Empirical Equations for Bubble Formation Frequency from Downward-Facing Nozzle with and without Rotating Flow Effects

Abstract

Bubble formation from a downward-facing single-hole nozzle immersed in a still circular water bath has been observed with a high-speed video. An empirical equation is derived for the frequency of bubble formation, f B0 , as a function of gas flow rate Q g , the inner and outer diameters of the nozzle, d ni and d no , the acceleration due to gravity, g, and the physical properties of fluids. A cross-flow is imposed on the nozzle by rotating the bath around its vertical axis. The frequency of bubble formation in the presence of the rotating flow, f B , is predicted using f B0 and the rotating flow velocity, v .

Experimental characterization of bubbling in submerged lance injection

“…Then, a kind of transition occurs, where F increases with q, and reaches a local maximum at about 3.5 l/s. The order of magnitude of F is perfectly consistent with data reported in literature (Neven, 2005;Goda et al, 2005). In contrast, the experimentally determined bubble diameters are a new piece of information.…”

“…At low submergence depths indeed, it is observed that the bath enters into a swirling motion, which may induce a premature detachment of the bubbles, and thus a higher frequency. Goda et al (2005) claim that the natural bubbling frequency can be multiplied by up to 3 with bath rotational velocities of only 0.2 m/s (for lance exit velocities between 1.5 and 20 m/s). It appears clearly in Fig.…”

“…Owing to the development of metal converters in the last decade, lance injection has recently drawn more interest, but still, very little is known about the bubbling phenomena in this injection configuration. On an experimental point of view, Goda et al (2005) provide one of the most extensive database for bubbling frequencies with and without swirling effect of the bath. From their measurements based on the observation of high-speed movies, they extract purely empirical correlations for the frequency in a water-air system, for different inner and outer lance diameters, gas flow rates and bath rotational velocities.…”

Experimental study and numerical modeling of mixing by air injection in yield stress fluids using the OpenFOAM software

“…Clearly, the downward bubble formation has received much less attention than the upward injection. More recently this configuration was considered by Tsuge et al, 5 Goda et al 6 and Wollants et al, 7 but always in flow conditions quite different from the ones considered in the present study. Tsuge et al 5 considered downward bubble injection with flow rate lower than that in the current study by 2 orders of magnitude (0.034 m 3 /h) and a ratio between the injection nozzle diameter and height clearance larger than 1, which leads to the absence of formation of air cavity and a flow with much lower inertial effects.…”

“…Tsuge et al 5 considered downward bubble injection with flow rate lower than that in the current study by 2 orders of magnitude (0.034 m 3 /h) and a ratio between the injection nozzle diameter and height clearance larger than 1, which leads to the absence of formation of air cavity and a flow with much lower inertial effects. Similarly, Goda et al 6 considered a downward injection but in Newtonian fluids with much lower injection flow rates (Q max ≈ 0.18 m 3 /h) and a different reactor geometry with a cylindrical shape and a much larger height clearance. They as well did not observe the formation of the air cavity and focused their work on studying the effects of rotating the reactor on bubble frequencies.…”