Spatial void fraction measurement in an upward gas–liquid flow on the slug regime

Flow Measurement and Instrumentation 46 (2015) 139–154

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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst

Spatial void fraction measurement in an upward gas–liquid flow on the slug regime Eugênio S. Rosa n, Marco A.S.F. Souza Mechanical Engineering School, University of Campinas, UNICAMP Campinas, SP 13083-890, Brazil

art ic l e i nf o

a b s t r a c t

Article history: Received 23 October 2014 Received in revised form 25 October 2015 Accepted 29 October 2015 Available online 31 October 2015

Spatial void fraction measurements of a vertical upward air–water flow on the slug regime are made. The experimental technique uses simultaneously a contact needle and two single wire sensors. The data processing combines the information of both types of sensors. The liquid slug local void fractions along the radial and axial directions are estimated employing time and ensemble averages. The spatial void fraction along the axial direction disclosed two patterns, one associated to the pipe core and the other near the wall. The data is further processed to render the average void fraction along the radial and axial directions and the slug unit void fraction profile. Uncertainty analysis and data consistency tests are applied the check data reliability. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Slug flow Spatial void fraction Contact needle sensor Gas entrainment Vertical flow

1. Introduction Slug flow is a gas–liquid flow regime occurring over a wide range of flow rates and found in many industrial processes. The regime is characterized by a quasi-periodic succession of aerated liquid slugs trailed by gas pockets surrounded by liquid films which do not repeat in time or in space. In vertical upward slug flow the gas pockets become axis-symmetric with a bullet shape, also called by Taylor bubble. The Taylor bubble moving faster than its upstream liquid slug transfers a fraction of the displaced volume to the downstream liquid slug as a free falling film. The gas is entrained into the downstream liquid slug due to the liquid film fragmentation at the Taylor bubble rear. The intermittent slug flow behavior allied to the intrinsic gas– liquid interactions is a complex phenomenon. One successful attempt to model slug flow is based on a steady state approximation by considering the existence of a repeating cell or unit cell [5]. There are several models employing the unit cell concept, among them we cite Taitel and Barnea [6] model as representative of this class. Unfortunately all the unit cell based models have more unknowns than equations and frequently the void fraction is supplied by closure equations. The accuracy of the void fraction estimate has influence on the predicted slug properties, certainly the most obvious one regards to the gas transport. Despite the major n

Corresponding author. E-mail addresses: [email protected] (E.S. Rosa), [email protected] (M.A.S.F. Souza). http://dx.doi.org/10.1016/j.flowmeasinst.2015.10.016 0955-5986/& 2015 Elsevier Ltd. All rights reserved.

fraction of the gas is transported by the Taylor bubble, the aerated liquid piston may transport not a negligible fraction of the total gas as we shall see through the experimental data. Relevant experimental data on liquid slug void fraction in vertical upward flow appeared during the late 70's. A selection of a few experimental databases concerning the volumetric averaged liquid slug void fractions are presented on Table 1. These databases were used to validate empirical liquid slug void fraction correlation, for example Felizola and Shoham [14] and Gomez et al. [15]. The empirical correlations are easy to evaluate but their usefulness is restricted to scenarios close to the experimental condition where they were developed. In an attempt to overcome this limitation new models based on a Taylor bubble gas balance were developed: Fernandes et al. [10], Kockx [21], Brauner and Ulmann [16] and Guet et al. [17]. These mechanistic models estimate the volumetric averaged void fraction of the liquid slug by modeling the liquid slug aeration process based on the downward gas flow induced by the liquid film [10] and [21], on the flux of energy [16] or on the pressure jump at the rear of the Taylor bubble [17]. Despite the available databases and the resourceful void fraction models there is little information regarding spatial void fraction measurements, a valuable source of information to develop mechanistic models to void fraction prediction. Nakoryakov et al. [1] and Mao and Dukler [2] were the first to address this issue in 1989. Nakoryakov et al. [1] measured: the radial and axial velocity profiles at the liquid slug employing a hot wire, the wall shear stress using a double wall shear stress probe and the radial void fraction profiles of the Taylor bubble region employing a

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V V* Ub

Nomenclature List of symbols A At C0 C0,B C1 D Dt F Frm g J JG JL LF LS LU N Q r R0 Rem S t tb ts TB TS TV* vG,J

pipe cross sectional area (m2) flow attachment point dimensionless distribution parameter for the kinematic law dimensionless distribution parameter for the kinematic law dimensionless drift parameter pipe diameter (m) flow detachment point slug frequency (Hz) Froude number gravity acceleration (m/s2) mixture velocity (m/s) gas superficial velocity (m/s) liquid superficial velocity (m/s) liquid film length (m) liquid slug length (m) slug unit length (m) number of samples volumetric flow rate (m3/s) radial coordinate (m) pipe radius (m) Reynolds number sensors axial spacing (m) time (s) residence time of the elongated bubble (s) residence time of the liquid slug (s) time of the bubble front (s) time of the slug front (s) dimensionless threshold value drift velocity (m/s)

Table 1 Experimental database for averaged liquid slug void fraction. Authors

Year

Schmidt [8] Koeck [9] Fernandes et al. [10] Fréchou [11] Fréchou [11] Nakoryakov et al. [1]

1977 1980 1981 1986 1986 1989

Mao and Dukler [2] Van Hout et al. [12] Felizola [13]

Fluids

Air–kerosene Air–water Air–water Air–water Air–oil Air–water solution 1989 Air–water solution 1992 Air–water 1992 Air–kerosene

Pipe diameter (cm)

Data points

5.10 4.40 5.07 5.36 5.36 1.5

15 25 24 7 7 6

5.08

5

5.00 5.10

6 9

contact needle probe. The experimental test section was a vertical 15 mm internal diameter pipe and the measurements were performed at 166D downstream the gas–liquid mixer. The working fluids were air and an electrolyte water based solution. Mao and Dukler [2] employed a double mass transfer sensors and a radio frequency local probe to disclose measurements of the wall shear stress and axial distribution of the void fraction at the pipe centerline. The data were taken in a vertical pipe with 5.08 cm in diameter and 175D in length. The working fluids were air and an electrolyte water based solution. The gas and liquid superficial velocities range were of (76–342) cm/s and (5–32) cm/s respectively. The experimental data disclose that the void fraction is high

UT XL z

voltage (v) dimensionless voltage dispersed bubble velocity (m/s) within the liquid slug (m/s) bubble nose translational velocity (m/s) liquid phase indicator function axial distance from the slug head (m)

Greek letters

αS,T αS,E αU β η μL ξ ρG ρL Δρ s

liquid slug void fraction employing time average liquid slug void fraction employing ensemble average unit void fraction dimensionless intermittence factor dimensionless radius liquid viscosity (N.s/m2) dimensionless axial distance gas phase density (kg/m3) liquid phase density (kg/m3) density difference (kg/m3) surface tension (N/m)

Operators 〈〉 {.} {〈.〉} 〈〈.〉〉

cross sectional average pipe axial average mixed average global average

Subscripts G L

gas phase liquid phase

just at the slug head and decays continuously throughout the measurement interval. Barnea and Shermer [18], in 1989, focused on slug flow characteristics and transition. They used a contact needle probe to detect the passage of the interfaces at the centerline of a vertical tube with 50 mm in diameter and 10 m long operating with air– water mixture. The experiments were carried out at constant liquid velocity of 1 cm/s and gas velocities spanning from (3– 400) cm/s encompassing bubbly, slug and churn regimes. The centerline void fraction measurements were taken at distances up to 5D downstream the slug head to reinsure the voidage decaying behavior observed by Mao and Dukler [2]. Furthermore, the liquid slug void fraction at the centerline was around 0.25 which is the bubbly flow transition for air–water flow. Van Hout et al. [12], in 1992, employed two fiber optic probes to measure the spatial distribution of the liquid slug void fraction in a vertical 50 mm internal diameter pipe. The measurements were carried out at a distance of 120D downstream the air–water mixer. The air and water superficial velocities range were of (10– 156) cm/s and (1–75) cm/s respectively. They found that the radial profiles were nearly flat with a tendency to peak near the wall. Reference [12] concluded that at distances greater than 10D from the Taylor bubble rear the radial and axial void fraction profile no longer change and exhibit values lower than the ones observed on the wake region. To get insight into the air entrainment process Delfos [19], in 1996, measured the gas loss at the rear of a Taylor bubble held stationary in vertical tube and proposed a gas entrainment model.

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His experimental work is also reported in Delfos et al. [20]. The test section was a vertical pipe with 5.4 m long with internal diameter of 99.7 mm. The entrained air was measured directly from a flow meter because the air flowed in a closed circuit. The averaged pipe cross section void fraction was estimated by measuring the axial pressure drop profile and using the one dimensional drift flux model. The radial void fraction profile was measured at 20D below the Taylor bubble using a glass fiber probe. New measurements on the characteristics of the falling film and on the air re-coalescence flux were carried out by Kockx et al. [21], in 2005, with the objective to get additional data to validate the air entrainment model proposed by Delfos [19]. The re-coalescence air flux was estimated indirectly using a helium injection technique. Zengh and Che [22] in 2006 employed different experimental techniques to study several hydrodynamic parameters of vertical slug flow. The test section consisted of a vertical Plexiglas pipe with 5 m long and 35 mm of internal diameter. The gas and liquid phases were nitrogen and an electrolyte water based solution operating with superficial velocities ranging from (15–45) cm/s to (34–65) cm/s, respectively. The void fraction data was measured using a contact needle probe. The distance from the measurement site to the gas–liquid mixer is not mentioned but it is certainly less than 143D. Reference [22] shows measurements regarding the slug flow properties such as lengths, bubble velocity, frequency, wall shear stress and liquid film thickness. It also includes the radial profile of the slug unit void fraction as well as the liquid slug void fraction along the axial direction for various radial positions. Kaji et al. [23], in 2009, experimentally assess the effects of the pipe entrance length on the slug flow properties. They employed a wire-mesh sensor to perform measurements on two vertical test facilities with same ID of 51.2 mm but with lengths of 3.5 m and 9 m. The operational fluids were air and water with superficial velocities of (10–400) cm/s and (10–160) cm/s respectively. The experimental data provided several mean slug flow properties, such as lengths, bubble velocity, frequency and void fraction probability density functions. The authors proposed to estimate the Taylor bubble and the liquid slug averaged void fractions as being the peak values of the experimentally determined void fraction pdf. Accordingly to [23], the void fractions corresponding to the Taylor bubbles and to the liquid slugs tend to increase with increasing the gas flow rates and decreasing liquid flow rates. Barnea et al. [24], in 2013, measured the liquid slug spatial void fraction in the whole range of pipe inclination using a wire mesh sensor. The working fluids were air and water flowing in a pipe of 54 mm in diameter. The air and water superficial velocities range were of (41–250) cm/s and (1–200) cm/s respectively. The measurements were taken at 148D downstream the air–water mixer. Of particular interest are the axial profiles of the liquid slug void fraction taken at different radial locations for various mixture velocities with the test section at the upright position. Abdulkadir et al. [25] in 2014, developed an experimental study of the hydrodynamic behavior of slug flow in a vertical riser employing an electrical capacitance tomography. The test section consisted of a transparent acrylic pipe of 6 m long and internal diameter of 67 mm. The gas and liquid phases were air and silicone oil with superficial velocities ranging (30–150) cm/s and (5– 38) cm/s. Reference [25] shows several slug flow properties including the volumetric averaged void fraction values for the liquid slug and for the Taylor bubble with an uncertainty of 710%. The list of fifteen reviewed works published along the past 25 years narrows to only three if one considers the experimental works that yielded detailed information on the spatial void fraction distribution: [12,22,24]. An examination on these references discloses differences among them which are briefed as: void fraction exhibiting core peaking or wall peaking; the

141

establishment of a stationary void fraction beyond 10D downstream the Taylor bubble rear or a non-stationary void fraction profile and the existence of a minimum void fraction downstream the Taylor bubble or not. These qualitative differences are still open issues considering the fact that the employed experimental facilities had similar pipe diameters, distance from the mixers, working fluids and phase velocities. The motivation of this research is to analyze the spatial void fraction distribution on the liquid slug. This work is primarily aimed to check some gaps left by the foregoing investigations. The structure of the work is as follows: the experimental apparatus and data processing procedures are in Sections 2 and 3, the experimental results are in Section 4 and the conclusions are in Section 5. 1.1. Description of the slug flow nomenclature, streamlines and wake regions The description of the slug flow nomenclature, streamlines and wake regions is introduced beforehand as a form to assist this paper reading. A schematic representation of a vertical upward slug flow and its nomenclature are shown in Fig. 1. The aerated liquid slug has length and void fraction labeled as LS and αS respectively. Furthermore, the upward velocities of the dispersed bubbles and of the liquid phase are represented by Ub and UL,S, respectively. The coordinate z is associated to the distance from a given pipe cross section, within a liquid slug, to the liquid slug head, see representation in Fig. 1. The Taylor bubble flows within the pipe core and is surrounded by a thin liquid film which is in contact with the wall. As the bubble nose displaces upward and the liquid film flows downward. The liquid film void fraction, the liquid film length and the bubble nose translational velocity are represented by αf, Lf and UT respectively. The liquid slug, trailed by an elongated gas bubble, forms a quasi-periodic flow structure hereafter called as slug unit which has length and void fraction defined by LU and αU respectively. The streamlines and the wake regions described in Fig. 1 { Slug head }

g z

Near wake Dt

Aerated liquid slug

Far wake UL,S LS LS, Fully developed flow

S

Ub

Far bubble nose At { Slug rear }

UT

Bubble nose

Taylor bubble LF, r

F

Bubble body

q Liquid film

Pi Pipe diameter

D

Fig. 1. Left side, slug flow schematic representation. Right side, the streamlines seen accordingly to a stationary observer and the associated wake zones on the right the instantaneous.

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Measuring Station

stainless steel pipe

g 200mm

elec tronic

Patm P

143.7mm

single wires

contact needle

330 mm elec tronic

flow

drop leg, 120mm

7.96 m

112.5mm elec tronic

measuring station

26mm

support the liquid slug void fraction characterization given in Section 4. The streamlines refer to a transient flow representation, at a given instant of time, viewed by a stationary frame of reference. A downward annular liquid film is discharged at Taylor bubble rear, similar to a wall jet, into the upward liquid slug. This phenomenon fragments the liquid film, entrains gas into the liquid piston and creates a wake downstream the Taylor bubble [7]. The wake region is split into two regions: a near wake and a far wake. The near wake starts at the slug head and finishes at a spot where the descendent wall jet detaches from the wall. This flow detachment point is represented in the figure as Dt. The far wake begins on the flow detachment point and extends downstream up to a region where the flow becomes eventually fully developed. The fully developed slug flow refers to a state where the liquid and gas velocity profiles no longer change within the liquid slug, the neighboring Taylor bubbles do not merge and the bubble coalescence rate is null. One of the differences between the near wake and the far wake regions is the existence of upward and downward flows on the former while the later has only upward flow. The fully developed region bridges the far wake to the far bubble nose region. This region may exist only if the liquid slug has enough length to achieve the fully developed state. Next there is the nose region where the flow is influenced by the Taylor bubble nose displacement. Complementary to the previous case, a flow attachment point, At, divides these nose regions into a region with reversed flow from another with downward flow only. Lastly, there is the Taylor bubble body next to bubble nose region. It is identified as a region where the downward liquid film is in equilibrium, i.e. the film velocity and the film thickness are constants. A new slug unit starts at the end of the bubble body region. The flow detachment and attachment points, also called as critical points, have null wall shear stress. The critical points were not cited before but the existence of null wall shear stress was confirmed through the change in sign of the wall shear stress within 3D to 5D downstream the Taylor bubble rear, [2]. The streamline patterns are indirectly confirmed through the experimentally determined vector plot obtained by Nogueira et al. [3,,4]. The critical points are relevant in this work because they define the boundary between the near and far wake regions. In a stable or developed aeration process the gas net flux crossing the Taylor bubble interface is null. Therefore the Taylor bubble absorbs the incoming flow of gas from the upstream liquid piston and sheds gas into to the trailing liquid piston at the rear. A fraction of the entrained gas return to the Taylor bubble while the remainder flows as dispersed bubbles on the trailing liquid piston.

6.68 m

142

plexiglass pipe

water reservoir

air-water mixer

Patm

water flow meter air flow meter P

air supply P

T

Fig. 2. Schematic diagram of the experimental apparatus and measuring station.

and 200 mm, respectively. The U bend discharges the air–water mixture into a vertical tube with 120 mm in diameter which has its upper end open to the atmosphere while the low end is connected to the water storage tank. This vertical drop leg, acts as air– water separator due to its larger diameter. The air is freely discharged into the atmosphere while the water goes into a 3 m3 water storage tank whose outlet feeds the water pump. The operational pressure and temperature were of 94.7 kPa and 23 °C which are close to the ambient conditions. The mixer is a Y connection where the water flows along the straight branch and the air is injected thru the side branch. Visual observations indicate the slug regime establishes at nearly 70D downstream the mixer and that the dispersed bubble diameters within the liquid slug span from 2 mm to 3 mm exhibiting distorted interfaces. 2.1. The measuring station

2. Experimental apparatus The experimental apparatus is schematically represented in Fig. 2. The test section consists of a straight vertical transparent Plexiglas pipe with 26 mm internal diameter and 7.96 m long or 306D. A centrifugal pump displaces the water in a closed loop. The water flow rate is monitored by a Metroval RH15 Coriolis mass flow meter accurate within 1%. Compressed air is stored into a 5 m3 vessel where the pressure ranges between 8 Barg and 10 Barg accordingly to on–off compressor pressure controller relay. The air storage vessel discharges to a supply line which has a mechanical pressure regulator to fix the downstream pressure to 2 Barg. The air flow rate is monitored by a laminar flow element Merian 50 MT10, with reported uncertainty of 1½%. The water and the air are mixed at the low end of the test section. The mixture flows upward along the test section, reaches the measuring station at 6.682 m, or 257D, downstream the mixer. At a distance of 49D downstream the measuring station, the flow exits the test section into U bend with internal diameter and curvature radius of 37 mm

The measuring station consists of four instruments: a pressure transducer, two single wire conductive sensors axially spaced and a contact needle conductivity sensor, see inset on Fig. 2. A section of a stainless steel pipe, with the same internal diameter of the test section and 400 mm long, houses the pressure transducer and the two single wire sensors. The pressure tap is at the mid section and the single wire conductive sensors are symmetrically spaced off the mid section by 56.25 mm. The contact needle probe is attached to the acrylic pipe wall and placed at 330 mm below the stainless steel pipe. The single wire conductive sensor consists of a bare stainless steel cylindrical rod with 0.6 mm in diameter stretched along the pipe diameter line resulting in a pipe cross section blockage less than 3%. Sleeves placed at the stainless steel pipe rim provides to the rod mechanical support, mechanical seal against leakages and electrical insulation. A description of the sensors mechanical assembly is in Rosa et al. [27]. The single wire sensors are used to detect the boundaries of the elongated gas bubble and of the liquid piston.

E.S. Rosa, M.A.S.F. Souza / Flow Measurement and Instrumentation 46 (2015) 139–154

2.2. Experimental procedure The flow rates are expressed in terms of the phases' superficial velocity or phases' volumetric fluxes defined as:

JL = Q L/A and JG = Q G/A,

(1)

where the subscripts L and G stand for the water and air phases, Q is the volumetric flow rate and A is the pipe cross section area. The mixture superficial velocity is defined as:

J = JL + JG .

(2)

1000

JL (cm/s)

The contact needle conductivity sensor consists of a tip of a non insulated gold wire of 108 μm in diameter facing the flow. The gold wire is insulated and housed by a stainless steel needle with an external diameter of 900 μm whose function is to give structural support to the gold wire tip and provide ground to the electronic circuit. The contact needle conductivity sensor is used to measure the local void fraction at distinct radial pipe positions employing a traverse mechanism driven by a micrometer. The sensor operational details and references of its application for local void fraction measurement are in Hewitt [28]. The single wire sensors and the contact needle probe have a signal proportional to the water electrical resistance path established within the pipe. The electrical resistance path to the single wire sensor is established between the wetted areas of the rod and of the pipe wall while for the contact probe it is established between the wetted areas of the wire tip and of the needle body. Both sensors share the same circuit driver which is based on a voltage divider driven by a 100 kHz sinusoidal oscillator signal with 10 V rms to minimize the polarization effects on the sensors’ contact surface. The water electrical resistance path is proportional to the voltage drop at the variable resistance on the voltage divider circuit. The output voltage signal carrier frequency of 100 kHz is removed employing a 10 kHz low pass filter. Next, the voltage signal goes through an amplifier and finally to a voltage–current converter to transform the voltage to a 4–20 mA signal. The signals are digitized at a sampling frequency of 3 kHz and stored in a National Instruments data acquisition system for further processing. It is observed that the chosen sampling frequency is much greater than the characteristic frequencies of the slugs, 1– 10 Hz, and of the dispersed bubbles within the liquid slugs, 10– 100 Hz. Nevertheless, it is necessary to have a sampling frequency of 3 kHz in order to accurately estimate the bubble nose velocity and the lengths of Taylor bubbles and liquid slugs. The signal sampling period was of 120 s for each experimental run.

143

100

10 1

10

100 JG (cm/s)

1000

10000

Fig. 3. Representation of tests #2, #3 and #4 velocities on the flow map [29].

for tests #2, #3 and #4. The slug flow regime predicted by the map and is also confirmed by visual observations. The local void fraction is measured along nine radial positions defined as r/R0 ¼ {0.0, 0.10, 0.30, 0.50., 0.60, 0.70, 0.80, 0.85, 0.90} where R0 ¼D/2 and r/R0 ¼ 0 represents the pipe centerline. The developed experimental procedure is based on following hypotheses: (i) the flow is isothermal with no phase change; (ii) no gas is in contact with the wall i.e., α ¼0 at r/R0 ¼1, and (iii) in average the flow is axially symmetric. The test starts by setting the JG and JL velocities and displacing the contact needle to a radial position. This step is repeated until the nine radial positions are scanned. After the scanning step is finished a new pair of JL and JG is set and the procedure is repeated until the all grid velocities are scanned. The execution time for a single pair JG and JL lasts approximately 60 min.

3. Data processing The data processing is developed along the next four sections. The first Section defines the phase indicator function. The second Section is devoted to the pair of single wire sensors and to the evaluation of the slug flow properties. The third Section shows the time average procedure to get the averaged radial profile. Finally, the fourth Section presents the ensemble average procedure to get the liquid slug void fraction profiles along the radial and axial directions. 3.1. The phase indicator function

Table 2 displays the test grid superficial velocities and the associated Reynolds and Froude numbers defined as: Rem ¼ ρL.D.J/μL and Frm ¼J/(gD)0.5 where ρL, μL, g and D represent the liquid density, liquid viscosity, gravity acceleration and pipe diameter, respectively. Test #1 differs from the remaining tests because JL is null; the flow is driven due to the Taylor bubble buoyancy. This operational condition was chosen to check if low liquid input induces changes on the void profiles. For referencing purposes Fig. 3 displays the grid velocities on the Taitel and Barnea [29] flow map

The sampled signals consist of time series stored at time intervals given by the reciprocal of sampling frequency. The data processing starts with the discrimination of the occurrence of the gas or liquid phase in contact with both types of conductive sensors. The contact needle and single wire sensors have a typical voltage span of 1–5 V. The occurrence of water or air is associated with high or low voltages readings respectively. The first step towards the phase indicator function is to normalize the sensors’ output voltage according to:

Table 2 Test grid phase superficial velocities and Rem and Frm.

V * (t ) =

Test #

JG (cm/s)

JL (cm/s)

J (cm/s)

Rem (-)

Frm (-)

1 2 3 4

59 52 88 105

0 31 29 61

59 83 117 166

1.6E þ04 2.2Eþ 04 3.0Eþ 04 4.3Eþ 04

1.2 1.6 2.3 3.3

V (t )−Vmin where 0 ≤ V * (t ) ≤ 1, Vmax−Vmin

(3)

where Vmax and Vmin represent the maximum and minimum voltage within the voltage time series. The next step defines a threshold value, TV*, which will discriminate the occurrence of water or air. The TV* is a reference value spanning along the interval:

0 ≤ TV * ≤ 1.

(4)

144

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Fig. 4. Point #4 sample of V* (black line extracted from the single wire probe) and XL (red line) functions and the associated time variables. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The liquid phase indicator function is then defined as a function of TV*:

XL (t ) = 1 if V * (t ) ≥ TV * and 0 otherwise.

(5)

Since the flow has only two phases, the gas phase indicator function is defined as:

X G (t ) = 1−XL (t ).

(6)

The optimum threshold values to the single wire probes are determined by counting the number of detected liquid pistons when TV* spans from 0.1 to 0.9 in 0.02 steps. It is found that the number of detected liquid pistons remains nearly constant within

Fig. 5. (a) V* versus time extracted from the contact needle (continuous black line), dashed red line representing the slug head and Taylor bubble nose evaluated by the twin sensors; (b) XL (scattered points) versus time along the slug unit and (c) XL (scattered points) versus time along each liquid slug. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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the interval 0.5 oTV* o0.8. Based on this analysis was chosen TV* of 0.7 to be applied through all tests. The contact needle probe threshold value was of TV* ¼0.5, [30]. For reference Figs. 4 and 5 display the liquid phase indicator function superposed to the dimensionless voltage time series for the single wire and contact needle sensors, respectively.

phase indicator function shown in Fig. 5b. Due to this sampling characteristic, the void fraction resulting from Eq. (8) is usually called unit void fraction, or αU. The averaged unit void fraction is estimated by the integral of the measured void fractions along the pipe radius:

αU 3.2. Estimating the slug flow properties with the pair of single wire sensors The pair of single wire sensors is used to detect the boundaries of the elongated gas bubble and liquid piston. Since they are displaced from each other by 112.5 mm (or 4.3D) the twin signal is strongly correlated as seen in Fig. 4. Employing a TV* of 0.7 it is possible to define the liquid slug and Taylor bubble boundaries in a form of a squared wave train as shown in Fig. 4. A software routine matches the set of square waves to determine the initial time of the slug head and of the Taylor bubble nose, TS and TB as well as their residence times, ts and tb respectively. These characteristic time intervals are represented in Fig. 4 with subscripts ‘u’ and ‘d’ indicating they belong to the upstream or to the downstream wire sensor. The nomenclature also employs numbers 1, 2, 3, etc. to associate them to a specific slug unit. Once the characteristic times of each slug and Taylor bubble are determined, the individual Taylor bubble nose velocity, UT, the film length LF, the slug length LS, the unit frequency, F, and the intermittency factor, β, are evaluated as:

UT = S/( TB d−TBu

)

L S = UT⋅ts

1 ≤ i ≤ N and 0 ≤ η ≤ 0. 90,

(8)

η is the dimensionless radial coordinate defined as:

η = r /R 0,

(10)

Ni

1 Nj

∑ ( 1−XLi ) for 1 ≤ i ≤ Nj and 1 ≤ j ≤ M, i=1

(11)

the subscripts ‘S’ and ‘T’ associate α to the liquid slug and to the time average procedure; Nj is the sample size of the jth liquid slug defined by the product of the sampling frequency and the residence time of the jth liquid slug. Once the void fraction of each liquid slug is known, the mean liquid slug void fraction at a given radial position is defined as a weighted average of the liquid slug void fraction by the associated liquid slug lengths:

}

j S,T (η) L S

αS,T

N i=1

α (η) η⋅dη .

=

M

j L Sj/ ∑ L Sj. ∑ αS,T j=1

j=1

(12)

The symbol {.} represents a weighted average. The mean liquid slug void fraction is evaluated taking the average at the pipe cross section of {αS,T}Ls:

The averages procedures defined along this section are refereed as time averages because they stem from simple manipulations of the experimentally determined time series. A typical V* signal of the contact needle at the pipe centerline is shown in Fig. 5a. Two quasi periodic regions are identified: one where V* stays zero during long periods and the other where V* spans 0.2–1 in a much shorter period. These are typical signals when the needle’s tip crosses a Taylor bubble and an aerated liquid piston respectively. Furthermore, the dashed red line represents the liquid indicator function, as estimated by the single wire sensors. It defines the interface position which separates the liquid slug of the Taylor bubble and, at the same time, defines an envelope where the liquid slugs can be sorted out. A typical contact needle probe signal sampled at the pipe centerline is shown in Fig. 5a. The corresponding liquid phase indicator functions, XL, for the slug unit and for each liquid slug are in Fig. 5b and c respectively. The air–water mixture void fraction, at a given radial position, is evaluated as:

where

j αS,T (η) =

(7)

3.3. Void fraction measurements by time averaging the contact needle signal

∑ ( 1−XLi ) for

1

M

where S represents the sensors' spacing, S¼ 112.5 mm.

1 N

∫0

The symbol 〈〈.〉〉 represents a global mean, condenses the void fraction measurements into a single value by averaging the local measurements along the streamwise and radial directions. The single wire sensor time series contains a sample with M slug units in which the initial and final times of each liquid slug are identified. This information allow us to sort, within the contact needle time series, sub sets corresponding to each slug as suggested in Fig. 5c. The jth liquid slug void fraction, at a given radial position, accordingly to:

{α

,

β = LF/ ( LF + L S )

α (η) =

=2

F = 1/(ts + tb)

LF = UT⋅tb

145

(9)

and N is the sample size defined as the product between the sampling frequency and the acquisition period. The alternating passage of the liquid slugs and of the Taylor bubbles are equally sampled by the contact needle and has its corresponding liquid

=2

1

∫0 { αS,T (η) }L η⋅dη . S

(13)

3.4. Void fraction measurements by ensemble averaging the contact needle signal The first step to the ensemble average is to sort and store the time series of each one of M liquid slugs for each one of the sampled radial positions. This procedure is done with the initial and final time of the jth slug given by the single wire sensors. For an equilibrium flow, it is supposed that the Taylor bubble nose and the slug front travel with the same speed, UT. This assumption allows us to transform each time series into a space series along the z direction, by multiplying the time step of each time series by its associated UT. The transformation of time to space series introduces a difficulty: the set along the z direction have data spacing and number of samples distinct from each other due to the fact that the liquid slug residence time and the associated UT change from unit to unit. At this stage, for each radial position, a set of M spline functions is applied from head to tail in each one of the M slugs to interpolate V* spanning from the slug head, z/D ¼0, up to z/D¼ 15 at fixed axial displacement of Δz/D¼ 1. The reason to choose z/D ¼15 as the end of interval is postponed to Section 4.1. This procedure renders an ensemble of V* with equally spaced data. Next, the TV* procedure is applied into the V* ensemble to get the liquid phase indicator for each radial and axial positions. The outcome is a series of 1 and 0 which are schematically represented in Fig. 6 at positions z/D¼ 0, 1, 2, etc for a given radial position. The local void fraction, at a given radial and axial position, is determined by:

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4. Experimental results 4.1. Global averages, experimental procedure validation and experimental technique limitations

Fig. 6. Ensemble of XL signals at given radial position. The mean void fraction, at a given z/D is obtained from the ensemble average.

αS,E (η, ξ ) = where

1 M

M

∑ ( 1−XLj ) for 1 ≤ j ≤ M,

(14)

j=1

ξ is the dimensionless axial coordinate defined as:

ξ = z/D ,

(15)

and the subscript E is used as label to identify that the result comes from an ensemble average procedure. The evaluation of Eq. (14) results in a matrix {16,10} where the 16 lines represent the set of axial displacements spanning from 0 to 15D in steps of 1D while the 10 columns represent the radial positions given on Section 2.2 plus the pipe wall, r/R0 ¼ 1 where α≡0. The average void fraction along the axial direction for a given radial position, for example η1 ¼r1/R0, is defined as:

{ αS,E (η1) } =

1 ξmax

∫0

ξmax

αS,E ( η1, ξ ) dξ ,

(16)

where ξmax ¼zmax/D¼15. The liquid slug average at the pipe cross section for a given axial position, for example ξ1 ¼ z1/D, is defined as:

αS, E (ξ1) = 2

∫0

1

αS, E ( η, ξ1) η⋅dη,

(17)

where the symbol 〈.〉 represents the cross section average operator. With the aid of Eq. (17), it is possible to define a mean liquid slug void fraction in terms of the liquid slug axial distance:

{

αS,E (λ )

} = 1λ ∫0

λ

αS,E (ξ ) dξ ,

(18)

where 0 ≤ λ ≤ zmax /D = 15. The global liquid slug void fraction is evaluated taking the average at the pipe cross section of the mean slug void fraction along the piston length {αS,E}Ls, or taking the average along the pipe axial direction of the mean void fraction at the cross section 〈αS,E〉:

αS,E where

=2

∫0

1

η { αS,E }z / D dη =

ξmax ¼ 15.

1 ξmax

∫0

ξmax

αS,E (ξ ) dξ ,

(19)

The simultaneous use of two single wire sensors and the contact needle sensor allowed us to determine the average lengths of the film and slug, the bubble nose translational velocity and the unit frequencies, as well as the averaged void fractions of the unit and of the liquid slug. The above mentioned quantities are in Table 3 for tests #1 to #4. The 2nd to the 7th columns display the averages of: film length, liquid slug length, intermittency factor β ¼Lf/(Lf þLS), Taylor bubble nose velocity, unit frequency and the number of slug samples. Lastly, the 8th, 9th and 10th columns display the unit void fraction and the liquid slug void fraction employing time and ensemble averaging procedures. Table 3 shows that the average liquid slug length spans from 15.9D to 16.7D. The average film length is sensitive to the phases' velocities but tests #2 and #3 disclose that keeping constant the liquid phase velocity Lf/D increases as the gas phase velocity grows. The bubble nose translational velocity is linearly proportional to the mixture velocity and the unit frequency is dependent on the liquid velocity and weakly dependent on gas velocity. The 7th column shows the number of detected slug units per test. The sample size is approximately 20% less than the product of the unit frequency by the acquisition time because the data processing fails to identify and match all slugs. The missing matches usually happen due short piston occurrence, typical of imminent Taylor bubble coalescence, and also to the presence of large bubbles within the liquid piston which reduces the voltage level and are interpreted as a gas occurrence. The slug units have void fractions spanning from 0.46 to 0.74 while the liquid slugs exhibit smaller void fraction values differing in a narrow range of 0.24–0.27. The void fraction differences between the slug unit and the liquid slug is an indicative of the major fraction of the gas phase is transported by the Taylor bubble. It is also observed that 〈〈αU〉〉 is proportional to JG/J. The reported time and ensemble void fractions, 〈〈αS,T〉〉 and 〈〈αS,E〉〉, compare with the reported values in [2,,10]. Furthermore, differences between the two average methods are bounded within 7 0.01 revealing the procedures consistency. 4.1.1. Consistency data checks We suggest, and use along this paper, two data consistency checks as a way to indirectly assess the reliability of the local void fraction measurement through the measured averaged void fraction values of 〈〈αU〉〉, 〈〈αS,T〉〉 and 〈〈αS,E〉〉. Namely they are: (i) the unit void fraction has to be bounded between the estimates arising from the no-slip flow (homogeneous flow) and from the maximum slip flow, see Eq. (22) and; (ii) the dispersed bubble velocity within the liquid slug has to be small or equal to the bubble nose velocity, see Eq. (27). The data checks require the knowledge of the void fraction values of the unit slug and of the liquid slug. Unfortunately few works measured the unit void fraction and also present the data in Table 3 Global averages of the slug flow properties. Test #

Lf/D (-)

LS/D (-)

β (-)

UT (cm/s)

F (Hz)

# Units (-)

〈〈αu〉〉 (-)

〈〈αS,T〉〉 (-)

〈〈αS,E〉〉 (-)

1 2 3 4

46.9 13.5 26.7 22.6

16.4 15.9 16.7 16.6

0.74 0.46 0.61 0.58

78 118 154 216

0.47 1.43 1.33 2.14

90 273 253 403

0.74 0.46 0.57 0.50

0.25 0.24 0.27 0.24

0.26 0.23 0.26 0.24

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147

table format to apply these checks. For example, references [12,18,23–25] do not have information concerning 〈〈αU〉〉 and show the void fraction data in graphical displays which make difficult to extract numerical information. Among the reviewed works [22] is the only reference that measured slug unit void fraction and published the data in table format. Unfortunately nearly one fourth their averaged data do not comply with data check (i). The unit void fraction check employs, simultaneously, the drift flux model [31] and the Taylor bubble nose translational velocity [32], also known as the kinematic law, as given by Eqs. (20) and (21):

defined by Eq. (23) is satisfied with an RMS difference of þ2 cm/s in favor of UT. The void fraction experimental data complies, in average, with the bounds defined by the drift flux model as well as the kinematic law restating the consistency of the experimental procedures. The check on the liquid slug void fraction measurement is performed indirectly by estimating the dispersed bubble velocity instead. The averaged velocity of the dispersed bubbles within the liquid slug is evaluated through a volumetric balance [6] employing experimentally determined variables:

JG / α U

Ub =

= C0 J + vG,J ,

UT = C0,B J + C∞ gD ,

(20)

(21)

where the parameters C0, C0,B, vG,J and C1 are flow pattern dependent. C0 is refereed as distribution parameter defined as C0 ¼〈 αU.J〉/(〈αU〉.〈J〉), which for air–water slug flow and Rem 4104, is approximately 1.2, [33] and [34]. Furthermore, the slug drift velocity for air–water flow in a 26 mm internal diameter pipe is vG,J = 0. 345 gD [33,,34]. Turning to the kinematic law, the C0,B is related to ratio between the maximum and the average velocities of the liquid slug ahead of the elongated gas bubble, Polonsky et al. [35]. For turbulent regime the accepted C0,B value is 1.2, [32]. The C1 parameter is associated to the rising velocity of a single bubble which for air–water flow is 0.345, Viana et al. [36]. Surprisingly, the parameters C0 and C0,B, as well as vG,J and C∞ gD , are coincidental despite arising from distinct physical principles. Recognizing that the velocity ratios, JG/UT and JG/J, represent the flows with maximum slip and no-slip (or homogenous flow) respectively [17], then the unit void fraction value is necessarily bounded by these extrema:

JG /UT ≤ α U ≤ JG /J .

(22)

It is possible to show with the inequality in Eq. (22) that:

JG /α U ≤ UT.

(23)

For non aerated liquid slugs it is possible to prove that JG/αU ¼UT. Simultaneous comparison of the experimentally determined JG /αU and UT and JG/αU estimated by the drift flux model, Eq. (20), are shown Fig. 7 as a function of J. The match of JG/αU against the drift flux model is off by 3 cm/s (rms value), which is within the model experimental uncertainties. Additionally, the inequality

JG −UT ( α U − αS

).

αS

(24)

The drift flux model can also be used to estimate Ub. The dispersed bubble velocity within the liquid slug is estimated as:

Ub = C0 J + vG,J ,

(25)

where the drift velocity, [6], is given by:

vG,J = 1. 54 ( 1− αS

⎡

⎤1/4

)1.75 ⎢⎢ σg Δ2 ρ ⎥⎥ ⎣ ρL ⎦

, (26)

and s and g represent the surface tension and the acceleration due to gravity. For distorted bubble regime, C0 spans from 0.9 to 1.2 depending on the shape of the radial void fraction profile [37]. The present work uses C0 ¼ 1.13 because the radial void fraction profiles are nearly flat, as will be shown on Section 4.5. Lastly, UT also defines an upper bound to Ub i.e., to exist aerated liquid pistons it is necessary that the dispersed bubble velocity be smaller than the Taylor bubble velocity,

Ub ≤ UT,

(27)

otherwise the dispersed bubbles would catch up the Taylor bubble [29] and 〈〈αS〉〉¼0. A comparison among Ub estimated by the volumetric balance, Eq. (24); Ub estimated by the drift flux model, Eq. (25), and the inequality in Eq. (27) is shown in Fig. 8 as a function of J. The Ub estimates have a RMS deviation of 4.3 cm/s against Eq. (25) when the mixture velocity spans from 59 cm/s to 166 cm/s. Also the RMS of the difference Ut  Ub [from Eq. (24)] is of 8.8 cm/s in favor to Ut indicating that in average UT is greater than Ub assuring the existence of aerated liquid pistons. The favorable comparisons support the employed procedures and validate the experimental and data processing procedures.

250

(ccm m/ss)

200 150 100 Ub Vol balance

50

Ub drift model d l UT Exp

0 0

50

100

150

200

250

/) J ((cm/s) Fig. 7. Comparison of the experimental JG/αU, and UT against the drift flux model (continuous line with C0 and C1 of 1.2 and 0.345).

Fig. 8. Comparison between Ub from volumetric balance, Eq. (24); Ub from the drift flux model, Eq. (25) and UT from the kinematic law, Eq. (21), against J.

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4.1.2. Experimental technique limitations One of the limitations of the proposed experimental technique regards to the discrimination of air–water interface separating the Taylor bubble rear from the liquid slug head. This interface takes almost the whole pipe cross section with fractions of it distributed at distinct pipe axial positions; see, for example, the sequence of images shown by Polonsky et al. [38]. This work determines the interface positioning through the phase indicator function employing the signals from the single wire sensors. The difficulty rests on the fact that the plane intercepted by the single wire sensors may not be the same plane intercepted by the contact needle. This uncertainty affects only the liquid slug void fraction measurements. Additional problems arise on the local void fraction measurements done by the contact needle sensor due to the change on the bubble trajectory, the interface piercing process, and the probe’s distance from the wall and threshold value. A detailed analyzes of each source of experimental uncertainty on the contact needle probe is in Cartellier and Achard [41]. Furthermore, the use of the contact needle sensor demands that the probe tip points toward the incoming flow. This condition is satisfied in most of the scanned regions where the flow is upward but the flow is downward close to the wall and near to the Taylor bubble rear. This region corresponds to a small fraction of the slug unit volume. At this region the entrained dispersed bubbles have a downward velocity inducing a void fraction measurement bias. To mitigate this difficulty the measurements were considered at radial positions defined by the interval 0 rr/R0 o0.9. A third limitation applies to the ensemble average procedures used to estimate the liquid slug void fraction at a given axial position downstream of the liquid slug head. During the ensemble procedure, the sorted liquid slugs form an ensemble with a cumulative slug length distribution shown in Fig. 9. The minimum measured liquid slug length is 4D, set by the single wire sensors spacing. Therefore, the probability of occurrence of LS/D¼ 4 is 100% because all measured slug lengths have at least LS/D ¼4. As the liquid slug length increases, the probability starts decreasing. As seen in the figure, the mean liquid slug ranges from 15D to 17D and the standard deviation is approximately 0.06. The ensemble average procedure is limited to z/Dr15 where the number of available samples is reduced to nearly one half of the original sample. For values of z/D 415 the average values start wiggling, see further discussion on Section 4.3. The last but not the least of the limitations concerns to the uncertainty of the phases flow rate, their influence on the mixture velocity, J, and the uncertainty propagation into the void fraction measurements. Each test lasts nearly 60 min and during this period is difficult to keep the flow rates at fixed value. The intrinsic

100% Test #1 Test T t #2 Test #3 Test #4

75%

25%

0% 10

30

20

40

LS/D Fig. 9. Probability functions of the liquid slug lengths.

Factors

Variable

Absolute uncertainty

Slug head position for αS Contact needle sensor Sample size for ensemble average Phase velocity fluctuations for αU Phase velocity fluctuations for αS

ΔP ΔCN ΔS ΔJ ΔJ

7 0.01 7 0.02 7 0.01 7 0.01 7 0.01

gas and liquid velocity fluctuations are estimated of 3% of J. The impact of phase velocity uncertainty on the void fraction measurement will be estimated on the next section. 4.1.3. Void fraction uncertainty estimate The data uncertainties [39] are estimated based on the set of assumptions given on the previous section and briefed on Table 4 for convenience. The 2th line attributes an uncertainty of 70.01 to αS to the liquid slug head position. The uncertainty on the local void fraction measurement due to the bubble trajectory deviation, the interface piercing process, the probe's distance from the wall and threshold values are represented as the contact needle uncertainty, ΔCN. It is estimated as ΔCN¼ 70.02 and shown on the 3rd line. The ΔCN value is estimated by similarity to previous experiments in air–water flows employing conductive contact needle which had their uncertainty determined against void fraction measurement through quick closing valves, see data report in Table 3 of [41]. The 4th line estimates the uncertainty due to the liquid slug sample size reduction as the liquid slug length increases. As the number of samples reduces the averaged value starts wiggling. Numerical simulations showed a void fraction uncertainty of 70.01 as the sample size reduced to half of the original size. Lastly, the 5th and 6th lines refer to the influence of the mixture velocity fluctuation on the void fraction values at the unit and at the liquid. The absolute uncertainties are estimated by assessing the void fraction sensitivity to J fluctuation employing the drift flux model, Eqs. (20) and (25). The uncertainties of αU and αS were of 7 0.01 for both void fractions. The absolute void fraction uncertainties are shown on Table 5. The columns, from left to right, presents: the variables, their equation of origin, the symbolic representation of the absolute uncertainty, the expression for the uncertainty evaluation and finally its absolute value. In order to perform the uncertainty evaluations the following is considered: (i) the mean slug length and its absolute uncertainty, L S/D and Δ(LS/D), are of 16 and 1 respectively and (ii) the mean liquid slug void fractions, {αS,T } and {αS,E }, are considered the same and equals to 0.26. The uncertainties shown on Table 5 are briefed as follows. The variables: αU(η), αS,T(η) and αS,E(η,ξ), have uncertainties of 70.02; 70.02 and 70.03, respectively. Additionally, the uncertainties of the global variables α U , αS,T and αS,E are, respectively, of 70.02; 70.03 and 7 0.04. 4.2. Unit void fraction radial profiles

50%

0

Table 4 αU or αS uncertainties estimates due primary factors.

50

The unit void fraction radial profiles, as defined in Eq. (8), are shown in Fig. 10. The high void fraction at the pipe core is due to the intermittent passage of the elongated gas bubble but, as the wall is approached, r/R0 40.8, it decreases reaching zero at the pipe wall. Tests #2 and #4, having a higher liquid to gas ratio, exhibit a slight tendency to void fraction peak at r/R0 ¼ 0.6 and then decreases towards the pipe centerline. The difference of the peak to the centerline position is less than 8% of the peak value. The existence of peaks off the pipe centerline are due to the wall peaking void fraction at the liquid slug, to be seen on Section 4.3,

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149

Table 5 Void fractions absolute uncertainties. Variable

Eq. of ref

Absolute uncertainty

α U (η )

Eq. (8)

Δα U

¼

αU

Eq. (10)

Δ αU

¼

Time average-liquid slug Eq. (11) α j (η ) S,T

Eq. (12)

{αS,T (η)}LS

Eq. (13)

αS,T

{αS,E (η1)} αS,E (ξ1)

{ αS,E (λ ) } αS,E

ΔαS,T

¼

Δ{αS,T }

≅

Δ

Ensemble average-liquid slug Eq. (14) αS,E (η, ξ )

Expression

¼

αS,T

ΔαS,E

¼

Eq. (16) Eq. (17)

Δ{αS,E } Δ αS,E

≅ ¼

Eq. (18)

Δ{ αS,E }

¼

Eq. (19)

Δ

≡

αS,E

1.0 10 08 0.8

U

06 0.6 00.4 4 Test #1 Test #2 Test #3 Test #4

0.2 0.0 00 00 0.0

02 0.2

04 0.4

06 0.6

08 0.8

1 1.0

r/R0 Fig. 10. Unit void fraction radial profile.

and to the off center position of the Taylor bubble nose reported in [40]. The void fraction profiles are easily distinguished from each other at the pipe core, r/R0 o0.6, with the values proportional to the ratio JG/J. The radial void profiles exhibited in Tests #2 and #4 are similar because they have the same JG/J. The shapes of the unit void profile shown in Fig. 10 are in qualitative agreement with the ones in [22]. Surprisingly the slug unit radial void fraction profile was just reported on [22] among all reviewed works. Lastly, the flatness of the unit void profile at the pipe core reassures the choice of the drift flux model distribution parameter, C0, of nearly 1.0. 4.3. The liquid slug void fraction profiles along the radial and axial directions

Value

(ΔJ )2 + (ΔCN )2 2 ∑10 i = 1 (2ηi Δηi ) ⋅Δα U ≅ Δα U

(ΔJ )2 + (ΔCN )2 + (ΔP )2 {αS,T }⋅ (

ΔαS,T {αS,T }

)2 + 2 (

ΔLS 2 ) LS

2 ∑10 i = 1 (2ηi Δηi ) ⋅Δ{αS,T } ≅ Δ{αS,T }

(ΔJ )2 + (ΔCN )2 + (ΔP )2 + (ΔS )2 σsv −σsl =σ lv cos θ 2 ∑10 i = 1 (2ηi Δηi ) ⋅ΔαS,E ≅ ΔαS,E

∑m i=1 (

Δξi 2 ) ⋅Δ ξm

αS,E ≡ Δ αS,E

Δ{ αS,E }

¼

70.02

¼

70.02

¼

70.02

¼

70.03

¼

70.03

¼

70.03

¼ ¼

70.04 70.04

¼

70.04

¼

70.04

as observed on Tests #2 to #4. Test #1, in particular, exhibits a less defined radial profile at plane z/D¼ 1 than other runs. It is supposed that the lack of liquid flow rate in Test #1 induces large fluctuations at the interface position not observed along the tests where JL 40. An interesting feature is observed tracking the centerline void fraction: it reaches a maximum at z/D ¼1, decays to a minimum at 3 oz/D o5 and then exhibits a mild growth as z/D increases. This behavior was also found in [24], it was partially detected in [12] and it was not identified in [22]. As the experimental data approaches the plane z/D¼ 15 a data wiggling is observed which is attributed to the data sample reduction discussed on Section 4.1. The shape of the radial void fraction becomes more defined at z/D 45 exhibiting a peak at r/R0 ¼0.80 approximately and then a mild decrease toward r/R0 ¼0. This feature was also observed in [12], partially observed in [22] but not in [24] where core peaking is observed. The observed void fraction wall peak is physically consistent with the gas entrainment process which occurs near the wall. The void profile along the axial direction experiences a sharp change within the near wake, 2D oz/D o5D but exhibits small increment changes at the far wake region, z/D45D, see Fig. 11. This information is in agreement with [24] but in disagreement with [12] and [22] which detected stationary void profile at distances ranging from 6D to 10D. In addition to what has been said, it is not expected that an axial distance of 10D is enough to achieve a stationary void profile within the liquid slug. Accordingly to Liu [26] it is necessary an entrance length of 60D for vertical upward bubble flow. Since liquid slugs seldom achieve lengths over 60D one may speculate that the void fraction within the liquid slugs does not achieve an stationary profile. 4.4. The near wake region void fraction profiles

The liquid slug void fraction profiles are shown in Fig. 1. The solid dots represent the experimental data while the continuous curves are fits along the (r/R0, α) plane to assist data visualization. The radial profiles are displayed at every two pipe diameter spacing in such way to suggest a 3D void fraction distribution as one observes the evolution of the curves (r/R0, α) along the z/D axis. The void fraction profile at the plane z/D ¼1 is usually not well defined due to the strong influence of the gas entrainment process

The near wake region is defined within 2D to 5D downstream the Taylor bubble rear. This region coincides with the region where was found the null shear stress point. It is characterized by an upward flow at the pipe core and by a downward flow near the wall; see streamlines schematic representation in Fig. 1. It is the place where the largest changes on the void fraction profile occurs, see Fig. 12. The near wake region is strongly influenced by the gas

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Fig. 11. Liquid slug void fraction profiles along the radial and axial directions for Tests #1 and #4.

production due the liquid film fragmentation and by the re-coalescence gas flux to the Taylor bubble due the upward flow of liquid and gas. The last mechanism is the responsible to the large changes on the void fraction values. The observed void fraction wall peaking in Tests #2 to #4 is due to the gas entrainment process which also occurs near the wall. As z/D increases the voidage progressively is displaced toward the

pipe centerline while the wall peak values stay approximately constant. Void fraction values reaching nearly 0.40 are observed at z/D o2, indicating an unstable bubbly regime. Test #1 has void fraction profiles near the wall similar to the ones observed in Tests #2 to #4 but they become non similar at the pipe core where the void fraction reaches values as high as 0.9. Test #1 void fraction is redistributed within the near wake zone

Fig. 12. The near wake void fraction profiles for Tests #1 and #4.

E.S. Rosa, M.A.S.F. Souza / Flow Measurement and Instrumentation 46 (2015) 139–154

151

0.5

0.5

T t #2 Test

Test #1 T

0.4

T

04 0.4

0.3 03

00.3 3

0.2

0.2

0.1

0.1 00 0.0

00 0.0 0.0 00

0.2 02

0.4 04

00.66

0.0 00

1.0 10

0.8 08

0.2 02

0.4 04

r/R0

0.6 06

0.8 08

1.0 10

r/R0

0.5 05

0.5 05

Test#3 0.4 0.

Test#4 00.44

E

0.3

0.3

0.2 02

0.2

01 0.1

01 0.1

0.0

0.0 0.0

0.2

0.4

0.6

0.8

1.0

r/R0

0.0

0.2

0.4

0.6

0.8

1.0

r/R0

Fig. 13. Average radial void fraction profile within the liquid slug employing the time and ensemble average procedures identified as ‘T’ and ‘E’ in the figure.

and at z/D¼ 5 the core peaking void fraction no longer exists. This feature is attributed to the lack of a net liquid flow rate in Test #1. 4.5. The liquid slug radial profiles The time and the ensemble averaged liquid slug radial profiles are shown in Fig. 13 as defined by Eqs. (12) and (16). The labels ‘T’ and ‘E’ stand, respectively, for the time and the ensemble average procedures. The continuous line and the open diamonds represent the time average data and the dotted line represents the ensemble average data. The time and the ensemble averages estimates differ by less than 0.04, are within the data uncertainty and lends reliability to the ensemble procedure which is more complex than the time average process. The radial profiles are nearly flat at the pipe core, peaks nearly r/R0 ¼ 0.8 and then drop to zero at the pipe wall. According to [37] this profile shape implies in a C0≅1, which supports the good match obtained on the dispersed bubble velocities shown in Fig. 8. The radial profiles’ shape are qualitatively similar to the ones shown in [12] but not with [22] which exhibits a core peaking tendency. Reference [24] does not show the liquid slug radial profile. 4.6. The liquid slug void fraction profile along the axial distance The local void fraction profiles as a function of the axial coordinate z/D for various radial positions are displayed in Fig. 14. They are grouped for radial positions representative of the pipe core in Fig. 14a, and of the near wall region in Fig. 14b. The split criterion is based on the approximated location of the peak value, r/R0≅0.8. As observed in Fig. 14a and b the axial void fraction profile at the pipe core has a different pattern from the profile near the wall. At the pipe core, the axial void fraction profile has a maximum at the Taylor bubble rear, decreases, reach a minimum at 2r z/D r5, and then exhibits a mild growth rate up to 15D. Near the wall the axial void fraction profile has also a maximum at the Taylor bubble rear, decreases, reach a minimum at 2 rz/Dr 5

and then remains roughly constant for 5 rz/Dr 15 in a regular sequence where the void grows as r/R increases. The axial distance (2 rz/Dr5) where the void fraction is minimum at the pipe core is coincident with the region where the flow detachment point and the null wall shear stress are, see Fig. 1. The superposition of these regions allow us to postulate that the minimum void fraction at the pipe core is induced by the flow detachment point which cause streamlines contraction, accelerate the mixture and decreases the void fraction. Complementary, it is anticipated that the streamlines bottlenecking is one of the flow mechanisms responsible to the gas re-coalescence flux to the Taylor bubble. The existence of a minimum void fraction at the pipe core followed by a mild growth rate was found for all tested points in this work. This behavior was also detected in [24] for liquid velocities lower than 100 cm/s. Reference [12] also detects a minimum and a mild growth rate up to 10D while reference [22] exhibits a monotonic void fraction decrease down to a minimum at 4D to 6D, where the void fraction values remain constant henceforward. The axial void fraction growth rate at the pipe core (r/R0 o0.8) and for 5 o z/D r15 is a puzzling feature observed by this work and also by [24]. This feature may be associated to void fraction redistribution due to the far wake liquid velocity profile. Complementary, at the near wall region (r/R0 o0.8) the void fraction profile for 5 oz/D r15 exhibits a roughly constant value. The observed local void fraction values as high as 0.35 suggest an unstable bubbly regime which probably persists due to the small residence time estimated as 0.72 s, 0.52 s, 0.37 s and 0.26 s for Test #1 thru Test #4 respectively. These complex issues are still open questions. The void fraction axial profile of the averaged liquid slug at the pipe cross section is estimated from Eq. (17). 〈αS,E〉 as a function of z/D is displayed in Fig. 15. The highest 〈αS,E〉 values are registered at the slug head, or z/D¼ 0. As z/D increases, 〈αS,E〉 decreases reaching a minimum within 3 rz/Dr 5 and experiences a mild growth up to z/D ¼15. The mild growth behavior is also inferred from reported data in [24], but this experimental observation is in

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1.0

0.6

Test#1

Test#2

0 10

0.5

r/R=0 70

0.6

0.4 04 S,E

S,E

0.8

/

0.3

0.4 0.2 00.2 2

0.1

0.0

0.0 0

5

10

15

0

5

z/D 00.66

0.5

0.4

0.4 S,E

S,E

Test#4

0.5

0.3

.

0.3

0.2

2 0.2 0

0.1

0.1

0.0

0.0 0

5

10

15

0

5

z/D 00.6 6

Test#1 0.5

10

15

10

15

z/D

0.6

Test#2

0.5

/

0.4

r/R=0.90

0.4 S,E

S,E

15

06 0.6 Test#3

0.3

0.3

0.2

0.2

0.1

0.1

0.0

0.0 0

5

z/D

10

15

0

5

0.6

0.6 Test#3

r/R=0 0 85

0.5

z/D Test#4

0.5 /

00.44 S,E

0.4 S,E

10 z/D

0.3

0.3

0.2

0.2

0.1 01

0.1 0.0

0.0 0

5

z/D

10

15

0

5

z/D

10

15

Fig. 14. Liquid slug void fraction profile along the z/D direction for various radial positions. (a) Axial void fraction profile at the pipe core, 0 rr/Rr 0.7; (b) Axial void fraction profile near the wall, 0.8 r r/R r1.

disagreement with [12] and [22] which measured a stationary void fraction at distances equal or even shorter than 10D. The void fraction mild tendency to grow as z/D is shadowed by the data uncertainty of 70.04 and by the sample size reduction due to the slug length at distances z/Dr15. These constraints limit the range of observation to ascertain if 〈αS,E〉 trend is to approach a constant value asymptotically or not at z/D higher than 15.

Nonetheless, at z/D ¼15 the 〈αS,E〉 values span from 0.25 to 0.28 (70.04) in agreement with the void fraction to bubbly flow regime before transition to the slug regime [29]. A final inspection of Fig. 15 discloses, beforehand, that the mean liquid slug void fraction is dependent on the slug length. A question of practical interest is the evaluation of the mean liquid slug void fraction in terms of the liquid slug axial distance. The

E.S. Rosa, M.A.S.F. Souza / Flow Measurement and Instrumentation 46 (2015) 139–154

0.5 0 5

0.5 Test #1

Test T #2

04 0.4

0.3

03 0.3

0.2

0.2

<

<

S

S,,E>

>

04 0.4

0.1

0.1

0.0

0.0 0

5

10

15

0

5

z/D

z/D

10

15

0.5

0.5 Test #3

Test #4

0.4

03 0.3

03 0.3 S,E E>

0.4

S,E E>

02 0.2

<

<

153

02 0.2 0.1

0.1

0.0

0.0 0

5

z/D

10

15

0

5

z/D

10

15

Fig. 15. Pipe cross section of liquid slug void fraction profile along the z/D direction, see mathematical definition on Eq. (17).

05 0.5 0.4 04

{< <

>}} S,E S >

03 0.3 02 0.2 Test T t #1 Test #2 Test #3 Test #4

01 0.1 00.00 0

5

10

15

z/D Fig. 16. Cross section liquid slug void fraction profile as a function of z/D, see definition on Eq. (18).

evaluation is carried out accordingly to Eq. (18) and is displayed in Fig. 16. The x axis represents the liquid slug axial distance and the y axis is the mean void fraction evaluated from z/D ¼0 to a given axial position. For example, at z/D¼7, the corresponding y scale reading will display the mean void fraction comprised 0 rz/Dr7. The figure shows that as z/D increases the mean void fraction decreases smoothly. It suggests at z/D 411 it approaches an asymptotic value. This implies that liquid slugs shorter than 11D have their void fraction dependent with the length while liquid slugs larger than 11D do not.

5. Conclusions This work combines the use of two distinct conductive sensors and post processing methods employing time and ensemble averages to evaluate the slug flow properties including the spatial liquid slug void fraction distributions as well as the radial void

fraction profile of the slug unit. The distinguished features of this experimental work are: new measurements on the spatial void fraction within the liquid slug, the post processing data procedures and the proposal of data consistence checks. The last feature, allied with the uncertainty analysis, assures the experimental data reliability. The liquid slug void fraction profile is better characterized splitting the liquid slug length into three distinct regions. Next to the Taylor bubble there is the near wake extending up to 5D downstream. The void fraction is highest at the Taylor bubble rear, it exhibits sharp decrease as the pipe axial distance increases reaching a local minimum value somewhere between 2D and 5D. Within the near wake the radial void fraction profile exhibits a peak near r/R0 E0.8 then a mild decrease toward the centerline. An exception applies to Test #1 which having JL ¼0, exhibits a core peaking void fraction. Inside the near wake region the flow has opposite directions: a downward stream close to the wall and an upward stream at the pipe core which is responsible to the gas entrainment and to the gas re-coalescence into the Taylor bubble, respectively. The penetration depth of the downward stream is defined by the axial position where the wall shear stress is null. The second region is the far wake which starts just after the near wake and the gas and liquid streams are on the upward direction. The void fraction grows with a mild rate as the axial distance increases. The radial void fraction distributions peak near r/R0 E0.8 but the difference with the centerline value diminishes, the profiles are almost flat. This behavior was observed for whole test matrix including Test#1 with JL ¼0 indicating that the lack of liquid flow rate did not alter the axial void fraction distribution. The liquid slug radial void fraction profiles changes are small at the pipe core but may exhibit a peak near the wall. Lastly, the third region is denoted as fully developed corresponding to a stationary void profile. This region was not detected experimentally within the experimental window of 15D downstream the Taylor bubble rear. The axial void fraction profile exhibits distinct behavior at the pipe core and near the wall along the near and far wake regions. At

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the pipe core the void fraction has a maximum at the Taylor bubble rear, attains a minimum at 3 rz/D r5 and has a mild growth up to the end of the measuring window. The near wall void fraction has a maximum next to the Taylor bubble rear; within 1 rz/Dr7 the void decays, attains a minimum and has a mild growth and at z/D4 7 it stays roughly constant from this point forward. The average liquid slug void fraction value may depend on the liquid slug length. Short slugs tend to have a higher void fraction value than longer slugs due to the sharp void fraction variations within the near wake region. The drift flux model can be applied successfully at the far wake but its application on the near wake is not advised unless a new value to the distribution parameter C0 is established to account to the two way flow characteristic of this region. Of practical interest are the estimates of the slug unit, the liquid slug average void fractions as well as the estimates of the gas and liquid volumetric fluxes at the liquid slug. The averaged slug unit void fractions are proportional to the gas to mixture velocity ratio. The averaged values of the liquid slug void fraction span from 0.24 to 0.27 despite of having local measurements which may attain as high as 0.40.

Acknowledgments M.A.S.F. acknowledges CNPq for the receipt of his doctoral scholarship during this work. The authors also acknowledge the receipt of a financial support from Petrobras, under Grant no. 0050.0022719.06.4.

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