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International audienceIn hot dip galvanizing, steel strip is coated by immersion in a bath of molten zinc. The principal reactions that occur at the steel/liquid zinc interface are (1) dissolution of iron and (2) nucleation and growth of intermetallic compounds. In order to improve the management of industrial galvanizing baths, it is essential to evaluate the flux of dissolved iron that diffuses into the bath from the sheet. For this purpose, a rotating disk device has been developed to study the dissolution and diffusion of iron in pure liquid zinc at the temperature usually employed in galvanizing baths (465degreesC). Since the dissolution reaction is controlled by diffusion under these conditions, the diffusion coefficient of iron in liquid zinc has been measured and found to be

The finite element method (FEM) is used in conjunction with plasticity theory in granular materials to derive the stress field and velocity field inside a small experimental apparatus reproducing the blast furnace. The theory used, called hypo-plasticity, gave satisfactory agreement between numerical and experimental time lines, and was able to predict the shape of the stagnant region in the bottom part, the so called dead man, without any adjustable parameters. Specific numerical methods, like iterative remeshing, allowed it to reach steady flow conditions in an Eulerian frame. The stress field is characterized by a plastic active state in the upper part, and a plastic passive state in the lower part. The velocity field is characterized by a plug flow in the upper part, and a funnel flow in the lower part. This model can also simulate granular flows in all type of vessels, like silos. In modeling blast furnaces, its usefulness lies in its connection with a multi-phase total model. KEY WORDS: blast furnace; finite element method; hypo-plasticity theory; granular material.

This article introduces an improvement of an existing blast furnace total model called the Four Fluid Flow Model, maintained by the last author. The derivation of solid phase motion in the former model is now replaced by an external numerical code, which implements a very specific granular flow theory called hypoplasticity. The calculation method in the external solid flow model is based on the finite element method (FEM), and differs from the method used in the fluid flow model (finite volume method or FVM), hence their separation. Both models are run one after the other by exchanging data such as solid velocity field, drag forces and solid voidage, until convergence. One major issue of the additional solid flow model is its ability to calculate the shape of the dead man (the name of the stagnant zone inside the blast furnace), whereas its shape was prescribed in the fluid model. The solid flow model also introduces stress state dependence on voidage, and takes into account source and sink terms related to solid phase physical and chemical transformations.KEY WORDS: blast furnace; finite element method; hypo-plasticity theory; metallurgical reactor.