Jet penetration correlation

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. 

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 ... 

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. 

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... 

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 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. 

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 ... 

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

Grid Jets as a Source of Attrition. Jet attrition affects only a limited bed volume above the distributor, which is defined by the jet length. As soon as the jet is fully submerged its contribution to the particle attrition remains constant with further increasing bed height. Figure 6 shows some respective experimental results by Werther and Xi (1993). The jet penetration length can be estimated by various correlations, e.g., Zenz (1968), Merry (1975), Yates et al. (1986) or Blake et al. (1990). 

Blake T. R., Webb H., and Sunderland P. B., The Nondimensionalization of Equations Describing Fluidization with Application to the Correlation of Jet Penetration Height, Chem. Eng. Sci., 45 365 (1990)... 

The literature contains many empirical correlations for estimating the mean depth of jet penetration [2-4] these must, however, be used with care and, whenever possible, only within the range of parameter values for which they were derived. By way of example, Merry gives the following correlations for vertical gas jets. [28] ... 

A major factor in fluidized bed behavior is the interaction between the gas flow from individual orifices and the particle and gas mixture within the bed. The jet penetration and the subsequent bubble formation have an important influence upon solids and gas mixing and, ultimately, upon the usefulness of the bed for reactor purposes. While flow visualization data are available at ambient pressures and temperatures, the natures of jet penetration and bubble development at high pressures and temperatures are not easily measured. Typical data on bubble size and bubble velocity at ambient conditions are shown, represented by the small size symbols, in Figure 2. It is well known that bubble volume can be correlated as a function of gas volumetric flow rate ( ) and that bubble velocity is related to the size of the bubble radius ( ). Such semi-empirical correlations are indicated as solid lines in that figure. 

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. 

Blake TR, Wen CY, Ku CA. The correlation of jet penetration measurements in fluidized beds using nondimensional hydrodynamic parameters. AIChE Symp Series 80(234) 42-51, 1984. 

Nz 5171 Jet penetration length increases existing correlations underestimate jet lengths. 

A considerable number of studies have been reported on jet penetration, and several correlations have been developed giving the penetration length as a function of the physical properties of gas and particles and of operating conditions (Knowlton and Hirsan, 1980). However, most of these correlations were produced from experimental data obtained at ambient conditions, and they fail when applied at elevated temperatures and pressures. Hirsan et al. (1980) measured jet penetrations in beds of Group B powders at pressures of up to 50 bar and produced a correlation for Ljnax (FiE- 5) in terms of the Froude number and the ratio of fluid to particle density ... 

Yates and Cheesman (1987) measured jet penetrations in three-dimensional beds of two coarse powders at pressures of up to 20 bar at ambient temperature and at temperatures of up to 800°C at ambient pressure. The pressure results gave a correlation identical to Eq. (31) but the high temperature measurements had slightly different values of the coefficient and exponent a correlation obtained from the combined results at temperature and pressure was... 

Blake TR, Webb H, Sunderland PB. The nondimensionaliza-tion of equations describing fluidization with application to the correlation of jet penetration height. Chem Eng Sci 45 365-371, 1990. 

If tuyeres with horizontal jets are used as gas distributors, they must be positioned so that they will not be eroded by jets issuing from adjacent tuyeres. Zenz [22] gives a correlation to calculate the penetration depth of horizontal jets into fluidized beds. He also gives a correlation to calculate the penetration depth of downward jets. This correlation would also be used to ensure that downward jets issuing from a pipe ring with downward-facing holes would not erode the support plate. 

Although various correlations offered for the spray penetration have used different functional dependence on xjd, most agree on a power of around 0.3-0.5 for q. This smaller power (compared to that of q in (29.7) for jet trajectory) is reasonable because the droplets forming the upper boundary of the spray plume are mainly... 

Authors Description of the study Correlations for jet spray penetration... 

To prevent severe erosion by jet impingement of internals such as heat exchanger tubes, one must know how far a vertical jet issuing from a distributor such as a perforated plate will penetrate into a fluidzed bed. This knowledge is also required to prevent piercing by jets of the surface of shallow beds. Blake et al. [58] reviewed the correlations and data available in the literature for the penetration depth of upward jets into fluidized beds. They proposed the following correlation ... 

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