experiments on the turbulent structure and the void

Multiphase Science and Technology, Vol. 16, Nos. 1-4, pp. 1-20, 2005

EXPERIMENTS ON THE TURBULENT STRUCTURE

AND THE VOID FRACTION DISTRIBUTION IN THE TAYLOR BUBBLE WAKE

L. Shemer, A. Gulitski and D. Barnea Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering, Tel-Aviv University, Ramat Aviv, Tel-Aviv 69978, Israel

Abstract. An experimental approach is developed to carry out PIV

measurements and to perform digital processing of the recorded PIV images to measure simultaneously the instantaneous turbulent velocity field and the void fraction distribution in the wake region of a Taylor bubble. Advanced methods of data processing, such as ensemble averaging and Proper Orthogonal Decomposition (POD), are applied. Results of measurements performed in our newly constructed experimental facility are presented. Two liquid flow rates were employed, corresponding to Reynolds numbers of 820 for laminar background flow and 7500 for turbulent flow. The mean characteristics of the velocity field in the wake region are calculated by ensemble-averaging the instantaneous velocity fields measured around 200 different bubbles. An algorithm to estimate the void fraction distribution in the axial pipe cross-section from the recorded PIV images is developed.

1. INTRODUCTION

Development of novel (mainly optical) experimental techniques allows getting insight into the transient and the instantaneous aspects of slug flow. Some preliminary measurements of the velocity field around Taylor bubbles, the coalescence process between two consecutive elongated bubbles, and of the dynamics of a swarm of small

2 L. SHEMER, A. GULITSKI and D. BARNEA

dispersed bubbles, etc., were carried out recently. However, in spite of the impressive progress achieved in this field, our understanding of the mechanisms governing the evolution of slug flow and its structure is still insufficient. In the present study an experimental approach is developed to carry out Particle Image Velocimetry (PIV) measurements and to perform digital processing of the recorded PIV images to measure simultaneously the instantaneous turbulent velocity field and the void fraction distribution in the wake region of a Taylor bubble. Advanced methods of data processing, such as ensemble averaging and Proper Orthogonal Decomposition (POD), are applied. Results of measurements performed in our newly constructed experimental facility are presented. Establishing the inter-relation between the velocity field and the void fraction distribution behind a Taylor bubble is of utmost importance for understanding the complex nature of slug flow.

Gas-liquid slug flow in pipes is one of the most complex flow patterns in two-phase flow. In vertical pipes the bulk of the gas is trapped inside large bullet-shaped (Taylor) bubbles that move upwards and are separated by liquid slugs that are sometimes aerated. The development of slug flow along the pipe is governed by the interaction between consecutive Taylor bubbles [1]. The first experimental study of the coalescence mechanism between two consecutive Taylor bubbles was carried out by Moissis and Griffith [2]. It was found that the trailing bubble accelerates with decreasing separation distance and its nose sways from side to side. More recently, Pinto and Campos [3] and Aladjem Talvy et al. [4] studied bubble coalescence using pressure transducers and image processing technique respectively.

It is generally assumed that the trailing bubble nose is affected by the velocity field in the liquid phase ahead of it [5], [6]. When the bubble moves in an unsteady velocity field induced by the wake of the leading bubble, the trailing bubble shape and movement become strongly affected by this velocity field. Information on the velocity distribution in the wake of the leading bubble is therefore indispensable for the understanding of the trailing bubble movement.

Polonsky et al. [6] determined the velocity field in front of a Taylor bubble rising in stagnant and upward flowing water using PIV. In stagnant water, far upstream (>10D) of the bubble nose, non-zero velocities, ranging between 1 mm/s for short bubbles (2.5D) to 3 mm/s for longer bubbles (9.0D), were detected due to bubble expansion. The onset of reversed flow occurred at approximately one pipe diameter in front of the bubble. This distance decreases with increasing liquid flow rate. Velocities in the falling liquid film around the bubble were determined by particle streaks. In all cases the flow in the liquid film was laminar over the whole bubble length.

Van Hout et al. [7] measured velocity characteristics of the flow field around a Taylor bubble rising in stagnant water in a vertical pipe using PIV and discussed the relation between the instantaneous velocity field and the movement of the trailing elongated bubble. Radial and axial distributions of the mean velocities and of the turbulent quantities measured in the wake of the Taylor bubble were presented. Numerical simulations of the instantaneous liquid velocity field in the Taylor bubble wake rising in a stagnant liquid were performed by Tomiyama et al. [8]. In a subsequent study, Tomiyama et al. [9] performed measurements of mean velocity and pressure distributions around Taylor bubbles. The variation of the axial velocity profiles in the near wake region obtained in [8] is in general agreement with the results of van Hout et

EXPERIMENTS IN THE TAYLOR BUBBLE WAKE 3

al. [7]. The maximum calculated values of the normal and shear Reynolds stresses reported in [8] are also in a qualitative agreement [7].

In the present paper measurements of the velocity field around a Taylor bubble are extended to non-stagnant co-flowing liquid. Two cases are considered, corresponding to laminar (Umean =0.0315 m/s, Re=820), and turbulent (Umean =0.29 m/s, Re=7500) undisturbed background flows.

2. EXPERIMENTAL FACILITY AND PROCEDURE The experimental facility enables controlled injection of a desired sequence of bubbles of prescribed length into a liquid flowing at a desired flow rate. This apparatus replaces our earlier set-up [4], [6], and its design was based on the experience gained in those studies. A schematic sketch of the experimental facility is given in Fig. 1. The facility consists of an air and water supply system and a test section made of three 6 m long vertical Perspex pipes that have internal diameters of 0.014 m, 0.026 m and 0.044 m. Note that only one pipe is shown in Fig. 1. In the present study, the pipe with the internal diameter of 0.026 m is used. Filtered tap water flowing in a closed loop is used as the working fluid. Water is then seeded by small, 20 µm to 40 µm nearly neutrally buoyant fluorescent particles to enable PIV measurements. Special care was taken to ensure symmetric and smooth entrance of water to the pipes. The inlet section of each pipe, presented in more detail in the insert of Fig. 1, consists of a large settling chamber, a honeycomb, a number of screens, and a converging nozzle. Water flow rate is monitored continuously by a magnetic flowmeter. Air is supplied from a central compressed air line. Air bubbles are injected via computer-controlled solenoid-activated ball valve from a common manifold through separate pipes with internal diameters identical to those of each test section. The air supply pipes protrude through the honeycomb and screens. The depth of intrusion of each pipe into the converging nozzle can be regulated to achieve the desired flow pattern. Adjustment of the air pressure in the manifold and the valve opening duration allows controlling the length of the injected bubbles. Each test section is equipped with a rectangular transparent box filled with running water, to reduce image distortion and to provide cooling against the heat from illumination.

Measurements are carried out at about 4 m from the pipe inlet. An optical switch located at some distance upstream of the measuring station generated a trigger pulse at the Taylor bubble passage that activates the PIV system. The timing of the recording was set up so that it started when the Taylor bubble head was few diameters from the measuring location. The PIV setup consists of a Kodak 1.0 ES 1K by 1K camera, Nd-Yag double-head pulsed laser with a light intensity of 50 mJ/pulse, a synchronizer unit and a PC equipped with an appropriate data acquisition system. The laser sheet is located in the axial plane of the pipe and its thickness is about 1 mm. The field of view of the PIV system is about 30 by 30 mm2, corresponding the spatial resolution of about 0.5 mm (interrogation window size of 32 by 32 pixels). Note that in this study, no special and time-consuming effort has been invested so far to resolve the flow in the very vicinity of the pipe wall, as it has been done in our previous work [7]. The acquisition frequency of the system is 14 frame pairs per second, and the time delay between the frames within each pair was set to 0.2 ms in the near wake region characterized by relatively high


Figure 1 Sketch of the experimental facility. Details of the inlet section are shown in the insert. instantaneous velocities, and to 1 ms far away from the bubble bottom. For every flow condition, at least 200 different elongated bubbles were injected. The synchronizing unit, triggered by an optical switch, controlled the laser pulses and the recording by the camera. Each recording session for a given injected bubble continued for few seconds, depending on flow conditions, and covered distances up to about 2 m (more than 70 pipe diameters D) from the bubble bottom. Therefore, up to 80 image pairs were recorded for every injected bubble. At any given location relative to the Taylor bubble, an accumulated set of 200 image pairs (400 snapshots) of the flow field allowed extracting the required quantitative information. The present investigation is aimed mainly at acquiring detailed data on the mean and instantaneous velocity fields around the Taylor bubble. In addition, the recorded images were used to extract information on the void fraction distribution in the Taylor bubble wake.


3. RESULTS 3.1 Laminar background flow Even when the background (undisturbed) flow in the pipe is laminar (Re=820), the PIV images of the instantaneous flow fields reveal quite a complicated irregular structure. However, the PIV maps of the mean flow field are quite regular (Fig. 2). Reduced resolution is used here for better visibility.

The PIV map of the velocity vector field, in the diameter plane of the pipe, immediately behind the bubble is show in Fig. 2a. The axial distance x is measured from the bottom of the bubble. A narrow toroidal vortex can be seen in this figure. To visualize better the vortex structure of the flow, it is often instructive to subtract the mean velocity of the flow from the measured velocity field [10]. The characteristic velocity scale in the near wake region is the translational velocity of the Taylor bubble Utr=0.24 m/s. When this translational velocity is subtracted from the absolute velocities in Fig. 2b (i.e. the transformation is carried out to the frame of references moving with Utr), the toroidal vortex becomes more visible.

Profiles of the mean axial velocities, U, derived from the PIV measurements are shown in Fig. 3 at various locations behind the Taylor bubble bottom.

Immediately behind the Taylor bubble (x/D=0.1) the velocity profile in Fig. 3a is nearly flat in the central region of the pipe, with the velocity magnitude being close to Utr. The induced toroidal vortex causes notable increase in the axial velocity in the central region of the pipe, that attains maximum approximately at x/D=0.9. The values of U in the central region of the pipe then decreases, and attains a minimum at approximately x/D=3.0. The velocity profile in the far wake (Fig. 3b) therefore starts to develop from a strongly disturbed shape, and does not attain a fully developed parabolic shape in the whole measurements domain.

The non-monotonous variation of the axial velocity component along the pipe axis, Fig. 4, indicates that the mean velocity field behind the Taylor bubble is characterized by a sequence of toroidal vortex rings with opposite sense of rotation. The effect of those vortices gradually decreases. so that for x/D > 10 the velocity at the center line gradually approaches the value in the fully developed flow, but it still does not attain this value even at x/D = 45.

The radial velocities V (Fig. 5) are quite strong in the near wake region, where the vortex ring shown in Fig. 2 was observed. At x/D > 5, the mean radial velocity component essentially vanishes. It should be stressed that contrary to the mean values, the instantaneous values of the radial velocity component remain significant even at much higher distances from the Taylor bubble.

Note that while the background flow is laminar (Re=820), the dominant velocity in the near wake, as mentioned above, is Utr and the corresponding Re equals 6250, so that the flow in that region is turbulent. The correlation coefficient between the velocity fluctuations in the axial and the radial directions is shown in Fig. 6.

The correlation coefficient value is small in the immediate vicinity of the bubble bottom, but increases fast, attaining maximum of about 0.6 around x/D = 1. The fluctuations, however, fast become uncorrelated, and for x/D > 5 the flow can be considered as essentially laminar, although uncorrelated velocity fluctuations remain up


Figure 2a Mean velocity field behind the bubble in laminar background flow.

Figure 2b As in Fig. 2a, but the velocity vectors are shifted by Utr = 0.24 m/s.


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Figure 3 Mean axial velocity profiles, laminar background flow. a) near wake region (0 , x/D < 5); b) far wake (x/D > 5).


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Figure 4 Variation of the axial velocity component at the center line of the pipe, laminar background flow.

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Figure 5 Mean radial velocity profiles, laminar background flow.


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Figure 6 Reynolds stress behind a Taylor bubble in laminar background flow. to much larger distances. This is in agreement with the results obtained for a Taylor bubble rising in stagnant liquid [7]. 3.2 Turbulent background flow The PIV measured mean turbulent velocity field, both in constant (Fig. 7a) and in moving with Utr = 0.535 m/s (Fig. 7b) frames of references, seems similar to the vortex ring pattern observed in laminar flow, Fig. 2. Comparison of Figs. 7a and 7b clearly demonstrates that the vortical nature of the mean flow is expressed well in the moving frame of references, as it was in the case of laminar background flow.

The profiles of the mean axial velocity U in turbulent flow are presented in Fig. 8. In the near wake region these profiles behave similar to their laminar counterparts. The initially flat U profile (with the values of U close to Utr) is transformed to a velocity distribution with higher velocities in the central region of the pipe at x/D = 0.6. The velocity profile then fast becomes nearly uniform at x/D = 2. This similarity apparently stems from the fact that the flow in this region is turbulent for the given pipe diameter for any background flow rate. In the case of turbulent background flow, the strong mixing, however, results in a U profile that already at x/D = 4 is very close to the fully-developed shape, Fig. 8, much faster than in the laminar case.

The radial distributions of the mean radial velocity component V, Fig. 9, resemble qualitatively those observed behind the Taylor bubble propagating in the laminar pipe flow that were presented in Fig. 5. The mean radial velocities remain significant only in the close vicinity to the Taylor bubble bottom, x/D < 2, and are characteristic of the toroidal vortex pattern. Similarly to the axial velocity profiles, the radial velocities approach the developed shape faster than in the laminar background flow.


Figure 7a Mean velocity field behind the bubble in turbulent background flow.

Figure 7b As in Fig. 7a, but the velocity vectors are shifted by Utr = 0.525 m/s.


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Figure 8 Mean axial velocity profiles, turbulent background flow.

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Figure 9 Mean radial velocity profiles, turbulent background flow.


The propagation velocity of the Taylor bubble moving in the wake of the leading bubble is strongly dependent on the instantaneous rather than the mean velocity field ahead of it [4]. It is therefore instructive to apply the proper orthogonal decomposition analysis (POD) that has been introduced in the field of hydrodynamics by Lumley [11], to provide an unbiased identification of coherent structures in turbulent flow in the near wake region of a Taylor bubble. The method is based on the second-order statistical properties of the experimental data which result in a set of optimal eigenfunctions. The 1st eigenfunction is identical to the mean flow (Fig. 7a), while the 2nd and 3rd eigenfunctions (Figs. 10a and b, respectively) represent vortices with opposite senses of rotation. It seems plausible to assume that these vortices are induced by the Taylor bubble bottom oscillations, [12, 4].

Quantitative information about the turbulent structure of the flow is obtained by analyzing the spatial distribution of the turbulent velocity fluctuations at different locations relative to the Taylor bubble bottom. It is customary to scale the magnitude of the turbulent velocity fluctuation by the characteristic flow velocity. In the flow under consideration, this characteristic velocity scale, however, does not remain constant, and decreases from Utr, (or possibly even a higher value, corresponding to the liquid film velocity of the order of 1 m/s in our experiments) close to the bubble bottom, to a significantly lower value of the order of Umean in the far wake.

The r.m.s. values of the axial u’ and radial velocity v’ fluctuations presented in Fig. 11 are normalized by Umean at all distances from Taylor bubble to enable quantitative comparison of various profiles. Following the gradual decrease of the characteristic velocity scale, the normalized values of the axial and radial velocity fluctuations also decrease with the distance from the Taylor bubble. Contrary to the fast adjustment of the mean velocity profiles as shown in Figs. 8 and 9, the relaxation of the turbulent velocity fluctuations is quite slow, even at a distance of 20D behind the bubble bottom the turbulent fluctuations are notably stronger than in the developed pipe flow, which is only attained at distances exceeding 50D from the Taylor bubble.

Variation of the Reynolds stress distribution with the distance from the Taylor bubble, Fig. 12, is of particular interest. In the immediate vicinity of the Taylor bubble bottom, at x/D=0.1, the strong fluctuations of the axial and the radial velocity components remain uncorrelated. The Reynolds stresses attain a maximum at about x/D = 1, and then decay strongly along the pipe, Fig. 12a. In the near wake region, the cross-correlation coefficient (Fig. 12b) varies similarly to what was observed in laminar flow, increasing initially and then decaying.. The most striking feature of this figure is that the cross-correlation coefficients essentially vanishes for 2 < x/D < 20 (see open symbols in Fig. 12b), so that the momentum transfer in this region is governed by molecular viscosity, as in laminar flow. The velocity fluctuations in the axial and in the radial directions decay monotonically along the pipe, as discussed above. The cross-correlation coefficient, however, does not behave in a similar fashion, and the fluctuation in the axial and the radial directions gradually become correlated again, for x/D > 20, but even at x/D = 50, when the r.m.s. values of the velocity fluctuations in Fig. 11 already attain distributions typical of the fully developed turbulent pipe flow, the values of the correlation coefficient are well below those in the fully-developed flow. The turbulent structure becomes fully developed only for x/D approaching 70. It thus appears that for a typical slug flow, where the distance between consecutive bubbles is much shorter than


Figure 10 The 2nd and 3rd optimal eigenfunctions in the near wake region of the Taylor bubble in turbulent background flow.


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x/D = 50 x/D = 70

b Figure 11 Radial distributions of the r.m.s. vlues of turbulent velocity fluctuations, normalized by Utr = 0.29 m/s : a) axial component, b) radial component. 70D, application of the quantities appropriate for a fully developed turbulent pipe flow for modeling of the slug flow can lead to erroneous results. 3.3 Void fraction distribution As mentioned above, for each flow condition at least 400 instantaneous snapshots of the flow field (corresponding to 200 PIV image pairs) were recorded at various distances


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b Figure 12 Radial distributions of : a) Reynolds stresses ; b) cross-correlation coefficient.


from the Taylor bubble bottom. In all those images the velocity field has been illuminated by a thin laser light sheet pulse (the pulse duration of few nanoseconds). As a result, in addition to the fluorescent particles, sharp boundaries of air bubbles in the illuminated diametral plane of the pipe can be clearly identified in the images, Fig. 13. An image processing algorithm has been developed that allows delineating the boundaries of the bubble present in each image. At each axial x and radial r location, the ratio of the number of pixels belonging to air bubbles, to the total number of recorded images at a given distance from the bubble bottom, corresponds to the local void fraction.

The resulting contours of the void fraction distribution in the wake of a single Taylor bubble rising in a pipe in turbulent background flow are presented in Fig. 14. Note that due to reflections from the pipe wall, the results in the vicinity of the wall are less reliable. For that reasons, void fraction distribution in Fig. 14 is shown only for 0 < r/D < 0.4.

Figure 13 A PIV image of the flow field with bubble in the illuminated plane clearly visible.


Figure 14 Contour plot of the void fraction distribution behind the Taylor bubble rising in turbulent flow.

It becomes clear from Fig. 14 that bubbles are mainly concentrated at a distance of

about 17D from the bubble bottom, while the domains in the immediate vicinity of the Taylor bubble, as well as far away for the bubble are practically free of small dispersed bubbles. Measurements were carried out at a distance of about 4 m, or 150D, from the pipe inlet. The results of Fig. 14 indicate that for our experimental conditions, no bubble shedding is observed from the bubble bottom, and the only dispersed bubbles present in the pipe are generated at the inlet in the process of bubble injection.

4. SUMMARY AND CONCLUSIONS Experiments with individual Taylor bubbles rising in a 0.026 m diameter, 6 m long vertical pipe were carried out. Measurements were performed with bubbles injected into either laminar (undisturbed background flow with mean velocity Umean= 0.0315 m/s, corresponding to Re = 820), or turbulent (Umean= 0.29 m/s and Re = 7500) co-flowing stream.


Mean and instantaneous PIV-measured velocity vector fields are discussed. For each flow condition and each location relative to the Taylor bubble, the data presented are based on an ensemble of at least 200 independent recordings.

The flow field in the Taylor bubble wake is characterized by different velocity scales, depending on the location relative to the bubble. The velocity scale in the immediate bubble vicinity is the translational Taylor bubble velocity Utr. For the pipe diameter in our experiments, D = 0.026 m, the Reynolds number based on this velocity, is Retr = 6,250 for the laminar background flow, and Retr = 13,650 for the turbulent background flow. As a result of that, the flow in the near wake region is turbulent for both flow rates investigated here.

Therefore, there is a considerable similarity in the flow fields observed in the laminar and the turbulent background flows, up to the distance of few pipe diameters from the Taylor bubble bottom. At both flow rates, the mean flow is characterized by toroidal vortex rings, which becomes more pronounced if the Galilean transform that shifts the velocity by the corresponding Utr values is applied, cf. Figs. 2 and 7. In the immediate vicinity of the Taylor bubble bottom, the mean velocity profile is nearly flat in the central region of the pipe, with the axial velocity being close to Utr, as expected from continuity. The vortex rings then induce much higher axial velocities at the pipe axis, the maximum is attained at approximately x/D = 0.9 for the lower flow rate, and at x/D = 0.6 for the higher flow rate. The radial velocity components also behave in agreement with the vortex ring pattern. Moreover, there is a considerable similarity in the turbulent structure observed for both laminar and turbulent background flows in this region. In particular, the Reynolds stresses are small immediately below the Taylor bubble bottom, and the strong turbulent velocity fluctuations in the axial and the radial direction in this region being essentially uncorrelated. The correlation coefficient then attain a very high maximum value of about 0.6 at about x/D = 1, and then decreases (Figs. 6 and 12).

The coherent structure of the instantaneous (contrary to the ensemble averaged) velocity field may be described using the Proper Orthogonal Decomposition (POD). The dominant eigenfunctions characterizing the instantaneous velocity field right below the Taylor bubble bottom indicate that the toroidal vortex pattern is only obtained on the average. The coherent part of the instantaneous velocity field in this region, presented in Fig. 10, seems to be mainly affected by the quasi-periodic oscillation of the Taylor bubble bottom, and is dominated by vortices that occupy the whole pipe cross-section and have opposite senses of rotation.

At larger distances from the Taylor bubble bottom, the mean flow velocity Umean gradually becomes the dominant velocity scale. The evolution of the mean velocity profiles with distance from the Taylor bubble bottom is therefore quite different for x/D > 3 for both laminar and turbulent background flow regimes. In the laminar flow, the mean velocity profile behind the bubble varies slowly and remains undeveloped at considerable distances (beyond 50D) from the Taylor bubble bottom, Figs. 3, 4. Variation of the axial velocity component at the center line of the pipe indicates that the mean flow field is affected by a sequence of vortex rings with alternating senses of rotation and decaying intensity. Reynolds stresses vanish for x/D > 3, but the uncorrelated velocity fluctuations decay slowly.


The results on the velocity field behind a Taylor bubble rising in co-flowing laminar liquid are consistent with our earlier measurements performed with a Taylor bubble rising in stagnant liquid [7].

For a bubble rising in a turbulent flowing liquid, the enhanced mixing results in mean velocity profiles that approach the fully developed shape already at x/D > 4. The turbulent structure relaxation is however much slower. The axial and radial velocity fluctuations decay gradually and do not exhibit fully-developed profiles even at x/D = 20, Fig. 11.

Quite strong velocity fluctuations measured at distances up to 20D behind the bubble and even beyond, remain nearly uncorrelated. The cross-correlation coefficient between the fluctuating velocity components u’ and v’ effectively vanishes for 3 <x/D < 20, and is gradually restored approaching the fully developed shape for x/D > 50. It thus may be concluded that the route of the turbulent structure in the liquid phase from that dominated by a mixing in a circumferential wall jet immediately behind the Taylor bubble, to fully developed turbulent pipe flow passes through an extensive effectively laminarized domain, where turbulent fluctuations do not contribute significantly to the momentum transfer. These results are significant for modeling of momentum and heat transfer in turbulent slug flow.

The analysis of the PIV images recorded in the course of this study revealed that many of them contain that clear boundaries of small air bubbles dispersed in the liquid. Fig. 13. It was thus concluded that in addition to the velocity data, the available snapshots can provide information on the void fraction distribution in the Taylor bubble wake. An appropriate image processing algorithm has been developed, and the spatial distribution of the void fraction behind a bubble rising in turbulent background flow was calculated, Fig. 14. No small bubble shedding from the Taylor bubble bottom can be identified in our experiments, and it appears that the only source of the dispersed bubbles in the flow is related to the injection procedure.

While the potential of simultaneous velocity field and void fraction measurements has been demonstrated here, considerable additional work is required to optimize the processing procedure and to carry out measurements for a wide range of flow parameters.

ACKNOWLEDGEMENT This work was supported by a grant from the Israel Science Foundation.

NOMENCLATURE D pipe diameter (m) r radial coordinate (m) u instantaneous axial velocity component (m/s) U mean axial velocity component u’ axial velocity fluctuation (m/s) v instantaneous radial velocity component (m/s)


V mean radial velocity component v’ radial velocity fluctuation (m/s) x distance from the Taylor bubble bottom, m Subscripts mean cross-sectional mean tr translational

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experiments on the turbulent structure and the void

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