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Modelling of metal flow and oxidation during furnace emptying using smoothed particle hydrodynamics
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 9 ( 2 0 0 9 ) 3396–3407
journal homepage: www.elsevier.com/locate/jmatprotec
Modelling of metal flow and oxidation during furnace emptying using smoothed particle hydrodynamics Mahesh Prakash a,∗ , Paul Cleary a , John Grandfield b a b
CRC for CAST Metals Manufacturing (CAST), CSIRO Mathematical and Information Sciences, Clayton, VIC 3169, Australia CRC for CAST Metals Manufacturing (CAST), CSIRO Manufacturing and Materials Technology, Clayton, VIC 3169, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history:
In this paper the grid-free smoothed particle hydrodynamics (SPH) method has been used to
Received 26 November 2007
predict the amount of oxide generated during a furnace tipping process, where the metal is
Received in revised form
poured into a launder. The free surface modelling capability of SPH and 3D visualisation of
28 July 2008
the fluid flow leads to a better understanding of the flow characteristics during the furnace
Accepted 29 July 2008
tipping phase of the operation. Experimental mass flow rate measurements are used to validate the SPH simulation predictions. The relative amount of oxide generated during the furnace tipping phase and the phase of metal discharge from the ingot wheel are then
Keywords:
predicted. Results indicate that the furnace tipping process can lead to as much as two
Ingot casting
thirds of the total oxide generated during melt transfer from the furnace to the ingot. This
CFD
suggests that optimisation of furnace design and the tipping process could lead to significant
SPH modelling
improvements in the quality of the downstream products, such as ingot castings.
Oxide generation
Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved.
Free surface flow
1.
Introduction
In cast houses, liquid metal is transferred from various crucibles and furnaces and finally to a casting process. Depending on the operation these transfers may involve pouring a crucible into a furnace, emptying a furnace to a launder trough or flow from a launder to a casting process. Oxidation can occur to varying degrees during these operations, the oxide layer created on top of the molten aluminium breaks up, exposing fresh melt to air leading to further oxide formation and a mixture of oxide and un-oxidised melt known as dross. Transfer operations are major contributors to total melt loss, a significant economic and environmental issue. The creation of oxide in the melt also reduces the finished quality of the final downstream products by introducing inclusions that then must be removed. Thus, the ability to model and predict the amount of oxidation and dross formation for a given configuration is
∗
greatly desired to aid in improving these operations. Many different configurations are used in industry for these operations. For example, crucibles can be emptied using siphons or simple tilted pouring metal into the furnace. In the case of furnace to launder transfer, this can be via a tap hole in a stationary furnace or using a tilting furnace in order to have no cascade of metal out of the furnace. The nature of metal flow will determine the amount of fragmentation and break-up of the oxide layer. This in turn depends on such parameters as the tilt rate of the furnace or crucible, the falling height and the container spout design. Therefore it is important to understand the flow characteristics of a furnace tipping operation and relate these to the formation of oxide. Solnordal et al. (2003) performed computational fluid dynamics (CFD) simulations of the flow and reactions in a flash furnace smelter. This work evaluated the gas flow in the furnace using a finite volume method and the associ-
Corresponding author. Tel.: +61 395458010; fax: +61 395458080. E-mail address: [email protected] (M. Prakash). 0924-0136/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.07.055
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ated flow of solid metal feed by Lagrangian particle tracking. Khoei et al. (2003) used a finite element code to predict the temperature distribution in a rotary furnace during the aluminium recycling process. De et al. (2004) developed an analytical solution to predict the early stage of oxide formation in molten aluminium–magnesium alloys in a reverberatory furnace. Yang et al. (2004) numerically modelled the entrainment of oxide film defects during the filling of aluminium alloy castings. They used a volume of fluid (VOF) approach to model the free surface flow behaviour of the metal. Zhou et al. (2006) modelled the melting behaviour of aluminium scrap in a rotary furnace using a finite difference method. A population balance model was used to define the scrap with different properties such as size and shape. Recently Dispinar and Campbell (2007) investigated the effect of casting conditions such as the use of diffusers and casting techniques to reduce turbulence and fragmentation in a holding furnace experimentally on re-melt aluminium metal quality. The studies reported here were undertaken as part of a project to develop a low oxide wheel design for ingot casting. This work involved the development of a series of wheel designs through trial simulations and experiments over a period of four years. Cleary et al. (2003) presents the early work carried out in this project. Prakash et al. (2007) provides more comprehensive details and a summary of the wheel design optimisation process. The experimental configuration used had a 500 kg crucible furnace emptying metal from a small drop (420 mm) into a launder feeding the casting wheel (Fig. 1). The relative contribution to dross levels in the ingot from the cascade from the furnace and the ingot mould filling needed
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to be ascertained for that project. This would be very difficult to do experimentally and thus numerical modelling was used. Currently, measurement of the amount of oxide generated during such operations is difficult. Available analysis methods include dissolution of the metal and weighing the remaining oxide as presented in Simensen et al. (1984). This type of analysis is only done on sample sizes less than 5 g or re-melting of the sample and passing a melt sample through a fine filter to collect and quantify the amount of oxide and other solids. Sampling issues arise due to the potential for oxide to settle or float1 and the question of introducing further oxide during the re-melting process. Simulation was therefore used to predict the amount of oxide generated during furnace tipping. The grid-free smoothed particle hydrodynamics (SPH) method first developed by Gingold and Monaghan (1977) was chosen for the simulations due to its inherent advantages in: (a) tracking free surface flows with fragmentation and breakup more accurately than is possible with traditional grid based methods; (b) the ability to easily predict oxide formation and to track the advection of this oxide through subsequent flow, and; (c) easy handling of the complicated motions of three dimensional objects involved in the furnace tipping operation. Previous work in simulating the wheel system for aluminium re-melt ingot casting presented in Prakash et al. (2007) is an example demonstrating this advantage of the SPH method. Simulated and experimentally measured mass flow rates are compared to ensure that the simulation predictions are representative of the real flow. The simulation results are then used to predict the relative amount of oxide generated during the furnace tipping and the re-melt ingot casting operations. This estimate is useful in understanding the extent to which oxide is generated during such melt transfer operations.
2.
The SPH method for fluid flow
The SPH method can be used for modelling coupled heat and mass flows. It is a particle based method and does not use conventional fixed grids or meshes to track the fluid and calculate the fluid velocities and therefore does not suffer from the inherent limitations of these methods for modelling moving bodies, complex fluid free surfaces and oxide formation. In SPH, material is represented as particles that move around in response to the fluid or solid stresses produced by the interaction with other particles. SPH is particularly well suited to momentum dominated flows, flows involving complex free surface behaviour and flows with complex physics such as solidification or flow through industrial porous media. In Cleary et al. (2002) SPH is used to model high pressure die casting (HPDC) and gravity die casting (GDC) processes. In this
Fig. 1 – Experimental set-up to test ingot wheel designs (a) furnace containing molten aluminium, and (b) the ingot wheel and launder.
1 Oxide species in dross generally include amorphous oxides of aluminium and magnesium in magnesium containing alloys whose density is greater than the melt. However, considerable porosity is trapped in the dross reducing the bulk density to less than the melt allowing it to float.
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paper the results are compared with experiments and Eulerian simulations using MAGMAsoft. It is shown that the mesh free nature of SPH allows it to better capture the free surface wave behaviour and the fine details of the flow in comparison with the Eulerian method. In Cleary et al. (2004) HPDC of large and complex industrial components such as an engine rocker cover and a cross-member are simulated using SPH allowing predictions of porosity defects and locations to place air-vents in these dies. It is also ideal for flows around moving objects, since there are no mesh structures to be affected. In Monaghan et al. (2003) SPH has been applied to fluid structure interaction of off shore structures. Gomme et al. (2006) used SPH for predicting shear stress levels in biological fluids passing through a lobe pump. Prakash et al. (2007) used SPH to model flow of molten aluminium through an ingot wheel system consisting of a rotating wheel and translating ingots. A brief summary of the SPH method is presented here. One can find more comprehensive details on the derivation of these equations in Monaghan (1992). The paper also provides information on the kernel functions used during the interpolation process. Cleary and Monaghan (1999) extended the method to accurately model processes involving heat transfer. The interpolated value of a function A at any position r can be expressed using SPH smoothing as: A(r) =
b
A mb b W(r − rb , h) b
(1)
where mb and rb are the mass and density of particle b and the sum is over all particles b within a radius 2h of r. Here W(r, h) is a C2 spline based interpolation or smoothing kernel with radius 2h, that approximates the shape of a Gaussian function but has compact support. The gradient of the function A is given by differentiating the interpolation equation (1) to give: ∇A(r) =
b
A mb b ∇W(r − rb , h) b
(2)
Using these interpolation formulae and suitable finite difference approximations for second order derivatives, one is able to convert parabolic partial differential equations into ordinary differential equations for the motion of the particles and the rates of change of their properties.
2.1.
Continuity equation
use of this form of the continuity equation is very important for predicting free surface flows of the present kind.
2.2.
Momentum equation
The SPH momentum equation used here is:
dva mb = g− dt
Pb b2
b
+
Pa
a2
× ∇a Wab
−
4a b vab rab a b (a + b ) r2 + 2 ab
(4)
where Pa and a are pressure and viscosity of particle a and vab = va − vb . Here is a factor associated with the viscous term evaluated by Cleary (1996), is a small parameter used to smooth out the singularity at rab = 0 and g is the gravity vector. The first two terms involving the pressure correspond to the pressure gradient term of the Navier–Stokes equation. The next term involving viscosities is the Newtonian viscous stress term. This form ensures that stress is automatically continuous across material interfaces and allows the viscosity to be variable or discontinuous.
2.3.
Equation of state
Since the SPH method used here is quasi-compressible one has to use an equation of state, giving the relationship between particle density and fluid pressure. This relationship is given by the expression: P = P0
0
−1
(5)
where P0 is the magnitude of the pressure and 0 is the reference density. For liquid metals we use = 7. This pressure is then used in the SPH momentum equation (4) to give the particle motion. The pressure scale factor P0 is given by: P0 = 100V 2 = cs2 0
(6)
where V is the characteristic or maximum fluid velocity. This ensures that the density variation is less than 1% and the flow can be regarded as incompressible.
From Cleary and Monaghan (1999), the SPH continuity equation is:
2.4.
da mb (va − vb ) · ∇Wab = dt
Similar to the fluid, solid boundaries are also represented as particles in SPH. Each solid particle has a normal associated with it. These particles are assigned physical properties (mass, position, density, temperature, etc.) in the same way as for the fluid particles. The boundary particles exert forces, typically with a Lennard–Jones form, on the fluid particles in the direction normal to the surfaces. Appropriate interpolation of these forces produces arbitrary, smoothly defined boundaries. For moving boundaries, the position and velocity of the boundary particles are updated at every time-step for translation. For rotational motion the direction of normal associated with each particle is also updated at each time-step.
(3)
b
where a is the density of particle a, with velocity va and mb is the mass of particle b. We denote the position vector from particle b to particle a by rab = ra − rb and let Wab = W(rab , h) be the interpolation kernel with smoothing length h evaluated for the distance |rab |. This form of the continuity equation is Galilean invariant (since the positions and velocities appear only as differences), has good numerical conservation properties and is not affected by free surfaces or density discontinuities. The
Motion of solid bodies
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lected at regular time intervals. The predicted flow rates are compared to those observed in the experiments. Prediction of oxide content is essentially dependent on the ability to predict liquid metal exposed to air (that is metal located at the free surface) and the duration of exposure. In conventional Computational Fluid Dynamics, this is a complex issue as information is only known about liquid metal that is currently at the free surface. There is no history available to indicate where the metal was at earlier times or where oxide formed at earlier times has moved. In SPH, each particle represents a specific volume of fluid and it can easily carry with it information on composition and the history of that composition. In this case we are interested in oxide. So in the Lagrangian framework used by SPH, the oxide prediction becomes very simple with the following key elements:
Fig. 2 – Two views of the simulation setup to match the experiment.
3. Determination of oxide content during furnace tipping A furnace tipping simulation modelled the aluminium ingot casting experiments (see Figs. 1 and 2). This setup simulates the flow of metal from the tilting furnace into the launder, up to the point where the metal exits the launder and flows into the wheel. A typical wheel setup used in aluminium ingot casting is shown in Fig. 3. At the point where the metal flows into the wheel, a computational plane was placed across the flow and the fluid particles passing through this plane were noted. This information allows the flow rate of the fluid to be calculated. Each of the particles passing through this plane also carries with it an amount of oxide (dependent on the specific history of each particle) which can be summed to provide information on the total oxide generated and the rate at which it passes through the plane. Flow rate and oxide data were col-
(a) Liquid metal particles oxidise for any period of time they are on the free surface. (b) Oxidation is tracked using a simple ordinary differential rate equation. (c) Liquid metal does not oxidise if it is not currently on the free surface. (d) Oxide already formed is carried (advected) with their host SPH particles, so the subsequent distribution of oxide produced by the fluid flow is automatically provided by the method.
The oxide content of any particle is given (in step b) by a rate equation. Here we use the linear oxide (Ox ) growth model suggested by Baker et al. (1995) for pure aluminium: dOx = kl dt
(7)
where kl is the rate constant and t is time. In Birks and Meier (1983), the rate constant was estimated to be kl = 10.9 × 10−3 kg/m2 s.
(8)
Note that this oxide model is suitable for instances where pure aluminium is being poured and can be assumed to be liquid throughout the duration of the pour.
Fig. 3 – Typical ingot wheel design for casting aluminium ingots showing the launder, wheel and ingot.
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3.1.
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Limitations of the oxide model
The following assumptions have been made during the implementation of the oxide model in the SPH code:
1. There is no density difference between the oxide and or dross and the liquid metal. In actual practice one would expect the oxide to have a slightly lower density than the liquid metal. This means the oxide formed is more readily able to entrain into the liquid metal. 2. It is assumed that the oxide created can instantaneously break down and entrain into the melt. In other words we do not associate any strength to the oxide film created. For the present application involving liquid metal throughout the pour and for relatively high pouring rates we can reasonably expect that such oxide films would not be long-lived. This is one of the major limitations of the oxide model presented here and will need to be resolved for applications in a wider operating range. 3. The model is essentially single phase and we have not included air entrainment into the liquid. Campbell (2006) has proposed that the entrainment of air inside surface oxide films creates air pockets or bubbles and unbonded double oxide interfaces in the liquid that act as cracks. The model in its current form will be unable to predict defects arising out of gas entrainment. Overcoming this limitation will need the inclusion of a second (gas) phase into the current model. Work is now underway to include the gas phase for such systems. The large density difference between the liquid and gas results in instabilities at the interface and requires special treatment at the interface. We have also found that the simulation time increases by approximately a factor of four due to the smaller time-steps needed for numerical stability.
4.
Furnace, launder and fluid configuration
4.1.
Furnace and launder geometry
• Coarse – 25.0 mm, • Medium – 15.625 mm, and • Fine – 12.5 mm. These particle sizes resulted in 11110, 47862 and 95130 SPH fluid particles for the coarse, medium and fine resolution simulations, respectively, for a fill level of around 75% of the furnace.
4.3.
Furnace tipping
In both the experiments and the simulations the furnace is tipped into the launder about the pivot shown in Fig. 2. For the experiments, it was observed that the metal started to flow into the launder when the furnace had rotated by about 20◦ about the pivot. It was also observed in the experiments that it takes about 60 s for nearly all the metal in the bath to be used up. This happens when the furnace has rotated by about 80–85◦ . Based on the experimental observations, the simulations were started with the furnace at an angle of 20◦ from the horizontal. The experiments used a slightly variable tilt rate to adjust the flow rate in order to get a more constant ingot fill level. The variation in the tilt rate was manual and was not recorded during the experiment. A constant representative tilt rate of 1◦ /s or 0.01745 rad/s was therefore used in the simulations. The fluid was allowed to settle down for about one second to allow the fluid to become quiescent before the furnace was rotated about the pivot (Fig. 2). The initial position of the fluid in the furnace at the start of the tipping part of the simulation is shown in Fig. 4.
5.
Description of furnace tipping operation
5.1.
Flow pattern
Fig. 5 shows a 3D oblique view of the furnace and launder at different times with the furnace rotating about its pivot.
The 500 kg furnace and launder arrangement used in the simulations is shown in Fig. 2. The furnace height is 660 mm and has an internal diameter of 715 mm and an external diameter of 1325 mm. The launder is 1450 mm long. The launder has a maximum width of 285 mm near the furnace and a minimum width of 128 mm near the ingot wheel. The maximum depth of the launder is 280 mm and occurs approximately at the centre. A dam with a thickness of 80 mm in the middle of the launder is intended to prevent the oxide formed during the furnace tipping operation from getting into the ingot wheel. The dam has a clearance of 80 mm from the base of the launder.
4.2.
SPH fluid setup
To match the experiments, the furnace was filled with SPH fluid particles to a depth of 500 mm. Simulations were carried out at three different resolutions with SPH interpolation lengths or particle size of:
Fig. 4 – Initial position of fluid (shown in blue) and furnace for the SPH simulations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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Fig. 5 – 3D oblique view of the flow of molten aluminium into the launder for the fine resolution simulation during a cycle of the furnace tipping operation. The fluid is coloured by aluminium oxide content with red being the current maximum and blue being zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
This figure shows the fine resolution simulation of the flow with the fluid coloured by the oxide fraction. In each frame, red represents the instantaneous maximum oxide mass per particle and blue represents the minimum of 0.0 g per particle.
The launder and furnace are made transparent to provide a clearer view of the fluid flow. At 2 s the fluid begins from rest as the furnace starts being rotated about its pivot. At this stage the bottom of the furnace
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is at an angle of 21◦ from the horizontal. The fluid has just begun flowing into the launder at this stage. At 10 s, a substantial amount of fluid has entered the launder. The furnace has tilted by 30◦ at this stage. The dam in the middle of the launder appears to mix the oxide generated in the tipping process into the liquid melt thus reducing the amount of surface oxide visible on the surface. This means oxide that may have reported to the product as surface dross is now distributed through the final product volume. For products such as primary ingots, where surface finish is the key requirement, this may lead to an improvement in perceived product quality. If total oxide content is the performance measure required, then this re-distribution of oxide has no effect. By about 20 s (when the furnace has rotated by 40◦ ), the fluid has almost fully filled the launder and starts flowing at an almost steady rate out the other end towards the location of the wheel (as shown in Fig. 3), through the oxide measuring plane. This steady rate of flow continues until about 40 s. Comparison of fluid level in the launder at 20, 30 and 40 s in Fig. 5 indicates that it remains essentially constant during this period. By about 50 s, a substantial fraction of fluid in the furnace has been emptied out. The furnace is at an angle of 70◦ to the horizontal at this stage. The flow from the furnace is not fully able to compensate for the flow out of the launder, so the liquid metal level in the launder declines. Fig. 6 shows a close-up of the fluid flowing from the furnace into the launder. The fluid is coloured by its local speed with red indicating maximum (3.0 m/s) and blue the minimum (of 0.0 m/s). At 10 s, a thin fragmented stream of fluid is seen to fill the launder. Due to the fragmented nature of this stream one can expect a larger surface area of fluid exposed to air leading to higher rates of oxide formation. At 20 s, the stream from the furnace to the launder becomes less fragmented and is more or less continuous. As the fluid hits the launder there is splashing with the fast moving fluid approaching the dam. However, due to a deeper liquid level in the middle of the launder and the presence of the dam the fluid quickly loses momentum. At 30 and 50 s, the stream of fluid from the furnace is still reasonably continuous indicating a steady flow pattern from the furnace to the launder. The predominantly blue coloured fluid beyond the dam at all times demonstrates that it tends to reduce the fluid speed in the launder before reaching the ingot wheel. The tilt speed of the furnace, the design of the lip of the furnace, the launder design and the location and design of the dam are important factors that will influence the amount of oxide being carried over downstream.
5.2. Comparison between different simulation resolutions Fig. 7 shows the flow pattern for the medium (frames on the left) and fine resolution (frames on the right) simulations. The fluid here is coloured by its speed with red representing the maximum speed (3.0 m/s) and blue is stationary. At 2 s, the fluid has just started flowing from the furnace into the launder in the medium resolution and fine resolution cases. The fine resolution case has progressed slightly further than the medium resolution one at this stage.
Fig. 6 – Close-up of the fluid flowing from the furnace into the launder. The fluid is coloured by its speed with red being maximum and blue being minimum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.) At 5 s when the furnace has rotated by 25◦ the fluid starts flowing into the launder as observed in the experiments. At this stage the fluid has filled the clearance between the dam and launder in both cases. At 10 s, a substantial amount of fluid has entered the launder. Strong similarities between the
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Fig. 7 – Flow pattern of the molten aluminium poured from the furnace into the feed launder for the medium and fine resolution simulations. The fluid is coloured by speed with red being the maximum (3.0 m/s) and blue being zero. Most of the fluid has emptied out from the furnace by 60 s. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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medium and fine resolution simulations can be observed in the following aspects of flow at this stage: • The stream of fluid coming from the furnace and feeding the launder is fragmented in both cases in similar ways. • The fill level of the fluid and its local speed (given by the fluid colour) are comparable in the region before and after the dam in the launder. • The level of fluid and the angle of the fluid free surface in the furnace are similar at both resolutions. At 20 s, the flow from the furnace to the launder is well established and the fluid stream emanating from the furnace is more or less continuous at both resolutions. The fill level of the fluid in the launder and the location at which the fluid hits the launder are noticeably similar for both resolutions. At about 60 s, almost all the fluid has been poured from the furnace into the launder. At this stage the bottom of the furnace is at an angle of about 80◦ from the horizontal. The level of fluid and free surface location in the furnace and launder are similar for both resolutions. This comparison demonstrates that the flow predicted is very similar for these two resolutions. They are also quite similar to the coarse solution (albeit with much more detail). The mass flow rates, oxide flow rates and oxide per unit of aluminium discharged (discussed below) all indicate that three simulations show similar trends. This gives us confidence that the solution is fairly insensitive to the numerical resolution used.
6.
Mass flow predictions
The furnace tipping speed was chosen to give an average mass flow rate of 30 tonnes/h or 8.33 kg/s. The time variation of the actual mass flow rates in the experiments was backcalculated from the observed ingot weights. Fig. 8 shows the experimental mass flow rate. One can observe a pattern with a lower mass flow rate in the initial stage with a relatively steady flow rate in between and with the flow rate declining back towards zero as the fluid empties out from the furnace. Fig. 9 – Mass flow rate in kg/s for (a) coarse, (b) medium and (c) fine resolution simulations.
Fig. 8 – Variation in mass flow rate (kg/s) with time (s) in the experiment.
In the experiment shown the flow rate remained reasonably steady until about 45 s. The peak experimental mass flow rate is about 32.7 tonnes/h or 9.1 kg/s. As mentioned earlier the experiments used a slightly variable tilt rate to maintain a reasonably constant ingot fill level. The local peaks in Fig. 7 correspond to the stages when such variable tilt rates were used in the experiment. The smoothed experimental mass flow rate (during the relatively constant middle stage of pouring) lies in the range of 24.0–32.7 tonnes/h or between 6.7 and 9.1 kg/s. Fig. 9 shows the predicted mass flow rate of the molten aluminium for the simulations carried out at the three different resolutions. These plots show that the mass flow predictions are acceptably consistent for the different resolutions. As for the experiments, one can see that the mass flow rate starts from zero attains a somewhat steady rate and drops down
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back to zero as the furnace empties out. Note that the peak mass flow rate for all three resolutions is about 9.5 kg/s and that between 20 and 40 s the mass flow rate varies consistently between 6.5 and 9.5 kg/s. This range of mass flow rate and the predicted fill time correlates well with the experimentally observed values.
7.
Oxide predictions
Fig. 10 shows the average oxide flow rate predicted from the fluid passing through the measuring plane at the end of the launder for the three simulation resolutions. The smoothed oxide flow rate varies in the range of 0.005 and 0.008 kg/s
Fig. 11 – Oxide content of aluminium in grams of oxide per kg of aluminium for (a) coarse, (b) medium and (c) fine resolution simulations.
Fig. 10 – Oxide flow rate in kg/s for (a) coarse, (b) medium and (c) fine resolution simulations.
between 20 and 50 s and then declines rapidly as the aluminium flow rate falls off at the end of the pour. Fig. 11 shows the oxide concentration in the aluminium as it flows out of the launder in grams of oxide per kilogram of aluminium for the three different resolutions. This is essentially obtained by dividing the oxide flow rate shown in Fig. 10 by the fluid flow rate shown in Fig. 9. Initially there is no oxide in the fluid. The first small peak (around 1 g oxide/kg of aluminium for the fine resolution simulation) before 10 s in Fig. 11 corresponds to the initial splash of leading edge fluid flying through the measuring plane. The oxide content starts to rise from 10 s as the leading edge of contiguous fluid reaches the plane. The oxide content rises rapidly to a peak of around 2.4 g/kg at around 15 s. This reflects both the very high and
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Table 1 – Comparison of average oxide content in the launder to that generated through the wheel for the original and optimised wheel design reported in Cleary et al. (2003) Wheel design Original Optimised
Total oxide content generated by the wheel (g/kg)
Average launder oxide content (g/kg)
% Oxide generated in the launder from the furnace tipping
1.035 1.035
52 67
0.95 0.52
Fig. 12 – Essential features of (a) the original poorer performing wheel design and (b) the new optimised wheel design. The liquid is coloured by velocity.
increasing surface area to volume ratio of the initially thin fluid flowing across the bottom of the launder and its very turbulent nature. As the launder fills the surface area of metal exposed remains fairly constant but the volume increases with depth so the fraction of metal exposed to oxidation steadily declines from its peak at 15 s. The increasing depth also damps the violent turbulent motions observed at shallow fill levels. This combination leads to a rapid decline in oxide content reporting to the wheel (by more than 60% from its peak) at 20 s. It continues to decline to a minimum of only 0.8 g/kg at around 30 s). After 30 s, the metal flow rate starts to drop and the fluid level in the launder starts to decline slowly. This leads to slow but steady increase in the ratio of surface area to volume of fluid in the launder thus increasing the oxide concentration measured at the sample plane. The gradient of the measured oxide content with time (as seen in Fig. 11) is constant from 30 s to around 70 s reflecting the steady linear decline in the launder fluid depth. By 75 s, the depth of metal in the launder has become very low and the turbulent motions from the flow from the furnace are no longer able to be damped by the fluid pool in the launder. This results in a sharp increase in gradient of oxide content with the oxide levels reaching and then exceeding the initial peak of around 2.4 g/kg. This indicates that the final residual parts of the flow are very oxide rich. This example demonstrates that SPH can be used to predict the oxide concentration at different stages in any melt transfer operation and to understand the importance of the different mechanisms driving oxide formation. Specifically, the role of the surface to volume ratio of the liquid metal and of the ability of the fluid pool to rapidly damp the turbulent flow entering the pool is identified. Between 20 and 50 s the oxide concentration varies in the range of 0.84–1.23 g/kg. Ingots with a standard weight
of around 22.5 kg are expected to be produced during this part of the furnace tipping process. Therefore the average value, 1.035 g/kg, of this oxide range is used to characterise the oxide content resulting from the furnace tipping phase of the process. This is compared with the oxide content predicted for the ingot pouring phase using wheel casters. Table 1, gives a comparison between oxide generated in the furnace/launder region and the oxide generated in the ingot moulds for the original and optimised ingot casting wheels (as reported in Cleary et al., 2003). The percentage of the total oxide formed in the launder resulting from the furnace tipping and launder flow is shown in the last column of Table 1. In both cases the oxide generation during the furnace pouring and launder flow is greater than that generated in the wheel. For the poorer performing original wheel, the amount of oxide is similar for both parts of the process, but for the new optimised wheel design, the furnace tipping phase generates the dominant fraction (67%) of the total oxide created in the experimental casting process. This demonstrates the critical importance of the furnace tipping phase of melt transfer processes in relation to the creation of oxide and thus the overall quality of finished products. Essential features of the original wheel design and the modified and optimised wheel design can be surmised from Fig. 12. Further information about the wheel design and optimisation process can be found in Prakash et al. (2007).
8.
Conclusions
SPH simulations were carried out at three different resolutions to understand the nature of the fluid flow and to predict the amount of oxide generated during the furnace tipping phase of an aluminium melt transfer process. The following conclusions can be drawn from these simulations:
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• Simulations at all three resolutions lead to comparable qualitative and quantitative results, demonstrating that the solutions are resolution independent. • Good agreement was reached between the mass flow rate predicted by the simulation and the experimental mass flow rate measurements. • SPH simulation has key advantages for modelling this process compared to conventional grid based CFD. These include the ability to easily predict complex splashing free surface flows, simulate moving objects and to predict oxide formation. These have enabled a detailed flow analysis that has led to a better understanding of the key mechanisms that control oxide generation in furnace tipping operations. • It was found that the oxide generated during the furnace tipping process was comparable or larger than the oxide generated during the flow of metal through various casting wheels and could be responsible for up to 67% of oxide creation for the better wheels. • Oxide formation is heavily influenced by the surface to volume ratio of liquid metal in the launder and to the degree of damping of turbulent free surface motion resulting from the entry of metal from the furnace into the launder pool. Increasing depth of the pool in the launder is favourable for both mechanisms but the damping of free surface motion is most critical for shallow pools. These results demonstrate that the furnace tipping stage of melt transfer and casting operations can have serious implications for the quality of the finished products. This suggests that there are likely to be strong benefits in optimising furnace designs and tipping processes to minimise oxide formation.
Acknowledgments This project was conducted by the Cooperative Research Centre for Cast Metals Manufacturing (CAST). CSIRO is a core participant in the CRC for Cast Metals Manufacturing (CAST), which was established under and is supported in part by the Australian Government’s Cooperative Research Centres scheme.
references
Baker, P.W., Nguyen, K., Kirkaldie, R., 1995. Dross formation during metal transfer operations. In: Nilmani, M. (Ed.), Aluminum Cast House Tech. 4th Australasian Asian Pacific Conference. TMS, Warrendale, PA, pp. 109–122. Birks, N., Meier, G.H., 1983. Introduction to High Temperature Oxidation of Metals. Edward Arnold, London, UK.
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Campbell, J., 2006. Modelling of entrainment defects. In: Proceedings of the 135th TMS Annual Conference, San Antonio, Texas, USA. Cleary, P.W., Monaghan, J.J., 1999. Conduction modeling using smoothed particle hydrodynamics. J. Comput. Phys. 148, 227–264. Cleary, P.W., Prakash, M., Sinnott, M., Grandfield, J., Alguine, V., Oswald, K., 2003. 3D SPH simulations of the aluminium ingot casting process. In: Proceedings of the 3rd International Conference on CFD in the Minerals & Process Industries, Melbourne, Australia, pp. 409–414. Cleary, P., 1996. New implementation of viscosity: tests with coquette flows, SPH Technical Note 8, CSIRO DMS, Technical Report DMS – C 96/32, 41 pp. Cleary, P., Grandfield, J., Prakash, M., Ha, J., Sinnott, M., Nguyen, T., 2004. Modelling of casting systems using smoothed particle hydrodynamics. JOM 56, 67–70. Cleary, P., Ha, J., Alguine, V., Nguyen, T., 2002. Flow modeling in casting processes. Appl. Math. Modell. 26, 171–190. De, A.K., Mukhopadhyay, A., Sen, S., Puri, I.K., 2004. Numerical simulation of early stages of oxide formation in molten aluminium-magnesium alloys in a reverberatory furnace. Modell. Simul. Mater. Sci. Eng. 12, 389–405. Dispinar, D., Campbell, J., 2007. Effect of casting conditions on aluminium metal quality. J. Mater. Proc. Tech. 182, 405–410. Gingold, R.A., Monaghan, J.J., 1977. Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389. Gomme, P.T., Prakash, M., Hunt, B., Stokes, N., Cleary, P., Tatford, O.C., Bertolini, J., 2006. Effect of lobe pumping on human albumin: development of a lobe pump simulator using smoothed particle hydrodynamics. Biotech. Appl. Biochem. 43, 113–120. Khoei, A.R., Masters, I., Gethin, D.T., 2003. Numerical modelling of the rotary furnace in aluminium recycling processes. J. Mater. Proc. Tech. 139, 567–572. Monaghan, J.J., 1992. Smoothed particle hydrodynamics. Ann. Rev. Astron. Astrophys. 30, 543–574. Monaghan, J.J., Kos, A., Issa, N., 2003. Fluid motion generated by impact. J. Wtrwy. Port Coast Oc. Eng. 129 (6), 250–259. Prakash, M., Cleary, P.W., Grandfield, J., Rohan, P., Nguyen, V., 2007. Optimization of ingot casting wheel design using SPH simulations. Prog. Comput. Fluid Dyn. 7 (2–4), 101–110. Simensen, C.J., Fartum, P., Andersen, A., 1984. Analysis of intermetallic particles in aluminium by dissolution of the sample in butanol. Fresenius’ Z. Anal. Chem. 319 (3), 286–292. Solnordal, B.C., Jorgensen, F.R.A., Koh, P.T.L., Hunt, A., 2003. CFD modeling of the flow and reactions in a flash furnace smelter reaction shaft. In: 3rd International Conference on CFD in the Minerals & Process Industries, Melbourne, Australia, pp. 161–166. Yang, X., Huang, X., Dai, X., Campbell, J., Tatler, J., 2004. Numerical modelling of entrainment of oxide film defects in filling of aluminium alloy castings. Int. J. Cast Metals Res. 17 (6), 321–331. Zhou, B., Yang, Y., Reuter, M.A., Boin, U.M.J., 2006. Modelling of aluminium scrap melting in a rotary furnace. Minerals Eng. 19, 299–308.
journal homepage: www.elsevier.com/locate/jmatprotec
Modelling of metal flow and oxidation during furnace emptying using smoothed particle hydrodynamics Mahesh Prakash a,∗ , Paul Cleary a , John Grandfield b a b
CRC for CAST Metals Manufacturing (CAST), CSIRO Mathematical and Information Sciences, Clayton, VIC 3169, Australia CRC for CAST Metals Manufacturing (CAST), CSIRO Manufacturing and Materials Technology, Clayton, VIC 3169, Australia
a r t i c l e
i n f o
a b s t r a c t
Article history:
In this paper the grid-free smoothed particle hydrodynamics (SPH) method has been used to
Received 26 November 2007
predict the amount of oxide generated during a furnace tipping process, where the metal is
Received in revised form
poured into a launder. The free surface modelling capability of SPH and 3D visualisation of
28 July 2008
the fluid flow leads to a better understanding of the flow characteristics during the furnace
Accepted 29 July 2008
tipping phase of the operation. Experimental mass flow rate measurements are used to validate the SPH simulation predictions. The relative amount of oxide generated during the furnace tipping phase and the phase of metal discharge from the ingot wheel are then
Keywords:
predicted. Results indicate that the furnace tipping process can lead to as much as two
Ingot casting
thirds of the total oxide generated during melt transfer from the furnace to the ingot. This
CFD
suggests that optimisation of furnace design and the tipping process could lead to significant
SPH modelling
improvements in the quality of the downstream products, such as ingot castings.
Oxide generation
Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved.
Free surface flow
1.
Introduction
In cast houses, liquid metal is transferred from various crucibles and furnaces and finally to a casting process. Depending on the operation these transfers may involve pouring a crucible into a furnace, emptying a furnace to a launder trough or flow from a launder to a casting process. Oxidation can occur to varying degrees during these operations, the oxide layer created on top of the molten aluminium breaks up, exposing fresh melt to air leading to further oxide formation and a mixture of oxide and un-oxidised melt known as dross. Transfer operations are major contributors to total melt loss, a significant economic and environmental issue. The creation of oxide in the melt also reduces the finished quality of the final downstream products by introducing inclusions that then must be removed. Thus, the ability to model and predict the amount of oxidation and dross formation for a given configuration is
∗
greatly desired to aid in improving these operations. Many different configurations are used in industry for these operations. For example, crucibles can be emptied using siphons or simple tilted pouring metal into the furnace. In the case of furnace to launder transfer, this can be via a tap hole in a stationary furnace or using a tilting furnace in order to have no cascade of metal out of the furnace. The nature of metal flow will determine the amount of fragmentation and break-up of the oxide layer. This in turn depends on such parameters as the tilt rate of the furnace or crucible, the falling height and the container spout design. Therefore it is important to understand the flow characteristics of a furnace tipping operation and relate these to the formation of oxide. Solnordal et al. (2003) performed computational fluid dynamics (CFD) simulations of the flow and reactions in a flash furnace smelter. This work evaluated the gas flow in the furnace using a finite volume method and the associ-
Corresponding author. Tel.: +61 395458010; fax: +61 395458080. E-mail address: [email protected] (M. Prakash). 0924-0136/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2008.07.055
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ated flow of solid metal feed by Lagrangian particle tracking. Khoei et al. (2003) used a finite element code to predict the temperature distribution in a rotary furnace during the aluminium recycling process. De et al. (2004) developed an analytical solution to predict the early stage of oxide formation in molten aluminium–magnesium alloys in a reverberatory furnace. Yang et al. (2004) numerically modelled the entrainment of oxide film defects during the filling of aluminium alloy castings. They used a volume of fluid (VOF) approach to model the free surface flow behaviour of the metal. Zhou et al. (2006) modelled the melting behaviour of aluminium scrap in a rotary furnace using a finite difference method. A population balance model was used to define the scrap with different properties such as size and shape. Recently Dispinar and Campbell (2007) investigated the effect of casting conditions such as the use of diffusers and casting techniques to reduce turbulence and fragmentation in a holding furnace experimentally on re-melt aluminium metal quality. The studies reported here were undertaken as part of a project to develop a low oxide wheel design for ingot casting. This work involved the development of a series of wheel designs through trial simulations and experiments over a period of four years. Cleary et al. (2003) presents the early work carried out in this project. Prakash et al. (2007) provides more comprehensive details and a summary of the wheel design optimisation process. The experimental configuration used had a 500 kg crucible furnace emptying metal from a small drop (420 mm) into a launder feeding the casting wheel (Fig. 1). The relative contribution to dross levels in the ingot from the cascade from the furnace and the ingot mould filling needed
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to be ascertained for that project. This would be very difficult to do experimentally and thus numerical modelling was used. Currently, measurement of the amount of oxide generated during such operations is difficult. Available analysis methods include dissolution of the metal and weighing the remaining oxide as presented in Simensen et al. (1984). This type of analysis is only done on sample sizes less than 5 g or re-melting of the sample and passing a melt sample through a fine filter to collect and quantify the amount of oxide and other solids. Sampling issues arise due to the potential for oxide to settle or float1 and the question of introducing further oxide during the re-melting process. Simulation was therefore used to predict the amount of oxide generated during furnace tipping. The grid-free smoothed particle hydrodynamics (SPH) method first developed by Gingold and Monaghan (1977) was chosen for the simulations due to its inherent advantages in: (a) tracking free surface flows with fragmentation and breakup more accurately than is possible with traditional grid based methods; (b) the ability to easily predict oxide formation and to track the advection of this oxide through subsequent flow, and; (c) easy handling of the complicated motions of three dimensional objects involved in the furnace tipping operation. Previous work in simulating the wheel system for aluminium re-melt ingot casting presented in Prakash et al. (2007) is an example demonstrating this advantage of the SPH method. Simulated and experimentally measured mass flow rates are compared to ensure that the simulation predictions are representative of the real flow. The simulation results are then used to predict the relative amount of oxide generated during the furnace tipping and the re-melt ingot casting operations. This estimate is useful in understanding the extent to which oxide is generated during such melt transfer operations.
2.
The SPH method for fluid flow
The SPH method can be used for modelling coupled heat and mass flows. It is a particle based method and does not use conventional fixed grids or meshes to track the fluid and calculate the fluid velocities and therefore does not suffer from the inherent limitations of these methods for modelling moving bodies, complex fluid free surfaces and oxide formation. In SPH, material is represented as particles that move around in response to the fluid or solid stresses produced by the interaction with other particles. SPH is particularly well suited to momentum dominated flows, flows involving complex free surface behaviour and flows with complex physics such as solidification or flow through industrial porous media. In Cleary et al. (2002) SPH is used to model high pressure die casting (HPDC) and gravity die casting (GDC) processes. In this
Fig. 1 – Experimental set-up to test ingot wheel designs (a) furnace containing molten aluminium, and (b) the ingot wheel and launder.
1 Oxide species in dross generally include amorphous oxides of aluminium and magnesium in magnesium containing alloys whose density is greater than the melt. However, considerable porosity is trapped in the dross reducing the bulk density to less than the melt allowing it to float.
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paper the results are compared with experiments and Eulerian simulations using MAGMAsoft. It is shown that the mesh free nature of SPH allows it to better capture the free surface wave behaviour and the fine details of the flow in comparison with the Eulerian method. In Cleary et al. (2004) HPDC of large and complex industrial components such as an engine rocker cover and a cross-member are simulated using SPH allowing predictions of porosity defects and locations to place air-vents in these dies. It is also ideal for flows around moving objects, since there are no mesh structures to be affected. In Monaghan et al. (2003) SPH has been applied to fluid structure interaction of off shore structures. Gomme et al. (2006) used SPH for predicting shear stress levels in biological fluids passing through a lobe pump. Prakash et al. (2007) used SPH to model flow of molten aluminium through an ingot wheel system consisting of a rotating wheel and translating ingots. A brief summary of the SPH method is presented here. One can find more comprehensive details on the derivation of these equations in Monaghan (1992). The paper also provides information on the kernel functions used during the interpolation process. Cleary and Monaghan (1999) extended the method to accurately model processes involving heat transfer. The interpolated value of a function A at any position r can be expressed using SPH smoothing as: A(r) =
b
A mb b W(r − rb , h) b
(1)
where mb and rb are the mass and density of particle b and the sum is over all particles b within a radius 2h of r. Here W(r, h) is a C2 spline based interpolation or smoothing kernel with radius 2h, that approximates the shape of a Gaussian function but has compact support. The gradient of the function A is given by differentiating the interpolation equation (1) to give: ∇A(r) =
b
A mb b ∇W(r − rb , h) b
(2)
Using these interpolation formulae and suitable finite difference approximations for second order derivatives, one is able to convert parabolic partial differential equations into ordinary differential equations for the motion of the particles and the rates of change of their properties.
2.1.
Continuity equation
use of this form of the continuity equation is very important for predicting free surface flows of the present kind.
2.2.
Momentum equation
The SPH momentum equation used here is:
dva mb = g− dt
Pb b2
b
+
Pa
a2
× ∇a Wab
−
4a b vab rab a b (a + b ) r2 + 2 ab
(4)
where Pa and a are pressure and viscosity of particle a and vab = va − vb . Here is a factor associated with the viscous term evaluated by Cleary (1996), is a small parameter used to smooth out the singularity at rab = 0 and g is the gravity vector. The first two terms involving the pressure correspond to the pressure gradient term of the Navier–Stokes equation. The next term involving viscosities is the Newtonian viscous stress term. This form ensures that stress is automatically continuous across material interfaces and allows the viscosity to be variable or discontinuous.
2.3.
Equation of state
Since the SPH method used here is quasi-compressible one has to use an equation of state, giving the relationship between particle density and fluid pressure. This relationship is given by the expression: P = P0
0
−1
(5)
where P0 is the magnitude of the pressure and 0 is the reference density. For liquid metals we use = 7. This pressure is then used in the SPH momentum equation (4) to give the particle motion. The pressure scale factor P0 is given by: P0 = 100V 2 = cs2 0
(6)
where V is the characteristic or maximum fluid velocity. This ensures that the density variation is less than 1% and the flow can be regarded as incompressible.
From Cleary and Monaghan (1999), the SPH continuity equation is:
2.4.
da mb (va − vb ) · ∇Wab = dt
Similar to the fluid, solid boundaries are also represented as particles in SPH. Each solid particle has a normal associated with it. These particles are assigned physical properties (mass, position, density, temperature, etc.) in the same way as for the fluid particles. The boundary particles exert forces, typically with a Lennard–Jones form, on the fluid particles in the direction normal to the surfaces. Appropriate interpolation of these forces produces arbitrary, smoothly defined boundaries. For moving boundaries, the position and velocity of the boundary particles are updated at every time-step for translation. For rotational motion the direction of normal associated with each particle is also updated at each time-step.
(3)
b
where a is the density of particle a, with velocity va and mb is the mass of particle b. We denote the position vector from particle b to particle a by rab = ra − rb and let Wab = W(rab , h) be the interpolation kernel with smoothing length h evaluated for the distance |rab |. This form of the continuity equation is Galilean invariant (since the positions and velocities appear only as differences), has good numerical conservation properties and is not affected by free surfaces or density discontinuities. The
Motion of solid bodies
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lected at regular time intervals. The predicted flow rates are compared to those observed in the experiments. Prediction of oxide content is essentially dependent on the ability to predict liquid metal exposed to air (that is metal located at the free surface) and the duration of exposure. In conventional Computational Fluid Dynamics, this is a complex issue as information is only known about liquid metal that is currently at the free surface. There is no history available to indicate where the metal was at earlier times or where oxide formed at earlier times has moved. In SPH, each particle represents a specific volume of fluid and it can easily carry with it information on composition and the history of that composition. In this case we are interested in oxide. So in the Lagrangian framework used by SPH, the oxide prediction becomes very simple with the following key elements:
Fig. 2 – Two views of the simulation setup to match the experiment.
3. Determination of oxide content during furnace tipping A furnace tipping simulation modelled the aluminium ingot casting experiments (see Figs. 1 and 2). This setup simulates the flow of metal from the tilting furnace into the launder, up to the point where the metal exits the launder and flows into the wheel. A typical wheel setup used in aluminium ingot casting is shown in Fig. 3. At the point where the metal flows into the wheel, a computational plane was placed across the flow and the fluid particles passing through this plane were noted. This information allows the flow rate of the fluid to be calculated. Each of the particles passing through this plane also carries with it an amount of oxide (dependent on the specific history of each particle) which can be summed to provide information on the total oxide generated and the rate at which it passes through the plane. Flow rate and oxide data were col-
(a) Liquid metal particles oxidise for any period of time they are on the free surface. (b) Oxidation is tracked using a simple ordinary differential rate equation. (c) Liquid metal does not oxidise if it is not currently on the free surface. (d) Oxide already formed is carried (advected) with their host SPH particles, so the subsequent distribution of oxide produced by the fluid flow is automatically provided by the method.
The oxide content of any particle is given (in step b) by a rate equation. Here we use the linear oxide (Ox ) growth model suggested by Baker et al. (1995) for pure aluminium: dOx = kl dt
(7)
where kl is the rate constant and t is time. In Birks and Meier (1983), the rate constant was estimated to be kl = 10.9 × 10−3 kg/m2 s.
(8)
Note that this oxide model is suitable for instances where pure aluminium is being poured and can be assumed to be liquid throughout the duration of the pour.
Fig. 3 – Typical ingot wheel design for casting aluminium ingots showing the launder, wheel and ingot.
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3.1.
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Limitations of the oxide model
The following assumptions have been made during the implementation of the oxide model in the SPH code:
1. There is no density difference between the oxide and or dross and the liquid metal. In actual practice one would expect the oxide to have a slightly lower density than the liquid metal. This means the oxide formed is more readily able to entrain into the liquid metal. 2. It is assumed that the oxide created can instantaneously break down and entrain into the melt. In other words we do not associate any strength to the oxide film created. For the present application involving liquid metal throughout the pour and for relatively high pouring rates we can reasonably expect that such oxide films would not be long-lived. This is one of the major limitations of the oxide model presented here and will need to be resolved for applications in a wider operating range. 3. The model is essentially single phase and we have not included air entrainment into the liquid. Campbell (2006) has proposed that the entrainment of air inside surface oxide films creates air pockets or bubbles and unbonded double oxide interfaces in the liquid that act as cracks. The model in its current form will be unable to predict defects arising out of gas entrainment. Overcoming this limitation will need the inclusion of a second (gas) phase into the current model. Work is now underway to include the gas phase for such systems. The large density difference between the liquid and gas results in instabilities at the interface and requires special treatment at the interface. We have also found that the simulation time increases by approximately a factor of four due to the smaller time-steps needed for numerical stability.
4.
Furnace, launder and fluid configuration
4.1.
Furnace and launder geometry
• Coarse – 25.0 mm, • Medium – 15.625 mm, and • Fine – 12.5 mm. These particle sizes resulted in 11110, 47862 and 95130 SPH fluid particles for the coarse, medium and fine resolution simulations, respectively, for a fill level of around 75% of the furnace.
4.3.
Furnace tipping
In both the experiments and the simulations the furnace is tipped into the launder about the pivot shown in Fig. 2. For the experiments, it was observed that the metal started to flow into the launder when the furnace had rotated by about 20◦ about the pivot. It was also observed in the experiments that it takes about 60 s for nearly all the metal in the bath to be used up. This happens when the furnace has rotated by about 80–85◦ . Based on the experimental observations, the simulations were started with the furnace at an angle of 20◦ from the horizontal. The experiments used a slightly variable tilt rate to adjust the flow rate in order to get a more constant ingot fill level. The variation in the tilt rate was manual and was not recorded during the experiment. A constant representative tilt rate of 1◦ /s or 0.01745 rad/s was therefore used in the simulations. The fluid was allowed to settle down for about one second to allow the fluid to become quiescent before the furnace was rotated about the pivot (Fig. 2). The initial position of the fluid in the furnace at the start of the tipping part of the simulation is shown in Fig. 4.
5.
Description of furnace tipping operation
5.1.
Flow pattern
Fig. 5 shows a 3D oblique view of the furnace and launder at different times with the furnace rotating about its pivot.
The 500 kg furnace and launder arrangement used in the simulations is shown in Fig. 2. The furnace height is 660 mm and has an internal diameter of 715 mm and an external diameter of 1325 mm. The launder is 1450 mm long. The launder has a maximum width of 285 mm near the furnace and a minimum width of 128 mm near the ingot wheel. The maximum depth of the launder is 280 mm and occurs approximately at the centre. A dam with a thickness of 80 mm in the middle of the launder is intended to prevent the oxide formed during the furnace tipping operation from getting into the ingot wheel. The dam has a clearance of 80 mm from the base of the launder.
4.2.
SPH fluid setup
To match the experiments, the furnace was filled with SPH fluid particles to a depth of 500 mm. Simulations were carried out at three different resolutions with SPH interpolation lengths or particle size of:
Fig. 4 – Initial position of fluid (shown in blue) and furnace for the SPH simulations. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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Fig. 5 – 3D oblique view of the flow of molten aluminium into the launder for the fine resolution simulation during a cycle of the furnace tipping operation. The fluid is coloured by aluminium oxide content with red being the current maximum and blue being zero. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
This figure shows the fine resolution simulation of the flow with the fluid coloured by the oxide fraction. In each frame, red represents the instantaneous maximum oxide mass per particle and blue represents the minimum of 0.0 g per particle.
The launder and furnace are made transparent to provide a clearer view of the fluid flow. At 2 s the fluid begins from rest as the furnace starts being rotated about its pivot. At this stage the bottom of the furnace
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is at an angle of 21◦ from the horizontal. The fluid has just begun flowing into the launder at this stage. At 10 s, a substantial amount of fluid has entered the launder. The furnace has tilted by 30◦ at this stage. The dam in the middle of the launder appears to mix the oxide generated in the tipping process into the liquid melt thus reducing the amount of surface oxide visible on the surface. This means oxide that may have reported to the product as surface dross is now distributed through the final product volume. For products such as primary ingots, where surface finish is the key requirement, this may lead to an improvement in perceived product quality. If total oxide content is the performance measure required, then this re-distribution of oxide has no effect. By about 20 s (when the furnace has rotated by 40◦ ), the fluid has almost fully filled the launder and starts flowing at an almost steady rate out the other end towards the location of the wheel (as shown in Fig. 3), through the oxide measuring plane. This steady rate of flow continues until about 40 s. Comparison of fluid level in the launder at 20, 30 and 40 s in Fig. 5 indicates that it remains essentially constant during this period. By about 50 s, a substantial fraction of fluid in the furnace has been emptied out. The furnace is at an angle of 70◦ to the horizontal at this stage. The flow from the furnace is not fully able to compensate for the flow out of the launder, so the liquid metal level in the launder declines. Fig. 6 shows a close-up of the fluid flowing from the furnace into the launder. The fluid is coloured by its local speed with red indicating maximum (3.0 m/s) and blue the minimum (of 0.0 m/s). At 10 s, a thin fragmented stream of fluid is seen to fill the launder. Due to the fragmented nature of this stream one can expect a larger surface area of fluid exposed to air leading to higher rates of oxide formation. At 20 s, the stream from the furnace to the launder becomes less fragmented and is more or less continuous. As the fluid hits the launder there is splashing with the fast moving fluid approaching the dam. However, due to a deeper liquid level in the middle of the launder and the presence of the dam the fluid quickly loses momentum. At 30 and 50 s, the stream of fluid from the furnace is still reasonably continuous indicating a steady flow pattern from the furnace to the launder. The predominantly blue coloured fluid beyond the dam at all times demonstrates that it tends to reduce the fluid speed in the launder before reaching the ingot wheel. The tilt speed of the furnace, the design of the lip of the furnace, the launder design and the location and design of the dam are important factors that will influence the amount of oxide being carried over downstream.
5.2. Comparison between different simulation resolutions Fig. 7 shows the flow pattern for the medium (frames on the left) and fine resolution (frames on the right) simulations. The fluid here is coloured by its speed with red representing the maximum speed (3.0 m/s) and blue is stationary. At 2 s, the fluid has just started flowing from the furnace into the launder in the medium resolution and fine resolution cases. The fine resolution case has progressed slightly further than the medium resolution one at this stage.
Fig. 6 – Close-up of the fluid flowing from the furnace into the launder. The fluid is coloured by its speed with red being maximum and blue being minimum. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.) At 5 s when the furnace has rotated by 25◦ the fluid starts flowing into the launder as observed in the experiments. At this stage the fluid has filled the clearance between the dam and launder in both cases. At 10 s, a substantial amount of fluid has entered the launder. Strong similarities between the
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Fig. 7 – Flow pattern of the molten aluminium poured from the furnace into the feed launder for the medium and fine resolution simulations. The fluid is coloured by speed with red being the maximum (3.0 m/s) and blue being zero. Most of the fluid has emptied out from the furnace by 60 s. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of the article.)
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medium and fine resolution simulations can be observed in the following aspects of flow at this stage: • The stream of fluid coming from the furnace and feeding the launder is fragmented in both cases in similar ways. • The fill level of the fluid and its local speed (given by the fluid colour) are comparable in the region before and after the dam in the launder. • The level of fluid and the angle of the fluid free surface in the furnace are similar at both resolutions. At 20 s, the flow from the furnace to the launder is well established and the fluid stream emanating from the furnace is more or less continuous at both resolutions. The fill level of the fluid in the launder and the location at which the fluid hits the launder are noticeably similar for both resolutions. At about 60 s, almost all the fluid has been poured from the furnace into the launder. At this stage the bottom of the furnace is at an angle of about 80◦ from the horizontal. The level of fluid and free surface location in the furnace and launder are similar for both resolutions. This comparison demonstrates that the flow predicted is very similar for these two resolutions. They are also quite similar to the coarse solution (albeit with much more detail). The mass flow rates, oxide flow rates and oxide per unit of aluminium discharged (discussed below) all indicate that three simulations show similar trends. This gives us confidence that the solution is fairly insensitive to the numerical resolution used.
6.
Mass flow predictions
The furnace tipping speed was chosen to give an average mass flow rate of 30 tonnes/h or 8.33 kg/s. The time variation of the actual mass flow rates in the experiments was backcalculated from the observed ingot weights. Fig. 8 shows the experimental mass flow rate. One can observe a pattern with a lower mass flow rate in the initial stage with a relatively steady flow rate in between and with the flow rate declining back towards zero as the fluid empties out from the furnace. Fig. 9 – Mass flow rate in kg/s for (a) coarse, (b) medium and (c) fine resolution simulations.
Fig. 8 – Variation in mass flow rate (kg/s) with time (s) in the experiment.
In the experiment shown the flow rate remained reasonably steady until about 45 s. The peak experimental mass flow rate is about 32.7 tonnes/h or 9.1 kg/s. As mentioned earlier the experiments used a slightly variable tilt rate to maintain a reasonably constant ingot fill level. The local peaks in Fig. 7 correspond to the stages when such variable tilt rates were used in the experiment. The smoothed experimental mass flow rate (during the relatively constant middle stage of pouring) lies in the range of 24.0–32.7 tonnes/h or between 6.7 and 9.1 kg/s. Fig. 9 shows the predicted mass flow rate of the molten aluminium for the simulations carried out at the three different resolutions. These plots show that the mass flow predictions are acceptably consistent for the different resolutions. As for the experiments, one can see that the mass flow rate starts from zero attains a somewhat steady rate and drops down
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back to zero as the furnace empties out. Note that the peak mass flow rate for all three resolutions is about 9.5 kg/s and that between 20 and 40 s the mass flow rate varies consistently between 6.5 and 9.5 kg/s. This range of mass flow rate and the predicted fill time correlates well with the experimentally observed values.
7.
Oxide predictions
Fig. 10 shows the average oxide flow rate predicted from the fluid passing through the measuring plane at the end of the launder for the three simulation resolutions. The smoothed oxide flow rate varies in the range of 0.005 and 0.008 kg/s
Fig. 11 – Oxide content of aluminium in grams of oxide per kg of aluminium for (a) coarse, (b) medium and (c) fine resolution simulations.
Fig. 10 – Oxide flow rate in kg/s for (a) coarse, (b) medium and (c) fine resolution simulations.
between 20 and 50 s and then declines rapidly as the aluminium flow rate falls off at the end of the pour. Fig. 11 shows the oxide concentration in the aluminium as it flows out of the launder in grams of oxide per kilogram of aluminium for the three different resolutions. This is essentially obtained by dividing the oxide flow rate shown in Fig. 10 by the fluid flow rate shown in Fig. 9. Initially there is no oxide in the fluid. The first small peak (around 1 g oxide/kg of aluminium for the fine resolution simulation) before 10 s in Fig. 11 corresponds to the initial splash of leading edge fluid flying through the measuring plane. The oxide content starts to rise from 10 s as the leading edge of contiguous fluid reaches the plane. The oxide content rises rapidly to a peak of around 2.4 g/kg at around 15 s. This reflects both the very high and
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Table 1 – Comparison of average oxide content in the launder to that generated through the wheel for the original and optimised wheel design reported in Cleary et al. (2003) Wheel design Original Optimised
Total oxide content generated by the wheel (g/kg)
Average launder oxide content (g/kg)
% Oxide generated in the launder from the furnace tipping
1.035 1.035
52 67
0.95 0.52
Fig. 12 – Essential features of (a) the original poorer performing wheel design and (b) the new optimised wheel design. The liquid is coloured by velocity.
increasing surface area to volume ratio of the initially thin fluid flowing across the bottom of the launder and its very turbulent nature. As the launder fills the surface area of metal exposed remains fairly constant but the volume increases with depth so the fraction of metal exposed to oxidation steadily declines from its peak at 15 s. The increasing depth also damps the violent turbulent motions observed at shallow fill levels. This combination leads to a rapid decline in oxide content reporting to the wheel (by more than 60% from its peak) at 20 s. It continues to decline to a minimum of only 0.8 g/kg at around 30 s). After 30 s, the metal flow rate starts to drop and the fluid level in the launder starts to decline slowly. This leads to slow but steady increase in the ratio of surface area to volume of fluid in the launder thus increasing the oxide concentration measured at the sample plane. The gradient of the measured oxide content with time (as seen in Fig. 11) is constant from 30 s to around 70 s reflecting the steady linear decline in the launder fluid depth. By 75 s, the depth of metal in the launder has become very low and the turbulent motions from the flow from the furnace are no longer able to be damped by the fluid pool in the launder. This results in a sharp increase in gradient of oxide content with the oxide levels reaching and then exceeding the initial peak of around 2.4 g/kg. This indicates that the final residual parts of the flow are very oxide rich. This example demonstrates that SPH can be used to predict the oxide concentration at different stages in any melt transfer operation and to understand the importance of the different mechanisms driving oxide formation. Specifically, the role of the surface to volume ratio of the liquid metal and of the ability of the fluid pool to rapidly damp the turbulent flow entering the pool is identified. Between 20 and 50 s the oxide concentration varies in the range of 0.84–1.23 g/kg. Ingots with a standard weight
of around 22.5 kg are expected to be produced during this part of the furnace tipping process. Therefore the average value, 1.035 g/kg, of this oxide range is used to characterise the oxide content resulting from the furnace tipping phase of the process. This is compared with the oxide content predicted for the ingot pouring phase using wheel casters. Table 1, gives a comparison between oxide generated in the furnace/launder region and the oxide generated in the ingot moulds for the original and optimised ingot casting wheels (as reported in Cleary et al., 2003). The percentage of the total oxide formed in the launder resulting from the furnace tipping and launder flow is shown in the last column of Table 1. In both cases the oxide generation during the furnace pouring and launder flow is greater than that generated in the wheel. For the poorer performing original wheel, the amount of oxide is similar for both parts of the process, but for the new optimised wheel design, the furnace tipping phase generates the dominant fraction (67%) of the total oxide created in the experimental casting process. This demonstrates the critical importance of the furnace tipping phase of melt transfer processes in relation to the creation of oxide and thus the overall quality of finished products. Essential features of the original wheel design and the modified and optimised wheel design can be surmised from Fig. 12. Further information about the wheel design and optimisation process can be found in Prakash et al. (2007).
8.
Conclusions
SPH simulations were carried out at three different resolutions to understand the nature of the fluid flow and to predict the amount of oxide generated during the furnace tipping phase of an aluminium melt transfer process. The following conclusions can be drawn from these simulations:
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• Simulations at all three resolutions lead to comparable qualitative and quantitative results, demonstrating that the solutions are resolution independent. • Good agreement was reached between the mass flow rate predicted by the simulation and the experimental mass flow rate measurements. • SPH simulation has key advantages for modelling this process compared to conventional grid based CFD. These include the ability to easily predict complex splashing free surface flows, simulate moving objects and to predict oxide formation. These have enabled a detailed flow analysis that has led to a better understanding of the key mechanisms that control oxide generation in furnace tipping operations. • It was found that the oxide generated during the furnace tipping process was comparable or larger than the oxide generated during the flow of metal through various casting wheels and could be responsible for up to 67% of oxide creation for the better wheels. • Oxide formation is heavily influenced by the surface to volume ratio of liquid metal in the launder and to the degree of damping of turbulent free surface motion resulting from the entry of metal from the furnace into the launder pool. Increasing depth of the pool in the launder is favourable for both mechanisms but the damping of free surface motion is most critical for shallow pools. These results demonstrate that the furnace tipping stage of melt transfer and casting operations can have serious implications for the quality of the finished products. This suggests that there are likely to be strong benefits in optimising furnace designs and tipping processes to minimise oxide formation.
Acknowledgments This project was conducted by the Cooperative Research Centre for Cast Metals Manufacturing (CAST). CSIRO is a core participant in the CRC for Cast Metals Manufacturing (CAST), which was established under and is supported in part by the Australian Government’s Cooperative Research Centres scheme.
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