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针对描述多相体系中成核、长大、聚并微观过程的群体平衡方程,提出了一种可以跟踪任意数目矩的定点矩方法.为便于方法处理,将间歇式和连续式两种不同操作过程下的群体平衡方程写成统一形式,并利用权值残差法导出统一形式矩方程,实现了两种操作条件下矩的直接跟踪.将数值密度函数简化为连续DiracDelta函数加权和,将积分或微分转化为连续求和.对连续式操作下的成核、长大微观过程和间歇式操作条件下的聚并、长大微观过程模拟结果表明:该方法具有较高数值精度,与分析解的相对误差在10-8%以内.对无分析解间歇式操作过程中成核、聚并、长大复合微观过程模拟,重现了复合过程微观行为,说明该算法的可行性.
In order to describe the population balance equation of nucleation, growth, aggregation and microscopic processes in multiphase system, a fixed moment method can be used to track arbitrary number of moments. To facilitate the processing of the method, two kinds of intermittent and continuous operation The population equilibrium equation under the process is written into a unified form, and the method of weight residuals is used to derive the unified form moment equation to realize the direct tracking of moment under the two operating conditions. The numerical density function is simplified as the weighted sum of continuous DiracDelta functions, Differential transformation into continuous summation.Under the continuous operation of the nucleation, growth and intermittent operating conditions under the conditions of the merger, the growth of micro-process simulation results show that: the method has a high numerical accuracy, and analytic solution The relative error is less than 10-8%. The microscopic process of nucleation, aggregation and growth in intermittent operation without analytic solution is simulated, and the microscopic behavior of compound process is reproduced. The feasibility of the algorithm is demonstrated.