Dynamic Behavior of a Rotationally Restrained Pipe Conveying Gas-Liquid Two-Phase Flow

Abstract

This study explores the dynamic behavior of a vertical pipe conveying gas-liquid two-phase flow with rotationally restrained boundaries, employing the generalized integral transform technique (GITT). The rotationally restrained boundary conditions are more realistic for practical engineering applications in comparison to the classical simply-supported and clamped boundary conditions, which can be viewed as limiting scenarios of the rotationally restrained boundary conditions when rotational stiffness approaches zero and infinity, respectively. Utilizing the small-deflection Euler-Bernoulli beam theory, the governing equation of motion for the deflection of the pipe is transformed into an infinite set of coupled ordinary differential equations, which is then numerically solved following truncation at a finite order NW. The proposed integral transform solution was initially validated against extant literature results. Numerical findings demonstrate that as the gas volume fraction increases, there is a reduction in both the first-order critical flow velocity and the vibration frequency of the pipe conveying two-phase flow. Conversely, as the rotational stiffness factor enhances, both the first-order critical velocity and vibration frequency increase, resulting in improved stability of the pipe. The impact of the bottom-end rotational stiffness factor r2 on the dynamic stability of the pipe is more pronounced compared to the top-end rotational factor r1. The variation in two-phase flow parameters is closely associated with the damping and stiffness matrices. Modifying the gas volume fraction in the two-phase flow alters the distribution of centrifugal and Coriolis forces within the pipeline system, thereby affecting the pipeline’s natural frequency. The results illustrate that an increase in the gas volume fraction leads to a decrease in both the pipeline’s critical velocity and vibration frequency, culminating in reduced stability. The findings suggest that both the gas volume fraction and boundary rotational stiffness exert a significant influence on the dynamic behavior and stability of the pipe conveying gas-liquid two-phase flow.

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