International audienceA finite element method has been used to model solid flow inside a cold blast furnace, based on a hypo-plastic constitutive equation. This equation was calibrated with data obtained from simple soil mechanics tests on coke material. The steady state velocity and stress fields were determined after an iterative enmeshment procedure. The most significant results include the computed shapes of the deadman zone and the active and passive state regions, the transition between plug flow in the shaft and funnel flow in the bosh, and the void ratio distribution fields

A new 3-D model has been developed to describe the interaction between a transferred electric arc and a liquid metal bath, and has been used to simulate a pilot axisymmetrical transferred arc furnace operating in the EDF Research and Development laboratory.This model enables calculations of the flow patterns, temperature distribution and electromagnetic fields in both the arc and the bath. The Navier-Stokes equation coupled with the electromagnetic relations are solved in each domain using a finite volume method. The source term in the radiative energy equation is modeled using the radiative transfer method in order to take into account the strong temperature variations in the electric arc. The transport and condensation of metal vapour in the arc domain are considered by solving a conservation equation for the vapour mass fraction. The arc flow calculation at the bath surface uses a one-dimensional sheath model taking account of the metal vapour, in order to ensure the coupling between the plasma and the bath by evaluating the boundary conditions at the arc/bath interface. The calculations were performed for an arc length of 0.25 m.Realistic predictions are obtained for the electrical, dynamic and thermal behaviour of the plasma and liquid metal, and also for the arc voltage. The results indicate that the effects of the arc impact and Lorentz forces are not sufficient to induce effective mixing throughout the metal bath, leading to a marked thermal stratification in the liquid metal. In the bath, the liquid/solid interface has been determined by calculations.

The solid flow inside a blast furnace is modelled using a standalone finite element program and a constitutive equation called hypo‐plastic, in order to better simulate the granular material behaviour. The parameters of this constitutive equation are calibrated using data obtained from simple soil mechanics tests on coke and sinter materials, such as triaxial and oedometric devices. Steady velocity, stress and void fraction fields are obtained after several iterations of the code. Knowledge of the solids velocity field makes it possible to determine the dead man profile, as well as its renewal kinetics. Burden trajectories and time lines are also computed. Knowledge of the stress field makes it possible to compute pressures acting on the burden as well as on the walls. Finally, knowledge of void fraction field makes it possible to determine gas paths. The solid flow model was validated on 2D and 3D small‐scale cold blast furnaces, but the simulations never required any tuning parameter. This code is in fact an invaluable tool to determine the effect of blast furnace profile on solid flow conditions, and reciprocally.

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