Mixing in a tundish and a choice of turbulence model for its prediction

Abstract

The Navier-Stokes equation and the species continuity equation have been solved numerically in a boundary fitted coordinate system comprising the geometry of a single strand bare tundish. The solution of the species continuity equation predicts the time evolution of the concentration of a tracer at the outlet of the tundish. The numerical prediction of the tracer concentration has been made with nine different turbulence models and has been compared with the experimental observation for the tundish. It has been found that the prediction from the standard k-1 model, the k-1 Chen-Kim (ck) and the standard k-1 with Yap correction (k-1 Yap), matches well with that of the experiment compared to the other turbulence models as far as gross quantities like the mean residence time and the ratio of mixed to dead volume are concerned. It has been found that the initial transient development of the tracer concentration is best predicted by the low Reynolds number Lam-Bremhorst model (LB model) and then by the k-1 RNG model, while these two models under predict the mean residence time as well as the ratio of mixed to dead volume. The Chen-Kim low Reynolds number (CK low Re) model (with and without Yap correction) as well as the constant effective viscosity model over predict the mixing parameters, i.e. the mean residence time and the ratio of mixed to dead volume. Taking the solution of the k-1 model as a starting guess for the large eddy simulation (LES), a solution for the LES could be arrived after adopting a local refinement of the cells twice so that the near wall y + could be set lower than 1. Such a refined grid gave a time-independent solution for the LES which was used to solve the species continuity equation. The LES solution slightly over predicted the mean residence time but could predict fairly well the mixed volume. However, the LES could not predict both the peaks in the tracer concentration like the k-1, RNG and the Lam-Bremhorst model. An analysis of the tracer concentration on the bottom plane of the tundish could help to understand the presence of plug and mixed flow in it.

Comparison between Standard and Renormalization Group k-.EPSILON. Models in Numerical Simulation of Swirling Flow Tundish

“…The standard k-e model is, therefore, only valid for fully turbulent flows with high Reynolds number. Although the standard k-e turbulence model has gained success in many cases, [1][2][3][4][5][6] it can over-predict the level of turbulence in more complex geometries 9) for example swirling flow tundish with dam and weir.…”

“…In these studies, the standard k-e turbulence model with two-equation was commonly adopted (He and Sahai, 1) LEE and KOO, 2) JHA, 3) Palafox-Ramos 4) and Fan 5) ). Nine kinds of turbulence models have been used for prediction of fluid mixing in tundish by JHA, 6) including the standard two-equation k-e turbulence model and the Renormalization Group (RNG) turbulence model. It's evident that the RNG turbulence model is seldom used by researchers in the simulation of metallurgical processes.…”

Assessment of Turbulence Models for Prediction of Intermixed Amount with Free Surface Variation Using Coupled Level-Set Volume of Fluid Method

“….............. (21) in which ϕ21 = V2 -V1, ϕ32 = V3 -V2. For constant value of grid refinement (r), the term of q(P) was selected as zero.…”

“…A detailed study have been carried by Jha et al 21) In that © 2014 ISIJ research work, nine different turbulence models have been studied. The observations carried out by them shows that the prediction from the standard k-ε model, the k-ε Chen-Kim (ck) and the standard k-ε with Yap correction (k-ε Yap), matches fairly with the mean residence time and the ratio of mixed to dead volume.…”

Numerical Investigation of Fluid Flow Phenomenon in a Curved Shape Tundish of Billet Caster

“…8) Zero shear stress boundary condition was applied for the free surface of the tundish according to references. 8,17) Pressure boundary condition of 1 atm was fixed at the outlets of the tundish. The tracer concentration was considered to be impervious for the walls of the tundish, hence a zero gradient or flux boundary condition was applied on the walls for the tracer dispersion equation.…”