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Design of Helical Capacitance Sensor for Holdup Measurement in Two-Phase Stratified Flow: A Sinusoidal Function Approach Lam Ghai Lim 1 , William K. S. Pao 2 , Nor Hisham Hamid 1 and Tong Boon Tang 1, * 1 2

*

Department of Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Malaysia; [email protected] (L.G.L.); [email protected] (N.H.H.) Department of Mechanical Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Malaysia; [email protected] Correspondence: [email protected]; Tel.: +60-5368-7801; Fax: +60-5365-7443

Academic Editor: Vittorio M. N. Passaro Received: 3 June 2016; Accepted: 30 June 2016; Published: 4 July 2016

Abstract: A 360˝ twisted helical capacitance sensor was developed for holdup measurement in horizontal two-phase stratified flow. Instead of suppressing nonlinear response, the sensor was optimized in such a way that a ‘sine-like’ function was displayed on top of the linear function. This concept of design had been implemented and verified in both software and hardware. A good agreement was achieved between the finite element model of proposed design and the approximation model (pure sinusoidal function), with a maximum difference of ˘1.2%. In addition, the design parameters of the sensor were analysed and investigated. It was found that the error in symmetry of the sinusoidal function could be minimized by adjusting the pitch of helix. The experiments of air-water and oil-water stratified flows were carried out and validated the sinusoidal relationship with a maximum difference of ˘1.2% and ˘1.3% for the range of water holdup from 0.15 to 0.85. The proposed design concept therefore may pose a promising alternative for the optimization of capacitance sensor design. Keywords: helical capacitance sensor; finite element method; two-phase flow; stratified flow; holdup measurement; sinusoidal

1. Introduction Horizontal two-phase flow occurs widely in the petroleum, nuclear, and chemical industries. Pipeline transportation of natural gas in the presence of a liquid phase or mixture of crude oil and water are examples of two-phase flow [1]. One of the most common observations in two-phase flow is the complete separation between the two phases at moderately low velocities, where such a phenomenon is known as stratified flow. On the other hands, bubbly, intermittent, and annular flows can be observed at higher velocities [2]. A number of techniques have been applied to measure the holdup in two-phase flow, e.g., X-ray, gamma ray, optical, ultrasonic, and capacitive method [3,4]. The definition of holdup can be found in [5]. Amongst all these, the capacitive method was often employed due to its relatively cheap cost, simple design, and non-invasive approach—one just needs to attach the electrodes on the outer surface of the nonconductive section of the pipe. Relatively high sensitivity to water content could be achieved in two-phase flow, owing to the disparity in their permittivity values [5–9]. The signals from the capacitance sensors had been studied to characterize and identify the flow patterns in horizontal two-phase flow [10–12]. In addition to two-phase flow measurements, the capacitive sensing technique has also been adopted in numerous applications, e.g., occupancy, motion, position, displacement, level, touch, pressure, humidity, and moisture detectors [13,14]. Sensors 2016, 16, 1032; doi:10.3390/s16071032

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Finite element method (FEM) is one of the most widely used design and analysis tools for capacitance sensor. Several configurations of two-electrode capacitance sensors have been proposed and analysed, i.e., concave, helical, and ring structures. Although increasing the number of electrodes (typically eight or more) to create an electrical capacitance tomography (ECT) has been explored [15], such a technique involves solving an inverse problem that is rather challenging in nature. A brief review of holdup measurement in horizontal two-phase flow using two-electrode capacitance system is presented in Table 1. Note that there were also other groups who conducted similar experiments on vertical two-phase flow [7,8,16–19]. Xie et al. [20] and An et al. [21] used two-dimensional (2D) finite element models to investigate and optimize the sensitivity distribution of concave electrode for holdup measurement in different flow patterns. In order to reduce the dependency of angle orientation in concave design, Hammer et al. [22] proposed a helical shape electrode of 180˝ and 360˝ . This was further validated by Tollefsen and Hammer [23] using a three-dimensional (3D) finite element model, where helical design was found to be more robust against the variation of flow patterns, specifically in stratified flow. Table 1. A brief review of holdup measurement in horizontal two-phase flow using two-electrode capacitance system. Authors

Electrode Design

Guard Electrodes

Inner Diameter of Pipe

Two-Phase Components

Geraest and Borst [24] Tollefsen and Hammer [23] Ahmed [25], Ahmed and Ismail [26] Caniere et al. [27] Demori et al. [9] and Strazza et al. [5] De Kerpel et al. [28] dos Reis and da Silva Cunha [29] An et al. [21] Zhai et al. [30] This paper

Helical Concave and helical Concave and ring Concave Concave Concave Concave, helical, and ring Concave Helical Helical

Yes No No Yes Yes Yes No Yes Yes No

5 mm and 50 mm 82 mm 12.7 mm 9 mm 21 mm 8 mm 33.85 mm 10 mm 20 mm 28.38 mm

Air-water Gas-oil, gas-water Air-oil Air-water Oil-water Vapour-liquid Air-water Oil-water Oil-water Air-water, oil-water

As compared to a concave design of the same spatial resolution, Ahmed [25] suggested that ring design was more sensitive to void fraction measurement. Similarly, Reis and Cunha [29] conducted an experimental study on several configurations of capacitance sensors for holdup measurement in air-water smooth stratified flow. They reported that ring design was the best configuration due to the least dependency of air-water distribution, but also found that all designs showed some levels of nonlinear response. Jaworek and Krupa [31] further pointed out that the electric field was strongly localized in the gap separating the rings, which in turn causes the ring design to be less sensitive to the changes of holdup. On the other hand, the design of the helical sensor could be optimized by adding guard electrodes to improve the homogeneity in the sensitivity distribution field of capacitance sensor [7,8,16]. Despite that, the nonlinearity in response still could not be eliminated completely due to the nonlinear behaviour of the electrostatic field [20,23]. Thus, De Kerpel et al. [28] proposed a flow pattern based calibration for capacitive void fraction sensor to counter the nonlinear response, albeit at the expense of computational cost. One of the major patterns observed for the holdup measurement in stratified flow was the nonlinear response assimilated to a sinusoidal function alongside the ideal response, and it was found in various sensor designs [23,27–29]. Instead of suppressing, we propose to exploit the sinusoidal response characteristics as a novel design concept of helical capacitance sensor for holdup measurement in two-phase stratified flow. Helical design is chosen because of its minimal dependency on angle orientation as compared to a concave design. At the same time, this is also due to its higher sensitivity as compared to a ring design [29]. The proposed design is simpler as guard electrodes are not required. We derive an approximation model of the sinusoidal relationship observed between the capacitance readings and the holdup values. Experimental studies based on air-water and oil-water two-phase stratified flows

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[29]. The proposed design is simpler as guard electrodes are not required. We derive an approximation model of the sinusoidal relationship observed between the capacitance readings and Sensors 2016, 16, 1032 3 of 15 the holdup values. Experimental studies based on air-water and oil-water two-phase stratified flows are carried out to validate the sinusoidal model. If modelled accurately, the approximation model can be usedout to to calibrate the the actual holdup for two-phasemodel stratified are carried validate thecapacitance sinusoidal sensor model. to If acquire modelled accurately, the approximation can flow. be used to calibrate the capacitance sensor to acquire the actual holdup for two-phase stratified flow. 2. Helical HelicalCapacitance CapacitanceSensor Sensor 2. 2.1. Conventional Conventional Design Design 2.1. ˝ ˝ Tollefsen and Tollefsen and Hammer Hammer [23] [23] demonstrated demonstrated that that 180 180° and and 360 360° twisted twisted helical helical sensors sensors exhibited exhibited similar trends of response between the capacitance value and holdup, but at different similar trends of response between the capacitance value and holdup, but at different measurement measurement ˝ ranges. In is is preferable in ranges. In this this case, case, aa larger largercapacitance capacitancevalue valueobtained obtainedfrom from360 360°helical helicalconfiguration configuration preferable order to increase the sensitivity of the sensor [20]. In addition, the pitch of helix is better correlated in order to increase the sensitivity of the sensor [20]. In addition, the pitch of helix is better correlated ˝ helical configuration. Thus, the 360˝ twisted electrode is selected. with with the the 360 360° helical configuration. Thus, the 360° twisted electrode is selected. ˝ twisted helical capacitance sensor in 2D and 3D views, Figure 1 shows the structure of of the the 360 Figure 1 shows the structure 360° twisted helical capacitance sensor in 2D and 3D views, which and detection electrodes. Parameters “W” “and”“θ” the are width opening which consists consistsofofsource source and detection electrodes. Parameters andare“θ” theand width and angle of source and detection electrodes, while “R ” and “R ” represent the inner radius and 2 1 opening angle of source and detection electrodes, while “ ” and “ ” represent the inner radiusouter and radius of the pipe. The thickness of the pipe wall is equivalent to R ´ R . The parameters W, θ, 2 1 outer radius of the pipe. The thickness of the pipe wall is equivalent to − . The parametersand, R are related by the following equation: θ,2and are related by the following equation:

= θR θ 2 W “

(1) (1)

where the unit of θ is in radian. The pitch of helix “ ” is defined as the length of one complete helix where the unit of θ is in radian. The pitch of helix “P” is defined as the length of one complete helix turn (360°), measured parallel to the axis of helix. In addition, the total length of the pipe covered by turn (360˝ ), measured parallel to the axis of helix. In addition, the total length of the pipe covered electrodes, denoted as “ ”, is obtained by duplicating the number of complete helix turns and by electrodes, denoted as “L”, is obtained by duplicating the number of complete helix turns and maintaining the pitch of the helix. This stage is crucial to minimize the fringe effect [20]. The relative maintaining the pitch of the helix. This stage is crucial to minimize the fringe effect [20]. The relative permittivity of wall, gas, and liquid are represented as “ε ”, “ε ”, and “ε ”, respectively. permittivity of wall, gas, and liquid are represented as “εwall ”, “εgas ”, and “εliquid ”, respectively.

Figure 1. The structure of 360˝ twisted helical capacitance sensor design in 2D and 3D views. Figure 1. The structure of 360° twisted helical capacitance sensor design in 2D and 3D views.

2.2. Finite Finite Element Element Model Model 2.2. FEM was was used usedto todesign, design,analyse, analyse,and andoptimize optimize the structure helical capacitance sensor in FEM the structure of of helical capacitance sensor in 3D 3D model. The voltage applied on the source electrode was 1 V and the detection electrode was 0 V. model. The voltage applied on the source electrode was 1 V and the detection electrode was 0 V. Due Due to the potential difference between the electrodes, the changes of the permittivity values in the measurement region can be observed through the capacitance value.

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to the potential difference between the electrodes, the changes of the permittivity values in the measurement region can be observed through the capacitance value. SensorsFigure 2016, 16,2 1032 4 of 15 displays 2D view of holdup values for air-water smooth stratified flow with different levels of water content, labelled as “ ”. The water holdup is represented as “ ”, where = 0 indicates the pipe is empty and = 1 indicates the pipe is filled completely with Figure 2 displays 2D view of holdup values for air-water smooth stratified flow with different water. The static response of the 3D helical model was simulated to obtain the capacitance value of levels of water content, labelled as “h”. The water holdup is represented as “Hwater ”, where Hwater “ 0 liquid holdups in stratified flow. By measuring the level of water content, the water holdup can be indicates the pipe is empty and Hwater “ 1 indicates the pipe is filled completely with water. The static calculated as follows [32]: response of the 3D helical model was simulated to obtain the capacitance value of liquid holdups − of water content, the water holdup can be calculated as in stratified flow. By measuring the level ( − ) 2 − follows [32]: , < ´ −¯ $ R ´h ? cos´1 1R 2 ’ p R ´hq 2R h´h 1 ’ ’ ´ 1 πR2 1 , h ă R1 = = 0.5 , (2) ’ π & 1 − Hwater “ (2) 0.5, ´ ¯ ( − )? 2 − h “ R1 ’ ´1 h´R1 + ’ 1’ − , cos ’ R1 ph´ R1 q 2R1 h´h2 % 1´ ` , h ą R1 π πR2 1

Figure 3 is an equivalent circuit representation of helical capacitance sensor displayed in Figure 3 is an equivalent circuit representation of helical capacitance sensor displayed in Figure 2. Figure 2. In general, this would include the capacitance of ambient air, in parallel and the In general, this would include the capacitance of ambient air, Cambient in parallel and the capacitance capacitance of pipe wall, in series with the capacitance of the two-phase components. However, of pipe wall, in parallel and the capacitance of pipe wall, Cwall in series with the capacitance of the note that and are the constant parameters. The normalized capacitance, , two-phase components. However, note that Cambient and Cwall are the constant parameters. ,, The obtained using FEM for air-water two-phase flow, can be defined as [28,29]: normalized capacitance, CN, f em , obtained using FEM for air-water two-phase flow, can be defined − as [28,29]: = C ´C (3) ,, e f f − min CN, f em “ (3) Cmax ´ Cmin is the effective total capacitance comprised of air and water, and and are the where where Ce f f and is the effective total capacitance comprised of=air and Cmax are the minimum maximum values of when 0 and and water, and = 1C , min respectively. In this minimum maximum values ofthe Ce f sensor “ 1,the respectively. In this context, water “ 0 and f whenisHfrom context, theand measurement range of to Hwaterand measurement span of the the measurement range of the sensor is from C to C and the measurement span of the sensor is max min sensor is equal to − . equal to Cmax ´ Cmin .

Figure 2. 2D view of different holdup values for air-water smooth stratified flow. Figure 2. 2D view of different holdup values for air-water smooth stratified flow.

Figure 3. 3. Equivalent Equivalent circuit circuit representation representation of of helical helical capacitance Figure capacitance sensor. sensor.

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2.3. Approximation Model An ideal capacitance sensor should display a linear relationship between CN, f em and Hwater . However, when Hwater was less than 0.5, CN, f em was observed to be larger than the actual Hwater due to the closer proximity of the water phase with the electrodes as compared to the air phase. The only possible match between CN, f em and Hwater happened when the two phase components were uniformly separated in half. In contrast, when Hwater was larger than 0.5, CN, f em was lower than the actual Hwater due to the closer proximity of the air phase with the electrodes as compared to the water phase. As observed, the values of CN, f em were shifted from the ideal linear output and behaved identically to a sinusoidal function. A similar pattern was observed in simulation by other groups [23,27,28]. Since the nonlinear response cannot be eliminated absolutely, the sensor was optimized and designed in such a way that a sinusoidal relationship was generated between the capacitance reading and the holdup. The simulated design parameters of the helical capacitance sensor and the geometry of the pipe are presented in Table 2. As shown in Figure 4, the resulted output CN, f em was optimized to match the intersection point at Hwater “ 0.5, closer to that of the ideal linear output. CN, f em also behaved as a symmetrical sinusoidal function throughout the entire range of Hwater . The obtained results can be fit closely with the approximation model as below: CN, approx “ Hwater ` Asin p2πHwater q

(4)

where A is the amplitude of the sinusoidal function. In this case, the value of A was 0.071. The obtained value of A is calculated as follows: A ` A2 A “ 1 (5) 2 where A1 and A2 are the absolute difference between CN, f em and Hwater at Hwater “ 0.25 and 0.75, respectively. The maximum absolute difference between CN, f em and CN, approx is displayed in Table 3, where a good agreement was achieved between 0.15 to 0.85 of water holdup. A slightly larger absolute difference was observed for water holdup of less than 0.15 and above 0.85, which needs to be further validated through experimental study. Importantly, the results showed that the sinusoidal output can be designed by modifying the pitch of the helix, regardless of other parameters. Table 2. Design parameters of helical capacitance sensor and geometry of pipe. Parameters

Values

R1 R2 P L θ εwall εgas εliquid

14.19 mm 16.85 mm 55 mm 110 mm 140˝ 3.2 1 80

Table 3. Maximum absolute difference between CN,

f em

and CN, approx .

Water Holdup

Maximum Absolute Difference (%)

Hwater ď 0.15 0.15 ă Hwater ă 0.85 Hwater ě 0.85

3.9 1.2 4.2

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Figure 4.

,

and

,

versus

.

3. Finite Element Analysis on Design Parameters By simulating several different sets of design parameters and testing conditions, the effective total capacitance and their impacts on the response of sinusoidal output were examined. 3.1. Relative Permittivity of Two-Phase Components Table 4 displays the capacitance values of different combinations of ε and ε . The values of were equal as the values of ε were kept constant, whereas the values of increased Figure 4. CN, f em and CN, approx versus Hwater . Figure 4. indicated and that versus . sensor increases due to the , , the sensitivity as the values of ε increased. This of the significant difference in permittivity values of the two-phase components. As the values of ε 3. FiniteElement ElementAnalysis Analysison on DesignParameters Parameters 3. Finite changed the values of , theDesign intersection point of sinusoidal output would be shifted, as displayed By several of of design parameters andand testing conditions, the effective total in Figure 5. By simulating simulating severaldifferent differentsets sets design parameters testing conditions, the effective capacitance and their impacts on the response of sinusoidal output were examined. total capacitance and their impacts on the response of sinusoidal output were examined. Table 4. Capacitance values of different combination of ε

and ε

.

3.1. Relative Permittivity of Two-Phase Components 3.1. Relative Permittivity of Two-Phase Components (pF) (pF) Table 4 displays the1.0 capacitance values of different combinations10.521 of εgas and εliquid . The values 5 5.987 Table 4 displays the capacitance values of different combinations of ε and ε . The values of Cmin were equal as the of ε 10were kept constant, the values of Cmax increased as 1.0values 5.987 whereas of were equal as the values of gas ε were kept constant, whereas13.945 the values of increased the values of εliquid increased. This indicated that the sensitivity of the sensor increases due to the 1.0 17.516 as the values of ε increased. This 20 indicated that 5.987 the sensitivity of the sensor increases due to the significant difference in1.0 permittivity values of the two-phase components. As the values of εliquid 40 5.987 20.606 As significant difference in permittivity values of the two-phase components. the values of ε changed the values of Cmax , the intersection of sinusoidal output would shifted, as displayed 80 point 5.987 22.476 be changed the values of 1.0 , the intersection point of sinusoidal output would be shifted, as displayed in Figure 5. in Figure 5. Table 4. Capacitance values of different combination of ε

1.0 1.0 1.0 1.0 1.0

(pF) 5.987 5.987 5.987 5.987 5.987

5 10 20 40 80

Figure Figure 5. 5. The The effect effect on on CN,,

f em

and ε

(pF) 10.521 13.945 17.516 20.606 22.476

due due to to variation variation of of εεliquid ..

Table 4. Capacitance values of different combination of εgas and εliquid . εgas

εliquid

Cmin (pF)

Cmax (pF)

1.0 1.0 1.0 1.0 1.0

5 10 20 40 80

5.987 5.987 5.987 5.987 5.987

10.521 13.945 17.516 20.606 22.476

Figure 5. The effect on

,

due to variation of ε

.

.

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3.2. Geometry of Pipe 3.2. 3.2.Geometry GeometryofofPipe Pipe The intersection point of sinusoidal output was observed to beto shifted down,down, towards the direction The observed to be shifted shifted down, towards the Theintersection intersection point point of of sinusoidal sinusoidal output was observed be towards the of H “ 0, when the relative permittivity of the wall increases, as demonstrated in Figure water direction ofof ==0,0, when of the the wall wall increases, increases,asasdemonstrated demonstrated6a. direction when the the relative relative permittivity permittivity of inin In contrast, moved in the opposite in the direction ofinin Hwater “ 1, when Figurethe 6a.intersection contrast,point the intersection intersection moved in opposite way, the ofofthe Figure 6a. InIn contrast, the point movedway, in the the opposite way, thedirection direction thickness = of pipethe wall increased, as shown in Figure 6b. The value of C were severely affected =1,the 1,when when the thickness of the pipe wall increased, as shown in Figure 6b. The value of max thickness of the pipe increased, as shown in Figure 6b. The value of by were the thickness ofaffected the pipeby wall, shown in 5. This caused the measurement spancaused of the the sensor were severely affected by theas thickness ofTable the pipe wall, as in severely the thickness wall, as shown shown in Table Table5.5.This This caused the measurement spanof ofthe sensor tobe beincreased. greatly reduced the increased. a athicker pipe to be greatly reduced as thesensor thickness Thus,as a thicker pipe wall madeThus, the sensor bulky and measurement span to greatly as the thickness thickness increased. Thus, thicker pipe wall madethe sensor bulky and less sensitive sensitive to the lesswall sensitive tothe the changes ofand holdup [30]. made sensor bulky less to the changes changes of of holdup holdup[30]. [30].

(a) (a) Figure 6. The effect on

due to variations of: (a) ε

(b) (b) ; (b)

−

.

, Figure 6. 6.The of: (a) (a) εεwall;; (b) (b) R2 − ´ R1. . Figure Theeffect effecton onCN, , f em due due to to variations variations of:

Table 5. Capacitance values of different thicknesses of pipe wall.

Table 5.5.Capacitance ofpipe pipewall. wall. Table Capacitancevalues valuesof of different different thicknesses thicknesses of − (mm) (pF) (pF) Measurement Span (pF) − R0.86 (mm) (pF) Measurement (pF)(pF) R2 ´ Cmin (pF) C(pF) Measurement 3.960 47.714 43.754 SpanSpan max (pF) 1 (mm)

0.86

3.960 47.714 43.75443.754 4.751 34.322 29.571 3.960 47.714 4.751 34.322 29.57129.571 4.751 34.322 5.495 26.866 21.371 5.495 26.866 5.495 26.866 21.37121.371 5.987 22.476 16.489 5.987 22.476 5.987 22.476 16.48916.489 6.553 19.800 13.247 6.553 19.800 13.247 3.26 6.553 19.800 13.247 On the other hand, the amplitude of sinusoidal output was enlarged symmetrically as the inner OnOn theof other hand, amplitude output wasenlarged enlarged symmetrically the inner the other hand,the the amplitude ofsinusoidal sinusoidal output symmetrically asas the inner radius pipe increased, as displayedof in Figure 7, while the was intersection point was not affected. This radius ofofpipe increased, as displayed displayed inFigure Figure 7, while the intersection point was not affected. radius pipe increased, while the intersection was not affected. This indicated that the nonlinear responseinwas more7, severe in larger pipes. point The absolute difference of |indicated and thethe values of response for different sizes ofsevere pipe are summarized in Table 6,absolute where it difference is seenof − |that indicated the nonlinear waswas more in larger pipes. The absolute difference This that nonlinear response more severe in larger pipes. The | | clearly that increased as indicated that increased and the small difference of − | | ofof A forfor different sizes of pipe are summarized in Table 6, where it is the seen of |A1 − ´ A2 | and andthe thevalues values different sizes of pipe are summarized in Table 6, where it is sinusoidal function was symmetrical. | | clearly that increased as as Rincreased indicated that the and the small difference of − seen clearly that A increased increased and the small difference of |A ´ A | indicated that the 2 1 1 sinusoidal function was symmetrical. sinusoidal function was symmetrical. 1.46 0.86 1.46 1.46 2.06 2.06 2.06 2.66 2.66 2.66 3.26 3.26

Figure 7. The effect on

,

due to variation of

.

Figure7.7.The Theeffect effecton onC , due to variation of . Figure N, f em due to variation of R1 .

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Table 6. Absolute difference of | − | and the values of for different . Table 6. Absolute difference of |A1 ´ A2 | and the values of A for different R1 . R1 (mm) 10.19 12.19 14.19 16.19 18.19

(mm) 10.19 A 0.06669 1 12.19 0.06726 0.06669 14.19 0.06726 0.07441 16.19 0.07441 0.07510 0.07510 18.19 0.07847 0.07847

0.06058 A2 0.07125 0.06058 0.06843 0.07125 0.07958 0.06843 0.07958 0.08583

Absolute Difference (%) 0.611 Difference (%)0.06364 Absolute 0.399 0.06926 0.611 0.598 0.399 0.07142 0.448 0.598 0.07734 0.448 0.736 0.08215

0.08583

0.736

A 0.06364 0.06926 0.07142 0.07734 0.08215

3.3. Design Parameters of the Sensor 3.3. Design Parameters of the Sensor The intersection point of sinusoidal output was found to be the same as the opening angles of The intersection of sinusoidal output was found be the same as the opening of electrode change, as point shown in Figure 8a. However, the to difference between and angles of the electrode as for shown in Figure 8a. of However, the difference A1 and A2 ofresponse the sinusoidal sinusoidalchange, function different values θ increased, resultingbetween in an asymmetrical of the function foroutput. different valuesthe of measurement θ increased, resulting in an asymmetrical response of the sinusoidal sinusoidal Besides, span of the sensor was strongly affected, which cannot output. Besides, the measurement span of the sensor was of strongly which cannot be observed | − affected, | and the be observed in Figure 8a. Hence, the absolute difference measurement span for in Figure 8a. Hence, the absolute difference of |A1 ´ A the measurement for different θ are | − |, an opening different θ are presented in Table 7. By comparing the absolute difference ofspan 2 | and |A1 ´ Afollowed presented in Table 7. yield By comparing absolute difference of output, of 50˝angle would angle of 50° would the most the symmetrical sinusoidal by anangle opening of 2 |, an opening ˝ . In this case, the yield the most symmetrical sinusoidal output, followed by an opening angle of 140 140°. In this case, the measurement span would be the next factor to consider when choosing measurement span would beθthe factor to consider when area choosing theelectrode, optimumwhere θ. Theoretically, optimum θ. Theoretically, is next related to the total surface of the greater θ θwould is related to athe total surface area the hence electrode, wheremeasurement greater θ would haveIna this larger surface area have larger areaofand a bigger span. case, a larger and hence a bigger In this case, a larger of measurement spanThus, is desirable to improve measurement spanmeasurement is desirable tospan. improve the sensitivity the sensor [20]. 140° was selected the sensitivity of θ. the sensor [20]. Thus, 140˝ was selected as the optimum θ. as the optimum

(a)

(b)

Figure 8. The effect on Figure 8. The effect on CN,,

f em

due to variations of: (a) θ; (b) . due to variations of: (a) θ; (b) P .

Table 7. Absolute difference of | − | and the measurement span for different θ. Table 7. Absolute difference of |A1 ´ A2 | and the measurement span for different θ .

(°)

θ (˝ ) 50 50 60 60 70 70 80 80 90 90 100 100 110 110 120 120 130 140 130 150 140 160 150

160

A1 0.07657 0.07657 0.07266 0.07266 0.06967 0.06967 0.06306 0.06306 0.06644 0.06644 0.06646 0.06646 0.06212 0.06212 0.06910 0.06910 0.06840 0.06840 0.07441 0.07441 0.06657 0.07046 0.06657 0.07046

Absolute Difference (%) Measurement Span (pF) Absolute Measurement Span (pF) 0.07174A2 0.482 Difference (%) 7.587 0.07174 0.07952 0.686 0.482 8.687 7.587 0.07952 0.686 0.08064 1.098 9.965 8.687 0.08064 1.098 9.965 0.08420 2.115 2.115 11.102 11.102 0.08420 0.07787 1.143 1.143 12.179 12.179 0.07787 0.08246 0.08246 1.600 1.600 13.199 13.199 0.08526 0.08526 2.314 2.314 14.174 14.174 0.08143 1.233 14.645 0.08143 1.233 14.645 0.07671 0.831 15.626 0.07671 0.831 0.598 15.626 16.489 0.06843 0.06843 0.598 2.378 16.489 17.272 0.09035 0.08755 1.709 0.09035 2.378 17.272 17.856 0.08755 1.709 17.856

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The sinusoidal output needs to be symmetrical before applying the approximation model The sinusoidal output needs to be symmetrical before theofapproximation model (Equation (4)), where the intersection point must lie closely to applying = 0.5 that ideal line. Since (Equation (4)), where the intersection point must lie closely to H “ 0.5 of that ideal line. Since water the pitch of the helix can control the intersection point, as demonstrated in Figure 8b, a perfectthe pitch of the helix can control the intersection point, as in Figure 8b, a perfect sinusoidal sinusoidal function can be obtained by optimizing thedemonstrated pitch of the helix. function can be obtained by optimizing the pitch of the helix. 4. Experimental Setup 4. Experimental Setup 4.1. Capacitance Interface Circuit 4.1. Capacitance Interface Circuit Figure 9 shows the schematic diagram of the capacitance interface circuit, which consists of Figure 9 shows the(C/V) schematic diagramconversion of the capacitance interface which consists capacitance-to-voltage and AC-to-DC circuits. The overall circuit, capacitance between the of capacitance-to-voltage (C/V) conversion circuits. The capacitance between electrodes was in the rangeand of AC-to-DC 10 to 40 pF. A stray-immune andoverall high signal-to-noise ratio themeasurement electrodes was in the range to ofmaximize 10 to 40 the pF. accuracy A stray-immune and high circuit is needed and sensitivity of thesignal-to-noise system. Thus, ratio an measurement circuit is needed maximizefor theC/V accuracy and sensitivity thecomposed system. Thus, AC-based method [33,34] wastoemployed conversion, where it of was of anan operational amplifier in inverting configuration , in parallel with a AC-based method [33,34](LT1360) was employed for C/V conversion,mode. whereAit resistor, was composed of an operational capacitor, , were as the feedback impedance. this experimental setup, 5 MΩ andC f , amplifier (LT1360) in chosen inverting configuration mode. A In resistor, R f , in parallel with a=capacitor, = 22 pF.as the feedback impedance. In this experimental setup, R f “ 5 MΩ and C f “ 22 pF. were chosen

Figure9.9.Schematic Schematicdiagram diagram of of the capacitance Figure capacitanceinterface interfacecircuit. circuit.

A sinusoidal voltageofof1 1VVpeak-to-peak peak-to-peak generated generated by (AFG-3081) A sinusoidal voltage by arbitrary arbitraryfunction functiongenerator generator (AFG-3081) was used to excite the source electrode at frequency = 1 MHz , as suggested by other was used to excite the source electrode at frequency f “ 1 MHz, as suggested by other authors [19,29]. authors [19,29]. The detection electrode was connected to the virtual ground of the operational The detection electrode was connected to the virtual ground of the operational amplifier. Since the amplifier. Since the sensor was not covered by any external shield, any objects in close proximity with sensor was not covered by any external shield, any objects in close proximity with the sensor can cause the sensor can cause significant interference to the capacitance reading. In our case, the surrounding significant interference to the capacitance reading. In our case, the surrounding of the sensor was not of the sensor was not interfered with by any other physical object, except the ambient air, which has interfered with by any other physical object, except the ambient air, which has been considered in been considered in our model presented in Section 2.2. The capacitance value of the sensor, , was ourlinearly model converted presentedtoinsinusoidal Section 2.2. The capacitance output voltage, . value of the sensor, C, was linearly converted to sinusoidal voltage, Vo . was comprised of active rectifier, peak detector, and an amplifier [35] Theoutput AC-to-DC conversion The AC-to-DC conversion rectifier, an amplifier [35] for converting and amplifyingwas the comprised sinusoidal of active into DC value, peak.detector, The finaland output, , was formeasured converting and amplifying the sinusoidal V into DC value, V . The final output, V , was o precision LCR meter meas (8110-G) with frequency meas of using a multimeter (GDM-8261A). A measured using (GDM-8261A). precision LCR with frequency of 1MHz 1MHz and 1Va multimeter AC was used to obtain the A capacitance valuemeter of the(8110-G) sensor for linearity inspection andbetween 1V AC was used to obtain capacitance value of the sensor for linearity between and for thethe same holdup values. The difference was found inspection to be within ±0.1%, C andwhich Vmeasindicated for the same holdup values. The difference was found to be within ˘0.1%, which indicated that the linearity error was within an acceptable range. The normalized output is as “ error ”,was which has an theacceptable same definition . thatdenoted the linearity within range.asThe ,normalized output is denoted as “VN, meas ”, , which has the same definition as CN, f em . 4.2. Fabrication of Capacitance Sensors

4.2. Fabrication ofshows Capacitance Sensors Figure 10 the actual photograph of helical capacitance sensors for air-water and oil-water stratified flow experiments, attached on theofouter surface of the pipe. Thefor electrodes were of Figure 10 shows the actual photograph helical capacitance sensors air-water andmade oil-water 0.075 mm thick copper foil coated with an electrically conductive acrylic adhesive surface. The pitch stratified flow experiments, attached on the outer surface of the pipe. The electrodes were made of of mm the helix air-water and oil-water experiments was determined to be 55surface. mm andThe 62 pitch mm, of 0.075 thick for copper foil coated with an electrically conductive acrylic adhesive respectively, from FEM simulation for achieving symmetrical sinusoidal outputs. In the design of the helix for air-water and oil-water experiments was determined to be 55 mm and 62 mm, respectively, from FEM simulation for achieving symmetrical sinusoidal outputs. In the design of sensors, the

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total complete turns of the helical were doubled, the totalthe length the pipe sensors, the total complete turns ofsensor the helical sensor were where doubled, where totalof length of thecovered pipe sensors, the total complete ofto the helical sensor were the oil-water total length of the pipe bycovered electrodes were equalwere to turns 110 mm and 124 air-water andwhere oil-water experiments. This step by electrodes equal 110 mmmm andfor 124 mmdoubled, for air-water and experiments. covered by electrodes were equal to 110 mm and 124 mm for air-water and oil-water experiments. This step wastonecessary the measurement range of the sensor and subsequently minimize was necessary increase to theincrease measurement range of the sensor and subsequently minimize the fringe Thisfringe step was necessary to increase the measurement range of the sensor and subsequently minimize the effect [20]. effect [20]. the fringe effect [20].

(a) (a)

(b) (b)

Figure Helicalcapacitance capacitance sensor sensor for: Oil-water. Pitch sizesize is shown for each design. Figure 10.10.Helical for:(a) (a)Air-water; Air-water;(b)(b) Oil-water. Pitch is shown for each design. Figure 10. Helical capacitance sensor for: (a) Air-water; (b) Oil-water. Pitch size is shown for each design.

4.3. Static Two-Phase Stratified Flow Setup 4.3.4.3. Static Two-Phase Static Two-PhaseStratified StratifiedFlow FlowSetup Setup The schematic of experimental setup for two-phase flow is illustrated in Figure 11. It was The ofofexperimental setup for two-phase two-phase flowwith illustrated Figure 11. was Theschematic schematic experimental flow isisillustrated inin Figure 11.injection It It was composed of a pipe made of polyvinyl setup chloride (PVC), connected PVC T-joint for liquid composed of a pipe made of polyvinyl chloride (PVC), connected with PVC T-joint for liquid injection composed of a pipe made of polyvinyl chloride (PVC), connected with PVC T-joint for liquid injection and sealed with a plug to prevent liquid leakage at both ends. The liquid tap was used to discharge and sealed witha aplug plug prevent liquid leakagewere ends. The used toto discharge and sealed with totoprevent at both both ends. Theliquid liquid tapwas was used discharge the liquid inside the pipe and theliquid retort leakage stands used to support thetap pipe horizontally at both the liquid inside the pipe and the retort stands were used to support the pipe horizontally both theends. liquid the pipe andwas the attached retort stands used toofsupport horizontally both Theinside capacitance sensor on the test section the pipethe andpipe the total volumeatofat the ends. The capacitance sensor was attached on the test section of the pipe and the total volume of the ends. The capacitance sensor was attached on the test section of the pipe and the total volume of pipe was measured. Due to the atmospheric pressure and density difference between the two-phasethe pipe was measured. Due the atmospheric pressure and density the two-phase pipe was measured. Due totothe andthe density difference between the two-phase components, stratified flow canatmospheric be observed pressure easily inside pipe difference as the lessbetween dense component (i.e., components, stratified flow can be observed easily inside the pipe as the less dense component (i.e.,air components, stratified flow float can be easily inside the pipe as the less denseHence, component (i.e., air or oil) would always onobserved the top of the denser component (i.e., water). the water air or oil) would always float on the top of the denser component (i.e., water). Hence, the water or holdup oil) would always float on the topratio of the denser component (i.e., water). Hence, thetotal water holdup is equivalent to the between the water poured into the pipe and the volume holdup is equivalent to the ratio between the water poured into the pipe and the total volume of the pipe. Hwater is equivalent to the ratio between the water poured into the pipe and the total volume of of the pipe. the pipe.

Figure 11. Schematic illustration of experimental setup for two-phase flow. Figure of experimental experimentalsetup setupfor fortwo-phase two-phase flow. Figure11. 11.Schematic Schematicillustration illustration of flow.

In this work, two static tests were conducted: air-water and oil-water stratified flow. Deionized this work, two statictests tests wereconducted: conducted: air-water and stratified flow. Deionized In In this work, two static were air-water andoil-water oil-water stratified flow. Deionized water was used to prevent the interference of the resistive component. A small quantity of gasoline water was used to prevent the interference of the resistive component. A small quantity of gasoline water usedofto748 prevent resistive During component. A small quantity of gasoline withwas density kg/m3 the wasinterference used as the of oilthe component. the experiment, the temperature with density was used usedbetween as the the oil oil component. During the the temperature 3 3was with density 748 as During theexperiment, experiment, the temperature was kept atof 25of ± 748 1 kg/m °C.kg/m The interface thecomponent. oil and water was allowed to settle down after each was kept 25 °C.The TheThe interface between the and was toto settle down after each change in at their outputbetween voltage was recorded using theallowed interface circuit, as discussed in was kept at 25 ˘ ±volumes. 1 1˝ C. interface the oil oil andwater water was allowed settle down after each change in their volumes. The output voltage was recorded using the interface circuit, as discussed in Section Table 8 lists the of the pipe for air-water and oil-water experiments. change in 4.1. their volumes. Thegeometry output voltage was used recorded using the interface circuit, as discussed in Section 4.1. Table 8 lists the geometry of the pipe used for air-water and oil-water experiments. Section 4.1. Table 8 lists the geometry of the pipe used for air-water and oil-water experiments. Table 8. Geometry of the pipe. Table 8. Geometry of the pipe. Table 8. Geometry of the pipe. Parameters Values

Parameters

Parameters

− ε− ε

R1 R2 R2 ´ R1 εwall

Values 14.19 mm 16.85 mm 16.85 mm 14.19 mm 2.66 mm 2.66 mm 16.85 mm 3.2 2.66 mm 3.2 Values14.19 mm

3.2

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5. 5. Results Resultsand andDiscussion Discussion 5.1. Air-Water Stratified Flow 5.1. Air-Water Stratified Flow Figure 12 12 shows thethe experimental results of of air-water stratified flow. It It was shown Figure shows experimental results air-water stratified flow. was shownclearly clearlythat thatthe output V behaved similar to a sinusoidal function, as observed in FEM simulation. The amplitude N, meas the output , behaved similar to a sinusoidal function, as observed in FEM simulation. The of the sinusoidal was equal to 0.071, on FEM The intersection point of amplitude of thefunction sinusoidal function was equalbased to 0.071, basedcalculation. on FEM calculation. The intersection VN,point located at Hlocated 0.5, indicates the sinusoidal was symmetrical. water “ at meas was of closely was closely = 0.5, indicates that the function function was ˇthat ˇ sinusoidal , ˇ ˇ ˇ ˇ ˇ symmetrical. Table 9 tabulates the maximum absolute difference of − and ˇ Table 9 tabulates the maximum absolute difference of ˇCN, f em ´ CN, approx ˇ and, VN, meas , ´ C N, approx − test. forfound air-water It was foundresults that the experimental results as had a higher to , , for air-water It was that test. the experimental had a higher accuracy compared accuracy as compared to the FEM simulation, particularly when water holdup was less than 0.15 and the FEM simulation, particularly when water holdup was less than 0.15 and greater than 0.85. Note greater than 0.85. Note that smooth stratified flow was simulated using FEM. However, in reality, that smooth stratified flow was simulated using FEM. However, in reality, smooth stratified flow was smooth stratified flow hardly the water full wasineither too due littletoorthe hardly observed when thewas amount of observed water waswhen either tooamount little orofalmost the pipe almost full in the of pipe due to the natural of water, cause the water natural properties water, which cause properties the distribution of which the water inthe thedistribution pipe to be of uneven. This in the pipe to be uneven. This could also be part of the reason why the range of water holdup could also be part of the reason why the range of water holdup p0.126 ď Hwater ď 0.773q was limited (0.126 ≤ ≤ 0.773) was limited in the experimental study of [29]. in the experimental study of [29].

Figure 12. and VN, versus Hwater for for air-water air-waterstratified stratifiedflow. flow. Figure 12.CN, ,f em ,, CN,, approx,, and , measversus ˇ Table 9. Maximum absolute differenceofofˇˇCN, absolute difference Table 9. Maximum stratified flow. stratified flow.

Water Holdup

Water Holdup

≤ 0.15 0.15 < < 0.85 Hwater ď 0.15 0.15 ă H≥ 0.85 ă 0.85 water

Hwater ě 0.85

,

f, em

ˇ ˇ ˇCN,

ˇ ˇ ˇ ˇ ˇ for air-water and ˇVN,, meas−´ C,N, approxfor air-water ´−CN,, approx ˇ and

Maximum Absolute Difference (%) Maximum Absolute Difference (%) − , − , ˇ ˇ ˇ , ˇ ˇ V ´ CN, approx ˇ ´ C ˇ 3.9 N, meas 2.6 N, approx f em 1.2 1.2 3.9 2.6 4.2 2.8 1.2 1.2 4.2

2.8

Two important properties that influence the experimental results are cohesion and adhesion of water. According to Marshall et al. [36], cohesion refers to the attraction of the same kind of Two important properties that influence the experimental results are cohesion and adhesion of molecules, where it holds hydrogen bonds together to create surface tension on water. On the other water. According Marshall al. [36], cohesion refers to the attraction of the same of molecules, hand, adhesionto refers to theetmolecular attractions at the interface of different kind kind of molecules. In where holds hydrogen bonds together to create surface On the other other rather hand, than adhesion this itcase, it has been observed that water molecules aretension inclinedontowater. stick to each to refers to thesurface molecular at the interface ofthan different kind of molecules. In cohesive this case,force it has the inner of theattractions pipe for water holdup of less 0.15, which indicates that the been observed molecules areSince inclined to amount stick to of each other rather thantotothe theinner inner surface was strongerthat thanwater the adhesive force. a trace water was attached surface of the pipe for the water holdup of less than 0.15,be which indicates cohesive force was stronger of the pipe, capacitance readings would expected to be that lowerthe than the simulated results in than the adhesive force. Since a trace amount of water was attached to the inner surface of the pipe,

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smooth stratified flow. As observed in Figure 12, , was smaller than for water holdup , of less than 0.15. the capacitance readings would be expected to be lower than the simulated results in smooth stratified Meanwhile, the adhesive and cohesive forces of water were almost equal for values of water flow. As observed in Figure 12, VN, meas was smaller than CN, f em for water holdup of less than 0.15. holdup from 0.15 to 0.85 as smooth stratified flow was easily formed inside the pipe. This showed Meanwhile, the adhesive and cohesive forces of water were almost equal for values of water that the simulation results and experimental results were close to each other. However, smooth holdup from 0.15 to 0.85 as smooth stratified flow was easily formed inside the pipe. This showed that stratified flow could not be generated as water holdup increased above 0.85. It was observed that the the simulation results and experimental results were close to each other. However, smooth stratified tendency of water to stick to the inner surface of the pipe was higher as adhesive force overwhelmed flow could not be generated as water holdup increased above 0.85. It was observed that the tendency cohesive force. Due to this phenomenon, the capacitance readings would be expected to be higher of water to stick to the inner surface of the pipe was higher as adhesive force overwhelmed cohesive than the simulated results in smooth stratified flow as more water attached to the inner surface of the force. Due to this phenomenon, the capacitance readings would be expected to be higher than the pipe. Thus, the results showed that the values of , were larger than for water holdup , simulated results in smooth stratified flow as more water attached to the inner surface of the pipe. of greater than 0.85, where this brought the values closer to the approximation model. In addition, Thus, the results showed that the values of VN, meas were larger than CN, f em for water holdup of greater the air-water distribution had been re-simulated in FEM to validate the experimental result for water than 0.85, where this brought the values closer to the approximation model. In addition, the air-water holdup of less than 0.15 and greater than 0.85. Overall, the output , obtained a good agreement distribution had been re-simulated in FEM to validate the experimental result for water holdup of with the approximation model, , where it was found to be even better than . , , less than 0.15 and greater than 0.85. Overall, the output VN, meas obtained a good agreement with the approximation model, CFlow N, approx , where it was found to be even better than C N, f em . 5.2. Oil-Water Stratified A clear and even separated interface between oil and water was observed after a few minutes 5.2. Oil-Water Stratified Flow for each change of holdup value. In addition, there were no cross-linking between oil and water when A clear and even separated interface between oil and water was observed after a few minutes for interfacial waves were absent, as reported by Al-Wahaibi and Angeli [37]. Thus, the flow pattern can each change of holdup value. In addition, there were no cross-linking between oil and water when be assumed to be smooth stratified. Figure 13 displays the experimental results of oil-water stratified interfacial waves were absent, as reported by Al-Wahaibi and Angeli [37]. Thus, the flow pattern can flow. It was clearly shown that the output, , , acted identically to a sinusoidal function, where be assumed to be smooth stratified. Figure 13 displays the experimental results of oil-water stratified the amplitude of the sinusoidal function was equal to 0.066. The sinusoidal function was proved to flow. It was clearly shown that the output, VN, meas , acted identically to a sinusoidal function, where be symmetrical as the intersection point of with the ideal line was nearly obtained at , the amplitude of the sinusoidal function was equal to 0.066. The sinusoidal function was proved to be = 0.5 . Table 10 presents the absolute difference of − , and − , , symmetrical as the intersection point of VN, measˇ with the ideal line was nearly obtained at Hwater “ 0.5. ˇ of the oil-water test, where the experimental result was to be very closeˇ to the ˇ , ˇ ˇ found Table 10 presents the absolute difference of ˇCN, f em ´ CN, approx ˇ and ˇVN, meas ´ CN, approx ˇ of the simulation result. oil-water test, where thethat experimental resultresponse was found to be very close thepermittivity simulation result. It was also noted the nonlinear was greater whentothe difference It was also noted that the nonlinear response was greater when the permittivity between the two-phase components increased. As the value of amplitude implies the difference degree of between the two-phase components increased. As the value of amplitude implies the degree of nonlinear response of sinusoidal output, the air-water stratified flow was found to be shifted more nonlinear response of sinusoidal output, the air-water stratified flow was found to be shifted more significantly from the ideal response, as compared to the oil-water flow. This is manifested by the significantly from the response, values as compared to the oil-water flow. Thistois oil-water. manifested Overall, by the larger larger difference in ideal permittivity of air-water as compared the difference in permittivity values of air-water as compared to oil-water. Overall, the approximation approximation model obtained a good agreement in air-water and oil-water stratified flow , model CN,holdup a good agreement approx obtained for water values from 0.15 to 0.85. in air-water and oil-water stratified flow for water holdup values from 0.15 to 0.85.

Figure 13. 13. CN, Figure ,

f em, ,

CN, approx, ,and and VN, measversus versus Hwater for for oil-water oil-water stratified stratified flow. flow. , ,

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ˇ ˇ Table 10. Maximum absolute difference of ˇCN, stratified flow. Water Holdup

Hwater ď 0.15 0.15 ă Hwater ă 0.85 Hwater ě 0.85

ˇ ˇ ˇCN,

ˇ ˇ ˇ ˇ ´ C ˇ and ˇVN, meas ´ CN, approx ˇ for oil-water N, approx f em

Maximum Absolute Difference (%) ˇ ˇ ˇ ˇ ˇVN, meas ´ CN, approx ˇ f em ´ C N, approx ˇ 3.1 1.1 3.6

3.0 1.3 3.3

6. Conclusions This paper reported a new and facile approach to the design and optimization of a helical capacitance sensor to measure the holdup of two-phase flow, specifically in a stratified pattern. The two phase components can either be gas and liquid or liquid and liquid. A sinusoidal relationship between the capacitance value and the holdup was observed and explored, where a good agreement was achieved between the FEM model and approximation model. In addition, all design parameters had been analysed and studied to determine their effects on the intersection point and symmetry of the sinusoidal function. The static experiments of stratified flow for air-water and oil-water further justified the proposed sinusoidal function with maximum differences of ˘1.2% and ˘1.3% for the range of water holdup from 0.15 to 0.85. In future, the flow loop test will be conducted to examine and investigate the performance of the sensor. Supplementary Materials: All relevant data are available from the database at the URL https://sites.google.com/ site/medicalelectronicslab/research/data-deposition. Acknowledgments: Lam Ghai Lim would like to thank Universiti Teknologi PETRONAS for the graduate assistantship. Author Contributions: Tong Boon Tang conceived the original idea and supervised the research. Lam Ghai Lim conducted the experiment and data analysis and prepared the manuscript. William K. S. Pao and Nor Hisham Hamid contributed to the project discussion and manuscript revision. Conflicts of Interest: The authors declare no conflict of interest.

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