Numerical Investigation of Shell Formation in Thin Slab Casting of Funnel-Type Mold A. VAKHRUSHEV, M. WU, A. LUDWIG, Y. TANG, G. HACKL, and G. NITZL The key issue for modeling thin slab casting (TSC) process is to consider the evolution of the solid shell including fully solidified strand and partially solidified dendritic mushy zone, which strongly interacts with the turbulent flow and in the meantime is subject to continuous defor- mation due to the funnel-type mold. Here an enthalpy-based mixture solidification model that considers turbulent flow [Prescott and Incropera, ASME HTD, 1994, vol. 280, pp. 59–69] is employed and further enhanced by including the motion of the solidifying and deforming solid shell. The motion of the solid phase is calculated with an incompressible rigid viscoplastic model on the basis of an assumed moving boundary velocity condition. In the first part, a 2D benchmark is simulated to mimic the solidification and motion of the solid shell. The impor- tance of numerical treatment of the advection of latent heat in the deforming solid shell (mushy zone) is specially addressed, and some interesting phenomena of interaction between the tur- bulent flow and the growing mushy zone are presented. In the second part, an example of 3D TSC is presented to demonstrate the model suitability. Finally, techniques for the improvement of calculation accuracy and computation efficiency as well as experimental evaluations are also discussed. DOI: 10.1007/s11663-014-0030-2 Ó The Minerals, Metals & Materials Society and ASM International 2014 I. INTRODUCTION THIN slab casting (TSC) is increasingly imple- mented, in competition with conventional slab casting, for producing flat/strip products due to its advantages of integrating the casting-rolling production chain, energy saving, high productivity, and near net shape. [1,2] How- ever, problems such as the sensitivity to breakout and edge/surface cracks were frequently reported. These problems have encouraged metallurgists to consider a special mold design, [3–5] cooling system, and submerge entry nozzle (SEN) [6–8] to use a special mold flux [9] and even to apply electromagnetic braking in the mold region. [7,8,10] The modeling approach becomes a useful tool to assist the system design. [5–8,10–18] One striking feature of TSC, different from that of conventional slab casting, is the use of the funnel-type mold, which provides the necessary space for the SEN to conduct liquid melt into the thin slab mold. Another important feature is the shell thickness which solidifies in the mold region: 40 to 50 pct of the slab thickness for TSC. [3] In comparison, there is only 20 to 30 pct of slab thickness which solidifies in the mold region for the conventional slab. [19,20] Therefore, the evolution of solid shell under the influence of turbulent flow and subject to the continuous shell deformation in TSC becomes a critical issue for the modeling approach. Different models were used to calculate solidification of TSC. One of these is the so-called ‘equivalent heat capacity model’, as proposed by Hsiao. [21] This model was originally proposed for the solidification without solid motion, as the transport of latent heat in the mushy zone due to the motion of the solid phase is not considered. According to recent investigations, [22,23] the transport of latent heat in the moving (deforming) mushy zone plays a very important part in continuously cast and solidified objects, e.g., continuous casting. The treatment of the motion of the solid phase has a significant influence on the advection of the latent heat, and hence on the evolution of the mushy zone. In order to consider the advection of latent heat under the condition of deforming and moving mushy zone, an enthalpy-based mixture solidification model is favored. [24–26] Another feature of the enthalpy-based model is to provide a possibility to consider the flow– solidification interaction in the mushy zone by introducing a volume-averaged parameter, i.e., permeability. The drag of the dendritic network of the crystals in the mush to the interdendritic flow is considered by the permeability, which is a function of the local solid fraction and the microstruc- tural parameters such as the primary dendrite arm space. This model was later extended by including the model of turbulence, [27–30] and applied to study the solidification and formation of macrosegregation under the influence of forced convection. A. VAKHRUSHEV, Senior Researcher, is with the Christian- Doppler Lab for Adv. Process Simulation of Solidification & Melting, Department of Metallurgy, University of Leoben, Franz-Josef-Str. 18, 8700 Leoben, Austria. M. WU, Associate Professor, is with the Christian-Doppler Lab for Adv. Process Simulation of Solidification & Melting, Department of Metallurgy, University of Leoben, and also Department of Metallurgy, University of Leoben. Contact e-mail: menghuai.wu@unileoben.ac.at A. LUDWIG, University Professor, is with the Department of Metallurgy, University of Leoben. Y. TANG and G. HACKL, Project Managers, are with the RHI AG, Technology Center, Magnesitstrasse 2, 8700 Leoben, Austria. G. NITZL, Product Manager, is with the RHI AG, Wienerbergstrasse 9, 1100 Vienna, Austria. Manuscript submitted July 3, 2013. Article published online February 20, 2014. 1024—VOLUME 45B, JUNE 2014 METALLURGICAL AND MATERIALS TRANSACTIONS B