Critical fluid-flow phenomenon in a gas-stirred ladle

Abstract

Measurement of the velocities of bubbles and liquid with a two-element electroresistivity probe and laser-Doppler velocimeter, respectively, during bottom injection of air into a water bath, has confirmed the existence of a critical gas-injection rate. Above the critical flow rate, the change of axial bubble velocity in the air jet, and of liquid velocity with increasing volume flow rate, diminishes markedly. The existence of the critical flow rate is explicable from high-speed motion pictures of the vertical gas jets, which reveal four zones of gas dispersion axially distributed above the orifice: primary bubble at the orifice, free bubble, plume consisting of disintegrated bubbles, and spout at the bath surface. With increasing gas-injection rate, the free-bubble zone expands such that the point of bubble disintegration rises closer to the bath surface. Above the critical flow rate, the free bubbles rise with minimal breakup and erupt from the bath surface with maximum energy discharge. The combined Kelvin-Helmholtz, Rayleigh-Taylor instability theory has been applied to analyze the bubble breakup in the bath and the critical gas-injection rate in a gas-stirred ladle. The criterion for the critical diameter of bubble breakup has been found to depend primarily on the surface tension and density of the liquid. In the analysis, the propagation time of a disturbance on a bubble surface at the “most unstable” wave number has been compared with the bubble rising time in the bath in order to determine the critical gas-flow rate. The predicted critical values are in close agreement with the measured results.