This paper presents a comparison of the analytical depth-integrated two-phase stratified flow model of Biberg (1) with CFD simulations using the k-? turbulence model. For simplicity, the Biberg model is based on channel flow geometry. The flow in both fluids is governed by an algebraic eddy viscosity distribution. Integration yields the corresponding analytical velocity distribution, which in turn leads to a consistent set of wall and interfacial friction formulas for the channel flow. Conveniently, the channel wall friction formula is given in the form of the classic Prandtl/Karman pipe flow friction laws, in which the two-phase effect is contained in a flow-dependent effective diameter. Thus, pipe flow friction formulas, ideally suited for 1-D computer models, are obtained from the channel flow expressions by use of a hydraulic similarity transformation of the effective flow diameters.
The Biberg model is compared with CFD simulations of single-phase flow influenced by a moving surface representing the effect of the other phase. First, this paper examines the Biberg model for stratified channel flow. Shown here is that the effective channel flow diameter and thus the wall and interfacial friction predicted by the model compare well with the CFD simulations and available experiments. In addition, cross-sectional details such as eddy viscosity and velocity distributions agree well. Second, this paper examines the Biberg model for stratified pipe flow. We find that the effective pipe flow diameter, as given by the hydraulic similarity transformation, compares well with the CFD simulations for favourable pressure gradients. Consequently, the pipe wall and interfacial friction also agree well. However, for adverse pressure gradients the Biberg model and the k-ω model show different trends. Incorrectly, the k-ω model predicts increasing wall friction for increasing adverse pressure gradients. Thus, the k-ω model over-predicts the wall friction compared with the Biberg model. The pipe flow friction formula as given by the Biberg model shows the correct trend and thus the channel to pipe flow transformation is confirmed as an effective modelling tool. Finally, this paper makes comparisons with standard friction models from the two-phase flow literature. The Biberg model is based on a velocity distribution relating the wall and interfacial friction, which is considered to be an improvement with respect to the standard friction models involving inconsistent (decoupled) expressions for wall and interfacial friction.
In conclusion, the Biberg model provides the potential for 1-D simulation of two-phase stratified flow in large pipeline systems with the consistency and accuracy of a cross-sectional model.
