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Pulse properties in gas–liquid flow through randomly packed beds under microgravity conditions
International Journal of Multiphase Flow 73 (2015) 11–16
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International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Brief communication
Pulse properties in gas–liquid flow through randomly packed beds under microgravity conditions Paul Salgi a,⇑, Vemuri Balakotaiah a, Enrique Ramé b, Brian J. Motil c a
Department of Chemical & Biomolecular Engineering, University of Houston, Houston, TX, USA National Center for Space Exploration and Research, c/o NASA Glenn Research Center, USA c NASA Glenn Research Center, Cleveland, OH, USA b
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 17 September 2014 Received in revised form 15 January 2015 Accepted 26 February 2015 Available online 7 March 2015
Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Packed beds Gas–liquid flow Pulse characteristics Microgravity
Introduction Packed bed reactors have been identified as a technology that could be used in support of long-duration manned space missions for such applications as wastewater treatment and air revitalization (NAS, 2000, 2011). Although packed beds have been extensively studied in 1 g, previous experimental work by Motil et al. (2003, 2006) has shown a significant impact of gravity on the location of flow regime transitions in gas–liquid concurrent flow through these reactors. In particular, under microgravity conditions and for packing sizes greater than 2 mm, pulse flow has been shown to exist over a much wider range of flow conditions. From a practical perspective, it is important to characterize the behavior of average pulse velocity and frequency as a function of flow conditions and system/fluid properties in order to develop predictive models for mass (and heat) transfer and reaction yield/selectivity (see, for instance, Wu et al., 1995, 1999). In this regard, we note that the columns that are currently in use for space applications have typical dimensions that are comparable to lab-scale packed beds and, hence, exhibit similar pulsing properties. It is wellknown that larger, industrial-scale beds do not necessarily show similar pulsing patterns (see, for instance, Christensen et al., 1986). On the other hand, the addition of microgravity data can help clarify the pulse patterns that have already been observed under normal gravity. In this note, we present new microgravity data for average pulse velocity and frequency as a function of both ⇑ Corresponding author. Tel.: +1 713 743 4169. E-mail address: [email protected] (P. Salgi). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.02.020 0301-9322/Ó 2015 Elsevier Ltd. All rights reserved.
the gas and liquid flow rates for the air–water system. We also show that the average amplitude of the pressure time variations at the bottom of the column, as measured by the standard deviation of the time signal, follows a similar pattern as the pulse amplitude when the flow conditions are changed. The packing consists of glass spheres that are 3 mm in diameter. In this preliminary study, no attempt is made at examining the effect of column/packing size or fluid properties on the pulse characteristics. In concurrent gas–liquid down flow under 1 g conditions (Boelhouwer et al., 2002), pulse velocity is known to increase with gas flow rate and to be relatively insensitive to the liquid superficial velocity, the small influence of the latter being attributed to an earlier inception point of the pulses in the column and, hence, a longer acceleration time available to the pulses. Also, as the gas flow rate is increased, pulse velocity reaches a limiting value that depends on the size of the packing. The pulse velocity is also found to be lower than the gas interstitial velocity (Rao and Drikenburg, 1983), the difference being small at low gas rates and increasingly larger at higher gas rates. For a given liquid flow rate, pulse frequency is found to increase with gas flow. At constant gas flow rate, the frequency increases with the liquid superficial velocity from about zero at the trickle to pulse transition to a limiting value (which depends on the gas flow) as the pulse flow transitions into dispersed bubble flow (Kolb et al., 1990; Boelhouwer et al., 2002). Previous studies related to the impact of gravity on the hydrodynamic behavior of packed-bed reactors include the work of Larachi and coworkers (Munteanu et al., 2005; Larachi and Munteanu, 2009; Munteanu and Larachi, 2009; Larachi and Munteanu, 2010a; Munteanu and Larachi, 2010; Larachi and
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Munteanu, 2010b), who have used inhomogeneous magnetic fields to generate a gravity-compensating body force and produce simulated microgravity conditions. These authors have found an increase in both liquid holdup and wetting efficiency (at relatively low liquid flow rates) with decreasing gravity level, as well as a significant impact of gravity on conversion rates and selectivity for similar flow conditions.
Experimental apparatus We used a cylindrical column 60 cm long and 5 cm in diameter packed randomly with 3 mm spherical glass beads. The column was made of Lexan Polycarbonate and was optically transparent. Gas and liquid were driven independently into a mixing chamber attached to the entrance to the column. The gas–liquid mixture then was driven through a perforated plate that spanned the entire column cross section. The plate, with 219 holes, 2.184 mm in diameter and arranged in a square pattern, acted as a flow distributor by virtue of its pressure drop and provided containment to the packing. A hard coating was applied to the interior wall of the column in order to protect the polycarbonate from abrasion by the glass beads. The test section was instrumented with five Kistler absolute pressure transducers (model 4045A), uniformly spaced through the entire column length. The axial separation between transducers was approximately 15 cm. High speed video of selected run conditions was recorded for two seconds each at about 9216 fps with a Vision Research Phantom 9 High-Speed CMOS Camera trained at a field of view (4.57 cm in the axial column direction by about 2.24 cm in the circumferential direction) located between the third and fourth pressure transducers. The illumination was provided by two white light LEDs, custom-mounted to a heat sink and fitted with a lens to cover the field of view of the high speed camera. Regular video was taken throughout the length of the runs and recorded to a Sony DVCAM digital cassette recorder. The pressure and video signals were time-synchronized. Clean air was supplied by a K-bottle regulated down to about 100 psig. One branch was piped through a mass flow controller and into the mixing chamber of the test section. Another branch was further regulated down to 40 psig and diverted to the top of a piston acting as a movable top lid in the liquid supply tank. The gas pressure allows the piston to move, thus displacing the liquid stored under it. This method has been used in low gravity two-phase flow experiments for many years and delivers a steady, oscillation-free liquid flow. The precise liquid flow rate was handregulated using a needle valve with the aid of the display from a liquid flow meter. At the exit of the test section, the two-phase mixture was sent to a screen phase separator. A fine screen mesh was installed such that it completely surrounds the gas outlet port in the top lid of the tank, thus setting up two partitions in the separator tank. The mixture was injected into the partition that does not contain the gas outlet. The small mesh pore size of the screen prevents liquid from breaking through but gas can flow unimpeded through the screen, thus reaching the gas outlet port. To draw out the liquid, it is necessary to wait for the high-g period that follows a low-g trajectory. During high-g, which lasts about 40 s and takes place while the airplane is climbing, the liquid drops to the bottom of the tank, from where a pump sends it back to the liquid supply tank. A total of 114 runs were carried out onboard the ZeroG Corp. aircraft over the span of 4 days. In the majority of the runs, water and air were flown at the desired rates for a period of about 20 s under reduced gravity conditions (typically ±0.03 g). After each low-g trajectory, the plane climbs back for about 40 s, during
which the effective gravity is about 1.8 g; this is usually called the ‘‘high-g period’’. Data analysis The data, collected at a rate of 100 Hz, consisted of the pressure traces at the five transducer locations, gas and liquid flow rates, gas and liquid temperatures, and the three components of the acceleration of gravity. For 27 of these runs, two seconds of highspeed video were captured at a rate of 9216 frames per second after allowing the flow to stabilize for a few seconds. Twelve out of these 27 runs were determined to be in the pulse regime and were used to obtain the preliminary results presented in this note. An average pulse frequency was determined by simply counting the number of pulses entering the camera’s field of view during the two-second time span of the video and dividing the result by that time span. An average pulse velocity was determined by locating the frame at which a pulse front first crosses into the camera’s field of view and the frame at which the front starts to move out. This measured time is then used along with the known width of the camera’s field of view (4.57 cm) to determine the pulse velocity. Each measurement was repeated many times (20–30) in order to provide a sense of the error from the calculated standard deviation. The error combines the human uncertainty in determining the time when a highly irregular front enters and leaves the field of view, and the error from one passing front to the other introduced in the irregular structure of the moving front. In accordance with previous observations in 1 g (Rao and Drikenburg, 1983), pulses do sometimes occur in groups of 2 or 3, but our goal here is to identify average properties and not the detailed geometry of these waves. The pulses did span the entire column cross-section in all but one of the twelve runs used in this analysis, but we still included this point because it led to reproducible average properties. With only about 20 s available for test runs under reduced gravity, the question arises as to whether fully-established flow conditions can be accessed. An estimate of the average residence time of the liquid can be made by using some characteristic velocity. Since part of the liquid is carried in high-velocity pulses, choosing the average liquid interstitial velocity as the characteristic velocity would provide an upper bound for the average residence time. Assuming the average liquid saturation in reduced gravity to be no more than 20% greater than that in normal gravity at the same flow conditions (based on predictions from Salgi and Balakotaiah, 2014), and for a bed length of 0.6 m and average bed porosity of 0.37, the average residence time is found to be well below 20 s for all points in our data set. Boelhouwer et al. (2002) have generated an extensive set of data for average pulse properties in 1 g down flow, which includes a system that is very similar to ours. We will frequently refer to these results for comparison with our own microgravity data. We have also included, for convenience, a limited number of 1 g data points that we have generated using our microgravity rig. Although very limited, these data confirm the similarities and differences identified through a comparison with the work of Boelhouwer et al. Results and discussion Before we present our data for the pulse characteristics in microgravity and determine how these results compare with those previously reported in 1 g (Rao and Drikenburg, 1983; Boelhouwer et al., 2002), we show in Fig. 1 a typical flow regime map for the air–water system in order to draw attention to two separate regions where qualitatively different approaches to the pulse transition are observed as the flow conditions are varied. This will help
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Fig. 1. Flow regime map for concurrent air–water flow (1 g down flow and ‘‘0 g’’) in a packed column (2 mm glass sphere). The solid lines drawn through Tosun’s data are just a guide for the eye.
clarify some of the differences/similarities that are seen in the 0 g and 1 g behavior of average pulse properties. Flow regime map in the high L region First, we focus on the region of the map corresponding to large liquid mass flux (L) values. Here the flow is seen to transition from a liquid-continuous (bubbly or dispersed bubbly) to a pulsing pattern as the gas mass flux G is increased at constant L. This transition, which is observed in both 1 g down flow and 0 g, is referred to as the ‘‘bubble-to-pulse transition’’. It is difficult to visualize pore-level flow patterns inside a packed bed and most observations are typically confined to a few packing diameters near the column wall. However, these observations do show increased bubble coalescence (with bubble lengths reaching sometimes several packing diameters) as G is increased, as if the flow is trying to become gas-continuous (Salgi and Balakotaiah, 2014). This tendency of the liquid-continuous pattern to transition to a gascontinuous pattern, as the gas flow rate is increased at constant liquid flow, is analogous to a transition from ‘‘slug flow’’ to ‘‘annular flow’’ in the capillary passages of the bed. This then suggests the following picture for the approach to pulsing. As G is increased, the liquid-continuous pattern (bubble flow) is first destabilized into an emerging gas-continuous flow, which itself is unstable (in this region of the map) and leads immediately to a pulsing pattern. If this picture is reasonable, is it consistent with experimental observations on flow regime maps for lab-scale packed beds? Also, what are the factors that affect the stability of the liquid-continuous pattern and that of the emerging gas-continuous pattern?
Before we answer these questions, we note that for a given system (column/packing and fluid properties) the minimum L value at which a liquid-continuous pattern (bubble flow) exists in the limit of vanishing G appears to be the same limiting value below which no pulsing is observed at higher G. In other words, for a given liquid mass flux L, no pulsing will be observed as G is increased if L does not fall in the liquid-continuous (bubbly) region in the limit of vanishing G (direct verification with traditional video observations is difficult but it seems reasonable for us to expect that if open channels occupied by ‘‘static’’ air are already available in the limit of vanishing G, then these channels should remain available for gas flow as G is increased at constant L). Physical factors affecting this limiting L value include liquid viscosity (which has a ‘‘favorable’’ effect, i.e. increasing viscosity leads to a lower limiting L value), gas–liquid surface tension (unfavorable), average bed porosity (unfavorable), and, most significantly, wettability of the packing by the liquid phase (very favorable). To explore the stability of the liquid-continuous pattern as G is increased at constant L, we note the work of Bordas et al. (2006) who found that bubbly flow in the limit of vanishing G is best described as ‘‘slug flow’’ at the pore level, with a bubble size of the same order as the pore size. As G is increased and the pulsing limit is approached, bubble size will increase and we can argue that, given two bubbly flows, the one with the smaller bubble size will be more stable. Laborie et al. (1999) studied ‘‘bubble-train’’ flow in circular capillaries of different sizes and with fluids of different properties. These authors’ experimental results on the average length of a gas slug indicate the following trends: (1) a decrease with increasing viscosity, (2) a relative insensitivity to surface tension at low gas flow
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10
2
L = 17 kg/m .s 2
L = 8.5 kg/m .s 2
L = 5.3 kg/m .s
Average Pulse Frequency (Hz)
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8
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G (kg/m .s) Fig. 2. Effect of gas flow on average pulse frequency. Solid symbols are microgravity data and open symbols are 1 g down flow data.
rates (but an increase with surface tension at higher gas flow rates), and (3) an increase with gas inertia. According to our picture, this should translate into the following effects on the liquid-continuous pattern (bubbly flow) in the packed bed: (1) a stabilizing effect of liquid viscosity, (2) a non-significant effect of surface tension (as interstitial gas velocities in the packed bed are in the lower range of gas velocities studied by Laborie et al.), and (3) a destabilizing effect of gas inertia. These are exactly the trends observed by Tosun (1984) and reproduced in his Figs. 2–4, respectively. Motil (2006), who studied the effect of liquid viscosity, also observed a stabilizing effect under microgravity conditions. Motil made the following additional observations: (1)
lowering gravity level has a destabilizing effect on bubbly flow (2) packing size has a non-significant effect in microgravity, and (3) decreasing packing size has a destabilizing effect in 1 g down flow. Strikingly enough, all these observations are consistent with the correlation proposed by Laborie et al. (1999) for the average gas slug length. These authors found that their data was best correlated in terms of a Reynolds number based on gas slug velocity and a Bond (or Eötvös) number based on the capillary diameter. More precisely, the data for the dimensionless (average) gas slug length scaled with respect to the capillary diameter was correlated using a group defined as the Reynolds number divided by the square of the Bond number. We should emphasize that the quantitative details of the correlation are not relevant for our purposes. Also, the surface tension effect included in the correlation was needed to account for all their data and not just the lower gas velocity limit. If, for a given L value, we think of the inverse of the average gas slug length as a measure of the size of the G interval over which bubbly flow is stable, then Laborie’s correlation would imply the following: (1) a decrease in g level leads to a decrease in the interval of stability (2) a decrease in packing diameter (and hence in pore size or ‘‘capillary diameter’’) leads to a decrease in the interval of stability, and (3) since the correlation actually involves the product of gravity level and capillary diameter, the effect of packing size should be much less significant in microgravity. Moreover, the data of Laborie et al. (1999) indicate that, for a given gas flow, the average slug length decreases with increasing liquid flow. Therefore, for the same G value, we would expect a bubbly flow to become more stable as L is increased, which is again consistent with the ‘‘upward slope’’ of the bubbleto-pulse transition (see Fig. 1). Lastly, we note that in the high L region of the flow map, when the liquid-continuous pattern loses its stability, the emerging gas-continuous pattern is not stable either and immediately gives way to a pulsing pattern, which may be viewed as a ‘‘hybrid’’ or ‘‘mixture’’ of alternating liquid and gas-continuous patterns (Boelhouwer et al., 2002). As argued in the next paragraph, we propose that the stability of the emerging gas-continuous pattern is driven mainly by a competition between gravity (stabilizing) and gas inertia (destabilizing) and -3
30x10 1.6
STD of Pressure Signal at Bottom of Column (Bar)
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L = 8.5 kg/m .s
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L = 17 kg/m .s
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1.2 1.0 0.8 0.6 0.4 0.2 0.0
L = 17 kg/m .s 2
L = 8.5 kg/m .s 2
L = 5.3 kg/m .s
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G (kg/m .s) Fig. 3. Effect of gas flow on average pulse velocity. Solid symbols are microgravity data and open symbols are 1 g down flow data.
0.2
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G (kg/m .s) Fig. 4. Effect of gas flow on average pulse ‘‘amplitude’’ (standard deviation of pressure signal). Solid symbols are microgravity data and open symbols are 1 g down flow data.
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that, in this region of the map (high L), the gas flow rates at which the liquid-continuous pattern becomes unstable are simply too high for the emerging gas-continuous pattern to be stable, even under 1 g conditions. The intermediate L interval of the flow map For intermediate L values, two different approaches to pulsing are observed as G is increased at constant L (see Fig. 1). In microgravity, the same behavior observed in the high L region is extended to lower liquid mass flux values, namely, a transition from a liquid-continuous (bubbly) to a pulsing pattern, which takes place at progressively smaller values of G as L is reduced. However, in 1 g down flow, we conjecture that the stability boundary of the liquid-continuous pattern falls rather sharply to ‘‘zero’’ gas flow rate at the same value of L below which no pulsing is observed. Direct verification of this ‘‘extinction’’ of the liquid-continuous pattern at low G values and a transition to gascontinuous pattern is difficult to achieve using traditional nearwall video observations. Perhaps tomographic techniques may be used in the future to check the validity of this picture. At any rate, it is reasonable to expect the 0 g stability boundary of the liquid-continuous phase to extend to lower L values as we would expect the presence of gravity to hinder the formation of a continuous liquid network. Also, the 0 g and 1 g stability boundaries of the liquid-continuous phase appear to intersect in about the same neighborhood of L where the two branches enclosing the pulsing region in 1 g meet each other (see Fig. 1). For intermediate liquid flow rates between the L value corresponding to this ‘‘point’’ and minimum L value corresponding to the extinction of the liquid-continuous pattern (in the limit of zero gas flow), the 1 g approach to pulsing consists of a transition from liquid-continuous to gas-continuous (trickle) followed by a transition from trickle to pulse. The latter takes place at increasingly higher G values as L is decreased, indicating an increase in the stability of the gas-continuous phase. For L values below this intermediate interval, no pulsing is observed in 1 g since the flow is already gas-continuous in the limit of vanishing G. ‘‘Left boundary’’ of pulsing region in microgravity In 1 g down flow, Boelhouwer et al. (2002) have shown that the pulsing pattern consists of alternating gas-rich regions, with average properties (e.g. liquid velocity and liquid holdup) that are similar to those of the limiting trickle flow at the same G value, and liquid-rich regions, with average properties that are similar to those of the limiting bubbly flow at the same G value. In 0 g, only a bubble to pulse transition has been observed, i.e., there is no documented gas-continuous pattern spanning the entire column. Then what does the ‘‘gas-rich’’ region look like in the 0 g pulse flow? Although direct observation is difficult, we propose that it is ‘‘mostly’’ a gas-continuous phase (that is the liquid may still contain a few bubbles). We also know that such a pattern cannot occupy the entire column. Our preliminary data (Figs. 2 and 3) show that, for L in the intermediate range described above, the 0 g average pulse frequency reaches a non-zero limiting value, which along with average velocity data, might give some indication on the maximum allowed (spatial) extent of the gas-continuous pattern in the column (for the particular system investigated). In 1 g, the average pulse frequency decreases steadily to a vanishing value (i.e., the gas-continuous pattern occupies the entire column) as the transition to trickle flow is approached. We do not speculate any further on this question as more detailed data is needed.
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Average pulse frequency In Fig. 2, we plot the average pulse frequency in microgravity as a function of gas flow rate for three different values of the liquid flow rate. The figure shows an almost linear increase with gas flow rate, in accordance with the pattern observed in 1 g down flow (Boelhouwer et al., 2002). However, the frequency appears to be rather insensitive to the liquid flow rate, in marked contrast with the observations in 1 g down flow. We note that the highest L value in Fig. 2 is close to the upper bound of the intermediate L interval described in the previous section (roughly the point where the two branches enclosing the pulsing region appear to meet each other). This implies that as L is decreased (at constant G) below this value, the 0 g frequency will stay about the same, whereas the 1 g frequency will continue to decrease and eventually vanish as the pulse to trickle transition is approached. Additional data is needed to better characterize the range of L values over which the 0 g pulse frequency is insensitive to liquid flow (for a given G). In particular, it would be interesting to know if the upper bound of this range is in fact the L value described above (or, as shown in Fig. 1, the slightly higher value corresponding to where the 1 g boundary of the dispersed bubbly flow starts to collapse). If that is the case, such L value may be used as an indication of when the presence of gravity will initiate a transition to a gas-continuous (trickle) flow pattern. Also, does this range of L signal the approach of a ‘‘left boundary’’ for pulse flow in 0 g? Our preliminary results indicate that as L is decreased below the intermediate range (lowest L value in Figs. 3 and 4), both the average velocity and the amplitude of the ‘‘pulse’’ drop significantly, consistent with a disintegration of the pulse pattern. These observations suggest that the disintegration of bed-wide pulses in microgravity is initiated in about the same range of L values as in 1 g. However, whereas this disintegration in 1 g is complete over a relatively short range of L values, in microgravity, large (bed-scale) chunks of continuous (aerated) liquid coexist with the gas continuous phase over a wider range of L values. This is consistent with a drop in average ‘‘pulse’’ velocity and amplitude as the gas continuous phase bypasses the large liquid chunks. Our observations also suggest that the average pulse frequency is related to the time scale associated with the evolution from pore-scale to bed-scale pulsing. As L values corresponding to the (1 g) trickle flow ‘‘boundary’’ are approached, this time becomes ‘‘infinite’’ in 1 g (zero frequency) but remains finite in microgravity (persistence of bed-scale aerated liquid chunks).
Average pulse velocity In Fig. 3, the average pulse velocity in microgravity is given as a function of gas flow rate for the same three values of the liquid flow rate shown in Fig. 2. The figure shows an initial increase followed by another region of more tapered increase, in accordance with the observed behavior in 1 g down flow for the same G interval. Our data does not cover a large enough G interval to determine whether the 1 g trend of an initial sharp increase followed by a plateau region (see Fig. 9c in Boelhouwer et al., 2002) is also followed in microgravity. To explain this well-documented behavior, Blok and Drinkenburg (1982) proposed that, as the gas flow rate is increased, the gas phase would infiltrate (bubble through) the liquid slugs, thus setting a limit on the piston effect that drives the pulses. This net transport of gas through the liquid is consistent with the observed gradual increase of the difference between pulse velocity and gas velocity as the gas rate is increased. It is also consistent with the observations of Lerou et al. (1980) on gas bubbling or fingering through liquid pulses. For large enough liquid flow rate (roughly higher than the lower limit required to sustain a pulsing
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pattern in 1 g), the average velocity also seems to be independent of liquid flow and of roughly the same magnitude as in 1 g down flow. However, the values measured at the lowest liquid flow are lower than those obtained at the two highest liquid flows. As discussed in the previous section, this probably signals a transition into a more uniform pattern, in which some ‘‘large chunks’’ of connected liquid are still present, but where much of the gas flows around these chunks.
the case of glass spheres and for similar flow conditions, both pulse velocity and frequency increase in 1 g as the sphere diameter is decreased (Boelhouwer et al., 2002). Would this effect increase, decrease, or remain roughly unchanged in microgravity? Similar questions apply to variations in packing type. Nevertheless, the work of Boelhouwer et al. (2002) suggests that the overall patterns of variation of pulse properties with flow conditions remain more or less unchanged when the packing size or type is changed.
Average pulse amplitude
Acknowledgement
In Fig. 4, the standard deviation of the pressure signal at the transducer located near the bottom of the column is plotted as a function of gas flow rate for the same three values of the liquid flow rate. At the two highest flow rates, the graph shows a gradual increase with gas flow rate, followed by a decrease after a weak maximum is reached. This trend is very similar to that observed by Boelhouwer et al. (2002) for the difference between the ‘‘base’’ liquid holdup (measured between pulses) and the pulse liquid holdup, which may be viewed as a measure of pulse amplitude. These authors observed an initial increase until a maximum is reached, followed by a subsequent decrease as spray flow is approached. The data of Boelhouwer et al. also indicates that this trend is independent of the liquid flow rate. At the lowest liquid flow rate, the ‘‘pulse’’ amplitude appears to be significantly lower and shows a much flatter profile. Again, as noted earlier, this is probably indicative of the proximity of the transition to a more uniform pattern. The limited number of available data points does not allow us to go beyond the general trends that we have just described. In particular, we cannot conclude from the figure how the pulse amplitude in microgravity compares with its value in 1 g down flow. Moreover, it would be interesting to identify changes in the wave geometry as the gravity level is decreased. In this regard, our video observations suggest the presence of pronounced ripples behind the microgravity pulse, which appear to be damped in the 1 g pulse.
This work was supported by a grant from the NASA Glenn Research Center (Grant # NNX14AD28G).
Summary and conclusions In this note, we have presented new microgravity data for the average pulse properties in concurrent gas/liquid flow through a randomly packed bed. The lab-scale column used to generate the data has similar dimensions to the columns that are currently in use for space applications. It is found that (for liquid flow rates higher than the limit required to sustain pulsing in 1 g) the average pulse velocity is relatively insensitive to gravity and shows similar behavior as the gas and/or liquid flow rate are varied. For lower liquid flow rates, pulse velocity decreases with L as the transition to a more uniform flow is approached. For the range of liquid flow rates over which a trickle–pulse transition is observed in 1 g, the pulse frequency in microgravity increases with gas flow rate but is independent of liquid flow rate. Our conclusions are based on an admittedly limited set of data and more detailed experiments are needed to refine these findings. Such experiments would ideally cover a wider range of flow conditions and provide a more complete picture of how average pulse properties vary across the relevant regions of the flow map. Also, additional work with variable fluid and packing properties is desirable to clarify how these properties might enhance or reduce the effect of gravity. For instance, in
References Blok, J.R., Drinkenburg, A.A.H., 1982. Hydrodynamic properties of pulses of twophase downflow operated packed columns. Chem. Eng. J. 25, 89–99. Boelhouwer, J.G., Piepers, H.W., Drinkenburg, A.A.H., 2002. Nature and characteristics of pulsing flow in packed bed reactors. Chem. Eng. Sci. 57, 4865–4876. Bordas, M.L., Cartellier, A., Sechet, P., Boyer, Ch., 2006. Bubbly flow through fixed beds: microscale experiments in the dilute regime and modeling. AIChE J. 52, 3722–3743. Christensen, G., McGovern, S.J., Sundaresan, S., 1986. Cocurrent flow of air and water in a two-dimensional packed column. AIChE J. 32, 1677–1689. Kolb, W.B., Melli, T.R., de Santos, J.M., Scriven, L.E., 1990. Cocurrent downflow in packed beds. Flow regimes and their acoustic signatures. Ind. Eng. Chem. Res. 29, 2380–2389. Laborie, S., Cabassud, C., Durand-Bourlier, L., Lainé, J.M., 1999. Characterization of gas–liquid two-phase flow inside capillaries. Chem. Eng. Sci. 54, 5723–5735. Larachi, F., Munteanu, M.C., 2009. Magnetic emulation of microgravity for earthbound multiphase catalytic reactor studies. Potentialities and limitations. AIChE J. 55, 1200–1216. Larachi, F., Munteanu, M.C., 2010a. Varying gravity force using magnetic-field emulated artificial gravity: application to cocurrent gas–liquid flows in porous media. Ind. Eng. Chem. Res. 49, 3623–3633. Larachi, F., Munteanu, M.C., 2010b. Gas–liquid flow solid-catalyzed reactions in magnetic-field emulated microgravity. J. Phys. Chem. C 114, 6534–6542. Lerou, J.L., Glasser, D., Luss, D., 1980. Packed bed liquid phase dispersion in pulsed gas–liquid downflow. Ind. Eng. Chem. Fund. 19, 66–71. Motil, B.J., 2006 Fundamental Studies on Gas–Liquid Two-Phase Flows Through Packed Reactors in Microgravity. PhD Dissertation – Case Western Reserve University. Motil, B.J., Balakotaiah, V., Kamotani, Y., 2003. Gas–liquid two-phase flow through packed beds in microgravity. AICHE J. 49, 557–565. Munteanu, M.C., Larachi, F., 2009. Flow regimes in trickle beds using magnetic emulation of micro/macrogravity. Chem. Eng. Sci. 64, 391–402. Munteanu, M.C., Larachi, F., 2010. Inhomogeneous magnetic field effects on the hydrodynamic properties of multiphase catalytic reactors. Int. Rev. Chem. Eng. 2, 150–154. Munteanu, M.C., Iliuta, I., Larachi, F., 2005. Process intensification in artificial gravity. Ind. Eng. Chem. Res. 44, 9384–9390. NAS, 2000. Microgravity Research in Support of Technologies for the Human Exploration and Development of Space and Planetary Bodies, ISBN: 0-30951867-9, Committee on Microgravity Research, Space Studies Board, National Research Council, National Academy Press. NAS 2011: Recapturing a Future for Space Exploration: Life and Physical Sciences Research for a New Era, ISBN 978-0-309-16384-2, Committee for the Decadal Survey on Biological and Physical Sciences in Space; National Research Council, The National Academies Press. Rao, V.G., Drikenburg, A.A.H., 1983. Pressure drop and hydrodynamic properties of pulses in two-phase gas–liquid downflow through packed beds. Can. J. Chem. Eng. 61, 158–167. Salgi, P., Balakotaiah, V., 2014. Impact of gravity on the bubble-to-pulse transition in packed beds. AIChE J. 60, 778–793. Tosun, G.A., 1984. Study of concurrent downflow of nonfoaming gas–liquid systems in a packed bed. Ind. Eng. Chem. Proc. Des. Dev. 23, 35–39. Wu, R., McCready, M.J., Varma, A., 1995. Influence of mass transfer coefficient fluctuation frequency on performance of three-phase packed-bed reactors. Chem. Eng. Sci. 50, 3333–3344. Wu, R., McCready, M.J., Varma, A., 1999. Effect of pulsing on reaction outcome in a gas–liquid catalytic packed-bed reactor. Catal. Today 48, 195–198.
Contents lists available at ScienceDirect
International Journal of Multiphase Flow j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j m u l fl o w
Brief communication
Pulse properties in gas–liquid flow through randomly packed beds under microgravity conditions Paul Salgi a,⇑, Vemuri Balakotaiah a, Enrique Ramé b, Brian J. Motil c a
Department of Chemical & Biomolecular Engineering, University of Houston, Houston, TX, USA National Center for Space Exploration and Research, c/o NASA Glenn Research Center, USA c NASA Glenn Research Center, Cleveland, OH, USA b
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 17 September 2014 Received in revised form 15 January 2015 Accepted 26 February 2015 Available online 7 March 2015
Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Packed beds Gas–liquid flow Pulse characteristics Microgravity
Introduction Packed bed reactors have been identified as a technology that could be used in support of long-duration manned space missions for such applications as wastewater treatment and air revitalization (NAS, 2000, 2011). Although packed beds have been extensively studied in 1 g, previous experimental work by Motil et al. (2003, 2006) has shown a significant impact of gravity on the location of flow regime transitions in gas–liquid concurrent flow through these reactors. In particular, under microgravity conditions and for packing sizes greater than 2 mm, pulse flow has been shown to exist over a much wider range of flow conditions. From a practical perspective, it is important to characterize the behavior of average pulse velocity and frequency as a function of flow conditions and system/fluid properties in order to develop predictive models for mass (and heat) transfer and reaction yield/selectivity (see, for instance, Wu et al., 1995, 1999). In this regard, we note that the columns that are currently in use for space applications have typical dimensions that are comparable to lab-scale packed beds and, hence, exhibit similar pulsing properties. It is wellknown that larger, industrial-scale beds do not necessarily show similar pulsing patterns (see, for instance, Christensen et al., 1986). On the other hand, the addition of microgravity data can help clarify the pulse patterns that have already been observed under normal gravity. In this note, we present new microgravity data for average pulse velocity and frequency as a function of both ⇑ Corresponding author. Tel.: +1 713 743 4169. E-mail address: [email protected] (P. Salgi). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2015.02.020 0301-9322/Ó 2015 Elsevier Ltd. All rights reserved.
the gas and liquid flow rates for the air–water system. We also show that the average amplitude of the pressure time variations at the bottom of the column, as measured by the standard deviation of the time signal, follows a similar pattern as the pulse amplitude when the flow conditions are changed. The packing consists of glass spheres that are 3 mm in diameter. In this preliminary study, no attempt is made at examining the effect of column/packing size or fluid properties on the pulse characteristics. In concurrent gas–liquid down flow under 1 g conditions (Boelhouwer et al., 2002), pulse velocity is known to increase with gas flow rate and to be relatively insensitive to the liquid superficial velocity, the small influence of the latter being attributed to an earlier inception point of the pulses in the column and, hence, a longer acceleration time available to the pulses. Also, as the gas flow rate is increased, pulse velocity reaches a limiting value that depends on the size of the packing. The pulse velocity is also found to be lower than the gas interstitial velocity (Rao and Drikenburg, 1983), the difference being small at low gas rates and increasingly larger at higher gas rates. For a given liquid flow rate, pulse frequency is found to increase with gas flow. At constant gas flow rate, the frequency increases with the liquid superficial velocity from about zero at the trickle to pulse transition to a limiting value (which depends on the gas flow) as the pulse flow transitions into dispersed bubble flow (Kolb et al., 1990; Boelhouwer et al., 2002). Previous studies related to the impact of gravity on the hydrodynamic behavior of packed-bed reactors include the work of Larachi and coworkers (Munteanu et al., 2005; Larachi and Munteanu, 2009; Munteanu and Larachi, 2009; Larachi and Munteanu, 2010a; Munteanu and Larachi, 2010; Larachi and
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Munteanu, 2010b), who have used inhomogeneous magnetic fields to generate a gravity-compensating body force and produce simulated microgravity conditions. These authors have found an increase in both liquid holdup and wetting efficiency (at relatively low liquid flow rates) with decreasing gravity level, as well as a significant impact of gravity on conversion rates and selectivity for similar flow conditions.
Experimental apparatus We used a cylindrical column 60 cm long and 5 cm in diameter packed randomly with 3 mm spherical glass beads. The column was made of Lexan Polycarbonate and was optically transparent. Gas and liquid were driven independently into a mixing chamber attached to the entrance to the column. The gas–liquid mixture then was driven through a perforated plate that spanned the entire column cross section. The plate, with 219 holes, 2.184 mm in diameter and arranged in a square pattern, acted as a flow distributor by virtue of its pressure drop and provided containment to the packing. A hard coating was applied to the interior wall of the column in order to protect the polycarbonate from abrasion by the glass beads. The test section was instrumented with five Kistler absolute pressure transducers (model 4045A), uniformly spaced through the entire column length. The axial separation between transducers was approximately 15 cm. High speed video of selected run conditions was recorded for two seconds each at about 9216 fps with a Vision Research Phantom 9 High-Speed CMOS Camera trained at a field of view (4.57 cm in the axial column direction by about 2.24 cm in the circumferential direction) located between the third and fourth pressure transducers. The illumination was provided by two white light LEDs, custom-mounted to a heat sink and fitted with a lens to cover the field of view of the high speed camera. Regular video was taken throughout the length of the runs and recorded to a Sony DVCAM digital cassette recorder. The pressure and video signals were time-synchronized. Clean air was supplied by a K-bottle regulated down to about 100 psig. One branch was piped through a mass flow controller and into the mixing chamber of the test section. Another branch was further regulated down to 40 psig and diverted to the top of a piston acting as a movable top lid in the liquid supply tank. The gas pressure allows the piston to move, thus displacing the liquid stored under it. This method has been used in low gravity two-phase flow experiments for many years and delivers a steady, oscillation-free liquid flow. The precise liquid flow rate was handregulated using a needle valve with the aid of the display from a liquid flow meter. At the exit of the test section, the two-phase mixture was sent to a screen phase separator. A fine screen mesh was installed such that it completely surrounds the gas outlet port in the top lid of the tank, thus setting up two partitions in the separator tank. The mixture was injected into the partition that does not contain the gas outlet. The small mesh pore size of the screen prevents liquid from breaking through but gas can flow unimpeded through the screen, thus reaching the gas outlet port. To draw out the liquid, it is necessary to wait for the high-g period that follows a low-g trajectory. During high-g, which lasts about 40 s and takes place while the airplane is climbing, the liquid drops to the bottom of the tank, from where a pump sends it back to the liquid supply tank. A total of 114 runs were carried out onboard the ZeroG Corp. aircraft over the span of 4 days. In the majority of the runs, water and air were flown at the desired rates for a period of about 20 s under reduced gravity conditions (typically ±0.03 g). After each low-g trajectory, the plane climbs back for about 40 s, during
which the effective gravity is about 1.8 g; this is usually called the ‘‘high-g period’’. Data analysis The data, collected at a rate of 100 Hz, consisted of the pressure traces at the five transducer locations, gas and liquid flow rates, gas and liquid temperatures, and the three components of the acceleration of gravity. For 27 of these runs, two seconds of highspeed video were captured at a rate of 9216 frames per second after allowing the flow to stabilize for a few seconds. Twelve out of these 27 runs were determined to be in the pulse regime and were used to obtain the preliminary results presented in this note. An average pulse frequency was determined by simply counting the number of pulses entering the camera’s field of view during the two-second time span of the video and dividing the result by that time span. An average pulse velocity was determined by locating the frame at which a pulse front first crosses into the camera’s field of view and the frame at which the front starts to move out. This measured time is then used along with the known width of the camera’s field of view (4.57 cm) to determine the pulse velocity. Each measurement was repeated many times (20–30) in order to provide a sense of the error from the calculated standard deviation. The error combines the human uncertainty in determining the time when a highly irregular front enters and leaves the field of view, and the error from one passing front to the other introduced in the irregular structure of the moving front. In accordance with previous observations in 1 g (Rao and Drikenburg, 1983), pulses do sometimes occur in groups of 2 or 3, but our goal here is to identify average properties and not the detailed geometry of these waves. The pulses did span the entire column cross-section in all but one of the twelve runs used in this analysis, but we still included this point because it led to reproducible average properties. With only about 20 s available for test runs under reduced gravity, the question arises as to whether fully-established flow conditions can be accessed. An estimate of the average residence time of the liquid can be made by using some characteristic velocity. Since part of the liquid is carried in high-velocity pulses, choosing the average liquid interstitial velocity as the characteristic velocity would provide an upper bound for the average residence time. Assuming the average liquid saturation in reduced gravity to be no more than 20% greater than that in normal gravity at the same flow conditions (based on predictions from Salgi and Balakotaiah, 2014), and for a bed length of 0.6 m and average bed porosity of 0.37, the average residence time is found to be well below 20 s for all points in our data set. Boelhouwer et al. (2002) have generated an extensive set of data for average pulse properties in 1 g down flow, which includes a system that is very similar to ours. We will frequently refer to these results for comparison with our own microgravity data. We have also included, for convenience, a limited number of 1 g data points that we have generated using our microgravity rig. Although very limited, these data confirm the similarities and differences identified through a comparison with the work of Boelhouwer et al. Results and discussion Before we present our data for the pulse characteristics in microgravity and determine how these results compare with those previously reported in 1 g (Rao and Drikenburg, 1983; Boelhouwer et al., 2002), we show in Fig. 1 a typical flow regime map for the air–water system in order to draw attention to two separate regions where qualitatively different approaches to the pulse transition are observed as the flow conditions are varied. This will help
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Fig. 1. Flow regime map for concurrent air–water flow (1 g down flow and ‘‘0 g’’) in a packed column (2 mm glass sphere). The solid lines drawn through Tosun’s data are just a guide for the eye.
clarify some of the differences/similarities that are seen in the 0 g and 1 g behavior of average pulse properties. Flow regime map in the high L region First, we focus on the region of the map corresponding to large liquid mass flux (L) values. Here the flow is seen to transition from a liquid-continuous (bubbly or dispersed bubbly) to a pulsing pattern as the gas mass flux G is increased at constant L. This transition, which is observed in both 1 g down flow and 0 g, is referred to as the ‘‘bubble-to-pulse transition’’. It is difficult to visualize pore-level flow patterns inside a packed bed and most observations are typically confined to a few packing diameters near the column wall. However, these observations do show increased bubble coalescence (with bubble lengths reaching sometimes several packing diameters) as G is increased, as if the flow is trying to become gas-continuous (Salgi and Balakotaiah, 2014). This tendency of the liquid-continuous pattern to transition to a gascontinuous pattern, as the gas flow rate is increased at constant liquid flow, is analogous to a transition from ‘‘slug flow’’ to ‘‘annular flow’’ in the capillary passages of the bed. This then suggests the following picture for the approach to pulsing. As G is increased, the liquid-continuous pattern (bubble flow) is first destabilized into an emerging gas-continuous flow, which itself is unstable (in this region of the map) and leads immediately to a pulsing pattern. If this picture is reasonable, is it consistent with experimental observations on flow regime maps for lab-scale packed beds? Also, what are the factors that affect the stability of the liquid-continuous pattern and that of the emerging gas-continuous pattern?
Before we answer these questions, we note that for a given system (column/packing and fluid properties) the minimum L value at which a liquid-continuous pattern (bubble flow) exists in the limit of vanishing G appears to be the same limiting value below which no pulsing is observed at higher G. In other words, for a given liquid mass flux L, no pulsing will be observed as G is increased if L does not fall in the liquid-continuous (bubbly) region in the limit of vanishing G (direct verification with traditional video observations is difficult but it seems reasonable for us to expect that if open channels occupied by ‘‘static’’ air are already available in the limit of vanishing G, then these channels should remain available for gas flow as G is increased at constant L). Physical factors affecting this limiting L value include liquid viscosity (which has a ‘‘favorable’’ effect, i.e. increasing viscosity leads to a lower limiting L value), gas–liquid surface tension (unfavorable), average bed porosity (unfavorable), and, most significantly, wettability of the packing by the liquid phase (very favorable). To explore the stability of the liquid-continuous pattern as G is increased at constant L, we note the work of Bordas et al. (2006) who found that bubbly flow in the limit of vanishing G is best described as ‘‘slug flow’’ at the pore level, with a bubble size of the same order as the pore size. As G is increased and the pulsing limit is approached, bubble size will increase and we can argue that, given two bubbly flows, the one with the smaller bubble size will be more stable. Laborie et al. (1999) studied ‘‘bubble-train’’ flow in circular capillaries of different sizes and with fluids of different properties. These authors’ experimental results on the average length of a gas slug indicate the following trends: (1) a decrease with increasing viscosity, (2) a relative insensitivity to surface tension at low gas flow
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10
2
L = 17 kg/m .s 2
L = 8.5 kg/m .s 2
L = 5.3 kg/m .s
Average Pulse Frequency (Hz)
2
L = 17 kg/m .s
8
2
L = 8.5 kg/m .s
6
4
2
0 0.0
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2
G (kg/m .s) Fig. 2. Effect of gas flow on average pulse frequency. Solid symbols are microgravity data and open symbols are 1 g down flow data.
rates (but an increase with surface tension at higher gas flow rates), and (3) an increase with gas inertia. According to our picture, this should translate into the following effects on the liquid-continuous pattern (bubbly flow) in the packed bed: (1) a stabilizing effect of liquid viscosity, (2) a non-significant effect of surface tension (as interstitial gas velocities in the packed bed are in the lower range of gas velocities studied by Laborie et al.), and (3) a destabilizing effect of gas inertia. These are exactly the trends observed by Tosun (1984) and reproduced in his Figs. 2–4, respectively. Motil (2006), who studied the effect of liquid viscosity, also observed a stabilizing effect under microgravity conditions. Motil made the following additional observations: (1)
lowering gravity level has a destabilizing effect on bubbly flow (2) packing size has a non-significant effect in microgravity, and (3) decreasing packing size has a destabilizing effect in 1 g down flow. Strikingly enough, all these observations are consistent with the correlation proposed by Laborie et al. (1999) for the average gas slug length. These authors found that their data was best correlated in terms of a Reynolds number based on gas slug velocity and a Bond (or Eötvös) number based on the capillary diameter. More precisely, the data for the dimensionless (average) gas slug length scaled with respect to the capillary diameter was correlated using a group defined as the Reynolds number divided by the square of the Bond number. We should emphasize that the quantitative details of the correlation are not relevant for our purposes. Also, the surface tension effect included in the correlation was needed to account for all their data and not just the lower gas velocity limit. If, for a given L value, we think of the inverse of the average gas slug length as a measure of the size of the G interval over which bubbly flow is stable, then Laborie’s correlation would imply the following: (1) a decrease in g level leads to a decrease in the interval of stability (2) a decrease in packing diameter (and hence in pore size or ‘‘capillary diameter’’) leads to a decrease in the interval of stability, and (3) since the correlation actually involves the product of gravity level and capillary diameter, the effect of packing size should be much less significant in microgravity. Moreover, the data of Laborie et al. (1999) indicate that, for a given gas flow, the average slug length decreases with increasing liquid flow. Therefore, for the same G value, we would expect a bubbly flow to become more stable as L is increased, which is again consistent with the ‘‘upward slope’’ of the bubbleto-pulse transition (see Fig. 1). Lastly, we note that in the high L region of the flow map, when the liquid-continuous pattern loses its stability, the emerging gas-continuous pattern is not stable either and immediately gives way to a pulsing pattern, which may be viewed as a ‘‘hybrid’’ or ‘‘mixture’’ of alternating liquid and gas-continuous patterns (Boelhouwer et al., 2002). As argued in the next paragraph, we propose that the stability of the emerging gas-continuous pattern is driven mainly by a competition between gravity (stabilizing) and gas inertia (destabilizing) and -3
30x10 1.6
STD of Pressure Signal at Bottom of Column (Bar)
2
2
L = 17 kg/m .s 2
L = 8.5 kg/m .s
1.4
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L = 5.3 kg/m .s 2
L = 17 kg/m .s
Average Pulse Velocity (m/s)
2
L = 8.5 kg/m .s
1.2 1.0 0.8 0.6 0.4 0.2 0.0
L = 17 kg/m .s 2
L = 8.5 kg/m .s 2
L = 5.3 kg/m .s
25
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L = 17 kg/m .s
20
15
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5
0 0.0
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G (kg/m .s) Fig. 3. Effect of gas flow on average pulse velocity. Solid symbols are microgravity data and open symbols are 1 g down flow data.
0.2
0.4
0.6
0.8
1.0
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G (kg/m .s) Fig. 4. Effect of gas flow on average pulse ‘‘amplitude’’ (standard deviation of pressure signal). Solid symbols are microgravity data and open symbols are 1 g down flow data.
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that, in this region of the map (high L), the gas flow rates at which the liquid-continuous pattern becomes unstable are simply too high for the emerging gas-continuous pattern to be stable, even under 1 g conditions. The intermediate L interval of the flow map For intermediate L values, two different approaches to pulsing are observed as G is increased at constant L (see Fig. 1). In microgravity, the same behavior observed in the high L region is extended to lower liquid mass flux values, namely, a transition from a liquid-continuous (bubbly) to a pulsing pattern, which takes place at progressively smaller values of G as L is reduced. However, in 1 g down flow, we conjecture that the stability boundary of the liquid-continuous pattern falls rather sharply to ‘‘zero’’ gas flow rate at the same value of L below which no pulsing is observed. Direct verification of this ‘‘extinction’’ of the liquid-continuous pattern at low G values and a transition to gascontinuous pattern is difficult to achieve using traditional nearwall video observations. Perhaps tomographic techniques may be used in the future to check the validity of this picture. At any rate, it is reasonable to expect the 0 g stability boundary of the liquid-continuous phase to extend to lower L values as we would expect the presence of gravity to hinder the formation of a continuous liquid network. Also, the 0 g and 1 g stability boundaries of the liquid-continuous phase appear to intersect in about the same neighborhood of L where the two branches enclosing the pulsing region in 1 g meet each other (see Fig. 1). For intermediate liquid flow rates between the L value corresponding to this ‘‘point’’ and minimum L value corresponding to the extinction of the liquid-continuous pattern (in the limit of zero gas flow), the 1 g approach to pulsing consists of a transition from liquid-continuous to gas-continuous (trickle) followed by a transition from trickle to pulse. The latter takes place at increasingly higher G values as L is decreased, indicating an increase in the stability of the gas-continuous phase. For L values below this intermediate interval, no pulsing is observed in 1 g since the flow is already gas-continuous in the limit of vanishing G. ‘‘Left boundary’’ of pulsing region in microgravity In 1 g down flow, Boelhouwer et al. (2002) have shown that the pulsing pattern consists of alternating gas-rich regions, with average properties (e.g. liquid velocity and liquid holdup) that are similar to those of the limiting trickle flow at the same G value, and liquid-rich regions, with average properties that are similar to those of the limiting bubbly flow at the same G value. In 0 g, only a bubble to pulse transition has been observed, i.e., there is no documented gas-continuous pattern spanning the entire column. Then what does the ‘‘gas-rich’’ region look like in the 0 g pulse flow? Although direct observation is difficult, we propose that it is ‘‘mostly’’ a gas-continuous phase (that is the liquid may still contain a few bubbles). We also know that such a pattern cannot occupy the entire column. Our preliminary data (Figs. 2 and 3) show that, for L in the intermediate range described above, the 0 g average pulse frequency reaches a non-zero limiting value, which along with average velocity data, might give some indication on the maximum allowed (spatial) extent of the gas-continuous pattern in the column (for the particular system investigated). In 1 g, the average pulse frequency decreases steadily to a vanishing value (i.e., the gas-continuous pattern occupies the entire column) as the transition to trickle flow is approached. We do not speculate any further on this question as more detailed data is needed.
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Average pulse frequency In Fig. 2, we plot the average pulse frequency in microgravity as a function of gas flow rate for three different values of the liquid flow rate. The figure shows an almost linear increase with gas flow rate, in accordance with the pattern observed in 1 g down flow (Boelhouwer et al., 2002). However, the frequency appears to be rather insensitive to the liquid flow rate, in marked contrast with the observations in 1 g down flow. We note that the highest L value in Fig. 2 is close to the upper bound of the intermediate L interval described in the previous section (roughly the point where the two branches enclosing the pulsing region appear to meet each other). This implies that as L is decreased (at constant G) below this value, the 0 g frequency will stay about the same, whereas the 1 g frequency will continue to decrease and eventually vanish as the pulse to trickle transition is approached. Additional data is needed to better characterize the range of L values over which the 0 g pulse frequency is insensitive to liquid flow (for a given G). In particular, it would be interesting to know if the upper bound of this range is in fact the L value described above (or, as shown in Fig. 1, the slightly higher value corresponding to where the 1 g boundary of the dispersed bubbly flow starts to collapse). If that is the case, such L value may be used as an indication of when the presence of gravity will initiate a transition to a gas-continuous (trickle) flow pattern. Also, does this range of L signal the approach of a ‘‘left boundary’’ for pulse flow in 0 g? Our preliminary results indicate that as L is decreased below the intermediate range (lowest L value in Figs. 3 and 4), both the average velocity and the amplitude of the ‘‘pulse’’ drop significantly, consistent with a disintegration of the pulse pattern. These observations suggest that the disintegration of bed-wide pulses in microgravity is initiated in about the same range of L values as in 1 g. However, whereas this disintegration in 1 g is complete over a relatively short range of L values, in microgravity, large (bed-scale) chunks of continuous (aerated) liquid coexist with the gas continuous phase over a wider range of L values. This is consistent with a drop in average ‘‘pulse’’ velocity and amplitude as the gas continuous phase bypasses the large liquid chunks. Our observations also suggest that the average pulse frequency is related to the time scale associated with the evolution from pore-scale to bed-scale pulsing. As L values corresponding to the (1 g) trickle flow ‘‘boundary’’ are approached, this time becomes ‘‘infinite’’ in 1 g (zero frequency) but remains finite in microgravity (persistence of bed-scale aerated liquid chunks).
Average pulse velocity In Fig. 3, the average pulse velocity in microgravity is given as a function of gas flow rate for the same three values of the liquid flow rate shown in Fig. 2. The figure shows an initial increase followed by another region of more tapered increase, in accordance with the observed behavior in 1 g down flow for the same G interval. Our data does not cover a large enough G interval to determine whether the 1 g trend of an initial sharp increase followed by a plateau region (see Fig. 9c in Boelhouwer et al., 2002) is also followed in microgravity. To explain this well-documented behavior, Blok and Drinkenburg (1982) proposed that, as the gas flow rate is increased, the gas phase would infiltrate (bubble through) the liquid slugs, thus setting a limit on the piston effect that drives the pulses. This net transport of gas through the liquid is consistent with the observed gradual increase of the difference between pulse velocity and gas velocity as the gas rate is increased. It is also consistent with the observations of Lerou et al. (1980) on gas bubbling or fingering through liquid pulses. For large enough liquid flow rate (roughly higher than the lower limit required to sustain a pulsing
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pattern in 1 g), the average velocity also seems to be independent of liquid flow and of roughly the same magnitude as in 1 g down flow. However, the values measured at the lowest liquid flow are lower than those obtained at the two highest liquid flows. As discussed in the previous section, this probably signals a transition into a more uniform pattern, in which some ‘‘large chunks’’ of connected liquid are still present, but where much of the gas flows around these chunks.
the case of glass spheres and for similar flow conditions, both pulse velocity and frequency increase in 1 g as the sphere diameter is decreased (Boelhouwer et al., 2002). Would this effect increase, decrease, or remain roughly unchanged in microgravity? Similar questions apply to variations in packing type. Nevertheless, the work of Boelhouwer et al. (2002) suggests that the overall patterns of variation of pulse properties with flow conditions remain more or less unchanged when the packing size or type is changed.
Average pulse amplitude
Acknowledgement
In Fig. 4, the standard deviation of the pressure signal at the transducer located near the bottom of the column is plotted as a function of gas flow rate for the same three values of the liquid flow rate. At the two highest flow rates, the graph shows a gradual increase with gas flow rate, followed by a decrease after a weak maximum is reached. This trend is very similar to that observed by Boelhouwer et al. (2002) for the difference between the ‘‘base’’ liquid holdup (measured between pulses) and the pulse liquid holdup, which may be viewed as a measure of pulse amplitude. These authors observed an initial increase until a maximum is reached, followed by a subsequent decrease as spray flow is approached. The data of Boelhouwer et al. also indicates that this trend is independent of the liquid flow rate. At the lowest liquid flow rate, the ‘‘pulse’’ amplitude appears to be significantly lower and shows a much flatter profile. Again, as noted earlier, this is probably indicative of the proximity of the transition to a more uniform pattern. The limited number of available data points does not allow us to go beyond the general trends that we have just described. In particular, we cannot conclude from the figure how the pulse amplitude in microgravity compares with its value in 1 g down flow. Moreover, it would be interesting to identify changes in the wave geometry as the gravity level is decreased. In this regard, our video observations suggest the presence of pronounced ripples behind the microgravity pulse, which appear to be damped in the 1 g pulse.
This work was supported by a grant from the NASA Glenn Research Center (Grant # NNX14AD28G).
Summary and conclusions In this note, we have presented new microgravity data for the average pulse properties in concurrent gas/liquid flow through a randomly packed bed. The lab-scale column used to generate the data has similar dimensions to the columns that are currently in use for space applications. It is found that (for liquid flow rates higher than the limit required to sustain pulsing in 1 g) the average pulse velocity is relatively insensitive to gravity and shows similar behavior as the gas and/or liquid flow rate are varied. For lower liquid flow rates, pulse velocity decreases with L as the transition to a more uniform flow is approached. For the range of liquid flow rates over which a trickle–pulse transition is observed in 1 g, the pulse frequency in microgravity increases with gas flow rate but is independent of liquid flow rate. Our conclusions are based on an admittedly limited set of data and more detailed experiments are needed to refine these findings. Such experiments would ideally cover a wider range of flow conditions and provide a more complete picture of how average pulse properties vary across the relevant regions of the flow map. Also, additional work with variable fluid and packing properties is desirable to clarify how these properties might enhance or reduce the effect of gravity. For instance, in
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