控制棒下落与流体流动的耦合状态方程及其保辛算法

The Coupling State Equations and the Symplectic Algorithm for Control Rod Drop and Fluid Flow

针对核反应堆内控制棒下落问题,提出了描述控制棒下落与流体流动的耦合非线性状态方程.该状态方程对于落棒过程内不同的流体状态,具有统一的表达形式,可以很方便地处理不同工况下的落棒问题.为高效分析落棒过程,准确捕捉落棒过程内流动状态的突变,并保证时程积分的数值稳定,提出了一种基于时间步长自适应的保辛算法.数值算例表明,提出的数值模型可以采用较大的时间步长精确计算控制棒在下落过程中的位移、速度、加速度、落棒时间等关键数据,计算结果与商业软件所得结果高度吻合.

The nonlinear state equations describing the coupling between control rod drop and fluid flow were proposed to solve the problem of control rod drop in nuclear reactors.The state equations have a uniform format for different fluid states in the process of control rod drop,which can conveniently deal with the problem for different working conditions.To efficiently analyze the falling process,accurately capture the sudden change of flow state and ensure the numerical stability of time integral,an adaptive time step-based symplecticity-preserving algorithm was proposed.Numerical examples show that,the proposed numerical model can accurately calculate the key data such as the displacement,the velocity,the acceleration and the falling time of the control rod in the falling process with a large time step,and the calculated results are in good agreement with those obtained the by the commercial software.