Determination of discharge coefficient in non-Boussinesq cases and application in emptying–filling boxes

Abstract

The effect of high buoyancy forces due to the density contrast between the fluids at either side of the vent on the discharge coefficient Cd was considered in emptying–filling boxes. Salt experiments were conducted at small scale in a large freshwater tank with saline to generate buoyancy force. In non-Boussinesq cases, a larger discharge parameter Γd at the vent may make plume-like flow contract further with a smaller value of the discharge coefficient. Simple draining flows with variant Cd at the upper vent is modeled when considering the emptying of an enclosure initially filled with a large amount of light fluid. The time in the non-dimensional form for draining light fluid fully out of the space for the analysis with a variable value is twice the time predicted with a constant value of Cd = 0.6. A theoretical model of displacement flow with a virtual source correction at the initial position of an internal source was developed to reveal a time-dependent movement of the layer interface, and comparisons were made with the experimental results. The oscillatory amplitude of the interface overshooting during the transient period was found to depend on a geometrical parameter Λ and a dimensionless parameter Θ that characterizes the source strength relative to the space height.