On the characteristics of the roll waves in gas–liquid stratified-wavy flow: A two-dimensional perspective

Experimental Thermal and Fluid Science 65 (2015) 90–102

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On the characteristics of the roll waves in gas–liquid stratified-wavy flow: A two-dimensional perspective Tayfun B. Aydin ⇑, Carlos F. Torres, Hamidreza Karami, Eduardo Pereyra, Cem Sarica McDougall School of Petroleum Engineering, The University of Tulsa, 800 South Tucker Drive, Tulsa, OK 74104, USA

a r t i c l e

i n f o

Article history: Received 4 September 2014 Received in revised form 22 December 2014 Accepted 12 February 2015 Available online 11 March 2015 Keywords: Stratified-wavy Two-phase flow Wave characteristics Wire Mesh

a b s t r a c t The characteristics of the roll waves in the oil–gas, stratified-wavy flow are studied experimentally in a 0.152 m ID horizontal pipe for superficial gas velocities between 7.45 m/s and 12.62 m/s at two different liquid superficial velocities, 1 and 2 cm/s. The liquid holdup, liquid film height, wetted wall perimeter decrease with the increasing superficial gas velocity. The interfacial surface area is calculated from the distinct interface between the phases from the experimental data without any assumptions on the interface geometry. The variation of the interfacial surface area is found to be closely related to the liquid holdup. The region where the interface fluctuations spread in the pipe cross-section is analyzed. For low gas flow rates, a small region exists where the fluctuations are negligible implying a continuous liquid contact with the pipe bottom. However, an increase in the superficial gas velocity extends the spatial reach of the interface fluctuations very close to the pipe wall at the bottom where the continuous liquid region diminishes. For all experimental conditions examined, the interface fluctuations occurring at a frequency range of 10 Hz < f < 40 Hz is hypothesized to be related to the capillary waves. At low superficial gas velocities, the roll wave topology is stretched toward the sides of the pipe. Moreover, the oscillations of these waves at different transverse locations are out-of-phase. With an increase in the gas flow rate, the wave oscillations are observed to be in-phase with each other and more coherent structures are detected. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction The physical understanding of the gas–liquid two-phase flow in a circular pipe is important for the flow assurance purposes in petroleum engineering applications, but it poses a great challenge due to the complexity of the flow field. In pursuit of a systematic investigation of this multi-phase flow phenomenon, past researchers have identified several flow regimes depending on a wide range of influential parameters such as the pipe geometry, flow conditions and physical properties of the fluids [1]. The segregated coflow of the liquid phase with the gas phase, referred to as stratified flow, is one of the flow regimes occurring in a horizontal pipe. Stratified flow with low liquid loading conditions is common in gas production wells and transmission pipelines, where low liquid loading refers to a ratio of the liquid volumetric flow rate to the gas volumetric flow rate (at standard conditions) less than 1100 m3/ MMsm3 [2]. In addition, small amounts of liquid present in this flow configuration is representative of the operational conditions for the wet-gas pipelines, where liquid condensation occurs during ⇑ Corresponding author. http://dx.doi.org/10.1016/j.expthermflusci.2015.02.013 0894-1777/Ó 2015 Elsevier Inc. All rights reserved.

the transport of the single-phase natural gas through the pipe. This can lead to a considerable increase in the pressure drop compared to the single-phase case [3]. Therefore, accurate predictions of insitu liquid holdup and pressure drop within in a pipeline is important especially for determining the pigging frequency, the design of the receiving facilities, and the required size and material of the pipe [4]. Several models have been proposed for the predictions of the pressure gradient and the liquid holdup related to the gas–liquid two-phase flow in horizontal pipes [1,3,5–10]. In these two-fluid models, the flow topology and friction factors are the major closure relationships in the combined momentum balance, and have direct impact on the accuracy of the predictions. The gas–liquid interface is one of the important closure parameters, and is subject to different approaches in the modeling such as flat interface [1,6], double circle [9] and apparent rough surface [3,8]. While these definitions aim to represent the time-average interface topology, the underlying physics is still not well understood. The flow structures at the interface are summarized by Hewitt and Hall-Taylor [11], and Chen et al. [9]. According to these studies, the interface changes from a smooth, flat surface to a wavy surface

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List of symbols

aG

gas void fraction arbitrary constants wave celerity based on hL wave celerity based on h pipe diameter time resolution pressure drop eL dielectric constant of the liquid eG dielectric constant of the gas em instantaneous permittivity values based on the Wire Mesh measurements 2HL uncertainty in liquid holdup q uncertainty in the variable of interest f frequency Df frequency resolution hL liquid film height HL liquid holdup i, j, k, m indices M, M0 number of intervals m degrees of freedom l dynamic viscosity q density s surface tension VL calibration measurements for the liquid VG calibration measurements for the gas c1, c2 C hL Ch D Dt dp/dL

as the superficial gas velocity is increased. These waves are classified as two-dimensional, three-dimensional (squalls) and roll waves (Kelvin–Helmholtz waves) with increasing gas flow rate. After a critical superficial gas velocity is achieved, the droplets of liquid are sheared from the interfacial waves and entrained into the gas phase. These flow structures are illustrated in Fig. 1, which is taken from Chen et al. [9]. Related to these flow structures, different mechanisms are proposed for the transport of the liquid phase; secondary gas flow structures [12], wave spreading [13], and entrainment/deposition [14,15]. There are several research studies on low-liquid loading [4,14–17]. Meng et al. [14] showed that liquid entrainment into the gas phase plays an important role in the variation of the liquid holdup. Badie et al. [15] showed that the intermittent waves on the gas–liquid interface are responsible for liquid entrainment. Fan [16] compared his experimental data with the Beggs and Brill correlation [18], Zhang et al. model [19] and Hart et al. model [8]. He showed that these models do not predict the pressure drop and the liquid holdup accurately, especially for larger pipe diameters. The incorporation of the flow physics associated with the stratified-wavy flow into the current mechanistical models is limited to one-dimensional analysis due to the complex flow field. The dynamics of the axial waves are not studied in detail from a two-dimensional perspective, which can limit our knowledge on the unsteady flow phenomenon occurring at the phase interface. It is also clear from the presented literature that there is still need for further understanding on the flow topology for larger pipe diameters, which will improve the closure relationships in the two-fluid models. In recent years, high-speed cameras and Wire Mesh sensors are used for the flow diagnostics tools in multiphase research, and yield detailed quantitative and qualitative information on the flow topology [20–22]. Therefore, this study focuses on the features of the interface topology and the wave dynamics in oil–gas, two-phase stratified-wavy flow at a large pipe diameter by facilitating the Wire Mesh sensors and a hi-speed camera.

Vlog

mSG mSL Qj qj  q s, s0 t tM,0.05 x, y h hL hR w wi

measured logarithmic signals at the crossings of the Wire Mesh sensor superficial gas velocity superficial liquid velocity normalized parameter mean of the variable of interest in the jth interval total mean of the variable of interest standard deviations time t percentile distribution with 95% confidence cartesian coordinates centered at the pipe center wetted wall perimeter wetted wall perimeter on the left side of the pipe wetted wall perimeter on the right side of the pipe weighting coefficient matrix ith wave defined based on the interface topology

Abbreviations QCV quick closing valve WMS Wire Mesh Sensor IC interface coordinate vector DFT Discrete Fourier Transformation PSD power spectrum density sys systematic ran random

2. Experimental setup and data processing techniques 2.1. Experimental Setup The experiments are conducted at the Tulsa University Fluid Flow Projects (TUFFP) low pressure flow loop (see Fig. 2). This flow loop is able to handle two-phase oil–gas flow. The test section consists of two runs, and each run is built with 0.152 m ID pipes running for 56.4 m in length. The pipe is made of acrylic glass at the section of data acquisition. The inclination angle of the test section is set to be horizontal. The liquid phase is mineral oil (IsoparL™, q = 760 kg/m3, l = 1.35 cP, s = 24 dynes/cm), and is pumped from the container tank by using a Blackmer™ progressive cavity pump (PV20B) with maximum pumping capacity of 11.5 GPM for the pressure and temperature conditions prevailing in the experiments. Compressed air is continuously supplied to the flow loop by a diesel powered portable rotary screw compressor, and an electric powered stationary two-stage compressor connected in parallel with a combined capacity of 1030 SCFM at 100 psig. The oil and the air are mixed using a specially designed mixing tee (for details, see Gawas [17]). After the oil and the air flow through the flow loop, the phases are separated by a preliminary separator followed by a vertical final separator. The air is vented out to the atmosphere, and the oil is re-circulated to the storage tank. During the experiments, the air flow rate is measured using Micro Motion CMF300 Coriolis mass flow meter located before the mixing tee. Oil flow rate and density are monitored using Micro Motion CMF100 mass flow meter. The calibrations of the flow meters are performed by the manufacturer and have a mass flow rate uncertainty of ±0.1% of the measured flow rate. The density measurements have an uncertainty of ±0.5% of the measured value. Table 1 presents the superficial velocities of the gas and the liquid phase for the cases investigated in this study. The uncertainty in the superficial velocities, also given in Table 1, represents the standard deviation of the flow rate measurements at the inlet by the aforementioned flow meters.

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HZDR-Innovation GmbH, Dresden, Germany. In this study, a dual sensor configuration, each sensor having a 32  32 wires, was utilized (Fig. 3). The use of dual WMS is for the purpose of the quantification of interfacial structure velocity at given experimental conditions, and is adopted by several other researchers in recent years [23–28]. However, the data from the first WMS is used to calculate time-averaged flow quantities such as liquid holdup, liquid film height, wetted wall perimeter and interfacial surface area. The effect of the WMS intrusiveness on these quantities is considered minimal based on the comparisons of WMS data with other non-intrusive tomographic techniques reported in the literature [29–35]. The sensors are installed in the second run of the flow loop (Fig. 2). The sensors are separated by a distance of 0.02 m from each other, which ensures a good cross-correlation peak from the signals. The data is acquired at a sampling frequency of 250 Hz for 200 s. 2.2. Data processing techniques 2.2.1. Spatially averaged liquid holdup The WMS data yields the instantaneous local mixture permittivity values, em(i, j, k), measured within a volume of 2.00 mm (distance between the transmitting and receiving wires of WMS)  4.75 mm (WMS grid resolution)  4.75 mm (WMS grid resolution) using the serial model [22] in conjunction with the gas and liquid calibration data, and is given by

Fig. 1. Regimes of horizontal stratified-wavy flow [9].

For each case considered, the liquid was trapped with two quick-closing ball valves (QCV) in the test section, and is drained from the pipe via a pigging mechanism. Then, the volume of the drained oil was measured with graduated cylinders. Finally, a liquid holdup value was calculated as the ratio of the volume of the drained liquid to the total volume between the two quick-closing valves (2  105 mL). The interface topology was visualized by using a high-speed camera (Photron FastCam SA3) operated at a sampling frequency of 500 Hz located at the first run of the flow loop (Fig. 2). In order to avoid image distortions, a visualization box has been installed. The camera is located at the bottom of the pipe, and is directed in an upward orientation with its axis perpendicular to the visualization box. An imaging lens (50 mm, f#1.8) is installed on the camera, and the still images of the flow are captured using a shutter speed of 1/40,000 s. Instantaneous phase distributions across the pipe cross-section are obtained by using the capacitance Wire Mesh Sensor (WMS) developed by Da Silva et al. [20] and supplied by

em ði; j; kÞ ¼ exp



 V log ði; j; kÞ  V G ði; jÞ lnðeL Þ : V L ði; jÞ  V G ði; jÞ

ð1Þ

In Eq. (1), the indices i, j and k represent the x and y coordinates for the measurement cell and data acquisition time, respectively. VG(i, j) and VL(i, j) are the local permittivity measurements for the same cell from the WMS calibration corresponding to the experimental conditions completely filled with gas (air) and liquid (oil), respectively. eL is the dielectric constant for the liquid phase (oil). Following the determination of em(i, j, k), the instantaneous percentile liquid holdup, HL(i, j, k), is calculated as

HL ði; j; kÞ ¼ 100  aG ði; j; kÞ ¼ 100 

eL ði; jÞ  em ði; j; kÞ ; eL ði; jÞ  eG ði; jÞ

ð2Þ

where the dielectric constant of the gaseous phase (air) eG is assumed to be 1. At this point, it is possible to compute the time traces of spatially averaged liquid holdup, HL(t), as

HL ðtÞ ¼ HL ðkÞ ¼

! 32 X 32 X HL ði; j; kÞwði; jÞ ;

ð3Þ

i¼1 j¼1

which represents the instantaneous liquid holdup measured by WMS. In Eq. (3), w(i, j) represents the weighting coefficient matrix

Fig. 2. Schematic of the flow loop and the layout of the measurement instrumentation. Schematic is not scaled. (DP: Differential Pressure Transducer).

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T.B. Aydin et al. / Experimental Thermal and Fluid Science 65 (2015) 90–102 Table 1 Superficial gas and liquid velocities, and associated uncertainties during the experiments. Case #

1

2

3

4

5

6

7

8

9

10

mSG (m/s) DmSG (m/s) mSL (cm/s) DmSL (cm/s)

7.94 0.675 1.00 0.003

9.32 0.526 1.00 0.004

10.69 0.664 1.00 0.004

11.96 0.386 1.00 0.002

12.34 0.326 1.00 0.002

7.45 0.348 1.98 0.005

9.25 0.602 1.99 0.010

10.83 0.626 2.00 0.006

12.12 0.390 2.00 0.002

12.62 0.178 1.99 0.003

Fig. 3. Two Wire Mesh sensors installed on the flow loop (left), and a close-up view of the sensor wires inside the pipe (right).

that accounts for the surface area over which HL(i, j, k) give the liquid holdup. 2.2.2. Liquid film height In this study, the liquid film height (hL) is defined as the lateral distance from the oil/gas interface to the pipe wall along the lateral line crossing through the pipe center. The evaluation of this length scale relies on the distinctive patterns of local liquid holdup values, HL(i, j, k), due to the lack of entrainment of the liquid phase into the gas phase or vice versa; the liquid phase is fully segregated from the gas phase via the gravitational force and is transported at the bottom of the pipe. In order to compute the film height, initially, the liquid holdup profile at the pipe center is extracted from WMS measurements by a spatial averaging given by,

HL ðj; kÞ ¼

 1 X17 HL ði; j; kÞ ; i¼16 2

ð4Þ

where the data columns with i = 16 and 17 correspond to the local holdup measurements at either sides of the lateral line passing the pipe center. Then, the measurement cell containing the phase interface is found with the use of the following two criteria given by

P32 HL ðj; kÞ > c1

j¼8 HL ðj; kÞ

25

ð5Þ

and

P32   dHL  H ðj; kÞ   ¼ HL ðj; kÞ  HL ðj; kÞ > c2 j¼8 L :  dy  25

ð6Þ

In Eqs. (5) and (6), the c1 and c2 are arbitrary constants, and the boundaries of the summation index (j) is selected such that the nodal points j = 8 and j = 32 correspond to the cell locations y/ D = 0.23 and 0.47, respectively, relative to the pipe center. Finally, the liquid film height is quantified using a linear interpolation based on the liquid holdup value of the cell identified using these two criteria; Eqs. (5) and (6). 2.2.3. Wetted wall perimeter The wetted wall perimeter is defined as the ratio of the circumferential arc length wetted by the liquid (oil) to the pipe circumference. This ratio is calculated, again, based on the distinctive patterns of the local holdup measurements encountered in all experiments, as mentioned in Section 2.2.2. The method can be

explained based on the sketch given in Fig. 4. Initially, the liquid holdup profile along the measurement cells closest to the pipe wall along its circumference for y/D < 0, is stored in a separate vector of variable. These cells are denoted in Fig. 4 with indices from m = 1 to 20. Then, the y coordinate of the phase interface at either side of the pipe centerline is identified from this liquid holdup vector by using Eqs. (5) and (6) and linear interpolation as discussed earlier. The locations of these interface points are given by points A and B in Fig. 4. From the locations of points A and B, the wetted perimeter (h) is calculated as

h ¼ hR þ hL :

ð7Þ

In the experimental data, there are WMS cells in which measurements of liquid holdup are not possible due to the WMS grid resolution (colored in 1red in Fig. 4). The unavailability of the liquid holdup information within those cells makes it necessary to model the interface shape across those red cells, i.e. from points A and B to the pipe wall. In this study, this assumed local interface shape is selected to be flat. Thus the y coordinates of points A and B are sufficient to quantify the wetted wall perimeter. This assumption on the local interface shape is considered to lead to minimal deviations from the actual interface since the highly curved shapes are modeled for smaller pipe diameters [3,8,9].

2.2.4. Random uncertainty in mean values of measured quantities The random uncertainty in the various flow quantities presented in this study is quantified based on a statistical approach previously proposed by Barral and Angeli [36]. This approach breaks down the whole data (50,000 data points sampled for 200 s) into smaller intervals with 2500 data points (10 s). Then, a normalized parameter (Qi) is calculated in order to compare with the t distribution percentile (90% confidence level) by

Qj ¼

j pffiffiffiffiffi jqj  q M; s

ð8Þ

where M = 20, qj is the mean value of the variable of interest in jth  and s are the total mean and the standard interval (j = 1, 2, . . . , 20), q deviation of the variable of interest. The intervals are accepted if 1 For interpretation of color in Figs. 4 and 8, the reader is referred to the web version of this article.

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Fig. 4. Determination of wetted wall perimeter.

Q j 6 t M;0:05 . Then, the random uncertainty in the estimation of the mean (for the variable of interest) is calculated by

s0 t m;0:05 ðeq Þran ¼  pffiffiffiffiffiffi0 ; M

ð9Þ

where s0 is the standard deviation of the M0 intervals which pass the evaluation based on Eq. (8), and m = M0  1. 3. Results The experimental results on the two-phase gas–oil flow will be presented in three sections; (i) time-averaged quantities (in Section 3.1), (ii) unsteady features (in Section 3.2) and (iii) wave topology (in Section 3.3). 3.1. Time-averaged quantities Variations of the pressure gradient (dp/dL) and liquid holdup (HL) are presented in Fig. 5 as a function of vSG, whose range is given in Table 1, for vSL of 1 and 2 cm/s. The pressure gradient and liquid holdup vary inversely related as the superficial gas velocity is increased; pressure drop increases from approximately 10 Pa/m to 30 Pa/m (for both vSL = 1 and 2 cm/s) and holdup decreases from 2.5% to 1.4% (for vSL = 1 cm/s) and from 4.6% to 2.5% (for vSL = 2 cm/s). While the change in the liquid flow rate does not have a significant impact on the variation of the pressure gradient, the holdup increases with the superficial liquid velocity at a constant superficial gas velocity. These variations are consistent with Fan [16]. In Fig. 5, the liquid holdup values are measured by QCV, which have a systematic uncertainty of ±5% of the measured value [16]. On the other hand, the error bars given for the pressure gradient represent the random uncertainty calculated as the standard deviation of the pressure drop measurements, which are averaged among the four measurement stations given in Fig. 2. Finally, the uncertainties presented for vSG in Fig. 5 are based on Table 1. As a next step, the mean values of the liquid holdup measured by WMS (over the pipe cross-section) are compared with the measurements by QCV. This comparison is given on the left side of Fig. 6, where the vertical and horizontal axes represent the results from WMS and QCV, respectively. In this figure, the uncertainty in QCV measurements (horizontal error bars) are the same with the uncertainties given in Fig. 5. The uncertainty in the WMS results (vertical error bars) is given as the combination of the systematic and random uncertainties using



eHL

WMS

¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  eHL sys þ eHL 2ran :

ð10Þ

In Eq. (10), ðeHL Þsys represents the systematic error in the measurements with WMS, and is quantified based on the measurements in a pipe segment outside the flow loop. In these

Fig. 5. Variation of the pressure drop and the liquid holdup as a function of vSL = 1 and 2 cm/s.

vSG at

calibration tests, a certain known amount of oil, measured by graduated cylinders, is filled into a horizontal pipe segment, in which WMS is installed. Then, WMS data is acquired in stagnant fluid conditions. The results from these tests are given on the right side of Fig. 6. The vertical axis of this plot represents the absolute value of the deviation in the liquid holdup measured by WMS from the values measured by the graduated cylinders. This deviation is considered as the systematic uncertainty, and the best power curve fit to the presented data (represented by the solid line in the plot to the right of Fig. 6) is given by

ðeHL Þsys ¼ expð0:388logðHL Þ  0:746Þ:

ð11Þ

In this Fig. 6, the upper limit for the liquid holdup is 9.8% which is well above the actual experimental results presented in Fig. 5. Therefore, the results of the static tests on WMS sensor are considered sufficient to quantify the systematic uncertainty in the liquid holdup measurements during the experiments. The comparison of the liquid holdup measured by WMS and QCV (in Fig. 6) shows that the WMS measurements are, overall, in good agreement with the values measured by QCV within the uncertainty bounds. The variations of the liquid film height, hL/D, and wetted wall perimeter, h, with the gas superficial velocity are given in Fig. 7 at superficial liquid velocities of vSL = 1 and 2 cm/s. The liquid film height and the wetted wall perimeter both decrease with increasing superficial gas velocity. This implies a decrease in the total liquid holdup with increasing superficial gas velocity, which is consistent with Fig. 5. On the other hand, at a constant vSG, increasing the

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Fig. 6. The comparison of the liquid holdup measured by WMS and QCV (on the left), and the calibration tests on WMS (on the right).

Fig. 7. The variations of the liquid film height (hL) and wetted wall perimeter (h) with the gas superficial velocity at different superficial liquid velocities.

superficial liquid velocity leads to an increase in both quantities which is, again, consistent with Fig. 5. Based on these variations (presented in Figs. 5–7), the total surface area through which the liquid flows can be shown to decrease with increasing gas flow rate. Although the actual phase velocity measurements are not conducted in this study, abovementioned situation implies an increase in the time-averaged linear momentum of the liquid phase. The increased momentum is a result of the increased energy transfer from the gas phase to the liquid phase. As shown in Fig. 5, the pressure drop values are shown to increase with the superficial gas velocity, which supports these described dynamics. 3.2. Unsteady features In this section, unsteady features of the roll waves are discussed. As a first step, spectral analysis is performed on the time traces of the liquid film height (hL), wetted wall perimeter (h) and the total liquid holdup in the pipe cross-section (HL) for vSG = 9.3 m/s and vSL = 1 cm/s, whose mean values were previously presented in Figs. 6 and 7. The analysis employs an ensemble averaged Discrete Fourier Transformation (DFT) on 48 windows, each with 1024 data points (4.1 s), formed from the long sample with 50,000 data points (200 s). The resulting normalized PSD

distributions are presented in Fig. 8(a)–(c) (red lines) for hL, h and HL, respectively. Since the sampling frequency of those signals is 250 Hz (as mentioned in Section 2), the Nyquist frequency is 125 Hz, and the frequency resolution in DFT analysis is Df = 0.24 Hz. However, the selection of this cut-off frequency needs justification. The information on the higher frequencies for each signal (125 Hz 6 f 6 1000 Hz) at the similar superficial gas and liquid velocities is provided by the blue lines in Fig. 8, which are obtained with a similar type of spectral analysis (with a window size of 4096 data points or a window duration of 1.6 s) applied on data sampled at 2500 Hz [37]. In Fig. 8, it can be observed that the PSD distributions given by the red lines (acquired at 250 Hz) coincide with the blue lines (acquired at 2500 Hz) in the frequency range of 10 Hz 6 f 6 125 Hz while some discrepancies are observed for low frequencies (f < 10 Hz) where the most dominant frequencies exist. Also, the spectral analysis represented by the red lines are accepted as a more accurate description of the wave frequencies, especially for the low frequencies, since the sampling time for the window (4 s) is larger compared to the window represented by the blue lines (1.6 s). Therefore, it is concluded that the cut-off frequency (125 Hz) provides sufficient information on the frequency components of the analyzed signals.

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Fig. 8. Normalized power spectrum density (PSD) distributions of the liquid film height (hL), wetted wall perimeter (h) and the total liquid holdup in the pipe cross-section (HL) given in (a), (b) and (c), respectively.

In order to explore the distributions of the frequency components with an increase in the superficial gas velocity, the spectral analysis is applied to both signals (hL, h) and the liquid holdup (HL) for two cases; (i) vSG = 7.9 m/s and vSG = 11.9 m/s (vSL = 1 cm/ s). The corresponding PSD distributions are given in Fig. 9. It is observed that the amplitude of oscillations inhabit a broad-band nature for a frequency range of 1 Hz 6 f 6 125 Hz. This is an expected behavior for the roll waves. However, there are some frequencies at which the spectral amplitudes attain large amplitudes. When the superficial gas velocity is high (vSG = 11.9 m/s), the visual inspection of the plot on the right side of Fig. 9 shows that there is a single dominant frequency (f1 = 4.4 Hz) in all PSD distributions. However, for the case with low superficial gas velocity (vSG = 7.9 m/s), the plot on the left side of Fig. 9 reveals two dominant frequencies for the wetted wall perimeter (f1 = 2.9 Hz and f2 = 5.6 Hz) while there is only one dominant frequency associated with the liquid holdup and liquid film height signals (f1 = 2.9 Hz). Another interesting finding derived from Fig. 9 is related to the relatively high amplitude of oscillations for the liquid film height signal at a frequency range of 10 Hz < f < 40 Hz. These frequencies represent a broad-band phenomenon, are typically higher than the roll wave frequencies (f < 10 Hz), and are hypothesized to contain oscillations originating from the capillary waves. In pursuit of an explanation for the multiple frequency peaks observed only for low gas flow rates, the signals of the liquid film

height and wetted wall perimeter obtained from dual WMS are cross-correlated. The analysis of liquid film height gives the wave celerity for the axial waves travelling at the pipe center. However, the wave celerity values obtained from the cross-correlation of the wetted wall perimeter signals are related to the passage of the axial waves at either sides of the pipe centerline close to the pipe wall. Therefore, the values of wave celerity based on the liquid film height (C hL ) and wetted wall perimeter (Ch) are associated with the axial waves travelling at different transverse locations within the pipe. Based on the analyses, the values of C hL and Ch are calculated as 0.743 m/s and 0.625 m/s for vSG = 7.9 m/s and vSL = 1 cm/s, respectively. On the other hand, for vSG = 11.9 m/s and vSL = 1 cm/s, these values increased to C hL ¼ C h ¼ 1:25 m=s. At first glance, for low superficial gas velocities, there seems to be a difference at the wave celerity values passing at different locations of the flow within the pipe while the waves seem to travel at the same speed at high superficial gas velocities. However, this might be a result of the temporal resolution of the data acquired at 250 Hz. In order to clarify this question, same analysis is applied to the data from Aydin et al. [37] for low gas flow rates that was acquired at 2500 Hz. Based on this analysis, it is found that C hL ¼ 0:86 m=s and Ch = 0.82 m/s for vSG = 9.2 m/s and vSL = 1 cm/s. These results conclude that the waves at different transverse locations travel at the same speed within the temporal resolution of the experimental data.

Fig. 9. PSD distributions for liquid film height (hL), wetted wall perimeter (h) and the total liquid holdup in the pipe cross-section (HL); vSG = 11.9 m/s on the right (both for vSL = 1 cm/s).

vSG = 7.9 m/s

on the left, and

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Fig. 10. Time traces of the liquid film height (hL), the wetted wall perimeter on the right and left sides of the pipe centerline (hR and hL) and the total wetted wall perimeter (h) given for 1 s at vSG = 7.9 m/s (top), and vSG = 11.9 m/s (bottom) both for vSL = 1 cm/s.

For a more in-depth understanding of the wave dynamics, the phase relationships in the liquid film height and wetted wall perimeter signals are presented in Fig. 10 for at vSG = 7.9 m/s (top), and vSG = 11.9 m/s (bottom) both for vSL = 1 cm/s. In this figure, the wetted perimeter oscillations at the right and left sides of the pipe centerline (hR and hL) are also given. Visual inspection of the signals show that, for vSG = 7.9 m/s, the correlation of hR and hL is weak. This implies that the waves with a frequency of f1 = 2.9 Hz are out-of-phase with each other at opposite sides of the pipe centerline, which, in return, leads to significant oscillations at a frequency (f2 = 5.6 Hz) almost twice of f1 = 2.9 Hz. On the other hand, for vSG = 11.9 m/s, the signals are well correlated,

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implying a more coherent wave structure along the transverse direction. This results in a single frequency peak (f1 = 4.4 Hz) in Fourier analysis, which was previously presented in Fig. 9. So far, these results have been compiled from the low superficial liquid velocity conditions. Therefore, it is of interest to expand similar analyses to the cases where the liquid flow rate is relatively higher, i.e. vSL = 2 cm/s. For this purpose, PSD distributions are presented in Fig. 11 for different gas flow rates; (i) vSG = 7.4 m/s (left), (ii) vSG = 10.8 m/s (middle) and (iii) vSG = 12.6 m/s (right). On the left side of Fig. 11, PSD distributions are observed to be similar to the case of vSG = 7.9 m/s and vSL = 1 cm/s (Fig. 9); the dominant frequencies in the wetted wall perimeter show an additional peak compared to the PSD distribution of the liquid film height. This result shows that the out-of-phase behavior of the axial waves that occur at different transverse locations prevail for higher superficial velocities of the liquid phase. On the other hand, as the gas flow rate is increased from vSG = 7.9 m/s to vSG = 12.6 m/s (at vSL = 2 cm/s), the PSD distributions (in Fig. 11) show that the dominant frequencies with high PSD amplitudes are shifted toward right along the frequency axis indicating an increase in wave frequencies with increasing gas flow rate (vSG). The ensemble averaged PSD distributions provided valuable information on the unsteady features of the interfacial roll waves in two-phase stratified-wavy flow. However, the presented PSD distributions can only be interpreted from a time-averaged perspective. To investigate the temporal features of PSD distributions, a special type of analysis is carried out on the wave signals for vSG = 7.9 m/s and vSG = 11.9 m/s (vSL = 1 cm/s), whose time-averaged PSD distributions were previously presented in Fig. 9. This analysis is referred to as time–frequency analysis, and employs the same DFT method used for ensemble averaged results. However, the whole signal is not broken down into 48 separate windows, as it was the case for the results presented in Figs. 8, 9 and 11. Instead, the window (with 1024 data points) is translated along time axis with a 95% overlap ratio between the consecutive windows. As a result, the temporal changes in PSD distributions can be stored in a two dimensional matrix, PSD(f, t). The iso-contours of this matrix are plotted in Figs. 12 and 13 for the superficial gas velocities of vSG = 7.9 m/s and vSG = 11.9 m/s (vSL = 1 cm/s), respectively. The contour plot is constructed such that the spectral amplitudes lower than 40% are masked (with black) to provide visual clarity, and the light gray colored contours represent amplitudes higher than 40%. On each figure, the analysis is performed for the liquid film height signal on the left, and the wetted wall perimeter on the right. Also, the resolution in the frequency and the time axes is Df = 0.24 Hz and Dt = 0.21 s, respectively. Based on the results presented in Figs. 12 and 13, the wave frequencies for both signals (at high and low superficial gas velocity)

Fig. 11. PSD distributions for liquid film height (hL), wetted wall perimeter (h) and the total liquid holdup in the pipe cross-section (HL) at vSL = 2 cm/s for vSG = 7.4 m/s (left), vSG = 10.8 m/s (middle) and vSG = 12.6 m/s (right).

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Fig. 12. Time–frequency analysis on the liquid film height signal (left) and the wetted wall perimeter wave signal (right) (vSG = 7.9 m/s and Dt = 0.21 s).

vSL = 1 cm/s,

Df = 0.24 Hz,

Fig. 13. Time–frequency analysis on the liquid film height signal (left) and the wetted wall perimeter signal (right) (vSG = 11.9 m/s and vSL = 1 cm/s, Df = 0.24 Hz, Dt = 0.21 s).

are observed to be highly unsteady and show a broad-band characteristic for the majority of the time. If the waves contained a stable wave frequency, then, one should see a horizontal line at a given frequency as opposed to the observed scattered contours. At vSG = 7.9 m/s (Fig. 12), the frequency range, at which the PSD amplitudes are high, is shifted slightly upwards for the wetted wall perimeter oscillations compared with the oscillations in liquid film height. This upward shift in frequency is in agreement with the previous discussion related to the out-of-phase relationship between the axial waves (Figs. 9 and 10). To provide visual reference to this shift in the dominant frequencies, red dashed lines are superimposed onto the contour plots in Fig. 12. On the other hand, at vSG = 11.9 m/s (Fig. 13), the frequency ranges with high amplitude oscillations for both signals coincide with each, which is, again, consistent with Fig. 9. Next, the spatial distribution of interfacial fluctuations is investigated in the pipe cross-section. For this purpose, DFT analysis is performed at each WMS measurement cell on the signals of the local liquid holdup. Then, the amplitude of resulting PSD distribution at a given frequency is stored in a two-dimensional matrix; PSD(fi). When the iso-contours of PSD(fi) are compared in Fig. 14(a) and (b), for fi = 2.9 and 5.6 Hz at vSG = 7.9 m/s, respectively, the spatial spread of the interfacial wave oscillations are observed by the high amplitude regions of PSD which are related to the wave occurrences. A small region is observed below the high amplitude PSD contours in Fig. 14(a)–(c). The low PSD amplitudes in this region implies that the oscillations in the interfacial waves do not have an amplitude high enough to touch the pipe bottom. Previously, it was shown that the liquid film height, wetted wall fraction and liquid holdup vary inversely with the superficial gas velocity (Figs. 5 and 6). With increasing mSG, the decrease in the liquid amount is consistent with the diminishing of the region with low PSD amplitudes below the phase interface, shown in Fig. 14(d) and (e). A final observation on Fig. 14(c) and (e) is that the spatial spread of the oscillations occurring at 20 Hz (hypothesized to be associated with capillary waves) seems very similar

to the axial waves instability region for both superficial gas velocities. 3.3. Wave topology In this section, experimental results on the features of the wave topology are presented. Initially, the flow visualization results are given in relevance to the previous discussions on the change in the phase relationship of the axial waves at different transverse locations from out-of-phase to in-phase oscillations as the superficial gas velocity is increased. From these findings, it should also be recalled that the investigated interfacial wave structures are highly unsteady. Therefore, the main goal of the flow visualization experiments is to reveal the variance in the wave topology in a qualitative manner. For this purpose, the wave structures are visualized for two cases; (i) vSG = 7.9 m/s and (ii) vSG = 11.9 m/s both for (vSL = 1 cm/s), and are given in Fig. 15. On each photograph given in Fig. 15, a length scale of 25.4 mm has been added, and the flow is from left to right. The presented snapshots in this figure are representative of oil/gas interface under the given flow conditions, and the actual visualization can be viewed from the movies in the following links; (i) movie 1 for vSG = 7.9 m/s and (ii) movie 2 for vSG = 11.9 m/s. Presented snapshots of the wave topology in Fig. 15 show that there is a distinct difference in the structure of the waves. For the low superficial gas velocity (vSG = 7.9 m/s), the waves are visualized to stretch from the pipe wall toward the pipe center while generating a smooth wave surface (image on the left side of Fig. 15). For this flow condition, it has been shown that the axial waves are out-of-phase with each other. This can be viewed in the movie 1 as well. When the superficial gas velocity is increased to vSG = 11.9 m/s, the topology of the interfacial waves (image on the right side of Fig. 15) is observed to inhabit smaller wavelengths but contains roll waves in a well defined manner. This result (also can be confirmed from the movie 2) in accord with the in-phase oscillations of the axial waves along the transverse direction.

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Fig. 14. Iso-contour plots of the normalized PSD amplitude at a selected frequency (fi) within the pipe cross-section; at (a) 2.9 Hz, (b) 5.6 Hz and (c) 20 Hz for and at f = 4.4 Hz and (e) 20 Hz for vSG = 11.9 m/s.

Fig. 15. Snapshots of the interface wave topology for (i) vSG = 7.9 m/s and vSL = 1 cm/s (on the left), and (ii) vSG = 11.9 m/s and vSL = 1 cm/s (on the right). Flow is from left to right.

The discussion on the flow visualization images (and movies) provide complimentary information related to the changes in the roll wave characteristics, but it is limited by the perspective of the imaging. Since the snapshots in Fig. 15 are taken from the bottom view of the flow, the three dimensional view of the interface topology is quantitatively visualized with the use of WMS data. This procedure facilitates the identification of the interface coordinates by using the same methodology used to quantify the liquid

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vSG = 7.9 m/s,

film height (hL), but applied to the data at each column of the WMS data in the pipe cross section, i.e. x location. The values of the interface coordinates are stored in a vector IC(x, t) as a function of time and space. Since the flow phenomenon investigated in this study consists of fully segregated co-flow of oil/gas, the regions below the interface coordinates, i.e. IC(x, t), can be assumed to contain liquid while the gas remains above the interface. Then, at each instance of measurement, a spline curve fit is applied to the interface coordinate matrix yielding a continuous line. The raw gas void fraction data matrix, which contains 32  32 cells, is refined by a factor of 5, and the final 160  160 matrix is reconstructed via the use of the continuous interface spline in binary file format where cells below this spline (liquid phase) are marked with a value of 100 and the cells above the spline (gas phase) are marked by 0. Further details on this technique are given by Schleicher et al. [38]. Reconstructed pseudo 3-D interface topology is presented for low (vSG = 7.9 m/s) and high (vSG = 11.9 m/s) gas superficial velocities in Fig. 16(a) and (b), respectively. For both cases, the topology is reconstructed for a time period of approximately 4 s. In this figure, the continuous white line represents the interface at the center of the pipe, i.e. hL(t). When the low gas flow rate is low, the well-defined stretching in the wave topology (Fig. 15) is not observed in the reconstructed image in Fig. 16(a). However, the appearance of various wave structures at different transverse locations without a significant coherency is in accord with the previous discussions for this experimental condition. When the gas flow rate is increased, the roll wave structures are more coherent with relatively higher wave amplitudes (Fig. 16b) while the fine details given in Fig. 15 are lost (due to the temporal resolution of the measurements). In addition, the liquid amount visualized in both parts of Fig. 16 show that the liquid holdup decreases with increasing

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Fig. 16. Pseudo 3-D interface reconstruction based on the WMS data for (a) numbered from i = 1 to n.

vSG = 7.9 m/s and (b) vSG = 11.9 m/s (both for vSL = 1 cm/s). The symbol wi denotes the wave

Fig. 17. The illustration of the procedure to calculate the interfacial surface are (Si) (vSG = 9.32 m/s and

vSL = 1 cm/s).

Fig. 18. Variations of the interfacial surface area with the superficial gas velocity at different liquid flow rates (on the left), and with the liquid holdup (on the right).

mSG, in accord with Fig. 5. Although the waves in Fig. 16(a) are not precisely visualized, their identification is still possible. When the number of the waves is counted within 4 s of the visualized data, it can be seen that there are more waves forming at mSG = 11.9 m/ s. Again, this is in perfect agreement with the findings presented in Fig. 9. Based on these findings, the increase in the gas flow rate leads to a more coherent wave structure with in-phase axial waves along the transverse direction. This finding is significant in explaining the increase in the pressure drop since these waves form a more roughened surface for the gas phase. While the reconstruction procedure yields a quantitative tool to visualize the interface topology, the refined meshes (with

160  160 cells) can be used to compute the interfacial surface area since the interface is well defined between the gas and liquid phases. An illustration for such a computation method is given in Fig. 17. In this figure, the instantaneous phase distribution is given as a sample to show the raw data from WMS sensor on the left for vSG = 9.32 m/s and vSL = 1 cm/s. On the right hand side of the same figure, the resulting refined phase distribution is given where the cells filled with liquid phase are marked with a value of 100, and the cells with filled with gas phase are marked with 0. The interfacial surface is marked with the white dashed lines, and its value, Si(t), can easily be calculated via a line integration.

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Combining the methodology described above to calculate Si(t) with Eq. (8), the variations of the mean values for the interfacial surface area are quantified and presented in Fig. 18 with the superficial gas velocity for different liquid flow rates on the left, and the liquid holdup on the right. The error bars in the mean values are, again, calculated according to Eq. (9). It can be seen that the interfacial surface area decreases with the decrease in the liquid flow rate or the increase in the gas flow rate. When Fig. 18 is analyzed together with the findings presented in Fig. 5, the topology of the liquid phase (HL, hL and h) and the interfacial surface area (Si) are associated with each other; the increase in the superficial gas velocity or liquid flow rate leads to a decrease in the liquid holdup in the pipe cross-section, and thus leading to a decrease in the wetted pipe perimeter, liquid film height and the interfacial surface area. The overall relationship between these important topology features for the roll waves is quite significant in relation to the mechanistical modeling of the stratified-wavy two-phase flow. Of particular interest, the variation of Si with liquid holdup provides a promising closure relationship, and is considered as a more accurate representation of the interface since its quantification process is independent of the assumptions on the interface geometry as in the models (i) flat interface [1,6], (ii) double circle [9], and (iii) apparent rough surface [3,8]. 4. Conclusions This study investigates the features of the roll waves in the oil– gas, stratified-wavy flow experimentally in a 0.152 m ID horizontal pipe with the use of capacitance based Wire Mesh sensors for 7.45 m/s < vSG < 12.62 m/s at two different liquid flow rates, i.e. vSL = 1 and 2 cm/s. The emphasis is given to the evaluation of the wave characteristics from a two-dimensional perspective, and significant novel understanding on the wave structures is achieved. These findings can be summarized as follows:  The total liquid holdup, liquid film height, wetted wall perimeter and interfacial surface are closely related to each other, and decrease with the increasing superficial gas velocity for both the superficial liquid velocities.  The spatial spread of the gas/liquid interface fluctuations is quantified. For low gas flow rates, there is a region beneath the interface that contains the liquid phase. However, with an increase in the superficial gas velocity, the liquid holdup decreases and the interface fluctuations occur very close to the pipe wall where the continuous liquid region diminishes.  The interface fluctuations occurring at a frequency range of 10 Hz < f < 40 Hz is hypothesized to be related to the capillary waves.  At low superficial gas velocities, the axial roll waves form a smooth surface with a stretched topology. Moreover, the oscillations of these waves at different transverse locations are outof-phase. With an increase in the gas flow rate, the wave oscillations are observed to be in-phase with each other and more coherent structures are detected.  A methodology for the quantification of the interfacial surface area is presented based on the experimental data, and is independent of the assumptions on the geometry of the interfacial surface.

Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.expthermflusci. 2015.02.013.

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