Vibration stability of a lifting pipe transporting solid-liquid two phase flow

A new mathematical model is developed to investigate the vibration stability of a lifting pipe induced by solid- liquid two phase flow. Three different slip models and the momentum conservation theorem are introduced to describe the slip characteristics of solid particles in two phase flow, which are coupled with the pipe vibration equations to establish a new governing equation and solved using the harmonic differential quadrature method. The mathematical model is validated by published data for the single-liquid flow case. Numerical results show that the slip model has noticeable effects on two phase flow-induced pipe vibration performance. The transport concentration of solid particles has a significant effect on the stability characteristic; however, the effect of particle size is very limited. The pipe flow mass ratio and the gravity coefficient are also key parameters affecting two phase flow-induced pipe vibration performance.