以体积为内部坐标数量平衡模型的矩直接积分方法

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

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．

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.