发展了一个元胞自动机模型来模拟定向凝固中枝晶阵列的一次间距选择. 在模型中通过采用简化的 生长动力学降低了计算复杂度, 并给出了判断系统达到稳定态的方法. 基于两种一次间距的调整机制-侧 枝不稳定性和湮没不稳定性, 分别采取两套不同的数值实验方法: 一套是种晶数目固定, 采用台阶变速方式; 另一套是种晶数目改变, 抽拉速度恒定. 确定了给定的生长条件下枝晶阵列的一次间距的允许范围. 模拟 结果表明, 一次间距的允许范围基本独立于数值实验方法, 而允许范围的上限λmax和下限 λmin可以一般化 地表示为抽拉速度的幂函数. 针对丁二腈-2.乙醇定向凝固枝晶的生长模拟得出的幂函数参数与文献的 实验结果吻合得很好, 模拟结果的下限与实验结果下限吻合的程度优于Hunt-Lu模型的下限.
A cellular automaton model was developed to simulate the primary spacing selection of dendritic array during directional solidification. A simplified growth kinetics was adopted, which could relax the computing complexity, and a strict method to determine the stable state of the system was proposed. Based on two type of primary spacing adjustment mechanisms in the simulation: branching-instability and submerging-instability, in order to determine the allowable range of primary spacing of dendritic arrays for given growth conditions, two different methods of tests were adopted, in one way the seeds number was fixed with a step-varying pulling velocity, and in another way the pulling velocity was constant with different seeds number. The simulated results showed that the allowable range is independent from test methods. The upper limit， λmax，and the lower limit， λmin， of the allowable range as the function of pulling velocity, V, can be generally expressed as the power function of the pulling velocity. During the simulation of the SCN-2.5%ethanol dendrite growth, the parameter of the power function were in good agreement with Huang’s experiments. The simulated lower limit was also in good agreement with Hunt-Lu model.
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