Gas-Liquid Two-Phase Flows in Cylindrical Bath

Mori and Sano stated, based on their experimental results, that the transition from bubbling to jetting occurs at a Mach number of unity [9], In other words, the transition occurs in the transonic region [10]. Recently, Chen and Richter [11] have developed an instability theory to explain the transition from bubbling to jetting by studying a circular compressible jet in a liquid. This theory indicates that small disturbances grow immediately in any position without limitation in the subsonic 

The dynamic behavior of bubbles rising in a bath is quantitatively characterized by the following parameters [12-15]  

Gas holdup and bubble frequency can be measured with a single-needle electroresistivity probe, while a two-needle probe is required for mean bubble rising velocity 

Bubbles are usually not perfectly spherical in shape. Accordingly, the mean chord length is used to represent the bubble size unless the bubble shape is radically different from spheroidal. For definition, the equivalent spherical bubble has the diameter d-Q. The mean bubble chord length Lb is given by [12]  

The units of a, /b, mb, and Lb are %, Hz, m/s, and m, respectively. In actual experiments some additional conditions are usually introduced in order to remove noise and enhance the measurement accuracy as much as possible [14], 

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