Numerical simulation of transient roll-waves in two-phase pipe flow

This paper presents a transient roll-wave simulator based on a one-dimensional incompressible two-fluid model. Using an efficient numerical method and a grid cell length of one pipe diameter, the simulator is able to accurately predict experimental data in the roll-wave regime. Essential to obtaining the stable roll-wave solutions is the use of a modified version of the Biberg friction model. Based on an algebraic eddy viscosity model, the Biberg model yields mechanistic expressions for the wall and interfacial shear stresses in stratified two-phase flow. Input to the model is closure relations for the turbulence levels at either side of the interface. In order to model the increased dissipation of energy in breaking wave fronts, we propose to modify the original closures by adding a term proportional to the negative gradient of the liquid height. As the waves grow and come close to breaking, this term redistributes the shear stresses such that the waves are stabilized. The numerical method used in the simulator is an extension of a previously presented pseudospectral Fourier method. In particular, spectral vanishing viscosity terms are introduced to stabilize short wavelengths inconsistent with the long wavelength approximation of the two-fluid model. The result is a simulator that provides reliable and convergent numerical solutions for all stratified flow conditions. In the last part of the paper, the simulator is tested against roll-wave experiments with horizontal and upward inclined flows of water and a dense gas in a 10 cm pipe. Wave heights and speeds as well as mean pressure drops and holdups are predicted within 20% accuracy when compared with 474 experiments. Furthermore, the transient simulations enable us to study the dynamics and interactions between waves. In agreement with experimental observations, two different wave growth mechanisms are identified, and their influence on the evolution of the roll-wave flow regime is analyzed.