Comparative Studyof Gas Oil and Gas Water 2 Phase Flows

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Chemical Engineering Science 65 (2010) 3836–3848

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Comparative study of gas–oil and gas–water two-phase flowin a vertical pipe

L. Szalinski a,�, L.A. Abdulkareem b, M.J. Da Silva a, S. Thiele a, M. Beyer a, D. Lucas a, V. Hernandez Perez b,U. Hampel a, B.J. Azzopardi b

a Institute of Safety Research, Forschungszentrum Dresden-Rossendorf e.V., Bautzner Landstraße 400, PO Box 510119, 01314 Dresden, Germanyb Process and Environmental Engineering Research Division, Faculty of Engineering, University of Nottingham, UK

a r t i c l e i n f o

Article history:

Received 21 August 2009

Received in revised form

10 March 2010

Accepted 16 March 2010Available online 27 March 2010

Keywords:

Multiphase flow

Air–water

Air–oil

Flow visualization

Wire-mesh sensor

Tomography

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ces.2010.03.024

esponding author. Tel.: +49 351 260 3408; fa

ail address: [email protected] (L. Szalinski).

a b s t r a c t

A wire-mesh sensor has been employed to study air/water and air/silicone oil two-phase flow in a

vertical pipe of 67 mm diameter and 6 m length. The sensor was operated with a conductivity-

measuring electronics for air/water flow and a permittivity-measuring one for air/silicone oil flow. The

experimental setup enabled a direct comparison of both two-phase flow types for the given pipe

geometry and volumetric flow rates of the flow constituents. The data have been interrogated at a

number of levels. The time series of cross-sectionally averaged void fraction was used to determine

characteristics in amplitude and frequency space. In a more three-dimensional examination, radial gas

volume fraction profiles and bubble size distributions were processed from the wire-mesh sensor data

and compared for both flow types. Information from time series and bubble size distribution data was

used to identify flow patterns for each of the flow rates studied.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Knowledge about multiphase flow phenomena is veryimportant from the perspective of basic research as well asapplications in process industry. Examples are chemical reactors,power plants and oil pipelines, where issues of efficiencyand safety are influenced by the behaviour of multiphaseflows. Furthermore, especially the research sector requiresreliable multiphase flow data for development and validationof flow mechanical and thermal hydraulic models as well ascomputational fluid dynamics (CFD) codes. This interest in high-resolution multiphase flow data is closely coupled to theavailability of appropriate measurement technology which allowsthe visualization of transient multiphase flows in all its details(Boyer et al., 2002, Dudukovic, 2002).

The literature in gas–liquid flow is dominated by a large baseof information on experiments carried out with air/water. Thishas been used in the development of many of the models andcorrelations available. Not surprisingly, engineers dealing withfluids typical of industrial applications complain that water hasinappropriate values of physical properties, particularly a surfacetension that is much higher than many of the materials they deal

ll rights reserved.

x: +49 351 260 1 3408.

with. Water is often used because it is cheap and relatively safe.Moreover, electrical resistance methods can be employed on it.Non-conducting organic liquids would have to employ the moredifficult capacitive approach. This work goes towards overcomingthe lack of data for low surface tension liquids and shows how theresults differ from the equivalent ones for water.

In the identification of the occurrence of flow patterns, anumber of mechanistic models have been proposed. The bound-ary for the occurrence of dispersed bubbly flow is assumed to bedue to the break up of bubbles by the turbulence. Here a modelfollowing the ideas of Taitel et al. (1980) is identified. For thebubble/slug transition an improvement of the model proposed byTaitel et al. (1980) is employed. The original model attributes thetransition to coalescence of bubbles. A constant critical voidfraction was proposed to define the transition. However, laterwork, starting with Song et al. (1995), indicates that the voidfraction at transition depends on the bubble size. Other work(Kytomaa and Brennen, 1991, Cheng et al., 2002, Guet et al., 2002),has considered a wider range of pipe diameters, 25–100 mm, andshows that the critical void fraction depends on the ratio of meanbubble size to pipe diameter. This is illustrated in Fig. 1. For theslug/churn transition the mechanism of transition was taken to bethe occurrence of flooding of the liquid film around the Taylorbubble as suggested by Jayanti and Hewitt (1992), Watson andHewitt (1999). For the churn/annular transition the model ofBarnea (1986) is used. This consists of two parts. At low liquid

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Fig. 1. Effect of bubble to pipe diameter ratio on critical void fraction for transition

to slug flow.

L. Szalinski et al. / Chemical Engineering Science 65 (2010) 3836–3848 3837

flow rates, the boundary is calculated as the gas velocity requiredcarry up drops. The size of the drops was taken to be themaximum stable drop size. This results in a critical Froudenumber in which the length scale is the length scale proposed byTaylor, lT¼O(s/[rLg]). Using this in place of the diameter resultsin a Froude number of the form:

Fr0 ¼

ffiffiffiffiffiffirGp

uGs

ð½rL�rG�gsÞ0:25

: ð1Þ

Here rL is the liquid density, rG is the gas density, g is thegravitational acceleration, s is the surface tension and uGs isthe gas superficial velocity. This is sometimes known as theKutateladze number and a value of 3.1 was proposed by Taitelet al. (1980). For this they proposed a critical Weber number of 30to specify the maximum drop size and a constant value of dragcoefficient of 0.44. Different values of these two items can be putforwards which would change the value of the Kutateladzenumber at transition. However, as the ratio of Weber number todrag coefficient are raised to the power of 0.25, big changes inthese are required to alter the transition gas superficial velocitysignificantly. For higher liquid flow the approach was slightlydifferent. Barnea suggested that the boundary would occur whenthe void fraction of two possible arrangement of the phases, i.e.,an annular flow and a bubbly flow were the same.

A number of different measuring techniques have been used toinvestigate gas–liquid flows. Some employ intrusive probes, forexample, Cartellier and Achard (1990). However, these probemeasurements are limited to one point in the flow so it isnecessary to use more then one probe or to scan the cross-sectionby moving the probe to determine cross-sectional information onthe flow. In contrast, there are methods which provide full cross-sectionally resolved information. These include: electrical tomo-graphy (York, 2001), X-ray tomography (Reinecke et al., 1998),gamma ray tomography (Johansen, 2005), magnetic resonanceimaging (Mantle and Sederman, 2003) and wire-mesh sensors(Prasser et al., 1998; Pietruske and Prasser, 2007; Da Silva et al.,2007). Electrical resistance tomography (ERT) and electricalcapacitance tomography (ECT) are able to acquire cross-sectionalgas phase distributions at sufficiently high frame rates. They offer,however, only very coarse spatial resolution because of the soft-field problem of electrical fields. For more detailed information

about the inner structure of two-phase flow, radiation-basedtomography techniques, like X-ray or gamma ray computedtomography can be used (Reinecke et al., 1998; Heindel et al.,2008). However, typical X-ray and gamma ray scanners have lowimaging speed and cannot be used for the visualization of rapid ortransient flows. Recently, a promising fast X-ray tomographymodality was introduced (Fischer et al., 2008). However, thistechnique is still rather complex, expensive and immobile. Thewire-mesh sensor described by Prasser et al. (1998) is acomparatively simple imaging sensor with adequate spatial andhigh temporal resolution. Wire-mesh sensors are composed ofthin wire electrodes forming a grid which is directly located in theflow. Whereas the spatial resolution of the wire-mesh sensorcorresponds to the in-plane wire separation the maximumtemporal resolution is predefined by the measuring electronics.Thereby measurements with temporal resolution of up to 10,000frames per second and spatial resolution of up to 2 mm arepossible (Prasser et al., 2002). The sensor scans an electricalproperty of the fluid at each crossing point, which maybe eitherelectrical conductivity or electrical permittivity. For mixture flowswith fluids of different electrical properties the sensor can thusproduce cross-sectional phase distribution images of the flow.Regarding intrusiveness wire-mesh sensors offer a compromise.The drawback of being invasive is partly compensated by theirhigh temporal resolution, low cost and functional simplicitycompared to other flow imaging techniques. A benchmark testbetween wire-mesh sensor and X-ray computer tomography (CT)was performed by Prasser et al. (2005b). Both measuring systemswere operated in a vertical air/water pipe flow simultaneously.The gained data both measuring systems, cross-section averagedvoid fractions and time series of them, radial void fraction profilesand visualizations, were directly compared. Prasser et al. (2005b)concluded in their study: (i) a good agreement in void fractiondata; (ii) a higher resolution in time and space of the wire-meshsensor; (iii) small bubbles are not seen by the X-ray tomograph;(iv) the wire-mesh sensor tends to underestimate the gas fractionin large bubbles; (v) the wire-mesh sensor distorts the shape ofTaylor bubbles at low liquid velocities. Results of this comparisonof non-intrusive X-ray CT and intrusive wire-mesh measurementsjustify the usage of wire-mesh sensor technique at the presentstudy in consideration of physical limits, e.g. minimum liquidvelocity and spatial resolution.

Here, two different two-phase flows, namely those involvingair/water and air/silicone oil, have been investigated in the samegeometry and at the same flow conditions. From visual inspectionand quantitative assessment of the wire-mesh sensor image datait was possible to compare the flows directly and so focus on theeffects of the different physical properties of the liquid phase. Thisis the first comparative two-phase flow study of this type with ahigh-speed cross-sectional imaging instrument which gives ushighly valuable data for the validation of mathematical models formulti-phase flow.

2. Experimental arrangement

2.1. Experimental setup

Experiments were carried out at a test facility of the ChemicalEngineering Laboratory in the Faculty of Engineering, Universityof Nottingham, UK. The facility had already been employed in anumber of earlier studies (Geraci et al., 2007, Hernandez Perezet al., 2007 and Da Silva et al., 2010). The heart of the facility is a67 mm diameter, 6 m long pipe which can be positioned at anyinclination from the horizontal to the vertical. In the studypresented here, the pipe was in the vertical position. The liquid

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Fig. 2. Scheme of the gas–liquid mixing device.

Table 1Selected physical properties of the liquids used in the study.

Parameter Water Silicone oil Unit

Electrical conductivity 400 0 mS/cm

Relative permittivity 80 2.7 –

Density 1000 900 kg/m3

Viscosity 1 5.25 mPa s

Surface tension 0.072 0.02 N/m

Fig. 3. Photograph of the wire-mesh sensor.

L. Szalinski et al. / Chemical Engineering Science 65 (2010) 3836–38483838

comes from a storage tank and air from the main compressed-airsystem of the laboratory. Liquid and air are mixed at the bottomof the pipe by a purpose-built mixing device (Fig. 2). The liquidenters the mixing chamber from one side and flows around aperforated cylinder. There, air is injected through a large numberof 3 mm diameter orifices. Thus, gas and liquid could be wellmixed at the test section entry. Inlet volumetric flow rates ofliquid and air are determined by a set of rotameters. The pipeoutlet is connected to a separator where air is released toatmosphere and the liquid is returned to the storage tank. A wire-mesh sensor was mounted into the pipe cross-section at a heightof 5 m from the inlet, i.e. at L/D¼74.6. L is the axial distance andD is the pipe diameter. Homogeneous mixing at the gas inlet aswell as the proper L/D ratio of the sensor position ensuresmeasurement of a fully developed two-phase flow. In principlefully developed two-phase flows exist if all the measuredproperties like cross-section averaged void fraction, radial voidfraction profiles and bubble size distributions do not change anymore with increasing L/D ratio. Regarding averaged void fractionand radial profiles this condition is reached clearly for L/D¼40 asmeasurements of vertical two-phase flows in a 51.2 mm diameterpipe at different L/D ratios and comparable flow conditions topresent study have shown (Lucas et al., 2005). For bubbles sizedistributions slight changes occur also for larger L/D ratios sincebubble coalescence still may go on. Nevertheless, the data showonly small changes of measured properties between L/D ratios of39.6 and 59.2. For this reason the flow can be termed as welldeveloped starting at L/D ratio of about 40. This is also confirmedfrom another measuring campaign performed in a 200 mmdiameter vertical pipe and presented by Prasser et al. (2007b)who describes the flow as fully developed at L/D ratio of 40. Forthe present study with an L/D ratio of 74.6 at a pipe diameter of67 mm the flow can be assumed as well developed.

In the first measuring campaign, the facility was run with tapwater as the liquid and air as the gas. For the second campaign thefacility was slightly modified in order to be run with silicone oiland air. Table 1 gives a summary of the physical parameters of

both the liquids used in the study. Experiments were performedat liquid superficial velocities of 0.2, 0.25 and 0.7 m/s and with gassuperficial velocities in the range of 0.05–5.7 m/s. As the gas flowrate depended on the flow meter reading and the pressure at therotameter and the latter was influenced by the void fraction in thetest pipe, though the same rotameter setting was employed thereare small differences in gas flow rate between the two liquids.Nevertheless, the experimental points are close enough forcomparison.

2.2. Wire-mesh sensor

In a wire-mesh sensor wire electrodes are stretched across theflow cross-section within two planes. Wires in the two planes areorthogonal. Those in one plane act as electrical transmitters, thewires in the opposite plane as electrical receivers. The wire-meshsensor electronics measures the local electrical conductivity orpermittivity in the gaps of all crossing points by successivelyapplying an excitation voltage to each one of the senderelectrodes while keeping all other sender electrodes at groundpotential and measuring, respectively, the dc or ac electricalcurrent flow to all receiver electrodes synchronously (for moredetails see Prasser et al., 1998, Da Silva et al., 2007). The sensoremployed in this study has 2�24 wires with an axial separationof 2 mm and an in-plane separation of 2.8 mm. Fig. 3 shows aphotograph of the wire-mesh sensor. The sensor was selectivelyoperated by two different electronic units. For air/water flow aconductivity-measuring electronics as described by Prasser et al.(1998) was applied while for air/silicone oil flow the permittivity-measuring electronics presented by Da Silva et al. (2007) wasused. Both measuring electronics were operated at a speed of1,000 cross-section images per second.

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For conductivity measurements the transmitter electrodes areexcited by a bipolar voltage pulse while for permittivitymeasurements a sinusoidally alternating voltage is applied. Inboth cases the receiver currents are converted to voltages by atransimpedance amplifier circuit. This is followed by a dc voltagedetector in the conductivity-measuring electronics and by a logdemodulation circuit in the permittivity-measuring electronics.For conductivity measurements the output voltages Vk of receivercircuits correspond to the conductivity value k at the crossingpoints according to

Vk ¼ K � k: ð2Þ

Here, K is a proportionality factor which depends on electroniccircuit constants. In this way, conducting and non-conductingphases (e.g., air and water) or components can be discriminatedby evaluating the output voltage Vk. In order to discriminate non-conducting fluids, such as air and oil, the capacitance or thepermittivity of a crossing point is measured. The permittivity-measuring electronics generates a voltage Ve which is propor-tional to logarithm of the rms-value of the transmitted ac currentwhich is itself proportional to the relative permittivity er of thefluid present at a crossing point (Da Silva et al., 2007). The relativepermittivity is related to the output voltage by

Ve ¼ a lnðerÞþb, ð3Þ

where a and b are constants determined by geometry and circuitparameters. An advantage of the log detection scheme is that itallows the measurement of electrical permittivity in a broadrange of substances. The electronic design is further optimized tosecure a fast time response of the log detector, which is in therange of a few microseconds.

The wire-mesh sensor produces sequences of cross-sectionalimages which are further processed as a three-dimensionaldata matrix of electrical voltage values denoted by V(i,j,k). Theycorrespond to either conductivity or permittivity values in thecrossing points, as described above. Further, i and j are the spatialindices of the image pixels (corresponding to the wire numbers)and k is the temporal index of each image. Eqs. (2) and (3) holdfor every crossing point in the wire grid. It is obvious thatthe constants in these equations are different for all crossingpoints. Thus, a calibration procedure is required to extract flowparameters from the raw data. Calibration is performed byacquiring data from measurements in conditions of ‘pipecompletely filled with liquid’ and ‘pipe completely filled withgas’. These data are saved into calibration matrices as describedbelow. In the case of conductivity-based electronics, due to thelinear relationship between measured voltage and liquid con-ductivity, only one reference point is required and the gas voidfraction matrix can be obtained by

aði,j,kÞ ¼ 1�Vk,mixði,j,kÞ

Vk,waterði,jÞð4Þ

where Vk,mix represents the measured voltage of the two-phasemixture and Vk,water is reference measurement with water. Eq. (4)assumes a linear relationship between gas phase fraction andconductivity values, as extensively used in earlier investigations(Prasser et al. 1998, 2001, 2002, 2005a; Richter et al., 2002). In asimilar way, for permittivity-based electronics an equivalentlinear relationship between gas void fraction a and relativepermittivity values can be assumed which is known as parallelmodel of mixture permittivity (McKeen and Pugsley, 2002)

a¼ er,oil�er,mix

er,oil�er,air: ð5Þ

However, due to the logarithmic dependence of the measuredvoltage Ve, with relative permittivity values, calculating gas void

fraction is not as simple as for conductivity-based electronics.Thus, measured mixture permittivity is calculated by

er,mix ¼ expVe,mixði,j,kÞ�Ve,airði,jÞ

Ve,oilði,jÞ�Ve,airði,jÞlnðer,oilÞ

� �, ð6Þ

where the subscripts ‘mix’ denotes the voltage measured of thetwo-phase mixture, ‘oil’ for the condition of pipe filled with oil, and‘air’ for empty pipe. In this way, the measured mixture permittivityalong with the known relative permittivity of oil and air are used inEq. (5) to obtain the gas void fraction matrix in the case of oil/airexperiments. A description of the calibration routine for permittiv-ity-based electronics is given by Da Silva et al. (2010).

From gas void fraction matrix aði,j,kÞ, axial and radial gasfraction profiles as well as integral gas fraction values can bedetermined by integration of the measured data over appropriatepartial volumes. Further post-processing of the matrix aði,j,kÞ canbe performed to identify single bubbles or determine character-istic bubble or interfacial area parameters (Richter et al., 2002,Prasser and Beyer, 2007a).

For the graphical presentation of the wire-mesh sensor datawe use two different visualization techniques: axial slice imagesand virtual side projections. The first method extracts the phasefraction distribution along a central chord of the cross-section.The resulting two-dimensional image shows the phase distribu-tion along the diameter (x-axis) for successive temporal steps(y-axis). Virtual side projections are obtained from application ofa simplified ray-tracing algorithm as described in detail by Prasseret al. (2005a). In this visualization technique an illumination ofthe three-dimensional phase fraction distribution by parallelwhite light is simulated and the light intensity emitted into thedirection of a virtual observer is calculated. This method gives aninstructive pseudo-3D view which is close to what one would getfrom flow observation with a video camera through a transparenttest section. In both cases the vertical axis represents a virtuallength which is scaled according to the averaged gas velocity. Thisscaling allows displaying gas structures of the flow in nearlycorrect length to width relation and thus visualizations ofdifferent gas velocities can be directly compared.

3. Results and discussion

3.1. Cross-sectionally averaged data

The three-dimensional, time-resolved information can beexamined at a number of levels. Before considering the three-dimensional structure of the flow, a great deal of information canbe obtained by considering the time series of the cross-sectionallyaveraged void fraction. An example of this for the two liquidsstudied is shown in Fig. 4. These are taken at gas superficialvelocity of 0.56 m/s and a liquid superficial velocity of 0.25 m/s. Inboth cases the results show the characteristic alternate regions ofhigher and lower void fractions which epitomise slug flow. It isclearly seen that the void fraction in the liquid slug part is higherfor the silicone oil than for the water data. This will be consideredfurther below.

These time series can be averaged to give the mean voidfraction. This quantity is important to many engineering calcula-tions particularly when pressure drop is involved as it is central tothe gravitational component. Fig. 5 shows how this parameterincreases systematically with increasing gas superficial velocity.The liquid superficial velocity is 0.25 m/s in this instant. Alsoshown are the predictions of rather older empirical correlationmethods which are still employed in some parts of industry.The first is the drift flux approach proposed by Zuber and

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Fig. 5. Mean void fraction—liquid superficial velocity¼0.25 m/s—closed sym-

bols¼water; open symbols¼silicone oil.

Fig. 6. Probability density function—air/water–liquid superficial velocity¼0.25 m/s.

Fig. 7. Probability density function—air/silicone oil–liquid superficial velocity

¼0.25 m/s.

Fig. 4. Time series of cross-sectionally averaged void fraction—gas superficial

velocity¼0.56 m/s; liquid superficial velocity¼0.25 m/s.


Findlay (1965) where the void fraction, ag is defined by

ag ¼uGs

CoðuGsþuLsÞþu1, ð7Þ

here uLs is the superficial velocity of the liquid. The radialdistribution parameter, Co, is given the value of 1.2. The driftvelocity, uN, can be calculated from either 0.35 O(gD) for slug flowor 1.53(sg[rL�rG]/rL

2)0.25 for bubbly flow. The former has a valueof 0.28 m/s for both liquids whilst the latter is 0.25 m/s for waterand 0.186 m/s for silicone oil, respectively. Though betteragreement might be achieved by tuning the value of Co, thiswould be empirical and not of wider applicability. The other twomethods use a separated flow approach and differ only in thedescription of the slip ratio. Chisholm (1973) proposed a simpleequation for this parameter (¼O[1�x(1�rL/rG)], where x is thegas mass fraction) whilst Premoli et al. (1971), whose correlationis usually known as CISE, suggested a more complex expressionalso having dependence on the mass flow rates, the pipe diameter,the liquid viscosity and surface tension. All methods predict lessdifference between the liquids than is seen experimentally. Thedrift flux method shows itself to be the most accurate whilst theCISE predictions are significantly high. This reinforces the need toprovide methods with a sound physical basis.

The time series data can be analysed further by considering thevariations in amplitude and frequency space. The former isexamined using the probability density function, how often each

value of void fraction occurs. As seen in Figs. 6 and 7, there aretypical shapes or signatures which are seen in these plots. Anarrow single peak at low void fraction is typical of bubbly flow. Adouble peak is usually found in slug flow. The low void fractionpeak corresponds to the liquid slug whilst that at the higher voidfraction is associated with the Taylor bubble region. The thirdtype, a single peak at high void fraction with a long tail down tolower void fractions is recognised as the signature of churn flow.As with the time traces presented in Fig. 4, the void fraction in theliquid slug is seen to have higher values for silicone oil than forwater. Fig. 8 shows how this is systematic over the range of gassuperficial velocities at which slug flow was present.

The examination of the time series in frequency space can becarried out using autocorrelation and power spectral density(PSD). These are described in Azzopardi et al. (2008) and Kaji et al.(2009a). If there is a dominant periodic structure, the PSD ischaracterised by a dominant peak at the frequency of thisperiodicity. For some flow rates it is easy to determine frequencyby counting the structures in the time series plot over a finitetime. However, it is not always clear which peaks are largeenough to be counted. It can be seen that though there isagreement between the values from counting and PSD in somecases, there are differences in others. The reason for this can beappreciated if the data in Fig. 4 is re-examined. There are regionsin time where, though there are peaks, it is not certain that theyare large enough to be counted. Examples of these smaller peaks

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Fig. 9. Frequency of periodic structures obtained from power spectral density

analysis.

Fig. 8. Void fraction in liquid slug—liquid superficial velocity¼0.25 m/s—closed

symbols¼water; open symbols¼silicone oil.


can be seen in the water data at 3 and 4.5 s. In this case the largepeaks correspond to the bullet shaped bubbles (Taylor bubbles)which almost entirely fill the pipe cross-section. The smallerpeaks are bubbles which have not grown sufficiently to fill thewhole cross-section of the pipe. The data in Fig. 9 show thatfrequencies are on the whole higher for silicone oil than for water.They are also greater the larger the liquid superficial velocity.The trend with gas superficial velocity is more complex. At lowvalues of this parameter there are contradictory trends. However,beyond 1 m/s, frequency decreases as the gas superficial velocityincreases. Examination of the probability density function plots ofthe cross-sectionally averaged time series of void fraction leads tothe conclusion these different trends are linked to changes in flowpattern.

3.2. Void fraction distribution

The wire-mesh sensors can provide very detailed informationabout the distribution of the liquid and gas phase in two-phaseflow. Many flow parameters, such as gas volume fraction orbubble size distribution, are encoded in these data but must be

extracted with appropriate processing algorithms (Prasser et al.,1998, 2001). The time-averaged but radially resolved distribu-tions of gas volume fractions have been computed from the data.These are illustrated in Fig. 10 and show that the time-averagedradial gas fraction profiles for air/water flow and air/silicone oilflow are qualitatively similar. In all cases gas fraction maxima arelocated in the pipe centre and these centreline values increaseswith increasing gas superficial velocity. At low gas superficialvelocities the radial gas fraction profiles of the air/silicone oil flowappear more flattened over the pipe radius compared to those forthe air/water flow. This is confirmed by fitting a power lawequation to these profiles. This can be written as

ag ¼ agCL 1�r

R

� �n� �

ð8Þ

The higher the value of the power law exponent, the closer theprofile converges to a horizontal line over the pipe radius. Fig. 11shows that though there is little difference between water andsilicone oil at higher gas superficial velocities, there is a verysystematic divergence at low velocities with the silicone oilhaving higher values.

The analysis can be applied selectively to the liquid slugregion. This has been carried out for the data shown in Fig. 4. Onlydata with cross-sectionally averaged void fractions o0.2 forwater and o0.3 for silicone oil were sampled. Though there islittle difference between the shape for the slug region and theshape for the whole data set for water, Fig. 12, plotting the localtime-averaged value of void fraction divided by the centrelinevalue, illustrates how the profile is the liquid slug region forsilicone oil is much flatter than the profile for data averagedover the whole flow, i.e., the small bubbles are not grouped in thecentre of the channel.

Temporally and spatially averaged bubble size distributionsare a useful indicator for the inner structure of the two-phaseflow. The modality for determining bubble size distributions fromwire-mesh sensor data was introduced by Prasser et al. (2001).Thereby bubble sizes are defined by the gas volume fractionwhich belongs to a bubble class related to the width of theclass. Figs. 13 and 14 showing the bubble size distributions forliquid superficial velocities of 0.25 and 0.7 m/s and different gassuperficial velocities. The x-axis represents the volume equivalentbubble diameter (Db) and the y-axis represents the gas fractionper bubble class (Da) divided by the width of the bubble class(DDb). Figs. 13 and 14 showing shows that air/silicone oil flowcontains more small bubbles then air/water flow, whereasair/water flow forms larger gas structures. So there is therelation between coalescence and breakup shifted towardsmore coalescence in air/water flow than in air/silicone oil flow.This effect is visible at gas superficial velocities of up to 1 m/s.At higher gas superficial velocities, this coalescence is lessnoticeable. The bubble size distributions showing anotherdifference between both two-phase flow types at small bubblesizes up to 20 mm diameter. For similar superficial velocities thelocal distribution maxima of the small bubbles in air/water floware located at smaller bubble diameters compared to the air/silicone oil flow. Furthermore the maximum shifts with increasinggas superficial velocity towards larger bubble sizes. This shift isrelatively low for air/water flow, but for the air/silicone oil flowthe shift is considerably larger.

3.3. Flow structure analysis

A strong theme in the modelling of two-phase flows is to usedifferent models for each flow pattern. Therefore it is important toidentify which flow pattern is present. The 3D image dataobtained from the visualization techniques described above

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Fig. 10. Time averaged radial gas volume fraction profiles for different gas and liquid superficial velocities. Left: air/water flow, right: air/silicone oil flow.


(Figs. 15 and 16) have been evaluated to extract flow patterns. Theflow patterns observed in the air/water flow are bubbly, bubble/spherical cap, slug and churn-turbulent flow. For the air/siliconeoil flows the annular flow pattern has also been observed.

Generally the definition of flow pattern in the transitionregions depends on the subjective assessment of the observer.Often, the characteristics of two different flow patterns can befound to occur simultaneously at the same pair of flow rates. Thiscan also be seen from Figs. 15 and 16. E.g. the left-most column inFig. 16 is characterised as bubbly flow, but contains also some capbubbles. Also in the central cut shown in Fig. 16 for a gassuperficial velocity of 0.56 m/s there is a Taylor bubble-likestructure in the upper part, but a heavily distorted gas structureindicating churn turbulent flow in the lower part.

For this reason in previous investigations using wire-meshsensors the size of the largest bubbles observed during themeasurement were used as a criterion to define the flow pattern.Lucas et al. (2005) defined the transition from bubbly to slug flow

on the condition, that the volume equivalent diameter of thelargest bubble observed exceeds the pipe diameter which wasabout 50 mm in those experiments. In this work we used also avolume equivalent bubble diameter of 50 mm to define thetransition between bubbly (resp. bubble/spherical cap) and slugflow.

In a similar manner, annular flow was assumed to be present ifthe volume equivalent bubble diameter exceeded 500 mm for thelargest gas structure observed. For an air superficial velocity of5.56 m/s and silicone oil superficial velocities of 0.2 and 0.25 m/sthe flow was identified as annular based on the interpretation of3D image data and if the bubble diameter limit of Db¼500 mmwas exceeded. Evaluation of the wire-mesh sensor data with thebubble identification algorithm proposed by Prasser et al. (2001)has shown that these annular flows are slightly unstable. Acontinuous gas core located in the pipe centre is characteristic forannular flows. During the measuring time of 40 s, a few shortintermissions into the gas core occur. These two measuring points

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Fig. 11. Variation of power law exponent of radial void fraction profile with gas

superficial velocity—closed symbols¼water; open symbols¼silicone oil.

Fig. 12. Radial profiles of void fraction non-dimensionalised with void fraction at

centre line. Examination of overall and values for liquid slug. Gas superficial

velocity¼0.56 m/s; liquid superficial velocity¼0.25 m/s.


probably indicate the start of the region of transition from churn-turbulent to stable annular flow. Here, these points are associatedwith annular flow to discriminate them from a pure churn-turbulent flow. There is also confirmation of annular flow fromthe probability density function plots shown in Figs. 6 and 7.Whilst that for water at the highest gas superficial velocity showsa long tail down to lower void fraction typical of churn flow, theequivalent for silicone oil does not have that tail. Instead, it hasthe characteristic shape, a narrow peak, typical of annular flow.

The slug to churn transition cannot be defined based on onlythe bubble sizes. In both cases a bimodal bubble size distributionis observed (Figs. 13 and 14). The main difference is the strongdistortion of the large gas structures in case of churn-turbulentflow. For this reason in this work the flow was defined as slug flowif Taylor-like bubbles were observed during the measurement.Indications of existing Taylor bubbles in present flows could befound at probability density functions and visualization images,but not at time series of the pipe core. Indeed the transitionbetween slug and churn turbulent flow pattern is hardly todetermine based on objective criteria. Slug flow exits due to theconfining action of the pipe. For pipe sizes larger than about50 mm in diameter Taylor bubbles are more and more distortedand there is a continuous transition to churn turbulent flow—

characterized by large gas structures but more or less far from theshape of Taylor bubbles. A study about the influence of pipediameter on the structure of a vertical two-phase flow presentedby Prasser et al. (2005a) has clearly shown that at pipe diameterof 50 mm a slug flow is present and at pipe diameter of 200 mmchurn-turbulent flow. The flow in 67 mm diameter pipe of presentstudy is located at a transition area where structures of slug andchurn-turbulent flow occurring simultaneously. Thus the abovementioned case for air/silicone oil flow at a liquid superficialvelocity of 0.25 m/s and a gas superficial velocity of 0.56 m/s wasdefined as slug flow.

That flooding of the film around the Taylor bubbles occurs atthe transition between slug and churn flow is not in doubt.Indeed, recent work by Kaji et al. (2009b) has identified that, forfixed inlet flow rates, some of the waves on the film around theTaylor bubble have downwards velocities, i.e., are unaffected bythe upwards gas flow, whilst others have upwards velocities, i.e.,they have undergone the flooding process. However, this in itselfdoes not cause the slug/churn transition. A clue to the mechanismmight be visible in the data plotted in Fig. 17, the PDF for air/silicone oil with a gas superficial velocity of 1.63 m/s and a liquidsuperficial velocity of 0.2 m/s. Unlike the signature for the flowpatterns, this has three peaks. The corresponding time series ofcross-sectionally averaged void fraction, Fig. 18, shows that thereare some of the liquid slugs are getting very full of small bubblesand so might not be able to remain as liquid continuous regions.They begin to be broken through. Is this a first stage to churn flowwith its continuous gas core? This aspect of the difficulty ofidentifying the slug/churn transition is supported by the work ofMao and Dukler (1993) and Hewitt and Jayanti (1993).

Since the experiments clearly show that there is no sharptransition between flow patterns, composite models to cover allflow patterns should apply blending functions in the transitionregions rather than switching sharply between the models foreach flow pattern.

Comparing air/water and air/silicone oil flow the physicalappearance of the gas phase in air/water flow is slightly morechurned up. This effect is evoked by a higher degree of turbulenceand can be explained by comparing the Reynolds numbers. TheReynolds number for two-phase flow is given by Azzopardi (2006)as Re¼ _mD=ZL where _m is the two-phase mass flux and ZL thedynamic viscosity of the liquid phase. For all experimental pointsReynolds numbers are larger than the critical Reynolds number(Re�2000) for single-phase pipe flow. Reynolds numbers in air/water experiments are approximately 5–6 times higher thenthose in air/silicone oil experiments.

3.4. Flow pattern map

For each flow condition studied a flow pattern was identified.This was carried out using a combination of: (i) the bubble sizedistribution data obtained from the methods described above; (ii)the probability density function signatures described earlier; (iii)inspection of the cross-sectionally averaged time traces; (iv) bystudying images such as Figs. 15 and 16; (v) as well as viewing themoving images of the cross-sectional position of the phases. Theresults are shown in Figs. 19 and 20 for air/water and air/siliconeoil, respectively. In those figures the experimental points areplotted as gas and liquid superficial velocities. Also shown are theflow pattern transition lines of the best models described in theintroduction above. It is noted that if the churn/annular transitionwere calculated using the modified Froude number/Kutateladzenumber defined in Eq. (1) is used the transition would occur at gassuperficial velocities of 14.6 m/s for air/water and 10.3 m/s for air/silicone oil.

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Fig. 13. Bubble size distributions for air/water flow and air/silicone oil flow at liquid superficial velocity¼0.25 m/s (left) and¼0.7 m/s (right).


For comparison of both two-phase flow types each measuringpoint is plotted with a symbol indicating the flow patternidentified. Transition from bubbly to slug flow is determined by

a maximum bubble diameter of Db¼50 mm. Classification of slugand churn-turbulent flow is performed by visual interpretation ofwire-mesh sensor images and evaluation of probability density

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Fig. 14. Bubble size distributions of air/water and air/silicone oil for gas superficial velocity range of 2.7–5.7 m/s.

Fig. 15. Visualization wire-mesh sensor data from air/water two-phase flow at liquid superficial velocity¼0.25 m/s and different gas superficial velocities. The gas phase is

represented by bright and the liquid phase by dark colour. Left: virtual side projection, right: axial slice images.

Fig. 16. Visualization of wire-mesh sensor data from air/silicone oil two-phase flow at liquid superficial velocity¼0.25 m/s and different gas superficial velocities. The gas

phase is represented by bright and the liquid phase by dark colour. Left: virtual side projection, right: axial slice images.


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Fig. 17. Probability density function plot for air/silicone oil. Gas superficial

velocity¼1.62 m/s, liquid superficial velocity¼0.2 m/s.

Fig. 18. Time series of cross-sectionally averaged void fraction for air/silicone oil.

Gas superficial velocity¼1.63 m/s, liquid superficial velocity¼0.2 m/s.

Fig. 19. Flow pattern map for air/water flow. Lines indicate flow pattern

transitions: bubble/dispersed bubble and bubble/slug—Taitel et al. (1980) (the

latter with a critical void fraction of 0.3 as deduced from Fig. 1); slug/

churn—Jayanti and Hewitt (1992), Watson and Hewitt (1999); churn/annular—

Barnea (1986).

Fig. 20. Flow pattern map for air/silicone oil flow. Lines indicate flow pattern

transitions: bubble/dispersed bubble and bubble/slug—Taitel et al. (1980) (the

latter with a critical void fraction of 0.3 as deduced from Fig. 1); slug/

churn—Jayanti and Hewitt (1992), Watson and Hewitt (1999); churn/annular—

Barnea (1986).


function plots. Whereas an existing slug flow is characterised byoccurrence of Taylor bubbles, a churn-turbulent flow is char-acterised by an inhomogeneous distributed gas phase into theflow. As described in Section 3.2, those runs which were identifiedas annular flow were classified according to the occurrence oflarge gas structures. The conditions corresponding to the alter-native version of the slug/churn transition identified in Figs. 17and 18 is marked by the dotted circle in Fig. 20.

One striking difference between both data from the two fluidpairs is the parameter range where bubbly flow occurs. At a liquidsuperficial velocity of 0.7 m/s bubbly flow in air/silicone oil flowoccurs at higher gas superficial velocities than for air/water flow.This can be taken another indication of a shift of the relationbetween coalescence and breakup towards more coalescence inair/water flow than in air/silicone oil flow.

The differences between the flow pattern maps for air/waterand air/silicone oil are most clearly seen the two extremes ofhighest and lowest air flow rates studied. At the lowest gasvelocities there is bubbly flow for the silicone oil case, whereas forwater the pattern is bubbly/spherical cap. At the next highest gasvelocity, for a liquid superficial velocity of 0.25 m/s, water hasmoved into slug flow whilst the silicone oil has only achievedbubbly/spherical cap. At the highest gas velocity, water is in churnflow whilst silicone oil is showing annular characteristics asdiscussed above. Though this does not agree with the predictionsof Barnea (1986), reasonable changes to the Weber number anddrag coefficient from which the transition Kutateladze number isobtained results in much better agreement with the presentexperimental results.

The models discussed in the introduction give a reasonableprediction if the bubbly and bubbly/spherical caps are taken onone side of the transition and slug flow on the other. The gassuperficial velocity at which the slug/churn transition is predictedto occur is much higher than that seen in the experimental data. Itis also higher than the alternative transition identified via Figs. 17and 18. The reason for this discrepancy could be due to the degreeto which the equations used to predict flooding by Jayanti andHewitt (1992), Watson and Hewitt (1999) apply. That equationwas developed from data for pipes of diameters smaller than thatof the present experiments. Measurements by Watson and Hewitt

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(1998) showed that though the flooding equation gave goodpredictions of flooding velocities for a pipe of 32 mm internaldiameter, it was much less effective for the larger diameter(80 mm) pipe.

4. Conclusions

A wire-mesh sensor operated with two different electronics hasbeen employed to study two different two-phase flow types in avertical pipe experimental test facility. The conductivity-measuringelectronics was used to investigate air/water flow and a permittiv-ity-measuring electronics for air/silicone oil flow. From the results ofthis study the following conclusions can be drawn:

1.
In the air/water flow there is the relation between coalescenceand breakup shifted towards more coalescence than in air/silicone oil flow. Bubbles in the air/water flow tend to be largerthan in air/silicone oil flow at similar superficial velocities.These differences in coalescence intensity are obviously due tothe different viscosities of the liquid phases. Bubble sizedistributions are showing local maxima at small bubble sizes.In air/water flow these maxima are located at smaller bubblediameters than in air/silicone oil flow for similar superficialvelocities. The observed shift of the maxima towards largerbubble diameters with increasing gas superficial velocity ishigher for air/silicone oil flow. A flow pattern map wasgenerated from the wire-mesh sensor data.
2.
There is a pattern (sub-pattern) between bubbly and slug—agood description is bubbly/spherical cap. It is analogous to theheterogeneous regime of bubble columns, the occurrence oflarge bubbles in a cloud of small ones.
3.
The churn/annular flow boundary is at lower gas velocities forthe silicone oil than for water.
4.
Though some of the best available transition models givereasonable predictions of flow patterns, the slug/churn andchurn/annular transitions were not well predicted.
Acknowledgements

�
This work has been undertaken within the Joint Project ontransient multiphase flows and flow assurance. The Author(s)wish to acknowledge the contributions made to this project bythe UK Engineering and Physical Sciences Research Council(EPSRC) and the following:-Advantica; BP Exploration; CD-adapco; Chevron; ConocoPhillips; ENI; ExxonMobil; FEESA; IFP;Institutt for Energiteknikk; PDVSA (INTEVEP); Petrobras; PETRO-NAS; Scandpower PT; Shell; SINTEF; StatoilHydro and TOTAL. TheAuthor(s) wish to express their sincere gratitude for this support. � The work is part of the collaborative agreement between
Forschungszentrum Dresden-Rossendorf and the University ofNottingham.
� L A Abdulkareem would like to thank the government of the
Kurdish region of Iraq for supporting his PhD study.

References

Azzopardi, B.J., 2006. Gas–Liquid Flows. Begell House Inc, New York.Azzopardi, B.J., Jackson, K., Robinson, J.P., Kaji, R., Byars, M., Hunt, A., 2008.

Fluctuations in dense phase pneumatic conveying of pulverised coal measuredusing electrical capacitance tomography. Chemical Engineering Science 63,2548–2558.

Barnea, D., 1986. Transition from annular flow and from dispersed bubble flow-unified models for the whole range of pipe inclinations. International Journalof Multiphase Flow 12, 733–744.

Boyer, C., Duquenne, A.-M., Wild, G., 2002. Measuring techniques in gas–liquid andgas–liquid–solid reactors. Chemical Engineering Science 57, 3185–3215.

Cartellier, A., Achard, J.L., 1990. Local phase detection probes in fluid/fluid two-phase flows. Review of Scientific Instruments 62, 279–303.

Cheng, H., Hills, J.H., Azzopardi, B.J., 2002. Effects of initial bubble size on flowpattern transition in a 28.9 mm diameter column. International Journal ofMultiphase Flow 28, 1047–1062.

Chisholm, D., 1973. Void fraction during two-phase flow. Journal of MechanicalEngineering Science 15, 235–236.

Da Silva, M.J., Schleicher, E., Hampel, U., 2007. Capacitance wire-mesh sensor forfast measurement of phase fraction distributions. Measurement Science andTechnology 18, 2245–2251.

Da Silva, M.J., Thiele, S., Abdulkareem, L., Azzopardi, B.J., Hampel, U., 2010. High-resolution gas-oil two-phase flow visualisation with a capacitance wire-meshsensor. Flow Measurement and Instrumentation, in press, doi:10.1016/j.flowmeasinst.2009.12.003.

Dudukovic, M.P., 2002. Opaque multiphase flows: experiments and modeling.Experimental Thermal and Fluid Science 26, 747–761.

Fischer, F., Hoppe, D., Schleicher, E., Mattausch, G., Flaske, H., Bartel, R., Hampel, U.,2008. An ultra fast electron beam X-ray tomography scanner. MeasurementScience and Technology 19, 094002.

Geraci, G., Azzopardi, B.J., van Maanen, H.R.E., 2007. Effect of inclination oncircumferential film thickness variation in annular gas/liquid flow. ChemicalEngineering Science 62, 3032–3042.

Guet, S., Ooms, G., Oliemans, R.V.A., 2002. Influence of bubble size on the transitionfrom low-Re bubbly flow to slug flow in a vertical pipe. Experimental Thermaland Fluid Science 26, 635–641.

Heindel, T.J., Gray, J.N., Jensen, T.C., 2008. An X-ray system for visualizing fluidflows. Flow Measurement and Instrumentation 19, 67–78.

Hernandez Perez, V., Azzopardi, B.J., Morvan, H., 2007. Slug flow in inclined pipes.In: Proceedings of 6th International Conference on Multiphase Flow 2007,Leipzig, Germany, July 9–13, Paper No. S5_Thu_C_53.

Hewitt, G.F., Jayanti, S., 1993. To churn or not to churn. International Journal ofMultiphase Flow 19, 527–529.

Jayanti, S., Hewitt, G.F., 1992. Prediction of the slug-to-churn transition in verticaltwo-phase flow. International Journal of Multiphase Flow 18, 847–860.

Johansen, G.A., 2005. Nuclear tomography methods in industry. Nuclear Physics A752, 696c–705c.

Kaji, R., Zhao, D., Licence, P., Azzopardi, B.J., 2009a. Studies of the interaction ofionic liquid and gas in a small diameter bubble column. Industrial andEngineering Chemistry Research 48, 7938–7944.

Kaji, R., Hills, J.H., Azzopardi, B.J., 2009b. Extracting information from time seriesdata in vertical up flow. Multiphase Science and Technology 21, 1–12.

Kytomaa, H.K., Brennen, C.E., 1991. Small amplitude kinematic wave propagationin two-component media. International Journal of Multiphase Flow 17, 13–26.

Lucas, D., Krepper, E., Prasser, H.-M., 2005. Development of co-current air-water flow in a vertical pipe. International Journal of Multiphase Flow 31,1304–1328.

Mantle, M.D., Sederman, A.J., 2003. Dynamic MRI in chemical process and reactionengineering. Progress in Nuclear Magnetic Resonance Spectroscopy 43, 3–60.

Mao, Z.S., Dukler, A.E., 1993. The myth of churn flow? International Journal ofMultiphase Flow 19 377–383.

McKeen, T.R., Pugsley, T.S., 2002. The influence of permittivity models on phantomimages obtained from electrical capacitance tomography. MeasurementScience and Technology 13, 1822–1830.

Pietruske, H., Prasser, H.-M., 2007. Wire-mesh sensors for high-resolving two-phase flow studies at high pressures and temperatures. Flow Measurementand Instrumentation 18, 87–94.

Prasser, H.-M., Bottger, A., Zschau, J., 1998. A new electrode-mesh tomograph forgas–liquid flows. Flow Measurement and Instrumentation 9, 111–119.

Prasser, H.-M., Scholz, D., Zippe, C., 2001. Bubble size measurement using wire-mesh sensors. Flow Measurement and Instrumentation 12, 299–312.

Prasser, H.-M., Zschau, J., Peters, D., Pietzsch, G., Taubert, W., Trepte, M., 2002. Fastwire-mesh sensors for gas–liquid flows—visualization with up to 10,000frames per second. In: International Congress on Advanced Nuclear PowerPlants (ICAPP 2002), Hollywood, Florida, June 9–13, Paper No. 1055.

Prasser, H.-M., Beyer, M., Bottger, A., Carl, H., Lucas, D., Schaffrath, A., Schutz, P.,Weiss, F.P., Zschau, J., 2005a. Influence of the pipe diameter on the structure ofthe gas–liquid interface in a vertical two-phase pipe flow. Nuclear Technology152, 3–22.

Prasser, H.-M., Misawa, M., Tiseanu, I., 2005b. Comparison between wire-meshsensor and ultra-fast X-ray tomograph for an air–water flow in a vertical pipe.Flow Measurement and Instrumentation 16, 73–83.

Prasser, H.-M., Beyer, M., 2007a. Bubble recognition algorithms for the processingof wire-mesh sensor data. In: Proceedings of 6th International Conference onMultiphase Flow 2007, Leipzig, Germany, July 9–13, Paper No. S7_THU_B_50.

Prasser, H.-M., Beyer, M., Carl, H., Gregor, S., Lucas, D., Pietruske, H., Schutz, P.,Weiss, F.-P., 2007b. Evolution of the structure of a gas–liquid two-phase flowin a large vertical pipe. Nuclear Engineering and Design 237, 1848–1861.

Premoli, A., Francesco, D., Prina, A., 1971. An empirical correlation for evaluatingtwo-phase mixture density under adiabatic conditions. La Termotecnica 25,17–26.

Richter, S., Aritomi, M., Prasser, H.-M., Hampel, R., 2002. Approach towards spatialphase reconstruction in transient bubbly flow using a wire-mesh sensor.International Journal of Heat and Mass Transfer 45, 1063–1075.

ARTICLE IN PRESS


Reinecke, N., Petritsch, G., Schmitz, D., Mewes, D., 1998. Tomographic measure-ment techniques: visualization of multiphase flows. Chemical Engineering andTechnology 21, 7–18.

Song, C.H., No, H.C., Chung, M.K., 1995. Investigation of bubble flow developmentsand its transition based on the instability of void fraction waves. InternationalJournal of Multiphase Flow 21, 381–404.

Taitel, Y., Barnea, D., Dukler, A.E., 1980. Modelling flow pattern transitionsfor steady upward gas–liquid flow in vertical tubes. AIChE Journal 26,345–354.

Watson, M.J., Hewitt, G.F., 1998. Effect of diameter on the flooding initiationmechanism. In: 3rd International Conference on Multiphase Flow, Lyon, June8–12.

Watson, M.J., Hewitt, G.F., 1999. Pressure effects on the slug to churn transition.International Journal of Multiphase Flow 25, 1225–1241.

York, T., 2001. Status of electrical tomography in industrial applications. Journal ofElectronic Imaging 10, 608–619.

Zuber, N., Findlay, J.A., 1965. Average volumetric concentration in two-phase flowsystems. Journal of Heat Transfer 87, 453–468.

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