Direct Quadrature Method of Moment on Characteristic Volume for Population Balance Equation

苏军伟 1; 顾兆林 2; 李云 1

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Direct Quadrature Method of Moment on Characteristic Volume for Population Balance Equation

更新时间：2025-12-08

- Direct Quadrature Method of Moment on Characteristic Volume for Population Balance Equation
- Vol. 41, Issue 5, Pages: 621-624+630(2007)
- 作者机构：
  
  西安交通大学能源与动力工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TQ021
- Online First：10 May 2007，
  
  Published：2007
- 稿件说明：
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苏军伟 1, 顾兆林 2, 李云 1. Direct Quadrature Method of Moment on Characteristic Volume for Population Balance Equation[J]. 2007, 41(5): 621-624+630.
DOI：

苏军伟 1, 顾兆林 2, 李云 1. Direct Quadrature Method of Moment on Characteristic Volume for Population Balance Equation[J]. 2007, 41(5): 621-624+630. DOI：

摘要

从体积为内部属性的数量平衡模型的一般形式出发

提出以体积为内部坐标的矩直接积分求解方法.该方法通过对实体数值密度分布引入高斯积分假设并进行矩变换

将颗粒固有属性从数值密度函数中分离出来

实现了实体属性及其实体分布的单独跟踪

从而降低了计算量.对各向同性系统的实体聚并、破碎和长大的模拟结果显示

该方法精度较高、计算量小.由于实体的数目及其体积在跟踪范围内

该方法具有数目和体积的自守恒性.以体积为内部属性的特点使其能够自动跟踪体积矩

从而使得该方法更适合描述结晶系统的沉积现象.考虑到离散相中体积和质量的密切关系

该方法能够直接应用到不可压缩流动的化学反应的传质模拟过程.

Abstract

Direct quadrature method of moment with nominal volume of entities for a general population balance model(PBE)is proposed. In order to lower time consumption in the simulation

the entity intrinsic property is extracted from the numerical density function of entity distribution by Gauss quadrature approximation and moment transformation. The higher accuracy and the lower time consumption are validated in aggregation

breakage and growth cases in isotropic system. The number or volume of the entities is self-conservative due to their automatic tracking in the simulation. With volume as internal coordinates

volume moment can be tracked

too. As a result

it is preferable for describing precipitation in crystal system. This method enables to solve mass transfer of incompressible multi-fluid systems with chemical reactions according to the proportional relationship between the mass of the disperse phase and its volume.

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references

苏军伟,顾兆林,李云. 各向同性颗粒系统数量平衡方程直接矩积分求解法的研究[J].化学反应工程与工艺,2006, 22(4):300-306.

Su Junwei, Gu Zhaolin, Li Yun. Study on direct quadrature method of moment for population balance equation in isotropic particle system[J]. Chemical Reaction Engineering and Technology, 2006,22(4):300-306.

Fan Rong, Marchisio M L, Fox R O. Application of the direct quadrature method of moments to polydisperse gas solid fluidized beds [J]. Powder Technology, 2004, 139(1): 7-20.

苏军伟,顾兆林,李云.颗粒数量平衡方程的直接矩积分求解[C]∥2006年中国工程热物理学会多相流学术会议论文集:上.重庆:中国工程热物理学会, 2006: 537-546.

Marchisio D L, Vigil R D, Fox R O. Quadrature method of moments for aggregation breakage processes [J]. Journal of Colloid and Interface Science, 2003, 258(2): 322-334.

Barrett J C, Webb N A. A comparison of some approximation methods for solving the aerosol general dynamic equation [J]. Journal Aerosol Sci, 1998, 19(1/2):31-39.

Bove S. Computational fluid dynamics of gas-liquid flows including bubble population balances [D]. Aalborg, Denmark: Aalborg University, Faculty of Engineering and Science, 2005.

Diemer R B, Olson J H. A moment methodology for coagulation and breakage problems, part 2:moment models and distribution reconstruction [J]. Chemical Engineering Science, 2002, 57(12): 2211-2228.

Alopaeus V, Laakkonen M, Aittamaa J. Numerical solution of moment-transformed population balance equation with fixed quadrature points[J]. Chemical Engineering Science, 2006, 61(15): 4919-4929.

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