Bubble characterization in horizontal air–water intermittent flow

International Journal of Multiphase Flow 69 (2015) 18–30

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

Bubble characterization in horizontal air–water intermittent flow W.R. de Oliveira, I.B. de Paula, F.J.W.A. Martins, P.S.C. Farias, L.F.A. Azevedo ⇑ Departamento de Engenharia Mecânica, Pontifícia Universidade Católica do Rio de Janeiro – PUC-Rio, Rio de Janeiro, Brazil

a r t i c l e

i n f o

Article history: Received 26 December 2013 Received in revised form 2 October 2014 Accepted 21 October 2014 Available online 29 October 2014 Keywords: Slug flow Elongated bubble Air–water flow Image processing

a b s t r a c t Elongated bubbles were characterized experimentally for air–water flow in a horizontal pipe at nearly atmospheric conditions. The range of flow rates employed covered regimes at the transition from elongated bubble to slug. Ensemble-averaged digital image processing techniques were applied for detection of the liquid–gas interface with aid of a set of photo gates to synchronize bubble passage with image acquisition. Quantitative data of front and tail parts of the bubbles were analysed for different mixture velocities and the results confirmed visual observations frequently reported in the literature. Close to transition, a linear tendency of the bubble nose to move towards the pipe centerline position, for increasingly higher values of the Froude numbers, was observed and quantified. Bubble tail shapes were quantified and the hydraulic jumps were shown to be dependent of Froude number, while the liquid film thicknesses were governed by the liquid volume fraction. Changes on the bubbles characteristics are apparently linked to variations in the bubble velocities and seem to reflect a competition between viscous and inertia effects. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction The transport of gas and liquid simultaneously in horizontal pipelines is present in many engineering applications. During the last decades, an intense effort has been devoted to the study and modelling of the flow characteristics in order to increase safety and profit margins in pipeline operations (see Havre et al., 2000, for a review). An important characteristic of two phase flows is the existence of a variety of flow regimes, depending, among other variables, on the flow rates of each phase. These regimes are defined based on the geometrical distribution of phases in the pipe cross section (see Mandhane et al., 1974; Taitel and Dukler, 1976). The present work is devoted to investigating the horizontal intermittent flow regime that is characterized by the passage of a succession of liquid slugs followed by elongated bubbles travelling above a thin liquid film. Intermittent flows can be subdivided into two sub-regimes: (i) plug or elongated bubble flow and (ii) slug flow. The plug flow regime is found at low flow rates. It is usually composed of liquid slugs with a low concentration of dispersed gas bubbles followed by elongated bubbles that move along the top of the pipe. According to Kadri et al. (2009), in this regime the liquid slugs can extend for more than 100 pipe diameters. The slug flow regime is characterized by the intermittent appearance of aerated liquid slugs,

⇑ Corresponding author. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2014.10.014 0301-9322/Ó 2014 Elsevier Ltd. All rights reserved.

separated from one another by gas bubbles, travelling near the centre of the pipe. In this last regime, the frequency of flow intermittence is higher when compared to plug flow. Also, the typical lengths of liquid slugs and bubbles are much shorter when compared to plug flow. In the oil and gas industry, significant capital losses can occur when long liquid slugs are present due to the elevated pressure levels generated by their passage that can, for safety reasons, require production shut down. Also, intermittent flows can induce severe transient loads on the structures with potentially catastrophic consequences. Although the slug and the plug flow regimes are both considered intermittent, the typical loads, lengths of slugs and bubbles and frequencies associated with each regime can be remarkably different (see Nydal et al., 1992; Hurlburt and Hanratty, 2002; Kadri et al., 2009). Thus, it is very important to distinguish between these regimes for a proper design of pipelines and damping devices, such as the slug catchers. According to the flow maps of Mandhane et al. (1974), Taitel and Dukler (1976), Barnea (1987), Lin and Hanratty (1987a), among others, for a given liquid superficial velocity, the transition from plug to slug regime is expected to occur above a threshold of gas velocities. However, at transition, these two regimes are not clearly distinguishable, especially for the case of horizontal pipes. The absence of dispersed gas bubbles was suggested by Barnea et al. (1980), as a criterion to distinguish plug from slug regime. Lin and Hanratty (1987b), used pressure measurements to define the transition threshold. Based on a photographic study, Ruder

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

et al. (1989), described plug flows as being an unaerated liquid slug followed by a gas bubble with characteristics similar to a ‘‘Benjamin bubble’’ (Benjamin, 1968). Later, this definition was extended by Ruder and Hanratty (1990), with the aid of pressure pulsation and void fraction measurements, and photographic visualization, to include qualitative characteristics of the front and rear part of the bubbles. They suggested that the transition from plug to slug regimes occurs when the tail of the bubble approximates the form of a single-stage hydraulic jump. Although they have measured different parameters of the flow, the major contribution to define plug flows was derived from qualitative analysis of a restricted number of images. Based on observations of different behaviours for the two regimes, Fagundes Netto et al. (1999) also suggested the use of the characteristic shapes of the front and rear of elongated bubbles as a means of accessing transition. They suggested the angle of the hydraulic jump at the rear of the bubble as a possible criterion to define this threshold. The goal of the present study is to apply quantitative visualization techniques to investigate the shape of the rear and front parts of the bubbles in the transition from plug to slug regimes. This work was motivated by the recent availability of high frame rate cameras that, combined with techniques for image analysis, added new possibilities to address the problem. The combination of these techniques have been used to investigate two-phase flows in several works, such as (Polonsky et al., 1999; Nogueira et al., 2003; Ursenbacher, 2004; Shemer et al., 2007; Mayor et al., 2007; Guo et al., 2010). The non-intrusive nature of these techniques make them suitable for studying flow regimes sensitive to disturbances, such as plug, slug and annular flows. The main drawback of the technique is the requirement of optical access to the flow. In the present work, procedures based on back-illuminated bubble images were combined with a high frame rate digital camera to enable the extraction of the bubble-slug interfaces at the transition from plug to slug flow. Back-illuminated bubble images have been widely used in the literature as a two-phase flow visualization technique (e.g. Bendiksen, 1984; Ruder and Hanratty, 1990). Also, the acquisition of images triggered by the passage of bubbles has been extensively applied to investigate bubble behaviour in two-phase pipe flow (e.g. Gopal and Jepson, 1998; Polonsky et al., 1999; van Hout et al., 2002; Nogueira et al., 2003; Ursenbacher, 2004; Mayor et al., 2007; Guo et al., 2010; Shemer et al., 2007). In the works of Polonsky et al. (1999), Pinto et al. (2001), Shemer et al. (2007), Mayor et al. (2007), the techniques for extraction of instantaneous and averaged bubble contours, as well as for quantitative measurements of the velocity field around the bubbles, were developed and validated. An improvement introduced here is the estimation of individual bubble velocity in real time, what allows for the utilization of an automatic adaptive adjustment of time delays used to synchronize each bubble passage with image acquisitions. By this technique, bubbles travelling at different velocities could still be captured within the field of view of the camera. This feature can aid in the study of plug and slug flows in horizontal pipes, since in these flows instantaneous bubbles can display variations in their velocities under the same nominal flow conditions. By the procedure used in the present work, hundreds of bubble contours could be ensemble averaged with increased efficiency, providing useful statistical information about the bubble characteristics.

Experiments The experiments were performed in a horizontal pipe with internal diameter (D) of 0.0508 m and length (L) of 23 m, yielding a length-to-diameter ratio of approximately 450. A schematic view of the apparatus is shown in Fig. 1. The test rig was built from

19

Fluorinated Ethylene Propylene (FEP) pipes, in order to reduce optical distortions during image acquisition. This material was previously used in the work of Hewitt et al. (1990), and it proved to reduce light scattering at the wall due to the matching of its refractive index with that of water. Air and water were injected into the section by a ‘‘Y’’ junction located at the inlet of the test pipe. A split plate was mounted inside the junction to reduce the level of flow fluctuations at the inlet. Water was pumped in closed loop at superficial liquid velocities up to 0.5 m/s. A centrifugal compressor provided air to the test section with velocities up to 40 m/s. The flow rates of air and water were measured using calibrated turbines, CONTECHÒ models SVTG G19 and SVTL L19, with experimental uncertainties estimated to be within 1% and 0.5%, respectively. At the end of the line, the air–water mixture was separated into two vessels from where the water was returned to the pump inlet, while the air was vented out of the laboratory space. The measurement section was located at a distance of approximately 400 pipe diameters from the inlet. It was composed of three infrared gate sensors, PASCOÒ model ME-9204B, a CMOS high frame rate camera (Motion Pro X3TM with 1.3MPixels), an illuminating panel of LEDs, and a visualization box. As will be described shortly, the infrared gates had a dual role in the experiments. They were used to measure slug statistics, such as slug length, velocity and frequency, as well as to provide a trigger signal for the image acquisition system. Downstream of the photo gates, the FEP tube was encased in a visualization box filled with water in order to reduce refractive indexes mismatches. On the opposite side of the camera, the panel of high power white LEDs was installed to provide background illumination for image acquisition with proper contrast. Measurement of bubble and slug statistics The three infrared photo gate sensors mentioned before are presented in more detail in Fig. 2. They were employed to measure the bubble and slug statistics of interest, namely, bubble front and rear velocities, slug length and slug frequency. These parameters were estimated as suggested in the work of Polonsky et al. (1999). The three infrared gates were installed orthogonally to the pipe, and spaced 0.3 m from each other (Ddgates). According to preliminary experiments, a sensible noise reduction in the signals from the photo gates was observed when the sensors were placed close to the centerline of the pipe. The reason for this behaviour is the high concentration of dispersed bubbles travelling close to the top of the pipe. However, for low Froude numbers the elongated bubbles also travel close to the top of the pipe. Therefore, the sensor is not sensitive to their passage when positioned at the centerline of the pipe. Thus, a good compromise between the detection of elongated bubbles and the noise reduction was found when the sensor was positioned at a height of 2/3 of the pipe diameter, as shown in Fig. 2. The first two photo gates were used to measure the front and rear velocities of the bubbles, while a third gate provided a trigger signal to start a quartz based clock, properly adjusted according to measured front or rear velocity. The clock was used to output signals for synchronization for image acquisitions. For fast measurements of the bubble front and rear velocities the output signals of gates 1 and 2 were fed to an external XOR logic circuit, which produced a single pulse of finite duration. The circuit provided a high state logical level during the passage of the front or the rear of the bubble through photo gates 1 and 2. This pulse width could be quickly and accurately measured at a rate of 20 MHz, using a built-in function of a multifunction D/A board model ATMIO-16X and Labview™ routines. The bubble front or rear velocity was then calculated as the ratio of the distance between the photo

20

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

Fig. 1. Schematic diagram of the test section.

Fig. 2. Schematic assembly of photo gates.

gates 1 and 2 and the measured pulse duration. In order to identify the pulses related to each part of the bubbles it was necessary to perform a logic AND operation using the XOR gate and the sensors output signals. This logic operation with the signal from photo gate Sensor 1 enabled the identification of pulses related to the rear part of the bubble, while the pulses associated with the front could be identified by using the signal from Sensor 2. A high amount of dispersed bubbles close to the front part of the elongated bubble was observed for high mixture velocities, causing high frequency oscillation in the output of the photo gates. In order to avoid such oscillations, the signals from the sensors were low-pass filtered using a cut-off frequency of 250 Hz. The length of a liquid slug was estimated by the product of measured bubble velocity (uB) and the time delay between two consecutive pulses. Similarly, the length of unit cells could be estimated by multiplying uB and the time delay between two consecutive passages of the bubble rear part (Dt). The inverse of the delay Dt provided information about the frequency of the slugs. A detailed description of these equations can be found in the literature (e.g. Polonsky et al., 1999). Due to the simplicity of the calculations performed, all parameters could be estimated in real time. Velocity information extracted from the infrared photo gate sensors was used in real time to provide a proper delay for synchronization of image acquisitions with bubble passage. Thus, a proper delay for image acquisition could be estimated and set to the hardware counter of the quartz based clock (20 MHz), before the bubble reached the third photo gate. The signal generated by the bubble passage through the third photo gate was used to start the counter and, immediately after finish counting, a high logic level signal was set to a digital gate of the D/A board. This procedure provided an accurate and adaptive time delay for the image acquisitions, which automatically compensated for slight variations in bubble velocities, thereby allowing that bubble front or rear images from different bubbles were properly captured at the same position in front of the camera field of view. The delayed trigger was used to start the camera synchronizer. At each trigger pulse, the synchronizer (model BNC-575) sent

pulses to the CMOS camera ordering it to capture 4 consecutive images of bubble front or rear. The time interval between the acquisitions was adjusted in the synchronizer according to the flow mixture velocities being studied. Intervals of 20 ms were set for cases with low mixture velocities (jm < 1.5 m/s), while 10–15 ms were used for other cases. Also, the camera exposition had to be adjusted according to the bubble speed in order to avoid image blurring. Downstream from the infrared gates, at the position of the visualization box, an array of 176 white light LEDs was installed to provide back illumination for the images. The intensity of the light was controlled by an adjustable power supply. To achieve uniform illumination in the background of the images, the light emitted by the LEDs was diffused by a sheet of white paper. The synchronization process developed guaranteed that the front or tail parts of the bubbles were exactly at the camera field of view at the moment of image capture, even though each individual bubble travelled at different velocities. This feature allowed for the capture of hundreds of bubble images that were later postprocessed to produce an ensemble-averaged bubble image, as will be described shortly. Ensemble-averaged bubble images are useful experimental information that can contribute to clarify the bubble behaviour. The main characteristic of the present study is the analysis of the bubble features based on ensemble-averaged interfaces constructed from hundreds of instantaneous bubbles images. This technique presents a significant advantage when compared to the widely used method of imaging a continuous interval of the fluid flow employing high frame rate digital cameras. The continuous imaging of only a few seconds of the bubble and slug passage at high frame rates and reasonable spatial resolution rapidly fills the camera memory space of currently available cameras. Most of the images acquired in this operating mode are related to the body of the bubbles, with only a few frames displaying the desired bubble nose or tail images. For instance, in the present experiments the highest shedding frequency of slugs was slightly below 0.5 Hz, while the lowest was close to 0.1 Hz. If one considers a typical frequency of 0.25 Hz for a rough estimate, it can be concluded

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

that 1 Gbyte of data is necessary to record the passage of only 5 slugs, when a camera of 1Mpixels is operated in continuous acquisition, at a rate of 50 Hz. Using the triggered image acquisition procedure employed in the present study, only images of bubble noses or tails are stored in the camera memory, what makes it possible to store hundreds of such images allowing for the computation of ensemble-averaged contours and other flow statistics. By using the proposed acquisition procedure, only 40 Mbytes are required to record the information of 5 consecutive slugs. Thus, a clear advantage of the method developed is the optimization of the camera memory and the reduced number of images used in the data processing. The main drawback of the method is the lack of continuous imaging of the flow, what does not allow for a complete reconstruction of the slugs. Image processing of bubble nose and tail The identification of bubble characteristics was performed using back-illuminated images, in a similar way as done previously in the work of Polonsky et al. (1999), Mayor et al. (2007), and Shemer et al. (2007). This is a simple, non-intrusive, optical technique suitable for measuring liquid and gas interfaces. It relies on the acquisition of images with an intense and uniform background illumination that passes through the flow. At the interface, the light transmission is attenuated, creating a shadow on the acquired image. Prior to analysis of the images, a calibration procedure was performed in order to convert from pixels to actual flow dimensions. To this end, a semi-cylindrical target marked with an array of spaced dots, was introduced into the pipe filled with water. After adjustment of the camera focus to the plane of the target, an image was acquired and the calibration factor extracted. The FEP pipes reduced the optical distortions induced by differences in the refraction indexes of water and the pipe. Thus a single calibration factor could be used for the complete area imaged by the camera. With the magnification selected for the measurements, a calibration factor of 11 pixels/mm was obtained. Although the refractions indexes of the pipe and the fluid were similar, their light absorption coefficients were not the same. Therefore, the light was significantly attenuated at locations very close to the top and the bottom of the pipe, hence reducing the region of measurements in 10% of the diameter. This effect is expected to occur also for different materials and can be reduced by using transparent pipes with reduced wall thickness. Due to the inaccuracy of the results at such locations, the bubble contours presented in the present study are shown within the limits of 5–95% of the pipe diameter. This is a conservative limit and it was chosen to ensure that no influence of the illumination intensity at the bottom and top of the pipe would be present in the obtained results. The procedures developed for analysis of bubble nose and tail images differed due to the nature of these images, but shared the same basic steps that will be outlined in the next subsections. All the image processing routines and bubble feature extraction routines were implemented using a Matlab platform. Bubble nose interface detection from instantaneous images The procedure used to extract the interfaces of individual instantaneous bubble images was applied to hundreds of images in order to allow the determination of statistically relevant information about the bubble contours. Each image of the bubble nose was cropped into a size of approximately one-by-one pipe diameter after the identification of the nose tip. The position of the bubble nose tip was used to align all the instantaneous images. Although the image triggering guaranteed that all bubbles were inside the camera field of view nearly at the same position, small shifts could be observed from image to image due to changes in

21

the bubble shapes. In cases with a high concentration of dispersed bubbles near the nose of the main bubble, an initial guess for the position of the nose tip was given by visual identification employing guided user interface (GUI) routines. This initial estimation of the nose tip was used to crop the images. It facilitated the automatic detection of the contour, which was performed afterwards. Other efforts in the literature have faced the same difficulty in identifying bubble interfaces in highly aerated flows, (e.g. van Hout et al., 2002). Standard pre-processing techniques, such as contrast enhancement, background subtraction and grey intensity normalization, were applied to each individual instantaneous cropped image, in order to remove any bias that could have been introduced by differences in illumination intensity (see Gonzales et al., 2009 for a review of the standard image processing routines). The standard techniques for image processing are capable to precisely detect the bubble interface in images having a low concentration of dispersed bubbles, such as the one of Fig. 3(a). For the detection of interfaces in images with a high concentration of dispersed bubbles, such as the one exemplified in Fig. 3(b), a low-pass digital filter was applied to the images before the processing. Thereby, it was possible to detect interfaces in the instantaneous images, even in the presence of dispersed bubbles. For each flow rate, a set of approximately 400 instantaneous interfaces was determined, producing statistic features about bubble nose shape and position. The ensemble-averaged interface shape was one of these features, and it was employed to yield all the results presented in the present study. Uncertainty estimation of bubble interface determination The image processing procedures just described for detecting the instantaneous bubble interfaces are associated with uncertainty levels that need to be estimated. The uncertainty on the binary operations employed to detect the interface position at a certain axial coordinate involve binarization of the original image and open and close binary operations. Tests on samples of the complete acquired image sets indicate that open and close operations with an average of 10 iterations were necessary to properly identify the bubble interface. An uncertainty of 1 pixel was associated with each of these iterations, totalling an uncertainty of 10 pixels for the interface detection. The uncertainty level associated with the image binarization procedure was found to be typically of 1 pixel, which can be considered negligible in face of the uncertainty levels on the interface detection. For the detection of the ensemble-averaged interfaces, a second source of uncertainty should be considered. It originates from the random nature of the bubble shapes that constitutes the set of images employed in the determination of the ensemble-averaged interfaces. This uncertainty contribution was estimated by the standard error, which is given by the standard deviation of the interface position at a particular axial location, divided by the square root of the number of bubble image samples used. The final uncertainty level was estimated by the square root of the sum of the squares of the two uncertainty contributions (JCGM, 2008). The estimated uncertainty levels for the results obtained in the present study are indicated in the figures as vertical bars. Bubble nose velocity from image analysis The velocity of the bubble nose was obtained using the displacement of the bubble nose between two consecutive captured images. Following the expressions given in the work of Polonsky et al. (1999), the velocity could be estimated by Eq. (1), since the time interval between the images was known.

uB ¼

1 Ddimages c Dt images

ð1Þ

22

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

Fig. 3. Example of images of bubble fronts for liquid superficial velocity jL = 0.2 m/s and gas superficial velocity jG = 0.7 m/s and jL = 0.2 m/s and jG = 1.9 m/s.

where c denotes the calibration factor (for the present work c = 11 pixels/mm), Ddimages and Dtimages denote, respectively, the horizontal image displacement extracted from two consecutive images and the time interval between the images. Fig. 4 presents a comparison of bubble velocities obtained from image analysis against those measured with the aid of photo gates. As can be seen in the figure, both techniques provided the same results within the expected experimental uncertainty levels. This good agreement suggests that no bias in the velocities was introduced by the measurement techniques employed. Bubble interface detection from ensemble-averaged image The processing of ensemble-averaged images for estimation of averaged liquid–gas interfaces can be an alternative to the method based on the processing of instantaneous images, just described. In the averaged bubble image, the most frequent positions of the interfaces are reinforced and seen as black shadows. Due to the random location of dispersed bubbles in the instantaneous images, the averaging procedure was capable of effectively removing noise induced by the presence of small bubbles, making the image processing simpler. The binarization of the averaged image was performed using a fixed threshold criterion determined by the minimum value of grey intensity in the column of the image corresponding to the nose position, which was detected during pre-processing. Standard, close, open and fill operations were used to smooth and close the main bubble interface. The processing was extremely fast, and most of the computational time was spent in reading the images. The main drawback of this procedure is the great number of images necessary to remove noise when the slugs are highly aerated, and the loss of other valuable statistical features. Fig. 5(a) and (b) present a comparison of mean bubble nose interfaces obtained from the ensemble average of 400 instantaneous bubble interfaces (dashed lines) with the interfaces

obtained from the ensemble-averaged image (dotted line). Cases with the same gas and liquid velocities as those from Fig. 3(a) and (b) are respectively analysed in Fig. 5(a) and (b). The bubble interfaces were shifted by the nose tip position (xB) in order to have all curves initiated at the same location. As can be seen, the resulting contours obtained from both methods can be considered coincident, within the levels of experimental uncertainties expected and indicated by the vertical bars. It is conceivable that under different flow conditions the two methodologies may present different results. However, it is important to emphasize that no significant differences were observed for all cases investigated in the present work. Bubble contours extracted from ensembleaveraged images are shown only in this section, for a comparative analysis against the ensemble-averaged contours obtained from instantaneous images descried before. As already mentioned, the latter technique was employed to obtain the results that are presented in the next sections of the present work. Bubble tail image analysis The methodology used to process the images of the bubble tail shares similar steps with the processing adopted for the detection of interfaces in the bubble nose images. However, due to the different characteristics of the images, specific steps had to be employed and the main differences are highlighted in this paragraph. The images were cropped into a length of 1.4D, as illustrated in Fig. 6. The cropping length was chosen according to the work of Fagundes Netto et al. (1999), where the hydraulic jumps presented lengths from 0.7D to 1.3D. The region upstream from the vertexes of the hydraulic jump typically displays a quiet liquid layer. Therefore this region was selected for the detection of the liquid film thickness (hL), as depicted in Fig. 6. The vertexes detected in instantaneous interfaces were shifted to the image origin and a least-squares linear fit procedure through all points of the interface was employed to determine the angle of the hydraulic jump. The shifting of the interfaces was implemented in order to reduce the influence of variations in the instantaneous film thickness on the estimation of the angle of the hydraulic jump. As demonstrated for the case of the bubble nose contours, the detection of the bubble tail characteristics from ensemble-averaged images provided similar results to those obtained from the methodology based on the ensemble-averaged interface from instantaneous images described in the above paragraph. However, results from ensemble-averaged images were not used in the present work since they do not yield statistical information about the interfaces. Results

Fig. 4. Comparison of bubble nose velocities measured by the photo gates and by the image processing techniques developed.

Modelling of intermittent two phase flow has been investigated by many research groups, as can be seen in the review paper of Fabre and Liné (1992). Valuable databases about the statistics of plug and slug flows are available in the literature for model validation, (e.g. Barnea, 1987; Nydal et al., 1992; Spedding and Spence, 1993; Fossa et al., 2003; Woods et al., 2006). However, the results

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

23

Fig. 5. Comparison of bubble front contours obtained from ensemble-averaged images and from ensemble-averaged interfaces of instantaneous images for: (a) jL = 0.2 m/s and jG = 0.7 m/s; (b) jL = 0.2 m/s and jG = 1.9 m/s.

Fig. 6. Example of image of bubble tail for liquid superficial velocity jL = 0.2 m/s and gas superficial velocity jG = 0.7 m/s.

from different research groups are not always in close agreement. According to Bendiksen and Malne (1987), the slug initiation can be significantly affected by inlet and outlet configurations of test rigs and hence have influence on slug statistics. This effect is more pronounced for short pipes. Therefore, long test rigs are often used to enable the development of slugs. For instance, the works of Wang et al. (2007) and Kadri et al. (2009) describe apparatus having lengths longer than 2500 pipe diameters. Indeed, long lines reduce significantly the influence of inlet conditions but, on the other hand, are associated with higher costs, being their real need justified only for the investigation of very long slugs. According to Kadri et al. (2009), this regime occurs for very low gas velocities that are lower than those covered by the present measurements. For higher mixture velocities, lines with lengths ranging from 350 to 500D have been used with success. For instance, the work of Nydal et al. (1992) provided statistical data about developed slugs using a test rig with a length of 360D.

environmental conditions. The validation of the test rig, including the measurement techniques, was done by comparing the results obtained with those from the literature. The range of phase velocities investigated is illustrated in the map of flow patterns shown in Fig. 7. The reference map was extracted from the work of Mandhane et al. (1974), which is based on several experimental results obtained under conditions similar to those of the present investigation. The same symbol is used to represent cases that share the same superficial liquid velocity. The range studied covers the transition from elongated bubble to slug regime, and it is located between cases of very long slugs, studied in the work of Kadri et al. (2009), and hydrodynamic slugs, investigated in Nydal et al. (1992). Although the range covers a gap existing between these two works, it still enables a comparison with those results. Following the concept of unit cell given by Dukler and Hubbard (1976), the slug flow can be seen as a sequence of similar slug units. At regions close to the onset of slugging, the slug units are

Preliminary assessment of the test section In view of the sensitivity of slug development to the inlet conditions, a series of preliminary tests was conducted to assess the quality of the results obtained from the test rig constructed and the experimental procedures developed. In particular, these preliminary tests were aimed at verifying that no bias was introduced into the results due to inlet and outlet configurations, and also due to the curves installed along the test pipe. These curves were installed to extend the pipe length while keeping the whole set-up inside the available laboratory space with controlled

Fig. 7. Flow regime map indicating the experimental conditions tested. The base map is extracted from Mandhane et al. (1974). The phase velocities covered in the present work are shown as symbols:: – jL = 0.2 m/s; – jL = 0.3 m/s; – jL = 0.4 m/s; – jL = 0.5 m/s. Shaded areas correspond to ranges covered in the works of Nydal et al. (1992) and Kadri et al. (2009).

24

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

Fig. 8. Comparison of translational velocities measured at the nose and tail of the bubble.

under development and may exhibit a different statistical behaviour from fully developed ones. According to Nydal et al. (1992) the existence of fully developed slug flow in pipes is a matter of definition, as gas expansion due to pressure losses along the pipe will cause an increase in the mixture velocity. However, they also mention that after an initial stage of development, the slug units change slowly along the pipe and mostly depend on the local value of the gas velocity and gas expansion rather than on the previous history of the flow. At this stage, the translational velocities of the front and rear part of the bubble would be similar, as suggested by Ruder et al. (1989). Therefore, the translational velocities of the front and the rear parts of the bubble were compared to each other prior to the statistical analysis of the slug units. The results presented in Fig. 8 shows that, within the experimental uncertainty levels, estimated according to the ISO guide for expression of uncertainties (JCGM, 2008), both velocities were close for most of the collected points. However, a small systematic difference is verified in the velocities of the rear part of the bubble that are slightly lower than the front. This might be related either to the gas expansion caused by pressure loss along the pipe or to the growth of the liquid slugs. In order to have a clearer picture about this behaviour it is necessary to analyse other statistics of the flow.

The measured mean lengths of the liquid slugs (LS) are depicted in Fig. 9(a). According to Nydal et al. (1992) and to Kadri et al. (2009), both liquid and gas superficial velocities can affect the length of the liquid slugs. Therefore, the mixture velocity was chosen to scale the data in Fig. 9(a), because it includes both velocities. For the range of flow velocities covered in the present experiments, the scaling was fairly good. However, for larger range of mixture velocities a scattering of the data can occur when using the mixture velocity to scale the slug lengths. The data indicate a change from long to short slug lengths for increasingly higher mixture velocities (jm). For high mixture velocities, experimental results asymptotically approach the lengths observed in Nydal et al. (1992). On the other end, for low mixture velocities the mean slug lengths were closer to those from the work of Kadri et al. (2009). For slugs under development, the measured lengths would be considerably shorter than those reported in the literature, which is not the case here. A comparison between the regimes measured in the present work with those reported in the work of Kadri et al. (2009) is shown in Fig. 9(b). The symbols used in Fig. 9(a) and (b) represent the same cases. A reasonable agreement is observed with the map given in the work of Kadri et al. (2009). This suggests that the typical slugs lengths observed at the measurement station location were of the order of those reported in the literature. Moreover, for mixture velocities lower than 1.5 m/s, the results show that small reductions in velocity may result in a remarkable increase in the length of the liquid slugs. The shedding frequency of the slugs is a relevant parameter to characterize the intermittent flow regime. According to Nydal et al. (1992), the frequency of non-developed slugs displays a probability density distribution with two peaks, with one of them having a high frequency, which is not typical for slugs at a given flow rate. This can shift the mean shedding frequency toward higher frequencies. The present results, depicted in Fig. 10, were compared against an empirical correlation proposed in the work of Fossa et al. (2003) which was based on several different databases reported in the literature. The correlation relates the dimensionless slug frequency, given in terms of a Strouhal number (St = fsD/jG), with the ratio of superficial liquid to mixture velocities (kL = jL/jm). Experimental results extracted from the work of Wang et al. (2007) for a pipe with approximately 2600D were also included in the figure as a second reference. The good agreement of the present results with those from literature is an indication of the presence of developed slugs at the region of measurement,

Fig. 9. Comparison of measured slug length with literature results for long and hydrodynamic slugs. (a) Length of the liquid slugs against the mixture velocity, (b) map of regimes extracted from the work of Kadri et al. (2009).

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

25

and suggests that the curves installed in the test section had no influence on the slug statistics. As already noted, the measured translational velocities of the front and rear part of the slugs, shown in Fig. 8, displayed small differences, suggesting that the slugs were still under development at the streamwise location where the measurements were carried out. However, the fact that the length and the intermittency of slugs, depicted in Figs. 9 and 10, are in agreement with those reported in the literature for well-developed slugs, is an indication that the slugs are developed or nearly close to this condition. The preliminary tests conducted were considered satisfactory, validating the test section constructed and the experimental procedures developed. Results for slug velocity and bubble characteristics will now be presented. Bubble nose translation velocities Fig. 10. Comparison of measured non-dimensional slug shedding frequencies with data from the literature.

Bubble front translation velocity is an important parameter for modelling intermittent two-phase flow. It is generally accepted that the bubble velocity (uB) is a function of the mixture velocity, jm, and drift velocity, ud (Bendiksen, 1984), as indicated by Eq. (2),

uB ¼ Cjm þ ud

Fig. 11. Comparison of measured and predicted bubble nose velocity as a function of mixture Froude numbers.

ð2Þ

The coefficient C is, in general, a function of the Reynolds, Froude, and Etvös numbers (Fabre and Liné, 1992). Several correlations are found in the literature for the bubble velocity in horizontal flows, and there is still not complete agreement with regard to the contribution of the drift pffiffiffiffiffiffivelocity for low values of the mixture velocity, i.e., for jm < 3:5 gD, where g is the gravitational acceleration. Bendiksen (1984) and Woods and Hanratty (1996) recognized the importance of the drift velocity in predicting bubble velocity, while other authors, as Cook and Behnia (1997) and van Hout et al. (2002), do not recommend its utilization, proposing that uB and jm be directly related by uB = 1.2jm Bendiksen (1984), discusses the change in the coefficient C in Eq. (2), indicating that its value reflects the competition between inertia and gravitational forces which determines the radial position of the bubble nose and, consequently, its velocity. For low values of the Froude number, gravitational forces dominate and the bubble travels at a position closer to the upper part of the pipe. For higher values of Froude, inertia forces dominate and the bubble is pushed toward the pipe

Fig. 12. Change in bubble nose shape and position with mixture Froude number.

26

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

uB ¼ 1:2jm ;

for Frm > 3:5

pffiffiffiffiffiffi where Frm ¼ jm = gD Woods and Hanratty (1996) introduced an intermediate Froude number regime where inertia and gravitational forces are comparable, proposing the following correlations for bubble velocity,

pffiffiffiffiffiffi uB ¼ 1:0jm þ 0:542 gD; pffiffiffiffiffiffi uB ¼ 1:1jm þ 0:542 gD; uB ¼ 1:2jm ;

Fig. 13. Measured bubble nose radial positions as a function of the mixture Froude number.

centerline. Based on these arguments, Bendiksen proposed a correlation that considers the low and high mixture Froude (Frm) number ranges,

pffiffiffiffiffiffi uB ¼ 1:05jm þ 0:542 gD;

for Frm < 3:5

ð3Þ

for Fr m < 2 for 2 < Fr m < 3:5

ð4Þ

for Fr m > 3:5

Fig. 11 presents a comparison of bubble velocities measured in the present study employing the optical techniques implemented, with the predictions of the correlations presented in Eqs. (3) and (4). Fig. 11 displays the comparisons of bubble velocities with the mixture Froude number. For the range of mixture velocities investigated in the present study, the results of Fig. 11 show that both correlations approximate reasonably well the bubble velocity data, with a better agreement observed for Woods and Hanratty (1996). This correlation considers a change in the coefficient C for an intermediate range of Froude numbers, or mixture velocities. Also plotted in Fig. 11 is the correlation that does not consider the effect of the drift velocity. As can be seen, comparison with experiments indicates that, for low values of the mixture velocity, the contribution of the drift velocity should not be neglected. In addition, the results clearly show the shift in bubble velocity at Froude number equal to 2, as proposed by Woods & Hanratty.

Fig. 14. Measured ensemble-averaged bubble shapes for different mixture velocities.

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

27

Fig. 15. Comparison between measured bubble shapes and prediction by Benjamin’s (1968) inviscid theory for jL = 0.2 m/s and jG = 0.18 m/s (a). Images (b) and (c) are examples of instantaneous bubbles used to compute the ensemble averaged contour.

Bubble nose radial position The change in the radial position of the bubble nose tip reflects the relative importance of gravitational and inertia effects. As the Froude number increases, inertia effects dominate and the bubble nose position tends to move to the pipe centerline. Also, the shapes of the bubbles tend to become narrower as Froude increases, with an impact on bubble velocity. Fig. 12 was prepared to demonstrate quantitatively the qualitative observations of the previous paragraph, and that were first mentioned in Bendiksen’s work. Fig. 12(a) is a reproduction of Fig. 11 without some of the experimental data in order to avoid overcrowding the figure. Fig. 12(b) presents bubble nose shapes corresponding to the same mixture Froude number as those represented in Fig. 12(a). The symbols plotted on the bubble shapes of Fig. 12(b) are related to those in Fig. 12(a). The bubble shapes presented in Fig. 12(b) were obtained by the optical techniques described previously, with each bubble contour representing an average of 400 instantaneous bubble contours. A careful observation on the results displayed in Fig. 12 demonstrate quantitatively the radial motion of the bubble nose tip toward the centre of the pipe for increasing values of the mixture Froude number. For the lowest values of Froude investigated, Frm = 1.28, the bubble nose tip is located at y ffi 0:75D, while for Froude equal to 2.98, this position moves downward to y ffi 0:6D. In the reference frame employed, y = 0D is at the lower wall of the horizontal pipe. Thus, y = 0.5D is at the pipe centerline. Fig. 13 displays the bubble nose position (yB) versus mixture Froude number measured for all tests conducted in the present work. The ordinate indicates the vertical bubble nose position measured from the lower pipe surface and made dimensionless by the pipe diameter. This figure indicates a nearly perfect linear relationship between bubble nose position and mixture Froude

number, for the range of parameters investigated. The results of Fig. 13 confirm quantitatively, seemingly for the first time, the qualitative observations of Bendiksen (1984) and Ruder and Hanratty (1990).

Bubble nose shape Ensemble-averaged bubble nose shapes obtained in the present work, as those presented in Fig. 12, allows for an analysis of the influence of liquid and gas superficial velocities on the bubble shapes. Fig. 14 was prepared to facilitate the analysis. Each figure corresponds to nose shapes measured for a fixed value of the mixture velocity. For the lowest value of mixture velocity studied, jm = 1.2 m/s, the results of Fig. 14(a) indicate that the bubble shapes are quite similar, having a nose position located at y=D ffi 0:75. As shown in Fig. 14(b)–(d), for increasingly higher velocities the bubbles display different shapes for different mixture velocities, becoming narrower. Narrowest shapes are found in Fig. 14(d). However, for the same mixture velocity the shapes are nearly the same in all cases analysed. This observation can be verified by comparing bubble shapes represented by dashed and dotted lines. As indicated in the figure, similar shapes are observed for the same mixture velocity, although these mixture velocities were obtained from different combinations of gas and liquid superficial velocities. It is interesting to relate the bubble shapes presented in Fig. 14 with the corresponding points in the flow map of Mandhane shown in Fig. 7. The fat bubbles of Fig. 14(a) fall in the elongated bubble regime, while the thinner shapes of (b), (c) and (d) fall in the slug regime. According to the experimental findings, the nose shapes are linked to the translational velocities, which are basically a function of the mixture Froude number (see Eqs. (3) and (4)).

28

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

Fig. 16. Variation of the liquid film thickness with the liquid volume fraction (kL).

Ruder and Hanratty (1990) and Woods and Hanratty (1996), observed good agreement between their experiments and the potential theory of Benjamin (1968), for the elongated bubble regime. Their conclusions on the agreement between experiments and theory were based not on full images of the bubble nose, but on measurements of average liquid film by conductive probes and on the visual observation of the bubble nose position near the pipe top surface. The present work provides complete images

of ensemble-averaged bubble noses that allow for a better comparison with Benjamin’s potential theory. Fig. 15 presents this comparison, where 300 instantaneous images of elongated bubbles were ensemble averaged for a liquid superficial velocity of 0.2 m/s and a gas superficial velocity of 0.18 m/s. The bubble shapes predicted by Benjamin’s theory are overlaid on the average contour in Fig. 15(a). A low level of agreement can be verified, indicating that the potential theory does not predict accurately the behaviour of the bubble, even for this case where the Froude number is equal to 0.45, which is certainly lower than the Froude numbers where slug flow regime is expected to prevail. Major differences are found around the tip of the bubble nose. Fig. 15(b) and (c) represent different samples of instantaneous images obtained under this experimental condition. It can be seen that one of the instantaneous bubbles is well represented by the shape given by Benjamin’s theory, as depicted in Fig. 15(b). However, shapes like this are a minor part of the total set of acquired images. Most images are similar to that of Fig. 15(c), in which bubble contours are rather different from the theoretical predictions. These results suggest that Benjamin’s solution might be valid for extremely low mixture velocities, which in practice do not correspond to slug regimes. Tests at even lower mixture velocities could not be performed in the present study since the required flow rates were below the values where stable conditions could be sustained in the test section available. Bubble tail shape The work of Fagundes Netto et al. (1999), pointed out for changes in the bubble tail during transition from the elongated

Fig. 17. Measured ensemble-averaged hydraulic jumps for different mixture velocities.

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

29

Fig. 18. Comparison of ensemble-averaged hydraulic jumps with the model proposed by Fagundes Netto et al. (1999).

bubble to the slug flow regime. According to their work, a measure of the bubble tail shape could be used as a criterion for the transition between those regimes. In the present work, ensembleaveraged bubble tail shapes were obtained and measured according to the procedures described previously in Section ‘Image processing of bubble nose and tail’. There, the bubble tail shape was characterized by the angle of the hydraulic jump and the liquid film thickness, hL. The analysis of the liquid film thickness has been performed separately from the analysis of the hydraulic jump, because they seem to be governed by different parameters of the flow. The variation in the liquid film thickness with the ratio of the superficial liquid velocity to the mixture velocity (kL) is presented in Fig. 16. A linear relationship of the film thickness with kL is observed. A least squares fit to the data is also plotted in the figure as a reference. The results suggest that, indeed, the film thickness is governed by the contribution of the liquid velocity to the total mixture velocity. Fig. 17 presents shapes of hydraulic jumps for fixed values of mixture velocities, obtained using the procedures described in Section ‘Image processing of bubble nose and tail’. The lengths of the bubbles associated with the hydraulic jumps were not the same for the various cases shown in this figure. Therefore, the horizontal positions of the curves representing the tails were shifted by the vertex position (xR) in order to have all hydraulic jumps initiated at the same location. Also, the liquid film thickness was subtracted from the curves in order to facilitate the comparison among the angles. As can be seen in Fig. 17, for the range of mixture velocities investigated, the angles of the hydraulic jumps for cases with different gas and liquid velocities, but with the same mixture velocity, are in excellent agreement. In all cases, the small deviations observed are well within the experimental uncertainty levels expected for the experiments, giving support to the idea of the dependency of the shape of hydraulic jumps on the flow mixture velocity. It is interesting also to note a steepening of the angles for higher mixture velocities. According to Mandhane’s map, the case with the lowest velocity shown in Fig. 17 falls within the plug flow regime, while the others fall in the slug flow regime. Fagundes Netto et al. (1999), suggested that a steepening of the angle of the hydraulic jump could be associated with a transition from plug to slug flow regimes. This angle variation was indeed observed in the experiments but, the differences were within the estimated uncertainty levels, what did not allow the confirmation of their proposition. Further investigation is necessary to clarify this possibility. In the work of Fagundes Netto et al. (1999), a one-dimensional model was proposed for predicting bubble characteristics. The

predictions given by the model are compared against the results of the present study, and are presented in Fig. 18. Due to constrains in the model, which is not valid for both low liquid velocities and very high mixture velocities, only cases having liquid velocities above 0.5 m/s are analyzed. Moreover, the length of the hydraulic jump in the model is fixed and assumed to be equal to 1D. Fig. 18(a) and (b) shows good agreement for the angle of the hydraulic jump and an excellent match for the liquid film thickness. These results suggest that the model proposed by Fagundes Netto et al. (1999), is potentially capable of predicting the behaviour of the bubble tail. However, a more detailed investigation for a wider range of liquid velocities is necessary.

Conclusions In the present work digital processing of back-illuminated bubble images in an intermittent flow regime of air and water in a horizontal pipe were employed to study the transition from elongated bubble to slug flow regimes. Original quantitative information about shapes of the bubble nose and tail could be obtained by using a set of procedures for image acquisition and processing. For image acquisition, a set of photo gates was used to measure in real time the velocity and the properties of the slugs. Based on the measured velocities, an adaptive delay could be adjusted in real time to trigger image acquisition with the passage of each bubble. Thus, hundreds of images from the bubble nose and tail could be captured and ensemble averaged. The detection of the bubble shape was performed on the instantaneous images and then ensemble averaged. An alternative methodology to process the images, based on ensemble averaged images, was also proposed. The results were validated against the ensemble averaged interfaces. It was observed that within the experimental uncertainty both results are equivalent. However, the method based on the ensemble averaged image does not provide statistical information about the bubble interfaces and therefore it was not used to obtain the results presented in this work. The results have shown that bubble translational velocities are dependent on the mixture Froude number, with rates close to those suggested by Woods and Hanratty (1996). This has evidenced the importance of the contribution of the drift velocity to the bubble translational velocity for low mixture velocities, as suggested in Bendiksen (1984). The radial movement of the bubble nose toward the pipe centerline as function of the mixture velocity was measured quantitatively, seemingly for the first time. The results indicated a linear

30

W.R. de Oliveira et al. / International Journal of Multiphase Flow 69 (2015) 18–30

dependence between bubble nose position and the mixture Froude number. In addition, the images have shown that, even for low values of mixture Froude numbers investigated, the inviscid theory of Benjamin (1968) does not accurately represent the shape of the bubble, especially at the region adjacent to the bubble nose. Changes in the shape of the bubble tail at the transition from elongated bubble to slug flow regimes were also measured. The liquid film thicknesses were shown to scale linearly with the ratio of the superficial liquid velocity to the mixture velocity. The angles of the hydraulic jumps were related mainly to the mixture velocities. Although a steepening of the angles could be observed for increasingly higher Froude numbers, the variation of the angles was within the experimental uncertainty of the measurements. Therefore, development of a criterion for characterizing the transition from plug to slug regimes based on the shape of the hydraulic jump, as suggested previously in the works of Ruder and Hanratty (1990) and of Fagundes Netto et al. (1999), still requires additional investigation. Acknowledgements The authors gratefully acknowledge the support awarded to this research by Petrobras R&D Center. Our gratitude is also extended to the Brazilian Government agencies CAPES and CNPq for the scholarships and continued support to our research activities. References Barnea, D., 1987. A Unified Model for predicting flow pattern transitions for the whole range of pipe inclinations. Int. J. Multiph. Flow 13, 1–12. Barnea, D., Shoham, O., Taitel, Y., Duckelr, A., 1980. Flow patterns transition for gas liquid flow in horizontal and inclined pipes. Int. J. Multiph. Flow, 217–225. Bendiksen, K.H., 1984. An experimental investigation of the motion of long bubbles in inclined tubes. Int. J. Multiph. Flow 10, 467–483. Bendiksen, K.H., Malne, D., 1987. Experimental data on inlet and outlet effects on the transition from stratified to slug flow in horizontal tubes. Int. J. Multiph. Flow 1, 131–135. Benjamin, T.B., 1968. Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248. Cook, M., Behnia, M., 1997. Film profiles behind liquid slugs in gas–liquid pipe flows. AIChE 43, 2180–2186. Dukler, A.E., Hubbard, M.G., 1976. A model for gas liquid slug flow in horizontal and near horizontal tubes. Ind. Eng. Chem. Fund., 337–347. Fabre, J., Liné, A., 1992. Modelling two-phase slug flow. Annu. Rev. Fluid Mech. 24, 21–46. Fagundes Netto, J.R., Fabre, J., Peresson, L., 1999. Shape of long bubbles in horizontal slug flow. Int. J. Multiph. Flow 25, 1129–1160. Fossa, M., Guglielmini, G., Marchitto, A., 2003. Intermittent flow parameters from void fraction analysis. Flow Meas. Instrum. 14, 161–168.

Gonzales, R.C., Woods, R.E., Eddins, S.L., 2009. Digital Image Processing Using Matlab, second ed. Gatesmark Publishing, s.l. Gopal, M., Jepson, W.P., 1998. The study of dynamic slug flow characteristics using digital image analysis. Part I: Flow visualization. J. Energy Resour. Technol. 120, 97–101. Guo, F., Yang, Y., Chen, B., Guo, L., 2010. A novel multi-scale edge detection technique based on wavelet analysis with application in multiphase flows. Powder Technol. 202, 171–177. Havre, K., Stornes, K., Stray, H., 2000. Taming Slug Flow in Pipelines, s.l.: s.n. Hewitt, G.F., Jayanti, S., Hope, C.B., 1990. Structure of thin liquid films in gas–liquid horizontal flow. Int. J. Multiph. Flow 16, 951–957. Hurlburt, E.T., Hanratty, T.J., 2002. Prediction of the transition from stratified to slug and plug flow for long pipes. Int. J. Multiph. Flow 28, 707–729. JCGM, 2008. JCGM 100:2008, Evaluation of Measurement data-Guide to the Expression of Uncertainty in Measurements. (accessed 31.05.14). Kadri, U., Zoeteweij, M.L., Mudde, R.F., Oliemand, R.V.A., 2009. A growth model for dynamic slugs in a gas liquid horizontal pipes. Int. J. Multiph. Flow 35, 439–449. Lin, P.Y., Hanratty, T.J., 1987a. Effect of pipe diameter on flow patterns for air-water flows in horizontal pipes. Int. J. Multiph. Flow 13, 549–563. Lin, P.Y., Hanratty, T.J., 1987b. Detection of slug from pressure measurements. Int. J. Multiph. Flow, 13–21. Mandhane, J.M., Gregory, G.A., Aziz, K., 1974. A flow pattern map for gas–liquid flow in horizontal pipes. Int. J. Multiph. Flow 1, 537–553. Mayor, T.S., Pinto, A.M.F.R., Campos, J.B.L.M., 2007. An image analysis technique for the study of gas–liquid slug flow along vertical pipes – associated uncertainty. Flow Meas. Instrum. 18, 139–147. Nogueira, S. et al., 2003. Simultaneous PIV and pulsed shadow technique in slug flow: a solution for optical problems. Exp. Fluids 35, 598–609. Nydal, O.J., Pintus, S., Andreussi, P., 1992. Statistical characterization of slug flow in horizontal pipes. Int. J. Multiph. Flow 3, 439–453. Pinto, A.M.F.R., Pinheiro, M.N.C., Campos, J.B.L.M., 2001. On the interaction of Taylor bubbles rising in two-phase co-current slug flow in vertical columns: turbulent wakes. Exp. Fluids 31, 643–652. Polonsky, S., Barnea, D., Shemer, L., 1999. Averaged and time-dependent characteristics of the motion of an elongated bubble in a vertical pipe. Int. J. Multiph. Flow 25, 795–812. Ruder, Z., Hanratty, P.J., Hanratty, T.J., 1989. Necessary conditions for existence of stable slugs. Int. J. Multiph. Flow 15, 209–226. Ruder, Z., Hanratty, T.J., 1990. A definition of gas–liquid plug flow in horizontal pipes. Int. J. Multiph. Flow 16, 233–242. Shemer, L., Gulistki, A., Barnea, D., 2007. On the turbulent structure in the wake of Taylor bubbles rising in vertical pipes. Phys. Fluids 19, 1–13. Spedding, P.L., Spence, D.R., 1993. Flow regimes in two-phase gas liquid flow. Int. J. Multiph. Flow 19, 245–280. Taitel, Y., Dukler, A.E., 1976. A model for predicting flow regime transitions in horizontal and near-horizontal gas–liquid flow. AIChE 22, 47–55. Ursenbacher, T., 2004. Interfacial measurements in stratified types of flow. Part I: New optical measurement technique and dry angle measurements. Int. J. Multiph. Flow 30, 107–124. van Hout, R., Barnea, D., Shemer, L., 2002. Translational velocities of elongated bubbles in continuous slug flow. Int. J. Multiph. Flow 28, 1333–1350. Wang, X., Guo, L., Zhang, X., 2007. An experimental study of the statistical parameters of gas–liquid two-phase slug flow in horizontal pipe. Int. J. Heat Mass Transf. 50, 2439–2443. Woods, B.D., Hanratty, T.J., 1996. Relation of slug stability to shedding rate. Int. J. Multiph. Flow 22, 809–828. Woods, B., Zhongliang, F., Hanratty, T.J., 2006. Frequency and development of slugs in a horizontal pipe at large liquid flows. Int. J. Multiph. Flow 32, 906–925.