Velocity profiles description and shape factors inclusion in a hyperbolic, one-dimensional, transient two-fluid model for stratified and slug flow simulations in pipes

In a previous work it has been shown that a one-dimensional, hyperbolic, transient five equations two-fluid model is able to numerically describe stratified, wavy, and slug flow in horizontal and near-horizontal pipes. Slug statistical characteristics can be numerically predicted with results in good agreement with experimental data and well-known empirical relations. In this model some approximated and simplified assumptions are adopted to describe shear stresses at wall and at phase interface. In this paper, we focus on the possibility to account for the cross sectional flow by inserting shape factors into the momentum balance equations of the aforementioned model. Velocity profiles are obtained by a pre-integrated model and they are computed at each time step and at each computational cell. Once that the velocity profiles are known, the obtained shape factors are inserted in the numerical resolution. In this way it is possible to recover part of the information lost due to the one-dimensional flow description. Velocity profiles computed in stratified conditions are compared against experimental profiles measured by PIV technique; a method to compute the velocity profile during slug initiation and growth has been developed and the computed velocity distribution in the liquid phase was compared against the one-seventh power law.