Closure relations for two-fluid models for two-phase stratified smooth and stratified wavy flows

The theory-based closure relations for the wall and interfacial shear stresses obtained previously for laminar stratified flow, are extended to be applicable also to turbulent flows in either or both of the phases. The closure relations are formulated in terms of the single-phase-based expressions, which are augmented by two-phase interaction factors, due to the flow of the two phases in the same channel. These closure relations, which are valid for smooth stratified flow in horizontal or inclined pipes, were used as a platform for introducing necessary empirical corrections required in the stratified wavy flow regime. Based on experimental data available from the literature, new empirical correlations for the wave effect on the interface curvature, on the interfacial shear and on the liquid wall shear were obtained. The predictions of the two-fluid model for the pressure gradient and holdup are tested against extensive data bank and some analytical solutions for stratified flows. The favorable comparison suggest that the new closure relations are essentially representing correctly the interaction between the phases over a wide range of flow parameters space in the stratified smooth and stratified wavy regimes. The difficulties encountered due the possibility of obtaining multiple solutions in inclined flows are discussed.