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Characterization of slug flows in horizontal piping by signal analysis from a capacitive probe
Flow Measurement and Instrumentation 21 (2010) 347–355
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Characterization of slug flows in horizontal piping by signal analysis from a capacitive probe Emerson dos Reis a,∗ , Leonardo Goldstein Jr. b a
Federal Institute of Education, Science and Technology of São Paulo, IFSP Campus of São João da Boa Vista - 13872-551 São João da Boa Vista, S. P., Brazil
b
College of Mechanical Engineering of the State University of Campinas, FEM / DETF / UNICAMP, Campus Zeferino Vaz, Barão Geraldo - 13.083-970 Campinas, S. P., Brazil
article
info
Article history: Received 4 August 2009 Received in revised form 26 March 2010 Accepted 23 April 2010 Keywords: Slug flow Capacitance probe Liquid layer thickness Signal analysis FFT PDF
abstract The slug flow is a common occurrence in gas–liquid piping flows. Usually it is an undesirable flow regime since the existence of long lumps of liquid slug moving at high speed is unfavorable to gas–liquid transportation, so that considerable effort has been devoted to study its hydrodynamic characteristics. In this work, a capacitive probe was used for dynamic measurements in the horizontal air–water slug flows, for several flow rates. The acquired signals were representative of the effective liquid layer thickness near every cross sectional area of the flow, instead of merely the holdup or void fraction in a finite volume of the flow. This was possible because probe had a thin sensing electrode that minimizes the axial length effect on the measurements. Tests were performed in a 34 mm i.d. acrylic pipe, 5 m long; in which slug flows as well as stratified-smooth and stratified-wavy flows were generated. Signal analysis techniques were applied for flow regime identification and toward characterization of these two-phase flows: Power Spectrum Density (PSD) from Fourier Transform and Probability Density Function (PDF) from Statistical Analysis. Therefore, PSD and PDF graphs were taken as signatures of each flow under test and a correlation was calculated for each PSD and PDF set of data, which showed to be a robust parameter for correct flow regime identification. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The complex nature of gas–liquid two-phase flows in pipelines has challenged researchers along the past few decades. Many of them directed their efforts in develop unambiguous techniques for characterizing multiphase flows from dynamic signals analysis acquired by using different types of sensors: pressure [1–3], holdup or volumetric concentration [4–7], or liquid film thickness [8]. Pressure and volumetric concentration sensors are attractive as they are non-intrusive, robust, inexpensive, relatively welldeveloped and, therefore, more likely to be applied in industrial systems. The most import characteristic of the gas–liquid flow in pipes is the flow regime, which concerns the special arrangement of the gas and the liquid into the pipe [9]. On a macro point of view over this special arrangement, the bubbly is typically an 1D flow regime, while stratified-smooth is 2D, and stratified-wavy and slug flow are 3D due to variations of local concentration of liquid and/or gas components along the same cross sectional area and along the axial pipe length. Consequently, some confusion occurs when analyzing signals from different flow regimes in time space,
∗
Corresponding author. Tel.: +55 19 3634 1100; fax: +55 19 3634 1100. E-mail address: [email protected] (E. dos Reis).
0955-5986/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2010.04.006
since the dimensional flow information contained in the signal depends on the probe type used. Therefore, one must consider that sensors with different sensing principles, such as conductive [6,8], photonic [10] and capacitive (discussed ahead), etc. have different perceptions of the fluid flow and this fact reflects on the signal generated by each different probe and, therefore, on the signal analysis results. Capacitive sensors are robust, inexpensive, safe, and widely used in industrial systems for concentration measurements. Das and Pattanayak [4], Costigan et al. [5], Geraest and Borst [11] and Elkow and Rezkallah [12] used them to identify two-phase flow regimes. The authors reported the successful application of PDF on signals for low flow rates of the liquid and gas phases. Little attention was paid to the use of PSD, mainly due to fact that the capacitance electrodes commonly are thicker in the axial flow direction (about 2 times the pipe diameter) to enhance its sensitivity, as required by the capacitance transducer circuit, and also to reduce the effect of the electrical field distortion near the electrode’s edges, which can cause distortions on the probe response [13]. In this case, however, the probe can also operate as a low-pass filter cutting off high frequency components related to the flowing mixture [14] and, as a result, a portion of the information is lost. The gas–liquid slug flow is one of the most common two-phase flow regimes over all pipeline’s inclination. It is characterized by an intrinsic unsteadiness, due to the alternation of liquid
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Fig. 1. Experimental installation schematic.
‘slugs’ containing small bubbles, that fill the whole pipe cross section, with regions in which the flow consists of a liquid layer over/around an horizontal/vertical elongated gas bubble [15]. This intermittent behavior causes high fluctuations of pressure, concentration and flow rate. As a result, an extremely careful design of the pipeline is required (valves, orifices, etc.). Moreover, the low ‘slugging’ frequency (few hertz) can be in resonance with the characteristic frequency of the pipeline itself, causing serious damage. For that reason, it is of essential importance [6,16] not only to identify the slug flow regime but also determine its main flow characteristics, providing useful information for the engineer in design and process control. This work propose is to utilize the capacitive non-intrusive probe presented by dos Reis and Goldstein Jr. [17], to determine the effective liquid layer thickness in about every cross sectional area, in a horizontal Plexiglas pipeline, for several flow regimes: slug, stratified-smooth and stratified-wavy, instead of measuring only the holdup or void fraction in a finite flow volume. The flow regimes were established for air superficial velocities varying from 1.3 to 6.0 m/s, and water from 0.08 to 0.80 m/s. The proposed capacitive technique allowed registering information of an effective cross sectional liquid layer thickness through the time, and this information could be used to identify whether the image of the two-phase flows were inherently 2D or 3D. Furthermore, PDF and PSD data analysis were used to determine several flow characteristics: flow regime, range of the liquid layer thickness, presence of waves, dominant frequencies, presence of hydraulic jumps, regions of signal concentration, range of frequencies, and amplitudes. 2. Experimental installation Fig. 1 shows a schematic of the experimental flow loop. The air supply system is composed of a reciprocating compressor producing 19.1 m3 /h at 830 kPa, an air reservoir, AR, of 400 liters, to reduce pressure oscillations downstream, an air filter and pressure regulator, two needle valves, VC1 and VC2, one for fine flow adjustment, and two turbine flow meters, TM1 and TM2, of 3/4 and 1 1/2 inches, for measurement of the volumetric airflow rate, QG , with ranges from 1.1 to 11.0 and 8.8 to 88.0 m3 /h, and calibrated measurement uncertainties of ±0.14 m3 /h and ±0.41 m3 /h, respectively. A type T thermocouple, T 3, and an electronic pressure gauge, P3, were used to measure the air temperature and gauge pressure, T3 and p3 , respectively. The water supply system was composed of a reservoir, WR, which also performed air–water separation; a centrifugal pump, P, with a capacity of 45 m3 /h at 274 kPa (75% efficiency); two water
filters, WF, operating in parallel; a double tube heat exchanger, HE; two control valves, VC3 and VC4, one for fine adjustment, and a turbine meter, TM3 to measure the volumetric water flow rate, QL , which ranged from 3.0 to 45 l/min, with a measurement uncertainty of ±0.23 l/min. A water-cooling system became necessary due to heating of the circulating liquid. A cooling tower supplied water close to the wet bulb temperature to the annular side of the heat exchanger. Tests were realized with deionized water to avoid fouling the internal pipe walls, meters and valves. A type T thermocouple, T 2, was used to measure the water temperature, T2 . The air–water flow system was composed of an 13 m long Plexiglas pipeline with an internal diameter, D, of 34 mm and 3 mm wall thickness, a junction with 45◦ branch arms, TM, which mixed water from the main arm with air from the branch arm on the top. The Plexiglas pipeline has about 5 m of length from MT to the tests section (150 D). A Type T thermocouple, T 1, and an electronic pressure gauge, P1, were used to measure the temperature of the air–water mixture, T1 and p1 , respectively. A data acquisition system composed of a microcomputer, AT-MIO16E10 board, connections block, and Labview 6.0, by National Instruments TM , was used to log all the data from instruments. 3. Capacitive probe description As discussed by dos Reis and Goldstein Jr. [17], the effective liquid layer thickness, hL , represented by HL1 in Fig. 1, was measured by a device composed of an capacitive source-sensor pair of electrodes, guard electrodes, sinusoidal signal source and capacitance transducer circuit, as shown in Fig. 2. The sensor electrode was connected to the capacitance transducer and the source electrode was connected to the sinusoidal signal source. In this probe, the sensor electrode has a minimum width of 3 mm (black), which allows the probe to detect high frequencies related to the gas–liquid flow. Almost only the liquid in the sectional volume limited by the sensing electrode affects the capacitance transducer response. Two guard electrodes mounted very close to the sensing electrode (0.5 mm) limit electric field distortions around edges [13]. The electric field created among the sensor electrode and guard electrodes is null due to the virtual ground condition imposed by careful design of the capacitance transducer circuit [18]. Consequently, the shorter width of the sensor electrode makes the system response closer to the mean liquid thickness measured at the cross sectional area of the pipe. This is important, for example, when measuring the amplitude of small waves. In that sense, the technical limitation is due to limitations of the sensitivity and speed of the capacitance
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Fig. 2. The thin electrode capacitance probe.
Fig. 3. Air–water flow regime map with experimental test point.
transducer circuit. Dos Reis [19] presented an analog transducer circuit suitable for this application. The sensibility was evaluated to be 7.0 mV/fF and the circuit settling time about 6 ms. The probe was calibrated and a measurement uncertainty of ±0.521 mm or ±1.53% of FS (confidence interval of 95%) was determined. 4. Experimental procedure and data reduction Fig. 3 presents a theoretical air–water flow map for a horizontal piping of 34 mm of diameter, D, according to Taitel and Dukler [9]. Thirteen flow conditions were tested in the slug, stratified-smooth and stratified-wavy flow regimes, in the region of the map where the flow regime transition lines were more concentrated. While some of test flow conditions were chosen distant from the transition lines, as test points 3, 10 and 13, other points were near the slug-stratified and slug-annular transition lines, such as 1, 7, 6, 8, 9 and 10. Therefore, six test points were near the stratifiedslug and slug-annular transition lines. Four test points, under smooth and wavy flow regimes, were also included for evaluating a proposed flow regime identification methodology, since signals from slug and stratified-wavy flows can generate similar profiles in PDF and PSD graphs, as discussed ahead. The air supply system was fitted with a control valve and two turbine meters, TM1 and TM2, as shown in Fig. 2, which enabled us to cover the air superficial velocities, uGS = QG /A, from 1.3 to 6.0 m/s. The water flow system had a single turbine meter, TM3, allowing water superficial velocities, uLS = QL /A, from 0.08 to 0.80 m/s. Flow rates of air and water, QG and QL , gauge pressure, p1 , and temperature of the air–water flow mixture, T1 , through P1 and
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T 1, temperature of water T2 through T 2, temperature and gauge pressure of air into the feeding line, T3 and p3 , through T 3 and P3, and signals from the capacitive probe, HL1, all these signals, which were produced in the tests, were logged by the data acquisition system and stored in a digital file. The data acquisition time, ta , was defined as equal to 300 s for each test (5 min). The number of samples, n, and the data acquisition rate, f , were chosen to keep the same acquisition time for all tests. The f values were previously determined to avoid an aliasing error: 800 Hz for tests 1, 2, 3, 9, 10 and 11, which had the smaller flow velocities (∼1.5 m/s); 1500 Hz for points 4, 7, 8, 12 and 13 (∼3.5 m/s); and 2,500 Hz for points 5 and 6 having the higher flow velocities (∼6.5 m/s). This corresponds, for example, to n = 240,000 samples acquired at 800 Hz. Therefore, the use of high data acquisition rates was due to the temporal resolution of the signals demanded by the cross correlation technique, which was used by dos Reis and Goldstein Jr [17] to measure the mean translational velocity of the slug flows. This fact does not represent a problem for PSD or PDF analysis, since if more information is made available it only increases the computational work. In the data reduction stage, the acquired signals from electrical voltages of temperature, volumetric flow rate and pressure meters were first averaged, being converted to measured values by the calibration curve of each instrument. Differently, the acquired signals from the capacitive probe were first converted to the respective non-dimensional liquid layer thickness measurements, hL /D, also by using the calibration curve. A technique was applied to correct for deviations of the dielectric permittivity of the water associated to temperature variations of the flow [20]. Again, the hL /D values in number of n were stored in a digital file. In the signal analysis stage, all hL /D data processing begun from raw data that was ten-point filtered to remove all high frequency noise (moving average filter). After that, the Probability Density Function — PDF was determined by constructing histograms [5, 21], each one with 30 intervals, that cover the range from the minimum to the maximum values registered of hL /D. From the histograms, the probability of each interval, i, was calculated as P (hL /D)i = (number of values of hL /D into the interval i) / number of samples, n. Following the Power Spectrum Density — PSD was calculated from the fast-Fourier transform-FFT algorithm as the magnitude of the complex numbers from 1 to n/2 + 1 [22]. Data of hL /D were used in FFT without previous filtering, and subsequently the PSD data was 20-point filtered to remove noise from the longer FFT and to provide a good frequency resolution. PSD graphs were plotted excluding the single component at 0 Hz, and from 0 to 10 Hz that concentrate almost the whole power spectrum in all tests. PDF and PSD were used to identify the flow regime by means of a correlation. Some PDF and PSD graphs were taken as flow regime signatures, while others were used for testing. For PDFs from test 1 to 13 in Fig. 3, there were originally 31 pairs of (hL /D)i versus P (hL /D)i representative of each interval i, with ranges between the minimum and the maximum of hL /D, and also for PSDs by interpolation, there were 3000 pairs of frequency component (fs )i versus component power S (fs )i , which were equally distributed from 0 to 10 Hz from the FFT. A normalized correlation was calculated, as given by Eqs. (1)–(4):
ρxy = p
Rxy
Rxx Ryy
Rxx =
Ryy =
N 1 X
N i =1 N 1 X
N i =1
(1)
x [i] x [i]
(2)
y [i] y [i]
(3)
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Table 1 Tests data. uGS (m/s)
ulS (m/s)
1 2 3 4 5 6 7 8 9
1.371 1.371 1.392 3.225 6.131 6.165 3.170 3.206 2.013
10 11 12 13
1.371 2.016 3.225 5.926
Test
Rxy =
N 1 X
N i=1
Flow regime observed
h¯ LE /D (–)
ShLE /D (–)
Range of hLE /D (–)
fsd (Hz)
Range of fs (Hz)
0.198 0.410 0.788 0.797 0.788 0.497 0.301 0.198 0.200
Slug
0.312 0.415 0.520 0.443 0.359 0.328 0.338 0.313 0.282
0.191 0.230 0.267 0.193 0.140 0.125 0.132 0.111 0.168
0.160–0.998 0.217–0.987 0.243–0.994 0.213–0.984 0.181–1.00 0.155–0.967 0.177–0.965 0.186–0.956 0.164–0.981
0.133 0.533 1.14 0.937 1.64 0.960 0.360 0.297 0.213
0–2.88 0–5.38 0–7.50 0–6.95 0–9.60 0–14.6 0–7.81 0–6.47 0–4.17
0.080 0.080 0.080 0.082
Smooth Wavy Wavy Wavy
0.421 0.407 0.338 0.173
0.00150 0.0185 0.0550 0.0767
0.417–0.424 0.371–0.433 0.274–0.461 0.0776–0.423
0.0667 5.48 0.0667 0.497
0–7.41 0–13.0 0–17.7 0–18.5
x [i] y [i]
(4)
where ρxy is the normalized correlation, Rxx and Ryy are the autocorrelations of x and y data, Rxy is the correlation of x and y, x or y are equal to P (hL /D) or S (fs ) and N is the amount of data to be computed. ρxy , in this case, ranged from 0 to 1, being equal to 1 when there is a perfect similarity of data. Eqs. (1)–(4) require that x and y be calculated on the same hL /D or fs for each i. However, PDF data had different ranges and a parameterization scheme was necessary. By using a spline interpolation algorithm, N = 500 pairs from hL /D = 0 to 1.0 were calculated for each original set of 31 pairs of (hL /D)i versus P (hL /D)i . Interpolations were performed only within the interval from the minimum and the maximum of (hL /D)i , otherwise, when determining the new P (hL /D)i = 0. N = 500 pairs were sufficient to reproduce each original PDF graph of test 1 to 13 with high fidelity. On the other hand, PSD data were already adequate for a correlation calculation with N = 3000, since n/f = 300 s for all tests and the frequency range was always the same as discussed next. The ‘‘normalized’’ correlation was calculated according to Eq. (5) instead of Eq. (1), taking advantage of the difference in scale of the power spectrum of signals related to different flow regimes. ∗ Therefore, ρxy was always equal to 1 under perfect similarity. However, it could be many times greater than 1, as discussed in item 5.2. ∗ ρxy =
Rxy Rxx
.
(5)
The hL /D, PDF and PSD were further manipulated and are presented in those data of Table 1. From basic Statistics, mean values of hL /D signals and standard deviations were calculated, h¯ LE /D and ShLE /D , as well as the dominant frequency of each signal fsd , and ranges of hL /D. The range of frequency fs in all PSDs varied from 0 Hz to 10 Hz, which was taken as an upper limit of 1/100 of the component power on the dominant frequency, since the power spectrum tended asymptotically to zero (right side of the PSD graphs presented in the next item). 5. Results and discussion Figs. 5–7 show three types of graphs for each test shown in the map of Fig. 3 as a experimental point from number 1 to 13: a sample graph of hL /D through a short time interval of only 30 s at the left, a PDF graph at the center, and a PSD graph at the right. From visual observations tests 1 to 9, in Figs. 5 and 6, their flow regimes were identified as slug, while in test 10 the flow regime was identified as stratified-smooth, and as stratified-wavy in tests 12 and 13, in agreement with the map of Fig. 3 [9]. For test point 11, in which the flow regime was expected to be stratified-smooth, it was observed
Fig. 4. Scheme of data analysis.
as stratified-wavy with small amplitude waves along the air–water interface. Therefore, it may be considered that, in the flow map of Fig. 3, the transition lines are representative in truth of a gradual regime transition that occurs across them. Test points 1, 6 8 and 9 are also near the transition lines (slug-stratified or slug-annular), and hybrid regime characteristics were impressed on the signals coming from the probe, as will be discussed. Individual flow characteristics of each test point shown in Fig. 3 are studied in item 5.1, while flow regime identification was studied in item 5.2. The information in item 5.1 is important in order to understand the flow regimes’ signatures in PDF and PSD graphs discussed in item 5.2. 5.1. Characterization of air–water flows This analysis follows data presented in Table 1, were h¯ LE /D detonates the mean liquid layer thickness, ShLE /D the standard deviation, and fsd the dominant frequency. The diagram shown in Fig. 4 concerns the variation of the superficial velocities of air and water over all tests according to the same polygon of Fig. 3. Fig. 4 is divided in two parts according to the flow regimes in the map: slug or stratified (smooth and wavy). Along the clockwise path indicated by arrows around the polygon, test 1 had the lowest superficial velocities of both phases under slug flow, while tests 2 and 3 had a higher liquid velocity, tests 4 and 5 had both higher liquid and gas flow rates, as well as all tests where near the slugannular and slug-stratified transition lines from tests 6 to 1. Further analysis of stratified flow data processed with tests 10 to 13 by increasing the airflow rate, while the water flow rate was kept constant. Fig. 4 also shows, on the top, a schematic of the horizontal Plexiglas pipeline and the test section position.
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351
Fig. 5. Graphs of tests under slug flow — Tests 1 to 5.
The liquid flow rate was increased by about 300% along the straight vertical line for tests 1 to 3, under slug flow, while the airflow rate was kept constant. Firstly, signal samples of tests 1, 2 and 3 in Fig. 5 indicate the presence of liquid slugs when hL /D is near 1.0, and regions of the elongated gaseous bubbles have lower values of hL /D separating them. The PDF graphs show hL /D signals occurring in a large range that decreases from test 1 to 3 as can be seem on Table 1, while the liquid layer above the elongated bubbles is thicker from hL /D = 0.160 in test 1 to hL /D = 0.243 in test 3. Therefore, the main characteristic of the PDF graphs is the presence of two peaks with a central region of lower signal probability, similar to results presented by Costigan and Whalley [5]. One of
those peaks is at about hL /D = 0.4, and the other is near hL /D = 1.0. They indicate the presence of two important values of hL /D: the left one is related to the presence of the elongated bubbles air–water interface and the right one to the liquid slugs. The peaks at the left, in general, are greater than the right ones, however, it should be observed that from tests 1 to 3 the peak’s height at the right becomes higher, and that there is an increase in the signals probability in the central region between the right and left peaks in each PDF graph, causing a more regular distribution of the probability. Furthermore, the presence of a hydraulic jump can be observed in tests 1 and 2, and a reduction of high waves into the elongated bubbles from test 1 to 3. A ‘‘mountain’’ shape
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Fig. 6. Graphs of tests under slug flow — Tests 6 to 9.
characterizes the PSD graph for the slug flow, with the highest peak corresponding to the dominant frequency, fsd . This frequency, fsd , is observed as increasing from about 0.133 Hz in test 1, through 0.533 Hz in test 2, and reaching 1.14 Hz in 3, as can be seen in Table 1. The liquid flow rate was kept high and constant from tests 3 to 5, while the airflow was increased about 360%. Thus, in tests 4, 5 and 6, it can be observed hL /D rarely reaching 1.0 in the presence of liquid slugs, as observed in tests 1, 2 and 3. This is due to the increased presence of small bubbles dispersed into the liquid slug body. The response of the capacitive probe is affected by their presence, since its signal is proportional to the effective dielectric permittivity of the mixture. Therefore, the population of bubbles increased with the flow velocity (airflow rate). The range of hL /D was not different to the previous tests, however, the PDF graphs show the disappearance of the right peaks related to the liquid slugs in tests 3 to 5, which occurred due to shaper peaks in hL /D signals, while the probability of the left region increases, and the PDF graph shows itself, again, like a chi-square probability distribution. High waves were also observed into the elongated bubbles region, as can be seen in the graphs of tests 4 and 5, in which their population increased from tests 3 to 5 in opposition to tests 1 to 3. The PDF graphs also show a reduction of the liquid layer thickness below the elongated bubbles from hL /D = 0.243 in test 3
to 0.181 in test 5. The graphs of PSD have the same ‘‘mountain’’ shape, however, with a larger decrease in the spectrum’s range to about half of those from tests 1, 2 and 3, with the appearance of some components of higher frequency from test 1 through 4 and 5. Furthermore, the PSDs show that the dominant frequency decreased from test 3 at about 1.14 Hz to 0.937 Hz in 4, and increased again to 1.64 Hz in test 5, as can be seen in Table 1. Consequently, this fact should state that the frequencies related to the hydrodynamics of the air–water slug flow aren’t a univocal function of the liquid and gas flow rates or superficial velocities. The liquid flow rate was decreased by about 60% from test 5 to 6, while the airflow rate was kept high, as shown in Figs. 5 and 6, with the flow condition in test 6 near the slug-annular transition line, as shown in Fig. 3. The sample graphs of hL /D signals show a reduction of the peak’s height, which show that the slugs were more aerated in test 6 than in test 5, and an increase in the mean time interval between two consecutive peaks, and also an increased presence of high waves in the flow. The PDF and PSD graphs are curiously very similar while showing a small reduction of the power spectrum range, with the dominant frequency falling from 1.64 Hz in test 5 to about 0.960 Hz in test 6. Both air and water flow rates were reduced by about 82% and 66%, from test 6 to 7, respectively. Peaks in the hL /D signals become more separated in time, and they still aren’t as high as hL /D = 1.0.
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Fig. 7. Graphs of tests under stratified-smooth and stratified.
The presence of high waves is also predominant as can be seen in PDF graphs, showing no large variations in the signals’ probability. However, huge variations occurred in the frequencies of hL /D signals as shown in the PSD graphs, since an alteration in the graphs’ shapes occurred, while the dominant frequency became smaller from 0.960 Hz in test 6 to about 0.360 Hz in test 7. The liquid flow rate was decreased again from test 7 to 8 by about 100%, while the airflow rate was the same. In a general way, all graphs of tests 7 and 8 are similar: signal sample, PDF and PSD, the same happening with graphs of test point 9 when the airflow rate was decreased from test 8 by about 65%. However, the PDF graph of test 9 showed the appearance of the right peak related to the liquid slug region, showing the presence of less aerated slugs as has occurred in tests 1, 2, 3 to 4. Concerning the developing pipeline length, x, necessary to the flow reach its complete full-developed fluidynamic, Nydal et al. [23] proposed that a ‘‘well defined statistical distribution of the slug holdup (only slug), with only a peak, may be a necessary condition for a developed slug flow’’. They demonstrated x as depending on both gas and liquid superficial velocities and that it ranges from 120 D to 400 D and over. Based on their own measurements in a 52 mm i.d. pipeline with a range of superficial velocities of air, uGS , from 0.5 to 20 m/s and of water, uLS , from 0.6 to 3.5 m/s, they obtained a map of minimum length for a developed slug flow. Based on this map, only flows in test points 2,
3 and 4 were under fully-developed conditions. However, one must consider that test points 1, 6, 7, 8 and 9 are near the flow regime transition lines, and their fluidynamic development does not occur according to the conditions proposed by Nydal and workers. Tests 10, 11, 12 and 13 are in the region of stratified-smooth and stratified-wavy flow regimes in Fig. 3, with the gaseous phase flowing separately over the liquid phase, as observed in graphs of Fig. 7. The airflow rate was increased by about 360% from tests 10 to 13, while the water flow rate was kept constant, about 150% below that of tests 1, 9 and 8 under slug flow. The signal graph of test 10 shows an almost constant value of hL /D about 0.42, throughout time. The PDF graph represents a single narrow band at 0.421, while the PSD graph shows this flow condition as having some frequency components different from 0 Hz, however, their amplitudes are small due to the range of the signal power spectrum. The PSD graph has two distinct regions: one at a low frequency range with a dominant frequency of about 0.1 Hz at the left; and another with a scattered spectrum around the dominant frequency, at about 4 Hz, at right. Also an increase in the airflow rate increased the oscillations in the air–water interface from test 10 to 12, with a decrease in the mean liquid layer thickness from h¯ L /D = 0.421 to 0.338, as can be seen in the signal samples and PDF graphs. The PSD graphs of tests 11 and 12 show a considerable increase in the amplitude of the waves, since the range of the power spectrum increased by about 1000% from test 10. The shapes
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Table 2 Correlation results for PDF data. Test
1 2 3 4 5 6 7 8 9 10 11 12 13
Flow regime observed
ρxy Ref. Point 3
Ref. Point 5
Ref. Point 10
Ref. Point 13
Slug
0.549 0.810 1.000 0.966 0.815 0.697 0.666 0.775 0.377
0.831 0.971 0.815 0.881 1.000 0.966 0.953 0.984 0.663
0.015 0.057 0.086 0.093 0.056 0.048 0.045 0.058 0.022
0.411 0.221 0.112 0.137 0.259 0.357 0.344 0.304 0.551
Smooth Wavy Wavy Wavy
0.086 0.276 0.862 0.112
0.056 0.176 0.743 0.259
1.000 0.305 0.021 0.001
0.001 0.006 0.098 1.000
Ref. Point 3
Ref. Point 5
Ref. Point 10
Ref. Point 13
Slug
0.260 0.567 1.000 0.724 0.442 0.440 0.177 0.264 0.250
0.419 0.827 1.394 1.152 1.000 0.715 0.296 0.443 0.392
11 157 14 083 16 599 18 848 16 147 12 527 7213 9879 8937
8.019 13.463 12.365 11.330 6.592 7.009 4.716 6.111 5.977
Smooth Wavy Wavy Wavy
0.000 0.000 0.009 0.045
0.000 0.002 0.026 0.075
1.000 96.60 802.7 1390
0.000 0.012 0.175 1.000
Table 3 Correlation results for PSD data. Test
1 2 3 4 5 6 7 8 9 10 11 12 13
Flow regime observed
∗ ρxy
were similar to those of test 10 with two distinct regions. They also show a large range of frequencies in test 12, with a dominant frequency at the right region about 4.5 Hz, which is narrowest in test 11, with a dominant frequency at the right region of about 5.8 Hz. The airflow rate was also increased about 82%, from test 12 to 13. The waves were higher while the liquid layer became thinner from about hL /D = 0.338 to 0.173, as seen in PDF graphs and in Table 1. However, the PDF graph is similar to that of tests 5 to 7 under slug flow as a chi-square probability distribution, which can cause some confusion; otherwise, both conditions have not different ranges of hL /D. Still the PSD graph of test 13 is similar to those of tests 1, 7, 8 and 9, under slug flow, which are near the slugstratified transition line, and also with a low dominant frequency of about 0.497 Hz close to those of tests 1, 7, 8 and 9. Although the PDF graphs presented a different shape for stratified and slug flows, since they presented a single peak for stratified and two peaks for slug flows, as shown on the graphs of tests 10, 11, 12, and 13, and 1 to 4, it is not true when the slug flow occurred under high airflow rate with slug bodies becoming highly aerated. In this condition, the right peak in PDF disappeared, and these graphs were similar to those under stratified-wavy flow, as in test 13. However, differently of those under slug flow, ranges of hL /D were always less than 0.5, while standard deviations ShLE /D were always less than 0.8 under stratified-smooth and wavy flows. PSD graphs were also useful tools when analyzing the frequencies related to the flow, although they also presented some problems in identifying stratified-wavy flow regimes with high airflow rates, test 13, and slug flow near the transition lines, tests 1, 6, 7, 8 and 9. However, the power spectrum range of the slug flow could be about 1500% greater than those from the wavy flows, which could be decisive when identifying the flow regime.
For example, by comparing both graphs of tests 6 or 7 and those of test 13, PSD graphs had ranges from 0 to about 30 [Power/Hz] against 0 to 3.0 [Power/Hz]. A similar analysis can be made from PDF graphs; however, the scales’ differences are smaller than from PSDs. 5.2. Flow regime identification Tables 2 and 3 present the correlation results calculated from Eqs. (1)–(4) for PDFs, and from Eq. (5) and (2)–(4) for PSDs. Test points 3, 5, 10 and 13 were chosen as references for the slug flow regime (3 and 5), stratified-smooth (1) and stratified-wavy (13), since they are distant from the transition lines in Fig. 3, and they imposed the signatures of each flow regime on the respective probes signals, as discussed in item 5.1. In a general way, ρxy in ∗ Table 2, or ρxy in Table 3, is equal to 1.000 if the reference and the test data are the same, such as 5–5 and 3–3. Additionally, ρxy is the same for PDFs if the reference and the test numbers are permuted, such as 3–5, and 5–3. From Table 2 for PDF data, when identifying the slug flow regime, ρxy was equal to 0.815 for test 3 with test 5 as the reference, being the smallest value equal to 0.663 for test 9, which is greater than those when test 3 was taken as the reference. This is an important result, since test 5 is more representative than test 3 according to the actual concept of ideal picture of PDF for slug flows. Additionally, ρxy was high and equal to 0.862 for test 12 under the stratified-wavy flow regime, with 5 as the reference. It was due to the concentrations of signals’ probability in the same range of hL /D, as can be observed in Figs. 5 and 7. When identifying the stratified-smooth flow regime, values of ρxy , with test 10 as the reference, were always less than 0.1, when the flow regime observed was slug or wavy, at least ρxy = 0.305 for test 11, this PDF shows some similar characteristics of the smooth
E. dos Reis, L. Goldstein Jr. / Flow Measurement and Instrumentation 21 (2010) 347–355
flow regime, as can be seen in Fig. 7. Otherwise, when identifying the stratified-wavy flow regime with test 13 as the reference, tests 11 and 12 under stratified-wavy didn’t present high values of ρxy . Different situations occurred for some tests under slug flows with a higher ρxy up to 0.551, such as 1 and 9 near the transition lines. From Table 3 for PSD data, when identifying the slug flow ∗ regime with test 3 as the reference, ρxy was as low as 0.177 for ∗ test 7 under slug flow, while ρxy was less than 0.045 (test 13) in all stratified flows. Analogous results were observed when test 5 ∗ was the reference, however, with a higher ρxy equal to 0.296 for test 7. Therefore, test 5 showed itself again as a better reference for identifying slug flows. Similar results were observed from PDFs as discussed previously. When identifying the stratified-smooth with test 10 as the ∗ reference, Table 3 shows values of ρxy many times greater than 1.0, for all tests under both slug and stratified-wavy flow regimes. Otherwise, when identifying the stratified-wavy regime with test ∗ 13 as the reference, all slug flow tests presented ρxy many times greater than 1.0, while it was less than 1.0 among all stratified flows. Therefore, test 13 as the reference is suitable to distinguish stratified and slug flow regimes. As discussed, a correlative technique applied to PSDs supplied a better parameter for correct flow regime identification than PDFs. 6. Conclusion and remarks This paper presented a study about the signal analysis of a capacitive probe used to register the liquid layer thickness variation in air–water two-phase flows under stratified-smooth, stratified-wavy and slug flow regimes, some of them being near the transition lines in the flow map. These flows were generated in a horizontal acrylic pipe, with a 34 mm diameter, and the probe was installed 150 D downstream from the phases mixing point. Both the probability function calculation and the fast-Fourier-transform were applied to the acquired signals, and graphs of probability distribution function – PDF – and power spectrum density – PSD – were produced. PDF and PSD graphs showed to be useful for evaluating characteristics of the flows: range of the liquid layer thickness, presence of waves, dominant frequencies, presence of hydraulic jumps, regions of signal concentration, range of signal frequencies and amplitudes. Both presented respectively similar graphs for stratified-wavy and slug flows with high gas flow rates. Different ranges of liquid layer thickness measurements in PDFs and of scales of power spectrums in PSDs were observed, which were more evident in PSDs. When applying correlation technique on PDF and PSD data, the results showed the PSD as more effective for flow regime identification in all 13 tested conditions, with 4 of them near the slug-stratified and slug-annular transitions lines on the flow regime map, which indicates that some computational algorithm can be implemented for use in practical situations. However, one must consider the following: (i) the power spectrum does not have a coherent scale, or a system of units, which can cause some confusion in practical situations; (ii) PDF calculations request minimal computational work if compared to PSD. In a future work, using more than one probe on the same pipe slice, but at a different angle would provide more information for correct flow regime identification. Therefore, a new assembly of electrodes from that of Reis and Goldstein [17], can be built. There are two ways to perform that: (i) two sensing electrodes mounted around the same pipe cross section; or (i) they can be mounted in different pipe sections with an independent source and guard electrodes. A study based in the Finite Element Method, for example, can help the researcher’s choice. Moreover, in horizontal flows, one should consider that if the new sensing electrode was
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installed in the upper or lower side of the pipe section, the effect of its major proximity to gas or liquid, due to gravity, would appear in the probe’s signals. Also, Wang et al. [24] reported a development length x as long as 1157 D, where slug still collapses and grows, as was observed by the authors. Then it can be seen that the subject treated is still open for research. Yet, the methodology proposed in the manuscript may be used by comparing PDF and FFT graphs in different measurement stations along the pipeline. Acknowledgement The support of FAPESP – Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazil, is deeply appreciated. References [1] França F, Acikgoz M, Lahey Jr RT, Clausse A. The use of fractal techniques for flow regime identification. International Journal of Multiphase Flow 1991; 17(4):545–52. [2] Shim W, Jo CH. Analysis of pressure fluctuations in two-phase vertical flow in annulus. Journal of Industrial and Engineering Chemistry (Seoul) 2000;6: 167–73. [3] Sun T, Zhang H, Hu C. Identification of gas–liquid two-phase flow regime and quality. In: IEEE instrumentation and measurement technology conference, 2002. [4] Das RK, Pattanayak S. Electrical impedance method for flow regime identification in vertical upward gas–liquid two-phase flow. Measurement Science and Technology 1993;4:1457–63. [5] Costigan G, Whalley PB. Slug flow regime identification from dynamic void fraction measurements in vertical air–water flows. International Journal of Multiphase Flow 1997;23:263–82. [6] Fossa M, Guglielmini G, Marchitto A. Intermittent flow parameters from void fraction analysis. Flow Measurement and Instrumentation 2003;14:161–8. [7] Mi Y, Ishii M, Tsoukalas LH. Investigation of vertical slug flow with advanced two-phase flow instrumentation. Nuclear Engineering Design 2001;204: 69–85. [8] Jana AK, Das G, Das PK. Flow regime identification of two-phase liquidliquid upflow through vertical pipe. Chemical Engineering Science 2006;61: 1500–15. [9] Taitel Y, Dukler AE. A model for predicting flow regime transitions in horizontal and near horizontal gas–liquid flow. AIChE Journal 1976;22:47–55. [10] Mouza AA, Vlachos NA, Paras SV, Karabelas AJ. Measurement of liquid thickness using a laser light absorption method. Experiments in Fluids 2000; 28:355–9. [11] Geraest JJM, Borst JC. A capacitance sensor for two-phase void fraction measurement and flow regime identification. International Journal of Multiphase Flow 1988;14(3):305–20. [12] Elkow KJ, Rezkallah KS. Void fraction measurements in gas–liquid flows using capacitance sensors. Measurement Science and Technology 1996;7(8): 1153–63. [13] Reinecke N, Mewes D. Recent developments and industrial/research applications of capacitance tomography. Measurement Science and Technology 1996; 7:233–46. [14] Ma J, Yan Y. Design and evaluation of electrostatic sensor for the measurement of velocity of pneumatically conveyed solids. Flow Measurement and Instrumentation 2000;11:195–204. [15] Taitel Y, Barnea D. Two-phase slug flow. Advances in Heat Transfer 1990;20: 83–132. [16] Nydal OJ, Pintus S, Andreussi P. Statistical characterization of slug flow in horizontal pipes. International Journal of Multiphase Flow 1992;18:439–53. [17] dos Reis E, Goldstein Jr L. A non-intrusive probe for bubble profile and velocity measurement in horizontal slug flow. Flow Measurement and Instrumentation 2005;16:229–39. [18] Yang WQ, Stott AL, Beck MS. High frequency and high resolution capacitance measuring circuit for process tomography. IEE Proc-Circuits Devices Systems 1994;141:215–9. [19] dos Reis E. Estudo do escoamento pistonado horizontal ar-água em tubulações com ramificação T: College of Mechanical Engineering, State University of Campinas (2003). Ph.D. thesis in Portuguese. [20] dos Reis E, Goldstein Jr L. A procedure to correct the effect of fluid flow temperature variation on the response of capacitive void fraction meters. Flow Measurement and Instrumentation 2005;16(4):267–74. [21] Walpole RE, Myers RH. Probability and statistics for engineers and scientists. New York: The Macmillan Company; 1973. [22] Oppenheim AV, Willisky AS, Nawab SH. Signals and systems. 2.ed Upper Saddle River, New Jersey: Prentice Hall; 1983. [23] Nydal OJ, Pintus S, Andreussi P. Statistical characterization of slug flow in horizontal pipes. International Journal of Multiphase Flow 1992;18(3): 439–53. [24] Wang X, Guo L, Zhang X. Development of liquid slug length in gas–liquid slug flow along horizontal pipeline: experiment and simulation. Chinese Journal of Chemical Engineering 2006;14(5):626–33.
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Characterization of slug flows in horizontal piping by signal analysis from a capacitive probe Emerson dos Reis a,∗ , Leonardo Goldstein Jr. b a
Federal Institute of Education, Science and Technology of São Paulo, IFSP Campus of São João da Boa Vista - 13872-551 São João da Boa Vista, S. P., Brazil
b
College of Mechanical Engineering of the State University of Campinas, FEM / DETF / UNICAMP, Campus Zeferino Vaz, Barão Geraldo - 13.083-970 Campinas, S. P., Brazil
article
info
Article history: Received 4 August 2009 Received in revised form 26 March 2010 Accepted 23 April 2010 Keywords: Slug flow Capacitance probe Liquid layer thickness Signal analysis FFT PDF
abstract The slug flow is a common occurrence in gas–liquid piping flows. Usually it is an undesirable flow regime since the existence of long lumps of liquid slug moving at high speed is unfavorable to gas–liquid transportation, so that considerable effort has been devoted to study its hydrodynamic characteristics. In this work, a capacitive probe was used for dynamic measurements in the horizontal air–water slug flows, for several flow rates. The acquired signals were representative of the effective liquid layer thickness near every cross sectional area of the flow, instead of merely the holdup or void fraction in a finite volume of the flow. This was possible because probe had a thin sensing electrode that minimizes the axial length effect on the measurements. Tests were performed in a 34 mm i.d. acrylic pipe, 5 m long; in which slug flows as well as stratified-smooth and stratified-wavy flows were generated. Signal analysis techniques were applied for flow regime identification and toward characterization of these two-phase flows: Power Spectrum Density (PSD) from Fourier Transform and Probability Density Function (PDF) from Statistical Analysis. Therefore, PSD and PDF graphs were taken as signatures of each flow under test and a correlation was calculated for each PSD and PDF set of data, which showed to be a robust parameter for correct flow regime identification. © 2010 Elsevier Ltd. All rights reserved.
1. Introduction The complex nature of gas–liquid two-phase flows in pipelines has challenged researchers along the past few decades. Many of them directed their efforts in develop unambiguous techniques for characterizing multiphase flows from dynamic signals analysis acquired by using different types of sensors: pressure [1–3], holdup or volumetric concentration [4–7], or liquid film thickness [8]. Pressure and volumetric concentration sensors are attractive as they are non-intrusive, robust, inexpensive, relatively welldeveloped and, therefore, more likely to be applied in industrial systems. The most import characteristic of the gas–liquid flow in pipes is the flow regime, which concerns the special arrangement of the gas and the liquid into the pipe [9]. On a macro point of view over this special arrangement, the bubbly is typically an 1D flow regime, while stratified-smooth is 2D, and stratified-wavy and slug flow are 3D due to variations of local concentration of liquid and/or gas components along the same cross sectional area and along the axial pipe length. Consequently, some confusion occurs when analyzing signals from different flow regimes in time space,
∗
Corresponding author. Tel.: +55 19 3634 1100; fax: +55 19 3634 1100. E-mail address: [email protected] (E. dos Reis).
0955-5986/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2010.04.006
since the dimensional flow information contained in the signal depends on the probe type used. Therefore, one must consider that sensors with different sensing principles, such as conductive [6,8], photonic [10] and capacitive (discussed ahead), etc. have different perceptions of the fluid flow and this fact reflects on the signal generated by each different probe and, therefore, on the signal analysis results. Capacitive sensors are robust, inexpensive, safe, and widely used in industrial systems for concentration measurements. Das and Pattanayak [4], Costigan et al. [5], Geraest and Borst [11] and Elkow and Rezkallah [12] used them to identify two-phase flow regimes. The authors reported the successful application of PDF on signals for low flow rates of the liquid and gas phases. Little attention was paid to the use of PSD, mainly due to fact that the capacitance electrodes commonly are thicker in the axial flow direction (about 2 times the pipe diameter) to enhance its sensitivity, as required by the capacitance transducer circuit, and also to reduce the effect of the electrical field distortion near the electrode’s edges, which can cause distortions on the probe response [13]. In this case, however, the probe can also operate as a low-pass filter cutting off high frequency components related to the flowing mixture [14] and, as a result, a portion of the information is lost. The gas–liquid slug flow is one of the most common two-phase flow regimes over all pipeline’s inclination. It is characterized by an intrinsic unsteadiness, due to the alternation of liquid
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Fig. 1. Experimental installation schematic.
‘slugs’ containing small bubbles, that fill the whole pipe cross section, with regions in which the flow consists of a liquid layer over/around an horizontal/vertical elongated gas bubble [15]. This intermittent behavior causes high fluctuations of pressure, concentration and flow rate. As a result, an extremely careful design of the pipeline is required (valves, orifices, etc.). Moreover, the low ‘slugging’ frequency (few hertz) can be in resonance with the characteristic frequency of the pipeline itself, causing serious damage. For that reason, it is of essential importance [6,16] not only to identify the slug flow regime but also determine its main flow characteristics, providing useful information for the engineer in design and process control. This work propose is to utilize the capacitive non-intrusive probe presented by dos Reis and Goldstein Jr. [17], to determine the effective liquid layer thickness in about every cross sectional area, in a horizontal Plexiglas pipeline, for several flow regimes: slug, stratified-smooth and stratified-wavy, instead of measuring only the holdup or void fraction in a finite flow volume. The flow regimes were established for air superficial velocities varying from 1.3 to 6.0 m/s, and water from 0.08 to 0.80 m/s. The proposed capacitive technique allowed registering information of an effective cross sectional liquid layer thickness through the time, and this information could be used to identify whether the image of the two-phase flows were inherently 2D or 3D. Furthermore, PDF and PSD data analysis were used to determine several flow characteristics: flow regime, range of the liquid layer thickness, presence of waves, dominant frequencies, presence of hydraulic jumps, regions of signal concentration, range of frequencies, and amplitudes. 2. Experimental installation Fig. 1 shows a schematic of the experimental flow loop. The air supply system is composed of a reciprocating compressor producing 19.1 m3 /h at 830 kPa, an air reservoir, AR, of 400 liters, to reduce pressure oscillations downstream, an air filter and pressure regulator, two needle valves, VC1 and VC2, one for fine flow adjustment, and two turbine flow meters, TM1 and TM2, of 3/4 and 1 1/2 inches, for measurement of the volumetric airflow rate, QG , with ranges from 1.1 to 11.0 and 8.8 to 88.0 m3 /h, and calibrated measurement uncertainties of ±0.14 m3 /h and ±0.41 m3 /h, respectively. A type T thermocouple, T 3, and an electronic pressure gauge, P3, were used to measure the air temperature and gauge pressure, T3 and p3 , respectively. The water supply system was composed of a reservoir, WR, which also performed air–water separation; a centrifugal pump, P, with a capacity of 45 m3 /h at 274 kPa (75% efficiency); two water
filters, WF, operating in parallel; a double tube heat exchanger, HE; two control valves, VC3 and VC4, one for fine adjustment, and a turbine meter, TM3 to measure the volumetric water flow rate, QL , which ranged from 3.0 to 45 l/min, with a measurement uncertainty of ±0.23 l/min. A water-cooling system became necessary due to heating of the circulating liquid. A cooling tower supplied water close to the wet bulb temperature to the annular side of the heat exchanger. Tests were realized with deionized water to avoid fouling the internal pipe walls, meters and valves. A type T thermocouple, T 2, was used to measure the water temperature, T2 . The air–water flow system was composed of an 13 m long Plexiglas pipeline with an internal diameter, D, of 34 mm and 3 mm wall thickness, a junction with 45◦ branch arms, TM, which mixed water from the main arm with air from the branch arm on the top. The Plexiglas pipeline has about 5 m of length from MT to the tests section (150 D). A Type T thermocouple, T 1, and an electronic pressure gauge, P1, were used to measure the temperature of the air–water mixture, T1 and p1 , respectively. A data acquisition system composed of a microcomputer, AT-MIO16E10 board, connections block, and Labview 6.0, by National Instruments TM , was used to log all the data from instruments. 3. Capacitive probe description As discussed by dos Reis and Goldstein Jr. [17], the effective liquid layer thickness, hL , represented by HL1 in Fig. 1, was measured by a device composed of an capacitive source-sensor pair of electrodes, guard electrodes, sinusoidal signal source and capacitance transducer circuit, as shown in Fig. 2. The sensor electrode was connected to the capacitance transducer and the source electrode was connected to the sinusoidal signal source. In this probe, the sensor electrode has a minimum width of 3 mm (black), which allows the probe to detect high frequencies related to the gas–liquid flow. Almost only the liquid in the sectional volume limited by the sensing electrode affects the capacitance transducer response. Two guard electrodes mounted very close to the sensing electrode (0.5 mm) limit electric field distortions around edges [13]. The electric field created among the sensor electrode and guard electrodes is null due to the virtual ground condition imposed by careful design of the capacitance transducer circuit [18]. Consequently, the shorter width of the sensor electrode makes the system response closer to the mean liquid thickness measured at the cross sectional area of the pipe. This is important, for example, when measuring the amplitude of small waves. In that sense, the technical limitation is due to limitations of the sensitivity and speed of the capacitance
E. dos Reis, L. Goldstein Jr. / Flow Measurement and Instrumentation 21 (2010) 347–355
Fig. 2. The thin electrode capacitance probe.
Fig. 3. Air–water flow regime map with experimental test point.
transducer circuit. Dos Reis [19] presented an analog transducer circuit suitable for this application. The sensibility was evaluated to be 7.0 mV/fF and the circuit settling time about 6 ms. The probe was calibrated and a measurement uncertainty of ±0.521 mm or ±1.53% of FS (confidence interval of 95%) was determined. 4. Experimental procedure and data reduction Fig. 3 presents a theoretical air–water flow map for a horizontal piping of 34 mm of diameter, D, according to Taitel and Dukler [9]. Thirteen flow conditions were tested in the slug, stratified-smooth and stratified-wavy flow regimes, in the region of the map where the flow regime transition lines were more concentrated. While some of test flow conditions were chosen distant from the transition lines, as test points 3, 10 and 13, other points were near the slug-stratified and slug-annular transition lines, such as 1, 7, 6, 8, 9 and 10. Therefore, six test points were near the stratifiedslug and slug-annular transition lines. Four test points, under smooth and wavy flow regimes, were also included for evaluating a proposed flow regime identification methodology, since signals from slug and stratified-wavy flows can generate similar profiles in PDF and PSD graphs, as discussed ahead. The air supply system was fitted with a control valve and two turbine meters, TM1 and TM2, as shown in Fig. 2, which enabled us to cover the air superficial velocities, uGS = QG /A, from 1.3 to 6.0 m/s. The water flow system had a single turbine meter, TM3, allowing water superficial velocities, uLS = QL /A, from 0.08 to 0.80 m/s. Flow rates of air and water, QG and QL , gauge pressure, p1 , and temperature of the air–water flow mixture, T1 , through P1 and
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T 1, temperature of water T2 through T 2, temperature and gauge pressure of air into the feeding line, T3 and p3 , through T 3 and P3, and signals from the capacitive probe, HL1, all these signals, which were produced in the tests, were logged by the data acquisition system and stored in a digital file. The data acquisition time, ta , was defined as equal to 300 s for each test (5 min). The number of samples, n, and the data acquisition rate, f , were chosen to keep the same acquisition time for all tests. The f values were previously determined to avoid an aliasing error: 800 Hz for tests 1, 2, 3, 9, 10 and 11, which had the smaller flow velocities (∼1.5 m/s); 1500 Hz for points 4, 7, 8, 12 and 13 (∼3.5 m/s); and 2,500 Hz for points 5 and 6 having the higher flow velocities (∼6.5 m/s). This corresponds, for example, to n = 240,000 samples acquired at 800 Hz. Therefore, the use of high data acquisition rates was due to the temporal resolution of the signals demanded by the cross correlation technique, which was used by dos Reis and Goldstein Jr [17] to measure the mean translational velocity of the slug flows. This fact does not represent a problem for PSD or PDF analysis, since if more information is made available it only increases the computational work. In the data reduction stage, the acquired signals from electrical voltages of temperature, volumetric flow rate and pressure meters were first averaged, being converted to measured values by the calibration curve of each instrument. Differently, the acquired signals from the capacitive probe were first converted to the respective non-dimensional liquid layer thickness measurements, hL /D, also by using the calibration curve. A technique was applied to correct for deviations of the dielectric permittivity of the water associated to temperature variations of the flow [20]. Again, the hL /D values in number of n were stored in a digital file. In the signal analysis stage, all hL /D data processing begun from raw data that was ten-point filtered to remove all high frequency noise (moving average filter). After that, the Probability Density Function — PDF was determined by constructing histograms [5, 21], each one with 30 intervals, that cover the range from the minimum to the maximum values registered of hL /D. From the histograms, the probability of each interval, i, was calculated as P (hL /D)i = (number of values of hL /D into the interval i) / number of samples, n. Following the Power Spectrum Density — PSD was calculated from the fast-Fourier transform-FFT algorithm as the magnitude of the complex numbers from 1 to n/2 + 1 [22]. Data of hL /D were used in FFT without previous filtering, and subsequently the PSD data was 20-point filtered to remove noise from the longer FFT and to provide a good frequency resolution. PSD graphs were plotted excluding the single component at 0 Hz, and from 0 to 10 Hz that concentrate almost the whole power spectrum in all tests. PDF and PSD were used to identify the flow regime by means of a correlation. Some PDF and PSD graphs were taken as flow regime signatures, while others were used for testing. For PDFs from test 1 to 13 in Fig. 3, there were originally 31 pairs of (hL /D)i versus P (hL /D)i representative of each interval i, with ranges between the minimum and the maximum of hL /D, and also for PSDs by interpolation, there were 3000 pairs of frequency component (fs )i versus component power S (fs )i , which were equally distributed from 0 to 10 Hz from the FFT. A normalized correlation was calculated, as given by Eqs. (1)–(4):
ρxy = p
Rxy
Rxx Ryy
Rxx =
Ryy =
N 1 X
N i =1 N 1 X
N i =1
(1)
x [i] x [i]
(2)
y [i] y [i]
(3)
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Table 1 Tests data. uGS (m/s)
ulS (m/s)
1 2 3 4 5 6 7 8 9
1.371 1.371 1.392 3.225 6.131 6.165 3.170 3.206 2.013
10 11 12 13
1.371 2.016 3.225 5.926
Test
Rxy =
N 1 X
N i=1
Flow regime observed
h¯ LE /D (–)
ShLE /D (–)
Range of hLE /D (–)
fsd (Hz)
Range of fs (Hz)
0.198 0.410 0.788 0.797 0.788 0.497 0.301 0.198 0.200
Slug
0.312 0.415 0.520 0.443 0.359 0.328 0.338 0.313 0.282
0.191 0.230 0.267 0.193 0.140 0.125 0.132 0.111 0.168
0.160–0.998 0.217–0.987 0.243–0.994 0.213–0.984 0.181–1.00 0.155–0.967 0.177–0.965 0.186–0.956 0.164–0.981
0.133 0.533 1.14 0.937 1.64 0.960 0.360 0.297 0.213
0–2.88 0–5.38 0–7.50 0–6.95 0–9.60 0–14.6 0–7.81 0–6.47 0–4.17
0.080 0.080 0.080 0.082
Smooth Wavy Wavy Wavy
0.421 0.407 0.338 0.173
0.00150 0.0185 0.0550 0.0767
0.417–0.424 0.371–0.433 0.274–0.461 0.0776–0.423
0.0667 5.48 0.0667 0.497
0–7.41 0–13.0 0–17.7 0–18.5
x [i] y [i]
(4)
where ρxy is the normalized correlation, Rxx and Ryy are the autocorrelations of x and y data, Rxy is the correlation of x and y, x or y are equal to P (hL /D) or S (fs ) and N is the amount of data to be computed. ρxy , in this case, ranged from 0 to 1, being equal to 1 when there is a perfect similarity of data. Eqs. (1)–(4) require that x and y be calculated on the same hL /D or fs for each i. However, PDF data had different ranges and a parameterization scheme was necessary. By using a spline interpolation algorithm, N = 500 pairs from hL /D = 0 to 1.0 were calculated for each original set of 31 pairs of (hL /D)i versus P (hL /D)i . Interpolations were performed only within the interval from the minimum and the maximum of (hL /D)i , otherwise, when determining the new P (hL /D)i = 0. N = 500 pairs were sufficient to reproduce each original PDF graph of test 1 to 13 with high fidelity. On the other hand, PSD data were already adequate for a correlation calculation with N = 3000, since n/f = 300 s for all tests and the frequency range was always the same as discussed next. The ‘‘normalized’’ correlation was calculated according to Eq. (5) instead of Eq. (1), taking advantage of the difference in scale of the power spectrum of signals related to different flow regimes. ∗ Therefore, ρxy was always equal to 1 under perfect similarity. However, it could be many times greater than 1, as discussed in item 5.2. ∗ ρxy =
Rxy Rxx
.
(5)
The hL /D, PDF and PSD were further manipulated and are presented in those data of Table 1. From basic Statistics, mean values of hL /D signals and standard deviations were calculated, h¯ LE /D and ShLE /D , as well as the dominant frequency of each signal fsd , and ranges of hL /D. The range of frequency fs in all PSDs varied from 0 Hz to 10 Hz, which was taken as an upper limit of 1/100 of the component power on the dominant frequency, since the power spectrum tended asymptotically to zero (right side of the PSD graphs presented in the next item). 5. Results and discussion Figs. 5–7 show three types of graphs for each test shown in the map of Fig. 3 as a experimental point from number 1 to 13: a sample graph of hL /D through a short time interval of only 30 s at the left, a PDF graph at the center, and a PSD graph at the right. From visual observations tests 1 to 9, in Figs. 5 and 6, their flow regimes were identified as slug, while in test 10 the flow regime was identified as stratified-smooth, and as stratified-wavy in tests 12 and 13, in agreement with the map of Fig. 3 [9]. For test point 11, in which the flow regime was expected to be stratified-smooth, it was observed
Fig. 4. Scheme of data analysis.
as stratified-wavy with small amplitude waves along the air–water interface. Therefore, it may be considered that, in the flow map of Fig. 3, the transition lines are representative in truth of a gradual regime transition that occurs across them. Test points 1, 6 8 and 9 are also near the transition lines (slug-stratified or slug-annular), and hybrid regime characteristics were impressed on the signals coming from the probe, as will be discussed. Individual flow characteristics of each test point shown in Fig. 3 are studied in item 5.1, while flow regime identification was studied in item 5.2. The information in item 5.1 is important in order to understand the flow regimes’ signatures in PDF and PSD graphs discussed in item 5.2. 5.1. Characterization of air–water flows This analysis follows data presented in Table 1, were h¯ LE /D detonates the mean liquid layer thickness, ShLE /D the standard deviation, and fsd the dominant frequency. The diagram shown in Fig. 4 concerns the variation of the superficial velocities of air and water over all tests according to the same polygon of Fig. 3. Fig. 4 is divided in two parts according to the flow regimes in the map: slug or stratified (smooth and wavy). Along the clockwise path indicated by arrows around the polygon, test 1 had the lowest superficial velocities of both phases under slug flow, while tests 2 and 3 had a higher liquid velocity, tests 4 and 5 had both higher liquid and gas flow rates, as well as all tests where near the slugannular and slug-stratified transition lines from tests 6 to 1. Further analysis of stratified flow data processed with tests 10 to 13 by increasing the airflow rate, while the water flow rate was kept constant. Fig. 4 also shows, on the top, a schematic of the horizontal Plexiglas pipeline and the test section position.
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Fig. 5. Graphs of tests under slug flow — Tests 1 to 5.
The liquid flow rate was increased by about 300% along the straight vertical line for tests 1 to 3, under slug flow, while the airflow rate was kept constant. Firstly, signal samples of tests 1, 2 and 3 in Fig. 5 indicate the presence of liquid slugs when hL /D is near 1.0, and regions of the elongated gaseous bubbles have lower values of hL /D separating them. The PDF graphs show hL /D signals occurring in a large range that decreases from test 1 to 3 as can be seem on Table 1, while the liquid layer above the elongated bubbles is thicker from hL /D = 0.160 in test 1 to hL /D = 0.243 in test 3. Therefore, the main characteristic of the PDF graphs is the presence of two peaks with a central region of lower signal probability, similar to results presented by Costigan and Whalley [5]. One of
those peaks is at about hL /D = 0.4, and the other is near hL /D = 1.0. They indicate the presence of two important values of hL /D: the left one is related to the presence of the elongated bubbles air–water interface and the right one to the liquid slugs. The peaks at the left, in general, are greater than the right ones, however, it should be observed that from tests 1 to 3 the peak’s height at the right becomes higher, and that there is an increase in the signals probability in the central region between the right and left peaks in each PDF graph, causing a more regular distribution of the probability. Furthermore, the presence of a hydraulic jump can be observed in tests 1 and 2, and a reduction of high waves into the elongated bubbles from test 1 to 3. A ‘‘mountain’’ shape
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Fig. 6. Graphs of tests under slug flow — Tests 6 to 9.
characterizes the PSD graph for the slug flow, with the highest peak corresponding to the dominant frequency, fsd . This frequency, fsd , is observed as increasing from about 0.133 Hz in test 1, through 0.533 Hz in test 2, and reaching 1.14 Hz in 3, as can be seen in Table 1. The liquid flow rate was kept high and constant from tests 3 to 5, while the airflow was increased about 360%. Thus, in tests 4, 5 and 6, it can be observed hL /D rarely reaching 1.0 in the presence of liquid slugs, as observed in tests 1, 2 and 3. This is due to the increased presence of small bubbles dispersed into the liquid slug body. The response of the capacitive probe is affected by their presence, since its signal is proportional to the effective dielectric permittivity of the mixture. Therefore, the population of bubbles increased with the flow velocity (airflow rate). The range of hL /D was not different to the previous tests, however, the PDF graphs show the disappearance of the right peaks related to the liquid slugs in tests 3 to 5, which occurred due to shaper peaks in hL /D signals, while the probability of the left region increases, and the PDF graph shows itself, again, like a chi-square probability distribution. High waves were also observed into the elongated bubbles region, as can be seen in the graphs of tests 4 and 5, in which their population increased from tests 3 to 5 in opposition to tests 1 to 3. The PDF graphs also show a reduction of the liquid layer thickness below the elongated bubbles from hL /D = 0.243 in test 3
to 0.181 in test 5. The graphs of PSD have the same ‘‘mountain’’ shape, however, with a larger decrease in the spectrum’s range to about half of those from tests 1, 2 and 3, with the appearance of some components of higher frequency from test 1 through 4 and 5. Furthermore, the PSDs show that the dominant frequency decreased from test 3 at about 1.14 Hz to 0.937 Hz in 4, and increased again to 1.64 Hz in test 5, as can be seen in Table 1. Consequently, this fact should state that the frequencies related to the hydrodynamics of the air–water slug flow aren’t a univocal function of the liquid and gas flow rates or superficial velocities. The liquid flow rate was decreased by about 60% from test 5 to 6, while the airflow rate was kept high, as shown in Figs. 5 and 6, with the flow condition in test 6 near the slug-annular transition line, as shown in Fig. 3. The sample graphs of hL /D signals show a reduction of the peak’s height, which show that the slugs were more aerated in test 6 than in test 5, and an increase in the mean time interval between two consecutive peaks, and also an increased presence of high waves in the flow. The PDF and PSD graphs are curiously very similar while showing a small reduction of the power spectrum range, with the dominant frequency falling from 1.64 Hz in test 5 to about 0.960 Hz in test 6. Both air and water flow rates were reduced by about 82% and 66%, from test 6 to 7, respectively. Peaks in the hL /D signals become more separated in time, and they still aren’t as high as hL /D = 1.0.
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Fig. 7. Graphs of tests under stratified-smooth and stratified.
The presence of high waves is also predominant as can be seen in PDF graphs, showing no large variations in the signals’ probability. However, huge variations occurred in the frequencies of hL /D signals as shown in the PSD graphs, since an alteration in the graphs’ shapes occurred, while the dominant frequency became smaller from 0.960 Hz in test 6 to about 0.360 Hz in test 7. The liquid flow rate was decreased again from test 7 to 8 by about 100%, while the airflow rate was the same. In a general way, all graphs of tests 7 and 8 are similar: signal sample, PDF and PSD, the same happening with graphs of test point 9 when the airflow rate was decreased from test 8 by about 65%. However, the PDF graph of test 9 showed the appearance of the right peak related to the liquid slug region, showing the presence of less aerated slugs as has occurred in tests 1, 2, 3 to 4. Concerning the developing pipeline length, x, necessary to the flow reach its complete full-developed fluidynamic, Nydal et al. [23] proposed that a ‘‘well defined statistical distribution of the slug holdup (only slug), with only a peak, may be a necessary condition for a developed slug flow’’. They demonstrated x as depending on both gas and liquid superficial velocities and that it ranges from 120 D to 400 D and over. Based on their own measurements in a 52 mm i.d. pipeline with a range of superficial velocities of air, uGS , from 0.5 to 20 m/s and of water, uLS , from 0.6 to 3.5 m/s, they obtained a map of minimum length for a developed slug flow. Based on this map, only flows in test points 2,
3 and 4 were under fully-developed conditions. However, one must consider that test points 1, 6, 7, 8 and 9 are near the flow regime transition lines, and their fluidynamic development does not occur according to the conditions proposed by Nydal and workers. Tests 10, 11, 12 and 13 are in the region of stratified-smooth and stratified-wavy flow regimes in Fig. 3, with the gaseous phase flowing separately over the liquid phase, as observed in graphs of Fig. 7. The airflow rate was increased by about 360% from tests 10 to 13, while the water flow rate was kept constant, about 150% below that of tests 1, 9 and 8 under slug flow. The signal graph of test 10 shows an almost constant value of hL /D about 0.42, throughout time. The PDF graph represents a single narrow band at 0.421, while the PSD graph shows this flow condition as having some frequency components different from 0 Hz, however, their amplitudes are small due to the range of the signal power spectrum. The PSD graph has two distinct regions: one at a low frequency range with a dominant frequency of about 0.1 Hz at the left; and another with a scattered spectrum around the dominant frequency, at about 4 Hz, at right. Also an increase in the airflow rate increased the oscillations in the air–water interface from test 10 to 12, with a decrease in the mean liquid layer thickness from h¯ L /D = 0.421 to 0.338, as can be seen in the signal samples and PDF graphs. The PSD graphs of tests 11 and 12 show a considerable increase in the amplitude of the waves, since the range of the power spectrum increased by about 1000% from test 10. The shapes
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Table 2 Correlation results for PDF data. Test
1 2 3 4 5 6 7 8 9 10 11 12 13
Flow regime observed
ρxy Ref. Point 3
Ref. Point 5
Ref. Point 10
Ref. Point 13
Slug
0.549 0.810 1.000 0.966 0.815 0.697 0.666 0.775 0.377
0.831 0.971 0.815 0.881 1.000 0.966 0.953 0.984 0.663
0.015 0.057 0.086 0.093 0.056 0.048 0.045 0.058 0.022
0.411 0.221 0.112 0.137 0.259 0.357 0.344 0.304 0.551
Smooth Wavy Wavy Wavy
0.086 0.276 0.862 0.112
0.056 0.176 0.743 0.259
1.000 0.305 0.021 0.001
0.001 0.006 0.098 1.000
Ref. Point 3
Ref. Point 5
Ref. Point 10
Ref. Point 13
Slug
0.260 0.567 1.000 0.724 0.442 0.440 0.177 0.264 0.250
0.419 0.827 1.394 1.152 1.000 0.715 0.296 0.443 0.392
11 157 14 083 16 599 18 848 16 147 12 527 7213 9879 8937
8.019 13.463 12.365 11.330 6.592 7.009 4.716 6.111 5.977
Smooth Wavy Wavy Wavy
0.000 0.000 0.009 0.045
0.000 0.002 0.026 0.075
1.000 96.60 802.7 1390
0.000 0.012 0.175 1.000
Table 3 Correlation results for PSD data. Test
1 2 3 4 5 6 7 8 9 10 11 12 13
Flow regime observed
∗ ρxy
were similar to those of test 10 with two distinct regions. They also show a large range of frequencies in test 12, with a dominant frequency at the right region about 4.5 Hz, which is narrowest in test 11, with a dominant frequency at the right region of about 5.8 Hz. The airflow rate was also increased about 82%, from test 12 to 13. The waves were higher while the liquid layer became thinner from about hL /D = 0.338 to 0.173, as seen in PDF graphs and in Table 1. However, the PDF graph is similar to that of tests 5 to 7 under slug flow as a chi-square probability distribution, which can cause some confusion; otherwise, both conditions have not different ranges of hL /D. Still the PSD graph of test 13 is similar to those of tests 1, 7, 8 and 9, under slug flow, which are near the slugstratified transition line, and also with a low dominant frequency of about 0.497 Hz close to those of tests 1, 7, 8 and 9. Although the PDF graphs presented a different shape for stratified and slug flows, since they presented a single peak for stratified and two peaks for slug flows, as shown on the graphs of tests 10, 11, 12, and 13, and 1 to 4, it is not true when the slug flow occurred under high airflow rate with slug bodies becoming highly aerated. In this condition, the right peak in PDF disappeared, and these graphs were similar to those under stratified-wavy flow, as in test 13. However, differently of those under slug flow, ranges of hL /D were always less than 0.5, while standard deviations ShLE /D were always less than 0.8 under stratified-smooth and wavy flows. PSD graphs were also useful tools when analyzing the frequencies related to the flow, although they also presented some problems in identifying stratified-wavy flow regimes with high airflow rates, test 13, and slug flow near the transition lines, tests 1, 6, 7, 8 and 9. However, the power spectrum range of the slug flow could be about 1500% greater than those from the wavy flows, which could be decisive when identifying the flow regime.
For example, by comparing both graphs of tests 6 or 7 and those of test 13, PSD graphs had ranges from 0 to about 30 [Power/Hz] against 0 to 3.0 [Power/Hz]. A similar analysis can be made from PDF graphs; however, the scales’ differences are smaller than from PSDs. 5.2. Flow regime identification Tables 2 and 3 present the correlation results calculated from Eqs. (1)–(4) for PDFs, and from Eq. (5) and (2)–(4) for PSDs. Test points 3, 5, 10 and 13 were chosen as references for the slug flow regime (3 and 5), stratified-smooth (1) and stratified-wavy (13), since they are distant from the transition lines in Fig. 3, and they imposed the signatures of each flow regime on the respective probes signals, as discussed in item 5.1. In a general way, ρxy in ∗ Table 2, or ρxy in Table 3, is equal to 1.000 if the reference and the test data are the same, such as 5–5 and 3–3. Additionally, ρxy is the same for PDFs if the reference and the test numbers are permuted, such as 3–5, and 5–3. From Table 2 for PDF data, when identifying the slug flow regime, ρxy was equal to 0.815 for test 3 with test 5 as the reference, being the smallest value equal to 0.663 for test 9, which is greater than those when test 3 was taken as the reference. This is an important result, since test 5 is more representative than test 3 according to the actual concept of ideal picture of PDF for slug flows. Additionally, ρxy was high and equal to 0.862 for test 12 under the stratified-wavy flow regime, with 5 as the reference. It was due to the concentrations of signals’ probability in the same range of hL /D, as can be observed in Figs. 5 and 7. When identifying the stratified-smooth flow regime, values of ρxy , with test 10 as the reference, were always less than 0.1, when the flow regime observed was slug or wavy, at least ρxy = 0.305 for test 11, this PDF shows some similar characteristics of the smooth
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flow regime, as can be seen in Fig. 7. Otherwise, when identifying the stratified-wavy flow regime with test 13 as the reference, tests 11 and 12 under stratified-wavy didn’t present high values of ρxy . Different situations occurred for some tests under slug flows with a higher ρxy up to 0.551, such as 1 and 9 near the transition lines. From Table 3 for PSD data, when identifying the slug flow ∗ regime with test 3 as the reference, ρxy was as low as 0.177 for ∗ test 7 under slug flow, while ρxy was less than 0.045 (test 13) in all stratified flows. Analogous results were observed when test 5 ∗ was the reference, however, with a higher ρxy equal to 0.296 for test 7. Therefore, test 5 showed itself again as a better reference for identifying slug flows. Similar results were observed from PDFs as discussed previously. When identifying the stratified-smooth with test 10 as the ∗ reference, Table 3 shows values of ρxy many times greater than 1.0, for all tests under both slug and stratified-wavy flow regimes. Otherwise, when identifying the stratified-wavy regime with test ∗ 13 as the reference, all slug flow tests presented ρxy many times greater than 1.0, while it was less than 1.0 among all stratified flows. Therefore, test 13 as the reference is suitable to distinguish stratified and slug flow regimes. As discussed, a correlative technique applied to PSDs supplied a better parameter for correct flow regime identification than PDFs. 6. Conclusion and remarks This paper presented a study about the signal analysis of a capacitive probe used to register the liquid layer thickness variation in air–water two-phase flows under stratified-smooth, stratified-wavy and slug flow regimes, some of them being near the transition lines in the flow map. These flows were generated in a horizontal acrylic pipe, with a 34 mm diameter, and the probe was installed 150 D downstream from the phases mixing point. Both the probability function calculation and the fast-Fourier-transform were applied to the acquired signals, and graphs of probability distribution function – PDF – and power spectrum density – PSD – were produced. PDF and PSD graphs showed to be useful for evaluating characteristics of the flows: range of the liquid layer thickness, presence of waves, dominant frequencies, presence of hydraulic jumps, regions of signal concentration, range of signal frequencies and amplitudes. Both presented respectively similar graphs for stratified-wavy and slug flows with high gas flow rates. Different ranges of liquid layer thickness measurements in PDFs and of scales of power spectrums in PSDs were observed, which were more evident in PSDs. When applying correlation technique on PDF and PSD data, the results showed the PSD as more effective for flow regime identification in all 13 tested conditions, with 4 of them near the slug-stratified and slug-annular transitions lines on the flow regime map, which indicates that some computational algorithm can be implemented for use in practical situations. However, one must consider the following: (i) the power spectrum does not have a coherent scale, or a system of units, which can cause some confusion in practical situations; (ii) PDF calculations request minimal computational work if compared to PSD. In a future work, using more than one probe on the same pipe slice, but at a different angle would provide more information for correct flow regime identification. Therefore, a new assembly of electrodes from that of Reis and Goldstein [17], can be built. There are two ways to perform that: (i) two sensing electrodes mounted around the same pipe cross section; or (i) they can be mounted in different pipe sections with an independent source and guard electrodes. A study based in the Finite Element Method, for example, can help the researcher’s choice. Moreover, in horizontal flows, one should consider that if the new sensing electrode was
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installed in the upper or lower side of the pipe section, the effect of its major proximity to gas or liquid, due to gravity, would appear in the probe’s signals. Also, Wang et al. [24] reported a development length x as long as 1157 D, where slug still collapses and grows, as was observed by the authors. Then it can be seen that the subject treated is still open for research. Yet, the methodology proposed in the manuscript may be used by comparing PDF and FFT graphs in different measurement stations along the pipeline. Acknowledgement The support of FAPESP – Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazil, is deeply appreciated. References [1] França F, Acikgoz M, Lahey Jr RT, Clausse A. The use of fractal techniques for flow regime identification. International Journal of Multiphase Flow 1991; 17(4):545–52. [2] Shim W, Jo CH. Analysis of pressure fluctuations in two-phase vertical flow in annulus. Journal of Industrial and Engineering Chemistry (Seoul) 2000;6: 167–73. [3] Sun T, Zhang H, Hu C. Identification of gas–liquid two-phase flow regime and quality. In: IEEE instrumentation and measurement technology conference, 2002. [4] Das RK, Pattanayak S. Electrical impedance method for flow regime identification in vertical upward gas–liquid two-phase flow. Measurement Science and Technology 1993;4:1457–63. [5] Costigan G, Whalley PB. Slug flow regime identification from dynamic void fraction measurements in vertical air–water flows. International Journal of Multiphase Flow 1997;23:263–82. [6] Fossa M, Guglielmini G, Marchitto A. Intermittent flow parameters from void fraction analysis. Flow Measurement and Instrumentation 2003;14:161–8. [7] Mi Y, Ishii M, Tsoukalas LH. Investigation of vertical slug flow with advanced two-phase flow instrumentation. Nuclear Engineering Design 2001;204: 69–85. [8] Jana AK, Das G, Das PK. Flow regime identification of two-phase liquidliquid upflow through vertical pipe. Chemical Engineering Science 2006;61: 1500–15. [9] Taitel Y, Dukler AE. A model for predicting flow regime transitions in horizontal and near horizontal gas–liquid flow. AIChE Journal 1976;22:47–55. [10] Mouza AA, Vlachos NA, Paras SV, Karabelas AJ. Measurement of liquid thickness using a laser light absorption method. Experiments in Fluids 2000; 28:355–9. [11] Geraest JJM, Borst JC. A capacitance sensor for two-phase void fraction measurement and flow regime identification. International Journal of Multiphase Flow 1988;14(3):305–20. [12] Elkow KJ, Rezkallah KS. Void fraction measurements in gas–liquid flows using capacitance sensors. Measurement Science and Technology 1996;7(8): 1153–63. [13] Reinecke N, Mewes D. Recent developments and industrial/research applications of capacitance tomography. Measurement Science and Technology 1996; 7:233–46. [14] Ma J, Yan Y. Design and evaluation of electrostatic sensor for the measurement of velocity of pneumatically conveyed solids. Flow Measurement and Instrumentation 2000;11:195–204. [15] Taitel Y, Barnea D. Two-phase slug flow. Advances in Heat Transfer 1990;20: 83–132. [16] Nydal OJ, Pintus S, Andreussi P. Statistical characterization of slug flow in horizontal pipes. International Journal of Multiphase Flow 1992;18:439–53. [17] dos Reis E, Goldstein Jr L. A non-intrusive probe for bubble profile and velocity measurement in horizontal slug flow. Flow Measurement and Instrumentation 2005;16:229–39. [18] Yang WQ, Stott AL, Beck MS. High frequency and high resolution capacitance measuring circuit for process tomography. IEE Proc-Circuits Devices Systems 1994;141:215–9. [19] dos Reis E. Estudo do escoamento pistonado horizontal ar-água em tubulações com ramificação T: College of Mechanical Engineering, State University of Campinas (2003). Ph.D. thesis in Portuguese. [20] dos Reis E, Goldstein Jr L. A procedure to correct the effect of fluid flow temperature variation on the response of capacitive void fraction meters. Flow Measurement and Instrumentation 2005;16(4):267–74. [21] Walpole RE, Myers RH. Probability and statistics for engineers and scientists. New York: The Macmillan Company; 1973. [22] Oppenheim AV, Willisky AS, Nawab SH. Signals and systems. 2.ed Upper Saddle River, New Jersey: Prentice Hall; 1983. [23] Nydal OJ, Pintus S, Andreussi P. Statistical characterization of slug flow in horizontal pipes. International Journal of Multiphase Flow 1992;18(3): 439–53. [24] Wang X, Guo L, Zhang X. Development of liquid slug length in gas–liquid slug flow along horizontal pipeline: experiment and simulation. Chinese Journal of Chemical Engineering 2006;14(5):626–33.