Method of finite difference solutions to the transient bubbly air–water flows

Abstract

A one-dimensional, time-dependent, isothermal, incompressible, Newtonian fluid, two-phase volume averaging model was developed to study momentum interaction effects in vertical ducts with bubble flow regime. For the evaluation of averaged description, potential inviscid flow around bubbles was considered in order to get closure relationships. The linear dynamic analysis is based on the eigenvalue technique, determining the domain of the hyperbolic behavior and the void fraction wave velocity, which are compared with previous models and experimental data. The solution to the partial differential equations is based on the finite difference technique implicit scheme. These schemes serve to demonstrate the numerical solution procedure. The numerical results are compared with analytical solution and experimental data for void fraction wave propagation. The importance of the surface tension effect in the behavior of the phases in transient conditions is shown. © 1998 John Wiley & Sons, Ltd.