Numerical Study of Multiphase Flow Dynamics of Plunging Jets of Liquid Steel and Trajectories of Ferroalloys Additions in a Ladle During Tapping Operations
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ISIJ International, Vol. 52 (2012), No. 5, pp. 814–822 Numerical Study of Multiphase Flow Dynamics of Plunging Jets of Liquid Steel and Trajectories of Ferroalloys Additions in a Ladle during Tapping Operations Jafeth RODRÍGUEZ-AVILA,1) Rodolfo D. MORALES2) and Alfonso NÁJERA-BASTIDA3) 1) Graduate Student, Instituto Politécnico Nacional-ESIQIE, Department of Metallurgy and Materials Engineering, Ed. 7, UPALM, Col. Lindavista, D.F. CP 07738 Mexico. E-mail: [email protected] 2) Instituto Politécnico Nacional-ESIQIE, Department of Metallurgy and Materials Engineering, Ed. 7, UPALM, Col. Lindavista, D.F. CP 07738 and K&E Technologies President, Manizales 88, Col. Residencial Zacatenco, D.F. CP 07369 Mexico. E-mail: [email protected], [email protected] 3) Formerly Graduate Student. Now at Instituto Politécnico Nacional-ESIQIE, Department of Metallurgy and Materials Engineering, Ed. 7, UPALM, Col. Lindavista, D.F. CP 07738 Mexico. (Received on September 27, 2011; accepted on November 24, 2011) A multiphase numerical analysis focused on flow dynamics and particle trajectories during steel tapping operations was developed. The numerical results indicate that lighter additions than steel (ferrosilicon and aluminum) are independent from bath level, fall height and flow dynamics of the melt. Neutral buoyant additions (Fe–Mn) are strongly dependent on fluid dynamics of the melt and bath height. Denser additions (like Fe–Nb) yields long residence time inside the melt before first emerging to the bath surface. However, when this ferroalloy is added at high bath levels, close to the end of tapping, the particles remain in the corner formed by the bottom and the wall of the ladle during long times prolonging their melting rates. KEY WORDS: tapping steel; air bubbles; additions; ferroalloys. ing into the melt. Final oxygen levels, assuming thermody- 1. Introduction namic equilibrium during steel tapping, depend then on Tapping is probably the most important operation leading efficient mixing and melting-dissolution processes of fer- to clean steel production since it is during this time that roalloys and aluminum. Due to these reasons it is important deoxidizers and alloying elements, in form of ferroalloys or to know the trajectories and residence times of particles of metallic, are added and slag carryover must be avoided to ferroalloys in molten steel. The problem this paper is deal- simplify later ladle furnace operations. Naturally, initial ing with had been already analyzed by Guthrie et al.6) who oxygen content in steel governs the efficiency of those addi- employed a balance of forces on a particle and evaluated the tions but certainly air entrainment by the plunging jet and importance of drag, buoyancy, added mass and history forces the bath surface turbulence contribute to form a multiphase acting on a particle submerged into a liquid. Their physical flow made of liquid steel, air and solid particles of deoxi- and mathematical models included experiments of wooden dizer. Under these circumstances excessive air entrainment particles with different densities into a tank of still water. works as a cushion dampening the steel motion and hinder- After the mathematical analysis of their experiments these ing the mixing and the melting-dissolution processes of fer- authors concluded that the history term in the balance of roalloys. Ferroalloy additions to molten steel initially freeze forces has negligible influence on the particle dynamics a shell of steel around the particles and this shell melts back emphasizing the importance of drag, buoyancy and mass after the ferroalloy or metal1–3) (like Al and Ni) addition has added forces. Maximum depth penetration of particles, for melted within this shell. Hereof, the residence time of fer- a given initial entry velocity, depend on the density ratio roalloys particles inside the melt during steel tapping is between the particle of ferroalloy and steel, higher ratios important to have high alloying and deoxidizing efficien- mean deeper penetrations. Tanaka et al.7) performed also cies. Assuming thermodynamic equilibrium, complete mix- physical and mathematical modeling for ferroalloys addi- ing conditions and efficient ferroalloys dissolution, the tions in a 250 ton steel ladle. They established, through group of the authors demonstrated that the amounts and dimensional analysis, modeling criteria for addition sizes types of inclusion chemistries depend on the addition and entry velocities between a model and the actual ladle sequence during steel tapping, steel level in the ladle and linked by the square root of the scale factor of the model. oxygen concentration in the melt.4,5) Therefore, those find- These authors simulated the effects of steel motion on ings underline the importance of an efficient mixing process spherical particle trajectories assuming a one-way coupling assisted by the momentum transfer effects of the jet plung- mechanism between liquid and particles (liquid steel flow © 2012 ISIJ 814 ISIJ International, Vol. 52 (2012), No. 5 influences particle dynamics). According with these authors main mechanisms for steel mixing during tapping. buoyant additions, such as aluminum and Fe–Si, are hardly • Plunging steel jet forms a perfect cylinder from the affected by the flow pattern of steel since buoyancy force is Eccentric Bottom Tapping (EBT) nozzle of the furnace so large that the dynamic behavior of these particles does to the bath surface or plunging point. not change even when compared with conditions of particles • The plunging jet is centered in the ladle geometric cen- in a stagnant liquid. The reverse is true for denser particles tre. whose trajectories are strongly influenced by fluid flow • The multiphase flow is one-way coupled, meaning that dynamics. The penetration of either, dense or light additions steel flow influences particle dynamics, but particles is improved when they are injected close or in the plunging motions do not affect liquid steel flow. steel jet. Maximum penetration depths and total immersion • There is not slag phase in the system, which implicitly times were substantially smaller when particles with differ- means that slag carryover does not exist attaining then ent geometries like cubes and cylinders are added to the an ideal perfect tapping operation. bath. However, as Guthrie et al.1,2) have shown, and cited • Steel throughput at tapping is constant. above, when a ferroalloy enters a bath of liquid steel, a solid The three-dimensional (3-D), multiphase and unsteady steel shell very rapidly forms around it. This shell formation turbulent fluid flow model of steel tapping operations was would tend to mask sharp irregularities in particle’s shape simulated through the solution of a set of continuity equa- maintaining valid the approximation of a spherical shape. In tions, one for each phase, and a set of momentum transfer another work, Mazumdar and Guthrie8) applied their model equations for all phases and the standard k-ε two-equation to the CAS (Composition Adjustment by sealed Argon turbulence model as is explained below. Bubbling Systems) process and found that the shape and size of particles have negligible effect on the overall nature 2.1.1. Continuity Equation of particle trajectories except for those with densities close The tracking of the interface(s) between each pair of to that of liquid steel. Efforts in the direction to model phys- phases is accomplished by the solution of the continuity ically plunging water jets dragging air have been reported equation for the volume fraction of one (or more) of the by Hammad9) using PIV measurements and Iguchi et al.10) phases. For the qth phase, this equation has the following who employed LDV measurements. The first authors found form: two-phase flow dynamics very sensitive to ambient pertur- 1 ⎡ ∂ ⎤ n bations, such as free surface instability and external vibra- ()αρqq+∇⋅() αρ qqqvS=+α () mm pq − qp (1) ρ ⎢∂t ⎥ q ∑ p=1 tions. On the other hand, LDV measurements were not pos- q ⎣ ⎦ sible in the developing region of the two-phase flow. where m pq is the mass transfer rate from phase q to phase Therefore, water models to explain plunging steel jets are p and m qp is the mass transfer from phase p to phase q. limited and can be used only for qualitative estimations of Since there is not a source term on the right-hand side of Eq. S these complex flows. In the present work mathematical (1), αq , is zero. Moreover assuming that air is essentially modeling approach is adopted since, possibly, it can provide insoluble in liquid steel there is not mass transfer between closer results to those observed in the steelmaking practice. both phases and mmpq== qp 0. Therefore, the full right Hereby, in order to complement the knowledge so far hand side of Eq. (1) is zero. Assuming that p is the primary developed in this field and to apply it to the actual steelmak- phase (liquid steel) and q is the secondary phase (air) Eq. (1) ing conditions various aspects, not considered in precedent is solved for air and the volume fraction of liquid steel will works, must be addressed. These aspects are the air dynam- be computed from the following constraint: ics during steel tapping, air entrainment by the plunging jet, n α = 1 ................................ (2) air bubbles dynamics generated and associated with the ∑ q=1 q entry jet and effects of steel level in the ladle at different Density and viscosity of the mixture are calculated stages of the steel tapping operation. The final aim of the through the weighted volume fraction of each phase accord- present work is then to build a frame where the factors influ- ing to the following Equations: encing ferroalloys efficiency may be identified considering n ραρ= conditions closer to those found in current steelmaking pro- ∑ q=1 qq............................. (3) cesses. n μαμ= ∑ q=1 q q ............................. (4) 2. Mathematical Model 2.1.2. Momentum Equation 2.1.