Applied Mechanics and Materials
ISSN: 1662-7482, Vols. 395-396, pp 1212-1217
doi:10.4028/www.scientific.net/AMM.395-396.1212
© 2013 Trans Tech Publications, Switzerland
Online: 2013-09-03
Numerical Simulation of Filling Process in Large Steel-ingot
Zhang Zhaohui ,Feng Lu, Zhao Fucai
School of Metallurgical Engineering， Xi’an University of Architecture and Technology， Xi’an
710055， Shaanxi， China
E-mail：[email protected]
Keywords: gas entrapment, the filling process , the numerical simulation
Abstract. A three dimensional incompressible gas-liquid two-phase flow model is proposed to
accurately simulate the fluid flow of casting's mould filling process. The gas entrapment during
mould filling is studied under different initial velocity and pressure conditions. The simulation
results show that the velocity of change has a larger effect on gas entrapment, Initial velocity affects
the distribution of temperature field,meanwhile gas entrapment parts specialized sampling is
proceeded for qualitative detection at the scene. The simulated result is consistent with the
experimental result, which can be reference for the process parameters selection and mold design of
filling process in large steel-ingot.
Introduction
Liquid metal during the mold filling process in practice cannot be observed in different time
phase changes of the flow field and temperature field, ingot casting numerical simulation is learned
the liquid metal free surface in contact with the air-liquid metal and surface formed in the interface.
As the initial temperature, filling pressure and the sprue gate parameters changes, the intinal
adjustment of ingot casting enchance the liquid metal flow and temperature field of ingot to achieve
optimal results. Firstly, reduce the gas entrapment in the process of filling and defects; Secondly, a
uniform temperature field and flow field should be provided as far as possible to solidification
phase.This article mainly aims at the numerical simulation of large steel ingot in the process of
filling and need know the arrival time of free surface condition, the gas-liquid phase transformation
is a process of change between the three-dimensional unsteady turbulent flow, large steel ingot
casting filling time is relatively longer than small mold filling time, because of the influence of the
gas back pressure , liquid steel in mold cavity through the sprue gate type and liquid metal into the
cavity of the inertia and the wall between the coefficient of thermal conductivity and consideration
of factors, makes the simulation of filling complex process comparatively. Smoothly to simulate
filling process conditions for computer configuration and the software itself is higher, Some initial
and boundary conditions need be simplified, resulting in the expense of calculation accuracy.
mathematical equation
2.1 Mathematical model of liquid flow
Liquid flow mathematical model for die casting during the filling process in order to improve the
calculation efficiency,should be accelerated the convergence and be reduced the computation time.
Simulation assumptions: (1) assume that the simulation of the metal liquid is incompressible and
viscous Newtonian fluid, (2) liquid flow in the cavity is the unsteady gas-liquid two phase turbulent
flow. (3) without regard to the effect of casting process during mould filling process. The model
follows the continuity equation, momentum equation and energy conservation equation[1].
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Applied Mechanics and Materials Vols. 395-396
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2.2 Free surface treatment
The most important task on the analysis of the movement of free surface flow is to move the free
surface position determined. Solutions to these questions are divided into two categories[2]:
Lagrangian method and eulerian method. Lagrange method adopted a mobile grid system, each of
compute grid on the free surface is mobile and distortion; Euler's method using a fixed grid system,
formed in the whole field and does not change calculation until could be finished. Considering the
advantages and disadvantages of this method ,and it is true that this method is more ideal algorithm.
however, Lagrange method, the change distorted grid in fluid transition is likely to result in
numerical error; Euler method for computing grid is generated in advance and is fixed in the whole
computing. Therefore, the deformation of the grid can reduce a lot of trouble. After how many years
of theory research and exploration in the euler method has been developed complex multiphase
flow simulation. The most important method contains: the tracking method, the marker particle
method, the volume of fluid method, the level set method. Volume of fluid method (VOF) is widely
used in the interface to capture method in the field of computational fluid dynamic, its adv
computation time. In fact, the melt instead of air in the die casting is neglected the influence of melt
movement in the air except gas entrapment area nearby. It is of importance to determine the
position of the gas entrapment area, rather than accurately solve the melt flow around the gas
entrapment. By increasing the assumptions to reduce the CPU time and give up some accuracy[3].
Single fluid simulation can not meet the actual needs of the current scene, VOF method during the
mold filling process is used to track the gas – liquid two-phase flow interface in this paper[4]. The
volume control fraction is varied from 0 to 1; F value is between 0 and 1 and indicates the gas liquid two-phase flow interface, F = 0 indicates that the cell contains only gas, F = 1 means that the
liquid fills the cell. F represents the volume fraction using ū continuity equation:antage is to ensure
that the fluid automatically follows the principle of conservation of mass,and is easy to simulate the
free surface separation and collision problem of nonlinear geometric topology. VOF method based
on single - fluid algorithms is used to track the free surface during casting by Sergey v. hepel etc. It
seeks fluid region instead of void region in this algorithm. It is not interaction between the fluid and
the void area. the equation which is solved does not take into account an empty area in order to
save.
+ ▽ ŪF =0
(1)
The group phase in each control volume determines the content in the transfer equation. The
density of the gas and the liquid phase using a linear relationship are considered , for each control
volume density can be expressed as:
ρ=F
+（1- F）
(2)
In the same manner as for other parameters are calculated.
Widely use of pressure can be divided into two basic methods[5]: the same as the SIMPLE
method is used to calculate the stability and low speed velocity of relaxation and some non-steady
two-phase methods for calculating instantaneous flow. Typical and similar SIMPLE methods have
SIMPLER, SIMPLEST-ANL, SIMPLEC. They have an important drawback when some methods
are used to calculate unsteady flow. Standard iterative scheme is unstable, there is the use of underrelaxation factor iterative scheme combined into one. SIMPLE and SIMPLEC algorithms are two
algorithms,that is step by step prediction and correction, but SIMPLE algorithm using nonstaggered grid, requires the solution of the momentum equation in order to control the surface
perpendicular to the velocity components, and requires an inverter velocity component[6]. PISO
was proposed pressure implicit operator splitting algorithms by Issa in 1986. The PISO algorithm
includes a prediction step and two correction steps, after the first correction step is completed and
1214
Advanced Materials and Processes III
then seek secondary value improvement, we can better meet the momentum equation and continuity
equation. PISO algorithm is the use of a prediction - correction to revise the steps, which can speed
up a single iteration step in the convergence speed.thus PISO algorithm solved twice the pressure
correction equation needs additional storage space to calculate the source term of secondary
pressure correction equation. Although this method involves more calculations, it is calculated very
quickly, overall efficiency is relatively high[7].
Experimental simulation and verification
3.1 Gas computing model.
Few of air to react with high temperature liquid metal is burned out in the filling process, the rest
are present in the form of air mass into the cavity. These air masses in their environment consider
can be divided into two situations: Firstly, liquid metal located in the forefront of the flow through
the overflow tank is connected with the outside air ventilation group; another is isolated air mass
formed within the liquid metal embroiled, the phenomenon of the gas entrapment is formed inside
the bubble liquid metal. The liquid is replaced by air in the process of mold filling, In addition to be
caught up in the area, other area of gas in the melt ignores the influence of movement of air.Our
main concern is the location of the air drawn into the region, rather than the exact solution of the
melt flow around them. So the main research of gas entrapment is determined the volume of gas as
well as regional location parameters affecting the region [3].Entrained gas prediction: prediction
entrapped gas chamber, the following is the current analysis assumptions: 1) the gas cavity is the
ideal gas; 2) cavity pressure, temperature, density is constant for each group in the gas.
Back pressure is used to solve each time step of the flow field in the pressure of boundary.
Therefore, the melt, gas exhaust and gas porosity in the mold filling process are coupled. This study
should be established the mathematical model in the process of die casting mould filling. The
simulation results in actual use of high-pressure die casting are compared with the experimental
analysis, the application of gas volume in the prediction and qualitative dimensions confirmed the
correctness of the method to be applied.
3.2 Simulation of large steel ingot
Type of
steel
Q345
liquid steel
density
(g/ m³)
7011
Specific heat
liquidus
Solidus
Thermal
conductivity(W/m.k) capacity(J/kg.K） temperature /˚C temperature/˚C
48
480
1496
1442
Firstly, against the ingot in Gambit software in meshing, you can learn to 257,740 nodes. Total
volume of 5.049237 m3. Multiphase fluid under non-steady-state pouring temperature is assumpion
of 1808 K, Assuming the initial mold temperature is generally normal temperature (about 25 ˚C).
Fig 1 shows the iterative calculations are more than five hundred thousand steps, the calculation
will be biased towards the stable, but it is difficult to converge and erative calculation based on a
certain time, the FLUENT software in the diagram can be observed velocity and temperature fields
trends, Fig 2 can be observed, as the initial speed external pressure, the liquid steel in the upward
inertia force of the jetting riser zone would be close to reach the molten steel due to the inertial
force of gravity above case, the metal liquid starts moving along the direction of gravity, but molten
metal in the joint action of two forces begins to flow along both sides of the wall, Fig 2 flow rate
diagram can be clearly reflected in the change of the mold, the Velocity along the Z axis are mainly
at the entrance direction;The liquid metal in the mold is gradually increased,so that this situation
Applied Mechanics and Materials Vols. 395-396
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leads to growing metal fluid gravity and promote speed riser area with shunt flow in the Y-axis
negative direction until the middle of the Z-axis, which is not completely out of the mold which the
air parcelled,so as to form a small flow area;The flow velocity diagram in Fig 3 observed in the
liquid metal flows in the Z-axis rate began to split along the inlet end to form symmetrical
recirculation zone.As for casting molten metal inside the parcel so that air can not flow,the
formation of gas entrapment, especially the most obvious is near the entrance. Resulting casting
defects of gas entrapment.
Fig 4 shows the initial speeds of 1 m/s, 2 m/s, 3 m/s when the midpoint of the mold along the Yaxis positive direction of velocity, temperature change map. According to the following diagram
analysis shows that With the increase of the initial speed, the bigger the temperature change; this
things can not give a smaller temperature gradient in the solidification process, which it is campared
with the mold filling process so that it is difficult to provide ideal conditions. But it is possible to
ensure the smooth progress during the mold filling process, as far as reducing the inlet velocity, so
that small fluctuations can cause steel surface and also inhibit the large grain production. Fig 5
shows that changing the initial pressure in the iterative calculation for the impact is not very
obvious, fluctuations in the calculations which the initial inlet velocity is changed are relatively
large and easy to diverge. Therefore, the fluid velocity is the main factor affecting the gas
entrapment defects in the ingot.
Fig 1 Iterative process diagram
Fig 2 YZ axial field diagram
300000 pa
350000 pa
400000 pa
450000 pa
0.05
0.04
V(m/s)
0.03
0.02
0.01
0.00
27.4
27.6
27.8
28.0
28.2
28.4
28.6
28.8
29.0
29.2
X/mm y=0.8
Fig 3 Z direction of flow Linear
Fig 5 Velocity change map
Advanced Materials and Processes III
1 m/s
2 m/s
3 m/s
0.8
1800
1 m/s
2 m/s
3 m/s
1600
0.16
0.7
0.14
1400
1200
0.12
1200
1000
0.10
V(m/s)
T/k
V(m/s)
0.4
800
0.3
600
0.2
1000
0.08
0.06
0.04
0.1
400
0.0
200
27.0
27.5
28.0
28.5
X(mm) Y=0.431
29.0
800
600
0.02
400
0.00
27.0
-0.1
1 m/s
2 m/s
3 m/s
1600
1400
0.6
0.5
1 m/s
2 m/s
3 m/s
T/k
1216
27.5
29.5
28.0
28.5
X(mm)Y=0.431
29.0
29.5
-0.02
200
27.4 27.6 27.8 28.0 28.2 28.4 28.6 28.8 29.0 29.2
X(mm)Y=0.8
27.4 27.6 27.8 28.0 28.2 28.4 28.6 28.8 29.0 29.2
X(mm) Y=0.8
Fig 4 Y = 0.431 m and Y=0.8 m velocity, temperature change map
Sample 1
Sample 2
Fig 6 Experimental samples
(a)
（b）
（c）
Fig 7 Phase diagrams
3.3 Experimental Verification
Simulation results can be obtained through the above pressure 300000 Pa, the initial velocity at
1.0 m/s case, the speed and temperature to meet at the filling process and the post-solidification
process requirements. However, according to the site of objective conditions, the latter ingot mold
filling process of quality assessment and numerical simulation of gas entrapment can not be truly
observed in the solidification process, According to preliminary filling process simulation result of
air entrainment defects, respectively, in positions A and B taken 1, 2(Fig 6), metallographic samples
were analyzed after solidification while taking the sample 2 which also has some slag. The gas
entrament during the mold filling can be defected location verification and analysis of causes. From
the above simulation results, respectively, it is true to separately conduct sampling and analysis in
the X-axis 28mm and 28.8mm, Fig 7 shows, (a) sample taken at the middle of the Z-axis, since it is
seen that the initial velocity must be along the Z-axis vertical upward flow, there is involved with
little air, so the air is pushed out of ingot, there is little situation of gas entrainment. (b) sample is
taken in the direction of the wall near the type specimen, the overall air entrainment isn’t a lot but
the wall near the type already start to solidify at the filling process, because of the absence of
sufficient time and the gas spread out so that there are a lot of big gas present in the ingot.
According to the solidification process along the wall to the center-type diffusion, (c) sample is
close to the ingress direction, temperature changes compared to the b-spline changes slowly, so you
can make the entrance be enough time to close out the liquid steel, then there are more gas and vent
clip small.
Applied Mechanics and Materials Vols. 395-396
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Conclusion
Through the large ingot casting process simulation and numerical simulation based on the folder
on the gas filling process to determine the location, in the latter part of the test specimen location
analysis, which can verify the simulation results, Taking into account the filling velocity changes in
the filling gas volumes produced during the flow field defect location and solidification process for
the latter to provide the appropriate temperature field; thus comparisons of the filling speed of 1m /
s, initial pressure of 300000Pa when compared to conform to the ingot mold filling process.
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Advanced Materials and Processes III
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Numerical Simulation of Filling Process in Large Steel-Ingot
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