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158
The Open Materials Science Journal, 2015, 9, 158-161
Open Access
Study on Influence of Water-Cooled Stool During the Process of
Unidirectional Solidification
Guangwu Ao1, Minggang Shen*,2, Zhenshan Zhang1 and Xiaodong Li2
1
School of Applied Technology, University of Science and Technology Liaoning, Anshan114011, China
2
School of Materials and Metallurgy, University of Science and Technology Liaoning, Anshan114051, China
Abstract: The heat flow control is an important link in directional solidification. Mathematical model for unidirectional
solidified ingot with multiple sets of cooling system was established. Temperature field and flow field influenced by
traditional water-cooled stool and improved one during solidification of a 45 t was carried out by using ProCAST
software. The results of temperature distribute and flow field show that the proposed chassis cooling system can improve
the axial temperature gradient. Uniform columnar grains from top to bottom are obtained and mechanical properties are
improved.
Keywords: Flow field, hollow lateral wall, temperature field, unidirectional solidification, water-cooled stool.
INTRODUCTION
Directional solidification has been widely used in
manufacturing the advanced material with special orientation
of the organization and excellent performance. Generally
speaking, there are three aspects in production technology of
directional solidified ingot such as sidewall insulation,
chassis cooling and liquid level. The side wall insulation
control mold temperature gradient from the bottom to the
top, and the solidification only in one direction from the top
of the bottom of the mold. In order to promote the directional
solidification, to increase the bottom cooling as much as
possible is also required. The reasonable chassis cooling
scheme will establish a bottom-up temperature gradient,
make the bottom nucleation of the lowest in the cooling
process and the crystal grows from the bottom up, form the
dendrite skeleton, which is the residual liquid metal.
Using the thick large chassis and forced cooling usually
with water are common practice. Tamaguchi Miyuki et al.
[1] thinks that whole thick stool should be divided into two
parts and only change the upper one after damage
considering too high cost. But a heat insulation layer will
form because the combination of upper and lower between
the two plates is not tight. Yuanyingshi et al. [2] think that
during the general directional solidification process, the
bottom will have a reverse contraction, thereby forming a
gap, and this gap can significantly reduce the thermal
conductivity between the chassis and the steel ingot, so the
height of directional solidification ingot is limited.
and finite element model respectively) which consists of
three blocks and lay inside the snake-shaped cooling pipe.
By using the method of the different intensity cooling of the
sub center, the chassis center can achieve the cooling
intensity and the cooling intensity of the chassis is small. At
the same time, the mathematical model on the temperature
field and flow field of heavy steel ingot was established and
numerical simulation on ingot solidification with
conventional water-cooled stool and the improved one was
carried out respectively. The chassis cooling parameters are
optimized.
Fig. (1). Geometrical model of optimized water-cooled stool.
According to the references, we put forward a new
cooling chassis with multiple sets of cooling system for
directional solidification (Figs. 1, 2) shows its geometrical
Fig. (2). Finite element model of unidirectional solidification with
optimized water-cooled stool.
1874-088X/15
2015 Bentham Open
Influence of Water-Cooled Stool During the Process of Unidirectional Solidification
1.
MATHEMATICAL
MODELING
TEMPERATURE FIELD SIMULATION
FOR
1.1. Basic Assumptions and the Control Equation
Heat transfer in casting is very complex, so it is very
difficult to give an accurate initial and boundary conditions.
The study on solidification simulation software is based on
establishing the mathematical model conforms to the actual
situation according to the solidification physical model, and
constantly revised to obtain accurate results. In the process
of establishing the physical model and mathematical model,
taking into account the current development of the theory
and the calculation conditions, make appropriate
assumptions and omission should be acceptable to the actual
situation. In order to simplify the model, this research is
based on the following assumptions [3-6]:
1.
2.
The filling process of liquid metal is instantaneous
and the beginning of solidification. Because some
initial conditions are based on this assumption, for
heavy plate steel ingot, because the ingot
solidification time is much longer than the casting
time, so it will not cause too much deviation;
In this paper, using the view of E A Mizikar, the heat
transfer rate of liquid metals is not considered, and
the heat transfer caused by the heat transfer of the
liquid metals is compensated by the appropriate
thermal conductivity of liquid metals;
3.
Density as
temperature;
constant
does
not
change
with
4.
The effective specific heat and the effective heat
conduction coefficient were respectively adopted for
the specific heat and the heat conduction coefficient
of the metal;
The Open Materials Science Journal, 2015, Volume 9
159
way, heat convection and radiation occurred mainly in the
boundary.
Although the steel liquid / heat transfer mold system is
based on three kinds of heat transfer in a comprehensive
way, but in the analysis of temperature field during
solidification of steel ingots, the basic mathematical model is
not stable heat conduction partial differential equations (Fu
Liye's law). In the general 3D problems, control equations
are as follows [7-9]:
𝜌𝑐!
!"
!"
=
!
!"
𝜆!
!"
!"
+
!
!"
𝜆!
!"
!"
+
!
!"
𝜆!
!"
!"
+ 𝜌𝑄
(1)
where ρ is the density(Kg/m3), Cp is latent heat (J/kg·k), λ
x,λy andλz are materal thermal conductivity along three
main directions as x, y and z(W/(m·k), T represents the
temperature(k),τrepresents the time(s) and Q=Q(x, y, z, τ)
represents the heat source density inside the object(W/kg).
The above equations coupled with the initial and
boundary conditions for solving the equations, constitutes a
mathematical model to describe the solidification process of
castings.
1.3. Solving Condition of Numerical Equation of Steel
Ingot Solidification Process
1.3.1. The Determination of Boundary Conditions
We put the bottom of the ingot and water cooling chassis
contact surface as a boundary condition of the third type, and
the ingot center symmetry plane and the outer surface of the
insulating board as the second boundary condition [10-13].
The upper part surface of the ingot: K
∂T
=q
∂x
5.
The materials that calculation involved are isotropic;
The lower part surface of the ingot: q = h(Tb − T f )
6.
Solidification was carried out under equilibrium
conditions;
Ingot around:
7.
The ingot deformation and volume change during
solidification is ignored.
∂T
=0
∂x
Ingot centre:
∂T
∂x
x=d/2
(4)
(5)
(6)
=0
1.2. Controlling Equation
x = d / 2 represents half the thickness of steel ingot.
The solidification process is a complex heat transfer
process. In the process of solidification, the liquid steel
transfer heat through a variety of ways to the mold and the
surrounding environment after pouring into a mold, the
temperature is falling, at the same time, environment and
surrounding medium, especially cast continuously absorb
heat and temperature rise. An unstable heat transfer
continuous process will be formed from one part to another
part in the above process. Heat transfer in a variety of ways:
before and after the solidification of liquid steel to cast, voids
and atmospheric radiation heat transfer; convective heat
transfer of liquid steel and casting mould and the atmosphere
within the different parts and between before and after
pouring; solidification liquid steel, steel liquid into the
internal mold and mold materials heat conduction, heat
transfer from the way, the cooling process is done by
radiation, convection and conduction three comprehensive
where: K is thermal conductivity coefficient (W/m°C),
(7)
q is heat density (W/m2),
h is heat exchange coefficient (W/m2°C),
Tb is the lower surface temperature of ingot (°C),
Tf is the temperature of cooling water (°C).
This paper take the wide and heavy plate steel ingot side
wall as an infinite plane wall and the thermal conductivity as
a one-dimensional non steady heat conduction. Therefore the
study deals with the initial conditions and three kinds of
boundary conditions in the following form:
AT T + BT Q = CT
Among the equation:
(8)
160 The Open Materials Science Journal, 2015, Volume 9
Guangwu et al.
T is the wall temperature (K),Q is the heat flux through the
wall(W/m2), AT, BT, CT are constants based on boundary
conditions.
When AT ＝1, BT ＝0 for the first boundary condition,
When AT ＝0, BT ＝1 for the second boundary condition,
When AT ≠0, BT≠0 for the third boundary condition.
For the third boundary condition, Q = h(Tinf – T) can be
changed into the form as hT+Q= hTinf, and AT, BT, CT can be
used to determine the boundary conditions of the third kind.
1.3.2. Initial Conditions
Because the solidification time is much longer than
pouring time during the casting process, the effect of the
filling process on the initial temperature field is ignored.
In this paper, the molten steel pouring temperature of
1560°C, the baking temperature of ingot mould is 80 °C and
atmospheric temperature is 25 C. The study set the heat
transfer coefficient of the traditional water cooling chassis as
5000 W/m**2/K during numerical simulation process. The
multi zone water cooling system is composed of three parts
and the heat transfer coefficient are set as 20000 W/m**2/K,
10000 W/m**2/K, and 5000 W/m**2/K respectively from
inside out [14].
Fig. (4). Heat flux of directionally solidified ingot with cooling
system.
Fig. (4) shows Heat flux of 45 t directionally solidified
ingot with conventional water-cooled stool(a) and optimized
one(b) respectively. From Fig. (2) we can see that heat flow
in one direction and perpendicular to the growth of the solidliquid interface. With optimized water-cooled stool and
previously studied hollow lateral wall, the majority of heat
flux is transferred along the direction of water cooling
chassis. Thus promote the directional solidification.
2. SIMULATION RESULTS AND ANALYSIS
Simulate the solidification process of steel ingot
temperature distribution and heat flux can be laid the
foundation for the evaluation of the ingot quality, and
prevent the shrinkage hole, shrinkage porosity, segregation,
hot crack defects so as to guide the production and improve
the quality of ingot.
Fig. (3a, b) is temperature distribution cross-section
contours of directionally solidified ingot which adopted
traditional chassis and the improved one respectively. From
Fig. (3) we can see that the solidification front in graph (b) is
pushed much more smoothly and evenly than that in graph
(a). The temperature gradient is increased so as to control the
grain orientation of the solidification structure.
Fig. (5). Temperature of the outer wall 1/2 position of steel ingot
mold with different water-cooled stool.
Fig. (5) is the outer wall of the location of 1/2 by
directional solidification ingot temperature time diagram of
different water-cooled chassis. From Fig. (5) we can see that
the sampling point temperature with optimized multi zone
cooling system is lower than that of the conventional one.
CONCLUSION
1)
Fig. (3). Temperature distribution cross-section contours of
directionally solidified ingot with different cooling system.
A new type of chassis, consisting of three cooling
regions is drawn. The solidification front with
improved cooling chassis is pushed much more
smoothly and evenly than that with traditional one.
Metal solidification heat is conducted away as soon as
possible.
Influence of Water-Cooled Stool During the Process of Unidirectional Solidification
2)
3)
The mathematical model on the temperature field and
flow field of 45 t directionally solidified ingot was
established and the model is feasible after
verification.
In the numerical simulation process, the quality of
casting is affected larger by water stool.
CONFLICT OF INTEREST
[1]
[2]
[3]
[4]
[6]
[7]
ACKNOWLEDGEMENTS
Conversations with Professor M.G. SHEN and workmate
Z.S. ZHANG have been most helpful. This work has been
supported by The Education Department of Liaoning
Province Key Laboratory Project under No.2008S122 and
the Metallurgical Engineering Laboratory, University of S. &
T. Liaoning.
This study was financially supported by The Education
Department of Liaoning Province Key Laboratory Project
under No.2008S122 (Technology development of
unidirectional solidification with hollow lateral wall
insulation for production of large heavy plate).
[8]
[9]
[10]
[11]
[12]
[13]
[14]
Received: February 17, 2015
161
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The authors confirm that this article content has no
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Accepted: June 9, 2015
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