Homogenised model for the electrical current distribution within a submerged arc furnace for silicon production

Luckins, Ellen K.; Oliver, James M.; Please, Colin P.; Sloman, Benjamin M.; Gorder, Robert A. Van

doi:10.1017/s0956792521000243

Cited by 6 publications

(36 citation statements)

References 36 publications

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“…1998; Luckins et al. 2022). As such, the contact points between the solid particles will actually have non-negligible surface area and so it is reasonable to expect heat conduction through the solid structure.…”

Section: Model Developmentmentioning

confidence: 99%

“…Our model is similar to that used by Luckins et al. (2022), although we now include the heat transfer between the phases which is important on the longer domain length scale now considered.…”

Section: Model Developmentmentioning

confidence: 99%

“…Thus the gas phase may be assumed to be quasi-steady on the slow time scale of variation in the solid phase (see Luckins et al. (2022) for a detailed dimensional analysis). In our one-dimensional geometry, the quasi-steady gas flow is fully described by the mass flux and we need not deal directly with the gas velocity.…”

Section: Model Developmentmentioning

confidence: 99%

“…Throughout, we assume that the dimensionless parameters , and in the model are of order unity (see Luckins et al. (2022) for justification in the case of a silicon furnace). The inverse Péclet number, , is expected to be of the order of (Luckins et al.…”

Section: Model Developmentmentioning

confidence: 99%

“…The inverse Péclet number, , is expected to be of the order of (Luckins et al. 2022), and is the smallest parameter in the system. The asymptotic analysis in this paper is in the limit of .…”

Section: Model Developmentmentioning

confidence: 99%

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Modelling and analysis of an endothermic reacting counter-current flow

Luckins

Oliver²,

Please³

et al. 2022

J. Fluid Mech.

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We study the endothermic reaction and flow of a granular solid reactant, where energy for the reaction is provided by a counter-current flow of hot gases through the porous reactant bed. Research into reacting flows typically focusses on exothermic combustion processes. However, endothermic processes are common in the metallurgy industry, including the production of cement, silicon and rutile titanium dioxide. Several common features are observed in experimental and numerical studies of these processes, including critical temperatures of the reactant at which the chemical reaction begins, and regions of the reactor with uniform reactant temperature. Motivated specifically by the processes in a silicon furnace, we analyse a model of endothermic, reacting counter-current flow using the method of matched asymptotic expansions. Assuming the Péclet number in the solid is large, we explore the full range of values for the dimensionless inter-phase heat-transfer rate, finding six distinguished limits. In all limits, we find a diffusive boundary layer in which there is a fast chemical reaction rate due to the high temperatures, analogous to exothermic flame fronts. Outside this region, the counter-current flow is crucial to the chemical processes. For intermediate values of the heat-transfer rate, we find the same qualitative properties as those observed across the metallurgy industry, and we quantify the dependence of these properties on the flow rate and heat-transfer rate. In the limit of large heat-transfer coefficient, we derive the single-temperature limit, in which the solution structure is dependent on the direction of net heat flux through the domain.

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Section: Model Developmentmentioning

confidence: 99%

Section: Model Developmentmentioning

confidence: 99%

Section: Model Developmentmentioning

confidence: 99%

Section: Model Developmentmentioning

confidence: 99%

Section: Model Developmentmentioning

confidence: 99%

See 3 more Smart Citations

Modelling and analysis of an endothermic reacting counter-current flow

Luckins

Oliver²,

Please³

et al. 2022

J. Fluid Mech.

Self Cite

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Modelling the reduction of quartz in a quartz–carbon pellet

et al. 2023

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Traditional refining of silicon generates carbon dioxide emissions that are released into the atmosphere. An alternative process under experimental exploration uses quartz particles coated in a layer of porous carbon as the raw material, instead of lumps of quartz and carbon. The quartz–carbon pellets are processed at a lower temperature than in an industrial furnace, and hence, different chemical reactions are dominant, reducing the greenhouse gas emissions. The quartz core shrinks as it is consumed, and the carbon is converted to silicon carbide, which can subsequently be processed into silicon. We develop a model for chemical and transfer processes within a single quartz–carbon pellet. We derive governing equations for the concentration of silicon monoxide, carbon monoxide, and carbon dioxide, and conservation equations on the moving quartz interface. Furthermore, we then focus on a reduced model in an industrially relevant distinguished limit, and solve numerically the resulting leading-order system. We show examples of reaction-limited behaviour as well as diffusion-limited behaviour. Both regimes are physically admissible due to the large potential range of the parameters. Finally, we sweep through the parameter space, and characterize the dynamics based on the utilization of the carbon and the silicon yield. We find that the diffusion-limited regime is best for carbon utilization and silicon yield, as the silicon monoxide reacts with the carbon before it is transported out of the pellet.

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