Interaction between a Fluidized Bed and Its Air-Supply System: Some

Jul 9, 2004 - fluctuations measured in the bed and the air plenum. 1. Introduction ..... 1.6 Hz) observed in the bed by pressure measurements and the ...
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Ind. Eng. Chem. Res. 2004, 43, 5730-5737

Interaction between a Fluidized Bed and Its Air-Supply System: Some Observations Srdjan Sasic, Filip Johnsson, and Bo Leckner* Department of Energy Conversion, Chalmers University of Technology, S-412 96 Go¨ teborg, Sweden

The interaction between a fluidized bed and its air-supply system was studied in a cold oneninth-scale model of a 12-MWth circulating-fluidized-bed (CFB) boiler and in a 0.7 × 0.12 × 8.5 m cold unit. Simultaneous measurements were carried out of pressure fluctuations in the bed and in the air plenum; of flow fluctuations in the air-supply ducts; and in the scale model, of bubble dynamics by an optical probe. It is shown that the fluid dynamics of the bed, represented by power spectra of pressure fluctuations in the bed and in the air plenum, depend significantly on the configuration of the air-supply system. In the scale model, three modes of bubble flow were identified: (1) the single-bubble regime, with the presence of one bubble at a time in the bed and with an interaction between the bed and the air-supply system at the bubble frequency; (2) a regime in which single bubbles still dominate the spectrum but another type of structure becomes significant at a frequency of its own (so-called exploding bubbles); (3) a regime in which exploding bubbles, acting as irregular voids stretching from the air distributor to the bed surface, dominate the spectrum and the bed is almost decoupled from the air-supply system. The cold CFB unit was operated at low velocity, either in the single-bubble regime or in a regime with numerous irregular bubbles, or at high velocity, in the exploding-bubble regime, with the same dominant frequency as for the single-bubble regime (the interaction with the air-supply system remains at that frequency). Pressure waves, resulting from the formation and eruption of bubbles, are identified as the main cause for the interaction between the bed and the air-supply system. These waves are recognized as the coherent part of the cross power spectra of pressure and flow fluctuations measured in the bed and the air plenum. 1. Introduction To reduce the cost of fan power, commercial fluidizedbed boilers, and sometimes also other fluidization equipment, are operated with low-pressure-drop air (or gas) distributors. Also, most practical air-supply systems have considerable lengths and volumes. Combined, these features enable propagation of pressure and flow waves throughout the entire system. This means that a coupled system is formed, consisting of the fluidized bed, air plenum, pipes, valves, and fan. Hence, the layout of the air-supply system can influence the fluidization behavior of the bed. Investigations1-3 show that the fluidized-bed dynamics are influenced by the design of the air distributor. Those studies were mainly focused on the quality of fluidization and provide no information on the interaction with the remaining part of the system. Moritomi et al.4 investigated the pressure response in the air plenum from imposed flow oscillations originating from the air-supply system. A strong correlation between bed and system was found. Svensson et al.5 studied the interaction between pressure fluctuations in the bed and air plenum by changing the pressure drop of the air distributor and the fluidization velocity in a cold circulating-fluidized-bed (CFB) unit. With a high airdistributor pressure drop, there was almost no interaction between the pressure fluctuations in the bed and the air plenum, whereas for low air-distributor pressure * To whom correspondence should be addressed. Tel.: +46 31 772 1431. Fax: +46 31 772 3592. E-mail: ble@ entek.chalmers.se.

drops, a clear interaction was found. Similar results were obtained by Johnsson et al.6 in a CFB boiler, where pressure fluctuations were recorded simultaneously in five positions in the system (three of them were in the air-supply system). Peirano et al.7 studied numerically the coupling between the bed and the air-supply system by introducing the air plenum in the computational domain. Because Peirano et al. experienced a lack of agreement with experimental data in the case of a lowpressure-drop air distributor, they concluded that, in such a case, the entire air-supply system should be included in the simulations. Johnsson et al.8 modeled pressure and flow fluctuations from the air-supply system by solving the continuity and momentum equations of the air flow and found the in-bed dynamics and flow fluctuations to be strongly linked. They concluded that modeling of the behavior of fluidized beds in industrial units should include information from the entire air-supply system, unless the pressure drop of the air distributor is high enough to decouple the bed and the air-supply system. In summary, the above-cited works identified three cases of interactions between the bed and the air-supply system: (1) no interaction, occurring in systems with high-pressure-drop air distributors; (2) interaction with air plenum only; and (3) interaction with the entire air-supply system. The aim of this work is to give further experimental basis in support of cases 2 and 3 and to systemize the interaction behavior with respect to principal fluidization regimes. This work also aims to identify mechanisms responsible for the interactions between the bed and the air-supply system.

10.1021/ie049763b CCC: $27.50 © 2004 American Chemical Society Published on Web 07/09/2004

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Figure 2. Time-averaged pressure along the air-supply system (unit II). Pressure drops at valve 1 (left-hand diagrams) and at valve 2 (right-hand diagrams) and finally at the air distributor. Figure 1. Simplified sketch of the air-supply systems of the units: unit I (top), unit II (bottom).

2. Experiments This work comprises measurements of in-bed and airplenum pressures, together with flow fluctuations in the air-supply part of two fluidized-bed systems. The systems are designed to allow for variations of the configuration of the air-supply system, and they are outlined in Figure 1 with the operating conditions summarized in Table 1. Unit I is approximately scaled9,10 to model the dynamical behavior of a 12-MWth CFB boiler, but during the present investigation, the unit was operated under noncirculating conditions. Two lengths of airsupply tubes were investigated (L ) 1 and 25 m). Air was supplied to the system by a centrifugal fan. The air distributor was a perforated plate with 2-mm holes (3.5% open area), yielding a pressure drop similar to that of the boiler under similar operating conditions. Unit II is a relatively large cold CFB test rig. In this unit, experiments were performed under both noncirculating and circulating conditions. The flow can be controlled by a valve that is located either near the air plenum (a gate valve, valve 1) or upstream of the fan (a nozzle valve, valve 2), yielding one case with the active air-supply system consisting of the air plenum only (L ≈ 0) and one case with a long air-supply tube (L ) 30 m). The time-averaged pressure along the air-supply system (from the fan to the bottom of the bed) is shown in Figure 2 for the cases investigated. A radial, highpressure fan operated at constant speed was used for the air supply. The air distributor was a perforated plate with 2-mm holes and 6.2% open area. Simultaneous measurements of pressure fluctuations in the bed and the air plenum and of flow fluctuations in the air-supply

system were performed in both units. In unit I, the bubble dynamics were also studied by an optical probe. The probe is a reflective fiber-optical sensor for emitting and recording light. The sensor has an infrared LED (light-emitting diode) and a phototransistor integrated into a small unit (such sensors are normally used for barcode-reading devices). The pressure fluctuations were measured (Honeywell pressure transducers, type 143PC03D) at the walls at 18 mm (unit I) and 0.2 m (unit II) above the air distributor and in the air plenum. The sampling frequency was 200 Hz in unit I and 20 Hz in unit II (enough to capture the major frequency content in the fluidized beds). The inflow of air to the plenum was investigated by using a Pitot tube connected to a micromanometer (Furnace Control, FC014). 3. Basis of Interpretation Davidson11 modeled the air plenum and the bed in analogy with a harmonic oscillator. The fluidized bed is seen as a mass oscillating on top of an air-filled cavity (the air plenum). Several research groups have accepted this concept and also included the resistance at the air distributor4 and the air-supply system.12 In the present work, it is sufficient to express the frequency of the oscillations (undamped or damped) as

f)

x

1 2π

κPAbed FbedHbedVgss

(1)

This frequency will be compared with the measured spectra. All measured signals are characterized in the frequency domain by power spectra, obtained as an

Table 1. Experimental and Operating Conditions unit I (scale model), Figure 1

unit II (CFB unit), Figure 1

temperature cross section (m x m) height of the unit (m) volume of the plenum (m3) volume of the air-supply tubes (m3) bed material particle diameter (mm) air feed system configuration

ambient 0.19 × 0.17 1.5 0.004 0.0016-0.02 bronze 0.10 L ) 1 and 25 m

fluidization velocity (m/s) minimum fluidization velocity (m/s) Terminal velocity of a single particle (m/s) flux of solids [kg/(m2 s)]

0.18, 0.37, 0.73 0.026 1.6 0

air-distributor pressure drop, ∆pdist (Pa) bed pressure drop, ∆pfb (Pa)

400, 520, 1000 2500

ambient 0.12 × 0.7 8.5 0.45 0-2.43 silica sand 0.32 flow control (by valves 1 and 2) near plenum (L ≈ 0) and upstream of fan (L ) 30 m) 0.80, 2.20 0.085 2.0 noncirculating conditions: 0 circulating conditions: ∼1 1000, 3200 5100

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Figure 3. Unit I. U ) 0.18 m/s. (a) Power spectra of pressure fluctuations in the bed and in the air plenum and of ∆p from the Pitot tube and the signal from the optical probe at L ) 1 m. (b) Power spectra of pressure fluctuations in the air plenum from L ) 1 and 25 m. The arrows indicate calculated (eq 1) fundamental frequencies with air-supply ducts of 1 and 25 m.

average from a number of subspectra (the number being chosen to obtain a good tradeoff between frequency resolution and statistical significance). In unit I, the power spectral density (PSD) and coherence were calculated for each data set of 1024 points, whereas in unit II, each set contained 512 points. In both units, the total duration of each run was 240 s. van der Schaaf et al.13 proposed a method to quantify the phenomena present in pressure time series recorded in a fluidized bed. The coherence between measurement positions was introduced

Cxy(f) )

Pxy(f) P/xy(f) , 0 e Cxy(f) e 1 Pxx(f) Pyy(f)

(2)

The power (Pyy) of the time series, measured at position y in the bed, is related to the time series measured in the air plenum (x) and expressed as the sum of the coherent (COPxy) and incoherent (IOPxy) parts as

Pyy(f ) ) COPxy(f) + IOPxy(f)

(3)

COPxy(f) ) CxyPyy

(4)

IOPxy(f) ) (1 - Cxy)Pyy

(5)

with

The coherent part of a power spectrum identifies pressure waves originating in the bed and possibly

Figure 4. Unit I. U ) 0.37 m/s. (a) Power spectra of pressure fluctuations in the bed and in the air plenum and of ∆p from the Pitot tube and the signal from the optical probe at L ) 1 m. (b) Power spectra of pressure fluctuations in the air plenum from L ) 1 and 25 m. The arrows indicate calculated (eq 1) fundamental frequencies with air-supply ducts of 1 and 25 m.

propagating through the entire system, whereas the incoherent part expresses the effect of local events in the bed (gas voids and turbulence). 4. Results Figures 3-5 show frequency spectra from unit I, operated with bronze particles and fluidization velocities of 0.18, 0.37, and 0.73 m/s. At low velocity and low pressure drop across the air distributor, one identifies a regime termed the single-bubble regime.5 A pistonlike movement of the bed as a whole and a strong periodicity in the formation and eruption of bubbles are observed. The bubble rises through the center of the bed. Figure 3a reveals that the dominant frequencies (the center point of the spectrum) of the pressure signals in the bed and the air plenum are identical and that they coincide with the inflow to the air plenum (denoted “tube”) and the optical probe: the pressure and flow fluctuations are accompanied by the movement of the bubbles. The influence of the configuration of the airsupply system during this regime is shown in Figure 3b, with only pressure fluctuations in the air plenum being presented because the dominant frequencies of all signals were identical. It is observed that the dominant frequency in the case of the longer air-supply tube (25 m) is somewhat lower than that with the shorter tube (1 m). When the gas velocity is increased to 0.37 m/s, the character of fluidization becomes more complex. Above the air distributor, there is a large number of small bubbles growing rapidly in size, yielding large pockets

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Figure 5. Unit I. U ) 0.73 m/s. (a) Power spectra of pressure fluctuations in the bed and in the air plenum and of ∆p from the Pitot tube and the signal from the optical probe at L ) 1 m. (b) Power spectra of pressure fluctuations in the air plenum from L ) 1 and 25 m.

of gas in the bed. The cross section of unit I is large enough for slugging not to occur. Figure 4a shows that the pressure fluctuations in the bed give a peak at approximately 1.6 Hz (not seen at 0.18 m/s). It is likely that this peak represents the so-called exploding bubbles.5 This explanation is further confirmed by spectral analysis of the optical probe signal, which gives a dominant peak at the same frequency, indicating that large voids of air are present in the bed. The peak at 1.6 Hz is not found in the air plenum or in the fluctuations of the air-supply tube. The high-frequency content of the signals, on the other hand, is similar to that of the single-bubble regime at 0.18 m/s and is present in all signals recorded but with a somewhat wider frequency distribution. Figure 4b illustrates that the pressure fluctuations in the air plenum lack almost all traces of the peak at 1.6 Hz but show the same shift of the dominant frequency when the pipe length is increased as experienced in the single-bubble regime (Figure 3b). Finally, when the gas velocity is increased to 0.73 m/s, large structures below 2 Hz dominate the signals (Figure 5a). The high-frequency content is still present and significant. The increased energy of the optical probe signal indicates that the exploding bubbles grow in size as the gas velocity increases. The position of the peak does not change with the change in velocity. Figure 5b shows that there is no clear difference in the distribution of the frequency content of the pressure fluctuations in the air plenum between the two lengths of the air-supply system. Again, the strong signal (at 1.6 Hz) observed in the bed by pressure measurements and the optical probe is not found in the air plenum.

Figure 6. Unit II, L ) 0 m, U ) 0.80 m/s. Power spectra of (a) pressure fluctuations, (b) flow fluctuations.

Figures 6-11 show frequency spectra from unit II operated at two fluidization velocities and with two configurations of the air-supply system (four cases). At U ) 0.8 m/s and L ≈ 0 (the flow is controlled by valve 2, Figure 2), the single-bubble regime is unambiguously identified (Figure 6a). The flow fluctuations in the airsupply system (deduced from the velocity as measured by a Pitot tube) show a dominant peak at the same frequency as the pressure fluctuations in the bed and in the air plenum (1 Hz, Figure 6b). At the same velocity and L ) 30 m (flow controlled by valve 2 while valve 1 is fully open, Figure 2), it is not straightforward to recognize the fluidization regime (Figure 7a). Note that the vertical scale differs from that in Figure 6a. The dominant frequency in the bed decreases to approximately 0.5 Hz, whereas the pressure fluctuations in the air plenum show two peaks, one that coincides with the dominant frequency in the bed (0.5 Hz) and one around 3 Hz that is not readily noticed in the bed if linear scales are used on both axes. A weak impact was detected, however, as one can see on logarithmic scales. The peak at 3 Hz is, indeed, present in the bed but with a far lower energy than the 0.5-Hz peak (Figure 8a). The flow fluctuations show peaks that coincide with the dominant frequencies identified above (0.5 and 3 Hz) in Figure 7b (or Figure 8b). Because the natural frequency of the duct is estimated to be around 3 Hz, it is likely that the corresponding frequency content in the air plenum and to some extent in the bed represents the effects of the air-supply system. In this regime, one observes that the bubbles are not as large as in the single-bubble regime and also that they are less uniform, despite the equality in fluidization velocity. At U ) 2.2 m/s and L ≈ 0, bubbles of an exploding character, extended vertically

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Figure 7. Unit II, L ) 30 m, U ) 0.80 m/s. Power spectra of (a) pressure fluctuations, (b) flow fluctuations.

all the way from the air distributor to the surface of the bed, dominate the flow field. A large portion of gas is in the form of a high throughflow, dominant over the gas flow in the particulate phase and the visible bubble flow.14 The dominant frequency in the in-bed and airplenum pressure fluctuations (Figure 9a) coincides with that observed in the single-bubble regime (1 Hz). The same can be said for the flow fluctuations in the airsupply system (Figure 9b). Finally, at U ) 2.2 m/s and L ) 30 m, the dominant frequency of the pressure fluctuations in the bed and in the air plenum remains at 1 Hz (i.e., it is not changed with a change of the configuration of the air-supply system, as in the lowvelocity case). The fluctuations in the air plenum show the presence of another peak at 3 Hz (Figure 10a), not seen in the bed, even on logarithmic scales (Figure 11a). Figure 10b (or Figure 11b) illustrates that the flow fluctuations have the same frequency distribution as the pressure fluctuations recorded in the air plenum. Figure 12 summarizes the fluidization regimes in the units treated (presenting the dependence of the pressure drop over the air distributor on the fluidization velocity, normalized by the terminal velocity of a single particle). 5. Interpretation Results from the model (eq 1) applied to the cases treated and a comparison with the corresponding experimental results are summarized in Table 2 (unit I) and Table 3 (unit II). At relatively low fluidization velocities and low airdistributor pressure drops, both units operate in the single-bubble regime. Because of the periodic nature of this regime, the dominant frequency of the in-bed and

Figure 8. Unit II, L ) 30 m, U ) 0.80 m/s. Power spectra of (a) pressure fluctuations (logarithmic scales), (b) flow fluctuations (logarithmic scales).

air-plenum pressure fluctuations can be modeled as a simple harmonic oscillator. The bed frequency obtained by this model agrees with the measurements in both units at fairly low velocities (Figures 3a,b 6a, and 7a), although in unit II, a change of the length of the tube gives rise to a different fluidization situation (the presence of smaller irregular bubbles and a frequency shift). Although the correct dominant frequency is obtained using eq 1, the model does not provide a physical explanation of the mechanisms responsible for the interaction between the bed and the remaining part of the system. For this purpose, Baskakov et al.15 explained the coupling in terms of the creation of a pressure wave after the collapse of the bed (i.e., after the bubble eruption) and its propagation throughout the whole system, given that the resistance of the distributor is low. In this regime, pressure fluctuations in the bed and in the air-supply system are almost entirely coherent, according to the model presented in eqs 3-5. By increasing the gas velocity in unit I, a complex flow field consisting of large (exploding bubbles) and structures of small and intermediate size (bubbles related to pressure waves) is established (Figure 4a,b). The model (eq 1) successfully predicts the frequency of the dominant bubbles, whose behavior still follows that of a harmonic oscillator, but it does not predict the occurrence of exploding bubbles (1.6 Hz). This is not surprising because these bubbles are not connected to the air-supply system; their effect is observed only in the bed. Furthermore, it is not understood why these bubbles, according to the observations supported by the optical probe measurements, occur at that specific frequency. The frequency position of the peak representing the exploding bubbles does not depend on the

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Figure 9. Unit II, L ) 0 m, U ) 2.20 m/s. Power spectra of (a) pressure fluctuations, (b) flow fluctuations.

Figure 10. Unit II, L ) 30 m, U ) 2.20 m/s. Power spectra of (a) pressure fluctuations, (b) flow fluctuations.

fluidization velocity or the configuration of the airsupply system, and also, this peak is not observed in

Figure 11. Unit II, L ) 30 m, U ) 2.20 m/s. Power spectra of (a) pressure fluctuations (logarithmic scales), (b) flow fluctuations (logarithmic scales).

the power spectra of the air plenum and the air-supply system (Figure 4a). Equations 3-5 applied to this case show that, although the incoherent part dominates at 1.6 Hz, a certain coherent part is found at that frequency as well. The lack of interaction in the case of exploding bubbles can be explained by conceiving those bubbles as shortcuts of gas from the air distributor through the bed into the splash zone, and no significant pressure wave is thereby created. On the other hand, the pressure waves, represented by the higher-frequency content, are felt throughout the entire system, although they are affected by damping in the system. Again, as shown in the lower-velocity case, the peak representing pressure waves is displaced with the change of the configuration of the air-supply system because of the different resonance volumes below the bed (Figure 4b). In addition to bubble eruption, which was identified as the cause for pressure waves in the single-bubble regime, bubble formation now also makes a significant contribution to the waves. In unit II, at U ) 2.2 m/s and L ≈ 0, the model (eq 1) seems to yield the correct dominant frequency of the inbed pressure fluctuations (Table 3), although the fluidization regime and the air-distributor pressure drop deviate from the assumptions of the model. It seems that, in this case, the exploding bubbles simply occur at the same frequency as the single bubbles. Calculation of the coherence between the bed and the air plenum supports the conclusions obtained on the basis of the power spectra (Figure 9a), but provides no further explanation of the event. At L ) 30 m, the fundamental frequency is not changed (Figure 10a), although the resonance volume now includes the volume of the air-

5736 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004 Table 2. Summary of Fundamental Frequencies, Measured and Calculated, for Unit I fluidization velocity (m/s):

0.18

0.37

length of duct (m):

1

25

fundamental frequency (Hz) (eq 1) fundamental frequency (Hz) (measured in the air plenum)

4.42 ∼4.5

4.05 ∼4.1

0.73

1

25

4.37 ∼4.5 and exploding bubbles in the bed (1.6 Hz)

4.01 ∼4.1 and exploding bubbles in the bed (1.6 Hz)

1

25

4.35 exploding bubbles dominate

4.00 exploding bubbles dominate

at any frequency that is significantly different from its own natural frequency. The experimental findings from the units treated in this work point out that, for a given fluidized bed, there exists a natural or fundamental frequency of the bed (the peak in the spectrum that also appears in the airplenum spectrum), such as has also been observed by Bi et al.16 Therefore, it seems that the volume of the plenum, combined with the length or volume of the supply tubes, is a key parameter in the interaction between the bed dynamics and the air-supply system. The dependence of the flow entering the bed (Qbed) on the flow entering the plenum (Qplenum) can be expressed, assuming small density and pressure [p(t)] variations in the plenum during a time ∆t, as

Qbed(t) ) Qplenum(t) -

Figure 12. Fluidization regimes in the units treated: (a) unit I, (b) unit II. Cases treated in this work are indicated by symbols. Table 3. Summary of Fundamental Frequencies, Measured and Calculated, for Unit II fluidization velocity (m/s): length of duct (m): fundamental frequency (Hz) (eq 1) fundamental frequency (Hz) (measured in the air plenum)

0.8

2.2

∼0

30

∼0

30

1.02

0.45

1.01

0.43

∼1

∼0.5

∼1

∼1

supply tubes. Therefore, the model (eq 1) becomes less suitable in this case as well (Table 3). Another important feature of unit II is the size of its air plenum compared to the size of the bed. The volume of the plenum is approximately 100 times larger in unit II than in unit I (with the cross section of the bed being only 3 times larger), and this makes the difference in interaction between the two duct lengths much greater in unit II than in unit I. At L ) 30 m and at both velocities used (0.8 and 2.2 m/s), the power spectra of the pressure fluctuations in the air plenum (and also flow fluctuations, Figures 7a,b and 10a,b) show two frequency peaks: the one that corresponds to the natural frequency of the bed (i.e., the frequency of the bubbles producing pressure waves) and the one that coincides with the natural frequency of the air-supply tubes. The latter is not present in the bed at high fluidization velocity (this is also confirmed by the analysis of the coherence between the air plenum and the bed). The hypothesis is that, in this case, a superposition of two effects takes place: First and probably dominant, the air-distributor pressure drop is high enough to reduce substantially the coupling at that frequency, and second, the bed “resists” the excitation

p(t) - p(t - ∆t) Vplenum (6) ∆t κp(t)

The larger the volume of the plenum (Vplenum), the larger the difference with respect to phase and amplitude between the flows to the plenum and to the bed. Therefore, the pressure and flow variations should be more pronounced in unit II than in unit I. In unit I, irrespective of the configuration of the air-supply system, the dynamics of the flow entering the plenum and the flow entering into the bed are almost the same. However, in both units, strong fluctuations in the flow entering the bed are expected. This differs from the assumption of constant inlet velocity made in most fluidized-bed studies. 6. Conclusions The interaction between a fluidized bed and its airsupply system has been studied in two different units provided with different configurations of air-supply systems. The units were operated in the laboratory under ambient conditions, and one of them was approximately scaled to model the behavior of a hot fluidized-bed boiler. Some general conclusions can be made. At low gas velocities and low pressure drops across the air distributor, single bubbles are observed, in agreement with previous experience. The bed interacts with the air-supply system at its fundamental frequency and produces pressure waves that propagate through the system. This behavior is well described by a simple harmonic oscillator that can also predict the effect of a change in the volume when longer air-supply ducts are applied. The fundamental frequency is noted also at higher fluidization velocities, even if the spectrum becomes wider (more bubbles are observed). The interaction between the bed and the air-supply system is clearly observed in this case as well. In the high-velocity range (closer to the terminal velocity), the bubbling behavior of the bed can be separated into the type of bubbles mentioned above (interacting with the air-supply system) and gaseous structures in the bed whose effects are not clearly

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observed in the air-supply system. The latter type of structures are the previously termed exploding bubbles. They constitute a gas bypass through the bed that is clearly noted by the optical probe and by the pressure transducers in the bed, but not by those in the air plenum and in the rest of the air-supply system. The waves are prevented from propagation only if the pressure drop over the air distributor is large enough to decouple the bed from its air-supply system (this means pressure drops on the order of magnitude of the pressure drop over the bed or greater). At all velocities, the position of the pressure peak that represents the exploding bubbles does not depend on the configuration of the air-supply system. The position (frequency) of exploding bubbles, however, cannot be predicted at present. The properties of exploding bubbles are not yet well understood, and in some cases, the exploding bubbles seem to be superimposed on normal bubbles, in which case they have the same frequency. The volume of the air-supply system (plenum and ducts) is an important parameter for the interaction. If the volume is large and if the pressure waves are enabled to propagate throughout the air-supply system, the power spectra of pressure fluctuations in the air plenum reflect both the waves from the bed and the effects from the air-supply ducts (at the same frequency as the natural frequency of the ducts). The latter fluctuations are not felt in the bed at high fluidization velocities. It is hypothesized that this is due to a combination of two effects: (1) the pressure drop caused by the increase of the fluidization velocity dampens the signals, and (2) to some extent, the bed resists excitation at any frequency deviating from its own natural frequency. Also, the tendency is that the greater the volumes of the system constituents, the more irregular the flow into the air plenum. This can cause a redistribution of bubble flow, at constant total (time-averaged) flow, between interacting (pressure waves) and noninteracting (exploding) bubble flow in the bed. This implies that, in the case of industrial fluidized-bed units with long airsupply tubes and relatively low air-distributor pressure drops, a uniform velocity profile should not be used as an inlet boundary condition for numerical simulations of the flow field. The details in the flow distribution over a gas distributor need to be studied further. Acknowledgment This work is financed by the Swedish National Energy Administration. Notation Abed ) bed cross-sectional area, m2 Cxy(f ) ) coherence between measurement positions f ) frequency, Hz Hbed ) bed height, m p, p(t) ) pressure, pressure in the plenum, Pa P ) average pressure in the air plenum (100 000 Pa) in eq 1 Pxx(f ), Pyy(f ) ) power spectral densities of pressure signals from the air plenum and the bed Pxy(f ) ) cross power spectral density ∆pad ) pressure drop at the air distributor, Pa ∆p ) dynamic pressure (Pitot tube), Pa

Qbed(t) ) flow into the bed, m3/s Qplenum(t) ) flow into the plenum, m3/s t, ∆t ) time, time interval, s U ) gas velocity (superficial), m/s Upt ) terminal velocity of a single particle, m/s Vgss ) volume of the air-supply system (air plenum and air-supply tubes), m3 Vplenum ) volume of the air plenum, m3 Greek Letters κ ) ratio of specific heats ) 1.4 Fbed ) average bed density, kg/m3

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Received for review March 25, 2004 Revised manuscript received May 8, 2004 Accepted May 11, 2004 IE049763B