International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
21
EFFECT OF THERMAL STRESS AND AXIAL LOAD ON COUPOLA FURNACE
METAL COMPONENTS
EJEHSON PHILIP SULE, 2ASHA SATURDAY,3 EZEONWUMELU OGECHUKWU,4 ONUOHA
EVARISTUS IROEME
1
1
ashiga4oxide@yahoo.com,2ejehsonadole@yahoo.com,3oscargulfecho@yahoo.com,4onuohairoe
me@yahoo.com
1,2,3,&4
Scientific Equipment Development Institute SEDI,P. O .BOX 3205,Enugu ,Enugu State,
Nigeria
ABSTRACT
When an unrestrained metallic material is heated or cooled, it dilates in accordance with its
characteristic coefficient of thermal expansion. But components that are restrained behave
differently to thermal effects as a result of the restraining loads this could lead to permanent
deformation of the surface due to rupture, wrinkles, crack, rumple etc. This study presents
analysis of axial loading and thermal stresses in an internally heated Copula furnace
component that is subjected to turbulent flow, and pulsating flow. The effect of flow
Reynolds number on thermal stresses in the insulated component close to the chimney or
exhaust channel ,the influence of hot fluid and axial load on components on the resulting
thermal stresses in steel material owning to temperature gradient and
with different
diameters, and thickness to diameter ratios are covered in this study to examine the
effects on thermal stresses and axial load. The amount of heat flux at the inner wall of the
Component with regard to regular use and unfriendly heat dissipation creating severe
temperature gradient on the inner and outer walls is also included in the study.
IJOART
KEY WORDS: axial load, thermal stress ,temperature gradient, rumpling ,copula furnace part.
INTRODUCTION
The mechanical behavior of materials when
subjected to thermal effects or thermal
environment is a factor to into consideration
when you are to design thermal machines or
systems. Meeting the need for materials,
which can function usefully at different
temperature levels, is one of the most
challenging problems facing some our
technology. Some examples are the
dilation effects like the strengthening of
bridges on a hot day or the bursting of
Copyright © 2016 SciResPub.
water pipes in freezing weather and
distortions set up in structures by thermal
gradients. Sometimes-drastic changes in
the properties of materials, such as tensile
strength fatigue and ductility as for the
metals could also result by the change in
material temperature ,also this is not limited
to the metals the plastics ,polymers or
elastomers even composites exhibit such
change in properties when subjected to
thermal environment. The elements of mild
steel component body expand with rising
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
temperature. Such an expansion generally
cannot proceed freely in a continuous
medium, and stresses due to the heating
are set-up. The difficulty is that operating
conditions
not
only
at
elevated
temperature levels, but frequently also at
severe
temperature
gradients.
Such
temperature differentials may produce
thermal stresses significantly high enough
to limit the material life. Fatigue failure
could also
occur due to temperature
fluctuations. Thermal cycling
process
which is the alternate heating and
cooling of a material until they
experience molecular reorganization which
tightens
or optimizes the particulate
structure of the material
throughout,
relieving stresses and making it denser
and uniform thereby minimizing flaws or
imperfections. Miner postulated that when a
component is fatigued, internal damage
takes place and the nature of the damage is
difficult to specify but it may help to regard
the damage as the slow internal spreading of
a crack, although this should not be taken
too literally. He also stated that the extent of
damage was directly proportional to the
number of cycles for a particular stress
level and quantified this by adding that
“the fraction of the total damage occurring
under one series of ycles at a particular
stress level, is given by the ratio of the
number of cycles actually endured (n) to the
number of cycles (N) required to break the
component at the same stress level” [3]
22
deformation is induced and thermal stresses
are developed. The resulting
thermal
stresses add to the stresses resulting from
internal and external pressures in the pipe
material. One of the causes of thermal
stresses in pipes is the non-uniform
heating or cooling; such a situation that
exists when for example pipes are welded,
causing residual
stresses.
Nuclear
engineering structures, military industries,
chemical and oil industries, gun tubes,
nozzle sections of rockets, composite
tubes
of automotive
suspension
components, launch tubes, landing gears,
turbines, jet engines and dies of hot forming
steels are typical examples.
The transfer of heat in a solid occurs in
virtue of heat conduction alone for time
periods longer than phonon relaxation time.
This does not have any macroscopic levels
of movement in the solid body such as
non-uniform electrons motion. At the
surface o f a body, heat transfer can occur in
three ways: heat conduction, convection, or
radiation. The heat exchange in the case
of convection occurs by virtue of the
motion of non-uniformly heated fluid or
gas
contiguous
with
the
body.
Convective heat transfer is the sum of the
heat carried by the fluid. Heat exchange
by means of electromagnetic waves takes
place between bodies separated by a
distance in the case of radiation. The pipe
flow subjected to conjugate heating, where
heat conduction in the solid interacts with
convection heat transfer in the fluid,
situations that result in large temperature
gradients finds wide applications in
engineering disciplines. This is due to the
fact that the thermal loading can have a
IJOART
For example, thick-walled pipes subjected
to internal heat flow are used in many
applications.
When a thick-walled
cylindrical body is subjected to a
temperature
gradient,
non-uniform
Copyright © 2016 SciResPub.
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
significant effect on the thermal resistance
of the pipe. Examples of systems, in
which the conjugate heat transfer exists,
include heat exchangers, geothermal
reservoirs, marine risers, sub-surface
pipelines
engineering
structures,
refrigeration ducts and nuclear reactors.
Based on the conditions of flow and heat
transfer,
the
temperature
gradients
resulting in pipes differ. The effect of
thermal cycling on a material cannot be
undermined because of its importance to the
design and manufacturing engineer. When a
material is subjected to a temperature
gradient it tends to expand differentially,
during this process thermal stresses are
induced. The source of heat that causes the
thermal gradient may be friction as in the
case of brake.
FLUID FLOW
23
the surface (the core region). Associated
with this condition, the enhanced mixing has
the effect of making velocity, temperature
and concentration profiles more uniform in
the core. As a result, the velocity gradient
in the surface region, and therefore, the
shear stress, is much mlarger for the
turbulent boundary layer than for the
laminar boundary layer. In a similar
manner, the surface temperature, and
therefore, the heat transfer rate is much
larger for turbulent flow than for laminar
flow. Due to this enhancement of convection
heat transfer rate, the existence of turbulent
flow can be advantageous in the sense of
providing improved heat transfer rates.
However, the increase in wall shear stresses
in the case of turbulent flow will have
the adverse effect of increasing pump or
fan power requirements. On the other
hand,
the
conductive
heat transfer
becomes more important in laminar flow
than the turbulent flow.
IJOART
The characteristic that distinguishes laminar
from turbulent flow is the ratio of inertial
force to viscous force, which can be
presented in terms of the Reynolds
number. Viscosity is a fluid property that
causes shear stresses in a moving fluid,
which in turn results in frictional losses.
This is more pronounced in laminar type of
flow; however, the viscous forces become
less important for turbulent flows. The
reason behind this is due to that in
turbulent flows random fluid motions,
superposed
on
the
average, create
apparent shear stresses that are more
important than those produced by the
viscous
shear
forces.
The eddy
diffusivities are much larger than the
molecular ones in the region o f a
turbulent boundary layer removed from
Copyright © 2016 SciResPub.
SCOPE
Investigating
the thermal stresses in
internal heated steel component when they
are subjected to different flow conditions
and it covers both the steady and the
unsteady types of flow. But thermal
recycling as well as fatigue could not be far
from this work. Since the temperature of
the solid-fluid boundary depends on the
fluid properties, the effect of the fluid
Prandtl number on thermal stresses is
investigated. In actual
practice,
the
temperature and heat flux distributions on
the boundary depend strongly on the
thermal
properties
and the flow
characteristics of the fluid as well as on
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
the properties of the wall. In order to
account for this effect, different pipe wall
materials are considered. Similarly, the
temperature level and the temperature
gradients within the solid are highly
influenced by the amount of heat flux
supplied at the outer wall of the pipe,
therefore, different heat flux levels are used
in the study to examine the effect of heat
flux on thermal stresses in pipes.The study
parameters also include the change of
thermal stresses with the pipe dimensions.
Different pipe diameters, thickness to
diameter ratios and length to diameter
ratios are also employed in the study.
AIMS AND OBJECTIVES
24
a.
b.
Fig 1.(a) and (b) pictoral view of a working
copula furnace with a rumpled or wrinkled
part
IJOART
This work is aimed at show casing the effect
of axial load and thermal stress on a
component of a cupola furnace with CAE
using Solid Works 2013,this can be
employed to estimate the service life of a
copula furnace since the steel shell whether
lagged with bricks or not are subjected
regularly to thermal stress and fatigue.
MODELING
Fig 2. Section Of The A Cylindrical Shell
Of Cuopular Furnace
𝑟0 = 𝑜𝑢𝑡𝑒𝑟 𝑡𝑎𝑑𝑖𝑢𝑠 𝑚,
𝑟𝑖 𝑖𝑠 𝑖𝑛𝑛𝑒𝑟 𝑟𝑎𝑑𝑖𝑢𝑠 ,
𝐿 , 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎 𝑐𝑦𝑙𝑖𝑛𝑑𝑟𝑖𝑐𝑎𝑙 𝑠ℎ𝑒𝑙𝑙 ,
𝑡 𝑖𝑠 𝑡𝑟ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑒𝑙𝑙
Copyright © 2016 SciResPub.
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
25
𝑞 𝑖𝑠 ℎ𝑒𝑎𝑡 𝑓𝑙𝑢𝑥 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑜𝑛 𝑡ℎ𝑒 𝑖𝑛𝑛𝑒𝑟 𝑤𝑎𝑙𝑙 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑒𝑙𝑙 ,
𝑢 , 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑜𝑤 𝑜𝑓 ℎ𝑜𝑡 𝑔𝑎𝑠 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛
𝑟 = 𝑟0
0≤𝑦≤𝐿
BOUNDARY CONDITIONS
The boundary conditions
for the
conservative equations of flow involving
fluid and solid are:
𝑇𝑆𝑜𝑙𝑖𝑑
E. The flow is assumed to be at uniform
temperature, i.e.:
A. At pipe axis:
Radial gradient of axial velocity and
temperature are set to zero, while the
radial
velocity is taken as zero, i.e.:
𝜕𝑈
𝜕𝑟
(𝑌, 0) = 0,
𝜕𝑇
𝜕𝑟
𝜕𝑇𝑠𝑜𝑙𝑖𝑑
𝜕𝑟
𝜕𝑇𝑓𝑙𝑢𝑖𝑑
= 𝐾𝑓𝑙𝑢𝑖𝑑
𝜕𝑟
= 𝑇𝑓𝑙𝑢𝑖𝑑
𝑞̇ 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑 = 𝐾𝑠𝑜𝑙𝑖𝑑
𝜕𝑇
(0, 𝑟, 𝑡) = 0
𝜕𝑟
The type of flow is specified based on the
considerations
made:Turbulent
flow:A
unidirectional flow with uniform inlet speed
is assumed.
IJOART
(𝑌, 0) = 0
and 𝑉 (𝑌, 𝑂)=O
B. At inner solid wall (r = rj, where r;
is pipe inner radius):
No-slip condition is assumed
𝑈(𝑌, 𝑟𝑖 )
𝑉 (𝑌, 𝑟𝑖 ) = 0
C. At outer surface of the pipe (r = r0,
where r0 is pipe outer radius):
Uniform heat flux is assumed, i.e.:
𝑟 = 𝑟0
0≤𝑥≤𝐿
D. A t solid-fluid interface, i.e.:
THERMAL STRESSES RELATIONS
In the solid, the governing heat conduction
equation for the steady-state cases
(applicable for fully developed laminar and
turbulent flow situations) is:
1 𝜕
𝑟 𝜕𝑟
�𝑟
𝜕𝑇
𝜕𝑟
�+
𝜕2𝑇
𝜕𝑌 2
=0
[1]
and for the transient case (pulsating flow):
𝜕𝑇
𝜕𝑡
= 𝑥�
1 𝜕
𝑟 𝜕𝑟
�𝑟
𝜕𝑇
𝜕𝑟
�+
𝜕 2𝑇
𝜕𝑌 2
�
[2]
The relation between thermal stress and
strain follows the thermoelasticity
formulae i.e.:
1
𝜀𝜃 = �𝜎𝜃 − 𝑣�𝜎𝑟 + 𝜎𝑦 �� + 𝛼𝑇
𝐸
Copyright © 2016 SciResPub.
[3]
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
1
𝐸𝛼
𝜀𝑟 = �𝜎𝑟 − 𝑣�𝜎𝑦 + 𝜎𝜃 �� + 𝛼𝑇
𝐸
1
[4]
𝜀𝑦 = �𝜎𝑦 − 𝑣 (𝜎𝑟 + 𝜎𝜃 )� + 𝛼𝑇
𝐸
𝜎𝑦 = (1−𝑣) �
[5]
𝜀 is
turbulent
dissipation
2⁄ 2
variable ( 𝑚 𝑠 ),𝜀𝑣 , tangential
strain
𝜀𝑟 radial strain
𝜀𝑥 axial strain
𝜎𝑣 effective stress (Pa)
𝜎𝑢 tangential stress (Pa)
𝜎𝑟 radial stress (Pa)
𝜎𝑦 axial stress (Pa)
T ;temperature at a grid point
K turbulent kinetic energy generation
variable (𝑚2 ⁄𝑠 2 )
𝐾𝑓 =thermal conductivity of the fluid
W/mk
𝐾𝑠 = thermal conductivity of the
solid W/mk
P Pressure Pa
Pr laminar prantl number
Prt turbulent prantl number
q heat flux
Re laminar Renolds number
Ret=turbulent Renolds number
R radial coordinate m
[8]
26
2
𝑟0 2−𝑟𝑖 2
𝑟
0
∫𝑟 𝑇. 𝑟𝑑𝑟 − 𝑇�
𝑖
The effective stress according to Von-Mises
theory [84] is:
𝜎𝑣 = �𝜎𝜃 2 + 𝜎𝑟 2 + 𝜎𝑦 2 −
�𝜎𝜃 𝜎𝑟 + 𝜎𝜃 𝜎𝑦 + 𝜎𝑟 𝜎𝑦 ��
𝜎𝜃 =
𝐸𝛼
(1−𝑣)𝑟 2
𝑇. 𝑟 2 �
�
𝑟 2−𝑟𝑖 2
𝑟
𝐸𝛼
𝑖
𝑟
𝑖
𝑖
[6]
𝑟 2−𝑟𝑖 2
𝜎𝑟 = (1−𝑣)𝑟 2 �𝑟
∫𝑟 𝑇. 𝑟𝑑𝑟�
𝑟
0
∫𝑟 𝑇. 𝑟𝑑𝑟 + ∫𝑟 𝑇. 𝑟𝑑𝑟 −
𝑟0 2 −𝑟𝑖 2
2
2
0 −𝑟𝑖
Copyright © 2016 SciResPub.
𝑟
0
∫𝑟 𝑇. 𝑟𝑑𝑟 −
𝑖
[7]
[9]
TURBULENT FLOW
The mean flow equations are simplified
after the consideration o f Boussinesq
approximations. In cylindrical polar
coordinates the conservation equations are
written.
Continuity:
IJOART
Solving the above equations for a hollow
cylinder results in [83]:
1�
2
𝜕𝑈
𝜕𝑦
+
1 𝜕𝑦
𝑟 𝜕𝑟
(𝑉𝑟) = 0
[10]
MOMENTUM
1 𝜕
𝑟 𝜕𝑟
1 𝜕
𝑟 𝜕𝑟
(𝑟𝑉𝑈𝜌) +
�𝑟(𝜇 + 𝜇𝑡 )
ENERGY
1 𝜕
𝑟 𝜕𝑟
1 𝜕
𝑟 𝜕𝑟
𝜕
(𝜌𝑈 2 ) = −
𝜕𝑌
𝜕𝑈
𝜕𝑟
�
[11]
(𝑟𝑉𝑇𝜌) +
�𝑟 �
𝜇
𝑃𝑟
𝜇
𝜕
𝜕𝑌
+ 𝑃𝑟𝑡 �
𝑡
𝑑𝑃
𝑑𝑌
+
(𝜌𝑈𝑇) =
𝜕𝑇
𝜕𝑟
� [12]
where Pr and Prt are bulk and turbulent
Prandtl numbers respectively. In order to
determine the turbulent viscosity and the
Prandtl number, the k-e model is used.
The constitutive equations for the turbulent
viscosity are as follows:
𝜇𝑡 = 𝐶𝜇 𝐶𝑑
𝜌𝐾2
𝜀
[13]
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
where k and 𝜀 are the turbulent kinetic
energy generation and the dissipation
variable respectively. The transport equation
for k is:
1 𝜕
(𝑟𝑉𝐾𝜌) +
𝑟 𝜕𝑟
𝜕𝑈 2
𝜇𝑡 � � +
𝜕𝑟
𝜌(𝜀 + 𝐷𝜀 )
1 𝜕
𝜕
(𝜌𝑈𝐾 ) =
𝜕𝑌
𝑟 𝜕𝑟
�𝑟 �𝜇 +
𝜇𝑡
�
𝑃𝑟
𝑡
[14]
𝜕𝐾 2
𝐷𝜀 = 2(𝜇 ⁄𝜌) � �
𝜕𝐾
𝜕𝑟
�−
[15]
𝜕𝑦
𝜀 attains zero at x = 0.The transport equation
for 𝜀 is:
1 𝜕
𝑟 𝜕𝑟
𝐶𝜀1
𝜇𝑡
𝜌𝜀
�
𝑃𝑟
𝑡
𝜕
(𝑟𝑉𝜀𝜌) +
𝐾
(𝜌𝑈𝜀 ) =
𝜕𝑌
𝜕𝑈 2
1 𝜕
𝜇𝑡 � � +
𝜕𝜀
𝜕𝑟
𝜕𝑟
𝑟 𝜕𝑟
�𝑟 �𝜇 +
[16]
𝜌𝜀 2
𝐾
+
2𝜇𝜇𝑡
𝜌
�
𝜕 2𝑊
𝜕𝑟 2
�
2
In order to minimize computer storage and
run times, the dependent variable at the
walls were linked to those at the first grid
from the wall by equations, which are
consistent with the logarithmic law of the
wall. Consequently, the resultant velocity
parallel to the wall in question and at a
distance xi (where x+ < 2) from it
corresponding to the first grid node was
assumed to be represented by the law of the
wall equations [85], i.e.:
𝑉0 𝐶𝑑 𝐶𝜇 𝐾1⁄2
1
𝐾
equations.The constants used in the transport
equations are:
𝐶𝜇 = 0.5478, 𝐶𝑑 = 0.1643 , 𝐶𝜀1
= 1.44 , 𝐶𝜀2
= 1.92 , 𝑃𝑟𝑘
= 1.0 , 𝑃𝑟𝜀 = 1.314
𝐾2
𝑅𝑒𝑡 = (𝜇⁄
𝜌 )𝜀
[18]
𝜇=fluid dynamic viscosity
𝜏𝑤𝑎𝑙𝑙 = 𝑤𝑎𝑙𝑙 𝑠ℎ𝑔𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑠𝑠 𝑃𝑎
𝑣 = 𝑝𝑜𝑖𝑠𝑠𝑜𝑛′ 𝑠𝑟𝑎𝑡𝑖𝑜𝑛
𝜇𝑡 = fluid dynamic turbulence
viscosity
𝜌 =density of fluid
𝜌𝑠𝑜𝑙𝑖𝑑 =density of the solid
THE
FLUID
AND
SOLID
TEMPERATURE FIELDS
The interior wall temperature at a
given axial plane is calculated
IJOART
� − 𝐶𝜀2
𝜏𝑤𝑎𝑙𝑙 ⁄𝜌
27
=
1⁄2
𝐼𝑛 �𝑒�𝐶𝑑 𝐶𝜇 �
𝐾 = 0.417
𝜌
𝐾 1⁄2 𝑦1 �
𝜇
𝑇𝑤 =
2∗𝑇𝑓𝑤 ∗𝑇𝑠𝑤
𝑇𝑓𝑤 +𝑇𝑠𝑤
[19]
𝑇𝑚𝑒𝑎𝑛 =mean temperature
𝑇𝑠𝑜𝑙𝑖𝑑 =solid side temperature
𝑇𝑓𝑙𝑢𝑖𝑑 =fluidside temperature
ANALYSIS WITH CAE
[17]
𝑎𝑛𝑑 𝑒 = 9.37
from which the wall shear stresses were
obtained by solving the momentum
Copyright © 2016 SciResPub.
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
The CAE analysis is done to verify
effect of axial load and thermal
stress in relation to the thickness of
the coupola
furnace component
which is uninsulated however this
does not mean that the internally
insulated parts are not affected but
this infect is gradual and minimal as
it depends on the type of insulation
i.e type of bricks used.
`ASSUMPTIONS
The following assumption are made
1. No slip on the hot gas stream
flow
2. No friction on application of
the axial load
3. The hot stream has a constant
temperature
4. The material is isotropic
5. The temperature difference is
constant.
6. Flow is turbulent nor
pulsating
Table 2.
28
MATERIAL PROPERTIES
Name:
Model type:
Default failure criterion:
Yield strength:
Tensile strength:
Elastic modulus:
Poisson's ratio:
Mass density:
Shear modulus:
Thermal expansion
coefficient:
AISI 1035 Steel
(SS)
Linear Elastic
Isotropic
Max von Mises
Stress
282.685 N/mm^2
585 N/mm^2
205000 N/mm^2
0.29
7850 g/cm^3
80000 N/mm^2
1.1e-005 /Kelvin
OF THE MODEL
IJOART
MESH PROPERTIES
TABLE1 properties of the mesh of the
parent model
Total Nodes
Aspect
Ratio
18097
91.5
Total
Elements
Mesh Type
Jacobian
Points
4 Points
Element Size
8929
Solid Mesh
35.852 mm
Copyright © 2016 SciResPub.
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
29
MODELS
ii.
Fig3. 3-D model of the cone
shell
IJOART
iii.
Fig4. 3-D mesh of the model
iv.
i.
Copyright © 2016 SciResPub.
fig.5, (i) to (ivi) deform models of the
cone part
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
30
Von Misses stress,MPa
effect of change in
thickness ,t,mm
Fig 6.deformed rumple cone part of the
cupola furnace due to exial laod and
regular heating
TABLE3. Simulated Results
Axial Load = 1800N
𝑇𝑖 =internal wall temperature =1900k
𝑇𝑜 =outer surface temperature =400k
4400
4200
4000
0
10
Strain
Element:
4597
Strain on the
component
Deformation
mm
Node: 1912
0.02
0.015
0.01
0.005
0
0
24
2
20
4251.1
0.0120281
3.44285
3
16
4222.11
0.0129057
3.43544
4
12
4542.29
0.0160067
3.38356
5
8
4039.12
0.0115654
3.29209
6
4
4260.11
0.011131
1.96201
0.012558
3.55025
10
20
30
Thickness,t,mm
Fig 8. Strain development on the
material with application of axial load
and temperature gradient
linear defomation
Displacement,mm
1
16081
4317.35
GRAPH
30
Thickness ,t,mm
IJOART
Von Misers
Stress
N/mm2 Node:
20
Fig 7. Stress development on the
material with application of axial load
and temperature gradient
Strain
S/N THICKNESS
mm
4600
4
3
2
1
0
0
10
20
Thickness,t,mm
Copyright © 2016 SciResPub.
IJOART
30
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
Fig 9.Linear deformation development
on the material with application of
axial load and temperature gradient
DISCUSSION
This study reveals the effect of thermal
stress on the cone model and the
rumple effect is more visualized than in
data form, see fig 5,iv and fig 6 ,there
is a clear similarity between the
pictorial view and the simulated model.
The value of the maximum stress is
used to predict the furnace column
shell model life based on fatigue
analysis. Thermal stress has more
effect on service life of a cupola
furnace than mechanical stress. Hence
,the material do not show distinct
variation on linear displacement of the
component as a whole, but the software
was able to show clearly the rumpling
of the material owning to the
temperature gradient since ductility of
a material increase with increase in
temperature in a thermal environment,
the axial load on the has to compress
as the material fails under thermal
environment. The table 3. shows that
the Von Misses stress increase as the
thickness decreases under the same
thermal condition and axial load. Thus,
to withstand axial load under severe
thermal conditions, thicker materials
should be used with or without
insulations especially areas from
charging door and above, but in
general,coupola furnace component
need to be limned internally with
insulating bricks to maximize the
31
performance and efficiency and as well
as extend the life of the metal parts due
to thermal recycling as foundry
operation is regular. Therefore, effect
of thermal stress on metallic material
like mild steel is minimized when they
are lagged internally.
CONCLUSION
Axial load and thermal stress has a
significant effect on failure of copula
furnace
parts. Proper Insulation
minimize or eliminate these effects
resulted from temperature difference
(gradient). The rumple and wrinkles
observed is as a result of thermal
stress on the constrained cone part by
axial load,this effect due to severe
temperature difference is minimized by
adapting thicker materials or insulating
their inner walls with good insulating
bricks.
IJOART
Copyright © 2016 SciResPub.
REFFERENCES
1. T. Inaba, “Longitudinal Heat
Transfer in Oscillatory Flows
in
Pipes
with Thermally
Permeable Wall”, Journal of
Heat Transfer, Vol. 177, pp.
884-888, November 1995.
2. L. Bauwens, “Oscillating Flow
of a Heat-Conducting Fluid in a
Narrow Tube”, J.
Fluid Mech., Vol. 324, pp.
135-161, 1996.
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
3. Miner, M. A., Cumulative
damage in fatigue transactions
ASME, 67, 1945.
4. J. Zhang and C. Dalton,
“Interaction of a
Steady
Approach Flow and a Circular
Cylinder Undergoing Forced
Oscillation”, Journal of Fluids
Engineering, Vol.
119, pp. 808-813, 1997.
5. Z. Guo and H. Sung,
“Analysis
of the Nusselt
Number in Pulsating
Pipe
Flow”,
Int. J. Heat Mass Transfer, Vol.
40, No. 10, pp. 2086-2489,
1997
32
with Various Wall Heat Flux
Distributions
and
Heat
Generation”, Journal of Heat
Transfer, Vol. 107, pp. 334337, 1985.
9. Kirk,E.,1899 copular furnace –
A practical treatise on the
construction and management
of
foundry
cupolas
,Philadelphia.,PA:Baird
10. Larsen.E.D.,Clark,D.E,Moore,
K.L.
&
King
,PE,1997.Intelligent control of
cupola
Melting
Lockheed
Martin Idalo Technologies
company
11. Bejan A 1993 Heat Transfer,
John Wiley & Sons, New York.
12. Holman JP 1989 Heat Transfer,
McGraw-Hill, Singapore.
13. Incropera FP and Dewitt DP
1990 Fundamentals of Heat
and Mass Transfer, John Wiley
& Sons,New York.
14. Ozisik MN 1968 Boundary
Value Problems of Heat
Conduction, International Text
Book Company,Scranton, PA.
15. N. Arai, A. Matsunami, S. W.
Churchil, 1996, A review of
measurements of heat flux
density applicable to the field of
combustion,
Experimental
Thermal and Fluid Science, ,
12, 452-460
IJOART
6. Davis, and W. Gill, “The
Effects of Axial Conduction
in The Wall on Heat
Transfer with Laminar Flow”,
Int. J. Heat Mass Transfer,
Vol. 13, pp. 459-470,
1970.
7. B. Kraishan, “On Conjugated
Heat Transfer in a Fully
developed Flow”,
Int. J. H eat Mass Transfer”,
Vol. 25, No.2, pp. 288-289,
1982.
8. O.A.
Amas, and M.A.
Ebadian, “Convective Heat
Transfer in A Circular Annulus
Copyright © 2016 SciResPub.
IJOART
International Journal of Advancements in Research & Technology, Volume 5, Issue 4, April-2016
ISSN 2278-7763
33
IJOART
Copyright © 2016 SciResPub.
IJOART