Incipient air entrainment in a translating axisymmetric plunging laminar jet

Abstract

Air entrainment due to a translating axisymmetric laminar water jet plunging into an otherwise quiescent pool of water was studied experimentally. The jet impact diameter, Dj, and velocity, Vj, ranged from 0.33 to 1.21 cm and 104 to 365 cm/s, respectively. For all of these jet flow conditions, the water surface around the jet impact site of the stationary jet is smooth and no air is entrained. When the jet is moving horizontally with velocity Vt, a depression of the free surface forms directly downstream of the jet. In any set of experiments with constant Vj and Dj, as Vt is increased, the depth and streamwise length of this depression increases and a cusp forms at the bottom of its upstream edge. Air entrainment first occurs in the form of discrete small bubbles with diameters of about 0.05 cm that are injected from the cusp when the Froude number (Fr=Vt/gDj, where g is the acceleration of gravity) exceeds a critical value of about 1.4 for Vj/Vt>5. At higher values of Vt, a separate mode of entrainment occurs where large pockets of air are injected from the cusp into the flow in the form of intermittent bursts. At still higher values of Vt, the high-entrainment-rate condition occurs continuously. High-speed flow visualization movies of the entrainment process show that in all entrainment regimes, the bubbles enter the water when vortices from the jet shear layer pass over the leading-edge cusp of the depression and that these bubbles are initially trapped within the vortices. The boundaries between the three entrainment regimes are determined and presented on a plot of Froude number versus velocity ratio (Vj/Vt).