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Dynamic forces on a horizontal slat immersed in a fluidized bed of fine particles
chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 604–613
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Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Dynamic forces on a horizontal slat immersed in a fluidized bed of fine particles Duiping Liu a , Shuhao Zhang a , Ruoyi Wang b , Yongmin Zhang a,∗ a b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, PR China Luoyang Petrochemical Engineering Corporation (LPEC)/SINOPEC, Luoyang 471003, PR China
a r t i c l e
i n f o
a b s t r a c t
Article history:
Forces on a single horizontal slat immersed in a fluidized bed of Geldart A particles were
Received 2 September 2016
investigated for the purpose of providing useful design guidelines for long-period relia-
Received in revised form 10
bility of horizontal baffles in industrial reactors. The characteristics of slat forces in the
November 2016
fluidized and de-fluidized states of a reactor were measured using adhered strain gauges.
Accepted 18 November 2016
The main parameters influencing these characteristics were superficial gas velocity, instal-
Available online 25 November 2016
lation height, inclination angle, and method of slat installation. The experimental results show that the measured force on the slat in the fluidized state is highly fluctuating, but its
Keywords:
root-mean-square is usually significantly lower than for the de-fluidized state, especially
Force
at the bottom of the bed. The effects of various operating and structural parameters were
Slat
determined. Critical locations and operating conditions under high load are indicated and
Measurement
warrant more attention in structural design of horizontal baffles.
Fluidized bed
© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Baffle
1.
Introduction
For their high efficiencies in mass and heat transfer and uniform temperature distribution, fluidized reactors are widely used in many important industrial processes, such as petroleum refining and chemical synthesis (Davidson et al., 1985; Kunii and Levenspiel, 1991). In these reactors, fine Geldart A particles and bubbling/turbulent regimes are often employed. However, the presence of bubbles promotes gas channeling, non-uniform gas distribution, and bubble coalescence, and hence results in poor gas–solids contact in industrial fluidized reactors. Another problem is strong gas/solids back-mixing induced by movement of bubbles, which contributes to a considerable non-uniform distribution in residence time of either gas or solids in the bed. For a specified fluidized reactor, the resulting consequences may be low
those with inclined slats, e.g., the louver baffle (Kwauk, 1996; Zhang et al., 2009, 2008), the ridge baffle proposed by Jin et al. (1986), and KFBE packing (Koch–Glitsch) (Rall and Demulder, 2000; Rall and Wichita, 2001) were reported to be more effective in breaking up bubbles and suppressing solids back-mixing in fluidized beds. They are often the choice in many industrial fluidized reactors. However, as chemical reactors are often required to operate continuously for years, forces arising from bubble and solids motions during operation may result in the vibration, material fatigue over time, and finally failure of the immersed baffles or their supports. If not designed properly, the baffles may deform excessively or even be destroyed because of their weight or squeezing of static material during a de-
conversion or poor product selectivity, both incurring low profitability.
fluidized state, which is more probable in an industrial reactor with a large bed diameter or high bed level. Here, squeezing means the solids material above the internals presses them downward due to gravity. To
To solve these problems, researchers found that adding baffles or internals in fluidized bed is an effective way to split bubbles and improve the lateral distribution of bubbles to enhance gas–solids con-
mitigate such problems, details of the forces acting on the baffles must be gathered to implement a better engineering design. However, few studies have been conducted in this aspect. Hosny
tact while suppressing gas/solids back-mixing to optimize residence time distributions (Dutta and Suciu, 1992; Harrison and Grace, 1971;
(1982) was one of the early researchers who has performed a systematical study of the characteristics of the dynamic forces on horizontal tubes immersed in a fluidized bed with a rectangular cross section of
Jin et al., 2003, 1986; Kwauk, 1996; Rall and Demulder, 2000; Rall and Wichita, 2001; Zhang et al., 2009, 2008). Of the various types of baffles,
∗
215 × 200 mm. Horizontal tubes are widely used as heat exchange tubes
Corresponding author. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.cherd.2016.11.018 0263-8762/© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 604–613
Nomenclature a b f F45 h H0 L M PSD q qAVG qRMS Sp t uc uf umf W x
Width of the test slat (m) Thickness of the test slat (m) Frequency (Hz) Fraction of fine particles with diameter less than 45 m (%) The distance of slat installed away the bottom gas distributor (m) Static bed height (m) Length of the test slat (m) Moment of the beam under an uniform load (N m) Power spectral density (MPa2 /Hz or Pa2 /Hz) An upward uniform load (N/m2 ) The effective load density in de-fluidized bed (N/m2 ) The effective load density in fluidized bed (N/m2 ) Standard deviation of the pressure fluctuation (kPa) Time (s) Onset velocity of the turbulent flow regime (m/s) Superficial gas velocity (m/s) Minimum fluidization velocity (m/s) Section modulus of the test slat (m3 ) The distance to the left fixed end (m)
Greek letters Inclination angle of the test slat (o ) Measured transient stress on the surface of the test slat (MPa) RMS stresses measured at different measuring RMS,i points (MPa) ˆ i i RMS ϕ
Calculated stresses at different measuring points (MPa) Measured stress at different time (MPa) RMS value of measured stress signal in a period (MPa) The sum of the square of the difference between nine measured RMS stresses and the absolute values of nine calculated stresses at the same positions (MPa2 )
in fluidized boilers. The effects of superficial gas velocity, static bed height, particle size and density, tube shape, tube array configuration on forces exerted on the tubes of various diameters were tested. The magnitude of the forces is strongly influenced by superficial gas velocity, slightly dependent on particle size, and moderately affected by bed depth and particle density. The horizontal force components have significantly lower magnitude than the vertical force components. The intensity of the force exerted on a single tube in a tube bundle is found to be reduced significantly, which was also proved by a later study by Nagahashi et al. (2008). Hosny and Grace (1984) also found that the upstream (lowermost) tubes in a bundle experienced the largest rootmean-square (RMS) forces, while tubes in the top row encountered the smallest RMS forces. Kennedy et al. (1981) and Donovan (1980) also measured forces on horizontal 50-mm-OD tubes of various lengths immersed in fluidized beds of different sizes. The dynamic forces were obtained by attaching strain-gauge load cells on the surface of each test tube. Their exper-
605
imental results showed that the magnitude of the forces depended roughly linearly with tube length. To understand the mechanism of bubble motion and transient forces, Nagahashi et al. (1998) measured the transient force on a single horizontal tube from a single injected bubble. The pressure profiles around the tube and the movement of the bubble were also measured by pressure transducers and recorded synchronously with a video camera. By comparing the transient force signal and the recorded bubble movement, they identified the key mechanisms relating to the forces buffeting tubes. The force from the impact of the bubble wake was found to be considerably higher than that caused by the gas pressure field. Levy et al. (1992a,b), also found similar results in their experiment. Recently, Nagahashi et al. (2013) also studied the dynamic forces on horizontal tubes of non-circular cross-section in a two-dimensional fluidized bed. The effects of tube cross-sectional shape were identified by image analysis similar to Nagahashi et al. (1998). The upward impulse force by wake particles, downward friction, and wake-shedding were found to be the predominant factors contributing to the force. Following these previous studies, a good understanding of the mechanism of forces on tubes caused by bubble motions has been obtained. However, most of the research effort was devoted to the dynamic forces on horizontal tubes in bubbling fluidized beds of Geldart B particles, and concerned mainly the heat exchange tubes found in most fluidized boilers. Little work was done on the baffles (usually inclined slats) in fluidized reactors with Geldart A particles typically operating in the high-velocity turbulent regime. As fluidized beds with different Geldart groups of particles present distinct hydrodynamic behavior (Davidson et al., 1985; Kunii and Levenspiel, 1991) and the effects of baffle shape on bed hydrodynamics are also very significant (Dutta and Suciu, 1992; Harrison and Grace, 1971; Zhang et al., 2009, 2008), the understanding obtained from previous studies on forces acting on the tube is insufficient and incomplete in guiding the design of baffles in these fluidized chemical reactors. In our study, we assembled a large cold-model fluidized bed of fluid catalytic cracking (FCC) particles (typical Geldart A particles). A single horizontal slat made of stainless steel, representing the most important component of typical baffles used in fluidized chemical reactors, was employed to study the dynamic forces acting on it in both fluidized and de-fluidized states. The main parameters varied in this study were superficial gas velocity, installation height, inclination angle and installation method of the slat. The objective of this study was to establish a fundamental understanding of the force characteristics acting on a single slat to build a strong knowledge base for better structural engineering design of horizontal baffles in industrial fluidized reactors.
2.
Experiment
2.1.
Experimental unit
Experiments were performed in a fluidized column of crosssection 300 × 300 mm and height 5 m (Fig. 1). The column walls were made of transparent plexiglass so as to observe the inner gas–solids flow. Fluidizing air was supplied into the bed using a Roots blower. A regulating valve controlled the superficial gas velocity in the bed, which was monitored using a digital turbine flowmeter installed in the pipeline. After passing through a plenum chamber, air was uniformly distributed into the bed by a perforated plate distributor of open-area ratio of 0.6%. A steel wire screen (200 mesh) covered the distributor from above to prevent fine particles from dropping into the plenum chamber. Particles entrained in the gas leaving the fluidized bed were recovered using two high-efficiency cyclones installed in series. The collected particles were returned to the dense bed via their diplegs. The total separation efficiency of the two cyclones was nearly 99%, which helped maintain the solids inventory and their particle size distribution in the bed unchanged over long periods. Meanwhile, particles escaping
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Fig. 1 – Schematic of the experimental unit. Table 1 – Major properties of the employed FCC particles. Properties
Value
Mean diameter (m) Particle density (kg/m3 ) Bulk density (kg/m3 ) F45 (%) umf (m/s)
77.4 1500 922 1.4 0.005
Fig. 4 – Positions of the five heights to install the test slat and the seven pressure taps (all units in millimeter).
it was first inserted into the two pre-positioned holes in the column wall. The diameter of the two holes was just slightly larger than that of the fixed flanges of the test slat. Second, the test slat was fixed with two blind flanges using screws. Third, the two blind flanges were screwed to the bed column wall. Rubber gaskets between the blind flanges and the column walls, as well as the fixed flanges of the test slat, were used to keep gas and particles from escaping from the bed.
2.3. Fig. 2 – Schematic of the test slat.
Fig. 3 – Schematic of the installation method of the test slat. from the exit of the second-stage cyclone were collected by a filter bag and regularly returned into the bed. The particles used were FCC equilibrium particles of density 1500 kg/m3 and mean diameter 77.4 m. More details of the particle properties are listed in Table 1.
2.2.
Structure and installation of the test slat
The test slat (Fig. 2) was structured from a slat and two circular fixed flanges, made of 304 stainless steel welded together. The size of the slat was 50 mm (width) × 300 mm (length) × 2 mm (thickness). The length of the test slat spanned the cross section of the bed. The fixed flanges had a thickness equal to that of the plexiglass column wall. In installing the test slat (Fig. 3),
Measurement method
The primary objective was to measure the dynamic force acting on the test slat under different conditions. During the experiment, the test slat was immersed in the dense bed. A specified bed height of 1.0 m was maintained throughout all test runs. In addition, the influencing parameters were monitored including the superficial gas velocity, the inclination angle and installation height of the slat (i.e., the central line of the slat) above the bottom gas distributor, and the method of fixing the slat. Here, the inclination angle is defined as the angle between the slat surface and the horizontal plane. To connect the test slat, 24 screw holes were drilled into the fixed flanges at 15◦ intervals, enabling the test slat to be inclined at various angles, specifically 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , 75◦ , and 90◦ . The test slat was horizontal (vertical) at the inclination angle of 0◦ (90◦ ). There were five positions preset along the centerline of the column (Fig. 4) that enabled the test slat to be installed at different heights, i.e., 100 mm, 300 mm, 500 mm, 700 mm, 900 mm above the bottom gas distributor. The superficial gas velocity ranged between 0.2–0.8 m/s, covering both the bubbling and turbulent regimes. To measure the dynamic force acting on the test slat, nine strain gauges were mounted on the surface of the slat (Fig. 3). One strain gauge was fixed in the middle of the slat and the other eight strain gauges were fixed symmetrically about the center of the slat at a pitch of 35 mm. The method of measurement employed in this study has been validated and results of the force on a cantilever slat immersed in a flu-
chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 604–613
idized bed have been reported (Wang et al., 2015). Each strain gauge was connected to a bridge module to monitor the small change in resistance and to amplify the electrical signal. After AD conversion and stress transformation (i.e., the measured strain multiplied by the elasticity modulus (206 GPa) of stainless steel of which the test slat was made), the final digital stress signal was recorded and displayed using a computer. The strain gauges employed were foil-type resistance strain gauges (KFG-5-120-C1-11, Kyowa, Japan) of resistance 120 , length 9.4 mm and width 2.8 mm. They were mounted (Fig. 2) to measure tensile strain along the length direction of the slat. A stress analysis system (DH5921, Donghua Instrument Co., Ltd., Jiangsu, China) was used to record the stress signals with a sampling frequency of 1000 Hz; the measurement accuracy of this system was within 0.5%. Usually, 4–6 repeated runs at a sampling time of 30 s were conducted during each test to obtain better data reproducibility. Similar to previous studies (Grace and Hosny, 1985; Hosny and Grace, 1984; Kennedy et al., 1981; Nagahashi et al., 2008), the RMS stress
N 1 RMS = 2 i
N
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Fig. 5 – Average bed voidage as a function of superficial gas velocity.
(1)
i=1
was used to characterize the average intensity of the measured dynamic stress signal. Different from an arithmetic mean, RMS avoids the offset effect of opposing stresses. Moreover, RMS emphasizes more the higher stress values that may dominate and therefore is more helpful when designing fluidized baffles. Except for stress signals, the dynamic pressure signals in the dense bed were also measured simultaneously during the experiment. There were seven pressure taps installed on the column wall (Fig. 4), situated 30 mm, 100 mm, 300 mm, 500 mm, 900 mm, and 970 mm above the bottom gas distributor. Both the bed pressure fluctuation and the axial profile of the particle concentration were thus obtainable. Pressure taps made of ID-8 mm steel tubing, the tips of which were connecting to the bed material, were inserted with 400-m stainless-steel mesh screens to prevent fine particles from leaking. CY201 gauge pressure transducers (Chengdutest Electrical Technology Co., Ltd., Chengdu, China) were used to measure the dynamic pressure signal. Their measurement range was 0–50 kPa with a measurement accuracy of 0.1% full scale. The sampling frequency for the pressure signal was 100 Hz.
3.
Results and discussion
3.1.
Macro flow characteristics
The average voidage in the dense bed measured by the pressure transducers (Fig. 5) at different superficial gas velocities show a gradual increase with increasing superficial gas velocity. Similar results were also reported in the literature (Zhang, 2008; Zhang and Lu, 2010). A common precept is that the superficial gas velocity corresponding to the maximum pressure fluctuations is the onset velocity of the turbulent flow regime (uc ) (Bi et al., 2000; Yerushalmi and Cankurt, 1979; Yerushalmi et al., 1978). The standard deviations of the measured gauge pressure signals (Fig. 6) at different superficial gas velocities in the dense bed shows that uc appears in the range 0.5–0.6 m/s. The bottom
Fig. 6 – Standard deviation of pressure fluctuations at different superficial gas velocities. section of the bed appears first to step into the turbulent flow regime earlier than the middle and top sections of the bed, as the superficial gas velocity corresponding to the maximum pressure fluctuation at h = 100 mm (uc = 0.5 m/s) is smaller. In the study of Zhu and Zhu (2008), a similar phenomenon was also observed.
3.2. Characteristics of typical dynamic stress signals measured in the dense bed During fluidization state, the test slat when immersed in the dense bed is subjected mainly to impacts induced by bubble movement. Dynamic stress signals (Fig. 7) measured using the strain gauges typically exhibit strong fluctuations. In previous studies of the mechanism (Levy et al., 1992a,b; Nagahashi et al., 1998, 2013), where a series of bubbles were created manually, a series of stress pulses induced by these observable and traceable bubbles were identified in the measured force signals. However, in a larger diameter three-dimensional fluidized bed, the test slat was relatively longer in length and hence subjected to simultaneous impacts from numerous bubbles. The measured stress signals (Fig. 7) show overlaps in impact impulses caused by these bubbles. Therefore, distinguishing each pulse is difficult. The range in magnitude of the measured stress signals for the test slat was typically 0–30 MPa. Also the average stress at = 0◦ is higher than that at = 90◦ . The stress values at = 90◦ oscillated above and below with an average value approximately equaling zero, but the stress values at = 0◦ are all
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Fig. 7 – Typical transient stress signals measured in the fluidized bed.
Fig. 9 – Power spectral density of measured dynamic pressure signal.
Fig. 10 – The RMS stress values at nine measuring points.
Fig. 8 – Corresponding power spectral densities of the two stress signals. positive (Fig. 7). Indeed, the averages of most measured stress signals in this study, except at = 90◦ , were positive indicating that the resultant force on the test slat in the fluidized bed is upward. In previous studies (Grace and Hosny, 1985; Hosny, 1982; Kennedy et al., 1981; Nagahashi et al., 2008), the vertical force acting on a round tube in a fluidized bed was also found to be positive on average with fluctuations similar to the measured stress signal acting on the test slat at = 0◦ in this study. However, the horizontal force acting on a round tube had a zero average as for the test slat at = 90◦ in this study. To obtain the frequency-domain characteristics of the measured stress signals (Fig. 8), a power spectral density (PSD) analysis was performed of the two measured stress signals
(Fig. 7). Here, the data used to compute the PSD were larger than that shown in Fig. 7. The effective frequency range of the stress signals is mainly in the range 0–10 Hz. The dominant frequencies corresponding to the maximum magnitude are usually less than 5 Hz. This result is consistent with previous studies on forces acting on horizontal tubes by Hosny (1982) and Kennedy et al. (1981). The PSD of the pressure signal (Fig. 9) measured synchronously as the stress signal shows that its macroscopic characteristics are similar to that of the measured stress signals. The effective frequency range and the dominant frequency of the pressure signal are also similar to the stress signals. Previous studies (Bi, 2007; van Ommen et al., 2011) have demonstrated clearly the close relationship between pressure fluctuations and bubble dynamics in the fluidized beds. These similarities here infer the common origin of both stress and pressure fluctuations in fluidized beds.
3.3. slat
Lateral profile of the measured stress along the
The lateral profiles of the RMS stress (Fig. 10) measured using the nine strain gauges mounted on the test slat (Fig. 3) show a nearly symmetric distribution over the center of the slat. The maximum RMS stress appears at both ends of the slat near the column wall, whereas the minimum RMS stress appears near Gauges #2 and #8 (Fig. 3). At the midpoint of the slat, the measured RMS stress is often peaked slightly lower than the RMS stress measured at the two ends of the slat. The above finding indicates that the two ends of the slat are vulnerable
chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 604–613
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Fig. 11 – Bending moment diagram of a beam fixed at both ends subjecting to a uniform load. regions for horizontal internals immersed in a fluidized bed in regard to engineering design. During fluidization of the bed, these locations of highest fluctuating stress would experience a higher probability of fatigue failure. The measured stress is not only affected by the force acting on the slat, the section modulus, an indicator of its stiffness, which is a function of the geometry (width and thickness) of the slat, also has a very big influence on the measured stress. Specifically, if the slat has a different thickness, the measured stress will change. Therefore, the influence of the slat stiffness must be decoupled from the measured stress signal to retain the effective force acting on the slat, as it is more universal and of interest to reactor designers. As the test slat was relatively longer in length and subjected to multiple bubble impacts, the load acting on the slat is more similar to an upward uniform load (Fig. 11). For a rectangular beam of length L, width a, and thickness b, fixed at both ends and subjected to an upward uniform load of load density q, the profile of the bending moment along the beam is
M (x) =
aq 6x2 + L2 − 6xL
(2)
12
obtained using the theory of material mechanics. Here, M is the profile of the bending moment, x the distance from the left end, and q the force acting on unit area. The profile of the tensile stress is computed from the profile of bending moment by dividing it by the section modulus of the slat W,
M ˆ (x) = = W
aq 6x2 + L2 − 6xL 12
=
/
ab3 2 · 12 b
q 6x2 + L2 − 6xL 2b2
(3)
The sum of the square of the difference between the nine measured RMS stresses and the absolute values of the nine calculated stresses at the same positions is
ϕ=
9
2
RMS,i − |ˆ i |
(4)
i=1
Here, RMS,i and ˆ i are the measured RMS stress and the calculated stress, respectively. Based on the least-squares method, an effective load density qRMS can be determined when ϕ is minimum. We used qRMS to quantify the force acting on the test slat. Comparing the profile of the measured RMS stresses and the calculated stresses under an effective load density determined by the above-described method (Fig. 10) shows that their trends are highly correlated. With this load density,
Fig. 12 – Transient stress signals at different superficial gas velocities. the stress profiles of internals with different geometries can also be estimated based on Eq. (3).
3.4.
Effect of superficial gas velocity
The transient stress signals for three different superficial gas velocities (Fig. 12) all measured at = 0◦ , where vertical impact area of the slat was maximum, indicate that the average as well as the magnitude of fluctuation of these signals increase with increasing superficial gas velocity in consequence of the increased number of bubbles and stronger bubble dynamics. To split the bubbles, horizontal baffles made of inclined slats are typically installed in the fluidized beds at inclination angles usually between 40–60◦ . In these situations, the effective load acting on a slat at different superficial gas velocities [Fig. 13(a)] shows that at three installation heights qRMS increases linearly with increasing velocity. This result is similar to those previously obtained from measured force characteristics on horizontal tubes immersed in fluidized beds (Hosny, 1982; Hosny and Grace, 1984; Kennedy et al., 1981; Nagahashi et al., 2008). These results can be attributed to the enhanced bubble motion and the stronger motion of solids induced in the bed at increasing superficial gas velocities. When gas velocity is close to the minimum fluidization velocity, at which the rising bubbles are small in size and their rising velocity is slow, the force on the slat is expected to be small. As the superficial gas velocity increases, the number of bubbles, their size and rising velocity increase at the same time. This then contributes to the increasing number of bubbles synchronously acting on the slat. The solids pressure from the upper layer of the rising bubbles is higher and the wake impact of the bubbles passing the slat is stronger, which ultimately leads to a higher force acting on the slat. Moreover, the internal solids circulation in the bed, i.e., the so called gulf streaming, also becomes stronger with increasing superficial gas velocity, which is another contributor to the higher force on the slat. At lower inclination angles [e.g., = 0◦ in Fig. 13(b)], the trend is similar to Fig. 13(a), but the measured qRMS s are comparable to those at = 45◦ . For many supporting internals installed in the fluidized reactors, their inclination angles are usually 90◦ . The force acting on them is similar to the curve for = 90◦ shown in Fig. 13(b). Unlike other inclination angles, qRMS is nearly unchanged and maintains a very low value with increasing superficial gas velocity. When studying the horizontal force
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Fig. 13 – Effective load densities at different superficial gas velocities.
Fig. 14 – Effective load densities at different installation heights.
on a round tube immersed in a fluidized bed, Hosny (1982) also found a big difference in the magnitudes of the measured vertical and horizontal forces. He also found that the horizontal force acting on a round tube was maintained at low values with very slow increment in magnitudes with increasing superficial gas velocity. Compared with the horizontal gas–solids movement, the vertical movement is well-known to be more dominant. Changing the inclination angle from 0◦ through to 90◦ decreases the impact area for vertically moving solids. Moreover, the offset effect of the buffeting forces on the two sides also reduces the total force on the slat. Previous studies on gas/solids dispersion in fluidized beds have shown that the coefficients of dispersion are usually an order higher for vertical than for lateral movement (Du et al., 2002; Geldart, 1997; van Deemter, 1980). As to the force characteristics acting on internals immersed in fluidized beds, it seems that a similar mechanism also exists.
Except at = 90◦ , a similar trend is seen in all other inclination angles [Figs. 14(a) and (b)]. The high qRMS s in the bed bottom may be related to gas jetting from the bottom gas distributor, causing a stronger movement of solids and a larger impact on the slat. Moreover, squeezing of the bed level above the slat is also a possible factor. On the top of the bed, the bursting of bubbles causes a large amount of solids to be ejected into the freeboard and allowed to re-enter the dense bed, contributing to a higher RMS stress. The high fluctuation magnitude of transient stress signal (i.e., h = 900 mm) is also a possible indicator of the strong solids movement caused by bursting bubbles near the bed surface. At = 90◦ , qRMS remains nearly constant [Fig. 14(b)]. Similar to the trend in Fig. 13(b), the installation height also has no significant effect on qRMS at = 90◦ . In an industrial fluidized bed, horizontal internals immersed in the bottom or near the bed surface should be strengthened if they are not installed vertically.
3.5.
3.6.
Effect of installation height
In the experiment, through observing the transient stress signals measured at three different installation heights, we found that the signal from the bottom of the bed (i.e., h = 100 mm) has the highest average but lowest fluctuation magnitude. Whereas, the stress signal measured in the top of the bed (i.e., h = 900 mm) has the highest fluctuation magnitude. From the axial profiles of the effective load density that were measured for typical horizontal baffles made of inclined slats (e.g., at = 45◦ in Fig. 14), the qRMS s are higher in the bottom and top of the bed giving a minimum qRMS in the middle.
Effect of inclination angle
In designing horizontal baffles for fluidized reactors, proper choice of the inclination angle of the slats is an important factor in achieving optimal results in enhancing gas–solids contact and obtaining the desired gas/solids back-mixing (Zhang, 2008; Zhang et al., 2007). By observing the measured transient stress signals at different inclination angles, we noticed that they exhibit similar fluctuation features although at = 90◦ the signal is distinctly lower with an average near 0 MPa (i.e., in Fig. 7). The stress signals all have positive averages except for at = 90◦ .
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Fig. 15 – Effect of inclination angle on the measured effective load densities.
Fig. 16 – Schematic of the test slat with one end fixed. Regardless of the fluctuation in experimental data, the measured effective load density qRMS is observed in general to decrease slightly with increasing inclination angle between = 0–75◦ (Fig. 15) but rapidly falls in value between = 75–90◦ . This trend can also be seen at other installation heights. Therefore, the effect of inclination angle on the force acting on the slats is expected to be small between = 40–60◦ at which the slats of typical horizontal baffles in industrial fluidized reactors are inclined.
3.7.
Effect of installation method
Usually, baffles of a fluidized reactor are fixed at one or both ends; both methods have advantages and disadvantages. A cantilever-like baffle is usually used when vertical thermal displacements occur between its two ends. In a cold-wall fluidized bed, a large temperature difference exists between the internal ends welded on the cold column wall and its main body which is usually immersed in the high-temperature bed. The cantilever-beam design permits larger lateral thermal displacements without compromising the structural integrity of the internal. However, internals with both ends fixed are more suitable in hot-wall fluidized beds. In this study, we also compared the forces acting on the slat in regard to the method of installation. The slat with one end fixed had the same width and thickness as the slat with both ends fixed (Cf. Figs. 2 and 16) although the length of the former was slightly smaller (298 mm). The geometrical details of the fixed flange and the mounting of the strain gauges were also the same (Figs. 2 and 3). Regarding installation method, the measured RMS stresses with signal data taken from Gauge #9 near the right end of the two slats (Figs. 2 and 16) exhibited the highest stresses for both test slats (Fig. 17). Their trends as superficial gas velocity increases are similar, but at = 0◦ the stresses found in the single fixed-end slat are about 1.5–2 times larger than that with ends fixed. At = 45◦ , the ratio appears to decrease slightly to 1.5 times, especially at lower gas velocities. At = 90◦ , there is
611
Fig. 17 – Comparison of the measured RMS stresses with one and both ends fixed. no significant difference between the measured RMS stresses for the two installation methods, as all the measured RMS stresses are very small in value. For a beam subjected to a uniform load, the calculated highest stress in the beam with a single fixed end is 6 times higher than with both ends fixed. The ratios measured in this study were much smaller. Because the flow is complex, a slat is impacted by upward and downward solids simultaneously, and it is this offsetting that produces the smaller ratios measured.
3.8.
Forces in the de-fluidized bed
Apart from the normal fluidized state, internals immersed in the bed may also experience abnormal operating conditions during the operation of a fluidized reactor, such as those for the de-fluidized state. There may be short periods of defluidization during the addition of solids or the unforeseen downtime of a blower following an unscheduled power-down of the plant. To ensure the safeguarding of internals, the force characteristics acting on the internals during de-fluidization also needs to be understood. During tests of the de-fluidized bed, the initial height (H0 ) was maintained at 1 m throughout all tests, as for tests in the fluidized state. Here, the slat is subjected to a static pressure induced by the weight of the solids in the bed. From the downward force of the solids material, the direction of the measured strain or stress opposes that measured in the fluidized beds. To guarantee data reproducibility, a standard operation procedure and three runs was followed for each test. Before each stress measurement, we first fluidized the bed at a low superficial gas velocity for several minutes and then closed the controlling valve in the gas pipeline. After a few minutes of deaeration of the bed material, measurements were taken when the static bed surface leveled out and the stress signal stabilized. From the measured RMS stresses, a similar effective load density was obtained using the method to obtain Fig. 10. For a horizontally placed slat (i.e., = 0◦ ), the effective load density (Fig. 18) decreases sharply with increasing installation height, as less solids weight acts on the slat. The highest effective load density appears when the slat is immersed in the bottom of the bed, which is 5–6 times higher than that for the fluidized state. This trend is different from that in the fluidized state where the lowest effective load density appears in the middle of the bed. In addition, the inclination angle also has a marked effect on the measured force in the de-fluidized bed (Fig. 19). The
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Fig. 18 – Effective load densities at different heights in the de-fluidized bed.
(1) The measured dynamic stresses on a slat immersed in a fluidized bed fluctuate over a range that is usually significantly lower than those measured in a de-fluidized bed, especially in the bed bottom. Their effective frequency range is mainly in the range of 0–10 Hz. (2) When the slat is oriented vertically (i.e., at = 90◦ ), the measured effective load density on the slat in both fluidized and de-fluidized states are low. Changing the operating and structural parameters have no significant effect. At other inclination angles, the measured effective load density in the fluidization state increases linearly with increasing superficial gas velocity. Along the height of the dense fluidized bed, higher effective load densities appear in the bottom and top of the dense bed, whereas a minimum effective load density appears in the middle of the bed. As the inclination angle increases, the measured effective load density decreases slightly at < 75◦ and then decreases rapidly to a low value at = 90◦ . (3) The lateral profile of the RMS stress in a fluidized bed is symmetric about the center of the slat, with the maximum RMS stress appearing at the ends near the column wall. (4) In a de-fluidized bed, a horizontal slat internal installed in the bottom of the bed encounters a very high load due to the weight of the static bed if they are installed at a low inclination angle. (5) Under the same operating conditions, the RMS stress value measured for a single fixed-end slat is about 1.5–2 times higher than that when both ends of the slat are fixed.
Acknowledgement
Fig. 19 – Effect of inclination angle on effective load density in the de-fluidized bed.
measured stress decreases with increasing inclination angle. Similar trends were observed in the fluidized state. When the slat is placed in the bottom of the bed, the highest load density measured at = 0◦ is about an order higher than at = 90◦ . In industrial fluidized reactors with high static beds and large diameters, an abrupt shut-down of the fluidizing gas stream may compromise some internals like baffles or other supporting structures with large horizontal spans. The strength of the internals near the bed bottom requires special attention. The squeezing of the high-level solids material and their large spans may result in a much higher local stress on these internals than that measured in this study. If not designed properly, stress fractures or plastic deformation of these internals may appear, resulting in a departure from their optimum structural design and failure or even jeopardizing the fluidized reactor. In these conditions, vertical slats or ones with high inclination angles are recommended to reduce the potential damage from the static bed material. Moreover, operation management protocols need to be established to avoid abnormal operation conditions or to mitigate their harmful effect.
4.
Conclusion
From our systematic study of the forces acting on a slat in a fluidized bed of Geldart A particles, the following conclusions can be drawn:
The authors acknowledge the financial supports by the National Natural Science Foundation of China (21276273), the Ministry of Science and Technology of China (2012CB215004), the Science Foundation of China University of Petroleum, Beijing (2462015YQ0312).
References Bi, H.T., 2007. A critical review of the complex pressure fluctuation phenomenon in gas–solids fluidized beds. Chem. Eng. Sci. 62, 3473–3493. Bi, H.T., Ellis, N., Abba, I.A., Grace, J.R., 2000. A state-of-the-art review of gas–solid turbulent fluidization. Chem. Eng. Sci. 55, 4789–4825. Davidson, J.F., Clift, R., Harrison, D., 1985. Fluidization, second ed. Academic press London, UK. Donovan, J.E., 1980. A Study of Forces on Simulated Heat Exchange Tubes Immersed in a Cold Fluidized Bed. Master Dissertation. Oregon State University. Du, B., Fan, L.-S., Wei, F., Warsito, W., 2002. Gas and solids mixing in a turbulent fluidized bed. AlChE J. 48, 1896–1909. Dutta, S., Suciu, G.D., 1992. An experimental study of the effectiveness of baffles and internals in breaking bubbles in fluid beds. J. Chem. Eng. 25, 345–348. Geldart, D., 1997. Mixing in fluidized beds. In: Harnby, N., Edwards, M.F., Nienow, A.W. (Eds.), Mixing in the Process Industries. , second ed. Butterworth-Heinemann, Oxford, pp. 62–78. Grace, J.R., Hosny, N., 1985. Forces on horizontal tubes in gas fluidized beds. Chem. Eng. Res. Des. 63, 191–198. Harrison, D., Grace, J.R., 1971. Fluidized beds with internal baffles. In: Davidson, J.F., Harrison, D. (Eds.), Fluidization. Academic Press London & New York, London & New York, pp. 599–624. Hosny, N.M., 1982. Forces on Tubes Immersed in a Fluidized Bed. Doctoral Dissertation. The University of British Columbia.
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Hosny, N.M., Grace, J.R., 1984. Transient forces on tubes within an array in a fluidized bed. AIChE J. 30, 974–976. Jin, Y., Wei, F., Wang, Y., 2003. Effect of internal tubes and baffles. In: Yang, W.C. (Ed.), Handbook of Fluidization and Fluid Particle Systems. Marcel Dekker Inc., New York, USA, pp. 171–200. Jin, Y., Yu, Z.Q., Zhang, L., Yao, W.H., Cai, P., 1986. Ridge type internal baffle for fluidized bed reactor. Petrochem. Eng. 15, 269–277 (in Chinese). Kennedy, T.C., Donovan, J.E., Trigas, A., 1981. Forces on immersed tubes in fluidized beds. AIChE J. 27, 351–357. Kunii, D., Levenspiel, O., 1991. Fluidization Engineering, second ed. Butterworth-Heinmann, Boston, USA. Kwauk, M., 1996. Fluidization. In: Shi, J., Wang, J. (Eds.), Chemical Engineering Handbook. , second ed. Chemical Industry Press, Beijng, Beijing, pp. 62–78 (in Chinese). Levy, E.K., Ayalon, A., Johnson, S., Sethu, H., Wagh, M., 1992a. Dynamic loading on a horizontal tube in a bubbling fluidized bed. AIChE Symp. Ser. 88, 99–106. Levy, E.K., Wagh, M., Sethu, H., Pinarbasi, A., 1992b. Pattern recognition analysis of bubbles impacting on tubes. Powder Technol. 70, 175–181. Nagahashi, Y., Asako, Y., Lim, K.S., Grace, J.R., 1998. Dynamic forces on a horizontal tube due to passing bubbles in fluidized beds. Powder Technol. 98, 177–182. Nagahashi, Y., Grace, J.R., Lim, K.-S., Asako, Y., 2008. Dynamic force reduction and heat transfer improvement for horizontal tubes in large-particle gas-fluidized beds. J. Therm. Sci. 17, 77–83. Nagahashi, Y., Yamamoto, D., Grace, J.R., Asako, Y., 2013. Forces on horizontal tubes of non-circular cross-section in fluidized beds. In: Kuipers, J.A.M., Mudde, R.F., van Ommen, J.R., Asako, Y. (Eds.), Fluidization XIV. , pp. 607–614. Rall, R.R., Demulder, B., 2000. New internal for maximizing performance of FCC catalyst strippers. In: Proceeding of the 12th Refining Seminar, San Francisco, California, USA. Rall, R.R., Wichita, K.S., 2001. Apparatus for contacting of gases and solids in fluidized beds. US Patent, 6224833.
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van Deemter, J.J., 1980. Mixing patterns in large-sacle fluidization beds. In: Grace, J.R., Matsen, J.M. (Eds.), Fluidization. Plenum Press, New York & London, pp. 62–78. van Ommen, J.R., Sasic, S., van der Schaaf, J., Gheorghiu, S., Johnsson, F., Coppens, M.-O., 2011. Time-series analysis of pressure fluctuations in gas–solid fluidized beds–a review. Int. J. Multiph. Flow 37, 403–428. Wang, R.Y., Liu, D.P., Li, Z., Zhang, Y.M., 2015. Experimental study on the force characteristics acting on the slat baffles in fine particles gas–solids fluidized bed. CJPE J. 15, 375–380 (in Chinese). Yerushalmi, J., Cankurt, N.T., 1979. Further studies of the regimes of fluidization. Powder Technol. 24, 187–205. Yerushalmi, J., Cankurt, N.T., Geldart, D., Liss, B., 1978. Flow regimes in vertical gas–solid contact systems. AlChE Symp. Ser. 74, 1–12. Zhang, Y.M., 2008. Hydrodynamic and Mixing Properties of a Novel Baffled Fluidized Bed. Doctoral Dissertation. China University of Petroleum. Zhang, Y.M., Grace, J.R., Bi, X., Lu, C., Shi, M., 2009. Effect of louver baffles on hydrodynamics and gas mixing in a fluidized bed of FCC particles. Chem. Eng. Sci. 64, 3270–3281. Zhang, Y.M., Lu, C.X., 2010. Fluidization quality and gas back-mixing in gas–solids fluidized beds of different shapes. CIESC J. 61, 2296–2304 (in Chinese). Zhang, Y.M., Lu, C.X., Grace, J.R., Bi, H.T., Shi, M.X., 2008. Gas back-mixing in a two-dimensional baffled turbulent fluidized bed. Ind. Eng. Chem. Res. 47, 8484–8491. Zhang, Y.M., Lu, C.X., Shi, M.X., 2007. Effects of structure parameters and arrangements of louver baffles on the hydrodynamics of turbulent fluidized beds of fine particles. Pet. Process. Petrochem. 38, 64–69 (in Chinese). Zhu, H., Zhu, J., 2008. New investigation in regime transition from bubbling to turbulent fluidization. Can. J. Chem. Eng. 86, 553–562.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Dynamic forces on a horizontal slat immersed in a fluidized bed of fine particles Duiping Liu a , Shuhao Zhang a , Ruoyi Wang b , Yongmin Zhang a,∗ a b
State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, PR China Luoyang Petrochemical Engineering Corporation (LPEC)/SINOPEC, Luoyang 471003, PR China
a r t i c l e
i n f o
a b s t r a c t
Article history:
Forces on a single horizontal slat immersed in a fluidized bed of Geldart A particles were
Received 2 September 2016
investigated for the purpose of providing useful design guidelines for long-period relia-
Received in revised form 10
bility of horizontal baffles in industrial reactors. The characteristics of slat forces in the
November 2016
fluidized and de-fluidized states of a reactor were measured using adhered strain gauges.
Accepted 18 November 2016
The main parameters influencing these characteristics were superficial gas velocity, instal-
Available online 25 November 2016
lation height, inclination angle, and method of slat installation. The experimental results show that the measured force on the slat in the fluidized state is highly fluctuating, but its
Keywords:
root-mean-square is usually significantly lower than for the de-fluidized state, especially
Force
at the bottom of the bed. The effects of various operating and structural parameters were
Slat
determined. Critical locations and operating conditions under high load are indicated and
Measurement
warrant more attention in structural design of horizontal baffles.
Fluidized bed
© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Baffle
1.
Introduction
For their high efficiencies in mass and heat transfer and uniform temperature distribution, fluidized reactors are widely used in many important industrial processes, such as petroleum refining and chemical synthesis (Davidson et al., 1985; Kunii and Levenspiel, 1991). In these reactors, fine Geldart A particles and bubbling/turbulent regimes are often employed. However, the presence of bubbles promotes gas channeling, non-uniform gas distribution, and bubble coalescence, and hence results in poor gas–solids contact in industrial fluidized reactors. Another problem is strong gas/solids back-mixing induced by movement of bubbles, which contributes to a considerable non-uniform distribution in residence time of either gas or solids in the bed. For a specified fluidized reactor, the resulting consequences may be low
those with inclined slats, e.g., the louver baffle (Kwauk, 1996; Zhang et al., 2009, 2008), the ridge baffle proposed by Jin et al. (1986), and KFBE packing (Koch–Glitsch) (Rall and Demulder, 2000; Rall and Wichita, 2001) were reported to be more effective in breaking up bubbles and suppressing solids back-mixing in fluidized beds. They are often the choice in many industrial fluidized reactors. However, as chemical reactors are often required to operate continuously for years, forces arising from bubble and solids motions during operation may result in the vibration, material fatigue over time, and finally failure of the immersed baffles or their supports. If not designed properly, the baffles may deform excessively or even be destroyed because of their weight or squeezing of static material during a de-
conversion or poor product selectivity, both incurring low profitability.
fluidized state, which is more probable in an industrial reactor with a large bed diameter or high bed level. Here, squeezing means the solids material above the internals presses them downward due to gravity. To
To solve these problems, researchers found that adding baffles or internals in fluidized bed is an effective way to split bubbles and improve the lateral distribution of bubbles to enhance gas–solids con-
mitigate such problems, details of the forces acting on the baffles must be gathered to implement a better engineering design. However, few studies have been conducted in this aspect. Hosny
tact while suppressing gas/solids back-mixing to optimize residence time distributions (Dutta and Suciu, 1992; Harrison and Grace, 1971;
(1982) was one of the early researchers who has performed a systematical study of the characteristics of the dynamic forces on horizontal tubes immersed in a fluidized bed with a rectangular cross section of
Jin et al., 2003, 1986; Kwauk, 1996; Rall and Demulder, 2000; Rall and Wichita, 2001; Zhang et al., 2009, 2008). Of the various types of baffles,
∗
215 × 200 mm. Horizontal tubes are widely used as heat exchange tubes
Corresponding author. E-mail address: [email protected] (Y. Zhang). http://dx.doi.org/10.1016/j.cherd.2016.11.018 0263-8762/© 2016 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 604–613
Nomenclature a b f F45 h H0 L M PSD q qAVG qRMS Sp t uc uf umf W x
Width of the test slat (m) Thickness of the test slat (m) Frequency (Hz) Fraction of fine particles with diameter less than 45 m (%) The distance of slat installed away the bottom gas distributor (m) Static bed height (m) Length of the test slat (m) Moment of the beam under an uniform load (N m) Power spectral density (MPa2 /Hz or Pa2 /Hz) An upward uniform load (N/m2 ) The effective load density in de-fluidized bed (N/m2 ) The effective load density in fluidized bed (N/m2 ) Standard deviation of the pressure fluctuation (kPa) Time (s) Onset velocity of the turbulent flow regime (m/s) Superficial gas velocity (m/s) Minimum fluidization velocity (m/s) Section modulus of the test slat (m3 ) The distance to the left fixed end (m)
Greek letters Inclination angle of the test slat (o ) Measured transient stress on the surface of the test slat (MPa) RMS stresses measured at different measuring RMS,i points (MPa) ˆ i i RMS ϕ
Calculated stresses at different measuring points (MPa) Measured stress at different time (MPa) RMS value of measured stress signal in a period (MPa) The sum of the square of the difference between nine measured RMS stresses and the absolute values of nine calculated stresses at the same positions (MPa2 )
in fluidized boilers. The effects of superficial gas velocity, static bed height, particle size and density, tube shape, tube array configuration on forces exerted on the tubes of various diameters were tested. The magnitude of the forces is strongly influenced by superficial gas velocity, slightly dependent on particle size, and moderately affected by bed depth and particle density. The horizontal force components have significantly lower magnitude than the vertical force components. The intensity of the force exerted on a single tube in a tube bundle is found to be reduced significantly, which was also proved by a later study by Nagahashi et al. (2008). Hosny and Grace (1984) also found that the upstream (lowermost) tubes in a bundle experienced the largest rootmean-square (RMS) forces, while tubes in the top row encountered the smallest RMS forces. Kennedy et al. (1981) and Donovan (1980) also measured forces on horizontal 50-mm-OD tubes of various lengths immersed in fluidized beds of different sizes. The dynamic forces were obtained by attaching strain-gauge load cells on the surface of each test tube. Their exper-
605
imental results showed that the magnitude of the forces depended roughly linearly with tube length. To understand the mechanism of bubble motion and transient forces, Nagahashi et al. (1998) measured the transient force on a single horizontal tube from a single injected bubble. The pressure profiles around the tube and the movement of the bubble were also measured by pressure transducers and recorded synchronously with a video camera. By comparing the transient force signal and the recorded bubble movement, they identified the key mechanisms relating to the forces buffeting tubes. The force from the impact of the bubble wake was found to be considerably higher than that caused by the gas pressure field. Levy et al. (1992a,b), also found similar results in their experiment. Recently, Nagahashi et al. (2013) also studied the dynamic forces on horizontal tubes of non-circular cross-section in a two-dimensional fluidized bed. The effects of tube cross-sectional shape were identified by image analysis similar to Nagahashi et al. (1998). The upward impulse force by wake particles, downward friction, and wake-shedding were found to be the predominant factors contributing to the force. Following these previous studies, a good understanding of the mechanism of forces on tubes caused by bubble motions has been obtained. However, most of the research effort was devoted to the dynamic forces on horizontal tubes in bubbling fluidized beds of Geldart B particles, and concerned mainly the heat exchange tubes found in most fluidized boilers. Little work was done on the baffles (usually inclined slats) in fluidized reactors with Geldart A particles typically operating in the high-velocity turbulent regime. As fluidized beds with different Geldart groups of particles present distinct hydrodynamic behavior (Davidson et al., 1985; Kunii and Levenspiel, 1991) and the effects of baffle shape on bed hydrodynamics are also very significant (Dutta and Suciu, 1992; Harrison and Grace, 1971; Zhang et al., 2009, 2008), the understanding obtained from previous studies on forces acting on the tube is insufficient and incomplete in guiding the design of baffles in these fluidized chemical reactors. In our study, we assembled a large cold-model fluidized bed of fluid catalytic cracking (FCC) particles (typical Geldart A particles). A single horizontal slat made of stainless steel, representing the most important component of typical baffles used in fluidized chemical reactors, was employed to study the dynamic forces acting on it in both fluidized and de-fluidized states. The main parameters varied in this study were superficial gas velocity, installation height, inclination angle and installation method of the slat. The objective of this study was to establish a fundamental understanding of the force characteristics acting on a single slat to build a strong knowledge base for better structural engineering design of horizontal baffles in industrial fluidized reactors.
2.
Experiment
2.1.
Experimental unit
Experiments were performed in a fluidized column of crosssection 300 × 300 mm and height 5 m (Fig. 1). The column walls were made of transparent plexiglass so as to observe the inner gas–solids flow. Fluidizing air was supplied into the bed using a Roots blower. A regulating valve controlled the superficial gas velocity in the bed, which was monitored using a digital turbine flowmeter installed in the pipeline. After passing through a plenum chamber, air was uniformly distributed into the bed by a perforated plate distributor of open-area ratio of 0.6%. A steel wire screen (200 mesh) covered the distributor from above to prevent fine particles from dropping into the plenum chamber. Particles entrained in the gas leaving the fluidized bed were recovered using two high-efficiency cyclones installed in series. The collected particles were returned to the dense bed via their diplegs. The total separation efficiency of the two cyclones was nearly 99%, which helped maintain the solids inventory and their particle size distribution in the bed unchanged over long periods. Meanwhile, particles escaping
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Fig. 1 – Schematic of the experimental unit. Table 1 – Major properties of the employed FCC particles. Properties
Value
Mean diameter (m) Particle density (kg/m3 ) Bulk density (kg/m3 ) F45 (%) umf (m/s)
77.4 1500 922 1.4 0.005
Fig. 4 – Positions of the five heights to install the test slat and the seven pressure taps (all units in millimeter).
it was first inserted into the two pre-positioned holes in the column wall. The diameter of the two holes was just slightly larger than that of the fixed flanges of the test slat. Second, the test slat was fixed with two blind flanges using screws. Third, the two blind flanges were screwed to the bed column wall. Rubber gaskets between the blind flanges and the column walls, as well as the fixed flanges of the test slat, were used to keep gas and particles from escaping from the bed.
2.3. Fig. 2 – Schematic of the test slat.
Fig. 3 – Schematic of the installation method of the test slat. from the exit of the second-stage cyclone were collected by a filter bag and regularly returned into the bed. The particles used were FCC equilibrium particles of density 1500 kg/m3 and mean diameter 77.4 m. More details of the particle properties are listed in Table 1.
2.2.
Structure and installation of the test slat
The test slat (Fig. 2) was structured from a slat and two circular fixed flanges, made of 304 stainless steel welded together. The size of the slat was 50 mm (width) × 300 mm (length) × 2 mm (thickness). The length of the test slat spanned the cross section of the bed. The fixed flanges had a thickness equal to that of the plexiglass column wall. In installing the test slat (Fig. 3),
Measurement method
The primary objective was to measure the dynamic force acting on the test slat under different conditions. During the experiment, the test slat was immersed in the dense bed. A specified bed height of 1.0 m was maintained throughout all test runs. In addition, the influencing parameters were monitored including the superficial gas velocity, the inclination angle and installation height of the slat (i.e., the central line of the slat) above the bottom gas distributor, and the method of fixing the slat. Here, the inclination angle is defined as the angle between the slat surface and the horizontal plane. To connect the test slat, 24 screw holes were drilled into the fixed flanges at 15◦ intervals, enabling the test slat to be inclined at various angles, specifically 0◦ , 15◦ , 30◦ , 45◦ , 60◦ , 75◦ , and 90◦ . The test slat was horizontal (vertical) at the inclination angle of 0◦ (90◦ ). There were five positions preset along the centerline of the column (Fig. 4) that enabled the test slat to be installed at different heights, i.e., 100 mm, 300 mm, 500 mm, 700 mm, 900 mm above the bottom gas distributor. The superficial gas velocity ranged between 0.2–0.8 m/s, covering both the bubbling and turbulent regimes. To measure the dynamic force acting on the test slat, nine strain gauges were mounted on the surface of the slat (Fig. 3). One strain gauge was fixed in the middle of the slat and the other eight strain gauges were fixed symmetrically about the center of the slat at a pitch of 35 mm. The method of measurement employed in this study has been validated and results of the force on a cantilever slat immersed in a flu-
chemical engineering research and design 1 1 7 ( 2 0 1 7 ) 604–613
idized bed have been reported (Wang et al., 2015). Each strain gauge was connected to a bridge module to monitor the small change in resistance and to amplify the electrical signal. After AD conversion and stress transformation (i.e., the measured strain multiplied by the elasticity modulus (206 GPa) of stainless steel of which the test slat was made), the final digital stress signal was recorded and displayed using a computer. The strain gauges employed were foil-type resistance strain gauges (KFG-5-120-C1-11, Kyowa, Japan) of resistance 120 , length 9.4 mm and width 2.8 mm. They were mounted (Fig. 2) to measure tensile strain along the length direction of the slat. A stress analysis system (DH5921, Donghua Instrument Co., Ltd., Jiangsu, China) was used to record the stress signals with a sampling frequency of 1000 Hz; the measurement accuracy of this system was within 0.5%. Usually, 4–6 repeated runs at a sampling time of 30 s were conducted during each test to obtain better data reproducibility. Similar to previous studies (Grace and Hosny, 1985; Hosny and Grace, 1984; Kennedy et al., 1981; Nagahashi et al., 2008), the RMS stress
N 1 RMS = 2 i
N
607
Fig. 5 – Average bed voidage as a function of superficial gas velocity.
(1)
i=1
was used to characterize the average intensity of the measured dynamic stress signal. Different from an arithmetic mean, RMS avoids the offset effect of opposing stresses. Moreover, RMS emphasizes more the higher stress values that may dominate and therefore is more helpful when designing fluidized baffles. Except for stress signals, the dynamic pressure signals in the dense bed were also measured simultaneously during the experiment. There were seven pressure taps installed on the column wall (Fig. 4), situated 30 mm, 100 mm, 300 mm, 500 mm, 900 mm, and 970 mm above the bottom gas distributor. Both the bed pressure fluctuation and the axial profile of the particle concentration were thus obtainable. Pressure taps made of ID-8 mm steel tubing, the tips of which were connecting to the bed material, were inserted with 400-m stainless-steel mesh screens to prevent fine particles from leaking. CY201 gauge pressure transducers (Chengdutest Electrical Technology Co., Ltd., Chengdu, China) were used to measure the dynamic pressure signal. Their measurement range was 0–50 kPa with a measurement accuracy of 0.1% full scale. The sampling frequency for the pressure signal was 100 Hz.
3.
Results and discussion
3.1.
Macro flow characteristics
The average voidage in the dense bed measured by the pressure transducers (Fig. 5) at different superficial gas velocities show a gradual increase with increasing superficial gas velocity. Similar results were also reported in the literature (Zhang, 2008; Zhang and Lu, 2010). A common precept is that the superficial gas velocity corresponding to the maximum pressure fluctuations is the onset velocity of the turbulent flow regime (uc ) (Bi et al., 2000; Yerushalmi and Cankurt, 1979; Yerushalmi et al., 1978). The standard deviations of the measured gauge pressure signals (Fig. 6) at different superficial gas velocities in the dense bed shows that uc appears in the range 0.5–0.6 m/s. The bottom
Fig. 6 – Standard deviation of pressure fluctuations at different superficial gas velocities. section of the bed appears first to step into the turbulent flow regime earlier than the middle and top sections of the bed, as the superficial gas velocity corresponding to the maximum pressure fluctuation at h = 100 mm (uc = 0.5 m/s) is smaller. In the study of Zhu and Zhu (2008), a similar phenomenon was also observed.
3.2. Characteristics of typical dynamic stress signals measured in the dense bed During fluidization state, the test slat when immersed in the dense bed is subjected mainly to impacts induced by bubble movement. Dynamic stress signals (Fig. 7) measured using the strain gauges typically exhibit strong fluctuations. In previous studies of the mechanism (Levy et al., 1992a,b; Nagahashi et al., 1998, 2013), where a series of bubbles were created manually, a series of stress pulses induced by these observable and traceable bubbles were identified in the measured force signals. However, in a larger diameter three-dimensional fluidized bed, the test slat was relatively longer in length and hence subjected to simultaneous impacts from numerous bubbles. The measured stress signals (Fig. 7) show overlaps in impact impulses caused by these bubbles. Therefore, distinguishing each pulse is difficult. The range in magnitude of the measured stress signals for the test slat was typically 0–30 MPa. Also the average stress at = 0◦ is higher than that at = 90◦ . The stress values at = 90◦ oscillated above and below with an average value approximately equaling zero, but the stress values at = 0◦ are all
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Fig. 7 – Typical transient stress signals measured in the fluidized bed.
Fig. 9 – Power spectral density of measured dynamic pressure signal.
Fig. 10 – The RMS stress values at nine measuring points.
Fig. 8 – Corresponding power spectral densities of the two stress signals. positive (Fig. 7). Indeed, the averages of most measured stress signals in this study, except at = 90◦ , were positive indicating that the resultant force on the test slat in the fluidized bed is upward. In previous studies (Grace and Hosny, 1985; Hosny, 1982; Kennedy et al., 1981; Nagahashi et al., 2008), the vertical force acting on a round tube in a fluidized bed was also found to be positive on average with fluctuations similar to the measured stress signal acting on the test slat at = 0◦ in this study. However, the horizontal force acting on a round tube had a zero average as for the test slat at = 90◦ in this study. To obtain the frequency-domain characteristics of the measured stress signals (Fig. 8), a power spectral density (PSD) analysis was performed of the two measured stress signals
(Fig. 7). Here, the data used to compute the PSD were larger than that shown in Fig. 7. The effective frequency range of the stress signals is mainly in the range 0–10 Hz. The dominant frequencies corresponding to the maximum magnitude are usually less than 5 Hz. This result is consistent with previous studies on forces acting on horizontal tubes by Hosny (1982) and Kennedy et al. (1981). The PSD of the pressure signal (Fig. 9) measured synchronously as the stress signal shows that its macroscopic characteristics are similar to that of the measured stress signals. The effective frequency range and the dominant frequency of the pressure signal are also similar to the stress signals. Previous studies (Bi, 2007; van Ommen et al., 2011) have demonstrated clearly the close relationship between pressure fluctuations and bubble dynamics in the fluidized beds. These similarities here infer the common origin of both stress and pressure fluctuations in fluidized beds.
3.3. slat
Lateral profile of the measured stress along the
The lateral profiles of the RMS stress (Fig. 10) measured using the nine strain gauges mounted on the test slat (Fig. 3) show a nearly symmetric distribution over the center of the slat. The maximum RMS stress appears at both ends of the slat near the column wall, whereas the minimum RMS stress appears near Gauges #2 and #8 (Fig. 3). At the midpoint of the slat, the measured RMS stress is often peaked slightly lower than the RMS stress measured at the two ends of the slat. The above finding indicates that the two ends of the slat are vulnerable
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609
Fig. 11 – Bending moment diagram of a beam fixed at both ends subjecting to a uniform load. regions for horizontal internals immersed in a fluidized bed in regard to engineering design. During fluidization of the bed, these locations of highest fluctuating stress would experience a higher probability of fatigue failure. The measured stress is not only affected by the force acting on the slat, the section modulus, an indicator of its stiffness, which is a function of the geometry (width and thickness) of the slat, also has a very big influence on the measured stress. Specifically, if the slat has a different thickness, the measured stress will change. Therefore, the influence of the slat stiffness must be decoupled from the measured stress signal to retain the effective force acting on the slat, as it is more universal and of interest to reactor designers. As the test slat was relatively longer in length and subjected to multiple bubble impacts, the load acting on the slat is more similar to an upward uniform load (Fig. 11). For a rectangular beam of length L, width a, and thickness b, fixed at both ends and subjected to an upward uniform load of load density q, the profile of the bending moment along the beam is
M (x) =
aq 6x2 + L2 − 6xL
(2)
12
obtained using the theory of material mechanics. Here, M is the profile of the bending moment, x the distance from the left end, and q the force acting on unit area. The profile of the tensile stress is computed from the profile of bending moment by dividing it by the section modulus of the slat W,
M ˆ (x) = = W
aq 6x2 + L2 − 6xL 12
=
/
ab3 2 · 12 b
q 6x2 + L2 − 6xL 2b2
(3)
The sum of the square of the difference between the nine measured RMS stresses and the absolute values of the nine calculated stresses at the same positions is
ϕ=
9
2
RMS,i − |ˆ i |
(4)
i=1
Here, RMS,i and ˆ i are the measured RMS stress and the calculated stress, respectively. Based on the least-squares method, an effective load density qRMS can be determined when ϕ is minimum. We used qRMS to quantify the force acting on the test slat. Comparing the profile of the measured RMS stresses and the calculated stresses under an effective load density determined by the above-described method (Fig. 10) shows that their trends are highly correlated. With this load density,
Fig. 12 – Transient stress signals at different superficial gas velocities. the stress profiles of internals with different geometries can also be estimated based on Eq. (3).
3.4.
Effect of superficial gas velocity
The transient stress signals for three different superficial gas velocities (Fig. 12) all measured at = 0◦ , where vertical impact area of the slat was maximum, indicate that the average as well as the magnitude of fluctuation of these signals increase with increasing superficial gas velocity in consequence of the increased number of bubbles and stronger bubble dynamics. To split the bubbles, horizontal baffles made of inclined slats are typically installed in the fluidized beds at inclination angles usually between 40–60◦ . In these situations, the effective load acting on a slat at different superficial gas velocities [Fig. 13(a)] shows that at three installation heights qRMS increases linearly with increasing velocity. This result is similar to those previously obtained from measured force characteristics on horizontal tubes immersed in fluidized beds (Hosny, 1982; Hosny and Grace, 1984; Kennedy et al., 1981; Nagahashi et al., 2008). These results can be attributed to the enhanced bubble motion and the stronger motion of solids induced in the bed at increasing superficial gas velocities. When gas velocity is close to the minimum fluidization velocity, at which the rising bubbles are small in size and their rising velocity is slow, the force on the slat is expected to be small. As the superficial gas velocity increases, the number of bubbles, their size and rising velocity increase at the same time. This then contributes to the increasing number of bubbles synchronously acting on the slat. The solids pressure from the upper layer of the rising bubbles is higher and the wake impact of the bubbles passing the slat is stronger, which ultimately leads to a higher force acting on the slat. Moreover, the internal solids circulation in the bed, i.e., the so called gulf streaming, also becomes stronger with increasing superficial gas velocity, which is another contributor to the higher force on the slat. At lower inclination angles [e.g., = 0◦ in Fig. 13(b)], the trend is similar to Fig. 13(a), but the measured qRMS s are comparable to those at = 45◦ . For many supporting internals installed in the fluidized reactors, their inclination angles are usually 90◦ . The force acting on them is similar to the curve for = 90◦ shown in Fig. 13(b). Unlike other inclination angles, qRMS is nearly unchanged and maintains a very low value with increasing superficial gas velocity. When studying the horizontal force
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Fig. 13 – Effective load densities at different superficial gas velocities.
Fig. 14 – Effective load densities at different installation heights.
on a round tube immersed in a fluidized bed, Hosny (1982) also found a big difference in the magnitudes of the measured vertical and horizontal forces. He also found that the horizontal force acting on a round tube was maintained at low values with very slow increment in magnitudes with increasing superficial gas velocity. Compared with the horizontal gas–solids movement, the vertical movement is well-known to be more dominant. Changing the inclination angle from 0◦ through to 90◦ decreases the impact area for vertically moving solids. Moreover, the offset effect of the buffeting forces on the two sides also reduces the total force on the slat. Previous studies on gas/solids dispersion in fluidized beds have shown that the coefficients of dispersion are usually an order higher for vertical than for lateral movement (Du et al., 2002; Geldart, 1997; van Deemter, 1980). As to the force characteristics acting on internals immersed in fluidized beds, it seems that a similar mechanism also exists.
Except at = 90◦ , a similar trend is seen in all other inclination angles [Figs. 14(a) and (b)]. The high qRMS s in the bed bottom may be related to gas jetting from the bottom gas distributor, causing a stronger movement of solids and a larger impact on the slat. Moreover, squeezing of the bed level above the slat is also a possible factor. On the top of the bed, the bursting of bubbles causes a large amount of solids to be ejected into the freeboard and allowed to re-enter the dense bed, contributing to a higher RMS stress. The high fluctuation magnitude of transient stress signal (i.e., h = 900 mm) is also a possible indicator of the strong solids movement caused by bursting bubbles near the bed surface. At = 90◦ , qRMS remains nearly constant [Fig. 14(b)]. Similar to the trend in Fig. 13(b), the installation height also has no significant effect on qRMS at = 90◦ . In an industrial fluidized bed, horizontal internals immersed in the bottom or near the bed surface should be strengthened if they are not installed vertically.
3.5.
3.6.
Effect of installation height
In the experiment, through observing the transient stress signals measured at three different installation heights, we found that the signal from the bottom of the bed (i.e., h = 100 mm) has the highest average but lowest fluctuation magnitude. Whereas, the stress signal measured in the top of the bed (i.e., h = 900 mm) has the highest fluctuation magnitude. From the axial profiles of the effective load density that were measured for typical horizontal baffles made of inclined slats (e.g., at = 45◦ in Fig. 14), the qRMS s are higher in the bottom and top of the bed giving a minimum qRMS in the middle.
Effect of inclination angle
In designing horizontal baffles for fluidized reactors, proper choice of the inclination angle of the slats is an important factor in achieving optimal results in enhancing gas–solids contact and obtaining the desired gas/solids back-mixing (Zhang, 2008; Zhang et al., 2007). By observing the measured transient stress signals at different inclination angles, we noticed that they exhibit similar fluctuation features although at = 90◦ the signal is distinctly lower with an average near 0 MPa (i.e., in Fig. 7). The stress signals all have positive averages except for at = 90◦ .
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Fig. 15 – Effect of inclination angle on the measured effective load densities.
Fig. 16 – Schematic of the test slat with one end fixed. Regardless of the fluctuation in experimental data, the measured effective load density qRMS is observed in general to decrease slightly with increasing inclination angle between = 0–75◦ (Fig. 15) but rapidly falls in value between = 75–90◦ . This trend can also be seen at other installation heights. Therefore, the effect of inclination angle on the force acting on the slats is expected to be small between = 40–60◦ at which the slats of typical horizontal baffles in industrial fluidized reactors are inclined.
3.7.
Effect of installation method
Usually, baffles of a fluidized reactor are fixed at one or both ends; both methods have advantages and disadvantages. A cantilever-like baffle is usually used when vertical thermal displacements occur between its two ends. In a cold-wall fluidized bed, a large temperature difference exists between the internal ends welded on the cold column wall and its main body which is usually immersed in the high-temperature bed. The cantilever-beam design permits larger lateral thermal displacements without compromising the structural integrity of the internal. However, internals with both ends fixed are more suitable in hot-wall fluidized beds. In this study, we also compared the forces acting on the slat in regard to the method of installation. The slat with one end fixed had the same width and thickness as the slat with both ends fixed (Cf. Figs. 2 and 16) although the length of the former was slightly smaller (298 mm). The geometrical details of the fixed flange and the mounting of the strain gauges were also the same (Figs. 2 and 3). Regarding installation method, the measured RMS stresses with signal data taken from Gauge #9 near the right end of the two slats (Figs. 2 and 16) exhibited the highest stresses for both test slats (Fig. 17). Their trends as superficial gas velocity increases are similar, but at = 0◦ the stresses found in the single fixed-end slat are about 1.5–2 times larger than that with ends fixed. At = 45◦ , the ratio appears to decrease slightly to 1.5 times, especially at lower gas velocities. At = 90◦ , there is
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Fig. 17 – Comparison of the measured RMS stresses with one and both ends fixed. no significant difference between the measured RMS stresses for the two installation methods, as all the measured RMS stresses are very small in value. For a beam subjected to a uniform load, the calculated highest stress in the beam with a single fixed end is 6 times higher than with both ends fixed. The ratios measured in this study were much smaller. Because the flow is complex, a slat is impacted by upward and downward solids simultaneously, and it is this offsetting that produces the smaller ratios measured.
3.8.
Forces in the de-fluidized bed
Apart from the normal fluidized state, internals immersed in the bed may also experience abnormal operating conditions during the operation of a fluidized reactor, such as those for the de-fluidized state. There may be short periods of defluidization during the addition of solids or the unforeseen downtime of a blower following an unscheduled power-down of the plant. To ensure the safeguarding of internals, the force characteristics acting on the internals during de-fluidization also needs to be understood. During tests of the de-fluidized bed, the initial height (H0 ) was maintained at 1 m throughout all tests, as for tests in the fluidized state. Here, the slat is subjected to a static pressure induced by the weight of the solids in the bed. From the downward force of the solids material, the direction of the measured strain or stress opposes that measured in the fluidized beds. To guarantee data reproducibility, a standard operation procedure and three runs was followed for each test. Before each stress measurement, we first fluidized the bed at a low superficial gas velocity for several minutes and then closed the controlling valve in the gas pipeline. After a few minutes of deaeration of the bed material, measurements were taken when the static bed surface leveled out and the stress signal stabilized. From the measured RMS stresses, a similar effective load density was obtained using the method to obtain Fig. 10. For a horizontally placed slat (i.e., = 0◦ ), the effective load density (Fig. 18) decreases sharply with increasing installation height, as less solids weight acts on the slat. The highest effective load density appears when the slat is immersed in the bottom of the bed, which is 5–6 times higher than that for the fluidized state. This trend is different from that in the fluidized state where the lowest effective load density appears in the middle of the bed. In addition, the inclination angle also has a marked effect on the measured force in the de-fluidized bed (Fig. 19). The
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Fig. 18 – Effective load densities at different heights in the de-fluidized bed.
(1) The measured dynamic stresses on a slat immersed in a fluidized bed fluctuate over a range that is usually significantly lower than those measured in a de-fluidized bed, especially in the bed bottom. Their effective frequency range is mainly in the range of 0–10 Hz. (2) When the slat is oriented vertically (i.e., at = 90◦ ), the measured effective load density on the slat in both fluidized and de-fluidized states are low. Changing the operating and structural parameters have no significant effect. At other inclination angles, the measured effective load density in the fluidization state increases linearly with increasing superficial gas velocity. Along the height of the dense fluidized bed, higher effective load densities appear in the bottom and top of the dense bed, whereas a minimum effective load density appears in the middle of the bed. As the inclination angle increases, the measured effective load density decreases slightly at < 75◦ and then decreases rapidly to a low value at = 90◦ . (3) The lateral profile of the RMS stress in a fluidized bed is symmetric about the center of the slat, with the maximum RMS stress appearing at the ends near the column wall. (4) In a de-fluidized bed, a horizontal slat internal installed in the bottom of the bed encounters a very high load due to the weight of the static bed if they are installed at a low inclination angle. (5) Under the same operating conditions, the RMS stress value measured for a single fixed-end slat is about 1.5–2 times higher than that when both ends of the slat are fixed.
Acknowledgement
Fig. 19 – Effect of inclination angle on effective load density in the de-fluidized bed.
measured stress decreases with increasing inclination angle. Similar trends were observed in the fluidized state. When the slat is placed in the bottom of the bed, the highest load density measured at = 0◦ is about an order higher than at = 90◦ . In industrial fluidized reactors with high static beds and large diameters, an abrupt shut-down of the fluidizing gas stream may compromise some internals like baffles or other supporting structures with large horizontal spans. The strength of the internals near the bed bottom requires special attention. The squeezing of the high-level solids material and their large spans may result in a much higher local stress on these internals than that measured in this study. If not designed properly, stress fractures or plastic deformation of these internals may appear, resulting in a departure from their optimum structural design and failure or even jeopardizing the fluidized reactor. In these conditions, vertical slats or ones with high inclination angles are recommended to reduce the potential damage from the static bed material. Moreover, operation management protocols need to be established to avoid abnormal operation conditions or to mitigate their harmful effect.
4.
Conclusion
From our systematic study of the forces acting on a slat in a fluidized bed of Geldart A particles, the following conclusions can be drawn:
The authors acknowledge the financial supports by the National Natural Science Foundation of China (21276273), the Ministry of Science and Technology of China (2012CB215004), the Science Foundation of China University of Petroleum, Beijing (2462015YQ0312).
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