| 结晶器数学模型的广义矩变换解法 |
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| 引用本文： | 王玉芳.结晶器数学模型的广义矩变换解法[J].沙洋师范高等专科学校学报,2005,6(5):5-7,13. |
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| 作者姓名： | 王玉芳 |
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| 作者单位： | 沙洋师专,数理系,湖北,沙洋,448200 |
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| 摘 要： | 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，为一组偏微分一常微分方程。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徽分方程组，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。
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| 关 键 词： | 广义矩变换 结晶器 数学模型 与粒度有关的晶体生长 |
| 文章编号： | 1672-0768（2005）05-0005-03 |
| 收稿时间： | 04 6 2005 12:00AM |
| 修稿时间： | 2005-04-06 |
Extended Moments Transformation-an Approach to Solve the Crystallizer Models |
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| WANG Yu-fang.Extended Moments Transformation-an Approach to Solve the Crystallizer Models[J].Journal of Shayang Teachers College,2005,6(5):5-7,13. |
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| Authors: | WANG Yu-fang |
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| Abstract: | 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. |
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| Keywords: | Extended moments transformation Crystallizer Modeling Size dependent crystal growth |
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