Dynamic response of pipes conveying two-phase flow based on Timoshenko beam model

Abstract

The dynamic behavior of pipes subjected to internal gas–liquid two-phase flow has been studied using the Timoshenko beam model and the slip-ratio factor model. In this paper, the governing equations were carried out using the generalized integral transform technique (GITT) by transforming the governing partial differential equations into a set of second-order ordinary differential equations. The comparison between Timoshenko beam model and Euler–Bernoulli beam model has been conducted through parametric study on dimensionless frequencies and amplitudes over various aspect ratios, internal fluid flow rates, and volumetric gas fractions. The results show that the frequencies of Timoshenko beam model are less and the amplitude is larger than that of Euler–Bernoulli beam model at low aspect ratio. In addition, the amplitude for Timoshenko beam model increases more dramatically than that of Euler–Bernoulli beam model when the pipe is about to lose stability. The high flow rate leads to the divergence of the dynamic system, as well as the two-phase flow accelerates the instability and has significant influence on the dynamic response when the pipe is long and the internal liquid flows fast.