结晶器数学模型的广义矩变换解法

Extended Moments Transformation-an Approach to Solve the Crystallizer Models

结晶器数学模型由粒数衡算方程、溶质质量衡算方程、晶体生长和成核动力学方程及相应的初值与边界条件组成,为一组偏微分-常微分方程。把矩变换的定义从整数域扩展到实数域并扩展定义晶体尺寸后,矩变换能将与粒度有关的生长的结晶器模型化为一组常微分方程。对Bransom模型、ASL模型、Strong模型描述的三种结晶器模型进行变换后导出了相应的常微分方程组,为最一般的结晶器数学模型的求解提供一种通用的方法。以分批式结晶器为例,给出了一个算例。

The crystallizer model was described by the population balance equation, the mass balance equation of solute, the crystal growth and nucleation rate equation, which was a group of partial - ordinary differential equations. When the growth rate is independent of crystal size, the moments transformation can reduce the crystallizer model into a set of ordinary equations, which can easily be solved by standard numerical method. When the growth rate is dependent of crystal size, the crystallizer model can be reduced into a set of ordinary equations by the moments transformation method which must be extended from integral number set to real number set. The detailed transformation process and the corresponded transformed ordinary equations are given for crystallizer models with size dependent crystal growth described by Bransom moedel, ASL model and Strong model. The extended moments transformation method is simple but powerful to solve the crystallizer model with size dependent growth kinetic equation, A sample calculation for batch, crystallization is provided.