Rise Height for Negatively Buoyant Fountains and Depth of Penetration for Negatively Buoyant Jets Impinging an Interface

Abstract

A vertical jet or fountain, whose velocity is opposite to the direction of its buoyant force, reverses direction after reaching a maximum penetration depth. This penetration depth is measured from the jet exit or, if present, the location of the undisturbed interface. This paper shows that the penetration depth is only a function of a Richardson number divided by a jet spreading factor. If no interface is present, the spreading factor is one; otherwise the spreading factor is only a function of distance between the jet exit and the interface. As long as the jet is fully turbulent, the penetration depth is independent of Reynolds and Weber numbers. These trends are applicable to a broad range of fluid systems including air jets impacting liquids as well as miscible and immiscible liquid-liquid systems with only slight density differences. [S0098-2202(00)00304-7]