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

Study on Direct Quadrature Method of Moment for Population Balance Equation in Isotropic Particle System

随着颗粒系统微观行为研究的深入,数量平衡方程越来越受到重视。一般数量平衡方程由于复杂难以得到解析解。比较数量平衡方程的求解方法—分组方法(CM)、矩方法(MOM)和在矩方法基础上发展起来的直接矩积分方法(DQMOM),发现DQMOM具有计算量小,容易和计算流体力学(CFD)耦合等优点。运用直接矩积分方法对各向同性系统的颗粒长大、聚并和破碎等微观行为进行模拟,对各向同性液固系统的颗粒长大行为模拟的结果与文献的解析解吻合较好,误差小于10-5,对于各向同性液固系统的颗粒聚并和破碎行为模拟的结果与CM方法的精确解相比误差在2%以内。可见直接矩积分求解法在液固多相系统是有效的,具有良好的应用前景。

With the development of particle system microcosmic behavior research, population balance equation （PBE） received more and more attention. PBE couldn＇t be solved by analytical methods because of its complexity, but by numeric methods. Numerical methods were divided into class method （CM） and method of moment （MOM）. The two methods and direct quadrature method of moment （DQMOM） were analyzed and compared, the results showed that DQMOM＇s computation amount was less than the others＇ and DQMOM was coupled with CFD more easily. DQMOM was used to simulate the particle growth, aggregation and breakage in homogeneous particle system, and the solutions agreed well with the analytical solution and literature solution, The results showed that DQMOM was promising in the liquid-solid particle system .