Mathematical Modeling and Computer Simulation of Molten Aluminum Purification by Flotation in Stirred Reactor

Abstract

The removal of inclusions by flotation in mechanically agitated vessels is widely used in liquid aluminum treatments. Originating from different sources (oxide skins, refractory, or recycling wastes), inclusions may have disastrous repercussions such as deterioration of the physical properties of the cast products or difficulties during forging processes. With the aim of both a better understanding of the physical processes acting during flotation and the optimization of the refining process, a mathematical modeling of the behavior of the population of inclusions has been set up. Transport phenomena, agglomeration of inclusions, and flotation are considered here. The model combines population balance with convective transport of the inclusions, in order to calculate the time evolution of the inclusion size distribution. An operator-splitting technique is employed to solve the coupled population balance equation (PBE) and the transport equation. The transport equation is solved using a finite volume technique associated with a total variation diminishing scheme, whereas the PBE resolution relies on the fixed pivot technique developed by Kumar and Ramkrishna. A laboratory-scale flotation vessel is modeled and the results of a two-dimensional (2-D) simulation are presented.

Numerical Modelling of Inclusion Behaviour in a Gas-stirred Ladle

“…This type of work, performed under the leadership of KTH in Stockholm 4) and the University of Urbana-Champaign, 5) can be considered as a benchmark in this field. A fairly comprehensive and recent presentation of the modelling approaches is given by Zhang 6) and an application to the aluminium industry is given by Mirgaux et al 7,8) However, most models used by these authors should be regarded as general models of processes that do not accurately describe the behaviour and the capture of particles at interfaces (refractory wall, surface and bubbles). Among the few experimental studies in this field, the contribution of Tohoku University 9) represents a laudable effort in order to make original experiments in hot or cold models.…”

Removal of Impurity Elements from Molten Aluminum: A Review

“…Zhao 1995; Mirgaux, Ablitzer, et al 2009). The flow from the top collides with the flow from the bottom at the half height of the rotor, causing a strong turbulence that shears the bubbles and disperses them outwards.…”

3D Modeling of the Aggregation of Oxide Inclusions in a Liquid Steel Ladle: Two Numerical Approaches

“…In this representation, the behavior of the dispersed phase (i.e., Ar bubbles) is governed by a set of partial differential equations that express continuity (1) and momentum transfer (2), similar to the continuous phase (i.e., liquid steel). This two-fluid model is expressed as follows:…”

“…The physical processes involved in gas stirred ladles are numerous and complex owing to the three dimensional and multiphase (metal-gas and inclusions) nature of the reactor. Despite these difficulties, the population balance equations (PBEs) can be implemented in CFD code [1,2] and combined CFD-PBM (computational fluid dynamicspopulation balance method) models are investigated for steel ladle processes [3,4] and produce very promising results in terms of inclusion removal efficiency. Current research focused on the mathematical formulation of the system and an approach, the quadrature method of moments (QMOM), has been formulated and applied.…”