Mean bubble chord length

In addition to optical methods, bubble size can be determined using optical probes and electrical conductivity (resistivity) probes (Saxena et al., 1988). For example, Magaud et al. (2001) used dual optical probes to determine the local instantaneous presence of the liquid or gas in a bubble column. With this information, local bubble chord length and bubble rise velocity can be determined. One advantage of optical probes is that its operation is independent of the electrical properties of the medium surrounding the probe (Saxena et al., 1988). Electrical conductivity or resistivity probes can be configured as needle probes, which have been used to determine mean bubble chord length, bubble size, and bubble rise 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] ... 

Gas holdup a, bubble frequency /b, mean bubble rising velocity b, and mean bubble chord length Lb were measured using a two-needle electroresistivity probe (not shown in Fig. 2.1). The vertical distance between the tips of the two electrode needles was set at 2 mm. The output signals of the electroresistivity probe system... 

Figures 2.4-2.7 show measured values of gas holdup, ad, bubble frequency, /s.d, mean bubble rising velocity, B,d, and mean bubble chord length, Lb,ci, where the subscript cl designates the value on the centerline of the bath. In Fig. 2.4, the...

Fig. 2.7 Axial distributions of mean bubble chord length on the centerline...

Figures 2.12 and 2.13 show the radial distributions of mean bubble rising velocity Mb and mean bubble chord length Lb, respectively. The measured values of mb and Lb at z = 1.5 cm were not plotted. The relatively large mb values near the centerline (r s 0) at z = 4 and 7 cm may be caused by the vertical elongation of bell-shaped bubbles [25]. The empirical correlation of mb proposed by Iguchi et al. [6,7] can predict the measured values only in the outer region of the bubbling jet. At every axial position, the measured Lb value is relatively small near the centerline, being caused by thinning of the bell-shaped bubbles. Any empirical correlations for the radial distributions of mb and Lb were not proposed by Xie et al.

The mean bubble rising velocity b and mean bubble chord length Lb measured at z = 1.5, 4.0, and 7.0 cm, exhibit a complex behavior in the radial direction. These radial distributions are also closely related to the shape of bubbles. An empirical correlation of b is proposed that could approximate the measurements only at the outer region of a bubbling jet. 

The bubble characteristics represented by the bubble frequency, gas holdup, mean bubble rising velocity, and mean bubble chord length were measured at z = 0.050, 0.100, 0.150, and 0.190m with a two-needle electroresistivity probe [14-20]. The inner and outer diameters of the nozzle were 2.0 x 10 and 4.0 x 10 m, respectively, and the distance 7 was 2 x 10 m. The gas flow rate gg was 41.4 X 10 , lOOx 10 , or 293x 10 m /s. Although the measurements were carried out in the r, 9, and z directions, the results obtained on the r — z plane (9 = 0) will be primarily presented to discuss the Coanda effect on an air-water bubbling jet rising near the side wall of a cylindrical vessel. 

Both the measured values of mean bubble rising velocity mb and mean bubble chord length Lb are approximately uniform in the horizontal direction, as illustrated... 

The maximum values of mean bubble rising velocity, mb,max, and mean bubble chord length, Lb,max, are shown in Figs. 3.12 and 3.13, respectively. In each figure the measurement for gg = 41.4 x 10 and 293 x 10" mVs can be approximated by the data obtained for the vertical bubbling jet that is free from the Coanda effect. 

Fig. 3.9 Mean bubble chord length near the side wall...

Fig. 3.13 Maximum value of mean bubble chord length...

In order to compare the experimental results for dual nozzle gas injection system, the two nozzles are removed, and subsequently gas is injected through a single-hole nozzle of inner diameter of 2.0 x 10 m. The center of the nozzle exit is placed at the origin of the coordinate system. The air flow rate is set to 80 x 10 m /s, being equal to the sum of ggi and 0g2. The center of the nozzle is placed at the vertical axis of the vessel. Bubble characteristics represented by gas holdup a, bubble frequency /b, mean bubble rising velocity b, and mean bubble chord length Lb are measured by making use of a two-needle electroresistivity probe [23,37]. 

The horizontal distributions of mean bubble chord length Lb are shown in Fig. 4.26. In the vicinity of the pl ate, j < 5 x 10 m, near the nozzle tip, z < 100 x 10 m, the measured value of Lb is larger for the plate with good wettability than that of the plate with poor wettability. There is a distinct peak in the measured Lb distributions for the highly wetted plate at z = 150 x 10 and 200 x 10 m. 

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