基于特征线法的群体平衡系统的数值模拟

SIMULATIONS OF POPULATION BALANCE SYSTEMS WITH THE CHARACTERISTIC LINE METHOD

本文利用有限元方法和特征线离散技术,对工业结晶过程中化学反应沉降过程进行数值模拟.该化学反应沉降过程被称作群体平衡系统,它由五个耦合的偏微分方程描述,分别是描述溶液流动的不可压Navier-Stokes方程,描述两个反应物在溶质中进行化学反应的非线性对流扩散反应方程,描述一个生成物在溶质中生成与成核的非线性对流扩散反应方程,描述沉淀颗粒性态的颗粒尺寸分布方程(也称粒数衡算方程).除了时间和空间坐标外,颗粒尺寸分布方程还包含一个描述颗粒大小的内部坐标.我们利用特征线方法,将这个高维方程的求解转化成一系列可以并行进行的低维问题的求解.基于对在方腔内的碳酸钙沉降过程的数值模拟,本文定性地给出反应物入流口位置和生成物出流口位置的相对关系对沉淀物颗粒大小的影响.

Precipitation processes are modeled by population balance systems consisting of equations describing the flow field,equations for the chemical reaction and an equation for the particle size distribution.The main difficulties for simulating the precipitation processes include the coupling of these equations,the solving of time dependent convection-dominated convection-diffusion-reaction equations and the high dimensional property of the particle size distribution equation.In this paper,using the characteristic line method solving the particle size distribution equation is replaced solving a series of low dimensional problems which can be carried out in the parallel way.The calcium carbonate deposition process is simulated in the square cavity.And the relationship bet ween the size of sedimen t particles and the positions of inflow and outflow is investigated qualitatively.