Ind. Eng. Chem. Res. 2001, 40, 3689-3696
3689
Gas Discharge Patterns in a Large Jetting Fluidized Bed with a Vertical Nozzle Qingjie Guo* and Guangxi Yue Department of Thermal Engineering, Tsinghua University, Beijing 100084, People’s Republic of China
Zhenyu Liu State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of Sciences, Taiyuan 030001, People’s Republic of China
The gas discharge patterns, a jet and a spout, generated by a vertical nozzle in an 8-m-high, 0.5-m-diameter jetting fluidized bed were investigated using frame-by-frame analysis and Sth VCD software analysis. The static bed height was varied from 0.38 to 0.66 m, and the nozzle jet velocity was varied from 16.1 to 64.26 m/s. A correlation was developed using experimental data to predict the transition of the flow pattern from a jet to a spout. The study shows that the major frequency in the power spectrum density function agrees with the jet collapse frequency measured by frame-by-frame analysis and Sth VCD software analysis. The major frequency in the power spectrum density function increases with increasing jet gas velocity. In addition, the jet velocity at the critical point in the curve of the major frequency versus the jet gas velocity corresponds to the gas velocity for the transition from a jet to a spout. Introduction Jets appear either at the nozzle exit of a fluidized bed or at the bed gas distributor. For a jet at the nozzle exit, gas injected vertically upward into the fluidized bed will cause various flow patterns such as a permanent cavity standing at the nozzle,1 a jet plume comprising a series of cavities separated by periodic constricted necks.2 The gas discharge patterns depend on the bed operating conditions, the gas discharge features, and the properties of the fluidized particles.3 Previous studies have shown that the gas discharge patterns at the nozzle exit influence the hydrodynamics in the fluidized bed. In addition, the gas discharge patterns affect effective gassolid contact and heat and mass transfer, as well as the chemical reaction. Therefore, many researchers pay attention to gas discharge patterns in fluidized beds. Huang et al.4 analyzed the power spectrum density function of the pressure fluctuations in a 400 mm × 15 mm two-dimensional fluidized bed to study the gas discharge transition from bubble plume to jet and then to spout. They then developed a correlation for predicting flow pattern variations. Kimura et al.5 employed a video recorder and an optical sensor in a 50-mm-i.d., 500-mm-high circular fluidized bed, an 80-mm-i.d., 500mm-high semicircular fluidized bed, and an 80-mm-i.d., 500-mm-high circular fluidized bed to examine the jet shape and its dynamic changes. They found that the penetration depth and the jet shape were strongly affected by the gas distributor shape. However, these studies of gas discharge patterns investigated smallscale fluidized beds, and there are great differences in gas discharge pattern transitions between small fluidized beds and large fluidized beds. A large jetting fluidized bed with a large central jet is commonly used * Corresponding author. E-mail:
[email protected]. Fax: 86-10-62781743. Tel.: +86-10-62781559.
in practice. Nevertheless, the reports about flow pattern transitions in large jetting fluidized beds are very sparse. In the present work, the flow pattern transitions are investigated using an 8.0-m-high, 0.5-m-i.d. jetting fluidized bed equipped with a semicircular nozzle. On the basis of the power spectrum density function of the pressure fluctuations, frame-by-frame video analysis, and Sth VCD software video analysis, a correlation for predicting flow pattern transitions is proposed. 2. Analysis 2.1. Dimensionless Analysis. Previous studies2,6,7 have indicated that the penetration depth increases with increasing jet gas velocity for a given nozzle diameter and that larger nozzle diameters caused larger penetration depths for the same jet gas velocity. Furthermore, at a given jet gas velocity, either larger particle sizes or larger particle densities can lead to smaller penetration depths.7 Thus, the penetration depth is a function of six variables
Lj ) f(d0,dp,u0,Fp,Fg,g)
(1)
Equation 1 has three basic dimensions: mass, length, and time. The Buckingham π theory shows that the above relationship reduces to a correlation of three dimensionless groups of variables related to the penetration depth. The dimensionless form of eq 1 can be expressed as
(
u02 Fg d0 Lj )f , , d0 gd0 Fp - Fg dp F/r
u02 Fg ) gd0 Fp - Fg
10.1021/ie000912+ CCC: $20.00 © 2001 American Chemical Society Published on Web 07/19/2001
)
(2)
(3)
3690
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
Figure 1. Schematic diagram of experimental and measuring system: 1, jetting fluidized bed; 2, coordinate origin; 3, semiconical gas distributor; 4, segregating column; 5, plenum chamber; 6, tank; 7, conveying pipeline; 8, cyclone; 9, flow meter; 10, accumulating tank; 11, pressure probe; 12, differential pressure transducer; 13, A/D converter; 14, computer; 15, jet nozzle; 16, pressure measurement tap.
F/r is the two-phase Froude number, which represents the ratio of the inertial force of the gas jet at the nozzle exit to the gravity force of the bed. It was first proposed by Yang.6 For convenience, a new parameter, Fd, is adopted to describe the effects of the various variables on the penetration depth and defined as
d0 u02 Fg d0 u02 Fg Fd ) F/r ) ) ) dp gd0 Fp - Fg dp gdp Fp - Fg
tuation time series are divided into k segments, each of length L, which are represented as
xi ) x(n + iL) n ) 1, 2, 3, ..., L; i ) 1, 2, ..., k (6) The average power spectrum is
Px )
{Re}p2 ) Frm (4) Ar
xi(n) w(n)e-j2πnk/N|2 ∑ ∑ | kLUi)1 n)1
(5)
Thus, two parameters, Fd and the ratio of the rest bed height (H0) to the nozzle diameter (d0), are utilized to describe flow pattern transitions. 2.2. Power Spectrum Density Function. The time series of pressure fluctuations can be analyzed using the power spectrum density function. The power spectrum illustrates how the energy is distributed over the frequency. To decrease the calculational error, the average of a number of subspectra is used to estimate the power spectrum. Consequently, the pressure fluc-
L
(7)
where U normalizes the power spectrum using a factor of the power in the window function, w(n)
As indicated above, Fd is the same as the modified Froude number.9 When spouts occur, the penetration depth must be greater than the static bed height
Lj H0 > d0 d0
k
1
U)
1
L
[w(n)2] ∑ Ln ) 1
(8)
A Hamming window applied in this study is a smooth one with a continuous first derivative; the window and its derivative are zero at the endpoints. That is
{(
1 πt 0.54 + 0.46 cos w(n) ) T T 0
)
0 e |t| e T |t| > T
(9)
The mean amplitude of the pressure fluctuations can be calculated as
σ)
x
1
n
∑(pi - pj )2 n - 1i)1
(10)
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3691
Figure 2. Series of photos at a jet gas velocity of 42.9 m/s and a static bed height of 0.66 m.
3692
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
The average pressure is n
p j)
pi ∑ i)1
(11)
3. Experimental Section 3.1. Experimental Setup. All experiments were performed in a cold-model jetting fluidized bed with an inside diameter of 0.5 m and a height of 8.0 m, as shown in Figure 1. The front bed plate is made of transparent Plexiglas to allow for the observation of the gas-solid flow behavior in the bed. The semicircular back plate is made of 10-mm cast steel. The semiconical gas distributor is located below the fluidized bed with an inclination angle of 70° and a height of 0.68 m. The inside diameter and height of the segregating column are 0.27 and 0.68 m, respectively. A semicircular jet nozzle 42 mm in diameter is located 15 mm from the flat front plate and 0.25 m above the gas distributor and injects gas at high velocity. The fluidizing gas used for the experiment is air at ambient conditions. Three rotameters are fitted into the line to measure the air flow rates of the jet, the segregating column, and the semicircular gas distributor. The static bed height was varied from 0.38 to 0.66 m above the nozzle exit, with particles in the region adjacent to the nozzle at the minimum fluidization condition. The segregating column flow rate and the semicircular distributor flow rate were adjusted to maintain minimum fluidization of the bed during the experiments. The jet gas velocity ranged from 16.1 to 60.0 m/s. A cyclone was installed at the bed gas exit, with the disengaged solid in the cyclone returned to the bed through a dipleg. Millet (Geldart Group D) with a density of 1474 kg/m3 and a mean diameter of 1.64 mm was used as the fluidized material. 3.2. Measurement Apparatus. The pressure sampling system included three pressure probes, three differential pressure transducers, an A/D converter, and a computer. Pressure taps were installed on the back semicircular wall of the fluidized bed at various height above the nozzle exit. Each pressure probe is made of 700-mm-long, 5-mm-i.d. copper pipe. To prevent particles from entering and blocking the probe, a piece of 200-µm stainless steel mesh screen was soldered to the
Figure 4. Jet penetration depth as a function of jet gas velocity at a static bed height of 0.66 m.
Figure 5. Effect of static bed height on the jet penetration depth.
pressure probe measuring port. The probe is connected to the high-pressure channel of a differential pressure transducer (Micro Switch 140PC 1D), whose full scale reading is 5000 Pa. The other channel is exposed to the atmosphere. Thus, the transducer produces an output voltage proportional to the pressure difference between these two channels. The sampling frequency is 110 Hz for all fluctuating signals, and 11 000 samples were taken, corresponding to 100 s of total sampling time. The origin is at the axis of the nozzle exit. The horizontal line along the front bed plate and the nozzle axis are the abscissa and ordinate, respectively, as shown in Figure 1. Three pressure transducers are mounted at (0 mm, -370 mm), (200 mm, 190 mm), and (200 mm, 310 mm). For all of the experimental conditions, the jet collapse positions in the bed are around 0.31 m. In this region of the bed where the jets are completely developed, the frequencies measured by the pressure probe are very close to the jet collapse frequencies measured using frame-by-frame analysis. Videos for each set of experimental conditions were recorded with a National M-7 video recorder for 180 s and then analyzed frame-by-frame using a Panasonic HD-100 player. The video images can be converted to VCD disks using a video converter and then analyzed using Sth VCD software. 4. Results and Discussion
Figure 3. Typical spout at a jet gas velocity of 42.9 m/s and a static bed height of 0.42 m.
4.1. Jet Development Process. A typical jet development process is shown in Figure 2 for a jet gas velocity
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3693
Figure 6. Pressure fluctuations at various jet gas velocities.
of 42.9 m/s. At t ) 0.04 s, a new jet forms, with some particles entrained into the jet after the former jet has collapsed and a bubble has formed. At t ) 0.08 s, the jet grows further, and a constriction appears as more particles enter the jet. In a typical jet, the top part swells like a mushroom cap, while the bottom part looks like a mushroom stem, with an obvious neck between these two parts at t ) 0.42 s. The jet collapses, and a new bubble is generated at t ) 0.72 s. Yang et al.,10 using high-speed motion pictures to visualize the flow in a two-dimensional fluidized bed and a semicircular fluidized bed, showed that crushed acrylic plastic with different particle sizes (Geldart Group B particles) led to the formation of permanent jets. Our observations are consistent with their conclusions. Knowlton and Hirsan11 summarized and classified the penetration depths using their definitions of Lb as the deepest penetration of bubbles into the bed before they lose their momentum, Lmax as the penetration depth of a series of interpenetrating cavities, and Lmin as the penetration depth of a cavity permanently attached to the nozzle. Merry et al.12 studied the maximum jet penetration depth and defined it as the vertical distance between the orifice and the lower edge of the bubble at the moment of bubble separation. Thus, the vertical dis-
Figure 7. Effect of jet gas velocity on the mean pressure for various static bed heights.
tance between the nozzle exit and the lower edge of the bubble at t ) 0.72 s is the penetration depth, which is 0.46 m, as shown in Figure 2. Observations indicate that the jets oscillate and the jet penetration depth at each cycle changes randomly. To decrease the experimental error, the penetration depth is the average of 60 jet collapses measured from the video player. Note that a new cycle begins at t ) 0.76 s. The periodic variation of
3694
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
Figure 8. Power spectrum density functions at various jet gas velocities.
the jets agrees well with Markhevka’s finding13 in a 130mm-i.d. fluidized bed. A spout forms when the jet gas velocity is increased and the static bed height is decreased. Figure 3 shows a typical spout, with gas jet passing through the bed surface and entrained solid particles carried through the bed and thrown up from the bed surface. The solid particles then descend along the boundaries of the gas fountain. 4.2. Effect of Jet Gas Velocity and Static Bed Height on the Penetration Depth. Figure 4 shows the influence of the jet gas velocity on the jet penetration depth. The jet penetration depth increases as the jet gas velocity increases, as the higher-velocity jet has more gas momentum. Figure 5 illustrates that the static bed height does not influence the jet penetration depth for the static bed height from 0.37 to 0.66 m when the jet gas velocity is 32.2 m/s. The experimental results for other jet gas velocities are similar. The static bed height should be sufficient to prevent the gas jet from passing through the bed surface and thus forming a spout. The jet penetration depth is independent of the static bed height because, as the static bed height increases, the bed pressure drop across the fluidized bed also increases, so that the inlet pressure must be increased to
maintain the jet gas flow rate. Thus, the resulting jet gas velocity is nearly the same. Because the large jetting fluidized bed contains about 800 kg of millet, it is difficult to obtain different-sized test material. Consequently, the effect of particle diameter on penetration depth in a large jetting fluidized bed was not investigated, and further work in this area is needed. The penetration depth in a large jetting fluidized bed can be predicted using Guo’s correlation,14,15 developed using experimental results from the same experimental setup as used in this study. 4.3. Power Spectrum Density Function of the Pressure Fluctuations. The static bed height and jet gas velocity are two important factors that influence flow transitions from a jet to a spout. Figure 6 illustrates pressure fluctuation diagrams for various jet gas velocities at a static bed height of 0.38 m. Jet gas velocities ranging from 16.1 to 32.2 m/s lead to pressure fluctuations with larger amplitudes because higher jet gas velocities result in larger jet region expansions and greater jet penetration depths. These four pressure fluctuation patterns are characterized by relatively large intensities with relatively slow oscillations. The videos indicate that each peak in these plots represents a jet collapse. It is interesting that the pressure fluctuations
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001 3695
Figure 9. Effect of jet gas velocity on the major frequency for various static bed heights.
at jet gas velocities of 42.9 and 60 m/s have smaller amplitudes and higher frequencies. In this case, the nozzle gas forms a spout that goes through the fountain at the bed axis. At a given static bed height, the effect of the jet gas velocity on the mean pressure fluctuation is shown in Figure 7, which illustrates that increasing the jet gas velocity increases the mean pressure fluctuation. However, at a given jet gas velocity, a large static bed height causes a large mean pressure fluctuation because the greater static bed height leads to a greater probability of bubble coalescence and larger bubble diameters. Typical power spectrum density function diagrams for the pressure fluctuations in a jet and a spout are presented in Figure 8. For the jet, the power spectrum density function has a large peak at less than 2 Hz and some peaks between 2 and 7 Hz. Compared to Figure 7, the major frequency has increased significantly to 5.25 Hz at a jet gas velocity of 42.9 m/s, indicating spout formation. The major frequency values are plotted for various jet gas velocities for four static bed heights in Figure 9. For H0 ) 0.66 m, the major frequency increases with jet gas velocity without a transition point. Static bed heights of 0.52 or 0.45 m have a frequency transition point at a jet gas velocity of 50.8 m/s. Frameby-frame video analysis reveals that the transition point corresponds to the transition from a jet to a spout. The bubble formation frequency measured in the present investigation is much lower than the 5-8 Hz value measured by Rowe et al.1 and the 20 Hz value measured by Hsing and Grace.16 In this study, only the spout has bubble formation frequencies near 5-8 Hz. The bubble frequency measured by Ettehadieh et al.17 in the upper portion of an 8-m-high, 3-m-diameter jetting fluidized bed was in the range 0-1 Hz, which is near the bubble frequency in the jet flow pattern of the present work. The lower bubble frequency measured in this study and in Ettehadieh’s work17 can be attributed to the dominant effect of the larger bed diameter and larger nozzle diameter. As discussed above, higher jet gas velocities and lower static bed heights often cause spouts, short circuiting much of the reaction gas and steam. This not only reduces the reaction efficiency but also wastes reaction gas and steam. Therefore, the spout pattern should be avoided in jetting fluidized beds. 4.4. Transition from Jets to Spouts. The flow pattern transition is a function of the static bed height and the jet gas velocity at the nozzle exit. Two param-
Figure 10. Jet to spout flow regime map.
eters, the ratio of the static bed height to the nozzle diameter and Fd, are employed to describe the transition from jet to spout (Figure 10). The boundary equation between the jet and spout regimes determined from the experimental data can be expressed by
Fd ) 0.0094
( ) H0 de
3.24
- 3.42
(11)
Equation 11 applies for
H0 14.59 e e 25.68 de 5. Conclusions The present work has obtained the following significant conclusions: (1) A complete jet period involves jet formation, jet development, and jet collapse. The jet formation frequency determined from the frame-by-frame analysis and the Sth VCD software analysis is consistent with the major frequency obtained from multistage power spectrum function of the pressure fluctuations. (2) The penetration depth increases with increasing jet gas velocity. For a given jet gas velocity and a range of static bed heights, the static bed height has little influence on the jet penetration depth as long as the static bed height is above the minimum required to prevent the gas jet from passing through the bed surface and thus forming a spout, as indicated in eq 11. (3) The jet formation frequency increases with increasing jet gas velocity. A transition point in the curve of the major frequency versus the jet gas velocity occurs at the transition from the jet to the spout regime. A correlation is presented to describe the transition from a jet to a spout. Acknowledgment The authors gratefully acknowledge financial support from the Chinese Postdoctoral Science Foundation. We also thank Peng Gui, Ronghu Kang, and Jianguo Liu of Taiyuan University of Technology for their assistance with this experimental work. Nomenclature d0 ) nozzle diameter, m dp ) particle diameter, m
3696
Ind. Eng. Chem. Res., Vol. 40, No. 16, 2001
de ) equivalent diameter, m F/r ) two-phase Froude number Fd, Frm ) dimensionless parameter defined in eq 4 g ) gravitational acceleration, m/s2 H0 ) static bed height, m k ) segment number in time series L ) individual length of each segment Lj, Lb, Lmax, Lmin ) penetration depth, m n ) pressure time series length t ) time, s T ) cycle time, s pi ) instantaneous pressure, Pa p j ) average pressure in a time series, Pa Px ) power spectrum density function u0 ) jet gas velocity at nozzle exit, m/s U ) nomalized power in the window function w(n) ) Hamming window function xi ) pressure fluctuation time series Greek Letters σ ) mean pressure fluctuation, Pa Fp ) particle density, kg/m3 Fg ) fluidization gas density, kg/m3
Literature Cited (1) Rowe, P. N.; Macgillivray, H. J.; Cheesman, D. J. Gas discharge from an orifice into a gas fluidized bed. Trans. Inst. Chem. Eng. 1979, 57, 194. (2) Kimura, T.; Matsuo, H.; Uemiya, S.; Kojima, T. Measurement of jet shape and its dynamic change in three-dimensional jetting fluidized beds. J. Chem. Eng. Jpn. 1994, 27, 602. (3) Massimilla, L. Gas jets in fluidized beds. In Fluidization, 2nd ed.; Davidson, J. F., Clift, R., Harrison, D., Eds.; Academic Press: New York, 1985; p 133. (4) Huang, C.; Chyang, C. Gas Discharge Modes at a Single Nozzle in Two-Dimensional Fluidized Beds. J. Chem. Eng. Jpn. 1991, 24, 633. (5) Kimura, T.; Horiuchi, K.; Watanabe, T.; Matsukata, M.; Kojima, T. Experimental study of gas and particle behavior in the
grid zone of a jetting fluidized bed cold model. Powder Technol. 1995, 82, 135. (6) Yang, W. C.; Keairns, D. L. Estimating the Jet Penetration Depth of Multiple Grid Jets. Ind. Eng. Chem. Fundam. 1979, 18, 317. (7) Guo, Q.; Yang, C.; Zhang, K.; Liu, Z.; Zhang, J. Study on Flow Characteristics in a Jetting Fluidized Bed. Eng. Chem. Metall. 1999, 20, 255. (8) Luo, G.; Zhang, J.; Zhang, B. Study on penetration depth in a jetting fluidized bed with multi-component. J. Chem. Ind. Eng. (China) 1996, 47, 96. (9) Kmiec, A. Expansion of Solid-Gas Spouted Beds. Chem. Eng. J. 1977, 13, 143. (10) Yang, W. C.; Revay, D.; Anderson, R. G.; Chelen, E. J.; Keairns, D. L.; Cicero, D. C. Fluidization Phenomena in a LargeScale, Cold-Flow Model. In Fluidization IV; Kunii, D., Toei, R., Eds.; Engineering Foundation: New York, 1983; pp 77-84. (11) Knowlton, T. M.; Hirsan, I. The Effect of Pressure on Jet Penetration Depth in Semi-Cylindrical Gas-Fluidized Beds. In Fluidization III, Grace, J. R., Matsen, J. M., Eds.; Plenum Press: New York, 1980; pp 315-324. (12) Merry, J. M. D. Penetration of vertical jets into fluidized beds. AIChE J. 1975, 21, 507. (13) Markhevka, V. I.; Basov, V. A.; Melik-Akhnazarov, T. K.; Orochko, D. I. The flow of a gas jet into a fluidized bed. Theor. Found. Chem. Eng. 1971, 5, 80. (14) Guo, Q. J.; Liu, Z. Y.; Zhang, J. Y. Flow characteristics in a large jetting fluidized bed with two nozzles. Ind. Eng. Chem. Res. 2000, 39, 746. (15) Guo, Q. J.; Yue, G. X.; Liu, Z. Y.; Zhang, J. Y. Hydrodynamics of large jetting fluidized bed. J. Chem. Eng. Jpn. 2000, 33, 855. (16) Hsing, T. P.; Grace, J. R. In Fluidization; Keairns, D. L., Davidson J. F., Eds.; Cambridge University Press: New York, 1978. (17) Ettehadieh, B.; Yang, W. C.; Haldipur, G. B. Motion of solids, jetting and bubbling dynamics in a large jetting fluidized bed. Powder Technol. 1988, 54, 243.
Received for review October 23, 2000 Revised manuscript received May 10, 2001 Accepted June 1, 2001 IE000912+
