Study of Melting of a Horizontal Ice Layer with a Combined Effect of Temperature and Concentration

对水平垂直冰板在方腔内融化成氯化钙水溶液进行了实验和数值研究。浸泡在水溶液中的冰板会自发融化，甚至在冰和水溶液之间没有温差的情况下也是如此，这是不可能通过热扩散控制的经典Stefan问题来预测的。采用质量扩散控制熔化的新概念的数值方法定量地预测了冰层温度的突然下降、瞬时融化质量和液体中的双扩散对流。由于浓度诱导的优势对流，熔体表面上方的熔融量约为下方的两倍。从下到下熔化的数值结果很好地预测了实验，但预测结果比实验预测的要少40%左右。现有的基于层流假设的数值处理方法很难预测熔化表面上的熔融量，因为在熔化表面上，由于浮力的作用，熔化表面出现了一个很小的喷口，就像盐指一样。此外，数值预报还发现，由于最接近熔化前沿的浓度边界层很薄，因此数值预报需要设置一个非常小的网格尺寸，小于0.1 mm。

Experimental and numerical investigations are carried out of the melting of a horizontal vertical ice plate into a calcium chloride aqueous solution inside a square cavity. The ice plate immersed into the aqueous solution melts spontaneously associated with temperature depression in the ice even when there is no temperature difference between the ice and the aqueous solution just beginning of the melting, which is not possible to predict through the classical Stefan problem controlled with a thermal diffusion. A numerical method with a new concept of a mass diffusion controlled melting predicts quantitatively an abrupt depression in the temperature of the ice, a transient melting mass, and a double diffusive convection in the liquid. The melting amount from above melting surface is about double larger than that from below due to the concentration induced predominant convection. The numerical results for the melting from below predicts well the experiment, however, predicts less about 40% compared with the experiment. The present numerical treatment based on the laminar assumption is difficult to predict the melting amount from above melting surface since it appeared a very small spouts induced with the buoyancy like a salt finger on the melting surface. Moreover, it is also found that the present numerical prediction will require to set a very smaller mesh size less than about 0.1mm due to the very thin concentration boundary layer closest to the melting front.