Nonlinear dynamics of horizontal pipes conveying two phase flow

Abstract

Two-phase flows are common in large-scale power systems and petroleum industry. During upstream oil and gas productions, crude oil, gas and sand eroded from formation zones are often conveyed as a mixture through horizontal pipes up to the well heads and between well heads and flow stations. In this work, governing equations and boundary conditions (BCs) for the motion of vibrating pipe conveying two phase flow were developed. Hamilton's principle was employed, where the kinetic energies of each phase and of the pipe were combined with the strain energy of the vibrating Euler-Bernoulli pipe. Solutions were presented for vibrating horizontal pipe using Eigenfunction expansion method and Runge Kutta technique. The linear frequencies were obtained for three different boundary conditions (BCs) where parametric analysis is performed to elucidate the effects of initial curvature amplitude, volume fraction and mass ratio. Furthermore, the developed model is used to investigate the effects of these parameters on the dynamic nonlinear behaviour of a pipe conveying two phase flow for vanishing and non-vanishing longitudinal vibrations. The linear analysis shows that as the volume fraction of the sand increases in the two phase flow, the natural frequencies decrease. The initial curvature has similar effect on the vanishing and non-vanishing longitudinal vibrations for all BCs considered. However, increase in volume fraction from low to mid value increases the nonlinear displacement of the pipe after the bifurcation point. Beyond the mid value of volume fraction, the nonlinear displacement reduces. This is absent in pipes conveying single phase flow.