Negatively buoyant starting jets

Abstract

The initial development of negatively buoyant jets has been investigated experimentally and numerically, focusing on the role played by gravity in the evolution of the leading vortex ring. Under the experimental conditions considered in this work, the densimetric Froude number, Fr= ρjU²j/[(ρ₀ − ρj) gD] , which represents the ratio between the jet momentum and the buoyancy forces, emerges as the most relevant parameter characterizing the dynamics of the flow. Two different flow regimes have been observed depending on the Froude number: for sufficiently small Fr, the vortex ring generated initially is pushed radially away by gravity forces before it has time to detach from the shear layer originating at the orifice. On the other hand, when the Froude number is larger than a critical value, Fr> Frc∼ 1, the vortex ring detaches from the injection orifice and propagates downstream into the stagnant ambient followed by a trailing jet until it eventually reaches a maximum penetration depth. In order to clarify the mechanisms leading to the transition between the two regimes, and to gain physical understanding of the formation dynamics of negatively buoyant starting jets, the total and the vortex circulation, as well as the trajectory of the vortex center, have been measured and compared to the case of neutrally buoyant jets. Finally, based on the experimental measurements and on the results of the numerical computations, a kinematic model that successfully describes the evolution of both total circulation and vortex trajectory is proposed.