2006 European Phoenics User Meeting, London
Applied CFD in the Metallurgical IndustryApplied CFD in the
Metallurgical Industry
Jonas Alexis MEFOS ABJonas Alexis MEFOS AB
2006 European Phoenics User Meeting, London
Outline
Why are MEFOS modelling Metallurgical processesWhat is applied CFD at MEFOSExample: Sulphur Refining of Steel— Transport description— Reaction model— Reaction Zone
* Scalar equation model* Empirical model
Validation— Transport Equation— Sulphur refining
Conclusions
2006 European Phoenics User Meeting, London
Why are MEFOS modelling metallurgical processes?
The goal for the metallurgical industry is to achieve the material properties needed for production of a given product. This requires control of the amount of:
• Alloying elements (C, Si, Mn, Cr, Al ..)• Other elements (S, N, H, P, Cu, Zn ..)• Unwanted non-metallic particles (Inclusions). Also composition and size distribution
•Continuous measurement and sampling for process control is difficult in most process steps. The models are therefore needed for:
• Optimisation of the different process steps • Development of process control systems• Enhanced understanding • Education
2006 European Phoenics User Meeting, London
What is applied CFD at MEFOS
When fundamental models are missing or impossible to realize because of the lack of data, which is often the case, other methods need to be utilised.
One example: Fundamental data needed to describe the slag/metal-interface in a stirred ladle during sulphur refining is missing. Instead, empirical models of that interface, based on sampling at the steel plant can be used. The use is necessary if sulphur-refining in a production ladle is to be simulated.
2006 European Phoenics User Meeting, London
Sulphur RefiningTransport description (Gas
Stirring)
Ladle Radius = 1.25 mSteel Weight = 65 tSlag Weight = 1200 kgGas Flow Rate = 100 Nl/min
Open eyes
2006 European Phoenics User Meeting, London
Slag Layer
Interface (Reaction zone)
Steel SurfaceGas Stirred Ladle
Sulphur RefiningTransport description (Gas
Stirring)
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Sulphur RefiningReaction Model
2[Al] + 3 [O] =
Al2O3
[Fe] + [O] = FeO
[Mn] + [O] = MnO
2[Si] + [O] =
SiO2
[S] + (O2-) = [O] +
(S2-)
5 equations 6 unknowns (Al, Fe, Mn, Si, S and O)!!!
2006 European Phoenics User Meeting, London
Sulphur RefiningReaction Model
Equation 1. Al is related to Al2O3
Equation 2. Fe is related to FeOEquation 3. Mn is related to MnOEquation 4. Si is related to SiO2
Equation 5. [S] is related to (S) O is related to:wt%O] = [wt%O]Al O + [wt%O]FeO +
[wt%O]MnO + [wt%O]SiO +[wt%O]S
2
2 3
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Reaction Zone Scalar Equation model
Top part of a Plane in the in the ladle, through the open eyes
Gas flow Directed Upwards
Steel Phase
Slag Phase
Reaction Zone (Mixed Steel and Slag)
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Reaction ZoneSampling (Empirical model)
Sampler
Sampling in the ladle
After sampling
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Reaction ZoneSampling (Empirical model)
After sampling and quenching, each sample was mechanically opened. The metal bulk, slag bulk and slag-metal interface can be easily identified. Thereafter, the slag part was physically divided into a number of zones on the basis of the distance from the slag-metal interface. The width of each zone was not constant for all the samples. Small pieces of collected slag were analyzed using light optical microscope (LOM) and scanning electron microscope (SEM). The chemical compositions of the slag samples were analyzed and the sulphur contents were determined.
2006 European Phoenics User Meeting, London
Reaction ZoneEmpirical Model
The figures shows schematically the contact of metal with the lowest layer of slag droplets and the flow of metal associated with slag droplets. The following assumptions are made:
1. After stabilization of the flow, the whole slag layer is in droplet form.2. All slag droplets are spherical and having the same size and shape.3. The linear velocity of the metal along the periphery of the slag droplet is equal to the
velocity of the bulk flow of the metal at the slag-metal interface.4. The contribution of the metal film covering each slag droplet to the rate of mass
exchange is negligible.
2006 European Phoenics User Meeting, London
Reaction ZoneEmpirical Model
The metal volume associated with each slag droplet can be expressed by:
(1)
The mass of the metal associated with all slag droplets is given by:
(2)
The average time to travel a distance of 2 r can be evaluated by
(3)
The time required to flush out all the metal can be written as
(4)
The flush-out rate of the metal in a unit cell can be expressed by:
(5)
Eqs. (2) to (5) lead to
(6)
()⎥⎦⎤⎢⎣⎡π−=33r34r221v () mcelltotal rarrM ρπ⎟⎟⎠⎞⎜⎜⎝⎛⎥⎦⎤⎢⎣⎡−= 2233_ 434221
⎟⎟⎠⎞⎜⎜⎝⎛+π=metalmetalav Vr2Vr21t ⎟⎟⎠⎞⎜⎜⎝⎛+π== metalmetalavflushVr2Vr21tt
flushcell_totalmetaltMK=
2metalmmetalaV185.0Kρ=
2006 European Phoenics User Meeting, London
Sulphur Refining and Reoxidation Model
0.0000.0020.0040.0070.0090.0110.0130.0150.0180.0200.0220.0240.0270.0290.031
0.0300.0330.0360.0390.0410.0440.0470.0500.0530.0560.0590.0610.0640.0670.070
1.1E-41.4E-41.6E-41.8E-42.2E-42.5E-42.7E-43.0E-43.3E-43.5E-43.8E-44.1E-44.4E-44.6E-44.9E-4
[%S] [%Al] [%O]
[%S] [%Al] [%O]
Steel/slag interface
2006 European Phoenics User Meeting, London
ValidationTransport description
Velocity measurements with graphite rods
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0.6 s efter start!
0,22
0,23
0,24
0,25
0,26
0,27
0,28
0,29
0,3
0,31
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 2
0,2 m/s0,3 m/s0,4 m/s0,5 m/s0,6 m/s1,0 m/s
0,2 m/s => = 0,2 H cm0,3 / => m s = 0,6 H cm0,4 / =>m s = 1,1 H cm0,5 / => m s = 2,0 H cm0,6 / =>m s = 3,1 H cm1,0 / => m s = 7,9H cm
ValidationWave Height Model
Simulated waveheight
Height above Fluid Surface
y = 1,4133x + 0,0002
0
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0,08
0,09
0 0,01 0,02 0,03 0,04 0,05 0,06
Height above fluid surface (m)
Total height (m)
2006 European Phoenics User Meeting, London
ValidationValidation of Wave Height
Model
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
0,00 0,01 0,02 0,03 0,04 0,05 0,06 0,07 0,08 0,09 0,10
Wave height (m)
Velocity (m/s)
Bernoulli CFD-model
Bernoulli’s equation for incompressible flow 101202 22tan2 ghvghvtConspghv =⇒=⇒=++ρ
Comparison between Bernoulli and simulation
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ValidationTransport Description
1 2
3
Measuring positions in the ladle
Induction stirrer
1 2
Porous plugs for gas injection
2006 European Phoenics User Meeting, London
ValidationTransport Description
Velocity measurements with graphite rods
2006 European Phoenics User Meeting, London
ValidationTransport Description
0
0,2
0,4
0,6
0,8
1
1,2
0 0,5 1 1,5 2 2,5 3 3,5
Distance from stirrer (m)
Steel velocity (m/s)
Worn ladle
Measured
Steel velocities in ladle during induction stirring
Predicted
2006 European Phoenics User Meeting, London
ValidationSulphur Refining and
ReoxidationFor a validation of the ”Sulphur refining and reoxidation predictions from the model a comparison between predicted results and data from the industry was performed. Slag and Steel was sampled before and after the sulphur refining process. The process took 850 seconds and was performed in vacuum making it impossible to sample during the process. The two sets of Slag and Steel samples were analysed and used as input data and resulting Steel analysis respectively.
2006 European Phoenics User Meeting, London
ValidationSulphur Refining and
Reoxidation
0,00
0,01
0,02
0,03
0,04
0,05
0,06
0,07
0 200 400 600 800Time [s]
wt% [Al], [O] and [S]
0,00
0,05
0,10
0,15
0,20
0,25
0,30
wt% [Mn] and
[Al]
[O]
[Mn]
[Si]
[S]
0,00
5,00
10,00
15,00
20,00
25,00
30,00
35,00
0 100 200 300 400 500 600 700 800 900
Time [s]
wt% (Al2O3), (MgO) and (SiO2)
0,00
0,40
0,80
1,20
1,60
2,00
2,40
wt% (FeO),(MnO) and (S)
(SiO2)
(Al2O3)
(MnO)
(FeO)(S)
(MgO)
Slag analysis Steel analysis
Meaured Predicted
2006 European Phoenics User Meeting, London
Conclusions
• For a Qualitative description (Parametric studies) a simpler reaction zone model can be used.
• For a Quantitative description of Sulphur refining, the development of empirical models describing the reaction zone in a steel ladle must be utilised due to the lack of data prohibiting development of a fundamental model.