Fluid bed characterization using Electrical Capacitance Volume Tomography (ECVT), compared to CPFD Software's Barracuda

Powder Technology 250 (2013) 138–146

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Powder Technology journal homepage: www.elsevier.com/locate/powtec

Fluid bed characterization using Electrical Capacitance Volume Tomography (ECVT), compared to CPFD Software's Barracuda Justin M. Weber ⁎, Ky J. Layfield 1, Dirk T. Van Essendelft, Joseph S. Mei National Energy Technology Laboratory, U. S. Department of Energy, 3610 Collins Ferry Road, Morgantown, WV 26507, USA

a r t i c l e

i n f o

Article history: Received 29 April 2013 Received in revised form 4 September 2013 Accepted 4 October 2013 Available online 18 October 2013 Keywords: Fluidization Electrical Capacitance Volume Tomography ECVT Computational fluid dynamics Multiphase flow Barracuda

a b s t r a c t Being able to accurately predict the performance and operation of multiphase flow systems continues to be a significant challenge. In order to continue the advancement of knowledge and to develop better models, a 10 cm diameter fluidized bed of 185 μm glass beads was used along with an Electrical Capacitance Volume Tomography (ECVT) sensor and high speed pressure measurements. Three dimensional images of the gas– solid flow structure were obtained and analyzed as well as frequency information from the high speed pressure transducers. The experimental data was then compared to four computational models performed with CPFD Software's Barracuda code exploring different techniques to handle the perforated distributor plate. Published by Elsevier B.V.

1. Introduction As the desire to use computational fluid dynamics (CFD) as a design tool for multiphase reacting, systems increases, it is important to understand how well the models perform and what assumptions can significantly affect the results. Therefore, it is important to compare physical experiments to computational models in order to continuously improve the understanding of how well these models can predict reality. Previous experimental studies of a 10 cm diameter cold flow fluidized bed have opened an opportunity to compare CFD models to a somewhat unique measurement technique, Electrical Capacitance Volume Tomography (ECVT) [1]. As the ECVT technique continues to improve and mature, it will provide useful measurements of solid concentrations in gas–solid or liquid–solid multiphase systems. The ECVT provides three dimensional non intrusive measurements of the flow structures much like X-ray tomography techniques [2–7] and magnetic resonance imaging (MRI) techniques [8–11], but does not have significant safety concerns, is geometrically flexible, and is not as expensive. The ECVT measurements can then be directly compared to CFD models such as what Yang et al. did when investigating bubble columns [12]. The aim of this work is to compare several CFD models to the measurements of the ECVT as well as high speed pressure measurements.

⁎ Corresponding author. Tel.: +1 304 285 5270; fax: +1 304 285 4403. E-mail address: [email protected] (J.M. Weber). 1 REM Engineering, 3566 Collins Ferry Road, Morgantown, West Virginia 26505, USA. 0032-5910/$ – see front matter. Published by Elsevier B.V. http://dx.doi.org/10.1016/j.powtec.2013.10.005

Due to the ease of use, computational speed, and ability to handle complex geometries, CPFD Software's Barracuda was chosen. 2. Experimental apparatus and test conditions The experimental apparatus, shown in Fig. 1, consists of a 10 cm diameter acrylic pipe standing 170 cm in height. At the exit of the experimental system, the piping reduces to a 5 cm diameter where a Micro Allergen filter bag was attached to capture any particles. Compressed air was used as the fluidizing gas and was controlled with a mass flow controller (Allicat Model MC-250LPM-8-1). A perforated plate, 6.35 mm in thickness, with 25 symmetrically located orifices, each being 1.59 mm in diameter, was used as the gas distributor. A stainless steel U.S. No. 325 mesh size (44 μm) screen was placed at the bottom of the distributor to prevent the bed material from entering the plenum. Two high-speed pressure transducers (Setra Model C239) were used in the experiments to record bubble frequency. The measurement range of the transducers was 0 to 9963 Pa and the sampling frequency was 100 Hz. One transducer measured the pressure drop across the distributor plate while the other measured the pressure across the fluidized bed. Glass beads were used as the bed material with a mean diameter of 185 μm, a mean sphericity of 0.98, a particle density of 2.483 g/cm3, a bulk density of 1.561 g/cm3, a packed solid fraction of 0.63, and a minimum fluidization velocity, Umf, of 3.17 cm/s. The measured particle size distribution is shown in Fig. 2. The static bed height was 26.2 cm, resulting in a bed mass of 3303.8 g. The bed was fluidized at a gas velocity of Ug/Umf = 4, or specifically 12.68 cm/s.

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Fig. 1. Experimental apparatus and gas distributor.

Cumulative

100% 80%

Cumulative

7%

Probability Density

6% 5%

60%

4% 3%

40%

2% 20% 0% 100

Probability Density

8%

120%

1% 125

150

175

200

225

0% 250

size [µm] Fig. 2. Glass bead particle size distribution, cumulative and volume.

The ECVT sensor, dimensioned 10 cm in diameter and 30 cm in height, was located 3.8 cm above the distributor from the bottom of the sensor. The sensor has 24 electrodes/channels and was used to collect three dimensional measurements of solid fraction at a frequency of 52 Hz. The sensor system was produced by Tech4Imaging, LLC and

consists of an ECVT sensor, data acquisition system, and a laptop, Fig. 3. The ECVT system measures capacitances with the electrodes and relates these physical measurements to solid fractions using a 3D neural network optimization reconstruction technique (3D-NN-MOIRT) [13,14]. This technique simultaneously optimizes four objective functions relating the measured capacitances to the solid fractions. Further details are described elsewhere [1,15–21]. The sensor was calibrated and normalized using the ‘empty’ and ‘full’ states before performing the experiments. The ECVT sensor reconstruction grid is 20 × 20 × 40 cells, thus providing a nominal resolution of 5 mm × 5 mm × 7.5 mm. However, the true resolution of the sensor is coarser then the nominal resolution due to the use of smoothing algorithms in the ECVT reconstruction. At this resolution, the interface between the bubble and emulsion phases cannot be sharply resolved, resulting in smeared bubble edges. This smearing presents a problem, when two or more bubbles are sufficiently close the ECVT will resolve the bubbles as a single bubble.

3. Computational fluid dynamics model In order to see how well a multiphase computational fluid dynamic (CFD) model compares to the data measured by the ECVT, several models were developed using CPFD Software's Barracuda (version

Fig. 3. Rendering of the electrical capacitance volume tomography system consisting of an ECVT sensor, data acquisition, and a laptop (left to right).

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Jets

Plenum

Discrete

Uniform

Pressure BC

Fig. 5. Discrete model flow boundary conditions locations.

Inlet Flow BC Fig. 4. The three models discussed in this paper.

15.0.3) and run on an Intel Xenon 5160 processor clocked at 3 GHz. Barracuda uses the multiphase particle-in-cell (MP-PIC) approach to modeling multiphase flows which is an Eulerian–Lagrangian approach where the fluid phase(s) are described as continuum while the solid phase(s) are described as discrete particles or particle clouds. Further details and mathematical descriptions of the CPFD Barracuda MP-PIC model are described elsewhere [22–26]. Four models were developed in an attempt to accurately model the experimental conditions and apparatus. The particle properties listed in the experimental section were used in the model, including the full particle size distribution. All three models were set up to be isothermal at 300 K, with compressible flow and air as the only gas in the domain. Maximum momentum redirection from collisions was set at 40% with the normal-to-wall and tangent-to-wall momentum retentions set at 0.33 and 0.99, respectively. The BGK collision model was not used. The Wen-Yu/Ergun drag model was used with Ergun's linear coefficient of 180 and non-linear coefficient of 2. The particles were initialized at a solid fraction of 0.63 at the experimental bed height. In all the simulations,

the bed mass in the model was matched to the experimental set-up within 1%. In all four models, a pressure boundary condition of 101,325 Pa was applied to the top of the geometry. The inlet flow boundary condition was identified as the critical influence on the formation, quantity, and size of the bubbles. Thus, four significantly different inlet flow conditions were modeled as shown in Fig. 4. The simplest and fastest operating model, referred to as the “uniform” model, had a uniform inlet flow boundary condition applied to all the cells at the bottom of the domain. The second model, referred to as the “discrete” model, has 25 discrete flow boundary conditions applied to the cells that line up best with the physical locations of the holes in the experimental distributor plate, displayed in Fig. 5. The total mass flow is divided evenly between all 25 discrete boundary conditions. The third model has the most complexity and is referenced as the “plenum” model. In this model, the entire plenum and distributor plate with each of the 25 individual holes are modeled, detailed by Fig. 6. This allows for the flow distribution between the holes in the distributor plate to be modeled dynamically, as well as the coupling of the fluid bed and plenum dynamics. The plenum model performed slowly because small cells with high velocity were needed to model the plenum holes which necessarily drove the allowable time step down. While this is truly the most accurate way to model the system, computationally it is by far the most costly. In an attempt to achieve

Individual hole Fig. 6. Plenum model grid at the distributor plate.

J.M. Weber et al. / Powder Technology 250 (2013) 138–146

similar results in a more timely fashion, a fourth model was developed referred to as the “jets” model. In this model, the flow boundary was represented by twenty five fluid injectors which were grouped into four sets according to their radial distances from the center of the plate. The velocity profile assigned to the groups of jets was calculated from the time averaged velocity profile from the plenum model shown in Fig. 7. The jets within each group had the same mass flow rate and velocity. The grid dimensions, cell counts, particle counts, computation time and average time steps are detailed in Table 1. In addition to the small cells driving the time step down, another issue with the grid resolution is exacerbated in the plenum model where there are smaller cells connected to significantly larger cells. There is a lack of grid resolution to resolve the individual jets at each of the distributor plate holes within the fluid field. Thus, there is a considerable amount of numerical diffusion, illustrated in Fig. 8, causing the jets to prematurely dissipate into the bottom of the bed. That said, resolving each of these jets would require a pronounced increase in the number of cells, bringing the simulation to a halt. For example, doubling the cell count on the horizontal axis caused the computation time to be reduced to 0.1 s/day which was too costly for the time available in this study. 4. Hydrodynamic model results and discussion 4.1. Gas velocity The four models provide significantly different boundaries at the bottom of the fluidized bed, specifically the gas velocity and distribution. At a selected instance in time for the Ug/Umf = 4condition, the uniform model shows a completely uniform velocity field at the bottom of the bed in Fig. 9. The discrete model has a non-uniform behavior with a peak average velocity of 2.2 m/s. Not surprisingly, the plenum model has a large amount of non-uniform behavior with an average maximum velocity through the inner ring of orifices of 45.7 m/s, as compared to the outer ring of orifices with an average velocity of 22 m/s. However, only two cells in the bed from the orifices, the velocity quickly was reduced to an average maximum velocity of 1.7 m/s. This rapid decrease in velocity is most likely due to the area difference between the orifice sizes and the adjacent cells. The jets model shows a very similar profile

Fig. 7. Injector distribution in the Jets model.

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Table 1 Summary of the three models developed in this paper. Note: “Fluid cells” is the number of cells that actually have fluid or particles in them. Also, “Clouds” are the total number of Barracuda's particle clouds used in the simulation. Finally, k = thousand and M = million. Model

Grid

Cells (fluid)

Particles (clouds)

Computation time

Average time step

Uniform Discrete Plenum Jets

20 × 20 × 65 23 × 23 × 65 22 × 22 × 107 23 × 23 × 64

26 k (22 k) 34 k (28 k) 52 k (45 k) 33 K (30 k)

61 M (0.5 M) 62 M (0.6 M) 62 M (0.8 M) 62 M (0.6 M)

63.5 s/day 21.7 s/day 0.98 s/day 29.9 s/day

2.98 × 10−3 s 2.24 × 10−3 s 4.01 × 10−5 s 2.80 × 10−3 s

to that of the plenum model because the input of the point source jet groups was calculated based on the plenum gas profile. The differences are due to the flow dynamics in the first row of cells. If the assumption is made that the gas is evenly distributed through each orifice, a velocity of 20.8 m/s is expected through each orifice, which is larger than the uniform and discrete models, as well as significantly less than the plenum model. The difference between the plenum model and the experimental system is due to the difference in cross-sectional areas. The orifices in the plenum model have a total area of 0.31 cm2, as compared to the experimental distributor's equaled to 0.49 cm2. The cause of this variation in area is associated to the gridding of the orifices. Four cells with a triangular cross-section are used to grid each circular orifice creating a square circumscribed in a circle. For the plenum model, if the flow is evenly distributed between all the orifices, an average velocity of 33.2 m/s is anticipated. The advantage of the plenum model is that it calculates the flow through each of the individual distributor plate holes, allowing for a dynamic coupling between the fluidized bed and the plenum chamber. Consequently, the total flow through the distributor plate is not constant and is calculated during the simulation, as shown in Fig. 10. Also, the dispersion of flow between the distributor plate holes is calculated dynamically, allowing for each hole to have a different flow rate, detailed by Fig. 11. Looking at a slice through the middle of the plenum model in Fig. 12, the model predicts that the inlet flow into the plenum stays intact, impinging on the distributor plate. This causes the flow through the center orifices to be higher than the orifices near the wall. 4.2. Solid fraction The ECVT allows for quantitative comparisons of the solid fraction between the experimental data and the models, both dynamic and time averaged. By qualitatively comparing the four models to the ECVT measurement at an instance in time, it is evident that the uniform and discrete models do not align well with the ECVT data, present in Fig. 13. Once the uniform model achieves steady state, the bed only forms small bubbles near the surface with uniform waves of lower solid fraction moving through the rest of the bed. The discrete model produces small bubbles that are mirrored about the center of the bed. The plenum model, and subsequently the jets model, seem to exhibit similar behavior as the ECVT, with large bubbles rising through the center of the bed. The plenum and jets models also exhibit vertical bubble coalescence. Both models appear to develop a pattern of one large bubble moving up through the bed with several smaller bubbles in the wake of the larger bubble until the smaller bubbles eventually coalesce with the large bubble. This pattern is also seen in the ECVT data. By qualitatively comparing a series of frames between the plenum model and ECVT data in Fig. 14, it suggests as if both the plenum and jets models are accurately capturing the bubble behavior as measured by the ECVT. By comparing the time averaged solid fraction of the four models to the ECVT measurement at a slice through the center of the bed, it can be quickly seen that there are significant differences, detailed by Fig. 15. The uniform model is essentially uniform through the entire bed with solids fractions only varying between 0.58 and 0.55, except at the top

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Z

Fig. 8. Plenum model's grid surrounding selected distributor holes, as colored by velocity in the Z direction.

of the bed. The discrete model shows a symmetric behavior about the centerline with the bubble tracks clearly visible, which do not agree with the ECVT measurement. The plenum and jets models preferably agree with the ECVT results, depicting a similar central area of low solid fraction with higher solid fraction at the walls. However, looking quantitatively at the solid fractions, it is evident that the plenum and jets models do not exactly match the ECVT measurement. Fig. 16 compares the solid fraction of the four models to the ECVT data at a height of 10.9 cm from the distributor plate. This comparison iterates that the uniform and discrete models differ significantly from the ECVT. The plenum model has a similar shape to the ECVT, despite the center region where the bubbles pass through being significantly narrower than the ECVT. The jets model accurately achieves the general shape; however, it maintains a higher solids fraction across the profile.

2.5 Plenum Model

Velocity [m/s]

2

Looking at the solid fraction profiles at a height of 18.4 cm from the distributor plate shows a similar trend as the 10.9 cm location in Fig. 17. Finally, comparing the solids fractions near the top of the bed at a height of 25.9 cm from the distributor plate once again shows a similar trend as the other two heights in Fig. 18. Nevertheless, the plenum model and jets models are much closer to the ECVT measurement at the center of the bed. Quite interestingly, at the top of the bed, the plenum and jets models are not symmetric about the center of the bed. Fig. 19 compares the radially averaged solid fraction as a function of height from the distributor plate between the four models and the ECVT measurement. All four models are consistent with each other except at the distributor plate. The models and the ECVT measurement do not agree well. The models maintain approximately 20% higher solid fractions than the ECVT measurement. This is consistent with the radial profiles where the models solid fractions are consistently higher than the ECVT measurement. From these profiles, it is possible to deduce the expanded bed heights by identifying the maximum change in slope near the top of the bed. The model bed heights range from 28.2 to 29.6cm, as compared to the experimental bed height of 32.6 cm, Table 2. The differences in bed heights between the models and the experiment are consistent with the models over predicting the solid fractions.

Jets Model

1.5

Discrete

4.3. Pressure

1 Uniform

0.5 0 -0.05

-0.03

-0.01

0.01

0.03

Pressure drops across the bed and where applicable, across the distributor plate are compared between the four models and the experiment, Table 3. The pressure drop across the bed should be dominated by the bed weight, neglecting other contributions to pressure.

0.05

Radius [m] Fig. 9. Velocity distributions at the centerline of the domain.

0.1 0.09 Radius

Mass Flow [g/s]

1.60

Mass Flow [g/s]

1.55 1.50 1.45 1.40 1.35 1.30

-3.675 -2.45

0.07

-1.225 0

0.06

1.225

0.05

2.45 3.675

0.04 0.03

1.25 1.20 10.0

0.08

0.02 10.0 10.2

10.4

10.6

10.8

11.0

10.2

10.4

10.6

10.8

11.0

Time [s]

Time [s] Fig. 10. A one second window of the total mass flow passing through the distributor.

Fig. 11. A one second window of the mass flow through seven individually selected orifices at the centerline.

J.M. Weber et al. / Powder Technology 250 (2013) 138–146

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models. This difference suggests that there is a dynamic in the experiment which contributes to larger bubble formation that is not captured in the models. It is also possible that this low frequency response is correlated to the average bubble width. 4.4. Model discussion

Fig. 12. Velocity field at the centerline of the plenum. Note. Vector lengths are on a log scale.

Therefore, it is not surprising that the pressure drop estimated from the bed mass of 3994 Pa by using Eq. (1), where m is the bed mass, g is acceleration due to gravity, and A is the bed cross sectional area, is very close to the experimental and model measurements. However, for some reason, the plenum model's pressure drop across the bed is approximately 300 Pa lower than the other three models. ΔP ¼

mg : A

ð1Þ

By calculating fast Fourier transforms on the pressure measurements from the experiment and models, quantitative comparisons of the dynamics can be made. A Hanning windowed fast Fourier transform was calculated for both of the experimental pressure measurements, Fig. 20, as well as the plenum, Fig. 21, and jets models, Fig. 22. Looking at the frequency response of the experiment, the dominate frequency across the bed is 1.9 Hz, while the dominate frequency across the distributor plate is 5 Hz. Surprisingly, the plenum model predicts a dominant frequency across the bed of 2 Hz, however, the dominate frequency across the distributor plate is 9 Hz. The jets model has a dominate frequency of 3.2 Hz across the bed. Furthermore, the experimental data shows significant frequency amplitude below 1 Hz which is not captured correctly by any of the

Uniform

Discrete

Reviewing the comparison between the four models and the experimental data for both pressure and ECVT measurements reveals the typical paradox of modeling complex systems. The more details incorporated into the computational model, the better the model. However, in order to incorporate these details, a significant penalty in performance is realized. Of the four “out of the box” models (uniform, discrete, plenum and jets), the plenum model compares best with the ECVT and transient pressure data, though it is the slowest model of all by far. The model also predicted a similar average solids fraction structure as measured by the ECVT, however not exactly matching. By using the gas distribution predicted by the plenum model and applying it to the jets model, a fairly comparable, fast operating model was developed. The jets model effectively operates 100 times faster than the plenum model. Out of all the models, the jets model compares best with the time averaged solid fraction, unfortunately, it does not accurately predict the transient pressure dynamics. What is clearly evident is the typical application of a uniform boundary condition to model a small fluidized bed that employs a perforated distributor plate is not accurate. The uniform model did not exhibit comparable bubble formation. Subsequently, the model also did not predict the average solid fraction correctly or any pressure dynamics. These comparisons lead to the conclusion that accurately modeling the distributor plate is critical to achieving accurate simulation results. The results also show that in order to achieve the correct dominate bubble frequency, the entire plenum chamber should also be included in the model since the air distribution can vary both in time and space. This result is similar to several other studies including a purely experimental case where the plenum chamber volume was varied, effecting the bed hydrodynamics [27], as well as several modeling papers [28,29], showing a strong coupling between the bed hydrodynamics and the plenum chamber. 5. Conclusion By comparing the physical measurements of the ECVT and pressure transducers to the CFD models, it is evident that depending upon how the distributor plate boundary condition is handled, the models can predict certain aspects of the fluidized system. However, the flow

Plenum

Jets

ECVT

Fig. 13. Typical solid fractions at an instance in time of the four models and the ECVT measurement at the center of the domain at a gas velocity of 4 ∗ Umf.

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Plenum Model ECVT Imaging Area

ECVT Fig. 14. Series of frames comparing the ECVT data to the plenum model at a gas velocity of 4 ∗ Umf.

Uniform

Discrete

Plenum

Jets

ECVT

Fig. 15. Time average solid fraction of the four models and the ECVT measurement at the center of the domain at a gas velocity of 4 ∗ Umf.

For this relatively simple case, as compared to an industrial scale process, the CFD model does well if enough details from the physical experiment are incorporated. The typical paradox between the predictive quality of a CFD model and the computational time is alive and well. Disclaimer This report was prepared as an account of a work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein

0.7

0.7

0.65

0.65

0.6 ECVT

0.55

Uniform

0.5

Discrete

0.45

Plenum

0.4

Jets

0.6 ECVT

0.55

Uniform

0.5

Discrete

0.45

Plenum

0.4

Jets

0.35

0.35 0.3 -6

Solid Fraction [-]

Solid Fraction [-]

distribution of the distributor plate is extremely important, especially in this specific system due to the small bed diameter and because the pressure drop across the distributor plate is only 24% of the pressure drop across the fluidized bed which is below the typical “rule of thumb” of 30% for good flow distribution. The non-uniformity of the gas distribution can be seen both experimentally in the ECVT images as well as computationally in the plenum model. Thus, for this experiment, the application of a uniform boundary condition, which is typically used in fluid bed modeling, is not applicable. It is recommended that if a perforated distributor plate is used, and non-uniformity of the gas distribution could be a reality, a model should be developed to predict this flow distribution. In order to develop a fast running CFD model, the predicted flow distribution can then be applied to individual injectors with reasonable results.

-4

-2

0

2

4

6

Radius [cm] Fig. 16. Time averaged solid fraction of the four models and the ECVT measurement at the center line at a height of 10.9 cm form the distributor plate.

0.3 -6

-4

-2

0

2

4

6

Radius [cm] Fig. 17. Time averaged solid fraction of the four models and the ECVT measurement at the center line at a height of 18.4 cm form the distributor plate.

J.M. Weber et al. / Powder Technology 250 (2013) 138–146

Solid Fraction [-]

0.65 0.6 ECVT

0.55

Uniform

0.5

Discrete

0.45 Plenum

0.4

Normalized Amplitude

0.7

Jets

145

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Distributor Bed Dist Mov Avg Bed Mov Avg

0

0.35

2

4

6

8

10

12

14

Frequency [Hz]

0.3 -6

-4

-2

0

2

4

6

Fig. 20. Frequency response of ΔP across distributor plate and fluidized bed. A 20 point moving average is also displayed.

Radius [cm]

Normalized Amplitude

Fig. 18. Time averaged solid fraction of the four models and the ECVT measurement at the center line at a height of 25.9 cm form the distributor plate.

35 30

Height [cm]

25 ECVT

20 Uniform

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Distributor Bed Dist Mov Avg Bed Mov Avg

0

2

4

Discrete

15

6

8

10

12

14

Frequency [Hz]

Plenum

10

Fig. 21. Plenum model frequency response of ΔP across distributor plate and fluidized bed. A 20 point moving average is also displayed.

Jets

0 0.3

0.4

0.5

0.6

Solid Fraction [-] Fig. 19. Radially averaged solid fraction profile, distributor plate is at a height of 0 cm.

to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

Table 2 Comparison of the expanded bed heights between the experiment and models. All values have units of centimeters.

Normalized Amplitude

5 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Bed Bed Mov Avg

0

2

4

6

8

10

12

14

Frequency [Hz] Fig. 22. Jets model frequency response of ΔP across the fluidized bed. A 20 point moving average is also displayed.

References

Models Experiment

Uniform

Discrete

Plenum

Jets

32.6

29.6

28.2

29.6

28.2

Table 3 Comparison of pressure measurements between the experiment and models. All values have units of Pascals. Models

Distributor Bed

Experiment

Uniform

Discrete

Plenum

Jets

931 3880

NA 3982

NA 3963

1115 3652

NA 3996

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