Abstract

An exact analytical solution has been obtained for fully developed laminar stratified flow in inclined pipes with a plane or curved interface. This solution is of practical significance mainly for studying liquid-liquid flows. However, it is also needed as a benchmark for testing the validity of numerical methods, and for testing closure relations for two-fluid models. Two-fluid models may yield poor predictions in inclined co-current and counter-current flows. The commonly used closure relations for the wall and interfacial shear stresses do not correctly represent the fine balance between the gravity body forces and viscous shear in inc]ined flows. The exact solution obtained for laminar flows is used to establish and validate new closure relations, which account for the interaction between the phases and are applicable also for turbulent stratifiecl flows.