Mean bubble rise velocity

Figure 11. Relationship between local mean bubble size and local mean bubble rise velocity in beds of different diameters (u0 = 9 cm/sec). (From Werther, 1974.)...

If the operations run in the semibatch mode and the linear superficial slurry velocity wsL is zero, the above equation would become the mean bubble rise velocity in the swarm (Shah et al, 1982). 

Here, it has to be noted that for calculating the Peclet number in fixed beds, the actual velocity has to be used, i.e. the interstitial velocity, which influences the degree of mixing. In slurry bubble column reactors, the real velocity of the fluid is the bubble velocity, which is much higher than the gas superficial velocity. The mean bubble rise velocity for a batch liquid is (eq (3.201))... 

In addition, the discussion of kL for single bubbles has indicated the importance of the bubble diameter which essentially influences the constitution of the gas-liquid interface and the mean bubble rise velocity. Initial bubble size dg generated from single-orifice spargers can be calculated from the empirical equation... 

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... 

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. 2.6 Axieil distributions of mean bubble rising velocity 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... 

Fig. 3.8 Mean bubble rising velocity near the side waU...

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. 3.12 Maximum value of mean bubble rising velocity...

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]. 

Figure 3.49 shows the horizontal distributions of mean bubble rising velocity mb in the x and y directions for z = 15.0 x 10 m. Just like the axial distributions, the horizontal distributions of b is not influenced by nozzle configuration and is satisfactorily predicted by the empirical equation proposed by Castello-Branco et al. [38] mainly in the central part of each bubbling jet. 

Figure 4.24 shows the experimental data on mean bubble rising velocity b. The data for the poorly wetted plate decrease monotonically in the y direction at every... 

As a consequence of bubble attachment to the poorly wetted plate, the measured bubble frequency /b, gas holdup a, mean bubble rising velocity b, and mean... 

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