Jet penetration

Vertical jet penetration in fluidized beds increases significantly with system pressure as shown in Fig. 18. Vertical jets fluctuate in the vertical direction between a minimum and a maximum value. Most jet penetration correlations are given in terms of the maximum jet penetration length which is designated Lmax (Hirsan et al. 1980). Over a pressure range of 1 to 50 bar with jet nozzles up to 3.8 cm in diameter, Hirsan et al. (1980) developed the following empirical correlation for the maximum jet penetration. 

This correlation predicts that the maximum vertical jet penetration into a fluidized bed varies with gas density to the 0.67 power, and decreases with increasing fluidizing gas velocity and increasing particle diameter. 

Yang (1981) incorporated the high-pressure data of Hirsan et al. (1980) to produce the following correlation forLmax 

Yates et al. (1986) varied system pressure up to 20 bar with jet nozzles of 2 and 4 mm diameter, and also found that the maximum jet penetration varied significantly with pressure. They then developed the following correlation for the maximum jet penetration  

Findlay and Knowlton (1985) investigated the effect of gas viscosity on jet penetration by varying system temperature while maintaining gas density constant. This was accomplished by adjusting system pressure at 

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Jet Penetration. At the high gas velocities used in commercial practice, there are jets of gas issuing from distributor holes. It is essential that jets not impinge on any internals, otherwise the internals may be quickly eroded. Figure 14 is a graphical correlation used to determine the jet penetration length as a function of gas velocity and gas density. Jets from horizontal and downflow holes are considerably shorter than those that are pointed upward. 

Fig. 14. (a) Correlation of jet penetration, P, from distributors iato fluidized beds where (—) represents upwardly directed jets and (-) downwardly and... 

This combustion product is diluted with air entering through holes on the liner to make the temperature appropriate for blade material and to have enough volume-flow in the dilution zone. Air is jet-penetrated mainly because of converging clearances and creates high local pressure. 

Figure 2.40 shows the unsteady flow upstream of the ONE in one of the parallel micro-channels of d = 130 pm at = 228kW/m, m = 0.044 g/s (Hetsroni et al. 2001b). In this part of the micro-channel single-phase water flow was mainly observed. Clusters of water appeared as a jet, penetrating the bulk of the water (Fig. 2.40a). The vapor jet moved in the upstream direction, and the space that it occupied increased (Fig. 2.40b). In Fig. 2.40a,b the flow moved from bottom to top. These pictures were obtained at the same part of the micro-channel but not simultaneously. The time interval between events shown in Fig. 2.40a and Fig. 2.40b is 0.055 s. As a result, the vapor accumulated in the inlet plenum and led to increased inlet temperature and to increased temperature and pressure fluctuations.

Figure 18. The effect of pressure on jet penetration. (Knowlton and Hirsan.)...

Overall bed-to-surface heat transfer coefficient = Gas convective heat transfer coefficient = Particle convective heat transfer coefficient = Radiant heat transfer coefficient = Jet penetration length = Width of cyclone inlet = Number of spirals in cyclone = Elasticity modulus for a fluidized bed = Elasticity modulus at minimum bubbling = Richardson-Zaki exponent... 

Gas flowing from the grid holes can either take the form of a series of bubbles or a permanent jet, depending on system parameters and operating conditions. However, a permanent jet prevails for most industrial conditions. Jet penetration is one of the most important design parameters since ithelpsin ... 

Figure 1. Jet penetrations at grid holes for different orientations.

There are numerous jet penetration correlations (Zenz, 1969 Shakhova, 1968 Merry, 1971 Yang and Keaims, 1979 Knowlton and Hirsan, 1980 Yates et al., 1986 Blake et al., 1990 Roach, 1993) in the literature. Massimilla (1985) and Karri (1990) have shown that the jet penetrations predicted by these correlations can vary by a factor of 100 or more. Among them, Merry s correlation for horizontal jets was shown (Karri Chen and Weinstein, 1993 Roach) to give reliable predictions. Merry s correlation to calculate the penetration of horizontal jets is ... 

The jet penetration lengths for upwardly and downwardly directed jets can be calculated from Eq. (1). These equations take into account the effects of pressure and temperature on jet penetration. Knowlton and Hirsan (1980) and Yates et al. found that the jet penetration increases significantly with system pressure. In addition, Sishtla et al. (1989) found that the jet penetration decreases with increasing system temperature. Bed... 

For a grid, achieving equal distribution of gas flow through many parallel paths requires equal resistances and sufficient resistance to equal or exceed the maximum value of any unsteady-state pressure fluctuation. It has been determined experimentally that the head of solids in some fluidized beds above an upwardly-directed grid port can vary momentarily by as much as 30%. This is due to large fluctuations in the jet penetration for an upwardly-directed jet as discussed in the previous section. The equivalent variation downstream of a downwardly-directed port is less than 10%. Thus, as a rule of thumb, the criteria for good gas distribution based on the direction of gas entry are ... 

System temperature and pressure affect the momentum of grid jets via the gas density (see Ch. 2). The momentum of the gas jets is p AC/A. When the temperature is increased, the gas density decreases. For the same gas jet velocity this decreases the momentum of the jets and, therefore, decreases the jet penetration and the attrition at the grid. Similarly, when system pressure is increased, gas density increases, gas jet momentum increases and, therefore, the jet penetration and the attrition at the grid are increased. 

Gas jet penetration depth using Merry s correlation (Eq. 2) for horizontal jets... 

Figure 19. Definition of jet penetration depth and jet half angle.

The good agreement obtained for all data using the modified Froude number signifies the physical significance of the parameter. In fact, the dependence of jet penetration on the two-phase Froude number can be derived theoretically from the buoyancy theory following that of Turner (1973). 

The characteristic length scale, L-, taken here to be the jet penetration depth is shown by Turner (1973) for a buoyancy jet to be... 

Jet Half Angle. Determination of jet half-angle is shown also in Fig. 19. The jet half-angle can thus be calculated from the experimentally measured bubble size and jet penetration depth as follows ... 

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