Dynamic analysis of a cantilevered pipe conveying fluid with density variation

The fluid flow conveyed by a cantilevered pipe might be a multi-phase flow, the density of which can fluctuate with time and space. In this paper, variable density fluid is simulated by a new mathematical model that satisfies the continuity of the fluid flow. The fluid forces acting on the pipe are derived from Newton's second law. Combined with a Bernoulli-Euler beam model, a new dynamic model for a cantilevered pipe conveying a variable density fluid is established. The numerical results of the present model can be obtained by utilizing finite difference methods and agree with the classical theoretical results. The influences of the fluctuating amplitude, wave number and initial phase angle of the fluid density on the stability and dynamics of the cantilevered pipe system are analysed in detail. It can be found that when the fluid density varies with a large amplitude, the cantilevered pipe system is prone to losing its stability, which consequently leads to flutter. A small wave number of the fluid density has a notable influence on the system's stability. Moreover, the stability of this system is seldom affected by the initial phase angle of the fluid density. Based on the current research work, an improved stability criterion is proposed with which the stability of the present system can be more precisely determined.