A Numerical Method for the Analysis of a New Model for Two-Phase Bubbly Flow in Elastic Pipes

A new approach and numerical method for study gas-liquid two-phase flows in elastic pipes is suggested. “A nonlinear wave dynamical model for liquid containing gas bubbles” is applied to derive governing equations for two-phase flow-filled pipelines. On assuming the hydraulic approximation the continuity and momentum equations of two-phase flow in a pipe are obtained for the first time. From these equations the inhomogeneous wave equation of Lighthill-type for two-phase flow in pipelines is derived. The shear stress at the tube surface, deformation of the tube cross-section, and liquid’s phase compressibility are taken into account. A high effectively and accurate finite difference technique for the exact solution of the basic equations in the case of Neumann boundary conditions is developed. Based on the proposed algorithm various numerical experiments have been carried out to investigate the major fluid dynamical features of hydraulic shocks and shock waves in the horizontal pipes. Comparisons with both the experimental data and computational results obtained with a second-order accurate predictor-corrector method support our numerical technique as well as the model.