Jet, penetration depth

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 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 ... 

Yang, W. C. and Keaims, D. L. (1979). Estimating the Jet Penetration Depth of Multiple Vertical Grid Jets. I EC Fund., 18, 317. 

The jets in fluidized beds have the following properties the jet penetration depth, the jet expansion angle (or the jet half angle), gas and solids entrainment, initial bubble size, and frequency issuing from the jets. They will be discussed now. 

There are at least a dozen proposed correlations in the literature for calculating the jet penetration depth for a vertical jet, they are summarized in Table 3. The jet penetration correlations were also reviewed by Blake et al. (1984), Massimilla (1985), and more recently Kimura et al. (1994, 1995). The discrepancy between the prediction from different correlations sometimes can be more than an order of magnitude on the dependency of gas velocity or operating pressure. The primary reason is because of the complex jetting modes observed experimentally, which create conflicting definitions of jet penetration depth by different researchers. Those by Merry (1975), Knowlton and Hirsan (1980), and Kececioglu et al. (1984) are presented in Fig. 19. 

The recommended approach to estimate the jet penetration depth is to make use of the two-phase Froude number defined as... 

The two-phase Froude number was first suggested by Yang and Keairns (1978) to calculate the jet penetration depth in the equation... 

This fundamental relationship has been elouded over the years by dilferent experimental arrangements, different definitions of jet penetration depth, and subjective observations of fluctuating jet penetration depth, which result in many jet penetration correlations that are inconsistent and of limited applicability. Equation (162) summarized the dependence of jet penetration... 

Figure 19 Different jet penetration depth definitions in the literature.

Based on the definition by Merry, the jet half angle can be calculated if the initial bubble size and the jet penetration depth are known. 

For multiple-jet systems such as that above a gas distributor plate, Wu and Whiting (1988) suggested to make use of the jet half angle discussed earlier to derive an equation for jet penetration depth. Their proposed equation is... 

Equation (176) predicts that the jet velocity does not affect the jet penetration depth in a multiple-jet system and infers that the jet region above the gas distributor has a constant height independent of the jet velocity. 

Yang and Keairns (1979) correlated the jet penetration depth data for multiple-grid jets and proposed an equation to estimate the jet penetration depth employing the two-phase Froude number. The resulting equation, as shown below, did show a decreasing, but not negligible, effect of jet velocity on jet penetration depth for multiple-jet systems. This obviously is due to the jet interaction observed experimentally. 

Yang WC, Keairns DL. Estimating the jet penetration depth of multiple vertical grid jets. I EC Fundamentals 18 317-320, 1979. 

Example 4. Design a flat perforated-plate grid for the polyethylene reactor schematically shown in Fig. 15 and calculate the gas jet penetration depth. Use a triangular pitch. System parameters are... 

In addition to the three solids circulation regions readily identifiable, the approximate jet penetration depth and bubble size can also be obtained from Fig. 8. The jetting region can be taken to be the maximum average value of jet penetration depth. From the jet... 

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