电磁成形定向凝固三维非线性温度场数学模型

Three dimension nonlinear mathematic model of temperature field of electromagnetic shaping directional solidification building

从基本物理模型出发,导出了电磁成形定向凝固稳态连铸过程中相变潜热在导热方程中的内热源处理形式,使之可以避免近似处理,而直接应用于数值模拟的推导过程.在此基础上,同时考虑涡电流加热、强制冷却、热辐射和热质运动等因素,建立了关于电磁成形定向凝固问题三维非线性温度场的完整导热微分方程.编程计算并与实验结果对比表明,模型正确有效.

Both melting and solidifying transfer of heat exist in electromagnetic shaping directional solidification and latent heat is very important for that temperature field numerical simulation. The traditional latent heat processing methods such as latent heat recovery, enthalpy and equivalent specific heat, are not suitable for accurate numerical calculation. Starting with the basic physical model, latent heat was introduced in the heat conduction equation as an inner heat source generation. This heat conduction equation can be employed directly for numerical simulation. Based on the analysis above, an integrated differential heat conduction equation was built that considered electric vortex heating, forced cooling, drawing rate, radiation and movement. The results of the numerical simulation agreed with the test result; that is, this mathematical model is correct and efficient.