An ironmaking blast furnace is a complex multiphase flow reactor involving gas, powder, liquid and solid phases. Understanding the flow behaviour of these phases is of paramount importance to the control and optimization of the process. Mathematical modelling, often coupled with physical modelling, plays an important role in this development. Yagi 1) gave a comprehensive review of the early studies in this area in 1993. Significant progress has since been made, partially driven by the needs in research but mainly as a result of the rapid development of computer and computational technologies. This paper reviews these developments, covering the formulation, validation and application of mathematical models for gas-solid, gas-liquid, gas-powder and multiphase flows. The need for further developments is also discussed.KEY WORDS: ironmaking; blast furnace; multiphase flow; two fluid model; discrete element method. Review development.
Mathematical ModellingGenerally speaking, the existing approaches to modelling the multiphase flow in a BF can be classified into two categories: continuum approach at a macroscopic level and discrete approach at a microscopic level. In the continuum approach, phases are generally considered as fully interpenetrating continuum media and described by separate conservation equations with appropriate constitutive relations and interaction terms representing the coupling between phases. The general governing equations are based on the so-called two fluid model (TFM), originally developed for gas-particle flow, [29][30][31] given by:Conservation The so-called Model A and Model B result from the treatment of the fluid pressure. For example, for gas-solid flow, Model A assumes the pressure is shared between the two phases, while in Model B, the pressure is attributed to gas phase only. 31) Model A formulation has been widely used in multiphase modelling, especially in process metallurgy. Model B formulation was recently used in the so called combined continuum and discrete method for coupled flow of continuum fluid and discrete particles. 32) The continuum approach is suitable for process modelling and applied research because of its computational convenience and efficiency. Indeed, most of the BF modelling is based on this approach. However, its effective use heavily depends on constitutive or closure relations and the momentum exchange between phases. For Newtonian fluids (gas and liquid here), these relations can be readily determined. For non-Newtonian fluids such as solids and powder, general theories are not yet available. In the past, various theories have been devised for different flow regimes (three flow regimes have been identified: quasi-static regime, rapid flow regime and a transitional regime that lies inbetween). For example, models have been proposed to derive the constitutive equations for the rate-independent deformation of granular materials based on either the plasticity theory or the double shearing theory; the rapid flow of granular materials has been described by extend...