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Modelling of transient magneto-hydrodynamic phenomena in Hall-Heroult cells
Abstract
Three dimensional flow field pattern and current density distribution in a Hall-Heroult cell is calculated with an extended version of the software package ESTER/PHOENICS. Boundary conditions for the electrical potential are derived from an electrical network simulation of the bus bar system. The magnetic effect of the steel parts is evaluated by the so-called direct method.
... These set the metal and the bath in motion and deform the metal-bath interface. The deformation of the interface perturbs the electric field in the liquids and subsequently the Lorentz forces, thus creating a self-exciting mechanism of bath-metal interface waves described by many authors [1][2][3][4][5][6][7][8][9][10][11][12]. This behavior is widely known in the aluminum industry as "metal pad roll". ...
... With the help of these models it was possible to increase cell currents and efficiency in many cases. In general, these models can be classified in two types: linear perturbation analysis of waves [1][2][3][4][5][6] and transient MHD analysis [7][8][9][10][11]. The latter uses transient shallow-water [7][8][9] or three-dimensional models [10][11]. ...
... In general, these models can be classified in two types: linear perturbation analysis of waves [1][2][3][4][5][6] and transient MHD analysis [7][8][9][10][11]. The latter uses transient shallow-water [7][8][9] or three-dimensional models [10][11]. In these models, cell stability is inferred from the decreasing or increasing wave amplitudes with time. ...
Numerical simulation of the magnetohydrodynamic (MHD) stability of the aluminum electrolysis cells has become an important tool for improving its design and operation efficiency. This paper presents a non-linear transient shallow water stability model and its application to the study on the stability of an existent cell. In the model, current density in the liquid metal pad, magnetic field generated by the currents inside the cell and subsequently, metal-bath interface wave shape are calculated at each time step. Anode changing greatly disturbs cell stability. During the anode change sequence, large current density disturbances occur, which produce a different MHD stability pattern after each anode change. We use the model to investigate the effect of different anode change patterns on MHD stability of the metal-bath interface. With the predictions of the model, it was possible to develop a new anode change sequence that improves cell stability.
... Steady-state and transient MHD of the cell have been described elsewhere [1]. Two kinds of cell stability model have been developed: linear perturbation analysis of waves [2][3][4] and transient MHD analysis [5][6][7]. The latter uses transient shallow water [5] or three-dimensional models [6][7]; in these models, cell stability is inferred from the decreasing or increasing wave amplitudes with time. ...
... Two kinds of cell stability model have been developed: linear perturbation analysis of waves [2][3][4] and transient MHD analysis [5][6][7]. The latter uses transient shallow water [5] or three-dimensional models [6][7]; in these models, cell stability is inferred from the decreasing or increasing wave amplitudes with time. In 3-D models, the amplitude can be as large as the ACD since the current density at each timestep is calculated from Laplace or Poisson equation without simplifications. ...
The aluminum industry is studying ways to increase the efficiency of reduction cells in new and retrofit smelters. Numerical simulation has become a very effective tool for analyzing such complex processes. This paper presents magneto-hydrodynamic (MHD) simulations of a cell technology case study. A three-dimensional (3-D) model was developed by coupling commercial codes ANSYS and CFX, via in-house programs and customization subroutines. A detailed electromagnetic model was built in ANSYS, which uses Finite Element Method. Steady state and transient MHD flows in the cell were calculated with CFX, which uses Finite Volume Method. Metal and bath were treated as multiphase flow. The homogeneous VOF (Volume of Fluid) model, available in CFX, was used to calculate bath-metal interface in steady state and transient regimes. The transient simulation of the bath-metal interface was used for the study of cell stability.
... As another example, CHAM produced the first Electrolytic SmelTER (ESTER) CFD code, for the aluminium-production industry, to simulate multi-anode electrolytic smelters of the Hall-cell type, in which electromagnetic effects and gravity waves on the molten-metal/electrolyte interface can interact to limit the performance of the equipment. Later on, ESTER was superseded by a PHOENICS-based product, Rosten [154], that was also used extensively by the industry [155][156][157]. Coal-and gas-fired furnaces, heat-exchangers, diesel and petrol (gasoline) engines, power condensers, steam generators, and natural-draught cooling towers were all among the equipment items for which CHAM produced the first CFD packages. ...
This paper presents a summary of some of the scientific and engineering contributions of Prof. D.B. Spalding up to the present time. Starting from early work on combustion, and his unique work in mass transfer theory, Spalding’s unpublished “unified theory” is described briefly. Subsequent to this, developments in algorithms by the Imperial College group led to the birth of modern computational fluid dynamics, including the well-known SIMPLE algorithm. Developments in combustion, multi-phase flow and turbulence modelling are also described. Finally, a number of academic and industrial applications of computational fluid dynamics and heat transfer applications considered in subsequent years are mentioned.
... Dans un contexte très simplifié, ilétablit un critère de stabilité empirique basé sur l'épaisseur des liquides et l'intensité des champsélectromagnétiques. D'autres auteurs obtiennent des résultats intéressants en exploitant des modèles 2D, 3D simplifiés ou de type "shallow water" ( [6,7,8]). ...
The purpose of this thesis is the study, from the numerical simulation point of view, of the aluminum electrolysis process. Navier-Stokes equations for the computation of a two fluids flow with free interface are coupled with Maxwell equations describing the electric current repartition and the magnetic induction field in an electrolysis reduction cell. The emphasis is set on an efficient method for the computation of the magnetic induction in an unbounded domain. The algorithm is based on a Schwarz domain decomposition method and on the Poisson integral representation formula for harmonic functions. The partial differential equations that rule the phenomena are discretized in space and time and implemented in an existing numerical simulation software. This code is then tested on an academic test case and also in a more realistic situation. The key parts of the mathematical model are emphasized. Finally the time-evolution model is compared with another approach, dealing with stationary situations and their linear stability.
Numerical simulation of coupled bath/metal magnetohydrodynamics (MHD) and MHD stability analysis allow the optimization of anode set pattern with respect to minimal cell disturbance. The contribution of anode gas-induced forces and the impact on the flow field are discussed.
During a complete anode set cycle, the anode current distribution changes significantly due to varying anode resistances, frozen bath and different metal pad heights. Typically the largest disturbance to cell stability occurs during a short time span after the anode change. With steady-state MHD simulations immediately before and after each anode change - following the sequence of the underlying set pattern - the relevant cell current and ACD distribution are determined. The impact of these parameters on cell stability is predicted with a linear MHD stability analysis for a complete anode change cycle.
The growth rate, period of oscillation, and spatial shape of interface waves in Hall-Héroult cells are determined from a linear stability analysis in the three-dimensional domain of liquid bath and metal. The linearized Maxwell and momentum equations together with the demand for hydrostatic balance at the interface describe a self-exciting oscillator. The corresponding eigenvalue problem for the interface movement is solved numerically. The resulting periods of typically 20–40s are in good agreement with measurements.
Both the steady-state as well as the oscillating component of the three-dimensional magnetic field and current density pattern are included. This gives a consistent description of different instability-driving mechanisms.
The spatial distribution of the electromagnetic to kinetic energy transfer is used to localize the regions in the cell which mainly cause instabilities . The influences of current intensity, ACD, metal pad height, and density ratio on strength and type of instability are demonstrated.
The bath flow was studied in prebake cells. The measurements were performed by recording the drop in bath temperature subsequent to alumina feeding as well as by adding tracer to the bath followed by subsequent bath sampling. The horizontal flow rate varied between 2 and 10 cm/s. It was found that the horizontal bath flow in the bulk above the working surface of the anodes and consequently the alumina distribution pattern are mainly determined by the bath flow from underneath the anodes. The quantity of anode gas which was drained into the centre channel was measured at different locations in a cell. The results showed that the distribution of the anode gas in the bath is strongly associated with the bath flow pattern under the anodes.
A CFD based numerical model for a realistic generic aluminium reduction cell is published. The model takes into account the complex physics of the magnetohydrodynamic problem in the reduction cell by coupling of two immiscible liquid flows, Lorenz force, flow turbulence and large length-scale with complex cell geometry. The current model extends the traditional box model with a detailed cell geometry including side and bottom ledge profiles and all channels (side, central and cross channels). The simulation tests of this model focus on quantifying the sensitivity of different side and bottom ledge profiles, and the cross channel by comparing the predicted metal flow and metal pad heaving. In addition, the model dependencies upon model assumptions of open/closed channel top are discussed. Finally a physical mechanism for the metal pad heaving that seems to explain at least parts of this complex phenomenon are highlighted.
A CFD based numerical model for a realistic generic aluminium reduction cell is published. The model takes into account the complex physics of the magnetohydrodynamic problem in the reduction cell by coupling of two immiscible liquid flows, Lorenz force, flow turbulence and large length-scale with complex cell geometry. The current model extends the traditional box model with a detailed cell geometry including side and bottom ledge profiles and all channels (side, central and cross channels). The simulation tests of this model focus on quantifying the sensitivity of different side and bottom ledge profiles, and the cross channel by comparing the predicted metal flow and metal pad heaving. In addition, the model dependencies upon model assumptions of open/closed channel top are discussed. Finally a physical mechanism for the metal pad heaving that seems to explain at least parts of this complex phenomenon are highlighted.
Introduction MHD Stability Analysis of Anode Set Pattern Optimization of Anode Set Pattern Effect of Gas Bubbles Conclusion
The bath flow was studied in prebake cells. The measurements were performed by recording the drop in bath temperature subsequent to alumina feeding as well as by adding tracer to the bath followed by subsequent bath sampling. The horizontal flow rate varied between 2 and 10 cm/s. It was found that the horizontal bath flow in the bulk above the working surface of the anodes and consequently the alumina distribution pattern are mainly determined by the bath flow from underneath the anodes. The quantity of anode gas which was drained into the centre channel was measured at different locations in a cell. The results showed that the distribution of the anode gas in the bath is strongly associated with the bath flow pattern under the anodes.
Stationary metal flow and metal heaving impact both heat balance and cell stability and affects pot tending as well. For improving cell performance and productivity, a good knowledge of these quantities is indispensable. However, limited access restricts the precise determination of the metal flow and heaving by measurements, and sought information must thus be derived from mathematical modeling of the magnetohydrodynamic (MHD) flow. The literature is scarce when it comes to benchmark problems for MHD flow in a cell and those cases which are available often suffer from insufficient level of detail, lack of input data and some inconsistencies. In this paper, a benchmark problem is given, resolving the deficiencies identified in the literature. A newly developed MHD model based on ANSYS FLUENT and User Defined Functions is applied to simulate the resulting flow pattern and interface heaving of the two immiscible bath/metal fluids in reduction cells.
Stationary metal flow and metal heaving impact both heat balance and cell stability and affects pot tending as well. For improving cell performance and productivity, a good knowledge of these quantities is indispensable. However, limited access restricts the precise determination of the metal flow and heaving by measurements, and sought information must thus be derived from mathematical modeling of the magnetohydrodynamic (MHD) How. The literature is scarce when it comes to benchmark problems for MHD flow in a cell and those cases which are available often suffer from insufficient level of detail, lack of input data and some inconsistencies. In this paper, a benchmark problem is given, resolving the deficiencies identified in the literature. A newly developed MHD model based on ANSYS FLUEN T and User Defined Functions is applied to simulate the resulting flow pattern and interface heaving of the two immiscible bath/metal fluids in reduction cells.
With the two commercial packages ANSYS and CFX, the electromagnetic driven flow field in the aluminum electrolysis cell was studied by finite element method and finite volume method. The flow field was simulated with the derived electromagnetic forces while two phase model and VOF method were employed to model the melt-bath mixture and its interface tracking. From the modeling it is shown that there are two vortexes in the liquid metal pad, and the disturbed horizontal current has significant effect on the magnetic field after corner anode changes and an eddy with larger velocity appears under the new anode while ACD decreases and magnetohydrodynamic instability increases.
Numerical simulations was conducted based on the commercial finite element method software package ANSYS to study the influences of electromagnetic field and electromagnetic force distribution on flow fields and fluctuations of the molten metal in a 75 kA drained cell. The results show that, the distribution of magnetic field and electromagnetic force in the aluminum film on the cathode slope are in symmetry to the long axis of the cell, especially the magnetic force is in the same direction as the gravity force, which is in favor of the aluminum discharging from the cathode slope. The highest fluctuation of aluminum pad surface in the accumulation sump is 0.021 m, which still remains within the safe range, and will not cause interpolar short circuit, so a normal operation process could be maintained with the same bus bar configuration as the current 75 kA aluminum reduction cells.
In order to understand both two-phase flow and interfacial fluctuation of magnetic fluid in an aluminum electrolysis cell, the two-phase flow numerical simulation for magnet fluid flow in a 160 kA aluminum electrolysis cell was performed through combing ANSYS with CFX software and taking Lorentz force as momentum source phase. The simulation results show that the flow of both aluminum liquid and electrolyte exhibits two vortexes. The average and maximum flow velocities of the aluminum liquid are 0.1476 m/s and 0.2879 m/s, respectively. The flow velocities of the electrolyte are slightly smaller, and the average and maximum flow velocities are 0.1165 m/s and 0.2866 m/s, respectively. The interfacial deformation range between the electrolyte and aluminum liquid is from -0.029 m to 0.035 m. The calculated results of flow velocities were compared with the measured values. The comparison results show that the two-phase flow based numerical simulation of magnet fluid in the aluminum electrolysis cell can be helpful for the understanding of flow field in the aluminum electrolysis cell, and can also provide the basis for further optimization research.
The growth rate, period of oscillation, and spatial shape of interface waves in Hall-Heroult cells are determined from a linear stability analysis in the three-dimensional domain of liquid bath and metal. The linearized Maxwell and momentum equations together with the demand for hydrostatic balance at the interface describe a self-exciting oscillator. The corresponding eigenvalue problem for the interface movement is solved numerically. The resulting periods of typically 20-40s are in good agreement with measurements. Both the steady-state as well as the oscillating component of the three-dimensional magnetic field and current density pattern are included. This gives a consistent description of different instability driving mechanisms. The spatial distributions of the electromagnetic to kinetic energy transfer is used to localize the regions in the cell which mainly cause instabilities. The influences of current intensity, ACD, metal pad height, and density ratio on strength and type of instability are demonstrated.
One of the key components of an aluminum reduction cell design is the potshell design. The potshell must be designed in such a way that it will not deform excessively in operation and will remain as much as possible in elastic deformation mode. Yet, over-designed potshell are very costly. So, it is important to achieve a design where all sections are getting their fair share of the total load and are being charged close to their elastic limit. It is obviously impossible to achieve such an optimal potshell design without extensive use of mathematical modeling tools. Three such tools are presented here in order of complexity namely the "empty shell", the "almost empty shell" and the "half empty shell" ANSYS ® based thermo-mechanical models. Results are presented for each model, both in elastic and plastic modes, as well as required CPU times.
Flow field in aluminum reduction cells is very important for the heat transfer, the mass transfer and the moment transfer. The gas-liquid-liquid flow in aluminum reduction cells was studied numerically by ANSYS and CFX. The study indicates that the anode bubbles present as a shallow layer. The bath-metal interface deformation of gas liquid-liquid three-phase flow model is larger than that of liquid-liquid two-phase flow model. The velocity magnitude and circulation flow direction of bath flow in the channels are affected by the anode bubbles. The anode bubbles play a major role in bath flow of the channels' domain only. The Lorentz force plays a major role in bath flow of other domain. The conclusion indicates that the gas-liquid-liquid three-phase model is necessary for the numerical simulation of flow field in aluminum reduction cells and the three-phase model provides basis for further optimization.
This survey focuses on the aluminium industry, mostly on process aspects as opposed to metallurgical aspects. It covers recent work on process models involving fluid flow and heat transfer, and extends to all important categories of processes encountered in the primary aluminium industry, from raw materials and reduction to cast shop and recycling. This includes a wide variety of processes from precipitators, calciners, rotary kilns, baking furnaces, reduction cells, casting and mixing furnaces to recycling furnaces and metal filtration. A review is carried out on the modelling work, the applications, and the needs expressed not only in analysis and design but also in process control, optimization and supervision, as well as operator training. A summary is given of the problems perceived, mainly in the field of model parameters and model validation. Indications on future trends are also given. Conclusions are drawn from the survey of this fast-expanding body of knowledge that suggests tough challenges as well as unprecedented opportunities. Suggestions are made as to how some of those challenges could be met.
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