One-dimensional prediction of the interface motion separating two immiscible fluids enclosed in a long duct

The numerical prediction for the time dependent interface location between two immiscible fluids is presented. The fluids have a small density difference and are contained in a closed duct of square cross section. The process starts when the duct, which is at first either horizontal or vertical, and at rest, is suddenly tilted. The problem is simulated by a one-dimensional, unsteady and laminar two phase model. The results are plausible and comparison with a simplified analytical solution is presented. Agreement is very good.