Simulation of Slag Freeze Layer Formation: Part II: Numerical Model
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many instances in the nonferrous metallurgical industry, a refractory wall in contact with molten slag will erode until a layer of slag freezes on the hot face of the refractory.[1–3] This frozen slag protects the refractory from subsequent erosion/corrosion by liquid slag. The cooling elements positioned behind the refractory are designed to control the slag freeze layer more accurately. Most smelters today operate for years by relying on the slag freeze layer formed with the aid of the cooling elements.[4,5] Processes such as Outokumpu and INCO flash converting/smelting furnaces,[6] HIsmelt,[7] ISASMELT,[8] electric slag cleaning furnaces,[9–11] and matte smelting furnaces[12] are some examples. Despite the importance of the slag freeze layer, there is no mathematical description of the fluid flow and heat transfer associated with the solidification of slag that have Prandtl numbers in the range of 50 to 150. There are many studies[13–19] related to the solidification of low Prandtl number fluids, such as water and molten metals. Worster[20] reviewed the problem of mathematical simulation in two-phase zone in binary alloys. The review focused buoyancy-driven convection in two-phase layers, paying particular attention to the complex interactions among heat transfer, flow, and solidification. The fundamental difference between low and high Prandtl number fluids is that the latter have hydrodynamic boundary layers that are much thicker than the thermal boundary layers.[21] This aspect requires accurate FERNANDO J. GUEVARA, Senior Mechanical Engineer, is with Fluor Canada Ltd., Vancouver, British Columbia V6E 4M7, Canada. GORDON A. IRONS, Director, is with the Steel Research Centre, McMaster University, Hamilton, Ontario L8S 4L7, Canada. Contact e-mail: [email protected] Manuscript submitted May 22, 2009. Article published online June 8, 2011. 664—VOLUME 42B, AUGUST 2011
resolution of the velocities in the thermal boundary layer. In addition, the viscosities and densities of nonferrous slag are temperature dependent close to the solidification point. In the literature, two major approaches can be found to compute macroscopic solidification problems numerically: interface tracking and fixed-grid formulations. A good description of these methods was presented recently by Jana et al.[15] Interface tracking methods use a heat balance at an assumed sharp interface to compute the moving boundary, usually called the Stefan boundary condition. The problem is solved with sets of governing equations for liquid and solid phase. Fixedgrid formulations solve one set of equations for the entire domain, which are usually based in the EnthalpyPorosity formulation proposed by Voller and Prakash.[22] The advantage of the fixed-grid method is that one set of equations and boundary conditions is used for the solid and liquid in the whole domain. It avoids the problem of tracking the solid–liquid interface, and it is easier to implement considerations of the two-phase zone. For a fixed-grid approach, null velocities in the solid phase must be achieve
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