Effect of pressure on two-phase stratified flow modeling

This paper reviews the use of the single-pressure model in two-phase flow modeling in previous literature, and develops and demonstrates the equations for the two-pressure model. Many of the models investigated previously suffer from an inability to achieve convergence and consistent results because they have complex characteristic values. Two different model specifications - single-pressure (ill-posed condition) and two-pressure (well-posed condition) are considered in this paper. Pressure effect was taken into account for both models. The models discussed in this paper were developed for the case of a transient two-phase air-water stratified flow in a horizontal duct. Terms that induce physical viscosity like surface tension, viscous stress, etc., were not included in the models. Both models were applied to the Kelvin-Helmholtz (K-H) instability case and the equations were solved numerically. The results showed that the two-phase two-pressure flow model pioneered by Ransom and Hicks overcomes the ill-posed condition. Convergence and consistence of results, which cannot be obtained by the ill-posed models, are established using the well-posed two-pressure model.