Axial mean velocity

First, however, consider that in turbulent Bunsen flames the axial component of the mean velocity along the centerline remains almost constant with height above the burner but away from the centerline, the axial mean velocity increases with height. The radial outflow component increases with distance from the centerline and reaches a peak outside the flame. Both axial and radial components of tuibulent velocity fluctuations show a complex variation with position and include peaks and troughs in the flame zone. Thus, there are indications of both generation and removal of turbulence within the flame. With increasing height above the burner. 

A co-swirl distribution in the burner increases both the droplet size and the axial mean velocity at all positions in the spray, including the longitudinal axis through the spray centerline and all radial positions downstream of the burner exit. This effect becomes more pronounced as the axial distance from the burner exit increases. The combustion airflow distribution in the burner has also been shown to have a significant effect on the size and velocity distribution of droplets in the spray flames. Since it is possible to change the droplet size, velocity, and number-density distribution in the spray flame using these techniques, it becomes possible to control the flame characteristics for any set of operating conditions of the combustor. 

Figure 2.14 shows the axial mean velocity on the centerline of the bath, Ua, and the root-mean-square values of the axial and radial turbulence components, M ms,ci and J.J, against the axial distance, z. The measured d value remains almost unchanged in the axial direction and approaches the following empirical correlations originally proposed for a water-air system [9] ... 

Fig. 2.14 Axial mean velocity and the rms values of turbulence components on the centerline as functions of axial distance...

The radial distribution of the axial mean velocity u measured at z = 4 cm is shown in Fig. 2.16. In the bubbling jet region r/b < 1.5) where almost all rising bubbles are present, the radial u distribution is approximated satisfactorily by a Gaussian distribution marked by the broken line, although the radial a distribution does not follow a Gaussian distribution, as shown in Fig. 2.7. Measured u values for z = 10 cm are also approximated by a Gaussian distribution. 

The experimental results suggest that empirical correlations of the bubble characteristics and the axial mean velocity and turbulence components of liquid flow, derived from cold model experiments, are applicable to actual reflning processes stirred by bottom gas injection when the radial distributions of gas holdup and bubble frequency follow Gaussian distributions. These distributions appear to be a result of the disintegration of rising bubbles due to highly turbulent liquid motion in the bath. 

The origin of the cylindrical coordinate system is placed at the center of the bath, as shown in Fig. 3.3. The horizontal distance from the side wall is designated by t] =R — r). The distance from the side wall to the nozzle exit, , is varied from 1.75 x 10 to 3.5 x 10 m. The horizontal position at which a peak appears in the gas holdup distribution is designated by a,max and the half-value width by > a,max/2,- These quantities are introduced to represent the horizontal extent of the bubble dispersion region. In the same manner, the peak position and half-value width of the axial mean velocity u are defined. These two representative scales will be discussed in a later section. The attachment length La is defined as the vertical distance from the nozzle exit to the position at which bubbles attach to the side wall. 

Maximum Axial Mean Velocity and Characteristic Length... 

Concerning the vertical bubbling jets free from the side wall, the half-value radius, bu, of the radial distribution of the axial mean velocity u is approximated by [21] ... 

Figure 3.30 shows nondimensionaUzed distributions of the axial mean velocity component. The data at three vertical positions above the attachment position, designated by the three open symbols, agree with one another. Consequently, the horizontal distributions of u are similar just like the horizontal distributions of... 

An air-water bubbling jet which is not subjected to the Coanda effect is known to rise straight upward while entraining the surrounding water into it [21]. As a result, the horizontal region in which water moves vertically upward spreads as z increases. The extent of this horizontal region can be represented, for example, by the half-value radius, of the horizontal distribution of the axial mean velocity of water flow, u (see Fig. 3.42). Based on existing experimental study, [21] can be approximated by... 

Figure 3.51 shows the axial mean velocity on the centerline of the bath, Ue, against the axial distance z. As in the case of the bubble characteristics, the axial position z = /fc is denoted by a broken line. The measured values of i/ci, for the two gas... 

Figure 4.58 shows the variation with gg, of the axial mean velocity d and the root-mean-square value of axial turbulence component M rms,ci. Both variables increase with gg. The turbulence intensity increases from 30% in the low gas flow... 

Fig. 4.58 Axial mean velocity and the root-mean-square value of axial turbulence component of water flow approaching a cylinder...

Fig. 7.6 Axial mean velocity u in the bath in disk model...

Figure 8.6 shows the vertical distribution of the axial mean velocity u normalized by the centerUne value for the single-phase water jet (gg = OcmVs), m,sw. The vertical distance y is nondimensionalized by the half-value radius for the single-phase... 

The root-mean-square values of the axial and radial turbulence components, n m and i/nns, are normalized by the axial mean velocity on the centerline of the singlephase water jet, Mm,sw, and plotted in Figs. 8.7 and 8.8, respectively. The vertical distance y is nondimensionalized in the same manner as in Fig. 8.6. The measured values of M mis/Mm,sw and v nns/ttm.sw for the single-phase water jet are close to the data of Wygnanski and Fiedler [19]. Below the x axis (y < 0) both M rms/ m,sw and v rms/Mm.sw are nearly independent of the gas flow rate while above the x axis (y > 0) they increase slightly with an increase in Qg. This is because turbulence is generated in the wake of the bubbles [20], and the number of bubbles increases as 2g increases. 

Accordingly, the vertical mean velocity component of water flow, v, is much smaller than the axial mean velocity component it. 

The mean bubble velocity b is equal to the axial mean velocity of water u in the control volume. 

The maximum value of the axial mean velocity component, Mm,sw, for the singlephase water jet, which occurs at the axis of the jet, is nondimensionalized by the water velocity at the pipe outlet, o. The results are plotted against x/rf i in Fig. 8.12. 

Fig. 8.12 Correlation of the maximum value of axial mean velocity in single-phase water jet...

The half-value radius of the vertical distribution of the axial mean velocity component is denoted by b. The measmed values shown in Fig. 8.15 can all be approximated by the solid line of the form ... 

Fig. 9.4 Predicted and measured axial mean velocity for water/silicon system ...

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