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Determination of flow regime and gas holdup in gas–liquid stirred tanks
Chemical Engineering Science 109 (2014) 264–275
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Determination of flow regime and gas holdup in gas–liquid stirred tanks Boung Wook Lee, Milorad P. Dudukovic n Chemical Reaction Engineering Laboratory (CREL), Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, St. Louis, MO 63130, United States
H I G H L I G H T S
Identification of flow regime in gas–liquid stirred tanks. Linear relationship of the Froude number with gas holdup quantified. Measurement errors of the probe used were found negligible.
art ic l e i nf o
a b s t r a c t
Article history: Received 11 November 2013 Received in revised form 16 January 2014 Accepted 27 January 2014 Available online 3 February 2014
This work provides an in-situ method for determining the flow regime in a lab scale gas–liquid stirred tank reactor based on optical probe measurements. Tapered (conical) end optical fibers, which can distinguish which phase their tips are surrounded by, were employed over the whole range of practical operating conditions achievable in our Chemical Reaction Engineering Laboratory (CREL). After checking for sources of error associated with the rise and fall times of the measured signals, gas holdup and bubble count profiles were obtained by processing the time-series data with appropriate in-house developed algorithms. The data were presented in terms of the two dimensionless numbers, the Flow Number (Fl) and the Froude Number (Fr). All experiments were executed with an air–water system but the technique can be employed with all liquids and gases. The results suggest that the optical probe, when strategically positioned, can successfully and readily determine which state of dispersion the reactor is in. This reveals the technique's potential usefulness as an important research and control tool. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Gas–liquid stirred tank Flow regime Gas dispersion Optical probe
1. Introduction Quantifying transport–kinetic interactions in gas–liquid stirred tank reactors (STRs) has been a crucial part of multiphase reaction engineering for several decades due to the tank's wide spread use in practice. STRs have been known to be one of the most effective gas– liquid contactors capable of handling numerous duties (Harnby et al., 1985), from the very basic chemical and petrochemical processes to the newly developed biochemical and biological processes. In 1991, it was estimated that nearly half of the chemical industry's output had passed through a STR at one point (Tatterson, 1991). In general, process efficiency of a gas–liquid STR highly depends on the degree of interfacial contacting. As the gas–liquid interfacial area per unit liquid volume (a) changes, so do other important operating parameters such as volumetric heat and mass transfer coefficients. Naturally, much effort was invested in developing useful
correlations for these parameters via means of proven experimental techniques and computational simulations (Cents et al., 2005; Ford et al., 2008; Khopkar and Ranade, 2006; Lane et al., 2002, 2005; Mueller, 2009; Mueller and Dudukovic, 2010; Wang et al., 2000, 2006). For a standard fully baffled gas–liquid STR equipped with central Rushton impeller which we investigated, several flow patterns (regimes) have been identified based on major bubble trajectories and are shown in Fig. 1. In the literature, three regimes have been reported and described using two dimensionless numbers. These three regimes are flooding, loading, and fully recirculated regimes (Bombač et al., 1997; Harnby et al., 1985; Tatterson, 1991), and the two dimensionless numbers are the Flow Number (Fl) and the Froude Number (Fr). The Fl number is the ratio between the gas flow rate and the impeller driven flow rate; the Fr number is the ratio between the impeller driven acceleration and gravity. In equation form,
n
Corresponding author. E-mail addresses: [email protected] (B.W. Lee), [email protected] (M.P. Dudukovic). http://dx.doi.org/10.1016/j.ces.2014.01.032 0009-2509 & 2014 Elsevier Ltd. All rights reserved.
Fl ¼
Qg ND3
ð1Þ
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Fr ¼
N2 D ; g
ð2Þ
where Qg is the gas flow rate from the sparger, N is the impeller rotational rate, D is the turbine diameter, and g is the gravitational constant. As the Fr number increases, i.e., by providing more acceleration by means of increased impeller rotational rate, the flow regime transitions from a less to a more dispersed state. Likewise, as the Fl decreases, i.e., by introducing less gas to be dispersed or by providing more acceleration by means of increased impeller rotational rate, the flow regime transitions from a less to a more dispersed state. A complete flow regime map for an air– water system has been provided by several researchers (Bombač et al., 1997; Jade et al., 2006; Khopkar and Ranade, 2006; Mueller, 2009; Warmoeskerken and Smith, 1985) and is shown in Fig. 2. In the flow regime map, cavity structures observed behind the impeller blades are also indicated, as different cavity structures have been well known to be associated with each flow regime (Bombač et al., 1997; Tatterson, 1991). VC represents the vortex clinging structure, S33 represents the small “3–3” structure, L33 represents the large “3–3”structure, and RC represents ragged cavities. The two transition lines, from flooding to loading and loading to fully recirculated regime, were first determined by observing at which operating conditions dominant bubble trajectories had changed, and
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later confirmed by determining the cavity structures. In dimensionless form, the two transition lines are Transition from flooding to loading regime ¼ FlF ¼ 30FrðT=DÞ 3:5 ð3Þ Transition from loading to recirculated regime ¼ FlCD ¼ 13Fr 2 ðT=DÞ 5 : ð4Þ Over recent years, the demand for more reliable experimental techniques for identification of the flow regimes has risen considerably partly due to ever increasing computational power and many computational fluid dynamic (CFD) models being readily available. As concluded by Rammohan (2002), Guha et al. (2007), and Mueller (2009), even the most detailed results obtained by the CFD models are subject to validation via proven experimental techniques due to numerous assumptions and closure models associated with them. While much success in modeling gas–liquid STRs had been reported, (e.g., Bakker and Van den Akker, 1994; Zhang et al., 2008), the results are almost always verified only at very few operating conditions. Whether the reported models can be used over the whole range of operating conditions remains to be verified, especially in the loading and fully recirculated regimes where most processes are operated and
Fig. 1. Flow regime transition from flooding to loading to the fully recirculated regime. As N (impeller rotational speed) increases, gas bubbles occupy more regions within the tank. Adapted from Mueller and Dudukovic (2010). Copyright 2010 American Chemical Society. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 2. Complete flow regime map for a standard fully baffled air–water STR.
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near the transition lines where the local flow properties are difficult to describe. In order to explore the potential of the optical probe technique for its usage as a process control tool for determining/monitoring the reactor state of dispersion, the use of an already proven singletip optical probe (Hamed, 2012; Mueller, 2009; Xue, 2004) is described here in a classical air–water STR. Optical probes can withstand harsh conditions including high pressures and temperatures, and can readily be implemented in industrial processes once proven useful. The objective of our study is therefore to assess whether our in-situ probe can provide quantitative information on the global reactor state of dispersion, while revealing relationships between the dimensionless numbers and local dispersion parameters. The ultimate goal of this research is to utilize similar optical probe techniques (including a four-point probe) and analysis methods in gas–liquid STRs equipped with different impeller types, chemicals, and scales. These studies will establish the important relationships between the flow regimes and key
Fig. 3. Gas–liquid STR and ring gas sparger. Sparger figure from Rammohan (2002).
operating parameters such as the bubble size distributions, bubble velocities, and interfacial areas.
2. Material and methods 2.1. Gas–liquid stirred tank reactor (STR) The gas–liquid STR used in our work is equivalent to that used by Rammohan et al. (2001), Khopkar et al. (2005), Guha et al. (2007), and Mueller (2009), and is of standard geometry. The setup consists of a central Rushton impeller at 1/3 the liquid height, a ring gas sparger at the bottom of the tank, and four baffles on the reactor cylindrical wall to prevent gross vortexing at high impeller speeds. Fig. 3 shows the STR and the gas sparger. For each run, the tank was filled with tap water up to Ht ¼20 cm, and air was used for gas. Data points were taken over the whole range of practical operating conditions achievable in
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CREL, which spanned the Fl number values from 0.025 to 0.06, and the Fr number values from 0.03 to 1.3. These correspond to impeller rotational rates between 126 and 830 rpm and the gas inlet flow rates between 2.08 and 30 ft3/h. 2.2. Optical probe in gas–liquid STR For our probes, 105/125/250 μm core/clad/coating diameter multimode optical fiber tips (Thorlabs AFS105/125Y) were first tapered and polished by methods outlined by Mueller (2009). The tapered (conical) end optical fibers were then glued into 1/8 in. diameter stainless steel tubes. The first probe was designed to have its tips facing inward positioned at the same radial position of 0.6R (R¼radius of the tank) from the center at axial (vertical distances) of (a) Ht/6 below the impeller discharge plane, (b) right at the impeller discharge plane, and (c) Ht/6 above the impeller discharge plane. The second probe was designed to have its tip facing downwards. Measurements were taken at the exact same locations for both probes as Mueller and Dudukovic (2010) suggested the usage of at least two orientations. Schematics of the two probes and the STR are shown in Fig. 4. For tips facing inward, data points were collected at three locations simultaneously. For tips facing downward, each data point was collected in a separate run to ensure probe tips' maximum exposure to the surrounding flow. Bombač et al. (1997) reported directional sensitivity of the single point conductance probe, which operates under similar principle as our optical probe, to be insignificant up to impact angles of 901. All the tips were positioned on the windward side to minimize the effect caused by the baffle. Before each run, the tank was allowed to reach a steady state by letting the reactor run for at least 5 min. Voltage signals from the photodiodes (Thorlabs PDA36A) were recorded at 40 kHz as suggested by Mueller (2009) through data acquisition system (PowerDAQ PD-BNC-16), for the duration of 138.24 s for each run.
3. Optical probe signal interpretation Based on the principle of total reflection versus refraction, a single point optical probe is able to capture three key parameters
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when employed in an air–water system (Mueller, 2009; Xue, 2004) local gas holdup, bubble count, and bubble frequency. When the tip is surrounded by a gas component whose refractive index is less than 1.15, all the light is reflected back. On the other hand, when the tip is surrounded by a liquid whose refractive index is greater than 1.15, all the light is refracted and dissipated away into the medium. One example of the probe's response to a gaseous bubble in a gas–liquid system is shown in Fig. 5. Using this principle, and by applying the ergodic theorem (which states that the volume-averaged holdup can be represented by the time-averaged measurement) to the original optical probe data, local gas holdup values for various reactor types have been measured by a number of researchers (Bakker and Van den Akker, 1994; Guet et al., 2003; Mueller, 2009; Mueller and Dudukovic, 2010; Xue, 2004; Youssef et al., 2012). In equation form, the ergodic theorem states εgas;local ¼
V gas;local t gas ¼ ; V liquid;local þ V gas;local t gas þ t liquid
ð5Þ
where ε is the phase holdup, V is the volume fraction, and t is the amount of time spent in a particular phase. In our group, Xue (2004) and Mueller (2009) also used the same fiber type to make the four-point optical probe for estimation of bubble size and bubble velocity distributions in bubble columns and STRs. Several other techniques which make use of the ergodic theorem for determination of local phase holdups include the resistivity probe (Bombač and Žun, 2000, 2006; Bombač et al., 1997; Gao et al., 2001) and the fiber optic reflectometer (Fordham et al., 1999a, 1999b, 1999c; Hamad et al., 1997, 2000; Rogerio et al., 2001). While the tapered optical fibers used for our work and by others, in theory, should result in binary signal distribution when employed in gas–liquid systems, several reviews have pointed out some sources of error (Cartellier, 1990, 1992; Cartellier and Achard, 1991; Julia et al., 2005) caused by the deformation of the phase interfaces at the probe tip. The error was found to always translate into longer rise and fall times, i.e., the time needed for the signal to rise from the liquid level to the gas level and vice versa. In this section, two major sources of errors outlined in these reviews are summarized, and several signal distributions from our results are presented for discussion regarding the accuracy of the results.
Fig. 4. Optical probe with its tips facing inward (left) and downward (right).
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Fig. 5. Refraction and reflection of light at the probe tip (left) and probe recorded response to a rising bubble striking the tip (right). Figure from Mueller (2009).
3.1. Sources of error 3.1.1. Piercing near the bubble edge Julia et al. (2005) investigated in detail the effect of piercing position on the rise and fall response curves. The results suggest that when the probe tip pierces the bubble near the edge, i.e., away from the equator, interpreting the raw signal as if the signal was binary (one for liquid, one for gas) and arbitrarily setting the cutoff-level somewhere in between the two levels may result in non-negligible error. The cutoff-level, or the signal criterion level, is the signal level at which the probe is considered to be completely immersed in the gas. Sample signal shapes as a function of piercing location are shown in Fig. 6. Signals of full amplitudes were found to be only observed for x/Ro0.9 and bell shaped signals were observed for x/R40.9, due to the wetting and de-wetting phenomena of the probe tip and their complex interaction with the light. Additionally, partial blinding effect associated with the bell shaped signals was also introduced. Fig. 7 shows this effect. While the full optical-physics calculations are required for a thorough explanation, so is the complete description of the wetting/de-wetting fluid dynamics. To our knowledge, only experimental description of the wetting/de-wetting and partial blinding phenomena has been reported based on the rise and the fall times of the detected signal (Cartellier, 1990, 1992; Cartellier and Achard, 1991; Julia et al., 2005), due to the difficulty of determining the exact tip shape and dynamics of liquid film removal/formation. After performing meticulous comparisons between the response curves and visual recordings, Julia et al. (2005) suggested the usage of a Lower Level Criterion (LLC)—defined as 10% of the maximum signal level—for differentiating which phase the tip is surrounded by.
3.1.2. Parallel piercing In addition to the piercing near the bubble edge, Cartellier (1990) and Julia et al. (2005) also suggested parallel piercing as a source of error. Instead of the monotonic signal rise, Cartellier (1990) reported two peaks of different amplitudes when the probe tip was pierced across a gas–liquid interface parallel to the tip long vertical axis orientation, thus parallel piercing. This phenomenon is illustrated in Fig. 8. The first peak occurs when the phase interface is disturbed by the tip, and the second peak occurs when the film is completely
Fig. 6. Signal shapes at various piercing positions for ellipsoidal bubbles traveling in shorter axis' direction. x Represents the distance away from the center of the bubble. Reprinted with permission from Julia et al. (2005). Copyright 2005, AIP Publishing LLC.
Fig. 7. Piercing of a bubble near the bubble edge and the blinding effect. Reprinted with permission from Julia et al. (2005). Copyright 2005, AIP Publishing LLC.
withdrawn from the tip. The duration of the signal rise (Tm)— which Cartellier (1990) defines as time to reach 90% of dry tip signal—was found to be very small when interfacial velocities were high. Specifically, for perpendicular piercing (gas–liquid interface perpendicular to the tip orientation), Tm was found to be less than
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Fig. 8. Signal change when the tip is pierced sideways (parallel piercing). Reprinted with permission from Cartellier (1990). Copyright 2005, AIP Publishing LLC.
0.3 ms for interphase velocities larger than 50 cm/s. For parallel piercing, Tm was found to be less than 0.8 ms for interphase velocities larger than 50 cm/s. Although the average bubble velocities in our reported setup are much higher than this value (Mueller, 2009), since Tm is also a function of the exact tip shape, it is unclear whether such effects are negligible. Further verification may be required. 3.2. Signal interpretation For our data, rather than obtaining visual images to quantify the two errors mentioned previously, the probability distributions of the signal levels were plotted. The rationale for this is as follows. Both studies by Cartellier (1990) and Julia et al. (2005) revealed a direct relationship between the two error types and the number of intermediate signal levels present. Thus, if negligible number of intermediate signals is observed, the above discussed errors can be neglected. On the other hand, if there is a significant number of intermediate signals present in our data, a new processing algorithm needs to be developed that takes into account these errors. Fig. 9 shows several signal level distributions at different flow regimes (flooding, loading, transition, and fully recirculated) for the tip that was placed at the impeller discharge plane facing inward. At this location and orientation, the majority of the bubbles at all conditions are known to travel in radial direction (Kerdouss et al., 2006; Khopkar et al., 2005), from the central to the reactor wall region. On the left hand side are the original timeseries data during the first 30 s. For each run, 5,529,600 points were collected at the frequency of 40 kHz for 138.24 s. After each set of experiment, collected signals were normalized by first subtracting the minimum voltage observed during the whole measurement time, and then dividing this value by the difference between the reference voltage and minimum voltage observed. The reference voltage was set to a value to have the dry tip signal be in between 0.8 and 1.2. In equation form, Voltagenormalized ¼
measured voltage minimum voltage : reference voltage minimum voltage
ð6Þ
As expected, as the flow regime transitioned from a less to a more dispersed regime, so did the number of detected peaks increase
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(bubbles being pierced by the probe). This directly translated into larger area underneath the higher value Voltagenormalized. Peaks at intermediate signal levels were found to be scarcely present at all operating conditions investigated, from which we concluded that the rise and fall times due to piercing near the bubble edge are negligible (since the probe tip is facing the major bubble movement trajectories, very little parallel piercing is expected). To investigate the degree of error due to parallel piercings, signal level distributions were also plotted for the tip that was placed at the same position as the previous tip while having its tip facing downwards. For this tip, the majority of the bubbles are pierced from the side (parallel piercing), since the probe tip is oriented in a perpendicular direction to the major bubble movement trajectories. Fig. 10 shows the four distributions at the same operating conditions as Fig. 9. Despite the difference in the tip orientation, only binary distributions were observed at all operating conditions. These results suggest that even when the parallel piercings may be dominant, our optical probes do not detect any intermediate level signals and therefore are free from effects reported by Cartellier (1990), most likely due to the high bubble speeds in gas–liquid STR. Mueller (2009) reported bubble speeds in the gas–liquid STR in the order of 50–100 cm/s. Similar distributions were observed for other positions at which our probes were employed. 3.3. Orientation dependency Orientation dependency of the optical probe data has been reported in the literature for some years (Groen et al., 1994; Julia et al., 2005; Mueller, 2009; Xue, 2004), and our results confirm such dependency. Comparing Figs. 9 and 10, the area underneath the higher value Voltagenormalized is consistently larger for the tip pointing inward, which was oriented to have its tip opposing the major bubble movement direction. For the probe tip positioned below the impeller discharge plane, the tip facing downward consistently showed larger area under the higher value Voltagenormalized, suggesting that more bubbles were traveling vertically in this region. For the probe tip positioned above the impeller discharge plane, the differences between the two orientations were found to be dependent on operating conditions.
4. Gas holdup and bubble count profiles After having verified the binary nature of our data, the ergodic theorem was invoked to process the data to obtain local gas holdups. For bubble counts, number of signal jumps—from liquid to gas—per second was obtained. All data points were processed by the MATLAB algorithm similar to the FORTRAN algorithm developed by Xue (2004) and used by Mueller (2009). The cutoff criterion between the liquid and the gas phase was set at 0.25 Voltagenormalized to match the algorithm developed by Xue (2004). This value is slightly higher than the low level criterion (LLC) suggested by Julia et al. (2005) of 0.1 Voltageplateau. The differences in our result due to the use of one or the other criterion were found to be negligible. 4.1. Tips facing the center Gas holdup and bubble count monotonically increased for the two tips that were positioned below and at the impeller discharge plane as the Fr number increased. This matches well with our visual observation, as the reactor transitioned to a more dispersed regime as the Fr number increased. For the tip that was placed above the impeller discharge plane, a rise-dip-and-rise pattern
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Fig. 9. Normalized voltage and corresponding signal level distributions for tips pointing inward. From top to bottom: flooding; loading; transition; and fully recirculated regime.
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Fig. 10. Normalized voltage signal and corresponding probability distributions for tips pointing downward. From top to bottom: flooding; loading; transition; and fully recirculated regime.
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was observed. Fig. 11 shows the 2-D plots when the Fl number is constant at 0.045, and Fig. 12 shows the 3-D plots. According to the previously reported correlation (Eq. (3)), the transition from the flooding to the loading regime occurs at FrF ¼ 0.07 when the Fl number is 0.045. Rather than being abrupt, this transition is very gradual and is therefore very difficult to
detect by the naked eye. Yet, the probe tip that was positioned at Ht/6 above the impeller discharge plane started detecting bubbles at the transition point, revealing the probe's potential as a control tool for determination of flooding to loading regime transition and vice versa. As the STR transitioned to an even more dispersed regime within the loading regime, two other tips positioned elsewhere also detected bubbles. For the tip positioned at Ht/6 below the impeller discharge plane, bubbles were detected from Fr ¼ 0.5; for the tip positioned at the impeller discharge plane, bubbles were detected from Fr ¼0.2. As the Fr number increased, the tip positioned above the impeller discharge plane showed a risedip-rise pattern, while two other tips showed a monotonically increasing trend. This pattern was observed at all ranges of the Fl number we investigated (Fig. 13). Since the majority of the industrial processes actually take place in the large cavity regimes (Bombač et al., 1997) which occur at the Fr number greater than 0.2, the best location to position the optical probe for in-situ characterization/determination of the flow regime was found to be at the impeller discharge plane. At this location, both parameters, i.e., the local gas holdup and bubble counts, have very small deviations and there is a clear linear relationship between the Fr number and the two parameters. While the same relationship was observed for the tip positioned below the discharge plane, this tip does not detect any bubbles until the flow pattern has almost reached the fully recirculated regime at the Fr ¼0.6, which is consistent with our knowledge of the fully recirculated regime. At the Fr ¼ 0.91, the STR flow pattern transitions to the fully recirculated regime when the Fl ¼0.045. Therefore, of the three locations investigated, we recommend positioning the optical probe right at the impeller discharge plane for an accurate description and fast in-situ determination of the overall STR dispersion state. Here, the correlation between the Fr number and the local gas holdup for the Fr range of 0.2–1.2 was found to be εG;idp;0:6R ð%Þ ¼ 5:6321 Fr 1:2143
Fig. 11. Gas holdup and bubble count for tips facing inward at Fl ¼0.045. From top to bottom: probe tip positioned below; on; and above impeller discharge plane at radial position of 0.6R (R¼ radius of the tank).
ð7Þ
where idp represents the impeller discharge plane, with the R2 value of 0.9955 (for Fl ¼0.045); the transition from the loading to the flooding regime occurs when εG;idp;0:6R ¼ 3:91%. The rise-dip-rise pattern observed for the tip positioned above impeller discharge plane is reproducible but does not correspond to an actual correlation between the local and the global STR states of dispersion. Rather, the pattern confirms the optical measurement's orientation dependency reported by Mueller and Dudukovic (2010). In the region where this tip was employed, bubbles change their dominant trajectories as the flow regime changes. In the flooding and loading regimes, the dominant bubble trajectories are vertical, from the lower to the upper regions as indicated by red lines in Fig. 1. In the fully recirculated regime, however, most bubbles move in horizontal direction, from the reactor wall region to the center region, as also indicated by red lines in Fig. 1. Since no one has yet quantified the effect of probe tip orientation when not opposing the dominant bubble trajectories to the author's knowledge, no correlation was made. In the region below the impeller discharge plane where our probe was positioned, no rise-dip-rise pattern was observed. This is because in the flooding and loading regimes, no bubbles are present in this region. It is not until the STR has reached the fully recirculated regime that there is vertical bubble movement from the lower to upper region. No conclusion regarding the effect of the Fl number on the optical probe measurements was reached due to the narrow operating range.
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Fig. 12. Gas holdup and bubble count for the tips facing inward. From top to bottom: probe tip positioned below; on; and above impeller discharge plane at radial position of 0.6R (R ¼radius of the tank).
4.2. Tips facing the bottom Orientation dependency of the optical probe measurements was found to be most pronounced in the region above the impeller discharge plane. Instead of the rise-dip-rise pattern observed for the tips that were facing the center, both gas holdup and bubble count increased monotonically with the Fr number and showed a rise-hold-rise pattern. The differences ranged from 1% to 1.5% the gas holdup and from 1 to 1.5 bubbles per second for the bubble count. Fig. 13 shows the gas holdup and bubble count profiles for the probe that was positioned above the impeller discharge plane. For tips positioned elsewhere, the gas holdups and bubble counts increased as the Fr number increased, but no linear correlations were found between the Fr number and the measured
parameters (Figs. 14 and 15). As expected, the holdup and bubble counts deviated from those results when the tips were facing inward. For the tip positioned at the impeller discharge plane, the differences ranged from 0% to 2.1% for the gas holdup and from 0 to 26 bubbles per second for the bubble count. For the tip positioned below the impeller discharge plane, the differences ranged from 0% to 4.5% for the gas holdup and 0 to 5.5 bubbles per second for the bubble count. No conclusion on the Fl number dependency was made due to narrow operational range. In conclusion, all the tips used in this work (except for one tip which captured the rise-dip-rise pattern) showed monotonically increasing patterns for gas holdup and bubble count when plotted as a function of the Fr number. Of the three positions and two orientations we examined, the tip placed at the impeller discharge
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Fig. 13. Gas holdups and bubble counts for the tip above the impeller discharge plane facing downward.
Fig. 14. Gas holdup and bubble count profiles below discharge plane.
plane facing inward was found to best represent the global reactor state of dispersion. The reasons are as follows: (1) the results from the tips positioned below the impeller discharge plane (facing both inward and downward) could not detect any bubbles until the operating conditions nearly reached the fully recirculated regime; (2) the results from the tip above impeller discharge plane pointed inward revealed the rise-dip-rise pattern; and (3) the deviations were too high for the measurements obtained from the tip positioned above discharge plane facing downward. This is consistent with what has previously been reported in the literature on the local flow fields associated with each flow regime (Fig. 1) and the directional sensitivity of the optical probe. Of the three locations and two orientations, only the tip placed at the impeller discharge plane facing inward opposes the major bubble trajectory at all three flow regimes.
5. Summary and conclusions Tapered end optical fiber probes were employed in a lab scale air–water STR at three positions and at two orientations. Two quantities obtainable by this technique, local gas holdup and local bubble counts, were acquired over the whole range of practical
Fig. 15. Gas holdup and bubble count profiles on discharge plane.
operating conditions achievable in CREL and were analyzed using two dimensionless numbers, the Fr number and the Fl number. The measured local gas holdup values was well within the range of what others have reported (e.g., Bakker and Van den Akker, 1994; Ford et al., 2008) when the tip was opposing the dominant bubble trajectories. Linear relationships between the Fr number and the two parameters were found for all but one location we investigated. Tips employed at several locations showed their potential usefulness as a key method for fast in-situ determination of the overall STR state of dispersion (flow regime). For determination of flow regime transition from the flooding regime to the loading regime, positioning the optical probe in the outer regions within the upper regions of a STR was found to be the best location as both tips (facing inward and downward) started detecting bubbles at the transition point. For STRs being operated under practical operating conditions (Fr number greater than 0.2), one tip location and orientation—at the impeller discharge plane facing inward—was found to best represent the global state of gas dispersion; the higher the gas holdup and bubble counts are at this location, the more dispersed the overall STR flow regime. Piercing of bubbles near the edge and parallel piercing were found to be negligible for the probe and the STR we investigated.
Acknowledgment The authors would like to thank the Chemical Reaction Engineering Laboratory (CREL) sponsors and the National Science Foundation (Grant: 0933780) for their financial support.
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Cents, A.H.G., Brilman, D.W.F., Versteeg, G.F., 2005. Ultrasonic investigation of hydrodynamics and mass transfer in a gas–liquid(–liquid) sitrred vessel. Int. J. Chem. React. Eng. 3, 32. Ford, J.J., Heindel, T.J., Jensen, T.C., Drake, J.B., 2008. X-ray computed tomography of a gas-sparged stirred-tank reactor. Chem. Eng. Sci. 63, 2075–2085. Fordham, E.J., Holmes, A., Ramos, R.T., Simonian, S., Huang, S.M., Lenn, C.P., 1999a. Multi-phase-fluid discrimination with local fibre-optical probes: I. Liquid/liquid flows. Meas. Sci. Technol. 10, 1329. Fordham, E.J., Ramos, R.T., Holmes, A., Simonian, S., Huang, S.M., Lenn, C.P., 1999b. Multi-phase-fluid discrimination with local fibre-optical probes: III. Threephase flows. Meas. Sci. Technol. 10, 1347. Fordham, E.J., Simonian, S., Ramos, R.T., Holmes, A., Huang, S.M., Lenn, C.P., 1999c. Multi-phase-fluid discrimination with local fibre-optical probes: II. Gas/liquid flows. Meas. Sci. Technol., 10; c p. 1338. Gao, Z., Smith, J.M., Müller-Steinhagen, H., 2001. Void fraction distribution in sparged and boiling reactors with modern impeller configuration. Chem. Eng. Process.: Process Intensif. 40, 489–497. Groen, J.S., Mudde, R.F., Van den Akker, H.E.A., 1994. Flow structures in bubble columns as obtained from glass fibre measurements and pressure fluctuations. In: Proceedings of the Seventh Workshop on Two-phase Flow Predictions. Erlangen, Germany. Guet, S., Fortunati, R.V., Mudde, R.F., Ooms, G., 2003. Bubble velocity and size measurement with a four-point optical fiber probe. Part. Part. Syst. Charact. 20, 219–230. Guha, D., Ramachandran, P.A., Dudukovic, M.P., 2007. Flow field of suspended solids in a stirred tank reactor by Lagrangian tracking. Chem. Eng. Sci. 62, 6143–6154. Hamad, F.A., Imberton, F., Bruun, H.H., 1997. An optical probe for measurements in liquid–liquid two-phase flow. Meas. Sci. Technol. 8, 1122. Hamad, F.A., Pierscionek, B.K., Bruun, H.H., 2000. A dual optical probe for volume fraction, drop velocity and drop size measurements in liquid–liquid two-phase flow. Meas. Sci. Technol. 11, 1307. Hamed, M.E., 2012. Hydrodynamics, Mixing, and Mass Transfer in Bubble Columns with Internals. Department of Energy, Environmental, and Chemical Engineering. Washington University, St. Louis. Harnby, N., Edwards, F., Nienow, A.W., 1985. Mixing in the Process Industries. Butterworths, London. Jade, A.M., Jayaraman, V.K., Kulkarni, B.D., Khopkar, A.R., Ranade, V.V., Ashutosh, S., 2006. A novel local singularity distribution based method for flow regime identification: gas–liquid stirred vessel with Rushton turbine. Chem. Eng. Sci. 61, 688–697. Julia, J.E., Harteveld, W.K., Mudde, R.F., Van den Akker, H.E.A., 2005. On the accuracy of the void fraction measurements using optical probes in bubbly flows. Rev. Sci. Instrum.76, 035103.
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Kerdouss, F., Bannari, A., Proulx, P., 2006. CFD modeling of gas dispersion and bubble size in a double turbine stirred tank. Chem. Eng. Sci. 61, 3313–3322. Khopkar, A.R., Rammohan, A.R., Ranade, V.V., Dudukovic, M.P., 2005. Gas–liquid flow generated by a Rushton turbine in stirred vessel: CARPT/CT measurements and CFD simulations. Chem. Eng. Sci. 60, 2215–2229. Khopkar, A.R., Ranade, V.V., 2006. CFD simulation of gas–liquid stirred vessel: VC, S33, and L33 flow regimes. AIChE J. 52, 1654–1672. Lane, G.L., Schwarz, M.P., Evans, G.M., 2002. Predicting gas–liquid flow in a mechanically stirred tank. Appl. Math. Model. 26, 223–235. Lane, G.L., Schwarz, M.P., Evans, G.M., 2005. Numerical modelling of gas–liquid flow in stirred tanks. Chem. Eng. Sci. 60, 2203–2214. Mueller, S.G., 2009. Optical Measurements in Gas–Liquid Stirred Tanks. Department of Energy, Environmental, and Chemical Engineering. Washington University in St. Louis, Saint Louis, Missouri. Mueller, S.G., Dudukovic, M.P., 2010. Gas holdup in gas–liquid stirred tanks. Ind. Eng. Chem. Res. 49, 10744–10750. Rammohan, A.R., 2002. Characterization of Single and Multiphase Flows in Stirred Tank Reactors. Department of Chemical Engineering. Washington University in St. Louis, Saint Louis, Missouri. Rammohan, A.R., Kemoun, A., Al-Dahhan, M.H., Dudukovic, M.P., 2001. A Lagrangian description of flows in stirred tanks via computer-automated radioactive particle tracking (CARPT). Chem. Eng. Sci. 56, 2629–2639. Rogerio, T.R., Andrew, H., Xu, W., Elizabeth, D., 2001. A local optical probe using fluorescence and reflectance for measurement of volume fractions in multiphase flows. Meas. Sci. Technol. 12, 871. Tatterson, G.B., 1991. Fluid Mixing and Gas Dispersion in Agitated Tanks. McGraw-Hill, New York. Wang, Mao, Z.-S., Yang, C., 2006. Experimental and numerical investigation on gas holdup and flooding in an aerated stirred tank with Rushton impeller. Ind. Eng. Chem. Res. 45, 1141–1151. Wang, M., Dorward, A., Vlaev, D., Mann, R., 2000. Measurements of gas–liquid mixing in a stirred vessel using electrical resistance tomography (ERT). Chem. Eng. J. 77, 93–98. Warmoeskerken, M.M.C.G., Smith, J.M., 1985. Flooding of disc turbines in gas–liquid dispersions: a new description of the phenomenon. Chem. Eng. Sci. 40, 2063–2071. Xue, J., 2004. Bubble Velocity, Size and Interfacial Area Measurements in Bubble Columns. Department of Chemical Engineering, Washington University, Saint Louis. Youssef, A.A., Hamed, M.E., Grimes, J.T., Al-Dahhan, M.H., Duduković, M.P., 2012. Hydrodynamics of pilot-scale bubble columns: effect of internals. Ind. Eng. Chem. Res 52, 43–55. Zhang, Y., Yang, C., Mao, Z.-S., 2008. Large eddy simulation of the gas–liquid flow in a stirred tank. AIChE J. 54, 1963–1974.
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Determination of flow regime and gas holdup in gas–liquid stirred tanks Boung Wook Lee, Milorad P. Dudukovic n Chemical Reaction Engineering Laboratory (CREL), Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, St. Louis, MO 63130, United States
H I G H L I G H T S
Identification of flow regime in gas–liquid stirred tanks. Linear relationship of the Froude number with gas holdup quantified. Measurement errors of the probe used were found negligible.
art ic l e i nf o
a b s t r a c t
Article history: Received 11 November 2013 Received in revised form 16 January 2014 Accepted 27 January 2014 Available online 3 February 2014
This work provides an in-situ method for determining the flow regime in a lab scale gas–liquid stirred tank reactor based on optical probe measurements. Tapered (conical) end optical fibers, which can distinguish which phase their tips are surrounded by, were employed over the whole range of practical operating conditions achievable in our Chemical Reaction Engineering Laboratory (CREL). After checking for sources of error associated with the rise and fall times of the measured signals, gas holdup and bubble count profiles were obtained by processing the time-series data with appropriate in-house developed algorithms. The data were presented in terms of the two dimensionless numbers, the Flow Number (Fl) and the Froude Number (Fr). All experiments were executed with an air–water system but the technique can be employed with all liquids and gases. The results suggest that the optical probe, when strategically positioned, can successfully and readily determine which state of dispersion the reactor is in. This reveals the technique's potential usefulness as an important research and control tool. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Gas–liquid stirred tank Flow regime Gas dispersion Optical probe
1. Introduction Quantifying transport–kinetic interactions in gas–liquid stirred tank reactors (STRs) has been a crucial part of multiphase reaction engineering for several decades due to the tank's wide spread use in practice. STRs have been known to be one of the most effective gas– liquid contactors capable of handling numerous duties (Harnby et al., 1985), from the very basic chemical and petrochemical processes to the newly developed biochemical and biological processes. In 1991, it was estimated that nearly half of the chemical industry's output had passed through a STR at one point (Tatterson, 1991). In general, process efficiency of a gas–liquid STR highly depends on the degree of interfacial contacting. As the gas–liquid interfacial area per unit liquid volume (a) changes, so do other important operating parameters such as volumetric heat and mass transfer coefficients. Naturally, much effort was invested in developing useful
correlations for these parameters via means of proven experimental techniques and computational simulations (Cents et al., 2005; Ford et al., 2008; Khopkar and Ranade, 2006; Lane et al., 2002, 2005; Mueller, 2009; Mueller and Dudukovic, 2010; Wang et al., 2000, 2006). For a standard fully baffled gas–liquid STR equipped with central Rushton impeller which we investigated, several flow patterns (regimes) have been identified based on major bubble trajectories and are shown in Fig. 1. In the literature, three regimes have been reported and described using two dimensionless numbers. These three regimes are flooding, loading, and fully recirculated regimes (Bombač et al., 1997; Harnby et al., 1985; Tatterson, 1991), and the two dimensionless numbers are the Flow Number (Fl) and the Froude Number (Fr). The Fl number is the ratio between the gas flow rate and the impeller driven flow rate; the Fr number is the ratio between the impeller driven acceleration and gravity. In equation form,
n
Corresponding author. E-mail addresses: [email protected] (B.W. Lee), [email protected] (M.P. Dudukovic). http://dx.doi.org/10.1016/j.ces.2014.01.032 0009-2509 & 2014 Elsevier Ltd. All rights reserved.
Fl ¼
Qg ND3
ð1Þ
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Fr ¼
N2 D ; g
ð2Þ
where Qg is the gas flow rate from the sparger, N is the impeller rotational rate, D is the turbine diameter, and g is the gravitational constant. As the Fr number increases, i.e., by providing more acceleration by means of increased impeller rotational rate, the flow regime transitions from a less to a more dispersed state. Likewise, as the Fl decreases, i.e., by introducing less gas to be dispersed or by providing more acceleration by means of increased impeller rotational rate, the flow regime transitions from a less to a more dispersed state. A complete flow regime map for an air– water system has been provided by several researchers (Bombač et al., 1997; Jade et al., 2006; Khopkar and Ranade, 2006; Mueller, 2009; Warmoeskerken and Smith, 1985) and is shown in Fig. 2. In the flow regime map, cavity structures observed behind the impeller blades are also indicated, as different cavity structures have been well known to be associated with each flow regime (Bombač et al., 1997; Tatterson, 1991). VC represents the vortex clinging structure, S33 represents the small “3–3” structure, L33 represents the large “3–3”structure, and RC represents ragged cavities. The two transition lines, from flooding to loading and loading to fully recirculated regime, were first determined by observing at which operating conditions dominant bubble trajectories had changed, and
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later confirmed by determining the cavity structures. In dimensionless form, the two transition lines are Transition from flooding to loading regime ¼ FlF ¼ 30FrðT=DÞ 3:5 ð3Þ Transition from loading to recirculated regime ¼ FlCD ¼ 13Fr 2 ðT=DÞ 5 : ð4Þ Over recent years, the demand for more reliable experimental techniques for identification of the flow regimes has risen considerably partly due to ever increasing computational power and many computational fluid dynamic (CFD) models being readily available. As concluded by Rammohan (2002), Guha et al. (2007), and Mueller (2009), even the most detailed results obtained by the CFD models are subject to validation via proven experimental techniques due to numerous assumptions and closure models associated with them. While much success in modeling gas–liquid STRs had been reported, (e.g., Bakker and Van den Akker, 1994; Zhang et al., 2008), the results are almost always verified only at very few operating conditions. Whether the reported models can be used over the whole range of operating conditions remains to be verified, especially in the loading and fully recirculated regimes where most processes are operated and
Fig. 1. Flow regime transition from flooding to loading to the fully recirculated regime. As N (impeller rotational speed) increases, gas bubbles occupy more regions within the tank. Adapted from Mueller and Dudukovic (2010). Copyright 2010 American Chemical Society. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
Fig. 2. Complete flow regime map for a standard fully baffled air–water STR.
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near the transition lines where the local flow properties are difficult to describe. In order to explore the potential of the optical probe technique for its usage as a process control tool for determining/monitoring the reactor state of dispersion, the use of an already proven singletip optical probe (Hamed, 2012; Mueller, 2009; Xue, 2004) is described here in a classical air–water STR. Optical probes can withstand harsh conditions including high pressures and temperatures, and can readily be implemented in industrial processes once proven useful. The objective of our study is therefore to assess whether our in-situ probe can provide quantitative information on the global reactor state of dispersion, while revealing relationships between the dimensionless numbers and local dispersion parameters. The ultimate goal of this research is to utilize similar optical probe techniques (including a four-point probe) and analysis methods in gas–liquid STRs equipped with different impeller types, chemicals, and scales. These studies will establish the important relationships between the flow regimes and key
Fig. 3. Gas–liquid STR and ring gas sparger. Sparger figure from Rammohan (2002).
operating parameters such as the bubble size distributions, bubble velocities, and interfacial areas.
2. Material and methods 2.1. Gas–liquid stirred tank reactor (STR) The gas–liquid STR used in our work is equivalent to that used by Rammohan et al. (2001), Khopkar et al. (2005), Guha et al. (2007), and Mueller (2009), and is of standard geometry. The setup consists of a central Rushton impeller at 1/3 the liquid height, a ring gas sparger at the bottom of the tank, and four baffles on the reactor cylindrical wall to prevent gross vortexing at high impeller speeds. Fig. 3 shows the STR and the gas sparger. For each run, the tank was filled with tap water up to Ht ¼20 cm, and air was used for gas. Data points were taken over the whole range of practical operating conditions achievable in
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CREL, which spanned the Fl number values from 0.025 to 0.06, and the Fr number values from 0.03 to 1.3. These correspond to impeller rotational rates between 126 and 830 rpm and the gas inlet flow rates between 2.08 and 30 ft3/h. 2.2. Optical probe in gas–liquid STR For our probes, 105/125/250 μm core/clad/coating diameter multimode optical fiber tips (Thorlabs AFS105/125Y) were first tapered and polished by methods outlined by Mueller (2009). The tapered (conical) end optical fibers were then glued into 1/8 in. diameter stainless steel tubes. The first probe was designed to have its tips facing inward positioned at the same radial position of 0.6R (R¼radius of the tank) from the center at axial (vertical distances) of (a) Ht/6 below the impeller discharge plane, (b) right at the impeller discharge plane, and (c) Ht/6 above the impeller discharge plane. The second probe was designed to have its tip facing downwards. Measurements were taken at the exact same locations for both probes as Mueller and Dudukovic (2010) suggested the usage of at least two orientations. Schematics of the two probes and the STR are shown in Fig. 4. For tips facing inward, data points were collected at three locations simultaneously. For tips facing downward, each data point was collected in a separate run to ensure probe tips' maximum exposure to the surrounding flow. Bombač et al. (1997) reported directional sensitivity of the single point conductance probe, which operates under similar principle as our optical probe, to be insignificant up to impact angles of 901. All the tips were positioned on the windward side to minimize the effect caused by the baffle. Before each run, the tank was allowed to reach a steady state by letting the reactor run for at least 5 min. Voltage signals from the photodiodes (Thorlabs PDA36A) were recorded at 40 kHz as suggested by Mueller (2009) through data acquisition system (PowerDAQ PD-BNC-16), for the duration of 138.24 s for each run.
3. Optical probe signal interpretation Based on the principle of total reflection versus refraction, a single point optical probe is able to capture three key parameters
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when employed in an air–water system (Mueller, 2009; Xue, 2004) local gas holdup, bubble count, and bubble frequency. When the tip is surrounded by a gas component whose refractive index is less than 1.15, all the light is reflected back. On the other hand, when the tip is surrounded by a liquid whose refractive index is greater than 1.15, all the light is refracted and dissipated away into the medium. One example of the probe's response to a gaseous bubble in a gas–liquid system is shown in Fig. 5. Using this principle, and by applying the ergodic theorem (which states that the volume-averaged holdup can be represented by the time-averaged measurement) to the original optical probe data, local gas holdup values for various reactor types have been measured by a number of researchers (Bakker and Van den Akker, 1994; Guet et al., 2003; Mueller, 2009; Mueller and Dudukovic, 2010; Xue, 2004; Youssef et al., 2012). In equation form, the ergodic theorem states εgas;local ¼
V gas;local t gas ¼ ; V liquid;local þ V gas;local t gas þ t liquid
ð5Þ
where ε is the phase holdup, V is the volume fraction, and t is the amount of time spent in a particular phase. In our group, Xue (2004) and Mueller (2009) also used the same fiber type to make the four-point optical probe for estimation of bubble size and bubble velocity distributions in bubble columns and STRs. Several other techniques which make use of the ergodic theorem for determination of local phase holdups include the resistivity probe (Bombač and Žun, 2000, 2006; Bombač et al., 1997; Gao et al., 2001) and the fiber optic reflectometer (Fordham et al., 1999a, 1999b, 1999c; Hamad et al., 1997, 2000; Rogerio et al., 2001). While the tapered optical fibers used for our work and by others, in theory, should result in binary signal distribution when employed in gas–liquid systems, several reviews have pointed out some sources of error (Cartellier, 1990, 1992; Cartellier and Achard, 1991; Julia et al., 2005) caused by the deformation of the phase interfaces at the probe tip. The error was found to always translate into longer rise and fall times, i.e., the time needed for the signal to rise from the liquid level to the gas level and vice versa. In this section, two major sources of errors outlined in these reviews are summarized, and several signal distributions from our results are presented for discussion regarding the accuracy of the results.
Fig. 4. Optical probe with its tips facing inward (left) and downward (right).
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Fig. 5. Refraction and reflection of light at the probe tip (left) and probe recorded response to a rising bubble striking the tip (right). Figure from Mueller (2009).
3.1. Sources of error 3.1.1. Piercing near the bubble edge Julia et al. (2005) investigated in detail the effect of piercing position on the rise and fall response curves. The results suggest that when the probe tip pierces the bubble near the edge, i.e., away from the equator, interpreting the raw signal as if the signal was binary (one for liquid, one for gas) and arbitrarily setting the cutoff-level somewhere in between the two levels may result in non-negligible error. The cutoff-level, or the signal criterion level, is the signal level at which the probe is considered to be completely immersed in the gas. Sample signal shapes as a function of piercing location are shown in Fig. 6. Signals of full amplitudes were found to be only observed for x/Ro0.9 and bell shaped signals were observed for x/R40.9, due to the wetting and de-wetting phenomena of the probe tip and their complex interaction with the light. Additionally, partial blinding effect associated with the bell shaped signals was also introduced. Fig. 7 shows this effect. While the full optical-physics calculations are required for a thorough explanation, so is the complete description of the wetting/de-wetting fluid dynamics. To our knowledge, only experimental description of the wetting/de-wetting and partial blinding phenomena has been reported based on the rise and the fall times of the detected signal (Cartellier, 1990, 1992; Cartellier and Achard, 1991; Julia et al., 2005), due to the difficulty of determining the exact tip shape and dynamics of liquid film removal/formation. After performing meticulous comparisons between the response curves and visual recordings, Julia et al. (2005) suggested the usage of a Lower Level Criterion (LLC)—defined as 10% of the maximum signal level—for differentiating which phase the tip is surrounded by.
3.1.2. Parallel piercing In addition to the piercing near the bubble edge, Cartellier (1990) and Julia et al. (2005) also suggested parallel piercing as a source of error. Instead of the monotonic signal rise, Cartellier (1990) reported two peaks of different amplitudes when the probe tip was pierced across a gas–liquid interface parallel to the tip long vertical axis orientation, thus parallel piercing. This phenomenon is illustrated in Fig. 8. The first peak occurs when the phase interface is disturbed by the tip, and the second peak occurs when the film is completely
Fig. 6. Signal shapes at various piercing positions for ellipsoidal bubbles traveling in shorter axis' direction. x Represents the distance away from the center of the bubble. Reprinted with permission from Julia et al. (2005). Copyright 2005, AIP Publishing LLC.
Fig. 7. Piercing of a bubble near the bubble edge and the blinding effect. Reprinted with permission from Julia et al. (2005). Copyright 2005, AIP Publishing LLC.
withdrawn from the tip. The duration of the signal rise (Tm)— which Cartellier (1990) defines as time to reach 90% of dry tip signal—was found to be very small when interfacial velocities were high. Specifically, for perpendicular piercing (gas–liquid interface perpendicular to the tip orientation), Tm was found to be less than
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Fig. 8. Signal change when the tip is pierced sideways (parallel piercing). Reprinted with permission from Cartellier (1990). Copyright 2005, AIP Publishing LLC.
0.3 ms for interphase velocities larger than 50 cm/s. For parallel piercing, Tm was found to be less than 0.8 ms for interphase velocities larger than 50 cm/s. Although the average bubble velocities in our reported setup are much higher than this value (Mueller, 2009), since Tm is also a function of the exact tip shape, it is unclear whether such effects are negligible. Further verification may be required. 3.2. Signal interpretation For our data, rather than obtaining visual images to quantify the two errors mentioned previously, the probability distributions of the signal levels were plotted. The rationale for this is as follows. Both studies by Cartellier (1990) and Julia et al. (2005) revealed a direct relationship between the two error types and the number of intermediate signal levels present. Thus, if negligible number of intermediate signals is observed, the above discussed errors can be neglected. On the other hand, if there is a significant number of intermediate signals present in our data, a new processing algorithm needs to be developed that takes into account these errors. Fig. 9 shows several signal level distributions at different flow regimes (flooding, loading, transition, and fully recirculated) for the tip that was placed at the impeller discharge plane facing inward. At this location and orientation, the majority of the bubbles at all conditions are known to travel in radial direction (Kerdouss et al., 2006; Khopkar et al., 2005), from the central to the reactor wall region. On the left hand side are the original timeseries data during the first 30 s. For each run, 5,529,600 points were collected at the frequency of 40 kHz for 138.24 s. After each set of experiment, collected signals were normalized by first subtracting the minimum voltage observed during the whole measurement time, and then dividing this value by the difference between the reference voltage and minimum voltage observed. The reference voltage was set to a value to have the dry tip signal be in between 0.8 and 1.2. In equation form, Voltagenormalized ¼
measured voltage minimum voltage : reference voltage minimum voltage
ð6Þ
As expected, as the flow regime transitioned from a less to a more dispersed regime, so did the number of detected peaks increase
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(bubbles being pierced by the probe). This directly translated into larger area underneath the higher value Voltagenormalized. Peaks at intermediate signal levels were found to be scarcely present at all operating conditions investigated, from which we concluded that the rise and fall times due to piercing near the bubble edge are negligible (since the probe tip is facing the major bubble movement trajectories, very little parallel piercing is expected). To investigate the degree of error due to parallel piercings, signal level distributions were also plotted for the tip that was placed at the same position as the previous tip while having its tip facing downwards. For this tip, the majority of the bubbles are pierced from the side (parallel piercing), since the probe tip is oriented in a perpendicular direction to the major bubble movement trajectories. Fig. 10 shows the four distributions at the same operating conditions as Fig. 9. Despite the difference in the tip orientation, only binary distributions were observed at all operating conditions. These results suggest that even when the parallel piercings may be dominant, our optical probes do not detect any intermediate level signals and therefore are free from effects reported by Cartellier (1990), most likely due to the high bubble speeds in gas–liquid STR. Mueller (2009) reported bubble speeds in the gas–liquid STR in the order of 50–100 cm/s. Similar distributions were observed for other positions at which our probes were employed. 3.3. Orientation dependency Orientation dependency of the optical probe data has been reported in the literature for some years (Groen et al., 1994; Julia et al., 2005; Mueller, 2009; Xue, 2004), and our results confirm such dependency. Comparing Figs. 9 and 10, the area underneath the higher value Voltagenormalized is consistently larger for the tip pointing inward, which was oriented to have its tip opposing the major bubble movement direction. For the probe tip positioned below the impeller discharge plane, the tip facing downward consistently showed larger area under the higher value Voltagenormalized, suggesting that more bubbles were traveling vertically in this region. For the probe tip positioned above the impeller discharge plane, the differences between the two orientations were found to be dependent on operating conditions.
4. Gas holdup and bubble count profiles After having verified the binary nature of our data, the ergodic theorem was invoked to process the data to obtain local gas holdups. For bubble counts, number of signal jumps—from liquid to gas—per second was obtained. All data points were processed by the MATLAB algorithm similar to the FORTRAN algorithm developed by Xue (2004) and used by Mueller (2009). The cutoff criterion between the liquid and the gas phase was set at 0.25 Voltagenormalized to match the algorithm developed by Xue (2004). This value is slightly higher than the low level criterion (LLC) suggested by Julia et al. (2005) of 0.1 Voltageplateau. The differences in our result due to the use of one or the other criterion were found to be negligible. 4.1. Tips facing the center Gas holdup and bubble count monotonically increased for the two tips that were positioned below and at the impeller discharge plane as the Fr number increased. This matches well with our visual observation, as the reactor transitioned to a more dispersed regime as the Fr number increased. For the tip that was placed above the impeller discharge plane, a rise-dip-and-rise pattern
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Fig. 9. Normalized voltage and corresponding signal level distributions for tips pointing inward. From top to bottom: flooding; loading; transition; and fully recirculated regime.
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Fig. 10. Normalized voltage signal and corresponding probability distributions for tips pointing downward. From top to bottom: flooding; loading; transition; and fully recirculated regime.
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was observed. Fig. 11 shows the 2-D plots when the Fl number is constant at 0.045, and Fig. 12 shows the 3-D plots. According to the previously reported correlation (Eq. (3)), the transition from the flooding to the loading regime occurs at FrF ¼ 0.07 when the Fl number is 0.045. Rather than being abrupt, this transition is very gradual and is therefore very difficult to
detect by the naked eye. Yet, the probe tip that was positioned at Ht/6 above the impeller discharge plane started detecting bubbles at the transition point, revealing the probe's potential as a control tool for determination of flooding to loading regime transition and vice versa. As the STR transitioned to an even more dispersed regime within the loading regime, two other tips positioned elsewhere also detected bubbles. For the tip positioned at Ht/6 below the impeller discharge plane, bubbles were detected from Fr ¼ 0.5; for the tip positioned at the impeller discharge plane, bubbles were detected from Fr ¼0.2. As the Fr number increased, the tip positioned above the impeller discharge plane showed a risedip-rise pattern, while two other tips showed a monotonically increasing trend. This pattern was observed at all ranges of the Fl number we investigated (Fig. 13). Since the majority of the industrial processes actually take place in the large cavity regimes (Bombač et al., 1997) which occur at the Fr number greater than 0.2, the best location to position the optical probe for in-situ characterization/determination of the flow regime was found to be at the impeller discharge plane. At this location, both parameters, i.e., the local gas holdup and bubble counts, have very small deviations and there is a clear linear relationship between the Fr number and the two parameters. While the same relationship was observed for the tip positioned below the discharge plane, this tip does not detect any bubbles until the flow pattern has almost reached the fully recirculated regime at the Fr ¼0.6, which is consistent with our knowledge of the fully recirculated regime. At the Fr ¼ 0.91, the STR flow pattern transitions to the fully recirculated regime when the Fl ¼0.045. Therefore, of the three locations investigated, we recommend positioning the optical probe right at the impeller discharge plane for an accurate description and fast in-situ determination of the overall STR dispersion state. Here, the correlation between the Fr number and the local gas holdup for the Fr range of 0.2–1.2 was found to be εG;idp;0:6R ð%Þ ¼ 5:6321 Fr 1:2143
Fig. 11. Gas holdup and bubble count for tips facing inward at Fl ¼0.045. From top to bottom: probe tip positioned below; on; and above impeller discharge plane at radial position of 0.6R (R¼ radius of the tank).
ð7Þ
where idp represents the impeller discharge plane, with the R2 value of 0.9955 (for Fl ¼0.045); the transition from the loading to the flooding regime occurs when εG;idp;0:6R ¼ 3:91%. The rise-dip-rise pattern observed for the tip positioned above impeller discharge plane is reproducible but does not correspond to an actual correlation between the local and the global STR states of dispersion. Rather, the pattern confirms the optical measurement's orientation dependency reported by Mueller and Dudukovic (2010). In the region where this tip was employed, bubbles change their dominant trajectories as the flow regime changes. In the flooding and loading regimes, the dominant bubble trajectories are vertical, from the lower to the upper regions as indicated by red lines in Fig. 1. In the fully recirculated regime, however, most bubbles move in horizontal direction, from the reactor wall region to the center region, as also indicated by red lines in Fig. 1. Since no one has yet quantified the effect of probe tip orientation when not opposing the dominant bubble trajectories to the author's knowledge, no correlation was made. In the region below the impeller discharge plane where our probe was positioned, no rise-dip-rise pattern was observed. This is because in the flooding and loading regimes, no bubbles are present in this region. It is not until the STR has reached the fully recirculated regime that there is vertical bubble movement from the lower to upper region. No conclusion regarding the effect of the Fl number on the optical probe measurements was reached due to the narrow operating range.
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Fig. 12. Gas holdup and bubble count for the tips facing inward. From top to bottom: probe tip positioned below; on; and above impeller discharge plane at radial position of 0.6R (R ¼radius of the tank).
4.2. Tips facing the bottom Orientation dependency of the optical probe measurements was found to be most pronounced in the region above the impeller discharge plane. Instead of the rise-dip-rise pattern observed for the tips that were facing the center, both gas holdup and bubble count increased monotonically with the Fr number and showed a rise-hold-rise pattern. The differences ranged from 1% to 1.5% the gas holdup and from 1 to 1.5 bubbles per second for the bubble count. Fig. 13 shows the gas holdup and bubble count profiles for the probe that was positioned above the impeller discharge plane. For tips positioned elsewhere, the gas holdups and bubble counts increased as the Fr number increased, but no linear correlations were found between the Fr number and the measured
parameters (Figs. 14 and 15). As expected, the holdup and bubble counts deviated from those results when the tips were facing inward. For the tip positioned at the impeller discharge plane, the differences ranged from 0% to 2.1% for the gas holdup and from 0 to 26 bubbles per second for the bubble count. For the tip positioned below the impeller discharge plane, the differences ranged from 0% to 4.5% for the gas holdup and 0 to 5.5 bubbles per second for the bubble count. No conclusion on the Fl number dependency was made due to narrow operational range. In conclusion, all the tips used in this work (except for one tip which captured the rise-dip-rise pattern) showed monotonically increasing patterns for gas holdup and bubble count when plotted as a function of the Fr number. Of the three positions and two orientations we examined, the tip placed at the impeller discharge
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Fig. 13. Gas holdups and bubble counts for the tip above the impeller discharge plane facing downward.
Fig. 14. Gas holdup and bubble count profiles below discharge plane.
plane facing inward was found to best represent the global reactor state of dispersion. The reasons are as follows: (1) the results from the tips positioned below the impeller discharge plane (facing both inward and downward) could not detect any bubbles until the operating conditions nearly reached the fully recirculated regime; (2) the results from the tip above impeller discharge plane pointed inward revealed the rise-dip-rise pattern; and (3) the deviations were too high for the measurements obtained from the tip positioned above discharge plane facing downward. This is consistent with what has previously been reported in the literature on the local flow fields associated with each flow regime (Fig. 1) and the directional sensitivity of the optical probe. Of the three locations and two orientations, only the tip placed at the impeller discharge plane facing inward opposes the major bubble trajectory at all three flow regimes.
5. Summary and conclusions Tapered end optical fiber probes were employed in a lab scale air–water STR at three positions and at two orientations. Two quantities obtainable by this technique, local gas holdup and local bubble counts, were acquired over the whole range of practical
Fig. 15. Gas holdup and bubble count profiles on discharge plane.
operating conditions achievable in CREL and were analyzed using two dimensionless numbers, the Fr number and the Fl number. The measured local gas holdup values was well within the range of what others have reported (e.g., Bakker and Van den Akker, 1994; Ford et al., 2008) when the tip was opposing the dominant bubble trajectories. Linear relationships between the Fr number and the two parameters were found for all but one location we investigated. Tips employed at several locations showed their potential usefulness as a key method for fast in-situ determination of the overall STR state of dispersion (flow regime). For determination of flow regime transition from the flooding regime to the loading regime, positioning the optical probe in the outer regions within the upper regions of a STR was found to be the best location as both tips (facing inward and downward) started detecting bubbles at the transition point. For STRs being operated under practical operating conditions (Fr number greater than 0.2), one tip location and orientation—at the impeller discharge plane facing inward—was found to best represent the global state of gas dispersion; the higher the gas holdup and bubble counts are at this location, the more dispersed the overall STR flow regime. Piercing of bubbles near the edge and parallel piercing were found to be negligible for the probe and the STR we investigated.
Acknowledgment The authors would like to thank the Chemical Reaction Engineering Laboratory (CREL) sponsors and the National Science Foundation (Grant: 0933780) for their financial support.
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