三维空间液滴运动模型数值解法研究

Study on Numerical Algorithm of Droplet Motion Model in Three-dimensional Space

提出了数值求解三维空间液滴运动模型的算子分裂算法(OS算法),并与常用的显式单步长Runge-Kutta(RK)算法进行了比较。简述了三维空间液滴运动模型的具体形式,提出了求解该模型的OS算法,以求解不同直径液滴在波形板汽水分离器内的运动轨迹作为算例,从OS算法的相容性、稳定性、计算精度和计算效率(CPU耗时)等方面,与4级4阶显式单步长RK算法进行了比较。结果表明,OS算法所构造的离散格式与液滴运动模型相容,采用此算法计算得到的液滴运动轨迹与RK算法得到的结果相似,而OS算法的稳定性和计算效率均优于RK算法。因此,OS算法的提出为数值计算波形板的分离效率提供了较为稳定、高效的算法。

An algorithm called operator-splitting （OS ） to solve the model of a single droplet moving in three-dimensional space was developed . At the same time , the algorithm was compared with the frequently used explicit single step Runge-Kutta （RK） algorithm .The droplet motion model in three-dimensional space was briefly introduced . The OS algorithm was showed in detail .Then the trajectories of droplets with different diameters in the wave-type plate separator were calculated numerically .In this example , the OS algorithm and the 4th order 4-step RK algorithm were both tested from the aspects of consistency , stability , numerical precision and calculating efficiency . T he results show that the trajectories acquired by these two algorithms are almost the same . However ,the stability and the calculating efficiency of the OS algorithm are both better than those of the RK algorithm .Therefore ,the OS algorithm is a relatively stable and efficient algorithm to numerically calculate the droplet separation efficiency of wave-type plate separator .