空化水射流空泡溃灭过程的数值分析

空化空泡发育与溃灭的计算是研究空化水射流的一个重点和难点.对比分析了空泡运动方程即Rayleigh-Plesset方程的不同数值解法,并针对固定时间步长的缺点,提出了变步长法解Rayleigh-Plesset方程的思路.通过优化系数λ=Ri/Ri-1,得出如下分析结果:在空泡内外压力变化的不同情况下,变步长法均优于固定步长法且没有奇异点.变步长法在节约计算量,保证结果精度等方面都有较好表现,该方法为研究空化水射流提供新的思路和算法.

Numerical Analysis on Collapse of Cavitation Bubble in a Water Jet Flow

Calculation on cavitation bubble growth and collapse is key to study the cavitating water jet.After the analysis of different numerical methods to Rayleigh-Plesset equation,a numerical method with variable-steps is developed that can overcome the weak point of constant time step method to solve the Rayleigh-Plesset equation.And it also learned that a constant time step is not appropriate for solving the Rayleigh-Plesset equation when dealing with large pressure variations or under the smaller pressure variation.The variable time step method can get a better result.What more,it is only after the variable time step method can be predicted without singularity.So the variable time step method is batter than the constant time step method in saving computational and keeping accuracy.This paper provides a new idea to solve Rayleigh-Plesset equation.