Estimation of time-dependent heat transfer coefficient in unidirectional casting using a numerical model coupled with solidification analysis and data assimilation

Abstract

We have recently developed a method to estimate the heat transfer coefficient based on data assimilation. To understand its usefulness for estimating the time-dependent heat transfer coefficient, herein we performed unidirectional casting experiments of Al-1mass%Si alloy and obtained the cooling curves during solidification. The experimental data were then used to validate the estimated time-dependent heat transfer coefficient. Consequently, the measured cooling curves could be accurately simulated, and the average errors between measured and simulated cooling curves were below 0.8%. The estimated time-dependent heat transfer coefficient was 29461.5 Wm−2K−1 at the initial stage of cooling, which rapidly decreased to about 6000 Wm−2K−1 and then gradually decreased to about 1000 Wm−2K−1. These values are reasonable as the heat transfer coefficients for castings of Al base alloys. Additionally, the effect of the setting parameters of the data assimilation were evaluated. It was found that the position of the cooling curve(s) used in the estimation was the most important factor and a cooling curve measured at the position near the surface of the mold should be utilized. This method allows the reasonable estimation of the time-dependent heat transfer coefficient between the mold and molten alloy for unidirectional castings without using trial and error, and experimentally measured cooling curves can be accurately reproduced by solidification analysis.