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Numerical analysis of wake flow on heated
cylinder
A PROJECT REPORT
Submitted by
DULARISH K A 312211114029
INTI SANDEEP 312211114043
in partial fulfillment for the award of degree of
BACHELOR OF ENGINEERING
in
MECHANICAL ENGINEERING
SSN COLLEGE OF ENGINEERING, CHENNAI -603110
ANNA UNIVERSITY: CHENNAI 600 025
APRIL 2015
ANNA UNIVERSITY: CHENNAI 600 025
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BONAFIDE CERTIFICATE
Certified that this project report Numerical analysis of wake
flow of
heated cylinder is the bonafide work of Dularish K A, Inti
Sandeep who carried out the project work under my
supervision.
SIGNATURE
Dr. V.E ANNAMALAI
HEAD OF THE DEPARTMENT
Mechanical Engineering,
SN College of Engineering,
OMR, Kalavakkam- 603110.
SIGNATURE
Dr. S. SOMA SUNDARAM
ASSOCIATE PROFESSOR
Mechanical Engineering
SSN College of Engineering,
OMR, Kalavakkam- 603110.
SUBMITTED FOR THE VIVA VOCE EXAM HELD ON: ___________
INTERNAL EXAMINER EXTERNAL EXAMINER
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ACKNOWLEDGEMENT
We are grateful to our Principal Dr. S. Salivahanan for
providing us a constructive environment for carrying
out our project.
We sincerely thank our Head of the Department,
Dr. V. E. Annamalai for giving us permission to carry
out our numerical analysis project.
We would like to express our gratitude to our guide
Dr. S.Soma Sundaram, for his valuable guidance and
support throughout the period of this project work.
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ABSTRACT
The thermal effects of the wake flow behind a heated
cylinder operating in mixed convection region is
studied numerically and is been compared with
experimental study. Water with constant temperature
flows under gravity from the top over a heated bluff
body maintained at a constant temperature. By adjusting
the surface temperature of solid, the corresponding
Richardson number is varied. This variation is observed
for different cross sectional bluff bodies. The optimal
cross section for which there is minimum heat transfer
and the one for which there is maximum heat transfer is
determined. The analysis was done on a CFD software
to determine the pattern of velocity and temperature
distribution. The study revealed that cross-section shape
changes the flow pattern significantly for the same area.
Heat transfer is maximum for circular cross section and
minimum in equilateral triangle . The change in
velocity pattern due to change of Richardson number is
negligible for a cross-section shape considered.
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TABLE OF CONTENTS
CHAPTER NO. TITLE PAGE NO.
ABSTRACT iv
LIST OF FIGURES vii
LIST OF SYMBOLS x
1. Introduction 1 1.1 Wake Flow 2 1.2 Vortex shedding 3 1.3
Reynolds Number 4 1.4 Turbulent flow 4 1.5 Nusselts number 5
2. Literature Survey 6
3. Procedure 9
4. Design Calculations 13 4.1 Time Step Calculation 13 4.2 No.
of Time Steps 13 4.3 Geometry 13 4.4 Mesh process 14 4.5
Assumptions 15 4.6 Boundary Conditions 15
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5. Numerical Results 16
5.1 Circular cross section cases 16 5.2 Equilateral triangle
cross section cases 22 5.3 Hexagon cross section cases 24 5.4
Inverse equilateral triangle cross section case 26 5.5 Square cross
section cases 28
6. Conclusions 33
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List of Figures & Tables
Figure 1.1 Wake flow
Figure 3.1 Temperature grid study
Figure 3.2 Velocity grid study
Figure 3.3 Temperature temporal study
Figure 3.4 Velocity temporal study
Figure 4.1 Geometry of circular cross section in cylindrical
pipe
Figure 4.2 Mesh Region
Figure 4.3 Prism layer and wake refinement
Table 5.1 Tabulation of cases considered
Figure 5.1 Velocity magnitude plot for circular cross
section
Figure 5.2 Temperature magnitude plot for circular cross
section
Figure 5.3 Temperature magnitude plot for circular cross
section
Figure 5.4 Temperature magnitude plot for circular cross
section
Figure 5.5 Temperature magnitude plot for circular cross
section
Figure 5.6 Temperature magnitude plot for circular cross
section
Figure 5.7 Temperature magnitude plot for circular cross
section
Figure 5.8 Velocity magnitude plot for circular cross
section
Figure 5.9 Temperature magnitude plot for equivalent triangle
cross
section
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Figure 5.10 Velocity magnitude plot for equivalent triangle
cross
section
Figure 5.11 Temperature magnitude plot for equivalent triangle
cross
section
Figure 5.12 Velocity magnitude plot for equivalent Triangle
cross
section
Figure 5.13 Temperature magnitude plot for hexagon cross
section
Figure 5.14 Velocity magnitude plot for hexagon cross
section
Figure 5.15 Temperature magnitude plot for hexagon cross
section
Figure 5.16 Velocity magnitude plot for hexagon cross
section
Figure 5.17 Temperature magnitude plot for inverse
equivalent
triangle cross section
Figure 5.18 Velocity magnitude plot for inverse equivalent
triangle
cross section
Figure 5.19 Temperature magnitude plot for inverse
equivalent
Triangle cross section
Figure 5.20 Velocity magnitude plot for inverse equivalent
triangle
cross section
Figure 5.21 Temperature magnitude plot for square cross
section
Figure 5.22 Velocity magnitude plot for square cross section
Figure 5.23 Temperature magnitude plot for square cross
section
Figure 5.24 Velocity magnitude plot for square cross section
Figure 5.25 Velocity with respect to position graph for circular
cross
section
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Figure 5.26 Temperature with respect to position graph for
circular
cross section
Figure 5.27 Temperature with respect to position graph for
different
geometries
Figure 5.28 Velocity with respect to position graph for
different
geometries
Table 5.2 Parameters along the probe
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x
LIST OF SYMBOLS, ABBREVIATIONS AND NOMENCLATURE
Re - Reynolds Number (no unit)
Gr - Grashof Number (no unit)
Ri - Richardson Number (no unit)
Pr - Prandtl Number (no unit)
St - Strouhl Number (no unit)
Nu - Nusselt Number (no unit)
f - Frequency (hertz)
D - Diameter Of Pipe (metre)
V - Velocity Of Fluid (m/s)
T - Time Period ( seconds )
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Chapter 1
Introduction
An understanding of the flow around a bluff body is of great
importance owing to its fundamental nature as well as its
many
related engineering applications. A circular cylinder is the
most
commonly studied bluff body. Despite its simple shape, a
circular
cylinder generates a wake that is dynamically complex. By
varying
the Reynolds number, a variety of flow patterns and vortex
shedding
characteristics in the wakes of circular cylinders have already
been
observed. The wake behaviour behind a heated cylinder is
physically
more complicated owing to the thermal effects added to the
viscous
phenomena. Heat transfer from a heated cylinder to the
surrounding
fluid can be either forced convection, mixed convection or pure
free
convection, depending on the ratio between the thermally
induced
buoyancy force and the inertial force, characterized by the
Richardson
number (Ri = Gr/Re2, where Gr is the Grashof number and Re is
the
Reynolds number). In forced convection (Ri >1), where the
flow inertial force is negligible, heat
transfer is a function of Grashof number (Gr) and Prandtl
number
(Pr). In mixed convection, both forced convention and free
convection
are important, and heat transfer is a function of Grashof number
(Gr),
Reynolds number (Re) and Prandtl number (Pr) as well as the
approaching forced flow direction. Despite the fact that
mixed
convection around bluff bodies is of great importance for
various
engineering applications such as electronics cooling, micro
heat
exchangers and fuel cells, the thermal effects on the wake
flow
behaviour behind a bluff body in the mixed convection regime
have
received little attention compared to those in the forced or
free
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convection. When a heated cylinder operates in the mixed
convection
regime, the thermally induced buoyancy force plays an important
role
in the flow behaviour in the wake. For a horizontally placed
heated
cylinder, the free-stream approach flow can be either
horizontal,
vertically upward or vertically downward, they are called
horizontal
cross-flow, parallel flow and contra-flow arrangements based on
the
angle between the approach flow direction and the thermally
induced
buoyancy force acting on the fluid surrounding the heated
cylinder.
1.1 Wake Flow The flow downstream of a body immersed in a stream
or the flow
behind a body propagating through a fluid. Wakes are narrow
elongated regions; filled with large and small eddies. The
wakes
eddies of a bridge pier immersed in a river stream, or of a
ship
propelled through the water, are often visible on the surface.
On
windy days, similar wakes form downstream of smoke stacks or
other
structures, but the eddies in the air are not visible unless
some smoke
or dust is entrained in them.
Turbulence in the wake of bluff bodies consists of all sizes of
eddies,
which interact with each other in their unruly motion. Yet, out
of this
chaos emerges some organization, whereby large groups of
eddies
form a well-ordered sequence of vortices. The sense of rotation
of
these vortices alternates and their spacing is quite regular. As
a result,
they can drive a structure that they encounter or they can exert
on the
body that created them a force alternating in sign with the
same
frequency as that of the formation of the vortices. Such forces
can
impose on structures unwanted vibrations which often lead to
serious
damage. Flow induced forces can be catastrophic if they are in
tune
with the frequency of vibration of the structure. Wakes are
sustained
for very large distances downstream of a body. Ship wakes
retain
their turbulent character for miles behind a vessel and can be
detected
by special satellites hours after their generation.
Similarly
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condensation in the wake of aircraft sometimes makes it look
like a
narrow braided cloud, traversing the sky.
Figure 1.1
1.2 Vortex Shedding
Vortex shedding is an oscillating flow that takes place when a
fluid
such as air or water flows past a bluff (as opposed to
streamlined)
body at certain velocities, depending on the size and shape of
the
body. In this flow, vortices are created at the back of the body
and
detach periodically from either side of the body. The fluid flow
past
the object creates alternating low-pressure vortices on the
downstream
side of the object. The object will tend to move toward the
low-
pressure zone. If the bluff structure is not mounted rigidly and
the
frequency of vortex shedding matches the resonance frequency of
the
structure, the structure can begin to resonate, vibrating with
harmonic
oscillations driven by the energy of the flow. This vibration is
the
cause of the singing of overhead power line wires in a wind, and
the fluttering of automobile whip radio antennas at some
speeds.
Tall chimneys constructed of thin-walled steel tube can be
sufficiently
flexible that, in air flow with a speed in the critical range,
vortex
shedding can drive the chimney into violent oscillations that
can
damage or destroy the chimney. These chimneys can be
protected
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from this phenomenon by installing a series of fences
(sometimes
called strakes or spoilers) at the top and running down the
exterior of
the chimney for approximately 20% of its length. The fences
are
usually located in a helical pattern.
The fences prevent strong vortex shedding with low
separation
frequencies. The optimal pitch for vortex shedding is a 5D pitch
(5 x
the diameter of the stack).
1.3 Reynolds Number
The Reynolds number is defined as the ratio of inertial
forces
to viscous forces and consequently quantifies the relative
importance
of these two types of forces for given flow conditions.
Reynolds
numbers frequently arise when performing scaling of fluid
dynamics
problems, and as such can be used to determine dynamic
similitude between two different cases of fluid flow. They are
also
used to characterize different flow regimes within a similar
fluid, such
as laminar or turbulent flow
Laminar flow occurs at low Reynolds numbers, where viscous
forces
are dominant, and is characterized by smooth, constant fluid
motion.
Turbulent flow occurs at high Reynolds numbers and is dominated
by
inertial forces, which tend to produce chaotic eddies, vortices
and
other flow instabilities.
1.4 Turbulent flow
Turbulent flow, type of fluid (gas or liquid) flow in which the
fluid
undergoes irregular fluctuations, or mixing, in contrast to
laminar
flow, in which the fluid moves in smooth paths or layers. In
turbulent
flow the speed of the fluid at a point is continuously
undergoing
changes in both magnitude and direction. The flow of wind and
rivers
is generally turbulent in this sense, even if the currents are
gentle. The
air or water swirls and eddies while its overall bulk moves
along a
specific direction.
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Most kinds of fluid flow are turbulent, except for laminar flow
at the
leading edge of solids moving relative to fluids or extremely
close to
solid surfaces, such as the inside wall of a pipe, or in cases
of fluids of
high viscosity (relatively great sluggishness) flowing slowly
through
small channels. Common examples of turbulent flow are blood
flow
in arteries, oil transport in pipelines, lava flow, atmosphere
and ocean
currents, the flow through pumps and turbines, and the flow in
boat
wakes and around aircraft-wing tips.
1.5 Nusselt Number
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Chapter 2
Literature Survey
2.1 The Thermal Effects on the Wake Flow behind a
Heated Circular Cylinder Operating In the Mixed
Convection Regime[1]
The thermal effects on the wake flow were investigated
experimentally. The experiment was conducted such that water
flows
in a channel over a heated cylinder which is maintained at a
particular
temperature. By controlling the temperature, Richardson number
is
varied from 0 to 1.04 resulting the heat transfer change from
forced
convection to buoyancy induced free convection. Molecular
Tagging
Velocimetry & Thermometry (MTV &T) technique is used
to
visualize velocity and temperature distribution. By varying
Richardson number, significant changes in the characteristics of
the
system such as recirculation distance, wake closure length,
vortex
shedding process. It was observed that when Richardson number
is
increased , the usual Karman vortices at the two sides of the
bluff
body is delayed and replaced by Kelvin-Helmholtz like vortex
structures and drag coefficients were found to be increased due
to
thermally induced flow. The average Nusselt number were found
to
be linearly decreasing with increasing Richardson numbers. A
numerical study yielded similar results in predicting wake
vortex
characteristics and flow pattern
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2.2 Passive Control of wake flow behind a
circular cylinder by parallel dual plates[2]
This is a numerical study on the effect of control device,
consisting of
two plates placed parallel to the wake centreline, on wake
characteristics with the objective of wake stabilization. Two
parallel
plates were placed behind the circular bluff body over which
flow
takes placed in a low Reynolds number regime. Extensive
studies
were performed by varying the angle of the plates and the number
of
plates. There was significant difference in the wake parameters
by
introducing plates at the rear of a bluff body and for thorough
wake
stabilization, the length of the plate must be 5 times that of
bluff body
diameter. The coefficient of drag experience change as high as
23%
close to L/D ratio of 1.5. Depending of the angle of the plates,
the
wake regime can be classified into three regimes, when the angle
of
the plates increased there was a decrease in coefficient of
drag. In this
paper, two mechanisms for the control of dual plates is
suggested.
First is the stabilization of free shear layer fluctuation and
the other
one is the basal cavity effect which accounts for pressure
redistribution upon the base surface region.
2.3 Heat Transfer From A Cylinder In The Wake
Flow[3] In this work, the effect of obstacle size and the shape
on the heat
transfer characteristics is studied. An additional cylinder is
placed
downstream of the bluff body and convective characteristics
are
determined. Conductive and radiation heat transfer is
considered
negligible. Lumped heat capacitance method is used in
determining
heat transfer coefficients. For every obstacle shape and size,
the effect
of spacing between obstacles and location of obstacles relative
to one
another is studied. It was observed that heat transfer did not
vary
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significantly at lower Reynolds number but when Reynolds
number
was higher, heat transfer was significantly higher. For
higher
Reynolds number, the larger the obstacle size, the higher was
the
average Nusselt number. When the obstacle was present just
behind
the circular object, the obstacle had a negative effect on the
heat
transfer, but for square cross section object, heat transfer
showed an
improvement.
2.4 Dependence of flow classification on the
Reynolds number for a two-cylinder wake[4]
This is a study on aerodynamic interference between multiple
structures. Flow behind two staggered cylinders is more
complicated
than with single cylinder configuration. Moreover, flow
characteristics depend on angle between the flow direction and
the
line joining two cylinders and the pitch distance between
two
cylinders. The experiments were performed in a wind tunnel
of
section 2.4m x 0.6m x 0.6m in which uniform flow takes place.
Two
hotwires are used to simultaneously measure velocity
fluctuation.
Flow modes are divided based on the values of pitch ratio and
angle.
An increase in Reynolds number reduces boundary layer
thickness,
causes a shift in separation point towards forward stagnation
point,
increases separation angle and decrease in vortex formation
length. It
was found that transition from one flow mode to another or the
border
of flow regime solely dependent on the variation of Reynolds
number.
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Chapter-3
Procedure
The analysis is attempted in a CFD software, and the final
results
are to be compared with experimental results. The properties
of
the fluid and temperature are considered same as experiment
performed.
The problem is modelled as per the experiment and suitable
boundary conditions and initial conditions are set. The
suitable
options in the models set are chosen.
Grid independence and temporal independence studies are done
in
order to determine base size and time step size. Too low
base
sizes and time step sizes would yield accurate results but
consume
unaffordable computational time. Large base and time step
sizes
would take less computational time but with a compromise on
accuracy. Therefore, base size and time step sizes must be
chosen
such that they give results of sufficient accuracy with
affordable
computational time.
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Figure 3.1
Figure 3.2
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After finalizing with base size and time step size, the analysis
of six
cases are performed. The temperature and velocity plots are
extracted
from scalar scene and to be compared with the plots from the
experiment.
Figure 3.3
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Figure 3.4
Additionally, the ideal geometries for minimum and maximum
heat
transfer are to be determined. So the other geometries that
are
considered include Equilateral Triangle, Inverse Equilateral
Triangle,
Square, Hexagon.
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Chapter 4
Design calculations
4.1 Time step calculation:
For flow over cylinders, strouhal number can be approximated to
0.2
St = f D / V
Where f is the frequency of vortex shedding.
By substituting D = 4.76mm & V = 0.026m/s
We get f =1.09 Hz, Time period = 0.917s.
So, we choose a standard time step close to 0.917s as 0.1s.
Temporal independence study is done by varying time period
below
0.1s.
4.2 Number of time steps:
We know distance of fluid travel = 200mm,
Velocity of fluid = 0.026m/s
Therefore, time taken for fluid to travel = 7.611s
For more accurate values, we take time as 20s.
For t = 0.1, No: of time steps: 20/0.1 = 200
For t = 0.01, No: of time steps: 20/0.01 = 2000
4.3 Geometry
Figure 3.1
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4.4 Mess process
Trimmer type elements are utilised in building up the
geometry.
Additionally, prism layer and wake refinement are
implemented
around the bluff body so as to obtain more accurate results.
Arbitrarily base size of 0.005m, which is close to the diameter
of the
cylinder is chosen. In the wake refinement region, the size is
6% of
base size. Grid independence study is performed by decreasing
the
base sizes below 0.005m. Due to the capability of the computers
we
possess, base sizes below 0.003m could not be meshed.
Figure 5.2
Prism Layer and wake refinement:
Figure 5.3
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4.5 Assumptions
The analysis is symmetric along the cross section. Hence
two-
dimensional analysis is sufficient. The fluid used is water
which is
incompressible and of constant density. Owing to Reynolds
number
being very low, laminar flow is assumed. Gravity function is
turned
on, as the water flows under gravity. Segregated flow is
assumed.
4.6 Boundary conditions
The temperature of the water is initially set as 24C and flows
with a
intial velocity of 0.026 m/s from the top edge. The temperature
of
bluff body is maintained constant throughout the analysis and
depends
on the specific case. The bottom edge of the section is
assumed
pressure outlet.
4.7 Converging criteria
Mass balance and enthalpy balance errors are calculated for
every
analysis done and made sure whether the errors are within
acceptable
limits. Mass balance is the difference between mass entering
through
the inlet and mass leaving the outlet. Similarly, enthalpy
balance is
the difference between enthalpy of the inlet edge and the
enthalpy
through the outer edge
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Chapter 5
Numerical Results
Considering for the below cases
Case
no.
Tw (0C) T (
0C) Re Gr Ri
1 24 24.0 135 0 0.00
2 35 24.0 135 3400 0.19
3 42 24.0 135 5600 0.31
4 53 24.0 135 9100 0.50
5 66 24.0 135 13100 0.72
6 85 24.0 135 19100 1.04
Table 5.1
5.1 Circular Cross section cases: Tw =240C
Velocity
Figure 5.1
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Temperature
Figure 5.2
Tw =350C:
Temperature
Figure 5.3
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Tw =420C:
Temperature
Figure 5.4
Tw =530C:
Temperature
Figure 5.5
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Tw =660C:
Temperature
Figure 5.6
Tw =850C:
Temperature
Figure 5.7
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Velocity
Figure 5.8
The change in velocity plot for different Richardson numbers
is
negligible. As the Richardson number increases, the temperature
in
the wake region increases considerably.
A central vertical probe is considered and the velocity and
temperature values are tabulated and analysed for
temperature
regainment distance and velocity recirculation distance. The
maximum temperature along the central probe is higher than that
of
other shapes under similar condition.
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5.2 Equilateral Triangle cross section Tw =240C
Temperature
Figure 5.9
Velocity
Figure 5.10
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Equilateral Triangle cross section Tw =850C
Temperature
Figure 5.11
Velocity
Figure 5.12
In case of Equilateral triangle, the wake vortices observed were
more
disorder and the peak velocity observed along the centreline
is
relatively higher when compared with other shapes. It has
the
maximum temperature regainment distance with the value 200%
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greater than that of circle and has velocity recirculation
distance 31%
lower than that of circle.
5.3 Hexagon cross section Tw =240C
Temperature
Figure 5.17
Velocity
Figure 5.18
Figure 5.13
Velocity
Figure 5.14
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Hexagon cross section Tw =850C
Temperature
Figure 5.15
Velocity
Figure 5.16
In case of hexagon, the wake plots are similar to circle but
with higher
velocity recirculation and temperature regainment distances.
Velocity
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recirculation distance is 18% higher than that of circle and
temperature regainment distance is 50% higher than that of
circle.
5.4 Inverse equilateral Triangle Tw =240C
Temperature
Figure 5.17
Velocity
Figure 5.18
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Inverse equilateral Triangle Tw =850C
Temperature
Figure 5.19
Velocity
Figure 5.20
In case of Inverted Equilateral triangle, the region where
buoyancy
forces are predominant is wider when compared to other
geometries.
It is interesting to note that the wake vortices formed are
exactly
behind the apex of the triangle, but they form behind the other
sides
too. Temperature regainment distance is 50% higher than that
of
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circle and velocity recirculation distance is 31% lower than
that of
circle.
5.5 Square cross section Tw =240C
Temperature
Figure 5.21
Velocity
Figure 5.22
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Square cross section Tw =850C
Temperature
Figure 5.23
Velocity
Figure 5.24
The temperature plot of Square cross section is similar to that
of
circular but the velocity plot differs significantly such that
it has the
maximum velocity recirculation distance among all the shapes
that
have been studied. Relatively lower values of peak temperature
and
peak velocity are observed. The velocity recirculation distance
is
37.5% higher than that of circle and temperature regainment
distance
is same as that of circle.
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Velocity with respect to Position graph for circular cross
section
Figure 5.25
Temperature with respect to Position graph for circular
cross
section
Figure 5.26
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Temperature with respect to Position graph for different
geometrical cross sections:
Figure 5.27
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Velocity with respect to Position graph for different
geometrical
cross sections:
Figure 5.28
There is no change in the values of velocity observed along
the
centreline probe for same cross section. However, for
different
geometries, there is a significant change in velocity
recirculation
distance and temperature regainment distance. As the
Richardson
number increases, the temperature peak increases. The change
in
temperature regainment distance can vary as much as 200% and
the
change in velocity recirculation distance can vary as much as
100%
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Parameters along the probe
Shapes Velocity
Recirculation
Region
Distance
(mm)
Temperature
Regainment
Distance
(mm)
Peak
Temperature
(Deg. C)
Peak
Velocity
(mm/s)
Equilateral
Triangle
11 12 35.5 12.81
Hexagon 19 6 62.47 6.26
Inverted
Equilateral
Triangle
11 6 48.85 8.84
Square 22 4 40 6.8
Circle 16 4 72.5 7.97
Table 5.2
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Chapter 6
Conclusions
It was observed that there was no velocity distribution along
the
centreline for the same cross section. The decreasing order
of
maximum temperature along the centreline is Circle, Hexagon,
Inverted Equilateral triangle, Square, Equilateral triangle.
The
decreasing order of peak velocity along the centreline is
Equilateral
triangle, Inverted Equilateral triangle, Circle, Square,
Hexagon.
Temperature regainment distance is maximum for Equilateral
triangle
and the decreasing order is Equilateral triangle, Hexagon,
Inverted
Equilateral triangle, Square, Circle. Velocity recirculation
distance is
maximum for Square and the decreasing order is Square,
Hexagon,
Circle, Inverted Equilateral triangle, Equilateral triangle.
In
applications where heat transfer is necessary, Circular cross
section
can be implemented and in applications where heat transfer is to
be
minimum, Equilateral triangle can be implemented as it has
the
maximum temperature regainment distance.
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References
[1] H. HU AND M. M. KOOCHESFAHANI 2011, Thermal effects on the
wake of heated cylinder operating in a mixed
convection regime, Cambridge University Press
[2] Y BAO, J TAO 2013, The passive control of wake flow behind a
circular cylinder by parallel dual plates, Journal of
fluids and structures
[3] A DALOGLU, A UNAL 2000, Heat transfer from a cylinder in the
wake flow
[4] C.W.WONG , Y.ZHOU, MD.MAHBUB ALAM , T.M.ZHOU , 2014,
Dependence of flow classification on
Reynolds number for a two-cylinder wake, Journal of fluids
and
structures