Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments

Chemical Engineering Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments Loveleen Sharma, K.D.P. Nigam, Shantanu Roy n Department of Chemical Engineering, Indian Institute of Technology – Delhi, New Delhi 110016, India

H I G H L I G H T S


Liquid phase Residence Time Distributions (RTD) are measured non-invasively.
Experiments are performed for single and two-phase (gas–liquid) flows through coiled geometry.
Quantified the axial dispersion and hence overall mixing over different flow regimes.

ar t ic l e i nf o

a b s t r a c t

Article history: Received 11 September 2015 Received in revised form 1 May 2016 Accepted 7 May 2016

Liquid phase residence time distributions (RTD) are reported by employing a novel experimental method of tracking a radioactive tracer particle during single phase and two-phase (gas–liquid) flows through a horizontal helical coil. Liquid and gas phase Reynolds numbers (NRe, L and NRe, G) were varied in the ranges from 1061 to 23, 150 and 130 to 100,000 respectively. As part of this work, we tracked the entry and exit of the tracer particle in the coiled flow structure using an array of strategically placed scintillation detectors. From these experiments, it became possible to extract the residence time distribution (RTD) by enumeration of the trajectories of the tracer particle through the flow system. The investigations have resulted in explaining mixing performance for gas–liquid (two-phase) flow in coiled geometry, based on the trends in liquid phase Peclet number (NPe), over varying liquid and gas phase velocities. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Axial dispersion Hydrodynamics Flow regimes RPT RTD

1. Introduction Fluid flow through coiled geometries is known to develop secondary flow patterns. Formation of such secondary flow patterns have been primarily attributed to centrifugal forces arising due to curved trajectories in such geometries. This kind of flow behaviour subsequently progresses into a double vortex circulation pattern in the cross-sectional plane perpendicular to the principal direction of flow at that point (as shown schematically in Fig. 1). These crosscirculating flow was first predicted from theoretical considerations by Dean (1927, 1928), and is hence referred to as Dean flow or Dean circulation. Such patterns are of great importance from hydrodynamics point of view, as they cause significant modification of the boundary layer structure and turbulent transition, and hence inspire the use of coiled tubes as laminar mixers or mixer-reactor (Vanka et al., 2004; Jiang et al., 2004; Kumar et al., 2006; Vashisth et al., 2008; Mridha and Nigam, 2008). Therefore, the examination of its performance across various flow regimes is in order. n

Corresponding author. E-mail address: [email protected] (S. Roy).

An extensive literature on flow through helical coils shows that coiled tubes are very effective in reducing that axial dispersion in single phase flow (Koutsky and Adler, 1964; Saxena and Nigam, 1979, 1981; Singh and Nigam, 1981; Saxena, 1983a, 1983b; Trivedi and Vasudeva, 1975; Castelain et al., 1997). However, application of coiled geometries are not restricted to single phase flows only; rather there are many reported applications in the process industry involving multiple phases wherein good radial mixing is desired within each phase. In all such cases, coiled tubes and modifications thereof are suitable candidates. Past studies on twophase coiled flows by Banerjee et al. (1969), Mujawar and Rao (1981), Saxena et al. (1990), Awwad et al. (1995), and Murai. et al., (2006) have focused on characterizing the holdup, pressure drop and visual observations (photography) of the flow pattern for coiled geometries. The measurements reported are based on gross estimates, such a holdup by collecting the total liquid held in the tubes, or overall pressure drop. Needless to say, there is interest and need to characterize multiphase flow properties by measuring local velocity or mixing characteristics, beyond mere visualization based observations. This is because owing to the complexity of multiphase flows, it is often argued that the gross flow measurements do not provide the much required deeper insights into the

http://dx.doi.org/10.1016/j.ces.2016.05.012 0009-2509/& 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Nomenclature dc dt D h Ku L l NRe, L NRe, G NPe RTD Sk t t

Diameter of coil (m) Inside diameter of tube (m) Effective dispersion coefficient (m2 /s) Pitch (m) Kurtosis (dimensionless) Tube length (m) Helical coil length (m) Liquid phase Reynolds number (dimensionless) Gas phase Reynolds number (dimensionless) Peclet number (dimensionless) Residence time distribution Skewness (dimensionless) Time (s) Mean residence time (s)

Fig. 1. Vortices or Dean vortices formation in a coiled tube.

flow. Flow visualization (photography), which has thus far been an important tool for characterization of two-phase flows in straight and coiled tubes, only provides a picture of the flow at the wall. Since phase segregation is known to be a common phenomenon even in straight tubes, and arguably in coiled tubes as well, clearly direct photography lead often to erroneous conclusions, biased largely by visual observations made at the wall. The curvature of the wall adds further challenges to clear visualization in the case of coiled tubes. Tomography would allay such concerns, but thus far nothing has been reported on tomographic investigations of twophase flows in coiled tubes. Furthermore, the problem of two-phase residence time distribution (RTD) measurements in two-phase flow in coiled tubes have also not attracted much attention. Performing classical tracer studies to get RTD are difficult in two phase systems since it is not very easy to clean “mixing cup” measurements, and online measurements are usually very noisy owing to the obstruction of the online probe by presence of the other phase. The only reported studies are by Rippel et al. (1966) and Saxena et al. (1996), which have been performed using classical tracer concentration measurement techniques in a limited set of air–water two-phase flow conditions. Rippel et al. (1966) compared the dispersion for two-

tL U VL VC QL

Liquid mean residence time, for two-phase flow (s) Liquid superficial velocity (m/s) Volume of liquid collected (m3) Volume of coil (m3) Volumetric flow rate of liquid (m3/s)

Greek symbols

σ2 σθ2 μ3 μ4 λ αL

Variance (s2) Dimensionless variance (dimensionless) Third moment about the mean (s3) Fourth moment about the mean (s4) Curvature ratio ( ¼dc/dt, (dimensionless)) Liquid holdup (dimensionless)

phase, and single phase flow through coiled geometry over a range of liquid Reynolds number (NRe, L) of 10–10,000. However, the gas flow conditions are not reported in that work. They reported the existence of three different dispersion patterns for two-phase flows. Furthermore, Saxena et al. (1996) investigated the twophase RTD using upward and downward arrangements of coiled geometries, in which the curvature ratio (λ) was used as a parameter over liquid and gas Reynolds numbers (NRe, L and NRe, G) in the range of 620–3200 and 1500–3000, respectively. The analysis from the two reported studies are not in complete agreement for two-phase flow in helical coils and also point towards discrepancy over their conclusions about flow regimes due to the limitation of flow range covered. Both studies suffer as well the typical problems faced by classical tracer injection techniques at high holdups of the dispersed gas phase. Also, the reported experimental work on helical configurations is only for smaller dimensions (order of 0.01 m or a few millimetres). One expects the flow behaviour and flow regime information to be markedly different on larger scales wherein surface tension is supposedly going to play a progressively lesser role, as compared to small of micro-channel helical coils. In view of these lacunae in the literature, the main objective of this study is to investigate the liquid phase RTD in single and twophase flows through a scaled-up helical coil (dt ¼0.05 m), over a wide range of liquid and gas Reynolds number (NRe). Further, these investigations have been done by tracking a single radioactive tracer particle (rendered neutrally buoyant with respect to the liquid phase), in line with the procedure outlined by Roy et al. (2001). Choice of this technique allowed us to probe the dispersion behaviour non-invasively without being constrained in any way to the flow regime and the corresponding gas holdup in the coiled tube. The highly penetrating gamma ray allowed us “optical access” into the coil (whose walls were opaque, being made of steel), and without any loss of accuracy due to two-phase interfaces. Details of this effort are reported in the flowing sections.

2. Experimental The present method of RTD measurement was inspired by previous studies by Roy et al. (2001) and Bhusarapu et al. (2004), for estimating the solid circulation rate in the closed loop system. The method proposed by these authors has been modified appropriately for measuring the residence time distribution (RTD) of a reasonably large diameter helical coil with a periodic tracer circulation scheme. Fabrication of the experimental setup was

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Fig. 2. (a) Schematic of helical coil flow setup (b) photograph of helical coil flow setup (c) schematic of detector arrangement to measure liquid phase RTD (d) photograph of detector arrangement (e) schematic for the circulation scheme.

done in two steps. In the first step, a helical coil of required dimensions was made with all necessary arrangements to study the single and two-phase flows through it. In the second step, the arrangement of detectors and associated electronics that allowed for the RTD measurements and radioactive particle circulation scheme was designed and installed. In some ways, the detector arrangement for RTD measurement was similar to the ideas used by Roy et al. (2005) in terms of having “sentry detectors” at the entry and exit of the coil. However, such a tracer particle circulation protocol has never been used before and was designed for the first time to make continuous RTD measurements using this method. Details of these experimental setups and protocol follow. 2.1. Helical coil setup Schematic of the helical coil flow setup used in the present study is shown in Fig. 2a. The single phase and two phase flow sections comprise of a helical coil made from 2 in. (0.05 m) diameter (dt) mild-steel tubing, which was wound on a cylindrical base to get a uniform curvature diameter (dc) of 19 in. (0.48 m).

This ratio of curvature to tube diameter (λ) was maintained uniform throughout the configuration. The coil was aligned horizontally and supported by a specially-fabricated support structure, which can be seen in the photograph in Fig. 2b, but not shown in the schematic of Fig. 2a for reasons of clarity. A total length (L) of about 780 in. (20 m) was used to obtain a helical coil of 2.3 in. (0.06 m) pitch, and 14 turns (l ¼ 0.88 m). A calculated (straight) entrance length of about 60 in. (1.5 m) was provided at the inlet of the horizontally placed helical coil to diminish all flow fluctuations offered by fittings and bends. For the purpose of estimating the exact volume of the test section, the entrance and exit planes were defined as the inlet and exit of the curved section of the helical coil. In order to manage the single and two-phase flows through the helical coil, an arrangement for maintaining a constant flow of air and water phases was ensured, the flows being constantly monitored using rotameters. Liquid and gas were fed to the test section via a T-connection, where liquid was made to flow through the straight T-run and gas was added from the cross T-section (as shown in Fig. 2a).

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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2.2. Particle tracking arrangement and recycling setup The schematic of the detector arrangement to measure the liquid phase RTD via tracing of the radioactive tracer particle for single and two-phase flows through the helical coil is shown in Fig. 2c (can also be seen in the installation photograph in Fig. 2d). For this measurement, a small radioactive tracer particle was prepared by encapsulating a small quantity of radioisotope of scandium (Sc-46) into a small PVC sphere, so that the effective density of the final tracer particle is precisely that of the water (continuous phase). During its sojourn through the helical coil, the tracer particle follows the liquid streamlines (since it is neutrally buoyant with respect to the liquid), while emitting gamma ray photons which are captured by detectors kept at the inlet and exit of the coil (Fig. 2c). Thus, in some sense the method employed resembles the more classical Radioactive Particle Tracking (RPT) method (Devanathan et al., 1990; Larachi et al., 1994; Roy et al., 2005); however we are not attempting to find local velocity in this work; rather only the distribution of sojourn times of residence times in the coil. Measurement of typical sojourn times or residence times of the tracer particle was accomplished in the following manner. The radiotracer was allowed to travel through coiled geometry along with the liquid phase (water) following the liquid streamlines. Entry and exit of the tracer particle in the coiled geometry (shown in Fig. 2c) was observed by mounting two NaI(Tl) scintillation detectors at specified entrance and exit locations. Each NaI(Tl) scintillation detector was collimated (using a lead casing) that allowed very narrow slit (of dimensions 0.002 m) for allowing the photon detection along the specified planes (i.e. entry and exit plane). The alignment of the detectors is precisely ensured to be perpendicular to the central axis of the coil. The output (photon counts) from detector, which has encased in itself both the radiation-sensitive crystal as well as a photomultiplier tube fitted with amplifiers, was acquired through suitable data acquisition electronic hardware system (MIDASs) at a set frequency of 50 Hz. By tracing multiple trajectories of the tracer particle from the inlet to exit of the coil, one obtains the time of residence of each trajectory. By recycling the tracer particle multiple times, a distribution of the times of residence between the inlet and the exit planes is obtained. On repeating this exercise many times, one obtains a distribution of residence times, which in fact under the assumption of ergodicity corresponds to the true residence time density function, E(t), as reported in standard texts in reaction engineering (Levenspiel, 1999; Nauman and Buffam, 1983; Wen and Fan, 1975). In order to realize this procedure mechanically, a circulation scheme was devised that could recirculate the tracer particle without disturbing the system steady-state condition. The challenge was to ensure that the particle, which is radioactive, is definitively prevented from entering rotameters, pumps and other flow restraining devices during its multiple sojourns through the coil (Fig. 2a). For ensuring this, the tracer circulation scheme was designed by an arrangement of valves and triggers. The schematic for the circulation scheme is shown in Fig. 2e. The line arrangement consisted of one main water tank, two centrifugal pumps (P1 and P2), two electrically actuated ball valves (B1 and B2) and four solenoid valves (S1, S2, S3 and S4). A crucial role was also played by the two “flow controlling detectors” D1 and D2. The choice of two ball valves (B1 and B2) was made to provide a clear flow path for the tracer during recirculation and thus ensuring a closed flow loop for the particle through the coil. Therefore, the two valves B1 and B2 were purposefully placed at the entrance and exit lines of the coiled geometry. By using pump P1, water was supplied to the coil through either valve S1 or S2, whereas by using pump P2 outflow from the coil was sucked through either valve S3 or S4. At

start of operation, pump P1 supplies a controlled water flow to the coil through valve S1 and B2; whereas pump P2 sucks outflow from the coil by using valve S3 (i.e. valves B2, S1, S3 opened, and B1, S2, S4 closed). During this stage of operation, the tracer particle is fed into the system via a funnel positioned at the outlet, that makes the tracer particle move towards the suction line of pump 2 (using valve S3). However, owing to the mesh at the T-section, the tracer particle is necessarily made to stop in front of the flow controlling detector D1. Once D1 detects the presence of radiotracer, the following control action is automatically taken: (1) B2, S1 closed, and S2 opened. (2) B1, S4 opened, and S3 closed. The completion of steps (1) and (2) makes the controlled flow of supply water to go into the coil via valve S2, and respective outflow to move towards suction valve S4. This combination of the valves (i.e. B1, S2, S4 opened and B2, S1, S3 closed) makes the tracer particle to follow the running suction line of pump P2 (using valve S4). However, again due to the placement of the mesh at T-section, tracer particle imposed to stop in front of the flow controlling detector D2. The moment tracer particle was detected by D2, the following steps were performed. (3) B1, S4 closed, and S3 opened. (4) B2, S1 opened, and S2 closed. The completion of steps (3) and (4) feeds the tracer particle back into the coil geometry. By following the same procedure, the tracer particle was recycled to make multiple sojourns through coiled geometry in an automated, fail-safe fashion without any human involvement. During each sojourn, the tracer particle follows a distinct trajectory and hence spent distinct residence time in the coiled geometry.

3. Results and discussion 3.1. Residence time distribution (RTD) measurement: typical data In order to determine RTD for a given flow condition, the photon counts time series recorded by two collimated detectors (entry and exit detectors in Fig. 2c) was analysed to identify the residence time of each trajectory. For each trajectory, the maxima in counts time series was obtained when the tracer particle was at the tube cross-section that is aligned with the central plane of the detector, and possibly at the closest position to the detector. Fig. 3a shows the typical data obtained from each detector over 500,000 events (10,000 s), where the maxima corresponding to each detector represents the time of entrance and exit successively. The data from each detector was smoothened out before further processing by taking a moving average. Fig. 3b shows the “zoomed-in” view of the same data over 5000 events (100 s). It is very clear from the figure that the maxima in counts series are well defined for both detectors, and indeed appears as a clear turning point in the counts graph. One also notices the characteristic periodicity in the counts graph with time, which seems to show progressive dampening. This happens because, during any one “turn” of the coil the counts recorded by either of the detectors (entry and exit) would be at the “turn-maximum” when the radial distance between the centre of the detector crystal and the tracer particle is minimum (or almost so, because it is possible that the solid angle subtended by the tracer particle on the detector crystal may in a minor way modify the exact value of the maximum counts recorded). Therefore, the entry detector shows a decreasing magnitude of the maximum recorded counts during one sojourn of the tracer particle, while the reverse is true for the exit detector. Since the data was acquired at a constant frequency (of 50 Hz), the time

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Fig. 3. (a) Raw data recorded by entry and exit detectors (b) “zoomed-in” view of entry and exit detector for one trajectory.

difference between two successive peaks in the recorded trace of the tracer particle, in its sojourn from the entry to the exit detector, represents the residence time of tracer particle in the helical coil during one visit (as shown in Fig. 3b). By estimating the time elapsed between all such peaks (recorded for multiple visits of tracer particle in helical coil, as shown in Fig. 3a), a histogram of residence time was plotted by binning all the trajectories into different time intervals. The fraction of such trajectories for each time interval with respect to total number of trajectories led to an estimation of exit age distribution function (E(t)). Indeed, this is the true “distribution of residence times” as envisaged by Danckwerts in his classic paper (Danckwerts, 1953). In fact, one may argue that the residence time distribution (RTD – a probability density function) extracted by a tracer test (such as that lucidly described in texts like Levenspiel (1999)), is only an ergodic equivalent of the true distribution of residence times that one can find with the radioactive particle tracing method. Of course, one has to ensure “closed–closed” boundary conditions in the experiment (Van Der Laan, (1958)) which of course we do ensure, by ensuring through the recorded photon trace that the tracer particle once entering the coiled tube continues in its trajectory to the exit plane without ever going back through the inlet plane, and also that it never re-enters through the exit plane once it leaves the tube. The only entry is from the inlet plane, and the only exit is through the exit plane. This is not a major concern actually in such a convection driven system like the present set of experiments, however our methodology is general and can be applied even if

the dispersion phenomena in the coiled tube were somehow dominating. One important and relevant question is: How many independent tracer particle trajectories are sufficient to estimate the RTD or flow pattern in the coiled tube (whether single phase or multiphase flow)? The number of particle trajectories required to estimate exit age distribution function (E(t)) are decided on the basis of the convergence of E(t)-curve with respect to number of tracer particle trajectories considered. Fig. 4a–f demonstrate, as an example, the convergence criteria of the E(t)-curve with accumulating the number of trajectories, wherein the mean ( t ) and normalized variance ( σθ2) were calculated for each case (by using (Eqs. (1)–3)). On reaching at such a situation, where there is no further change in normalized variance ( σθ2) of E(t)-curve by accumulating further number of trajectories, the convergence of the E(t)-curve is assumed to have been reached. The shape, as well as the absolute magnitude of the normalized histograms of the trajectory time distributions, resulted into a convergent E(t)-curve (as shown in Fig. 4a–f). Moreover to establish a reliability of the analysis, skewness (Sk, related to the third moment of the RTD) and kurtosis (Ku, related to the fourth moment of the RTD) of the E(t)-curve were also calculated (by using Eqs. (4) and (5)) for each case (as shown in Fig. 4a–f). This also verified the convergence of E(t)-curve beyond 750 trajectories. Notice that all the trajectories are taken from the same flow pattern, and indeed the same experiment (the 150, 300, 450, etc., were randomly chosen from experimental data collected for 900 trajectories (Fig. 4f)). Also, note that both the

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Fig. 4. Convergence of E(t) curve by considering different number trajectories (a) 150 (b) 300 (c) 450 (d) 600 (e) 750 (f) 900.

abscissa and the ordinate have been kept the same between the six different plots in Fig. 4, for ready comparison. From Fig. 4 we conclude that beyond a minimum requirement, even if we were to consider a higher number of trajectories, the exit age distribution (E(t)) was not changing further after sufficient number of trajectories have been considered. In other words, the measured “normalized” E(t) is convergent with number trajectories considered, beyond a minimum. For instance, in Fig. 4e and f, it is clear that between 750 trajectories and 900 trajectories, the E(t) is convergent. Of course, when considering a lesser number of trajectories (Fig. 4a–d), one observes some variation with the curve getting progressively convergent as the number of trajectories considered is increased. Once the E(t) curves have been extracted thus, it is trivial to find the moments of this distribution and relate them to various flow models for comparison. For instance, the mean ( t ) and normalized variance ( σθ2) of RTD are calculated to evaluate the flow system by using (Eqs. (1)–3). From the dimensionless second central moment (normalized variance), an estimate of liquid phase Peclet number (NPe) was made (defined by Eq. (6)) that helped in quantifying the axial mixing based on the tube length (L)

corresponding to making the coil alone (starting from entry plane to exit plane). A high Peclet number (NPe) indicates a small axial dispersion based on the tube length (L) and superficial velocity (U) of the flow system.

Mean residence time ( t ):

Variance ( σ 2):

σ2 =

t=

∫0

Dimensionless variance (σθ2 ):

Skewness (Sk )

Kurtosis (Ku)

Sk =

Ku =

μ3 σ3

μ4 σ4

∞

∫0

∞

tE (t ) dt

(t − t )2E (t ) dt

σθ2 =

σ2 (t )2

(1)

(2)

(3)

(4)

(5)

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Table 1 Experimental flow conditions. System

Tube dia., dt (m)

Coil pitch, h (m)

Length, L (m)

Coil dia., dc (m)

Liquid phase Reynolds number, NRe,

Single phase Two-phase

0.05

0.06

20

0.48

1061–23,150 1061–23,150

Pecletnumber ( NPe )

NPe =

UL D

(6)

In the following sections, the RTD analysis on single phase and two phase flows through the helical coil is discussed in detail. The experimental conditions for single and two-phase flows are tabulated in Table 1. 3.2. Single phase flow through coiled tube Single phase flows through coiled tubes have been analysed to assess the performance of scaled up helical geometry over laminar and turbulent flow regimes (mentioned in Table 1). Though, some literature reports are available for single phase RTD measurement in coiled tubes (Koutsky and Adler, 1964; Trivedi and Vasudeva, 1975; Saxena and Nigam, 1979; Saxena,1983a, 1983b; Saxena and Nigam, 1984), however the spectrum of flow conditions in terms of investigations has never been wide. Further, the investigations in this work are also being done at larger scales and non-invasively with the tracing of a single radioactive particle. Therefore, it was of great importance to validate the scale up and technique at pilot plant scale. The typical results of single phase RTD at two different liquid Reynolds number (NRe, L) of 1061 and 2986 are shown in Fig. 5a and b. In our method overall material balance is trivially satisfied, because all trajectories are actually accounted for (in classical pulse injection technique, mass conservation is not trivially satisfied and needs to be accounted for through the total area under the RTD curve). The real test for our methodology is to satisfy the so-called “central volume principle”, i.e., the mean of the RTD curves like that shown in Fig. 4e and f and Fig. 5a and b should also be equal to the overall mean time of contact. Indeed, this is well satisfied overall range of Reynolds number (NRe) (as can be seen in the first three columns of Table 2). Table 2 presents the results of the whole analysis at various flow conditions, and shows that the estimates of mean residence time obtained from the tracer particle tracking is very closely matching with what is obtained from overall flow measurements. Table 2 also shows that with increasing flow velocity the dimensionless variance is significantly reduced, leading to larger values of Peclet numbers (NPe). As we increase the Reynolds

L

(–)

Gas phase Reynolds number, NRe,

G

(–)

– 130–100,000

number, the strength of secondary flow increases leading to more uniform cross-sectional mixing even when Reynolds number may be well within the laminar range. As we increase the Reynolds number further, turbulent transition occurs which further leads to uniform cross-sectional mixing. In fact, in some earlier works (Trivedi and Vasudeva, 1975; Saxena and Nigam, 1984; Sharma et al., 2014) the liquid tracers were employed to measure the RTD using conventional tracer methods in smaller diameter coiled tubes. Those results, and the results of the current work can be readily compared in dimensionless coordinates, which we have plotted in Fig. 6. Indeed, the good agreement seen in this graph also points to the efficacy of the radioactive particle tracing technique, since it reproduces with cross-validates with the classical liquid tracer RTD technique on dimensionless coordinates very well (even though experiments with either technique were performed with different diameter tubes and different flow rates). 3.3. Two-phase flow through coiled tube Once the experimental protocol was finalized, the choice of two-phase system was made to present a clear picture of axial dispersion behaviour in helical tubes. Very little literature is available on two-phase flows that can capture the axial dispersion behaviour and hence convey the mixing behaviour over a wide flow range. The detailed description of flow map for helical geometry was made by Kaji et al. (1984) and Murai. et al., (2006), who studied the flow regime in helical tubes by using classical map of Mandhane et al. (1974) for straight tubes and showed qualitative similarities of helical flow regimes with that of straight tubes. In the current work as well, the regime information presented by Mandhane et al. (1974) was used to decide the flow range to perform RTD experiments in different flow regimes. The results of RTD analysis, using liquid and gas Reynolds number (NRe, L and NRe, G) of 1061–23,150 and 130–100,000 respectively, shows the reduction in mean residence time with increasing gas phase velocity (as shown in Fig. 7a). This change in mean residence time was caused due to the partial occupancy of the available volume by gas phase, which causes the velocity of the liquid phase to alter and hence the mean residence time. Therefore, an estimation of overall liquid hold up for an alternate comparison while verifying the veracity of the obtained results.

Fig. 5. Exit age distribution (E(t)) curve using single phase (water) flow at different liquid Reynolds number (NRe, L) (a) 1061 (b) 2986.

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Table 2 Parameters from single phase RTD. Liquid phase Reynolds number, NRe, 1061 1700 2986 5060 7997 10,500

L

(–)

Exp. mean residence time (s)

Theo. mean residence time (s)

Dimensionless variance (–)

Peclet number (NPe, (–))

828.9 523.3 284.1 173.7 101.3 89.3

834.8 521.3 296.7 175.1 110.8 84.4

0.031 0.030 0.029 0.022 0.015 0.009

64.9 66.1 68.2 92.9 136.2 222.9

Fig. 6. Comparison of RTD measurement by using liquid tracer and radioactive particle tracking technique.

The measurements for overall liquid holdup were made by locking the running steady state condition with quickly shutting off the valves at the inlet and outlet of the coil. The trapped water was then blown out from the coil into a graduated beaker. This small quantity of water that can be ascribed to wall-wetting was equivalently added to the measured water volume, to be taken as the total liquid volume VL, which is in turn used to estimate the liquid holdup, as per Eq. (7) (below). This gives an estimate of the proportion of coil volume occupied by water for each flow condition and hence liquid holdup (αL ). The measured values of overall liquid holdup for each flow condition are given in Table 3. From overall liquid holdup measurements, the liquid mean residence time ( tL ) for two-phase was calculated by using Eq. (8) (below). A parity plot of the experimental liquid mean residence time and those calculated by using theoretical mean residence time of the vessel ( t ) and liquid holdup ( αL ) data is shown in Fig. 7b. The agreement between the experimental liquid mean residence time and calculated liquid mean residence time (tL ) for two-phase flows is quite acceptable, given the inaccuracies involved in the water collection method to estimate liquid holdup. In fact, it shows very good consistency between different methods to estimate the overall flow characteristics of the two-phase flow.

V Liquid holdup ( αL ): αL = L VC Liquid mean residence time for two − phaseflow: tL =

(7) αL VC QL

(8)

The trends of liquid Peclet number (NPe) experienced by the helical flow using variable gas to liquid flow velocities are shown in Fig. 8a and b. In Fig. 8a, one clearly observes the different regions in the flow map that describes the different flow regimes offered by Mandhane et al. (1974). Also, the magnitude of Peclet

Fig. 7. (a) Mean residence time for two-phase flows through the helical coil (b) parity plot of the experimental liquid mean residence time and calculated liquid mean residence time by using theoretical mean residence time of the vessel (t ) and liquid holdup ( αL ) data.

number (NPe) in each flow regime is presented by following the stems of the markers. For more clarity, the trends of Peclet number (NPe) are shown by Fig. 8b for each liquid flow condition over variable gas flow conditions. The results from Fig. 8a and b are used to further explain the mixing behaviour based on the effective liquid phase Peclet number (NPe) (shown in Fig. 9), which represents a wide range of liquid and gas phase Reynolds numbers. On analysing the Peclet number (NPe) in each flow regime, it is seen that at low liquid and gas velocities (defined by stratified flow regime in Fig. 9, as per Mandhane et al. (1974)), there is an increase in axial dispersion with increasing gas velocity at a fixed liquid velocity. In this flow

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Table 3 Liquid holdup ( αL ). NRe,

L

1061 1700 2986 5060 7997 10,500 15,888 23,150

Liquid holdup  10  2 (–) NRe, G ¼130

NRe, G ¼ 296

NRe, G ¼650

NRe, G ¼ 1650

NRe, G ¼4000

NRe, G ¼9000

NRe, G ¼24,350

NRe, G ¼56,000

NRe, G ¼ 100,000

56.91 59.87 71.45 73.95 78.60 91.35 93.40 96.92

25.40 46.23 47.96 51.39 65.34 72.51 80.67 92.48

17.98 28.03 35.39 35.46 50.54 65.40 75.48 94.04

7.03 9.98 17.59 18.27 29.15 37.91 38.19 48.07

4.22 7.68 6.74 11.99 18.05 18.01 25.10 31.61

3.64 5.95 12.84 5.82 8.12 9.48 10.94 13.06

0.85 1.55 1.69 1.71 3.97 4.38 6.27 11.23

0.60 0.77 0.84 1.20 1.35 2.37 3.60 4.18

0.18 0.40 0.47 0.57 0.90 0.95 1.97 2.87

Fig. 9. Flow map for two-phase flows through helical coil using Peclet number (NPe) variation with changing liquid and gas phase velocities.

Fig. 8. Peclet number (NPe) variation for two-phase flows through helical coil over different flow regimes (a) top view (b) side view.

regime, separate layers of gas and liquid move owing to density difference; where the liquid water occupying the outer edge of curvature due to greater experience of centrifugal forces in comparison to air (owing to their difference in densities). Thus, the relative increase in the gas velocity causes the liquid in the vicinity of gas to move faster than rest of the liquid phase and hence causes flow to scatter; which in turns increases the axial dispersion. However, as we keep on increasing the gas velocity, we enter into a wavy flow regime (shown in Fig. 9) which causes the interface of gas and liquid to disturbed by small amplitude waves, and hence we get lesser axial dispersion in comparison to

stratified flow. In annular flow regime (shown in Fig. 9), the gas at the centre of pipe causes the liquid along the walls to move at higher velocities and hence gives lesser back-mixing (or axial dispersion) with an enhancement in gas and liquid velocities. The fluid in bubbly flow regime shows a reduction in axial dispersion with increasing gas velocity (as shown in Fig. 9), because with increasing gas velocity the turbulence caused by the bubbles makes the liquid to mix in the radial direction. Further, as we move in slug flow regime (shown in Fig. 9), the rate of decrease in axial dispersion dampens due to the aggregation of the bubbles into slugs. This causes lesser liquid to mix in comparison to bubbly flow. Similar observations were made by Saxena et al. (1996) on examining the two-phase flows in the approximate slug flow regime (using NRe, L from 620 to 3200 and NRe, G from 1500 to 3000), which showed that an increasing gas velocity at fixed liquid velocity caused more axial dispersion to happen in the liquid phase. Further, on analysing the dispersion as a function of liquid phase Reynolds number (NRe, L) for different gas phase Reynolds number (NRe, G), an important claim made by Rippel et al. (1966) becomes clearer. We see this when we compare the axial dispersion through helical coils using single phase and two-phase flows. Rippel et al. (1966) claimed that the relatively higher gas-to-liquid rates results in higher axial dispersion for two-phase in comparison to single phase. However, on examining the various flow regimes (NRe, L from 1061 to 23,150 and NRe, G from 130 to 100,000 respectively), we have found that this statement can be considered to be valid only when the two-phase flows have low liquid and gas phase velocities (i.e. in stratified regime). Fig. 10a shows the complete map of dispersion behaviour observed by using the analysis from current study and Rippel et al. (1966) (for air–water system), wherein on zooming the section of single phase (using liquid phase only) and two-phase flows observed in this study (Fig. 10b) it is observed that as long as the liquid and gas phase Reynolds numbers are within the stratified regime (i.e.

Please cite this article as: Sharma, L., et al., Axial dispersion in single and multiphase flows in coiled geometries: Radioactive particle tracking experiments. Chem. Eng. Sci. (2016), http://dx.doi.org/10.1016/j.ces.2016.05.012i

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Using single phase mixing information available in the literature, and comparing with our method, we have benchmarked the technique for laboratory as well as for pilot plant scale. Indeed, our investigations have yielded hitherto unreported information on two-phase flows in helical coils by investigating the trends of liquid Peclet numbers (NPe) over variable liquid and gas phase velocities. By analyzing the information of Peclet numbers (NPe) for different rates of gas to liquid flows (i.e. using different flow regimes), a bridge between the earlier reported studies (Rippel et al., 1966; Saxena et al., 1996) has been provided. The current work and the earlier reported works relate to different flow regimes, a gap that has been bridged by this contribution.. The types of the interactions experienced by the two phases through geometry, causes the axial dispersion to change much and hence mixing performance. This has been summarily captured in the flow regime map. Finally, it can be said that the single radioactive particle tracking technique as employed in this work opens up possibilities of using this technique in more complex geometries, such as combination of connected coiled tubes of coiled flow inverters. Further, clear possibilities exist for the use of this method for studying two-phase liquid-liquid flows (immiscible liquid) or slurry flow through coiled tubes. Indeed, some of these investigations will be subjects of our future contributions.

References

Fig. 10. (a) Liquid dispersion for single and two-phase flows (b) “zoomed-in” region of liquid dispersion for single and two-phase flows (this study).

NRe, G ≤ 24350 and NRe, L ≤ 5060 approx.), the axial dispersion is increasing with increasing gas phase flows. Once, the flow is out from this regime, there is no long validity of the statement. This is because in stratified flow regime (when both phases have low velocities), the relatively higher gas phase velocity than liquid phase velocity makes the liquid phase to distribute and hence offers higher axial dispersion in contrast to single phase flow. However, as the liquid phase velocity is increased in comparison to gas phase velocity, the two-phase flow gave higher Peclet number (NPe). It is also seen that as we are approaching towards higher liquid and gas velocities, this difference in Peclet number (NPe) is becoming insignificant due to shift in flow regime.

4. Summary and conclusions In this contribution, we have presented a non-intrusive method to measure liquid phase RTD for the helical flow system with continuous tracer particle circulation. This method is scalable to larger scales, and indeed the dimensions of the coil we have employed can be argued to be at a scale typical of pilot plants. The method employed was shown to yield accurate exit age distribution (E(t)), which is otherwise almost impossible to obtain with classical RTD techniques in large scale units and particularly in two phase flow units (owing to noise brought in by the second phase in the measured signal of the RTD). The approach was designed to obtain the information on axial dispersion over different flow regimes using single and two-phase flows through helical coils.

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