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Influence of the nature of the Roots blower on pressure fluctuations in a fluidized bed
Powder Technology 127 (2002) 19 – 31 www.elsevier.com/locate/powtec
Influence of the nature of the Roots blower on pressure fluctuations in a fluidized bed Chien-Song Chyang *, Yen-Chin Lin Department of Chemical Engineering, Chung Yuan Christian University, Chung-Li 320, Taiwan, ROC Received 27 March 2001; received in revised form 6 June 2001; accepted 31 January 2002
Abstract Experiments were conducted in a 0.29-m I.D. fluidized-bed cold model with fluidizing air supplied by a Roots blower. To investigate the influence of the air-supply equipment on the pressure fluctuations, another experiment was carried out in a 0.10-m I.D. cold model with fluidizing air supplied by a compressor. In this work, the effects of superficial air velocity, static bed height and windbox volume were studied. The pressure pulsation frequency caused by the Roots blower was identified successfully from the pressure fluctuation frequency spectrum. This pulsation frequency was found to be related to the blower impeller rotary speed and exhibited a good linear relationship. The experimental results indicated that the blower possesses its own pressure pulsation frequency vs. superficial air velocity characteristic curve. At a given air flow rate, a larger-scale blower produced a lower pulsation frequency, higher pulsation intensity and a higher coefficient of variation for pressure fluctuations in the bed. With increasing superficial air velocity, the pulsation intensity abated and became less influential on the pressure fluctuations in the bed. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Pressure fluctuations; Pulsation; Roots blower; Fluidized bed; Windbox
1. Introduction 1.1. Background Numerous researchers implemented pressure fluctuation measurements to investigate the hydrodynamic behavior of fluidized beds. However, pressure fluctuations in a fluidized bed can be induced by various sources, such as bubbles, bed-height oscillations, the line configuration and even the air supply. The influence of the blower on the hydrodynamic behavior in a fluidized bed has been noted for decades. Botterill et al. [1] reported that the pulsed air flow resulted from the Roots blower affects the voidage of the packed bed and the shape of the bed pressure drop vs. air flow rate curve. The minimum fluidization velocity estimated using the pressure fluctuation method is affected by the blower characteristics. Geldart [2] stated that the pressure pulsations resulted from the blower can alter the fluidization behavior. Dhodapkar and Klinzing [3] also pointed out that the rotating lobes in Roots blower can cause pressure fluctuations. However, no signifi*
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cant evidence has been reported to confirm the extent of this influence on the pressure fluctuations in the fluidized bed. In order to avoid the destructive measurement within the bed and prevent the pressure probe from erosion or clogging by the bed material, some investigators have made the pressure fluctuation measurements in the windbox. Lirag and Littman [4] measured pressure fluctuations in both the bed and windbox and analyzed the signals using probability density, autocorrelation, and power spectral density functions. Baird and Kelein [5] detected the pressure fluctuations in the windbox to investigate the spontaneous oscillation of the gas-fluidized bed. Kage et al. [6,7] measured and analyzed pressure fluctuation data detected in the windbox using the power spectral density function. Wilkinson [8] calculated the standard deviation of the pressure fluctuations, rp, detected in the windbox to evaluate the minimum fluidization velocity, U mf , via the linear relationship between U and rp proposed by Puncˇocha´rˇ et al. [9]. Svensson et al. [10] conducted experiments in a 12 MWth Circulating Fluidized Bed (CFB) boiler and a cold CFB. They made comparisons between the frequency spectra obtained from the bed and windbox. From the research mentioned above, measuring pressure fluctuations in the windbox has been a trend.
0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 ( 0 2 ) 0 0 0 9 2 - X
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Am, density of 2540 kg/m3, subjected to Geldart Group B particles, were used as the bed material.
Fig. 1. The schematic diagram of the 0.29-m I.D. fluidized-bed cold model.
Moritomi et al. [11] recorded the pressure histories to investigate the influence of the pressure pulsation on the pressure fluctuations within the bed by mandatory adjustment on inlet air flow. It showed that the pressure responses could be classified in terms of both the inlet frequency and the gas flow rate. Instead of using the pressure record, the frequency spectral analysis by Fast Fourier Transform (FFT) was used in this work to investigate the influence of the Roots blower’s mechanical nature of air transport. Whether the measurements were conducted in the bed or windbox, the pressure fluctuations were probably influenced to some extent by the nature of the blower. To assess the blower influence on pressure fluctuations, measurements were made both in the bed and windbox in this work.
2.1.1. 0.29-m I.D. cold model The fluidized bed was fabricated with an acrylic column, 0.29 m in diameter and 1.0 m in height. A schematic diagram of the experimental apparatus is shown in Fig. 1. Twenty-two horizontal nozzles, 90j-bent carbon steel tubes with an inside diameter of 6.8 mm, were mounted on an 8mm-thick plate as a distributor. The horizontal nozzles were arranged in three concentric circles with all discharge exits directed clockwise, as shown in Fig. 2. The windbox, with a volume of V = 0.04 m3 (0.6-m high), was made of iron. In order to explore the windbox volume effect on the pressure fluctuations, windboxes with volumes of 0.5, 1.5 and 2V were used as well. Two Roots blowers, with a maximum air capacity rate of 10 and 15 Nm3/min, respectively, were used to estimate the blower scale effect. An orifice-plate flow meter was used to measure the fluidizing air flow rate. 2.1.2. 0.10-m I.D. cold model The fluidized bed was made of an acrylic column, 0.10 m in diameter, 0.74 m in height, and equipped with a porous plate as an air distributor. A 10-hp compressor was used to provide the fluidized air with the flow rate measured using a rotameter. This apparatus was employed only to explore the effect of the air-supply equipment. Most experiments were conducted in the 0.29-m I.D. cold model.
1.2. Principle of the Roots blower Two impellers, rotating in opposite directions, were installed inside a Roots blower case. The clearance between the impellers or the lobe and the case was extremely small, about 0.08 –0.3 mm. When the two impellers rotate, the inlet volume is enlarged to cause a low-pressure area to draw air in. When the impeller blade rotates, it forms a transient closed space with the case that traps a certain amount of air. As the impeller blade rotates to the outlet, the captured air is discharged from the blower. In this way, the air-transport process in the blower is completed.
2. Experimental 2.1. Apparatus Experiments were carried out in 0.29- and 0.10-m I.D. fluidized-bed models. Glass beads with a diameter of 545
Fig. 2. The illustration of the multi-horizontal nozzle distributor (top-view).
C.-S. Chyang, Y.-C. Lin / Powder Technology 127 (2002) 19–31 Table 1 Experimental conditions Experimental unit
0.29-m I.D. cold model *
0.10-m I.D. cold model
Air-supply equipment
Roots blower (1) 15-hp, Qmax = 10 Nm3/min * (2) 15-hp, Qmax = 15 Nm3/min
Compressor (1) 10-hp
0.05
None
0.065
0.035
Glass bead 2540 545 0.205
None – – –
Measuring position (centrally) Distance above the distributor (m) Distance below the distributor (m) Bed material Material Density (kg/m3) Diameter (Am) Minimum fluidization velocity, Umf (m/s) Air distributor Type Orifice diameter (mm) Superficial air velocity, U (m/s) Static bed height, Hs (m) Windbox volume, Vw (m3)
21
where DPi is the instantaneous value of the pressure drop, and N is the number of sampling points. The coefficient of the variation for the pressure fluctuations, C.V., indicates the extent of the pressure fluctuations and is defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX u ðDPi DPÞ2 t i¼1 ; rp N1 ð2Þ ¼ C:V: ¼ DP DP where rp is the standard deviation of the pressure fluctuations, i.e. mean of the amplitude of the pressure fluctuations. 2.3.2. Frequency spectral analysis The Fourier transform used in this study is as follows [12]: gðtÞ ¼ a0 þ
Multi-horizontal nozzle distributor 6.8
Porous plate
0.205 – 1.23 (0.615*) 0.15, 0.20*, 0.25, 0.30, 0.35 0.02, 0.04*, 0.06, 0.08
0.615
–
l X
cn cosðnx0 t þ dn Þ;
ð3Þ
n¼1
1 a0 ¼ T
Z
aþT
gðtÞdt;
ð4Þ
a
where g(t) is a periodic function with period T, cn is harmonic amplitudes,
None 0.001
The asterisk symbol ‘‘ * ’’ denotes the normal operating conditions in this work.
cn ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2n þ b2n ;
ð5Þ
and 2 an ¼ T
2.2. Data acquisition Pressure taps were located along the column wall so that the pressure probe, made of a 2.5-mm I.D. stainless steel tube, could be inserted into the bed horizontally and moved in radial direction. Pressure fluctuation data were acquired using a high performance data-acquisition card (AdvanTech, PCL-818H) coupled with a pressure transmitter (Rosemount, Model 1151DP), and further analyzed using PCbased software (DASYTEC, DASYLab v. 5.0). In this work, the sampling rate was set at 100 Hz and the sampling points for each run were 8192. The comprehensive operating conditions are tabulated in Table 1. 2.3. Data analysis 2.3.1. Statistical analysis Mean of pressure fluctuations, DP, represents the mean pressure drop at a certain position during a certain period of time, and is given by N X
DP ¼
2 bn ¼ T
Z
aþT
gðtÞcosðnx0 tÞdt;
ð6Þ
gðtÞsinðnx0 tÞdt;
ð7Þ
a
Z
aþT
a
dn is phase angles, dn ¼ tan
1
bn ; an
x0 ¼ 2p=T
ð8Þ ð9Þ
Amplitude spectrum, the plot of c0 at 0 with c0 = Aa0A (in this work, the DC component was suppressed so c0 = 0) and, for n z 1, cn/2 vs. frequency, was used.
3. Results and discussion 3.1. Measuring location of pressure fluctuations
DPi
i¼1
N
ð1Þ
Usually, the pressure signals were measured along the central line within the bed (e.g., Refs. [8,9,13,14]). Hong
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et al. [13] suggested that a higher level in the bed is more appropriate for measurement. However, Wilkinson [8] determined the minimum fluidization velocity using the pressure fluctuation standard deviation and his results showed that the values obtained from the bottom of the bed (height = 0 cm) or the windbox were extremely good. Svoboda et al. [15,16] reported that the frequency spectrum was affected considerably less than the pressure amplitude when the pressure probe was located along the axial positions. Baskakov et al. [17] also stated that pressure fluctuations along the bed height occur synchronically. For the 0.29-m I.D. cold model, pressure taps were installed along the column 0.05, 0.07, 0.10, 0.15 m above and 0.065 m below the distributor, respectively. The pressure probe was inserted into the center of the bed
horizontally to measure the central pressure signals. Experimental results indicated that the frequency spectra obtained from various positions within the bed were very similar, while the amplitudes decreased with the height of the tap location. Hence, the locations, 0.05 m above and 0.065 m below the distributor, were chosen as the measurement positions in the bed and windbox, respectively. For the 0.10-m I.D. cold model, pressure signals were measured only in the windbox, at a position 0.035 m below the distributor. 3.2. The pressure pulsation frequency, fp The frequency spectra, detected in the bed and windbox at different operating conditions, are shown in Fig. 3. No pressure fluctuation signals could be measured in the bed
Fig. 3. The frequency spectra, detected in the bed and windbox at different operating conditions. A Roots blower with Qmax = 10 Nm3/min was employed. U = 0.615 m/s. Hs = 0.20 m.
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Fig. 4. Effect of superficial air velocity on frequency spectra detected in the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. Hs = 0.20 m.
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while the distributor was absent (Fig. 3(a)), or present without bed material (Fig. 3(c)). When the distributor was present without bed material, pressure signals could be detected in the windbox. One remarkable pressure fluctuation frequency (about 4.5 Hz) was detected in the windbox (Fig. 3(b)). Pressure fluctuation signals could be measured both in the bed and windbox with bed material present (Fig. 3(d) and (e)). Comparing Fig. 3(b) and (d), it can be seen that the frequency exists whether the bed material is present or not. Evidently, this characteristic frequency, denoted as fc, is irrelevant to the fluidization of the bed material. Comparing Fig. 3(d) and (e), it is observed that the pressure fluctuations, caused by the hydrodynamic behavior of the bed, are able to propagate downwards to the windbox. These pressure fluctuations feature a broad frequency band in the spectrum, with an intensity less than that in the bed due to the impediment caused by the distributor. This is in agreement with the results reported by Lirag and Littman [4]. Similarly, we can infer that the pressure fluctuations at the characteristic frequency can propagate upwards to the bed as well, but overlap with the pressure fluctuations caused by the bed, as shown in Fig. 3(e). It is interesting to discover the origin which causes the fluctuations at the characteristic frequency, fc. Effects of superficial air velocity, static bed height, and windbox volume on fc are taken into account in the following sections. 3.2.1. Effect of superficial air velocity, U The frequency spectra, detected in the bed and windbox with a superficial air velocity in the range of 2 – 6 Umf, are shown in Fig. 4. From Fig. 4(a) – (e), fc was affected significantly and increased almost linearly with U (see Fig. 5). The increase in gas velocity accelerated the formation of bubbles and promoted bubble coalescence. Large bubbles resulted in strong bed height oscillations and responded with a more intense and broader frequency band in the spectra (see Fig. 4(f) – (j)). 3.2.2. Effect of static bed height, Hs The frequency spectra, obtained from the bed and windbox with static bed height from 0.15 to 0.35 m, are shown in Fig. 6. From Fig. 6(a) – (e), fc was almost unaffected by Hs. A deeper static bed height enabled the bubbles to fully develop, accompanied with great bed height oscillations. A more intense and broader frequency band in the spectrum was observed (see Fig. 6(f) –(j)). 3.2.3. Effect of windbox volume, Vw The frequency spectra, obtained with windbox volumes varied from 0.08 to 0.318 m3 by changing the windbox height, but not affecting the superficial air velocity, are shown in Fig. 7. From Fig. 7(a) – (d), it can be seen that fc was independent of Vw. The intensity of the pressure fluctuations in the bed abated a little bit when a larger-size
Fig. 5. The characteristic frequency, fc, detected in the windbox as a function of superficial air velocity, U. A Roots blower with Qmax = 10 Nm3/ min was employed. Hs = 0.20 m.
windbox was employed (see Fig. 7(e) – (h)). This was probably attributed to the buffer effect from the enlarged windbox volume. According to the experimental results reported above, the characteristic frequency, fc, is only related to the superficial air velocity and is independent of the static bed height and windbox volume. Although spontaneous oscillations described by Baird and Kelein [5] can be neglected in this study, a pressure accumulation may have occurred within the windbox. Therefore, a comparison between the experimental results obtained in this study and that reported by Baird and Kelein [5] should be conducted. Baird and Kelein [5] measured the pressure fluctuations in the windbox to investigate the spontaneous oscillation phenomenon. They proposed that the pressureaccumulated frequency of the fluidizing air within the windbox increased first and then leveled off with superficial air velocity; and decreased with an increase in the static bed height and windbox volume. Apparently, their results were different from our findings. Hence, the source of the characteristic frequency, fc, is not due to the accumulation of fluidizing air within the windbox. It is known that the fluidizing air supplied by the Roots blower possesses pulsation characteristics. From the Roots blower’s principle discussed earlier in this work, it is understandable that the pulsation frequency of the fluidizing air increases with an increase in the rotary speed of the blower impellers. Since the characteristic frequency, fc, is only related to the superficial air velocity, it is quite possible that fc is induced by the nature of the Roots blower, i.e. pressure pulsations produced by the blower
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Fig. 6. Effect of static bed height on frequency spectra detected in the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. U = 0.82 m/s.
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Fig. 7. Effect of windbox volume on frequency spectra detected in the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. U = 0.615 m/s. Hs = 0.20 m.
rotating lobes. In order to prove this, a test was conducted by bypassing the fluidizing air. In this way, the amount of air entering the windbox could be altered by adjusting the valve aperture percentage on the bypass, /v, without having to adjust the speed of the impellers. The test results revealed that fc became independent of the superficial air velocity (see Fig. 8). In other words, fc is constant when the speed of the impellers is fixed. Therefore, it is evident that
the fluctuations at the characteristic frequency, fc, result from the nature of the blower. This pressure pulsation frequency of the fluidizing air is denoted as fp in this work, and its intensity is denoted as Ip. From Fig. 8, the pressure pulsation intensity, Ip, decreased due to the decreasing amount of fluidizing air into the windbox. It is noted that the fp can be the dominant frequency in the spectrum obtained from the windbox under the follow-
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3.3. Interaction between the pressure fluctuations from the bed and windbox
Fig. 8. Effect of the valve aperture percentage on the bypass on the characteristic frequency detected in the windbox without bed material. A Roots blower with Qmax = 10 Nm3/min was employed.
ing operating conditions: low superficial air velocity (Fig. 4(a)), low static bed height (Fig. 6(a)) and large windbox volume (Fig. 7(d)). This is because low superficial air velocity and small static bed height tend to result in a gentle fluidization, leading to smaller pressure fluctuations. A large windbox volume can buffer the pressure fluctuations propagated from the bed. In some cases, fp may overlap with the frequency band caused by the fluidization behavior within the bed and it is difficult to distinguish, even in the windbox. Therefore, if one attempts to measure the pressure fluctuations of the fluidized bed in the windbox, a preliminary experiment should be conducted to identify fp. The procedure is to measure the pressure fluctuations within the windbox with bed material absent under various superficial air velocities and then the fp at the corresponding air velocity can be clearly identified from the frequency spectrum.
It has been demonstrated that the pressure fluctuations in a fluidized bed with a Roots blower employed result from two major sources. The first is the hydrodynamic behavior in the bed, such as the formation and motion of bubbles. It results in a frequency band in the frequency spectrum of pressure fluctuations, which is associated with the superficial air velocity, static bed height, particle size and distributor design, as demonstrated by Fan et al. [18]. The second is the nature of the Roots blower. It features a specific frequency in the spectrum. These two sources have different influences on the pressure fluctuations in the bed and windbox. Among all of the operating parameters, superficial air velocity is the most important. The frequency spectra, obtained from the bed and windbox with various superficial air velocities, are shown in Fig. 9. From Fig. 9(a) and (f), the pressure fluctuations in the bed are in accord with those in the windbox. Meanwhile, the pressure fluctuations in the bed are dominated by the pressure fluctuation pattern in the windbox. Before the hydrodynamic behavior in the bed (such as bubbling and jetting) develops, the pressure fluctuations within the bed are caused by the interstitial air through the bed at the pulsation frequency, fp, which is corresponding to the socalled pulsed fluidization region [11]. At a higher air velocity, it can be observed from Fig. 9(d) and (i) that the frequency band is broadened which responds to the developing bed hydrodynamic behavior. With a further increase in air velocity, the pressure fluctuations within the bed become more intense, and gradually dominate the fluctuation pattern in the windbox. It should be noted that the pressure fluctuation intensity would abate while propagating across the distributor pressure drop from windbox to bed, and vice versa. With increasing air velocity or static bed height, the distributor pressure drop increases accordingly, leading to an incremental difficulty of pressure fluctuation propagation. Comparing Fig. 9(e) and (j), when the superficial air velocity reached 3Umf, the pulsation intensity in the bed fades out and is overlapped by the pressure fluctuation intensity caused by the well-developed bed hydrodynamic behavior, which is subjected to the socalled free fluidization region [11]. At this point, the pulsation frequency, fp, cannot be distinguished from the frequency spectrum obtained from the bed. Moreover, from Fig. 9, it is evident that the pressure fluctuations in the fluidized bed propagate both upwards and downwards. 3.4. Effect of the air-supply equipment on the pressure fluctuations The frequency spectra, obtained from the windbox at U = 0.615 m/s with the bed material absent and various types of air-supply equipment employed, are shown in Fig. 10. From Fig. 10(a) and (b), it is indicated that the pulsation
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Fig. 9. The interaction between the pressure fluctuations from the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. Hs = 0.20 m.
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pressure fluctuations. Hence, the pulsation frequency cannot be found in the pressure fluctuation frequency spectrum when a compressor is used (Fig. 10(c)). Fig. 11 shows the pulsation frequency, fp, obtained from the windbox as a function of the superficial air velocity, U, with bed material present and a Roots blower with Qmax = 10 and 15 Nm3/min employed, respectively. From Fig. 11, a good linear relationship between fp and U is observed. It is evident that the air output has less impact on the impeller rotary speed of the larger-scale blower. Therefore, the fp vs. U curve has a smaller slope. It is clear that the Roots blower possesses its own fp vs. U characteristic curve, depending on its scale. Fig. 12(a) shows the ratio of the pressure drop detected in the windbox with and without bed material, DPw/DPd, as a function of the superficial air velocity, U. When air velocity exceeds the minimum fluidization velocity, the bed pressure drop is constant and the distributor pressure drop increases. The ratio DPw/DPd approaches unity. It can be found from Fig. 12(b) that the two values for Ip, detected in the windbox with and without bed material, approach each other. This result confirms that Ip is related to the back resistance. A higher back resistance results in greater pulsation intensity. It can be found as well that an Ip produced by a larger-scale blower is more sensitive to the air output. Fig. 12(c) shows the coefficient of variance for the pressure fluctuations in the bed, C.V.b, as a function of the superficial air velocity, U. Comparing Fig. 12(b) and (c), it is indicated that a higher Ip results in greater pressure fluctuations in the bed. However, at high air velocity, Ip is abated due to the shortened pulsation period and Ip values
Fig. 10. Effect of the air-supply equipment on the pressure fluctuations detected in the windbox without bed material. U = 0.615 m/s.
frequency depends on the blower scale. A blower with Qmax = 15 Nm3/min produced a lower pulsation frequency and greater pulsation intensity than that produced by a blower with Qmax = 10 Nm3/min, under the same superficial air velocity. The reason is that a lower impeller rotary speed is required for a larger-scale blower than for a smaller-scale blower under the same air output. This leads to a lower pressure pulsation frequency. A lower pulsation frequency indicates a longer pulsation period, which results in greater pressure amplitude, i.e. greater pressure pulsation intensity. The air pressure supplied by a compressor is always constant due to a surge tank employed to damp out the
Fig. 11. The pressure pulsation frequency, fp, detected in the windbox as a function of superficial air velocity, U. A Roots blower with Qmax = 10 and 15 Nm3/min was employed respectively. Hs = 0.20 m.
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possibly becomes the dominant frequency. If one attempts to investigate the hydrodynamic behavior of a fluidized bed using spectral analysis in the windbox, a preliminary experiment should be conducted to identify the fp in the spectrum. Although the nature of the Roots blower affects the pressure fluctuations in the fluidized bed, a pulsed flow is favorable from the view of the fluidized-bed reactor design. The pulsed flow was deliberately introduced into the bed to promote mixing (e.g., Refs. [19 –21]). Therefore, it seems unnecessary to damp out the pulsation intensity from the blower. However, the knowledge of the pulsing air supply is required to avoid data-analysis confusion.
4. Conclusions
List of symbols a real number a0 coefficient defined in Eq. (4) an coefficient defined in Eq. (6) bn coefficient defined in Eq. (7) c0 = Aa0A ; in this work, the DC component was suppressed so c0 = 0 cn harmonic amplitudes, defined in Eq. (5) C.V. coefficient of variance for the pressure fluctuations, defined in Eq. (2) C.V.b coefficient of variance for the pressure fluctuations in the bed, dimensionless fc characteristic frequency, Hz fp pressure pulsation frequency caused by Roots blower, Hz g(t) periodic function, defined in Eq. (3) Hs static bed height, m Ip pressure pulsation intensity caused by Roots blower, kPa N sampling points of pressure fluctuations for each run DP mean of pressure fluctuations, defined in Eq. (1) DPd pressure drop across the distributor, kPa DPi instantaneous value of the pressure drop DPw pressure drop across the distributor and bed material, kPa Qmax maximum air capacity rate of Roots blower under the normal condition of 0 jC and 1 atm, Nm3/min t time T period U superficial air velocity, m/s Umf minimum fluidization velocity, m/s V = 0.159 m3, windbox volume in normal condition Vw windbox volume, m3
It has been demonstrated experimentally that the pressure fluctuations in a fluidized bed with a Roots blower result from two major sources. The first is the hydrodynamic behavior within the bed and the second is the nature of the Roots blower, which significantly influences the pressure fluctuations in the windbox. At low superficial air velocity, the pressure pulsation frequency, fp, quite
Greek letters dn phase angle, defined in Eq. (8) /v valve aperture percentage on the bypass, % p = pi rp standard deviation of pressure fluctuations, defined in Eq. (2) x0 = 2p/T
Fig. 12. (a) The ratio of the pressure drop detected in the windbox with and without bed material, DPw/DPd; (b) the pressure pulsation intensity, Ip, detected in the windbox; (c) the coefficient of variance for the pressure fluctuations in the bed, C.V.b, as a function of the superficial air velocity, U. Hs = 0.20 m.
produced by various blower scales are close, as seen in Fig. 12(b). This means that the influence of the nature of the blower on the pressure fluctuations in the bed tends to be minimum at high air velocity. Therefore, the C.V.b values for various blowers employed gradually approached each other with the increasing air velocity, as shown in Fig. 12(c).
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References [1] J.S.M. Botterill, Y. Teoman, K.R. Yu¨regir, The effect of operating temperature on the velocity of minimum fluidization, bed voidage and general behaviour, Powder Technol. 31 (1982) 101 – 110. [2] D. Geldart, Gas Fluidization Technology, Wiley, Chichester, UK, 1986. [3] S.V. Dhodapkar, G.E. Klinzing, Pressure fluctuations in pneumatic conveying systems, Powder Technol. 74 (1993) 179 – 195. [4] R.C. Lirag Jr., H. Littman, Statistical study of the pressure fluctuations in a fluidized bed, AIChE Symp. Ser. 67 (116) (1971) 11 – 22. [5] M.H.I. Baird, A.J. Kelein, Spontaneous oscillation of a gas-fluidised bed, Chem. Eng. Sci. 28 (1973) 1039 – 1048. [6] H. Kage, N. Iwasaki, H. Yamaguchi, Y. Matsuno, Frequency analysis of pressure fluctuation in fluidized bed plenum, J. Chem. Eng. Jpn. 24 (1) (1991) 76 – 81. [7] H. Kage, N. Iwasaki, Y. Matsuno, Frequency analysis of pressure fluctuation in plenum as a diagnostic method for fluidized beds, AIChE Symp. Ser. 89 (296) (1993) 184 – 190. [8] D. Wilkinson, Determination of minimum fluidization velocity by pressure fluctuation measurement, Can. J. Chem. Eng. 73 (1995) 562 – 565. [9] M. Puncˇocha´rˇ, J. Drahosˇ, J. Cˇerma´k, K. Selucky´, Evaluation of minimum fluidizing velocity in gas fluidized bed from pressure fluctuations, Chem. Eng. Commun. 35 (1985) 81 – 87. [10] A. Svensson, F. Johnsson, B. Leckner, Fluidization regimes in nonslugging fluidized beds: the influence of pressure drop across the air distributor, Powder Technol. 86 (1996) 299 – 312. [11] H. Moritomi, S. Mori, K. Araki, A. Moriyama, Periodic pressure fluctuation in a gaseous fluidized-bed, Kagaku Kogaku Ronbunshu 6 (4) (1980) 392 – 396.
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[12] P.V. O’Neil, Advanced Engineering Mathematics, 3rd edn., Wadsworth, Belmont, CA, 1991. [13] S.C. Hong, B.R. Jo, D.S. Doh, Determination of minimum fluidization velocity by the statistical analysis of pressure fluctuations in a gas – solid fluidized bed, Powder Technol. 60 (1990) 215 – 221. [14] L.P. Leu, C.W. Lan, Measurement of pressure fluctuations in twodimensional gas – solid fluidized beds at elevated temperatures, J. Chem. Eng. Jpn. 23 (5) (1990) 555 – 562. [15] K. Svobda, J. Cˇerma´k, M. Hartman, J. Drahosˇ, K. Selucky´, Pressure fluctuations in gas-fluidized beds at elevated temperatures, Ind. Eng. Chem. Process Des. Dev. 22 (1983) 514 – 520. [16] K. Svobda, J. Cˇerma´k, M. Hartman, J. Drahosˇ, K. Selucky´, Influence of particle size on the pressure fluctuations and slugging in a fluidized bed, AIChE J. 30 (3) (1984) 513 – 517. [17] A.P. Baskakov, V.G. Tuponogov, N.F. Filippovsky, A study of pressure fluctuations in a bubbling fluidized bed, Powder Technol. 45 (1986) 113 – 117. [18] L.T. Fan, T.C. Ho, S. Hiraoka, W.P. Walawender, AIChE J. 27 (3) (1981) 388 – 396. [19] M.T. Moreira, A. Sanroma´n, G. Feijoo, J.M. Lema, Control of pellet morphology of filamentous fungi in fluidized bed bioreactors by means of a pulsing flow. Application to Aspergillus niger and Phanerochaete chrysosporium, Enzyme Microb. Technol. 19 (1996) 261 – 266. [20] M.T. Moreira, C. Palma, G. Feijoo, J.M. Lema, Strategies for the continuous production of ligninolytic enzymes in fixed and fluidized bed bioreactors, J. Biotechnol. 66 (1998) 27 – 39. [21] L.A.M. van der Wielen, C.A.P.M. van Nunen, K.Ch.A.M. Luyben, Pulsed adsorbent transport in a countercurrent adsorptive reactor, AIChE J. 44 (1) (1998) 83 – 92.
Influence of the nature of the Roots blower on pressure fluctuations in a fluidized bed Chien-Song Chyang *, Yen-Chin Lin Department of Chemical Engineering, Chung Yuan Christian University, Chung-Li 320, Taiwan, ROC Received 27 March 2001; received in revised form 6 June 2001; accepted 31 January 2002
Abstract Experiments were conducted in a 0.29-m I.D. fluidized-bed cold model with fluidizing air supplied by a Roots blower. To investigate the influence of the air-supply equipment on the pressure fluctuations, another experiment was carried out in a 0.10-m I.D. cold model with fluidizing air supplied by a compressor. In this work, the effects of superficial air velocity, static bed height and windbox volume were studied. The pressure pulsation frequency caused by the Roots blower was identified successfully from the pressure fluctuation frequency spectrum. This pulsation frequency was found to be related to the blower impeller rotary speed and exhibited a good linear relationship. The experimental results indicated that the blower possesses its own pressure pulsation frequency vs. superficial air velocity characteristic curve. At a given air flow rate, a larger-scale blower produced a lower pulsation frequency, higher pulsation intensity and a higher coefficient of variation for pressure fluctuations in the bed. With increasing superficial air velocity, the pulsation intensity abated and became less influential on the pressure fluctuations in the bed. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Pressure fluctuations; Pulsation; Roots blower; Fluidized bed; Windbox
1. Introduction 1.1. Background Numerous researchers implemented pressure fluctuation measurements to investigate the hydrodynamic behavior of fluidized beds. However, pressure fluctuations in a fluidized bed can be induced by various sources, such as bubbles, bed-height oscillations, the line configuration and even the air supply. The influence of the blower on the hydrodynamic behavior in a fluidized bed has been noted for decades. Botterill et al. [1] reported that the pulsed air flow resulted from the Roots blower affects the voidage of the packed bed and the shape of the bed pressure drop vs. air flow rate curve. The minimum fluidization velocity estimated using the pressure fluctuation method is affected by the blower characteristics. Geldart [2] stated that the pressure pulsations resulted from the blower can alter the fluidization behavior. Dhodapkar and Klinzing [3] also pointed out that the rotating lobes in Roots blower can cause pressure fluctuations. However, no signifi*
Corresponding author. Tel.: +886-3-4563495; fax: +886-3-4636242. E-mail address: [email protected] (C.-S. Chyang).
cant evidence has been reported to confirm the extent of this influence on the pressure fluctuations in the fluidized bed. In order to avoid the destructive measurement within the bed and prevent the pressure probe from erosion or clogging by the bed material, some investigators have made the pressure fluctuation measurements in the windbox. Lirag and Littman [4] measured pressure fluctuations in both the bed and windbox and analyzed the signals using probability density, autocorrelation, and power spectral density functions. Baird and Kelein [5] detected the pressure fluctuations in the windbox to investigate the spontaneous oscillation of the gas-fluidized bed. Kage et al. [6,7] measured and analyzed pressure fluctuation data detected in the windbox using the power spectral density function. Wilkinson [8] calculated the standard deviation of the pressure fluctuations, rp, detected in the windbox to evaluate the minimum fluidization velocity, U mf , via the linear relationship between U and rp proposed by Puncˇocha´rˇ et al. [9]. Svensson et al. [10] conducted experiments in a 12 MWth Circulating Fluidized Bed (CFB) boiler and a cold CFB. They made comparisons between the frequency spectra obtained from the bed and windbox. From the research mentioned above, measuring pressure fluctuations in the windbox has been a trend.
0032-5910/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 2 - 5 9 1 0 ( 0 2 ) 0 0 0 9 2 - X
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Am, density of 2540 kg/m3, subjected to Geldart Group B particles, were used as the bed material.
Fig. 1. The schematic diagram of the 0.29-m I.D. fluidized-bed cold model.
Moritomi et al. [11] recorded the pressure histories to investigate the influence of the pressure pulsation on the pressure fluctuations within the bed by mandatory adjustment on inlet air flow. It showed that the pressure responses could be classified in terms of both the inlet frequency and the gas flow rate. Instead of using the pressure record, the frequency spectral analysis by Fast Fourier Transform (FFT) was used in this work to investigate the influence of the Roots blower’s mechanical nature of air transport. Whether the measurements were conducted in the bed or windbox, the pressure fluctuations were probably influenced to some extent by the nature of the blower. To assess the blower influence on pressure fluctuations, measurements were made both in the bed and windbox in this work.
2.1.1. 0.29-m I.D. cold model The fluidized bed was fabricated with an acrylic column, 0.29 m in diameter and 1.0 m in height. A schematic diagram of the experimental apparatus is shown in Fig. 1. Twenty-two horizontal nozzles, 90j-bent carbon steel tubes with an inside diameter of 6.8 mm, were mounted on an 8mm-thick plate as a distributor. The horizontal nozzles were arranged in three concentric circles with all discharge exits directed clockwise, as shown in Fig. 2. The windbox, with a volume of V = 0.04 m3 (0.6-m high), was made of iron. In order to explore the windbox volume effect on the pressure fluctuations, windboxes with volumes of 0.5, 1.5 and 2V were used as well. Two Roots blowers, with a maximum air capacity rate of 10 and 15 Nm3/min, respectively, were used to estimate the blower scale effect. An orifice-plate flow meter was used to measure the fluidizing air flow rate. 2.1.2. 0.10-m I.D. cold model The fluidized bed was made of an acrylic column, 0.10 m in diameter, 0.74 m in height, and equipped with a porous plate as an air distributor. A 10-hp compressor was used to provide the fluidized air with the flow rate measured using a rotameter. This apparatus was employed only to explore the effect of the air-supply equipment. Most experiments were conducted in the 0.29-m I.D. cold model.
1.2. Principle of the Roots blower Two impellers, rotating in opposite directions, were installed inside a Roots blower case. The clearance between the impellers or the lobe and the case was extremely small, about 0.08 –0.3 mm. When the two impellers rotate, the inlet volume is enlarged to cause a low-pressure area to draw air in. When the impeller blade rotates, it forms a transient closed space with the case that traps a certain amount of air. As the impeller blade rotates to the outlet, the captured air is discharged from the blower. In this way, the air-transport process in the blower is completed.
2. Experimental 2.1. Apparatus Experiments were carried out in 0.29- and 0.10-m I.D. fluidized-bed models. Glass beads with a diameter of 545
Fig. 2. The illustration of the multi-horizontal nozzle distributor (top-view).
C.-S. Chyang, Y.-C. Lin / Powder Technology 127 (2002) 19–31 Table 1 Experimental conditions Experimental unit
0.29-m I.D. cold model *
0.10-m I.D. cold model
Air-supply equipment
Roots blower (1) 15-hp, Qmax = 10 Nm3/min * (2) 15-hp, Qmax = 15 Nm3/min
Compressor (1) 10-hp
0.05
None
0.065
0.035
Glass bead 2540 545 0.205
None – – –
Measuring position (centrally) Distance above the distributor (m) Distance below the distributor (m) Bed material Material Density (kg/m3) Diameter (Am) Minimum fluidization velocity, Umf (m/s) Air distributor Type Orifice diameter (mm) Superficial air velocity, U (m/s) Static bed height, Hs (m) Windbox volume, Vw (m3)
21
where DPi is the instantaneous value of the pressure drop, and N is the number of sampling points. The coefficient of the variation for the pressure fluctuations, C.V., indicates the extent of the pressure fluctuations and is defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N uX u ðDPi DPÞ2 t i¼1 ; rp N1 ð2Þ ¼ C:V: ¼ DP DP where rp is the standard deviation of the pressure fluctuations, i.e. mean of the amplitude of the pressure fluctuations. 2.3.2. Frequency spectral analysis The Fourier transform used in this study is as follows [12]: gðtÞ ¼ a0 þ
Multi-horizontal nozzle distributor 6.8
Porous plate
0.205 – 1.23 (0.615*) 0.15, 0.20*, 0.25, 0.30, 0.35 0.02, 0.04*, 0.06, 0.08
0.615
–
l X
cn cosðnx0 t þ dn Þ;
ð3Þ
n¼1
1 a0 ¼ T
Z
aþT
gðtÞdt;
ð4Þ
a
where g(t) is a periodic function with period T, cn is harmonic amplitudes,
None 0.001
The asterisk symbol ‘‘ * ’’ denotes the normal operating conditions in this work.
cn ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2n þ b2n ;
ð5Þ
and 2 an ¼ T
2.2. Data acquisition Pressure taps were located along the column wall so that the pressure probe, made of a 2.5-mm I.D. stainless steel tube, could be inserted into the bed horizontally and moved in radial direction. Pressure fluctuation data were acquired using a high performance data-acquisition card (AdvanTech, PCL-818H) coupled with a pressure transmitter (Rosemount, Model 1151DP), and further analyzed using PCbased software (DASYTEC, DASYLab v. 5.0). In this work, the sampling rate was set at 100 Hz and the sampling points for each run were 8192. The comprehensive operating conditions are tabulated in Table 1. 2.3. Data analysis 2.3.1. Statistical analysis Mean of pressure fluctuations, DP, represents the mean pressure drop at a certain position during a certain period of time, and is given by N X
DP ¼
2 bn ¼ T
Z
aþT
gðtÞcosðnx0 tÞdt;
ð6Þ
gðtÞsinðnx0 tÞdt;
ð7Þ
a
Z
aþT
a
dn is phase angles, dn ¼ tan
1
bn ; an
x0 ¼ 2p=T
ð8Þ ð9Þ
Amplitude spectrum, the plot of c0 at 0 with c0 = Aa0A (in this work, the DC component was suppressed so c0 = 0) and, for n z 1, cn/2 vs. frequency, was used.
3. Results and discussion 3.1. Measuring location of pressure fluctuations
DPi
i¼1
N
ð1Þ
Usually, the pressure signals were measured along the central line within the bed (e.g., Refs. [8,9,13,14]). Hong
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et al. [13] suggested that a higher level in the bed is more appropriate for measurement. However, Wilkinson [8] determined the minimum fluidization velocity using the pressure fluctuation standard deviation and his results showed that the values obtained from the bottom of the bed (height = 0 cm) or the windbox were extremely good. Svoboda et al. [15,16] reported that the frequency spectrum was affected considerably less than the pressure amplitude when the pressure probe was located along the axial positions. Baskakov et al. [17] also stated that pressure fluctuations along the bed height occur synchronically. For the 0.29-m I.D. cold model, pressure taps were installed along the column 0.05, 0.07, 0.10, 0.15 m above and 0.065 m below the distributor, respectively. The pressure probe was inserted into the center of the bed
horizontally to measure the central pressure signals. Experimental results indicated that the frequency spectra obtained from various positions within the bed were very similar, while the amplitudes decreased with the height of the tap location. Hence, the locations, 0.05 m above and 0.065 m below the distributor, were chosen as the measurement positions in the bed and windbox, respectively. For the 0.10-m I.D. cold model, pressure signals were measured only in the windbox, at a position 0.035 m below the distributor. 3.2. The pressure pulsation frequency, fp The frequency spectra, detected in the bed and windbox at different operating conditions, are shown in Fig. 3. No pressure fluctuation signals could be measured in the bed
Fig. 3. The frequency spectra, detected in the bed and windbox at different operating conditions. A Roots blower with Qmax = 10 Nm3/min was employed. U = 0.615 m/s. Hs = 0.20 m.
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Fig. 4. Effect of superficial air velocity on frequency spectra detected in the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. Hs = 0.20 m.
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while the distributor was absent (Fig. 3(a)), or present without bed material (Fig. 3(c)). When the distributor was present without bed material, pressure signals could be detected in the windbox. One remarkable pressure fluctuation frequency (about 4.5 Hz) was detected in the windbox (Fig. 3(b)). Pressure fluctuation signals could be measured both in the bed and windbox with bed material present (Fig. 3(d) and (e)). Comparing Fig. 3(b) and (d), it can be seen that the frequency exists whether the bed material is present or not. Evidently, this characteristic frequency, denoted as fc, is irrelevant to the fluidization of the bed material. Comparing Fig. 3(d) and (e), it is observed that the pressure fluctuations, caused by the hydrodynamic behavior of the bed, are able to propagate downwards to the windbox. These pressure fluctuations feature a broad frequency band in the spectrum, with an intensity less than that in the bed due to the impediment caused by the distributor. This is in agreement with the results reported by Lirag and Littman [4]. Similarly, we can infer that the pressure fluctuations at the characteristic frequency can propagate upwards to the bed as well, but overlap with the pressure fluctuations caused by the bed, as shown in Fig. 3(e). It is interesting to discover the origin which causes the fluctuations at the characteristic frequency, fc. Effects of superficial air velocity, static bed height, and windbox volume on fc are taken into account in the following sections. 3.2.1. Effect of superficial air velocity, U The frequency spectra, detected in the bed and windbox with a superficial air velocity in the range of 2 – 6 Umf, are shown in Fig. 4. From Fig. 4(a) – (e), fc was affected significantly and increased almost linearly with U (see Fig. 5). The increase in gas velocity accelerated the formation of bubbles and promoted bubble coalescence. Large bubbles resulted in strong bed height oscillations and responded with a more intense and broader frequency band in the spectra (see Fig. 4(f) – (j)). 3.2.2. Effect of static bed height, Hs The frequency spectra, obtained from the bed and windbox with static bed height from 0.15 to 0.35 m, are shown in Fig. 6. From Fig. 6(a) – (e), fc was almost unaffected by Hs. A deeper static bed height enabled the bubbles to fully develop, accompanied with great bed height oscillations. A more intense and broader frequency band in the spectrum was observed (see Fig. 6(f) –(j)). 3.2.3. Effect of windbox volume, Vw The frequency spectra, obtained with windbox volumes varied from 0.08 to 0.318 m3 by changing the windbox height, but not affecting the superficial air velocity, are shown in Fig. 7. From Fig. 7(a) – (d), it can be seen that fc was independent of Vw. The intensity of the pressure fluctuations in the bed abated a little bit when a larger-size
Fig. 5. The characteristic frequency, fc, detected in the windbox as a function of superficial air velocity, U. A Roots blower with Qmax = 10 Nm3/ min was employed. Hs = 0.20 m.
windbox was employed (see Fig. 7(e) – (h)). This was probably attributed to the buffer effect from the enlarged windbox volume. According to the experimental results reported above, the characteristic frequency, fc, is only related to the superficial air velocity and is independent of the static bed height and windbox volume. Although spontaneous oscillations described by Baird and Kelein [5] can be neglected in this study, a pressure accumulation may have occurred within the windbox. Therefore, a comparison between the experimental results obtained in this study and that reported by Baird and Kelein [5] should be conducted. Baird and Kelein [5] measured the pressure fluctuations in the windbox to investigate the spontaneous oscillation phenomenon. They proposed that the pressureaccumulated frequency of the fluidizing air within the windbox increased first and then leveled off with superficial air velocity; and decreased with an increase in the static bed height and windbox volume. Apparently, their results were different from our findings. Hence, the source of the characteristic frequency, fc, is not due to the accumulation of fluidizing air within the windbox. It is known that the fluidizing air supplied by the Roots blower possesses pulsation characteristics. From the Roots blower’s principle discussed earlier in this work, it is understandable that the pulsation frequency of the fluidizing air increases with an increase in the rotary speed of the blower impellers. Since the characteristic frequency, fc, is only related to the superficial air velocity, it is quite possible that fc is induced by the nature of the Roots blower, i.e. pressure pulsations produced by the blower
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Fig. 6. Effect of static bed height on frequency spectra detected in the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. U = 0.82 m/s.
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Fig. 7. Effect of windbox volume on frequency spectra detected in the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. U = 0.615 m/s. Hs = 0.20 m.
rotating lobes. In order to prove this, a test was conducted by bypassing the fluidizing air. In this way, the amount of air entering the windbox could be altered by adjusting the valve aperture percentage on the bypass, /v, without having to adjust the speed of the impellers. The test results revealed that fc became independent of the superficial air velocity (see Fig. 8). In other words, fc is constant when the speed of the impellers is fixed. Therefore, it is evident that
the fluctuations at the characteristic frequency, fc, result from the nature of the blower. This pressure pulsation frequency of the fluidizing air is denoted as fp in this work, and its intensity is denoted as Ip. From Fig. 8, the pressure pulsation intensity, Ip, decreased due to the decreasing amount of fluidizing air into the windbox. It is noted that the fp can be the dominant frequency in the spectrum obtained from the windbox under the follow-
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27
3.3. Interaction between the pressure fluctuations from the bed and windbox
Fig. 8. Effect of the valve aperture percentage on the bypass on the characteristic frequency detected in the windbox without bed material. A Roots blower with Qmax = 10 Nm3/min was employed.
ing operating conditions: low superficial air velocity (Fig. 4(a)), low static bed height (Fig. 6(a)) and large windbox volume (Fig. 7(d)). This is because low superficial air velocity and small static bed height tend to result in a gentle fluidization, leading to smaller pressure fluctuations. A large windbox volume can buffer the pressure fluctuations propagated from the bed. In some cases, fp may overlap with the frequency band caused by the fluidization behavior within the bed and it is difficult to distinguish, even in the windbox. Therefore, if one attempts to measure the pressure fluctuations of the fluidized bed in the windbox, a preliminary experiment should be conducted to identify fp. The procedure is to measure the pressure fluctuations within the windbox with bed material absent under various superficial air velocities and then the fp at the corresponding air velocity can be clearly identified from the frequency spectrum.
It has been demonstrated that the pressure fluctuations in a fluidized bed with a Roots blower employed result from two major sources. The first is the hydrodynamic behavior in the bed, such as the formation and motion of bubbles. It results in a frequency band in the frequency spectrum of pressure fluctuations, which is associated with the superficial air velocity, static bed height, particle size and distributor design, as demonstrated by Fan et al. [18]. The second is the nature of the Roots blower. It features a specific frequency in the spectrum. These two sources have different influences on the pressure fluctuations in the bed and windbox. Among all of the operating parameters, superficial air velocity is the most important. The frequency spectra, obtained from the bed and windbox with various superficial air velocities, are shown in Fig. 9. From Fig. 9(a) and (f), the pressure fluctuations in the bed are in accord with those in the windbox. Meanwhile, the pressure fluctuations in the bed are dominated by the pressure fluctuation pattern in the windbox. Before the hydrodynamic behavior in the bed (such as bubbling and jetting) develops, the pressure fluctuations within the bed are caused by the interstitial air through the bed at the pulsation frequency, fp, which is corresponding to the socalled pulsed fluidization region [11]. At a higher air velocity, it can be observed from Fig. 9(d) and (i) that the frequency band is broadened which responds to the developing bed hydrodynamic behavior. With a further increase in air velocity, the pressure fluctuations within the bed become more intense, and gradually dominate the fluctuation pattern in the windbox. It should be noted that the pressure fluctuation intensity would abate while propagating across the distributor pressure drop from windbox to bed, and vice versa. With increasing air velocity or static bed height, the distributor pressure drop increases accordingly, leading to an incremental difficulty of pressure fluctuation propagation. Comparing Fig. 9(e) and (j), when the superficial air velocity reached 3Umf, the pulsation intensity in the bed fades out and is overlapped by the pressure fluctuation intensity caused by the well-developed bed hydrodynamic behavior, which is subjected to the socalled free fluidization region [11]. At this point, the pulsation frequency, fp, cannot be distinguished from the frequency spectrum obtained from the bed. Moreover, from Fig. 9, it is evident that the pressure fluctuations in the fluidized bed propagate both upwards and downwards. 3.4. Effect of the air-supply equipment on the pressure fluctuations The frequency spectra, obtained from the windbox at U = 0.615 m/s with the bed material absent and various types of air-supply equipment employed, are shown in Fig. 10. From Fig. 10(a) and (b), it is indicated that the pulsation
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Fig. 9. The interaction between the pressure fluctuations from the bed and windbox. A Roots blower with Qmax = 10 Nm3/min was employed. Hs = 0.20 m.
C.-S. Chyang, Y.-C. Lin / Powder Technology 127 (2002) 19–31
29
pressure fluctuations. Hence, the pulsation frequency cannot be found in the pressure fluctuation frequency spectrum when a compressor is used (Fig. 10(c)). Fig. 11 shows the pulsation frequency, fp, obtained from the windbox as a function of the superficial air velocity, U, with bed material present and a Roots blower with Qmax = 10 and 15 Nm3/min employed, respectively. From Fig. 11, a good linear relationship between fp and U is observed. It is evident that the air output has less impact on the impeller rotary speed of the larger-scale blower. Therefore, the fp vs. U curve has a smaller slope. It is clear that the Roots blower possesses its own fp vs. U characteristic curve, depending on its scale. Fig. 12(a) shows the ratio of the pressure drop detected in the windbox with and without bed material, DPw/DPd, as a function of the superficial air velocity, U. When air velocity exceeds the minimum fluidization velocity, the bed pressure drop is constant and the distributor pressure drop increases. The ratio DPw/DPd approaches unity. It can be found from Fig. 12(b) that the two values for Ip, detected in the windbox with and without bed material, approach each other. This result confirms that Ip is related to the back resistance. A higher back resistance results in greater pulsation intensity. It can be found as well that an Ip produced by a larger-scale blower is more sensitive to the air output. Fig. 12(c) shows the coefficient of variance for the pressure fluctuations in the bed, C.V.b, as a function of the superficial air velocity, U. Comparing Fig. 12(b) and (c), it is indicated that a higher Ip results in greater pressure fluctuations in the bed. However, at high air velocity, Ip is abated due to the shortened pulsation period and Ip values
Fig. 10. Effect of the air-supply equipment on the pressure fluctuations detected in the windbox without bed material. U = 0.615 m/s.
frequency depends on the blower scale. A blower with Qmax = 15 Nm3/min produced a lower pulsation frequency and greater pulsation intensity than that produced by a blower with Qmax = 10 Nm3/min, under the same superficial air velocity. The reason is that a lower impeller rotary speed is required for a larger-scale blower than for a smaller-scale blower under the same air output. This leads to a lower pressure pulsation frequency. A lower pulsation frequency indicates a longer pulsation period, which results in greater pressure amplitude, i.e. greater pressure pulsation intensity. The air pressure supplied by a compressor is always constant due to a surge tank employed to damp out the
Fig. 11. The pressure pulsation frequency, fp, detected in the windbox as a function of superficial air velocity, U. A Roots blower with Qmax = 10 and 15 Nm3/min was employed respectively. Hs = 0.20 m.
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possibly becomes the dominant frequency. If one attempts to investigate the hydrodynamic behavior of a fluidized bed using spectral analysis in the windbox, a preliminary experiment should be conducted to identify the fp in the spectrum. Although the nature of the Roots blower affects the pressure fluctuations in the fluidized bed, a pulsed flow is favorable from the view of the fluidized-bed reactor design. The pulsed flow was deliberately introduced into the bed to promote mixing (e.g., Refs. [19 –21]). Therefore, it seems unnecessary to damp out the pulsation intensity from the blower. However, the knowledge of the pulsing air supply is required to avoid data-analysis confusion.
4. Conclusions
List of symbols a real number a0 coefficient defined in Eq. (4) an coefficient defined in Eq. (6) bn coefficient defined in Eq. (7) c0 = Aa0A ; in this work, the DC component was suppressed so c0 = 0 cn harmonic amplitudes, defined in Eq. (5) C.V. coefficient of variance for the pressure fluctuations, defined in Eq. (2) C.V.b coefficient of variance for the pressure fluctuations in the bed, dimensionless fc characteristic frequency, Hz fp pressure pulsation frequency caused by Roots blower, Hz g(t) periodic function, defined in Eq. (3) Hs static bed height, m Ip pressure pulsation intensity caused by Roots blower, kPa N sampling points of pressure fluctuations for each run DP mean of pressure fluctuations, defined in Eq. (1) DPd pressure drop across the distributor, kPa DPi instantaneous value of the pressure drop DPw pressure drop across the distributor and bed material, kPa Qmax maximum air capacity rate of Roots blower under the normal condition of 0 jC and 1 atm, Nm3/min t time T period U superficial air velocity, m/s Umf minimum fluidization velocity, m/s V = 0.159 m3, windbox volume in normal condition Vw windbox volume, m3
It has been demonstrated experimentally that the pressure fluctuations in a fluidized bed with a Roots blower result from two major sources. The first is the hydrodynamic behavior within the bed and the second is the nature of the Roots blower, which significantly influences the pressure fluctuations in the windbox. At low superficial air velocity, the pressure pulsation frequency, fp, quite
Greek letters dn phase angle, defined in Eq. (8) /v valve aperture percentage on the bypass, % p = pi rp standard deviation of pressure fluctuations, defined in Eq. (2) x0 = 2p/T
Fig. 12. (a) The ratio of the pressure drop detected in the windbox with and without bed material, DPw/DPd; (b) the pressure pulsation intensity, Ip, detected in the windbox; (c) the coefficient of variance for the pressure fluctuations in the bed, C.V.b, as a function of the superficial air velocity, U. Hs = 0.20 m.
produced by various blower scales are close, as seen in Fig. 12(b). This means that the influence of the nature of the blower on the pressure fluctuations in the bed tends to be minimum at high air velocity. Therefore, the C.V.b values for various blowers employed gradually approached each other with the increasing air velocity, as shown in Fig. 12(c).
C.-S. Chyang, Y.-C. Lin / Powder Technology 127 (2002) 19–31
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