from square
to circle. The author has made the opinion that the
drag coefficient and reattachment length decreases
independent of the Reynolds number. It is also
commented that the drag coefficient of a rounded-
corner square cylinder can be lower than the circular
cylinder of the same size. Poussou and Plesniak,
[22], have observed experimentally the wake
formed due to a bluff body propagating through a
recirculating flow using Particle Image Velocimetry.
Lander, Letchford, Amitay and Kopp, [23], have
investigated the influence of bluff body shear layer
formation and the resulting impact on flow
characteristics using two-dimensional square prism
with the help of Particle Image Velocimetry.
Bandyopadhyay, Sarkar, Roy and Chanda, [24],
have experimentally found the flow field in a
rectangular diffuser using a bluff body. The authors
have remarked that the boundary layer thickness is
somewhat lower at higher inlet velocity and
maximum momentum occurs near the bluff body.
Nasr, Abdel-Fattah and EI-Askary, [25], have
investigated the effect of the number of ribbed walls
on heat transfer surface and friction property. In
[25] the authors have commented that ribs mounted
on the heat transfer surface make disturbance on the
boundary layer growth and augmentation of heat
transfer from the surface to the fluid and better
mixing is possible. The useful scientific idea
regarding flow separation and recirculation bubble
formation near the bluff bodies is still very scarce in
the published literature. The present experimental
work is associated with the diffusing air fluid flow
with generation of recirculation. The main objective
of the present study is to explore the turbulent air
flow behaviour experimentally at normal
atmospheric pressure and temperature in an
asymmetric two dimensional diffuser of rectangular
cross section fitted with single and twin bluff bodies
respectively.
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
Rabin Debnath, Snehamoy Majumder
E-ISSN: 2945-0489
49
Volume 1, 2022
2 Experimental Method
The experiment has been conducted in an
asymmetric horizontal rectangular diffuser
maintaining similarity with the geometry of the
experimental set up used by Buice and Eaton, [1].
The lower portion of the diffuser is horizontal and
its upper one is tilted. The inlet section of the
diffuser is 0.015 × 0.200 m which is combined with
the outlet section of the air blower. The aspect ratio
of the diffuser and the horizontal length of the inlet
channel are (13.33:1) and 0.83 m respectively. For
maintaining similarity with the experimental set up
used by Buice and Eaton, [1], the normal height of
the downstream tail end of the diffuser is
H7.4
and
the axial length of the diffuser is
H21
with an
inclination angle of 10°. The outlet section of the
diffuser of rectangular shape is 0.07 × 0.2 m
extending the length up to
H77
. Both the upper and
lower walls of the diffuser are made of 0.006 m
thick Plexi-glass sheet. The side walls of the
diffuser are constructed of plain transparent glass
sheet of 0.004 m thickness. The turbulent air from
the blower finally enters the inlet section of the
diffuser after passing through the vibration absorber,
wire-mesh and honey comb chamber accommodated
in between the blower and the diffuser. This type of
construction ensures the uniform turbulent fluid
flow through the inlet section of the diffuser. The
blower which is coupled with a D.C. motor supplies
air to the diffuser. Pressure Transducer is used in the
experimental work for measuring stagnation and
static pressure difference at a certain location inside
the diffuser. The specification of the Pressure
Transducer used is as follows: Model-CP300-HOP,
Sl.No.-12040821, Type-304, and Range: -
10000/10000 Pa, Air velocity range - 2 to 100 m/s
with accuracy: ± 0.5% of reading ± 1 Pa. The
measured pressure difference is utilised to calculate
the axial mean velocity of the turbulent fluid flow.
The calibrated Pitot tube has been used to determine
pressure heads. The probe is introduced from
numbers of drilled holes situated over the top
inclined surface along the mid-stream plane
at different station locations along the
diffuser length. Pressure differences (Δp Pa)
between the stagnation and static pressures are
calculated at various vertical heights measured from
the bottom horizontal wall by using Pitot tubes
mounted on a traversing equipment. Thermometer
and Barometer are employed for taking the reading
of local atmospheric temperature and pressure inside
the laboratory. The diffuser is installed perfectly on
a wooden frame structure. The working fluid is air
assuming its density ρ = 1.132 kg/m3 at normal
room temperature (300 K) and pressure (101.6 KPa)
inside the laboratory.
At first, the current experimental work for validation
of the results using the set up without a bluff body
has been carried over only at Reynolds number
equal to 1.367 × 104. The two-dimensional
parameters measured for the mean turbulent fluid
velocity profile have been plotted comparing the
benchmark experimental results of Buice and Eaton,
[1].
Secondly, a single polished wooden bluff body
made of dimension 0.20 × 0.02 × 0.02 m is placed
over the horizontal bottom wall at a distance of
0.18m from the inlet section of the diffuser. For
third experimentation work utilising the same set up,
two wooden bluff bodies, each of equal dimensions
of 0.20 × 0.02 × 0.02 m, are placed on the bottom
wall at the distances of 0.18 m and 0.30 m
respectively from the inlet section of the diffuser
and a clear gap existing between them is 0.12 m. For
second and third experimental works the inlet flow
condition is turbulent with Re = 1.36104, 1.749×
104 and 1.833× 104 respectively. Reynolds numbers
are calculated based on the inlet height of the
diffuser and axial mean flow velocity. Here also
two-dimensional measurements have been taken in
the mid-stream plane
XX
. The velocity
distribution curves are obtained at different stations
along the horizontal length of the diffuser.
The equations for the mean velocity of fluid u, uavg
m/s, Reynolds numbers and coefficient of skin
friction of the working fluid flowing passing
through the diffuser Cf are hereby given below:
sm
p
u/
81.92
(1)
H
b
U
Re
(2)
2
2
1
/
avg
u
dydu
f
C
(3)
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DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
Rabin Debnath, Snehamoy Majumder
E-ISSN: 2945-0489
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Fig. 1 Schematic diagram of the experimental set up (using twin bluff bodies/baffles)
Fig. 2 Schematic diagram of the diffuser using twin bluff bodies/baffles (not to scale), all dimensions are in mm
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Fig.3 Photograph of the Experimental Set Up
In figures 1 and 2 the schematic diagrams of an
experimental setup fitted with two bluff bodies and
holes on the inclined surface at different station
distances have been shown. For the case of the
experiment with a single bluff body, the diagrams
are necessary to be modified by replacing the
double bluff body with the single one.
3 Results and Discussion
3.1 Diffuser without Bluff body and
Validation of Results
The experimental results shown in Fig.4 (a and b)
of turbulent air flow through the asymmetric
rectangular diffuser used in the experimental work
have been validated with the published
experimental work of Buice and Eaton, [1].
Recirculation and reattachment of the flow have
been found out inside the diffuser adjacent to the
inclined surface. The velocity distributions are
presented in the two-dimensional coordinate
system in which
X
-axis is parallel to the inlet
upstream flow and the origin of
X
- axis is lying at
the onset of diffuser after the constant rectangular
section while the
Y
axis is normal to
X
- axis. The
centre-line velocity at the inlet is
b
U14.1
where
b
U
is obtained as 12.0 m/s and the corresponding
Reynolds number is calculated using the equation
(2) or Re =1.367×104.
Fig.(a)
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Fig.(b)
Fig. 4 Validation of the current experimental results with the results of Buice and Eaton, [1]
At the station
035.0X
m i.e.
405.310 b
U
U
H
X
the velocity profile shows
no sign of the presence of flow separation. In fact,
this is the just outer section of the inlet rectangular
section receiving the incoming flow in the settling
chamber which is 0.083m long. The height of the
settling chamber is 0.015m; therefore, the ratio of
the length of the settling chamber and height for this
section is almost 53.33. It is observed that the
velocity distribution along vertical Axis-Y obtained
from the present experiment agrees very well with
that of Buice and Eaton, [1], experimental work.
The same good agreement has also been observed at
a station distance
09.0X
m
for
0.610 b
U
U
H
X
, but no phenomena of any
recirculation i.e. separation or the reattachment of
the turbulent flow has occurred. This is due to the
fact that the flow is still not facing sufficient adverse
pressure to have a backflow near the wall. But the
presence of a separating flow is clearly observed at
the axial distances
mandmX 30.020.0
respectively
corresponding to
2.204.1310 and
U
U
H
Xb
with
a clear similarity and of the same nature of the back
flows shown by Buice and Eaton, [1]. At a station of
distance
mX 39.0
for
08.2710 b
U
U
H
X
the
recirculation bubbles disappear showing the
reattachment of the separating flow. The other axial
station distances chosen for the current
experimentation are
mandmmmX 90.080.0,70.0,60.0
respectively with
the corresponding non-dimensional values of
6033.53,67.46,4020 and
U
U
H
Xb
respectively.
In all of the above cases the current results agree
well with the experimental results of Buice and
Eaton, [1].
3.2 Diffuser with Single and Twin Bluff
bodies:
The present investigation provides a complete set of
information in the upstream position, diffuser region
and downstream of the diffuser model of 10°
inclinations. The single bluff body of size 0.20 ×
0.02 × 0.02 m is placed over the bottom horizontal
wall at a distance of 0.18 m from the inlet section of
the diffuser. The inlet condition of the air flow is
turbulent with
Re
=1.367× 104, 1.749× 104 and
1.833× 104 respectively. Measurements have been
taken in the mid-stream plane
XX
.
O Buice and Eaton, [1]
Present Experiment
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(a)
(b)
(c)
(d)
Fig. 5 Transverse distribution of Stream wise velocity (for single bluff body)
Figures 5(a) to 5(d) illustrate the distributions of
mean velocities of fluid at different axial station
distances along the
X
-axis from the inlet cross
section of the diffuser. From the figure 5(a), it has
been observed that no generation of recirculation
occurs before the edge of the bluff body, the
measurements being taken from the lower horizontal
wall of the diffuser towards the upper inclined wall.
As the measurements are conducted in the
downstream direction it has been found that there
exists recirculation of the turbulent flow adjacent to
the inclined surface. The recirculation occurs at a
distance of 0.075 m away from the inlet of the
diffuser and it ends at a distance of 0.535 m away
from the inlet of the diffuser. The effective
recirculation bubble length therefore equals to 0.460
m. Flow separation is generated due to the adverse
pressure gradient of the flow caused by the gradual
expansion of the volume of flow with larger
inclination angle of the diffuser.
When two bluff bodies of equal size are placed,
measurements have been carried out over the top
surfaces of the bluff bodies at the station distances
of 0.18 m to 0.20 m and 0.30 m to 0.32 m
respectively. Recirculation occurs in the region
between the distances of 0.075 m and 0.535 m away
from the inlet section of the diffuser. Figure 5(d) as
well as 6(f) clearly depicts the occurrence of re-
attachment of the flow in the downstream region of
the diffuser. From figures 5(b) to 5(c) and figures
6(b) to 6(e), it has been observed that recirculation
size is somewhat smaller above the top surface of
the baffles than that in other locations. Recirculation
bubble generated before the second baffle towards
the inlet section is smaller in size than that
generated just after the baffle in the downstream
region inside the diffuser. From the figures 5(a) to
5(d) and 6(a) to 6(f) it is also evident that the axial
mean velocity increases with increase of Reynolds
number.
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(a)
(b)
(c)
(d)
(e)
(f)
Fig. 6 Transverse distribution of Stream wise velocity (for double bluff bodies)
Lower Wall
Upper Wall
Single Bluff body
(a)
(b)
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Twin Bluff bodies
(c) Lower Wall
Fig. 7 Variation of Coefficient of Friction
(d) Upper Wall
Figures 7(a) to 7(d) illustrate the values of
coefficient of skin friction on the lower and upper
walls at different Reynolds numbers for the cases of
single and double bluff bodies respectively. Friction
force increases as the solid surface of the bluff
bodies are introduced disrupting the fluid flow and it
is clearly evident from the figures 7(a) to 7(d). From
the figures 7(a) to 7(d), it is observed that
coefficient of friction decreases with increase of
axial distance measured from the inlet section of the
diffuser and is found negative at the recirculation
zones. Coefficient of skin friction reaches nearly a
constant value at the outlet of the diffuser. It has
been also seen from the figures 7(a) to 7(d),
coefficient of skin friction increases with the
increase of Reynolds number of the turbulent flow
in a diffuser. The curves so obtained are drooping in
nature where the value of coefficient of skin friction
decreases with the increase of station distances.
Single Bluff body
(a)
Twin Bluff bodies
(b)
Fig.8 Variation of Coefficient of friction with Re
Figures 8(a) and 8(b) show the variation of
coefficient of skin friction with the increase of
Reynolds numbers for the cases of single and twin
bluff bodies respectively. The current experimental
value of the coefficient of friction correlates as the
function of Reynolds number and the relevant
correlations achieved for upper wall as well as lower
wall of the diffuser are given in Table1. These
correlations are valid for Re=1.367 × 104, 1.749
×104 and 1.833 × 104. Table 1
Lower Wall
Upper Wall
Single
Bluff
Body
58
213
101Re102
Re106
f
C
002.0Re103
Re101
7
211
f
C
Twin
Bluff
Bodies
Re109
Re102
8
212
f
C
001.0Re102
Re108
7
212
f
C
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DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
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3.3 Uncertainty of experimental results
Uncertainty has been calculated for the fluid flow
parameters measured as (i) for Reynolds number =
3.3% to 3.4% and (ii) for Coefficient of friction =
1.198% to1.67% respectively.
4 Conclusion
The present experimental results are validated with
the benchmark work of Buice and Eaton, [1],
considering the same geometry of diffuser and
boundary conditions of the turbulent flow in an
asymmetric diffuser. The current study shows a
good agreement with Buice and Eaton, [1]. This
validation approves the authenticity and accuracy of
the experimental set up designed, developed and
fabricated to measure the turbulent flow parameters
through a rectangular diffuser. The matching of the
velocity distribution also confirms the authenticity
of the current experimental methodology.
The present experiment has been aimed to
distinguish the effect of single and double bluff
bodies of identical geometry in shape and size fitted
on the bottom wall of an asymmetrical two
dimensional horizontal diffuser with an inclination
angle of 10° on the turbulent fluid flow. It has been
observed that recirculation zones are generated due
to the presence of the bluff bodies opposite to the
flow direction. Recirculation occurs on the top of
the bluff body for the case of single bluff body.
Thereafter it exists after the bluff body towards the
outlet of the diffuser with larger size. For the case of
twin bluff bodies, recirculation also exists between
the spacing of the two bluff bodies. Coefficient of
skin friction increases with the increase of Reynolds
number. With the increase of axial distance
measured from the inlet section of the diffuser,
coefficient of skin friction decreases and is found to
be negative at the recirculation zones. Coefficient of
skin friction reaches a constant value at the
downstream side of the diffuser. The value of
coefficient of skin friction is lesser in the upper wall
and higher in the lower wall in case of the flow
through the diffuser. Some relevant correlations
have also been established between the coefficient
of skin friction and Reynolds number which is
shown in Table no.1. These correlations are valid
for corresponding Reynolds numbers of 1.367× 104,
1.749×104 and 1.833× 104 respectively.
The significant use of the bluff bodies of different
sizes at different spacing and orientations inside the
diffuser duly validated with the results of Buice and
Eaton, [1], makes it possible to optimize the length
of the diffuser and it economises the industrial use
of the diffuser.
Acknowledgment:
The authors express their sincere thanks and
gratitude to all who have extended their helping
hands by giving valuable suggestions and technical
support for this experimental work done at
Hydraulics Laboratory, Mechanical Engineering
Department, Jadavpur University, Kolkata (India).
Nomenclature
f
C
Coefficient of Skin friction
H
Inlet height of the diffuser, m
dy
du
Velocity gradient of the upper and
lower wall of the diffuser
Re
Reynolds number
X, x, S
The distance of the station
measured from the inlet end of the
diffuser, m
Ub
Bulk average velocity, m/s
U
Velocity at certain location and
height, m/s
avg
u
Average Velocity of Fluid, m/s
p
Difference of Stagnation and Static
pressure, Pa
ρ
Density of air, kg/m3
μ
Co-efficient Dynamic viscosity of
fluid at room temperature, Pa-s
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Investigation of Flow through an
Asymmetric Plane Diffuser, Journal of
Fluids Engineering, Vol. 122, 2000, pp.
433-435.
[2] Obi, S., Aoki, K. and Masuda, S.,
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[3] Obi, S., Ohizumi, K., Aoki, K. and
Masuda, S., Turbulent Separation Control
in a Plane Asymmetric Diffuser by Periodic
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International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
Rabin Debnath, Snehamoy Majumder
E-ISSN: 2945-0489
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Volume 1, 2022
[4] Gullman-Strand, J., Törnblom, O.,
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A. V., Numerical and experimental study
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International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
Rabin Debnath, Snehamoy Majumder
E-ISSN: 2945-0489
58
Volume 1, 2022
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Authors’ Contributions:
Dr. Somnath Bhattaharjee, Dr. Arindam Mandal and
Dr. Rabin Debnath have conducted research and
performed the experimental process including
validation. Dr. Somnath Bhattacharjee (the
corresponding author) has developed the
methodology and prepared the initial draft as well as
edited subsequently. Prof. (Dr.) Snehamoy
Majumder has coordinated the execution of the
research work with his immense depth of
knowledge and mentorship. His discretionary power
and editing capability make the research work more
enriched with scientific innovation.
Sources of funding for research
presented in a scientific article or
scientific article itself
No specific financial support for research is
received to carry out this experimental study.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
International Journal on Applied Physics and Engineering
DOI: 10.37394/232030.2022.1.7
Somnath Bhattacharjee, Arindam Mandal,
Rabin Debnath, Snehamoy Majumder
E-ISSN: 2945-0489
59
Volume 1, 2022