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本文作了用焓法数值求解合金凝固温度场的尝试。首先,从合金相图出发,导得在固—液两相区内固相百分数和温度间的函数关系;建立了合金凝固传热的数学模型。然后,据此提出一个能反映合金凝固过程中潜热释放规律的、能为大多数合金适用的焓模型,并从数学上证明了与此焓模型相应的积分形式焓方程是等价于描述合金凝固的导热微分方程组。最后,以圆柱体中带有过热度的铝硅合金的凝固为例,采用有限差分隐式格式,求解了与此焓模型相应的焓方程。数值解的结果与实验测得值的吻合较好。
This paper made an attempt to solve the solidification temperature field of alloy by the method of enthalpy. First, starting from the alloy phase diagram, the function relationship between the solid fraction and the temperature in the solid-liquid two-phase zone is derived. A mathematical model for the solidification heat transfer of the alloy is established. Based on this, an enthalpy model that can reflect the rule of latent heat release during the solidification of the alloy and can be applied to most alloys is obtained. It is mathematically proved that the enthalpy equation of integral form corresponding to this enthalpy model is equivalent to describing the solidification of the alloy Thermal differential equations. Finally, taking the solidification of the Al-Si alloy with superheat in the cylinder as an example, the enthalpy equation corresponding to this enthalpy model is solved by using the finite difference implicit scheme. The result of numerical solution is in good agreement with the experimentally measured value.