(425e) Understanding the Origin of Pressure Oscillations in Fluidized Beds
AIChE Annual Meeting
2013
2013 AIChE Annual Meeting
Particle Technology Forum
Fundamentals of Fluidization II
Wednesday, November 6, 2013 - 9:58am to 10:20am
The origin of pressure
oscillations in fluidized beds has stood for a long time as a major question in
the understanding of two-phase granular flow. Pressure oscillations are
important to understand because they can easily be measured on fluidized beds
of all sizes and their relation to the passage of void regions has led to their
use in defining different flow regimes of fluidization [1]. While it has long
been understood that pressure oscillations correlate well with bubble passage
through fluidized beds, there has been contention as to whether pressure
oscillations are tied to bubble formation [2], coalescence [3], or eruption [4].
This paper compares detailed results from a recently developed computational
model [5] with experimental results [4] to shed light on the origin of pressure
oscillations in bubbling fluidized beds. A bubbling fluidized
bed with a diameter of Dbed
= 50 mm, filled with dp
= 1.2 mm diameter particles to various tapped bed heights, H0, was modelled computationally for direct comparison
to combined magnetic resonance (MR) imaging and pressure sensor experiments conducted
by Müller et al. [4] on
the same bed. A 3D cylindrical discrete element model with computational fluid
dynamics (DEM-CFD) described and validated for simulating bubbling fluidized
beds elsewhere [4] was used to model the fluidized bed. The bed was fluidized
at excess gas velocity (U-Umf) = 0.263 m/s for direct comparison of
model and experiment. Figure 1 shows
simulation results of the bed with initial height H0 = 40 mm over 275 ms of
steady bubbling. The first two rows show voidage (ε) and differential pressure drop
in the vertical direction (-dp/dz) maps of the bed every
25 ms. The third row gives the pressure drop across
the bed over the time period and the fourth row gives the 1D voidage traces at the bottom and top of the bed, capturing
bubble formation and eruption, respectively, with spikes in voidage.
The results show that bubbles form and erupt at the same frequency, since
bubbles form, rise and erupt without interacting with bubbles above or below
them in this short bed. Pressure drop occurs most rapidly in regions dense with
particles due to the drag force on these particles. Almost no pressure drop
occurs in the vertical region spanning from the bottom to the top of a bubble,
since the lack of particles in the bubble provides a free path through which
fluid can pass. The pressure drop across the entire bed is at a minimum when a
single, fully-formed bubble is rising through the bed because the bubble
provides a long path of low resistance for fluid. The pressure drop reaches a
maximum just as a bubble erupts because the free path for fluid disappears and
the fluid now has to pass through a tall region dense with particles. Figure 2 gives the same
sequence of simulation results of the same bed, except with initial height H0 = 50 mm, and voidage and differential pressure drop maps every 50 ms over a period of 550 ms. Approximately
every 260 ms, a large bubble forms and begins to
rise, spanning almost the entire diameter of the bed. Soon after, a smaller
bubble forms in its wake and rises more quickly behind the first large bubble.
The first bubble erupts, followed by the second in quick succession. The
pressure drop across the entire bed is at a minimum the entire time the first
bubble rises, but begins to increase dramatically as the first bubble erupts
since the free path for fluid created by this large bubble suddenly disappears.
The pressure drop reaches a maximum just as the second bubble erupts, since the
next large bubble has not formed yet and the bed is left with a large height of
dense particles, through which fluid must pass. Table 1 gives the
frequency of oscillations in pressure drop, bubble formation and bubble
eruption for various bed heights, determined by taking the Fourier transform of
the respective traces shown in the third and fourth rows of Figures 1 and 2 over
2.1 seconds of steady bubbling. In the 40 mm tall bed, bubble formation,
eruption and pressure oscillations all occur at the same frequency, since the
bubbles do not interact, and thus the same particle arrangements which create
easy and difficult paths for fluid passage occur for every bubble formed. In
the 50 mm tall bed, the frequency of bubble formation is twice that of bubble
eruption and pressure oscillations. Even though the bubbles do not fully
coalesce, they strongly interact, causing the arrangement of particles around
the first bubble to be vastly different from the second. Since, due to drag,
arrangements sparse in particles allow for little pressure drop over a vertical
distance and arrangements dense in particles create large pressure drops,
maxima in pressure drop occur only once for every two bubbles formed. While the
bubbles do not erupt at exactly the same time, the second bubble erupts in the
wake of the first eruption, causing the frequency of the oscillations of the voidage trace at the top of the bed to be half of that at
the bottom. The results for the
four bed heights in Table 1 demonstrate H0
= 50 mm to be a critical height at which two consecutive bubbles begin to
interact, and thus the frequency of bubble eruption and pressure oscillations
suddenly half, deviating significantly from the frequency of bubble formation. This
result matches well with experiments conducted on the same bed [4], which
showed a sudden decrease in bubble eruption and pressure oscillation frequency
at H0 = 50 mm, as shown in
Table 1. Finding the same frequency of bubble eruption and pressure oscillation
beds with H0 ranging from
20-161 mm, but vastly different frequencies of bubble formation in beds 50 mm
or taller, Müller
et al. [4] postulate that pressure
oscillations in fluidized beds are derived from bubble eruption. The detailed
results provided by the DEM-CFD simulations show that maxima in pressure drop
across narrow fluidized beds occur just after bubble eruption due to the large
height of dense particles left behind by the bubbles. Müller et al. [4] also found that the
transition point in pressure fluctuations occurred at a bed height at which the
theoretical value for effective bubble diameter, De, became large enough that the bed entered the
slugging regime, defined as De/Dbed > 0.6. This hypothesis is confirmed by DEM-CFD results,
shown in Table 1, which saw a drastic increase in average De, with the bed entering the slugging regime between H0 = 40 mm and H0 = 50 mm. This paper will further investigate the origin of pressure
oscillations in fluidized beds by using the DEM-CFD model to look at pressure
oscillations in beds ranging from 30-156 mm in tapped bed height and further comparing
to the results of Müller et al. [4]. Investigating
this larger range of heights will provide understanding on how bubble
coalescence and a variety of types of slugging affect pressure oscillations. References: [1] Bi, H.T. (2007). Chem. Eng. Sci., 62, 3473-3493.
[2] Fan, L.T.,
Ho, T., Hiraoka, S. and Walawender,
W.P. (1981). AIChE J., 27, 388-396. [3] Littman, H.
and Homolka, G. (1973). Chem. Eng. Sci., 28, 2231-2243. [4] Müller,
C.R., Davidson, J.F., Dennis, J.S., Fennell, P.F., Gladden, L.F., Hayhurst, A.N., Mantle, M.D., Rees, A.C., Sederman, A.J. (2007). Powder Technol., 177, 87-98. [5] Boyce, C.M., Holland, D.J., Scott, S.A., Dennis,
J.S. (submitted 2013). Phys. Rev. E. Figures:
Figure 1.
Analysis of pressure oscillations in a fluidized bed with H0 = 40 mm and Dbed = 50 mm. Over 275 ms
this figure gives: voidage maps (first row) and
differential pressure drop in the vertical direction maps (second row) every 25
ms, as well as traces of pressure drop across the
entire bed (third row) and 1-D voidage at the top and
bottom of the bed (fourth row).
Figure 2.
Analysis of pressure oscillations in a fluidized bed with H0 = 50 mm and Dbed = 50 mm. Over 550 ms
this figure gives: voidage maps (first row) and
differential pressure drop in the vertical direction maps (second row) every 50
ms, as well as traces of pressure drop across the
entire bed (third row) and 1-D voidage at the top and
bottom of the bed (fourth row). Tables: Table 1. Frequencies of bubble
formation (fform),
bubble eruption (ferupt)
and oscillations in pressure drop (fΔP), as well as the ratio of effective
bubble diameter to bed diameter (De/Dbed) in a 50 mm diameter bubbling fluidized
bed with varying tapped bed heights (H0).
The results are given for a DEM-CFD model as compared to experiments [4] using
a combination of magnetic resonance (MR) imaging and a pressure sensor.
oscillations in fluidized beds has stood for a long time as a major question in
the understanding of two-phase granular flow. Pressure oscillations are
important to understand because they can easily be measured on fluidized beds
of all sizes and their relation to the passage of void regions has led to their
use in defining different flow regimes of fluidization [1]. While it has long
been understood that pressure oscillations correlate well with bubble passage
through fluidized beds, there has been contention as to whether pressure
oscillations are tied to bubble formation [2], coalescence [3], or eruption [4].
This paper compares detailed results from a recently developed computational
model [5] with experimental results [4] to shed light on the origin of pressure
oscillations in bubbling fluidized beds. A bubbling fluidized
bed with a diameter of Dbed
= 50 mm, filled with dp
= 1.2 mm diameter particles to various tapped bed heights, H0, was modelled computationally for direct comparison
to combined magnetic resonance (MR) imaging and pressure sensor experiments conducted
by Müller et al. [4] on
the same bed. A 3D cylindrical discrete element model with computational fluid
dynamics (DEM-CFD) described and validated for simulating bubbling fluidized
beds elsewhere [4] was used to model the fluidized bed. The bed was fluidized
at excess gas velocity (U-Umf) = 0.263 m/s for direct comparison of
model and experiment. Figure 1 shows
simulation results of the bed with initial height H0 = 40 mm over 275 ms of
steady bubbling. The first two rows show voidage (ε) and differential pressure drop
in the vertical direction (-dp/dz) maps of the bed every
25 ms. The third row gives the pressure drop across
the bed over the time period and the fourth row gives the 1D voidage traces at the bottom and top of the bed, capturing
bubble formation and eruption, respectively, with spikes in voidage.
The results show that bubbles form and erupt at the same frequency, since
bubbles form, rise and erupt without interacting with bubbles above or below
them in this short bed. Pressure drop occurs most rapidly in regions dense with
particles due to the drag force on these particles. Almost no pressure drop
occurs in the vertical region spanning from the bottom to the top of a bubble,
since the lack of particles in the bubble provides a free path through which
fluid can pass. The pressure drop across the entire bed is at a minimum when a
single, fully-formed bubble is rising through the bed because the bubble
provides a long path of low resistance for fluid. The pressure drop reaches a
maximum just as a bubble erupts because the free path for fluid disappears and
the fluid now has to pass through a tall region dense with particles. Figure 2 gives the same
sequence of simulation results of the same bed, except with initial height H0 = 50 mm, and voidage and differential pressure drop maps every 50 ms over a period of 550 ms. Approximately
every 260 ms, a large bubble forms and begins to
rise, spanning almost the entire diameter of the bed. Soon after, a smaller
bubble forms in its wake and rises more quickly behind the first large bubble.
The first bubble erupts, followed by the second in quick succession. The
pressure drop across the entire bed is at a minimum the entire time the first
bubble rises, but begins to increase dramatically as the first bubble erupts
since the free path for fluid created by this large bubble suddenly disappears.
The pressure drop reaches a maximum just as the second bubble erupts, since the
next large bubble has not formed yet and the bed is left with a large height of
dense particles, through which fluid must pass. Table 1 gives the
frequency of oscillations in pressure drop, bubble formation and bubble
eruption for various bed heights, determined by taking the Fourier transform of
the respective traces shown in the third and fourth rows of Figures 1 and 2 over
2.1 seconds of steady bubbling. In the 40 mm tall bed, bubble formation,
eruption and pressure oscillations all occur at the same frequency, since the
bubbles do not interact, and thus the same particle arrangements which create
easy and difficult paths for fluid passage occur for every bubble formed. In
the 50 mm tall bed, the frequency of bubble formation is twice that of bubble
eruption and pressure oscillations. Even though the bubbles do not fully
coalesce, they strongly interact, causing the arrangement of particles around
the first bubble to be vastly different from the second. Since, due to drag,
arrangements sparse in particles allow for little pressure drop over a vertical
distance and arrangements dense in particles create large pressure drops,
maxima in pressure drop occur only once for every two bubbles formed. While the
bubbles do not erupt at exactly the same time, the second bubble erupts in the
wake of the first eruption, causing the frequency of the oscillations of the voidage trace at the top of the bed to be half of that at
the bottom. The results for the
four bed heights in Table 1 demonstrate H0
= 50 mm to be a critical height at which two consecutive bubbles begin to
interact, and thus the frequency of bubble eruption and pressure oscillations
suddenly half, deviating significantly from the frequency of bubble formation. This
result matches well with experiments conducted on the same bed [4], which
showed a sudden decrease in bubble eruption and pressure oscillation frequency
at H0 = 50 mm, as shown in
Table 1. Finding the same frequency of bubble eruption and pressure oscillation
beds with H0 ranging from
20-161 mm, but vastly different frequencies of bubble formation in beds 50 mm
or taller, Müller
et al. [4] postulate that pressure
oscillations in fluidized beds are derived from bubble eruption. The detailed
results provided by the DEM-CFD simulations show that maxima in pressure drop
across narrow fluidized beds occur just after bubble eruption due to the large
height of dense particles left behind by the bubbles. Müller et al. [4] also found that the
transition point in pressure fluctuations occurred at a bed height at which the
theoretical value for effective bubble diameter, De, became large enough that the bed entered the
slugging regime, defined as De/Dbed > 0.6. This hypothesis is confirmed by DEM-CFD results,
shown in Table 1, which saw a drastic increase in average De, with the bed entering the slugging regime between H0 = 40 mm and H0 = 50 mm. This paper will further investigate the origin of pressure
oscillations in fluidized beds by using the DEM-CFD model to look at pressure
oscillations in beds ranging from 30-156 mm in tapped bed height and further comparing
to the results of Müller et al. [4]. Investigating
this larger range of heights will provide understanding on how bubble
coalescence and a variety of types of slugging affect pressure oscillations. References: [1] Bi, H.T. (2007). Chem. Eng. Sci., 62, 3473-3493.
[2] Fan, L.T.,
Ho, T., Hiraoka, S. and Walawender,
W.P. (1981). AIChE J., 27, 388-396. [3] Littman, H.
and Homolka, G. (1973). Chem. Eng. Sci., 28, 2231-2243. [4] Müller,
C.R., Davidson, J.F., Dennis, J.S., Fennell, P.F., Gladden, L.F., Hayhurst, A.N., Mantle, M.D., Rees, A.C., Sederman, A.J. (2007). Powder Technol., 177, 87-98. [5] Boyce, C.M., Holland, D.J., Scott, S.A., Dennis,
J.S. (submitted 2013). Phys. Rev. E. Figures:
Figure 1.Analysis of pressure oscillations in a fluidized bed with H0 = 40 mm and Dbed = 50 mm. Over 275 ms
this figure gives: voidage maps (first row) and
differential pressure drop in the vertical direction maps (second row) every 25
ms, as well as traces of pressure drop across the
entire bed (third row) and 1-D voidage at the top and
bottom of the bed (fourth row).
Figure 2.Analysis of pressure oscillations in a fluidized bed with H0 = 50 mm and Dbed = 50 mm. Over 550 ms
this figure gives: voidage maps (first row) and
differential pressure drop in the vertical direction maps (second row) every 50
ms, as well as traces of pressure drop across the
entire bed (third row) and 1-D voidage at the top and
bottom of the bed (fourth row). Tables: Table 1. Frequencies of bubble
formation (fform),
bubble eruption (ferupt)
and oscillations in pressure drop (fΔP), as well as the ratio of effective
bubble diameter to bed diameter (De/Dbed) in a 50 mm diameter bubbling fluidized
bed with varying tapped bed heights (H0).
The results are given for a DEM-CFD model as compared to experiments [4] using
a combination of magnetic resonance (MR) imaging and a pressure sensor.
| DEM-CFD Results | Experimental Results | |||||
| H0 (mm) | fform (Hz) | ferupt (Hz) | fΔP (Hz) | De/Dbed | ferupt (Hz) | fΔP (Hz) |
| 30 | 6.96 | 6.96 | 6.96 | 0.41 | 6.4 | 6.0 |
| 40 | 7.12 | 7.14 | 7.15 | 0.44 | 5.6 | 5.5 |
| 50 | 7.42 | 3.73 | 3.72 | 0.66 | 2.9 | 3.0 |
| 60 | 7.57 | 3.75 | 3.79 | 0.65 | 2.9 | 3.1 |