A nonlinear wave dynamical model for two-phase flows and its numerical solutions
A new approach intended for describing two-phase bubbly flows is suggested. The fundamental idea of our approach is to construct a simple model that incorporates the essential physics of dispersed gas phase and where the liquid phase obeys the desired macroscopic equations. The generalized inhomogeneous wave equation of Lighthill-type was obtained for a carrier liquid. A highly effective and accurate finite difference technique for the exact solution of the basic equations has been developed. Our approach is implemented and tested for hydraulic shock in pipes. Comparisons with both experimental data and computational results obtained with a second-order predictor-corrector method support our model as well as the numerical technique. In the high-frequency limit the Klein-Gordon equations with quadratic and cubic nonlinearity are obtained. We show that well-known models are particular cases of our model. (C) 2002 Elsevier Science B.V. All rights reserved.
two-phase flow hydraulic shock bubble dynamics oscillatory solitary wave precursor solitary wave tails