Abstract

In the field of pyrometallurgy there is a complex interplay between many physical phenomena such as convective, conductive, and radiative heat transfer, stress and strain, electrical current flow, fluid flow, magnetohydrodynamics, phase change, reaction kinetics, and combustion. Including all of these physical phenomena into a single monolithic solver that is stable and applying it to a complex multi-region domain can however be difficult. An alternative to this is to instead develop simpler solvers that model only the necessary physics in each domain and thereafter coupling them together in an efficient manner. This work details the use of such a coupled multi-domain modeling approach to model and estimate feed throughput (melting rate) in a six in line electric arc furnace while incorporating the effects of electromagnetics, hydrodynamics, heat transfer and phase change.

The opensource coupling package preCICE [1] was used with custom interface conditions to couple various multiphysics solvers that were implemented in OpenFOAM to solve for the necessary physics in each domain of the furnace. Electrical current flow is modeled within all regions [2], with the resulting Joule heating and Lorentz forces inducing heating and buoyant flow within the molten slag and alloy baths where fluid solvers are used. A solid thermal conduction solver is utilized for furnace solid regions such as the refractory, while radiative heat transfer is modeled in the gaseous freeboard region with associated radiative heat transfer interface conditions implemented in preCICE [3]. Finally a throughput model is presented that models phase change and approximate particle movement within the feedpiles. This model estimates feed throughput for the given system state while maintaining the global furnace energy balance. To account for the difference in temperature that would exist between the top surface of the feed pile and its input temperature, a mass energy transport term is added to the interface condition between the freeboard and feed heaps using preCICE.

This coupled multiphysics model was used to study the influence of furnace geometry, operating conditions and material properties on the estimated feed throughput using a sensitivity analysis with the insight gained used to inform optimal furnace design and operation.

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Reference

[1] Chourdakis, G., Davis, K., Rodenberg, B., Schulte, M., Simonis, F., Uekermann, B., Abrams, G., Bungartz, HJ., Cheung Yau, L., Desai, I., Eder, K., Hertrich, R., Lindner, F., Rusch, A., Sashko, D., Schneider, D., Totounferoush, A., Vol.,, D., Vollmer, P., & Koseomur, OZ. (2023). preCICE v2: A sustainable and user-friendly coupling library. Open Research Europe.

[2] Bogaers, A.E.J, Roos, W., Reynold, Q., & Zietsman, J.H. (2023). Implementation and formulation of a multi-region, electromagnetic solver for discontinuous media. International Conference on Computational Methods for Coupled Problems in Science and Engineering.

[3] Bogaers, A.E.J, Heyns, J.A., Reynold, Q., & Zietsman, J.H. (2020). Partitioned Conjugate Heat Transfer with High Intensity Radiation. 12th South African Conference on Computational and Applied Mechanics.