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Ind. Eng. Chem. Res. 2004, 43, 5466-5473
Hydrodynamic Similarity in Bubbling Fluidized Beds: The Importance of the Solid-to-Gas Density Ratio P. John Sanderson,†,‡ K. Seng Lim,*,† Igor Sidorenko,‡,§ and Martin J. Rhodes§ CSIRO Minerals, Box 312 Clayton South, Victoria, Australia 3169, CRC for Clean Power from Lignite, 8-677 Springvale Road, Mulgrave, Victoria, Australia 3170, and Department of Chemical Engineering, Monash University, P.O. Box 36, Victoria, Australia 3800
Since bubbling fluidized-bed scaling laws were first developed, there has been some debate about their correct application and the relative importance of the various scaling parameters, in particular, the solid-to-gas density ratio. In this paper, we highlight the differences in the existing literature and present the results from experimental fluidized-bed systems where the solid-togas density ratio has been changed by varying degrees. From our results, we conclude that there is some flexibility for altering the solid-to-gas density ratio when scaling bubbling beds of Geldart group B materials up to particle Reynolds numbers of at least 12, but further work is needed to clarify the range of particle Reynolds numbers over which the density ratio requirement can be relaxed. In contrast, when scaling group A materials, we find that the density ratio is an important parameter even if the particle Reynolds number is small. Introduction Because of the commercial risks associated with scaling up of a fluidized-bed process, the effect of a scale change on the bubbling bed behavior has received much attention over the years. In the early 1980s, hydrodynamic similarity criteria were recognized as one possible way of predicting the physical behavior of a large bubbling fluidized bed based on measurements made in a small one. These similarity criteria, or “scaling laws”, could be summarized by equations or a set of dimensionless groups that, when applied to two fluidized-bed units of different size, should ensure that the physical phenomena occurring in the beds were scaled with their size. Fitzgerald et al.1,2 first suggested and tested the similarity approach on bubbling fluidized beds. Glicksman3 proposed a similar set of dimensionless groups but considered the cases of inertial-dominated and viscousdominated flow separately, so that simplifications could be made to the set of dimensionless groups under those conditions. Horio et al.4 suggested an alternative form of scaling relationship expressed as a pair of equations that were later shown5 to be equivalent to the viscousdominated version of Glicksman’s scaling relationships. Foscolo et al.6 showed that scaling criteria derived from their generalized particle-bed model of fluidization were consistent with the aforementioned scaling laws of Fitzgerald and Glicksman and, importantly, implied the successful application of scaling criteria to systems of group A materials from a fluid-dynamic basis (i.e., without the need to include any additional criteria for non-fluid-dynamic interparticle forces). This proposal was soon verified by the work of Rapagna et al.7 and Di Felice et al.8 The solid-to-gas density ratio is of particular interest because its inclusion in the so-called “simplified” scaling * To whom correspondence should be addressed. Tel.: +61 3 9545 8500. Fax: +61 3 9562 8919. E-mail:
[email protected]. † CSIRO Minerals. ‡ CRC for Clean Power from Lignite. § Monash University.
criteria is open to different interpretations in the literature. While the scaling relationship of Horio et al.4 does not explicitly require the solid-to-gas density ratio to be matched between the two scaled systems, it has often been experimentally evaluated in situations where a constant solid-to-gas density ratio has been maintained inadvertently (by virtue of using the same fluidization media at both scales), for example.4,9,10 On the other hand, Glicksman et al.11 specifically include the solid-to-gas density ratio in their development of a generally applicable simplified scaling law. Their reasoning is that for fluidization conditions with particle Reynolds numbers exceeding Rep ) 4 (the limit for viscous-dominated drag forces) the inertial drag term can no longer be neglected in the Ergun12 equation and thus the density ratio should be included in the scaling law.
Scaling law of Horio et al.:4 Condition 1: U2 - Umf2 ) xm(U1 - Umf1) Condition 2: Umf2 ) xmUmf1 similar bed geometry
(1)
Simplified scaling law of Glicksman et al.:11 L 1 Fs U2 U , , , gL Umf L2 Ff
(2)
Note that eqs 1 and 2 are equivalent except for the solidto-gas density ratio requirement in the latter. Note also that the additional particle-related requirements of similar size distribution and sphericity should also be considered in practice. Because the only difference between the scaling law of Horio et al.4 and the simplified scaling law of Glicksman et al.11 is the inclusion of the density ratio in the latter, further work is needed to clarify the significance of this parameter when applying scaling laws in practice.
10.1021/ie0341810 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/05/2004
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Figure 1. (a) Physical arrangement of the ambient-air fluidized bed used in system 1. Note that pressure probe and ECT measurements were carried out in separate runs. (b) Comparison of the cumulative particle size distributions for silica and garnet sands.
Literature Review The issue of matching the solid-to-gas density ratio was highlighted by Broadhurst and Becker13 in their early dimensional analysis study of bubbling fluidization. In their comparison of four different-sized columns, they found that the solid-to-gas density ratio was important for phenomena such as the minimum bubbling velocity. The question of matching the solid-togas density ratio with the simplified scaling parameters was pointed out by Glicksman et al.,11 experimentally reported on by Farrel et al.,14 and also highlighted by Glicksman.15 Glicksman et al.11 explained the reasoning behind the inclusion of the parameter in their simplified scaling laws as follows: Because the minimum fluidization velocity is a function of the particle-to-gas density ratio, if the density ratio is altered in the small-scale model (scaled by the simplified parameters), the required particle diameter must then be changed in order that the minimum fluidization velocity is still scaled correctly between the two units. Changing the particle diameter will thus alter the particle Reynolds number, which may significantly increase the error in the drag coefficient in the scale model. Thus, for scaling beds with intermediate or large Reynolds numbers, the solid-to-gas density ratio should be included in the set of scaling parameters. A number of experimental investigations have explored the use of the simplified scaling laws with mismatched solid-to-gas density ratios. Roy and Davidson16 conducted several runs with a density ratio mismatch in which it could be argued that the simplified criteria were met and concluded that for particle Reynolds numbers of less than 30, the solid-to-gas density ratio was unimportant (i.e., Glicksman’s requirement for Rep < 4 was conservative). Leu and Lan17 also investigated a density mismatch with the use of the simplified scaling criteria. Contrary to Roy and Davidson, they found that similarity was not achieved, even though their experiments were conducted at low particle Reynolds numbers (6 < Rep < 14 and 2 < Rep < 8) and they satisfied both requirements of the similarity rule in their first comparison and condition 2 alone in the second. van der Stappen18 also explored a density mismatch for the range 10 < Rep < 35 and found that similarity was not achieved for gas velocities exceeding 2.5Umf (corresponding to Rep ) 13), although the particle size distribution and sphericity were also mismatched and the choice of the distributor may also have influenced the results. Farrel et al.14 carefully matched all
parameters except the density ratio in their study of the simplified scaling law and found that similarity was not achieved at all for 10 < Rep < 25. Finally, Stein et al.19,20 carried out runs in their study of the simplified criteria in which the density ratio was mis-matched (for 17 < Rep < 42), and they did claim to find similar behavior, tentatively suggesting that the range for the viscous limit scaling criteria could be as high as Rep ) 100. Given the somewhat contradictory evidence from the previous studies and the differences in the approaches of Horio et al.4 and Glicksman et al.,11 it can only be concluded from a review of the literature that further work is needed to clarify situations when the gas-tosolid density ratio should be included and when it can be safely ignored. In the present work, experimental verification of the simplified scaling laws is undertaken with the specific objective of mismatching the solid-to-gas density ratio while maintaining the other parameters constant. In this way, we seek to determine the importance of this parameter for scaling in both Geldart group A and B materials at various particle Reynolds numbers. Experimental Section Two small-scale bubbling bed models were used in the experimental tests. Both were cylindrical in cross section and had vessel internal diameters of 146 mm. Henceforth, they shall be referred to as systems 1 and 2 for clarity. System 1 was designed to operate at ambient pressure and consisted of an acrylic column and bubble cap distributor with bed materials fluidized by ambient air. Figure 1a shows the overall arrangement. Measurements of fluidization properties were undertaken using either a single pressure probe located 103 mm above the distributor or a single-plane 12-electrode electrical capacitance tomography (ECT) system with electrode axial centers located 150 mm above the distributor. The measurement electrodes were 50 mm high and located between pairs of driven shield electrodes. The pressure probe, designed according to the guidelines of van Ommen et al.,21 was used to generate absolute pressure fluctuation signals detected by a Data Instruments XCX01DNQ pressure transducer. For each condition, over 16 000 data points were sampled to a personal computer at a rate of approximately 250 Hz. ECT data were sampled at approximately 80 Hz, and 16 000
5468 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 Table 1. Specifics of System 1 (Ambient Conditions, Group B Materials) system 1 bed diameter D (mm) bed material static bed height Hs (mm) Sauter mean particle diameter dsv (µm) minimum fluidization velocity Umf (m/s) particle density Fs (kg/m3) gas velocity U (m/s) Froude number Fr particle Reynolds number Rep density ratio Fs/Ff
Figure 2. Process instrumentation diagram for the pressurized cold fluidized-bed model used in system 2: V1, V3, V5-V7, V10V13, isolation valves; V2, V9, flow control valves; V4, nonreturn valve; V8, safety relief valve; P1-P4, pressure gauges; T1, temperature indicator; F1, line filter; PVC1, line service unit consisting of a pressure regulator, air filter, and moisture trap; R1-R3, rotameters Krohne H250; R4, rotameter with flow controller Krohne DK32; PVC2, manifold pressure regulator; PVC3, backpressure control valve Samson 3510 with an integral positioner; BD1, safety bursting disk; DP1, bed differential pressure transmitter Honeywell STD-924; PC, universal digital controller Honeywell UDC300.
frames were recorded for each condition. Both ECT and pressure measurement runs were repeated three times for each operating condition to get an indication of the extent of random error. As may be seen in Figure 1b, the two bed materials used in this system (garnet sand and silica sand) had similarly shaped particle size distributions, although the particle size distributions were somewhat wide, which may be the reason the measured minimum fluidization velocities were lower than those predicted by the Wen and Yu correlation. An examination under an optical microscope showed that both of the materials consisted of rounded sandlike particles with similar shape. Further details of the equipment and procedure may be found in work by Sanderson.22 System 1 was used to compare situations in which the solid density was changed while the gas density remained the same. System 2 was designed to operate at ambient as well as elevated pressures, up to 2500 kPa (25 bar). It consisted of an acrylic column and sintered bronze distributor (nominal pore size 12 µm) housed within a pressure vessel. The bed was fluidized by compressed air for pressures of up to 6 bar and by compressed nitrogen for pressures above this. Figure 2 shows the process and instrumentation diagram. For experiments reported here, measurements in the pressurized bed were undertaken using the single-plane 12-electrode ECT system with an electrode axial center located 250 mm above the distributor plate and electrode dimensions identical with those in system 1. Full details of the pressurized fluidized-bed equipment may be found in work by Sidorenko.23 System 2 was used to compare situations in which the gas density was altered by changing the system pressure while the solid density remained the same. The tests were carried out for both Geldart group A and B materials (henceforth referred to as systems 2A and 2B, respectively).
146 silica sand 295 337
146 garnet sand 295 300
0.085
0.082
2650 0.101-0.327 0.0071-0.075 2.2-7.2 2190
4100 0.101-0.402 0.0071-0.113 2.0-7.9 3390
Note that when the gas density is altered in this way, it is important to consider the impact of any inadvertent changes to the gas viscosity and minimum fluidization velocity that result from altering the gas pressure. While there is negligible change in the air viscosity at the pressures involved, the measured minimum fluidization velocity (Umf) is altered (see Table 2) for both bed materials.23 To account for this, the variation in the minimum fluidization velocity has been incorporated into our calculation of the dimensionless gas velocity (U/Umf) for proper comparison of dimensionless results. The fluidization parameters for the two separate experimental setups are shown in Tables 1 and 2. Note that a complete verification test was conducted in each of systems 1, 2A, and 2B; there is no attempt to match the parameters or achieve similarity between these systems. Results from System 1: Change in the Solid Density for Geldart Group B Materials As can be seen from Table 1, the comparison undertaken in system 1 involved two Geldart group B powders, well matched in terms of the simplified scaling criteria but with a mismatched solid-to-gas density ratio as a consequence different particle densities. Figure 3 shows a comparison of the dimensionless average pressure and dimensionless average absolute deviation of pressure recorded by the pressure probe system for the full range of gas velocities investigated. Pressure measurements were nondimensionalized via
P* ) P/FbgHs
(3)
where P is the measured pressure (Pa), Fb is the packedbed bulk density (kg/m3), g is the acceleration due to gravity (m/s2), and Hs is the settled bed height (m). The results indicate similar bed expansion and pressure fluctuation amplitude characteristics for both materials. Figures 4 and 5 show comparisons of the probability density function and amplitude spectrum, respectively, from the pressure fluctuation signals corresponding to a midrange gas velocity. The distributions were normalized to ensure that the area under each was the same, and for consistency with the simplified criteria, frequency was nondimensionalized via
f* ) fD/Umf
(4)
where f is the measured frequency (Hz) and D is the bed diameter (m). These results are typical of those obtained throughout the velocity range investigated.21
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5469 Table 2. Specifics of System 2 (High Pressure, Tests on Both Group A and B Materials) bed diameter D (mm) bed material Sauter mean particle diameter dsv (µm) particle density Fs (kg/m3) superficial gas velocity U (m/s) Froude number Fr operating pressure (bar, abs.) gas density (kg/m3) minimum fluidization velocitya Umf (m/s) particle Reynolds number Rep density ratio Fs/Ff a
system 2A
system 2B
146 FCC powder 77 1330 0.005-0.059 1.7 × 10-5-2.4 × 10-3 3-19 3.6-22.8 0.0028-0.0021 0.13-2.3 370-58
146 silica sand 203 2650 0.033-0.15 8.6 × 10-4-1.6 × 10-2 1-21 1.2-25.2 0.033-0.028 0.5-12 2190-105
Note that the minimum fluidization velocity is weakly affected by pressure and decreases with increasing pressure.
Figure 3. Variation in dimensionless average pressure (Av.) and average absolute deviation in dimensionless pressure (AAD) with dimensionless gas velocity for system 1 using silica and garnet sands.
Figure 4. Comparison of the normalized probability distribution of pressure fluctuations for system 1 (silica and garnet sands) at similar dimensionless superficial gas velocities.
ECT results were compared by calculating the average voidage across the measured cross section (i.e., a cylinder of 146 mm diameter and 50 mm height) for each frame of data and using these data to generate a spatially averaged bed voidage time sequence. The chosen ECT measurement provides a means of comparing the ensemble-averaged property of the fluidization hydrodynamics across a section of the bed. From this sequence, data were compared in a number of ways. Figure 6 shows the time average and average absolute deviation of the overall average bed voidage for the full range of gas velocities investigated. The trends in the results are entirely consistent with those recorded by the pressure probe in Figure 3. Figure 7 shows the average cycle frequency (calculated as half the number of times the signal crosses its own average per unit time) for the voidage fluctuation time sequence, indicating that the two systems have similar time scales (although
Figure 5. Comparison of dimensionless amplitude spectra of pressure fluctuations for system 1 (silica and garnet sands) at similar dimensionless superficial gas velocities.
Figure 6. Variation in the overall average voidage (Av.) and average absolute deviation in voidage (AAD) from ECT measurements for system 1 (silica and garnet sands) at a range of dimensionless superficial gas velocities.
there is some indication that at higher velocities the trends may be starting to diverge). The similarity of both the magnitude and time scale of voidage fluctuations for the two materials is further confirmed by normalized probability density functions (e.g., Figure 8) and amplitude spectra (e.g., Figure 9), both of which are typical of the agreement seen across the velocity range studied. Results from System 2A: Changes in the Gas Density for Geldart Group A Materials In the system 2 tests, ECT results were used as the main method of comparing hydrodynamic phenomena and were processed in the same way as that described for system 1. In system 2, spatially averaged ECT data are taken from a measurement volume of 146 mm in
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Figure 7. Comparison of the dimensionless average cycle frequency from ECT voidage fluctuations for system 1 (silica and garnet sands) as a function of the gas velocity.
Figure 8. Comparison of the normalized probability distribution of measured ECT voidage fluctuations for system 1 (silica and garnet sands) at similar dimensionless superficial gas velocities.
Figure 9. Comparison of the dimensionless amplitude spectra of ECT voidage fluctuations for system 1 (silica and garnet sands) at similar dimensionless superficial gas velocities.
diameter and 50 mm height, located 250 mm above the distributor plate. Results presented in Figure 10 show the variation in the average bed voidage with gas velocity for the FCC powder at a range of solid-to-gas density ratios, clearly indicating that an increase in the gas density results in a reduction of the average bed voidage. Interestingly, it was shown elsewhere23 that the bed voidage at minimum bubbling conditions for system 2A remains virtually constant across the range of gas pressures used, varying only from 0.47 to 0.50 at pressures from 1 to 21 bar, respectively (a result very similar to that of Rapagna et al.7). Figure 11 shows the
Figure 10. Variation in the average bed voidage (from ECT measurement) with dimensionless superficial gas velocity for system 2A (FCC powder) for a range of solid-to-gas density ratios (DR). Lines are used to guide the eye.
Figure 11. Variation in the average absolute deviation of bed voidage (from ECT measurement) with dimensionless superficial gas velocities for system 2A (FCC powder) for a range of solid-togas density ratios (DR). Lines are used to guide the eye.
Figure 12. Variation in the dimensionless average cycle frequency of bed voidage fluctuations (from ECT measurement) with dimensionless superficial gas velocities for system 2A (FCC powder) for a range of solid-to-gas density ratios (DR). Lines are used to guide the eye.
variation in the average absolute deviation of the bed voidage with gas velocity at a range of solid-to-gas density ratios. The increasing gas density results in a decrease in the average absolute deviation corresponding to more uniform bubbling. Figure 12 shows the variation in the average cycle frequency with gas velocity and solid-to-gas density ratio. The frequency decreases with a large increase in the gas density. In the intermediate region between minimum fluidization
Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 5471
Figure 13. Variation in the average bed voidage (from ECT measurement) with dimensionless superficial gas velocity for system 2B (silica sand) for a range of solid-to-gas density ratios (DR). Lines are used to guide the eye.
Figure 15. Variation in the dimensionless average cycle frequency of bed voidage fluctuations (from ECT measurement) with dimensionless superficial gas velocities for system 2B (silica sand) for a range of solid-to-gas density ratios (DR). Lines are used to guide the eye.
Discussion
Figure 14. Variation in the average absolute deviation of bed voidage (from ECT measurement) with dimensionless superficial gas velocities for system 2B (silica sand) for a range of solid-togas density ratios (DR). Lines are used to guide the eye.
and minimum bubbling conditions, the average cycle frequency is very sensitive to small disturbances apparently caused by experimental noise and typically shows a decrease and then an increase with increasing gas velocity, a trend that has also been reported by other workers.24,25 Results from System 2B: Changes in the Gas Density for Geldart Group B Materials In these tests, ECT results were again used as the main method of comparing hydrodynamic phenomena but this time in the evaluation of Geldart group B material behavior as shown in Table 2. Figure 13 shows the variation in the average bed voidage with gas velocity and density ratio for the silica sand and indicates that the decreasing solid-to-gas density ratio results in an increase in the average bed voidage, which is small for small changes in the density ratio but more dramatic for larger changes in the density ratio. Figure 14 shows the variation in the average absolute deviation of bed voidage with gas velocity for the same material and, importantly, indicates that the change in the density ratio has a relatively minor effect on the magnitude of the fluctuations. Figure 15 shows the variation in the average cycle frequency with gas velocity for the same experiments and indicates that the change in the density ratio has a relatively small effect on the time scale of the fluctuations.
For system 1, the comprehensive analysis of both pressure and voidage fluctuation signals indicates closely matched bubbling bed hydrodynamics, in terms of both the time scale and magnitude of the observed fluctuations. The results also serve to reinforce the validity of conclusions drawn from the ECT data in this situation because they correspond well with the more conventional pressure fluctuation measurements. Although in this work we do not present a deliberately mis-scaled scenario to test the measurement techniques, our previous work22,26 demonstrates that both the pressure and voidage fluctuation measurements we have undertaken can correctly distinguish between scaled and mis-scaled systems. In the system 1 time-scale comparisons, the nondimensionalization of the frequency is carried out for completeness rather than necessity because neither the bed diameter nor the minimum fluidization velocity is significantly altered between the two cases. The particle Reynolds numbers over which the system 1 comparison has been evaluated are in the range 2 < Rep < 7, thus spanning the viscous limit (Rep ) 4) suggested by Glicksman.3 We find that the density ratio mismatch in this system (2190 for silica sand and 3390 for garnet sand) does not cause any significant difference in the hydrodynamics for this range of particle Reynolds numbers. However, the voidage fluctuation average cycle frequencies in Figure 7 tend to suggest that the time scales for the two systems may be just starting to diverge at higher velocities, an observation also made by Farrel et al.14 and something to be evaluated in future work at higher velocities. For system 2B, also involving a Geldart B material, we find some differences in the measured bed expansion at different solid-to-gas density ratios that are more dramatic for a large change in the density ratio than for a small one. The magnitudes of the voidage fluctuations show a reasonable agreement and no clear trend with changing density ratio. The frequencies of the voidage fluctuations also show reasonable agreement; at low velocities, there is no clear trend with the density ratio, but at higher gas velocities, the frequency increases slightly with a 3-fold increase in the density ratio. So, in the pressurized group B system, we find that it is only for significant differences in the solid-togas density ratio and/or higher gas velocities that there is a measurable difference in the hydrodynamics.
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Note that both Farrel et al.14 and van der Stappen,18 who observed a mismatch in systems scaled by the simplified scaling criteria and incorporating a mismatched density ratio, did so at particle Reynolds numbers generally higher than those considered in this work (roughly above Rep ) 10), although other workers16,20 claim to have found well-matched behavior at still higher particle Reynolds numbers (suggesting up to 30 and 100, respectively). Interestingly, we note that our results for both the ambient and pressurized systems are in direct contradiction to the results presented by Leu and Lan,17 who explored a density ratio mismatch with Geldart B powders in a Reynolds number range similar to that of this work, albeit with one system at elevated temperature. Leu and Lan observed a mismatch in the fluctuation frequency for the ambient-temperature systems in which they mismatched the density ratio, and they observed a mismatch in the fluctuation amplitude between hot- and cold-scaled models (also involving a mismatched density ratio), although the fluctuation frequencies coincided. We do not observe these differences in our results, and at present we can offer no definitive explanation for the difference but acknowledge that the study was conducted in a two-dimensional bed as opposed to our three-dimensional system. We therefore consider an experimental evaluation of fluidparticle systems similar to those used by Leu and Lan (e.g., involving elevated temperature) as grounds for future work. In contrast to the observations of Geldart group B materials, the results from the pressurized experiments of system 2A demonstrate that matching the solid-togas density ratio is an important requirement when scaling systems of Geldart group A powders, even if the particle Reynolds number is very low. Our ECT-based measurements indicate that differences in the bed expansion, magnitude, and frequency of voidage fluctuations occur if the density ratio is mismatched, with the most significant differences occurring for large changes in the density ratio. (For comparison, we plan further evaluation with pressure measurements in future work.) Although the maximum change in the bed expansion for the group A case is of magnitude similar to that observed in the group B case (comparing Figure 10 with Figure 13), the density ratios have not been altered as dramatically to achieve it. Note that our observations for the group A system cover a range of low particle Reynolds numbers of 0.1 < Rep < 3, implying that the criteria for viscous limit scaling may require further evaluation. These findings are also in agreement with the recommendations of Rapagna et al.,7 who advised “extreme caution” when considering neglect of the density ratio in group A systems due to its strong influence on the minimum bubbling voidage.
group B systems, we found that for the range of particle Reynolds numbers considered (up to Rep ) 12), the effect of mismatch of the solid-to-gas density ratio was small and only identifiable at higher gas velocities or where the change in the density ratio was large. This suggests that there is more flexibility with group B materials than the “traditional” viscous limit value of Rep ) 4 would imply. However, further work on group B materials is required to better define the range in which the density ratio can be neglected. In contrast, we found that the solid-to-gas density ratio is an important parameter when scaling systems with Geldart group A powders and attempts should be made to match it even when the particle Reynolds numbers are small and within the range of the viscous limit. Further study is required to address these issues in order to develop more definitive scaling procedures. Acknowledgment The authors gratefully acknowledge the financial and other support received for this research from the CRC for Clean Power from Lignite, which is established under the Australian Government’s Cooperative Research Centres Scheme. Nomenclature D ) bed diameter (m) dsv ) Sauter mean particle diameter (µm) f ) frequency (Hz) g ) acceleration due to gravity (m/s2) L ) length dimension (m) m ) scaling factor; ratio of length dimensions Hs ) settled bed height (m) P ) pressure (Pa) Umf ) minimum fluidization velocity (m/s) U ) superficial gas velocity (m/s) Greek Letters µ ) fluid viscosity (kg/ms) Fb ) bed bulk density (kg/m3) Ff ) fluid density (kg/m3) Fs ) particle density (kg/m3) Dimensionless Groups Rep ) particle Reynolds number, Rep ) dsvUFf/µ Fr ) simplified Froude number, Fr ) U2/gD Superscript * ) nondimensional form Subscript 1, 2 ) parameters from different scaled systems
Literature Cited Conclusions An evaluation of the effect of mismatch of the solidto-gas density ratio in bubbling bed systems scaled by the simplified scaling parameters was carried out in small-scale cold models. Measurements of pressure fluctuations (from the pressure probe) and voidage fluctuations (from the ECT) were carried out. We investigated both Geldart group A and B systems and manipulated the density ratio via either choice of solids or alteration of the system gas pressure. For Geldart
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Received for review October 14, 2003 Revised manuscript received January 7, 2004 Accepted January 13, 2004 IE0341810
