分层两相流曲管的耦合振动建模研究

Mathematical modeling of coupled vibration of curved pipes conveying stratified two-phase flow

针对两相流曲管振动的复杂特点,对分层两相流曲管的耦合振动建模进行了专题研究。在前人的基础上,增加了对两相流中气、液两相不同的质量分量和速度的考虑,同时考虑了气相在振动过程中的势能变化,求解出曲管和流体微元的总能量;再通过总能量变分法原理,运用欧拉方程推导出了分层两相流曲管的振动控制微分方程;对微分方程进行量纲归一化处理后,最终得到了简化的分层两相流曲管振动微分方程。采用有限元法对分层两相流曲管振动方程进行求解,并将求解的结果应用到实际算例中,得出了分层两相流曲管的临界流速与曲管直径、管壁厚度、管道内径的关系曲线,还得出了分层两相流曲管的固有频率与流体流速、管壁厚度、管道内径的关系曲线。本文方法可以用于分析曲管中分层两相流、环状流的耦合振动问题。

Known that curved pipes conveying two-phase flow has complex features, this paper specially studies the coupled vibration modeling of curved pipes conveying stratified two-phase flow. On the base of the existing research, this paper considers the respective masses and velocities of the gas and liquid in the curved pipes, and also considers the effect of gas potential energy. Calculating the total energy of the unit including the curved pipe, the gas, and the liquid, the paper applies energy method to analyze the curved pipes' vibration conveying stratified two-phase flow, and use Euler equation to derive the pipe's vibration equation. Through variable replacement the simplified equation is obtained. The paper also shows how to use finite unit method to solve the vibration equation and how to use the method to analyze the concrete examples. Through the examples we sketch the curve of the critical velocity to the major radius, the thickness and the inside radius of the pipe. We also sketch the curve of the natural frequency to the velocity of the flow, the inside radius and the thickness of the pipe. This method can be used for analyzing the curved pipes conveying not only stratified flow but also annular flow.