Flows and mass transfers in two superimposed liquid layers in an induction furnace Cyril Courtessole ⇑ , Jacqueline Etay SIMaP, Grenoble INP, UJF, CNRS, BP 75, 38402 Saint-Martin d’Hères, France article info Article history: Received 4 February 2013 Received in revised form 13 June 2013 Accepted 14 June 2013 Available online 30 July 2013 Keywords: Mass transfers Liquid–liquid interface Electromagnetic stirring abstract In foundry, induction furnace is a well-known, clean, energy-efficient and well-controllable melting pro- cess. In order to improve its refining capacity, a salty or oxide liquid layer can be added at the surface of the liquid metal. This paper aims to simulate numerically mass transfers that occur at the liquid–liquid interface between these two liquid layers. To achieve this, the flows in both salty and metallic phases are calculated, taking into account all the present phenomena in the bulks (i.e. electromagnetic stirring, buoyancy, turbulence, heat transfer), as well as those at the interface (i.e. electromagnetic shaping, vis- cous shear driving). Comparison is made with literature experimental measurements. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The metal-refining step in metallurgy, or in spent nuclear fuels reprocessing, is based on a liquid–liquid extraction that aims to transfer a pollutant from one phase to another. In the reactor, two immiscible liquid layers (a metallic phase lying below a salty or an oxide phase) are separated by an interface where mass ex- change occurs via redox reaction. Kinetics of mass transfer, as well as its overall rate, are strongly dependent on the motions in the two layers, as well as the motion of the interface itself. Thus, stir- ring reduces mass transfer resistances by: – promoting the renewal of species in the vicinity of the interface by advection in the bulk of both phases, – increasing the apparent diffusion thanks to the contribution of turbulence with, correspondingly, a decrease of the thickness of the diffusion sub-layers. Numerical simulation is of great help to optimise such reactors. However, although mass transfers through an interface separating a liquid metal and a molten salt or oxide are at the heart of metal- lurgical processes, we do not find a satisfactory description of such transfers in the literature. The computation of an entire reactor is a tough task, not only because lake in mass transfers description, but also because it in- volves strongly coupled physical phenomena. In this article, we present a pragmatically conducted study. The choice of each model is explained and limitations are highlighted. We applied to validate each of the selected models. After a brief description of a pyrometallurgical reactor able to promote such mass transfers, we focus on the various physical phenomena and quantify them. Then, the strategy chosen to per- form the simulation is explained. The implementation of coupling between the two fluid flows is presented, and a focus is made on the numerical description of the interfacial shear stresses. The modelling choices attached to this description are validated on a simple flow (i.e. two-layers laminar plane Couette flow), whose analytical expression is easy to derive. Stationary flows in the stud- ied reactor are then presented and the promoted mass transfers are calculated finally as a post-process. The time-dependent concen- tration of the pollutant in the metallic phase is compared with experimental results from the literature. 2. Simulated reactor and attached physical phenomena A sketch of the experimental reactor is shown in Fig. 1. It corre- sponds to a reactor described by Perrier [1]. Two liquid layers are lying in a graphite crucible located in an electromagnetic field gen- erated by a 6-turn coil. The internal radius of the crucible is a = 4.5 cm. The thicknesses of the metallic and salty layers are 4 and 2 cm, respectively. This configuration has been used by Saadi [2], to study mass transfer of cerium from a fluoride molten salt to a metallic alloy. The respective chemical compositions of each phase are Sb-Li (10 mol.%) and LiF–CeF3 (2 mol.%) for the metallic and salty layers. The physical properties of involved materials are summarized in Tables 1 and 2. These properties are assumed to be constant; i.e. 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.06.025 ⇑ Corresponding author. Tel.: +33 4 76 82 52 53; fax: +33 4 76 82 52 49. E-mail address: cyril.courtessole@simap.grenoble-inp.fr (C. Courtessole). International Journal of Heat and Mass Transfer 65 (2013) 893–906 Contents lists available at SciVerse ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt