2D and 3D Numerical Modeling of Solidification Benchmark of Sn-3Pb (%wt.) Alloy under Natural Convection

"Comparison of experimental data obtained in a benchmark experiment of solidification of a Sn-3%wt.Pb ingot and numerical results of two-dimensional and three-dimensional simulations of the process is presented. The benchmark experiment consisted in solidifying a rectangular ingot of Sn-3%wt.Pb alloy using two heat exchangers. Conditions of solidification were thoroughly controlled due to six thermocouples embedded into each heat exchanger. Due to another array of thermocouples the evolution of the temperature field at a lateral wall of the crucible was registered during the whole experiment. A treatment of the temperature data provided an estimation of the velocity field in the experiment. Post-mortem analyses of the sample provided the pattern of macrostructure of the sample and qualitative segregations pattern. 2D and 3D numerical solidification models are developed to give the distribution of the solute in a solidified sample.IntroductionConvection, either natural or forced, plays a very important role during the solidification. Its intensity and flow pattern affect heat and mass transfer and, consequently, macrostructure and segregation in a solidified ingot [1-4]. The effect of buoyancy convection during solidification has been studied in many laboratory-scale experiments [5-6]. Due to these experiments a general comprehension of formation of various defects in the ingot has been achieved. However, mentioned studies were not consistent since alloys, solidification conditions and configurations were every time chosen arbitrary. That is why the role of each parameter characterizing solidification process remains unclear. Moreover, the question of reproducibility of defects under the same solidification conditions still exists. In addition, most of the experiments suffer from the insufficient knowledge of control parameters that makes difficult their use for validation of models for solidification. These parameters serve as boundary conditions for numerical modeling and their incomplete description leads unavoidably to the errors in simulations. This situation motivated us to develop a setup for benchmark solidification experiments and to perform a set of the solidification experiments which we reported in [7]. Here we presented a comparison between results obtained in a benchmark experiment of solidification of Sn-3%wtPb ingot and its numerical modeling, which was performed in two-dimensional and three-dimensional configurations."