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Mass measurement based calibration of a capacitive sensor to measure void fraction for R134a in smooth tubes
International Journal of Refrigeration 110 (2020) 168–177
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International Journal of Refrigeration journal homepage: www.elsevier.com/locate/ijrefrig
Mass measurement based calibration of a capacitive sensor to measure void fraction for R134a in smooth tubes Hongliang Qian a, Pega Hrnjak a,b,∗ a b
Air Conditioning and Refrigeration Center, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA Creative Thermal Solutions, 2209 Willow Rd., Urbana, IL, USA
a r t i c l e
i n f o
Article history: Received 2 July 2019 Revised 18 October 2019 Accepted 19 October 2019 Available online 23 October 2019 Keywords: Capacitive sensor Void fraction Quick-closing valve Calibration
a b s t r a c t This paper presents a new capacitive sensor built and used to measure void fraction of both horizontal and vertical upward flow in the low mass flux range in circular tubes with an inner diameter of 7 mm. Three sensors with different axial lengths (D, 2D/3, and D/2) are built and evaluated to examine the possibility of utilizing shorter sensors in applications with space limitations. Results show all three sensors have the capability to measure void fraction. Due to the nonlinear relation between capacitive signals and void fraction, a calibration procedure based on mass measurement (quick-closing valve technique, QCV) is proposed. After the calibration procedure, most void fraction data measured by the sensor falls into the ±15% deviations of the experimental results by QCV for horizontal flow and ±10% for vertical upward flow. Sensors with the same design can be utilized directly to measure void fraction for the similar test conditions in the future studies. © 2019 Elsevier Ltd and IIR. All rights reserved.
Étalonnage basé sur la mesure de masse d’un capteur capacitif pour mesurer la fraction de vide pour le R134a dans des tubes lisses Mots-clés: Capteur capacitif; Fraction de vide; Vanne à fermeture rapide; Étalonnage
1. Introduction Void fraction is generally defined as the ratio of the volume occupied by vapor over the total control volume. It is one of the most important parameters to characterize two-phase flow. It has been studied experimentally during the past several decades. Some common methods used to measure void fraction in experiments are X-ray/γ -ray absorption (Isbin et al., 1957), optical (Wojtan et al., 2005), wire mesh probe (Da Silva et al., 2010), quick-closing valves (QCV) (Beggs, 1973; Pabon et al., 2019; Qian and Hrnjak, 2019) and capacitive method (Abouelwafa and Kendall, 1980; De Kerpel et al., 2013, Olivier et al., 2016). However, some of the methods are not widely used because of inherent limitations. X-ray/γ -ray absorption method is relatively expensive and may cause safety issues. Transparent tubes are required for optical method, but it is
∗ Corresponding author at: Air Conditioning and Refrigeration Center, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA. E-mail address: [email protected] (P. Hrnjak).
https://doi.org/10.1016/j.ijrefrig.2019.10.019 0140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.
somewhat difficult to measure vapor volume by visualization results. Wire mesh probe is an intrusive method, and the sensor affects original flow patterns and void fraction. QCV is a relatively easy and straightforward experimental method to measure void fraction. By closing two valves simultaneously at both ends of a test section and measure the weight of fluid inside, the average void fraction is calculated. This method has a low uncertainty and can be used as a calibration standard when calibrating other void fraction sensors (Rocha and SimõesMoreira, 2008). The capacitive method utilizes different electrical properties between the liquid and vapor phases to measure void fraction and detect flow regimes in two-phase flow. The electrical impedance is defined as in Eq. (1), where R is the resistive term, and ωC is the capacitive term. If the working media has very high resistance and/or it is measured by a high-frequency circuit, the influence of resistivity can be neglected (Canière, 2010; Jaworek and Krupa, 2004). The signals mainly depend on the capacitance component within the sensor. Capacitive method can be used in this
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two concave electrodes to characterize two-phase flow in horizontal tubes also on charge/discharge principle. Jaworek and Krupa (2004) used two concave electrodes with a circuit measuring changes of frequency to measure gas/liquid ratio. The frequency changes were generated by a reference oscillator and the sensor. Later, Jaworek and Krupa (2010) proposed a new circuit measuring phase shift between a reference signal and a sinusoidal signal passing the sensors to measure void fraction. Most of the previous studies focused on measuring volumetric void fraction. Some studies on measuring semi-cross-sectional void fraction were proposed recently. Cross-sectional void fraction is essential to local heat transfer coefficient and pressure drop calculation. This kind of sensor can also be used in more compact applications thanks to its smaller size. Table 1 gives a brief review of experiments on void fraction measurements with capacitive sensors. Two-concave-plate configuration (Fig. 1a) is often used in the literature. In comparison to other configurations, it has the following advantages:
Nomenclature cross-sectional area (m2 ) capacitive signal (pF) inner diameter (m) mass flux (kg m−2 s−1 ) length (m) refrigerant recycling weight (g) pressure (Pa) shield inner diameter (m) temperature (°C) electrical impedance () mass flow rate (g s−1 ) dielectric layer thickness (m) vapor quality electric potential (V) void fraction electrode angle (o ) permittivity (F m−1 ) density (kg m−3 )
A C D G L M P R T Z m t x
α β ε ρ Subscripts r w Vapor Liquid measured norm
1) relatively easy to be built, especially for sensors on smaller tubes or complicated geometries. 2) higher sensitivity compared to double-helix configuration (Abouelwafa and Kendall, 1980). 3) possibility to measure semi-cross-sectional void fraction by reducing sensor axial length.
refrigerant water vapor phase liquid phase measured value normalized value
way.
Z=R+
1 jω C
169
(1)
The capacitive method is a nonintrusive method with lower cost. This method usually does not involve safety issues and is easy to implement. Abouelwafa and Kendall (1980) applied the capacitive sensors to measure phase percentage and compared different electrodes configurations. Later on, various sensor designs (electrodes configurations, Fig. 1) and electrical measuring circuits (transmitter/transducer) were proposed. Some (Ahmed and Ismail, 2008) directly measured the capacitance within the sensors with different electrode configurations to determine void fraction and/or flow regimes. Elkow and Rezkallah (1996) used concave and helical wound electrodes to measure void fraction on charge/discharge principle. Canière et al. (20 07, 20 08) used
The electrical field within some sensors (such as two concave plates) is not uniform. The signals obtained from capacitive sensors depend on both void fraction and flow patterns within the sensor. The relation between capacitive signals and void fraction is thus not linear. Hence, to measure void fraction of two-phase flow, the capacitive sensors must be calibrated first. Kerpel et al. (2014, 2013) calibrated the sensor developed by Canière et al. (2007) based on flow regimes or signal features for horizontal flow. In these two calibration methods, void fraction predicted by correlations from Rouhani and Axelsson (1970) was set to be calibration standard void fraction. Finite element method (FEM) was used to obtain capacitance and void fraction relations of different flow regimes. Olivier et al. (2016) used the calibrated sensor to measure void fraction in a smooth tube with different inclination angles during condensation. However, the difference between predicted void fraction from correlations and real values cannot be neglected for a calibration procedure. It is more reasonable to use mass measurement based method to calibrate the capacitive sensor. We selected Quick-closing valve method (QCV). FEM may also not provide the precise capacitance and void fraction relations due to the difference between the real flow regime and simulated models. Besides, both horizontal and vertical flow are encountered in HVAC systems. It is necessary to calibrate the capacitive sensor for both orientations. 2. Design of capacitive sensor 2.1. Capacitance governing equations and relative permittivity Volume resistivity and relative permittivity for different working media are shown in Table 2. The working fluid in this paper is R134a, whose resistivity is very high. Hence, capacitive methods that neglect conductivity effects are used. Canière (2010) proposed a general governing equation of capacitance between two electrodes:
C = −ε0 Fig. 1. Some typical electrode configurations (Jaworek and Krupa, 2004). (a) Two concave plates. (b) Four concave plates. (c) Six concave plates. (d) Rings. (e) Double helix.
S
εr (r )∇ · dA S − d
(2)
where S is source electrodes electric potential, d is detector electrodes electric potentials, is spatial potential distribution, ɛr is relative permittivity and ɛ0 is vacuum permittivity. Eq. (2) must
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Table 1 Review of experiments on void fraction measurements with capacitive sensors. Authors
Electrodes configuration
Pipe ID and orientation
Working media
Approach
Abouelwafa and Kendall (1980) Geraets and Borst (1988)
6 configurations Helical
12.7 – 50 mm 5 and 50 mm
Volumetric Volumetric
Kendoush and Sarkis (1995) K. J. Elkow and Rezkallah (1997) Jaworek and Krupa (2004) Ahmed and Ismail (2008) De Kerpel et al. (2014, 2013)
5 configurations Helical and concave 5 configurations Ring, concave (up and down) Concave
26–49 mm 9.53 mm, vertical 32 mm (ID), vertical 12.7 mm, horizontal 8 mm, horizontal
Air, water, and oil Air, water, glycerin and acrylate mock-ups Air and nonflow mock-ups Air–water Air–watter Air–oil R134a, R410A
De Kerpel (2015) Olivier et al. (2016) Sakamoto et al. (2019) This paper
Concave Concave Asymmetric Concave
8 mm, horizontal 8 mm (8.38 mm tube) 15 mm, horizontal 7 mm, horizontal and vertical upward
R134a, R410A R134a Hydrogen R134a
Volumetric Volumetric Semi-cross-sectional Volumetric/Semi-cross-sectional Calibration procedure for Semi-cross-sectional Semi-cross-sectional Semi-cross-sectional Semi-cross-sectional Semi-cross-sectional
Table 2 Conductivity and relative permittivity for some working media (ASHRAE, 2013). Volume resistivity (M m)
Working media Air (0 °C) Pure water (25 °C) (Haynes, 2014) R134a liquid between 23 and 26 °C (Meurer et al., 2001) R134a liquid at 25 °C R134a vapor at 25 °C R410A liquid between 23 and 26 °C (Meurer et al., 2001) R410A liquid at 25 °C R410A vapor at 25 °C
0.182 10,890
3920
be solved to get analytical solutions of capacitance for different void fraction and flow regimes. However, precise analytical solutions to some flow regimes are difficult to obtain. Experimental measurement is thus preferred. Eq. (2) also shows the overall capacitance is dependent on relative permittivity. It is important to examine relative permittivities of different working media before utilizing the capacitive method. Relative permittivity (ɛr ) is also called dielectric constant, which is a material property and temperature dependent. The permittivity is defined as ε = ε0 εr , the product of vacuum permittivity (ε0 = 8.854 × 10−12 F m−1 ) and relative permittivity. The relative permittivity of water at 25 °C is much larger than that of liquid R134a at the same temperature (Table 2). The absolute capacitive signals measured from R134a two-phase mixture are thus smaller than that from the air-water mixture. In addition, the relative permittivity difference between water and air is much bigger than that between R134a liquid phase and vapor phase. As a result, overall capacitance signal difference measured between full liquid phase and full vapor phase of R134a is smaller (Eq. (3)). Whether the sensor has the capability to measure small capacitive signals (signals of R134a mixture are typically in the order of pF and CR134a is about 1 pF) is a limitation to the sensor and transducer/transmitter design. Hence, to utilize capacitive sensors to refrigerant flow, some designs aimed to other working media from literature must be modified first.
CR134a = Cfull liquid − Cfull vapor < CWater−Air = Cfull water − Cfull air (3) The relative permittivity is a temperature dependent property. For R134a, researches (Feja, 2012) reported it decreased as temperature increased. Measured capacitance would be affected if the temperature of R134a changes. However, if the temperature is kept constant, this effect can be eliminated. This situation can be achieved when refrigerant is evaporating/condensing in the twophase zone or refrigerant flow in an adiabatic part, such as headers of microchannel heat exchangers. If the temperature varies and
Relative permittivity (domensionless) 1.00059 79.55 9.24 9.87 1.0125 7.78 5.37 1.0078
Fig. 2. Cross-sectional view of the capacitive sensor.
cannot be kept constant, dos Reis and Goldstein (2005) developed a procedure to correct the effect. 2.2. Determination of key parameters The capacitive sensor used in this paper is similar to Canière et al. (2007). To make the sensor suitable for more configurations other than only for horizontal tubes, some modifications and further developments are made. Figs. 2 and 3 show the cross-sectional and side view of the capacitive sensor. Two-phase refrigerant flows in a thin tube (diameter of D) made up with a dielectric layer. Sensors (two concave electrodes, each with central angle of β ) are outside the dielectric layer, connecting to copper wires. Outermost layer is a grounded metal shield. Some key parameters are necessary to be determined during the sensor design: dielectric layer thickness t, electrodes angle β , shield diameter R, orientation of the electrodes for horizontal configuration and electrode axial length L. To obtain a higher homogeneity for the electric filed within the sensor and larger overall capacitance difference between full liquid phase and full vapor phase, Canière (2010) suggested smaller shield radius, thinner dielectric layer thickness, larger electrode angle
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Fig. 3. Side view of the capacitive sensor.
Table 3 Dimensions of key parameters. Key parameter
Dimension
Inner tube diameter, D Electrode axial length, L Electrode angle, β Dielectric layer thickness, t Shield inner diameter, R
7 mm D, 2D/3, D/2 160° 0.05 mm 42.8 mm
for the sensor and perpendicular towards gravity as the orientation of electrodes for horizontal configuration should be applied. Similar FEM simulations to the work from Canière (2010) are made, and the results agree well to his. Canière (2010) selected the axial length of electrode (L) equal to one inner diameter (D) and claimed it could be further reduced if the transducer could be improved. Many researches (Elkow and Rezkallah, 1996; Jaworek and Krupa, 2010) used two-concave-plate configuration sensors with axial length more than one diameter. No open literature used sensors with this configuration with axial length shorter than tube diameter and compared the signals from sensors with different lengths, to our best knowledge. If shorter sensors can work as functionally as ones with longer electrodes, the sensor will be more capable to measure cross-sectional void fraction in different situations. Three sensors with axial length of one inner diameter (D), 2D/3 and D/2 are studied in this paper. From the discussion above, Table 3 lists the most important parameters of the capacitive sensor. 3. Building of the capacitive sensor The dielectric layer and electrodes are made up with the lamR inate circuit material Ultralam 3850. It is has three layers: the dielectric layer is in the middle with two copper layers on both sides. Following properties are desirable for the dielectric layer: 1) extremely low moisture absorption. 2) high electrical volume resistivity. 3) very thin thickness (0.05 mm) and excellent thickness uniformity.
Fig. 4. Configuration of the electrodes.
Precise shape and location of electrodes on dielectric layer is achieved by the etching technique. A photomask with the desired pattern of electrodes is made first. After the circuit material is attached to a silicon wafer, photoresistive material is spun onto the surface with a programmable spinner. Then ABM Flood Exposure Model 60 is used to apply UV light onto the mask and the circuit material. After photoresistive pattern is developed onto the circuit material surface, etching is applied to eliminate other parts of copper. Seven pairs of electrodes (1–7) with three different axial lengths are located in a row (Fig. 4). The gap between each pair of electrodes is half diameter (D/2, D = 7 mm). First three pairs from the left (1–3) have the axial length of one diameter (D). The axial length of the two pairs of electrodes in the middle (4 and 5) is 2D/3 and the last two pairs (6 and 7) is D/2. The dielectric layer with electrodes is made into a tube with a diameter (D) of 7 mm. Copper wires are then soldered onto the electrodes. Four pairs of electrodes (1, 3, 5 and 7) are connected to the ground as guarding electrodes. The other three pairs with
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Fig. 5. Capacitive sensor.
Fig. 6. Void fraction measured by the uncalibrated sensor (assuming linear relation between capacitance and void fraction) compared with experimentally measured void fraction by QCV, correlation by Dix (1971), and homogeneous correlation.
different axial lengths measure the capacitance signal within the electric field. 3D printed parts are mounted outside of this tube to support the structure. Outside of the inner design of the sensor, a piece of aluminum tube which is connected to the ground is used as a shield. This shield is used to reduce outside influence. The gap between the 3D printed parts and the aluminum tube is filled with resin. The resin acts also as a shield and helps the sensor withstand higher pressure. Fig. 5 shows the final schematic of the capacitive sensor. The capacitive signals measured by the sensors are in the order of pF. Hence, the transmitter/transducer must be capable to measure such small signals with reasonable high resolutions. Many researchers designed and built their own transducers/transmitters based on several techniques: charge/discharge (Canière, 2010; Canière et al., 2007, 2008; Elkow and Rezkallah, 1996), frequency deviation (Jaworek and Krupa, 2004) and phase shift (Jaworek and Krupa, 2010). Some were designed to measure air-water two-phase mixtures and may not be suitable for refrigerant flow due to the electric property difference mentioned above. Canière (2010) developed a transducer for refrigerant flow that can measure capac-
Fig. 7. Uncalibrated sensor failed to measure void fraction in the test condition explored (horizontal).
itive signals in 0–10 pF range. However, this design is not open in the literature. This transducer is hard to be duplicated in other research groups. We have used a commercially available transmitter which can directly measure capacitive signals from custom sensors. It is capable to read such small capacitive signals and provide relatively good resolutions (approx. 0.001 pF). 4. Calibration method The signals measured by the capacitive sensor depends on both void fraction and phase distribution. The capacitive signals do not vary linearly with void fraction. If the sensor measures void fraction directly without any calibration procedure (assuming a linear relation between capacitance and void fraction), the error is significant and cannot be neglected (Fig. 6). Uncalibrated results are lower compared to experimental data, and void fraction correlations (Dix, 1971) recommended in the previous work (Qian and Hrnjak, 2019) especially in the high vapor quality region. Homogeneous correlation, which is the upper limit of void fraction in horizontal and vertical upward flow, is shown for comparison. Other mass flux and flow orientation conditions have similar results.
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conditions, void fraction measured by the uncalibrated sensor is lower than those measured by QCV. The error is over 20%. Hence, a calibration procedure is necessary before utilizing this sensor to measure void fraction. In this paper, the capacitive sensor is calibrated by mass measurement based method (i.e. QCV). For each quality, time-averaged capacitive signals from all three sensors (D, 2D/3, and D/2) are related to void fraction obtained by QCV. Signals from three sensors are compared first to study the possibility of utilizing smaller sensor. The relation (polynomial equations) between experimentally measured void fraction and time-averaged signals will then be obtained by curve fitting for each flow orientation. If the test conditions are similar in the further studies, void fraction will be measured directly by reading capacitive signals. Detailed facility and test condition will be shown in the following section. 5. Facility
Fig. 8. Uncalibrated sensor failed to measure void fraction in the test condition explored (vertical).
Figs. 7 and 8 show the comparison between uncalibrated void fraction measurement from the sensor and experimental measured values by QCV. For both flow directions and all the mass flux
The schematic drawing of the calibration facility is shown in Fig. 9. The facility is similar to that in the previous study (Qian and Hrnjak, 2019) except the test section. Basically, it is a gear pump facility without oil. Refrigerant is first heated into superheat vapor and then condensed to the desired quality. In the test section, two quick-closing valves A and B are used to measured void fraction. A high-speed camera is used to capture high-speed video of flow regimes. The capacitive sensor is located right after the visualization part (Fig. 10). Flow regime characterization with the capacitive signals will be reported in the further study. Before the
Test secon bypass loop Capacitive sensor
P
Pre-cooler
Visualizaon part
T
C
QCV A
High-speed camera
C Vacuum
QCV B
T
T
T
Transmier
T P
Refrigerant removal tank (cooled in liquid nitrogen)
P Aer-cooler
Chilled water
T
AC
Pre-heater
Chilled water
Glycol (-2°C) Pressure and temperature transducers Bypass Filter valve
Mass flow meter
Sub-cooler
Charge port (in a water bath)
High/low temp refrigerant Water Chilled water (7°C)
Mixer
Glycol Pump bypass valve
Gear pump Fig. 9. Schematic drawing of calibration facility, test section in red box. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 10. Schematic drawing of the test section, horizontal and vertical. Table 4 Experimental conditions. Working media
R134a
Refrigerant saturation temperature Test section orientation Test section length Mass flux Quality
33 °C Horizontal and vertical Horizontal: 1500 mm (∼214 diameters)Vertical: 750 mm (∼107 diameters) Horizontal: 40, 80 and 115 kg/m2 sVertical: 65, 80 and 115 kg/m2 s 0.05–0.9
visualization section, 600 mm (∼86D) of the same PVC tube for the horizontal configuration and 170 mm (∼25D) for the vertical configuration is utilized to ensure the flow is fully developed. In addition, for the vertical configuration, 460 mm (∼66D) of the tube is maintained before the lower quick-closing valve to eliminate liquid pools within the test section. Hence, void fraction and flow regime in the test section are assumed to be constant. The experimental conditions are listed in Table 4. The mass flux is adjusted by the gear pump. After the system becomes stable (temperature, pressure, and refrigerant vapor quality do not change in the test section), capacitive signals are recorded by the sensor for a period of time. The time-averaged signal is obtained for each tested vapor quality. Then QCV technique is utilized to measure average void fraction in the test section. For the QCV technique, refrigerant in the test section is first sucked (or recovered) into a vacuumed tank that is cooled with liquid nitrogen. Thanks to liquid nitrogen’s extremely low temperature, it keeps the pressure in the tank very low. Once all the refrigerant from the test section is transferred into the tank, the weight of the
refrigerant in the tank is measured, and the average void fraction in the test section between valves A and B as shown in Fig. 9 can then be calculated. The time-averaged signals and measured void fraction for each test condition are then related. The detailed procedure of QCV to obtain void fraction can be found in Qian and Hrnjak (2019). 6. Data reduction and uncertainty Data reduction and uncertainty analysis of void fraction measurement can be found in the previous study (Qian and Hrnjak, 2019). The measurement uncertainties are shown in Table 5. Error propagation rule is given in Eq. (4). It estimates overall uncertainty based on measured values.
uc =
N i=1
∂y ∂ xi
2
u2 ( xi )
(4)
where uc is combined standard uncertainty, y is calculated values, xi are measured values and u(xi ) is the uncertainty of xi . This
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Table 5 Measurement uncertainties. Measurement point
Variable
Instrument
Uncertainty
Refrigerant and water temperature Absolute pressure in the mixer and after the test section Refrigerant mass flow rate Refrigerant recycling weight
Tr , Tw P mr M
Sheathed T-type thermocouple Absolute pressure transducer Coriolis mass flow meter Scale (calibrated)
±0.05 K ±0.073% FS ±0.1 g s−1 ±0.1 g
Table 6 Range of CL-V for different sets of experiments for horizontal and vertical configurations with R134a, axial length of L = D/2, 2D/3 and D, pF.
Horizontal Vertical
D/2
2D/3
D
1.119±0.057 1.319±0.011
1.224±0.05 1.363±0.017
1.797±0.069 1.853±0.01
equation is built in EES, following the procedure outlined in where the results are obtained. The median value of uncertainties of measured void fraction for horizontal flow is 1.7% and 5.5% for vertical upward flow. The maximum of uncertainties of void fraction measurement (α ±0.0405) happens at the lowest tested vapor quality condition (x = 0.05) for vertical upward flow. For each test condition, the time-averaged capacitive signals are read in pF. Before each set of experiments is conducted, capacitive signals for two base points are measured: capacitive signals for full vapor phase (CVapor ) and full liquid phase (CLiquid ). CLiquid is obtained at °C. Some researches (dos Reis and Goldstein, 2005; Olivier et al., 2015) indicated the effect of temperature on relative permittivity of refrigerant vapor phase could be neglected. Hence, CVapor is measured at room temperature. After signals of the two base points are determined, the capacitive signals for other test conditions (Cmeasured ) are measured. Time-averaged CVapor , CLiquid and Cmeasured are then calculated: CVapor , CLiquid and Cmeasured . Normalized capacitance Cnorm is defined as follows:
Cnorm =
Cmeasured − CVapor CLiquid − CVapor
(5)
The denominator shows the entire range of signal difference (quality from 0 to 1 for each mass flux). It is assumed constant for the duration of the one set of experiments. The numerator shows how much larger the measured signal is than the full vapor condition. Hence, the normalized signals are typically from 0 (fully vapor) to 1 (fully liquid). As the quality increases, the normalized signals decrease. Though the absolute values of CLiquid and CVapor may shift among different sets of experiments, the difference between CLiquid and CVapor ( CL−V ) keeps quite constant with little fluctuations as the temperature keeps constant in this study (Table 6). De Kerpel et al. (2013) proposed that normalized calibration curves would not be affected if CL−V remained the same. 7. Results 7.1. Signal analysis among sensors with different axial lengths Fig. 11 shows the comparison of normalized signals obtained from sensors with different axial lengths corresponding to the measured void fraction for horizontal flow (G = 40 kg m−2 s−1 ). All the three mass flux conditions of both orientations are compared. The results are similar and not shown here due to the space limitation. Three series of signals have the same trend: as the void fraction increases, the normalized signals decrease. When the sensors with different axial lengths measure the same void fraction, the values of normalized signals are nearly the same. The signal
Fig. 11. Comparison of signals from electrodes with different widths: D/2, 2D/3, D (Horizontal, G = 40 kg m−2 s−1 ).
values from electrodes with axial length of D/2 are close to those of D. However, the signal values of electrodes with length of 2D/3 are slightly lower than those from the other two. This may due to the configuration of the electrodes or instrumentation errors. The pair of electrodes with 2D/3 axial length is located in the middle, where more grounded guarding electrodes are on both sides. This configuration may have resulted in lower values of signals. Nevertheless, the normalized signals obtained from all three sensors have the capability to measure void fraction of both horizontal and vertical upward flow. Hence, narrower electrodes (D/2) can be used and is calibrated to measure void fraction in the next section.
7.2. Calibrated relationship between signal and void fraction As mentioned in the former sections, the capacitive sensors are calibrated by experimentally measured void fraction (Quick-closing valves). QCV technique has a low uncertainty and is often used as a calibration standard. Void fraction measured by QCV technique has definitely higher fidelity than those predicted by correlations. When calibrating a new sensor, this method is thus much more preferred. The calibration curve shows the relation between normalized capacitive signal (from D/2 sensor) and void fraction for horizontal flow (Fig. 12) and vertical upward flow (Fig. 13) in this mass flux range. Results from all three mass flux conditions of either orientation are put together to obtain a general curve. This is because mass flux has a small influence on the relation between void fraction and normalized signals in this mass flux range. Besides, the calibrated curve can be used as a mass flux independent equation in future studies if used within this mass flux range. With these two calibrated curves, the capacitive sensor can be used to measure void fraction in horizontal and vertical upward flow with R134a in similar test conditions.
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Fig. 12. Calibrated relationship for horizontal flow at low mass flux, R134a.
Fig. 15. Measurements by sensor vs. QVC for vertical upward flow at low mass flux.
Figs. 14 and 15 show comparisons between void fraction measured by the calibrated sensor and QCV technique. Compared to results obtained from the uncalibrated sensor (Figs. 7 and 8), the error is reduced significantly. After the calibration procedure, most void fraction data measured by the sensor falls into the ±15% deviations of the experimental results by ACV for horizontal flow and ±10% for vertical upward flow. 8. Conclusions
Fig. 13. Calibrated relationship for vertical upward flow at low mass flux, R134a.
A capacitive sensor based on the work from Canière (2010) is designed, built and further developed. To evaluate the influence of the axial length of the sensor and the possibility of utilizing shorter sensors in applications with space limitation, three sensors with different axial lengths are set in a row. Relations between measured void fraction and normalized signals from each sensor are compared (Fig. 11). Results show that signals are independent of the sensor axial length (D, 2D/3 and D/2) in the test conditions explored. This justifies the use of the shorter sensors in many applications, such as to measure void fraction along the headers of microchannel heat exchangers. The mass measurement based calibrated curves of void fraction and normalized signal for both horizontal and vertical flow are proposed (Figs. 12 and 13). Calibrated sensors provide more accurate void fraction measurement compared to the uncalibrated (Figs. 14 and 15). With these two calibrated relationships, the sensor can be utilized directly to measure void fraction in the smooth circular tubes with similar test conditions in the future studies. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References
Fig. 14. Measurements by sensor vs. QVC for horizontal flow at low mass flux.
Abouelwafa, M.S.A., Kendall, E.J.M., 1980. The use of capacitance sensors for phase percentage determination in multiphase pipelines. IEEE Trans. Instrum. Meas. 29 (1), 24–27.
H. Qian and P. Hrnjak / International Journal of Refrigeration 110 (2020) 168–177 Ahmed, W.H., Ismail, B.I., 2008. Innovative techniques for two-phase flow measurements. Recent Patents Electr. Electron. Eng. (Formerly Recent Patents on Electrical Engineering) 1 (1), 1–13. ASHRAE, 2013. 2013 ASHRAE Handbook – Fundamentals, I-P Ed. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Beggs, H.D. (1973). An Experimental Study of Two-Phase Flow in Inclined Pipes. Canière, H., 2010. Flow Pattern Mapping of Horizontal Evaporating Refrigerant Flow Based on Capacitive Void Fraction Measurements Ph.D. thesis. Ghent University. Canière, H., T’Joen, C., Willockx, A., De Paepe, M., Christians, M., Van Rooyen, E., … Meyer, J., 2007. Horizontal two-phase flow characterization for small diameter tubes with a capacitance sensor. Meas. Sci. Technol. 18 (9), 2898. Canière, H., T’Joen, C., Willockx, A., De Paepe, M., 2008. Capacitance signal analysis of horizontal two-phase flow in a small diameter tube. Exp. Thermal Fluid Sci. 32 (3), 892–904. Da Silva, M., Thiele, S., Abdulkareem, L., Azzopardi, B., Hampel, U., 2010. High-resolution gas–oil two-phase flow visualization with a capacitance wire-mesh sensor. Flow Meas. Instrum. 21 (3), 191–197. De Kerpel, K., 2015. Refrigerant Two-Phase Flow Behaviour and Pressure Drop Up-And Downstream of a Sharp Return Bend. Ghent University. De Kerpel, K., Ameel, B., De Schampheleire, S., T’Joen, C., Canière, H., De Paepe, M., 2014. Calibration of a capacitive void fraction sensor for small diameter tubes based on capacitive signal features. Appl. Therm. Eng. 63 (1), 77–83. doi:10. 1016/j.applthermaleng.2013.11.006. De Kerpel, K., Ameel, B., T’Joen, C., Canière, H., De Paepe, M., 2013. Flow regime based calibration of a capacitive void fraction sensor for small diameter tubes. Int. J. Refrig. 36 (2), 390–401. Dix, G.E., 1971. Vapor Void Fractions for Forced Convection With Subcooled Boiling at Low Flow Rates. University of California, Berkeley. dos Reis, E., Goldstein, L., 2005. A procedure for correcting for the effect of fluid flow temperature variation on the response of capacitive void fraction meters. Flow Meas. Instrum. 16 (4), 267–274. Elkow, K.J., Rezkallah, K.S., 1996. Void fraction measurements in gas-liquid flows using capacitance sensors. Meas. Sci. Technol. 7 (8), 1153. Elkow, K.J., Rezkallah, K.S., 1997. Void fraction measurements in gas-liquid flows under 1 - g and μ - g conditions using capacitance sensors. Int. J. Multiph. Flow 23 (5), 815–829. doi:10.1016/S0301-9322(97)0 0 020-7. Feja, S., 2012. Measurement of electrical properties of refrigerants and refrigerant– oil mixtures. Int. J. Refrig. 35 (5), 1367–1371. doi:10.1016/j.ijrefrig.2012.03.011.
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Geraets, J., Borst, J., 1988. A capacitance sensor for two-phase void fraction measurement and flow pattern identification. Int. J. Multiph. Flow 14 (3), 305–320. Haynes, W.M., 2014. CRC Handbook of Chemistry and Physics. CRC Press. Isbin, H.S., Sher, N.C., Eddy, K.C., 1957. Void fractions in two-phase steam-water flow. AIChE J. 3 (1), 136–142. doi:10.10 02/aic.690 030122. Jaworek, A., Krupa, A., 2004. Gas/liquid ratio measurements by rf resonance capacitance sensor. Sens. Actuat. A: Phys. 113 (2), 133–139. Jaworek, A., Krupa, A., 2010. Phase-shift detection for capacitance sensor measuring void fraction in two-phase flow. Sens. Actuat.s A: Phys. 160 (1), 78–86. Kendoush, A.A., Sarkis, Z.A., 1995. Improving the accuracy of the capacitance method for void fraction measurement. Exp. Therm. Fluid Sci. 11 (4), 321–326. Meurer, C., Pietsch, G., Haacke, M., 2001. Electrical properties of CFC-and HCFC-substitutes. Int. J. Refrig. 24 (2), 171–175. Olivier, S., Meyer, J., Elton, L., Müller, C., Martin, S.J., Huisseune, H., … Marzo, S., 2015. Measured void fraction and heat transfer coefficients during condensation. Sort 100, 250. Olivier, S.P., Meyer, J.P., De Paepe, M., De Kerpel, K., 2016. The influence of inclination angle on void fraction and heat transfer during condensation inside a smooth tube. Int. J. Multiph. Flow 80, 1–14. Pabon, J.J.G., Pereira, L.C., Humia, G., Khosravi, A., Revellin, R., Bonjour, J., Machado, L., 2019. Experimental study on the void fraction during two-phase flow of R1234yf in smooth horizontal tubes. Int. J. Refrig. 104, 103–112. doi:10. 1016/j.ijrefrig.2019.05.007. Qian, H., Hrnjak, P., 2019. Void fraction measurement and flow regimes visualization of R134a in horizontal and vertical id 7mm circular tubes. Int. J. Refrig. doi:10. 1016/j.ijrefrig.2019.04.018. Rocha, M.d.S., Simões-Moreira, J., 2008. Void fraction measurement and signal analysis from multiple-electrode impedance sensors. Heat Transf. Eng. 29 (11), 924–935. Rouhani, S.Z., Axelsson, E., 1970. Calculation of void volume fraction in the subcooled and quality boiling regions. Int. J. Heat Mass Transf. 13 (2), 383–393. Sakamoto, Y., Kobayashi, H., Naruo, Y., Takesaki, Y., Nakajima, Y., Furuichi, A., … Sato, T., 2019. Investigation of the void fraction–quality correlations for twophase hydrogen flow based on the capacitive void fraction measurement. Int. J. Hydrogen Energy 44 (33), 18483–18495. doi:10.1016/j.ijhydene.2019.05.066. Wojtan, L., Ursenbacher, T., Thome, J.R., 2005. Measurement of dynamic void fractions in stratified types of flow. Exp. Therm. Fluid Sci. 29 (3), 383–392. doi:10. 1016/j.expthermflusci.2004.05.017.
Contents lists available at ScienceDirect
International Journal of Refrigeration journal homepage: www.elsevier.com/locate/ijrefrig
Mass measurement based calibration of a capacitive sensor to measure void fraction for R134a in smooth tubes Hongliang Qian a, Pega Hrnjak a,b,∗ a b
Air Conditioning and Refrigeration Center, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA Creative Thermal Solutions, 2209 Willow Rd., Urbana, IL, USA
a r t i c l e
i n f o
Article history: Received 2 July 2019 Revised 18 October 2019 Accepted 19 October 2019 Available online 23 October 2019 Keywords: Capacitive sensor Void fraction Quick-closing valve Calibration
a b s t r a c t This paper presents a new capacitive sensor built and used to measure void fraction of both horizontal and vertical upward flow in the low mass flux range in circular tubes with an inner diameter of 7 mm. Three sensors with different axial lengths (D, 2D/3, and D/2) are built and evaluated to examine the possibility of utilizing shorter sensors in applications with space limitations. Results show all three sensors have the capability to measure void fraction. Due to the nonlinear relation between capacitive signals and void fraction, a calibration procedure based on mass measurement (quick-closing valve technique, QCV) is proposed. After the calibration procedure, most void fraction data measured by the sensor falls into the ±15% deviations of the experimental results by QCV for horizontal flow and ±10% for vertical upward flow. Sensors with the same design can be utilized directly to measure void fraction for the similar test conditions in the future studies. © 2019 Elsevier Ltd and IIR. All rights reserved.
Étalonnage basé sur la mesure de masse d’un capteur capacitif pour mesurer la fraction de vide pour le R134a dans des tubes lisses Mots-clés: Capteur capacitif; Fraction de vide; Vanne à fermeture rapide; Étalonnage
1. Introduction Void fraction is generally defined as the ratio of the volume occupied by vapor over the total control volume. It is one of the most important parameters to characterize two-phase flow. It has been studied experimentally during the past several decades. Some common methods used to measure void fraction in experiments are X-ray/γ -ray absorption (Isbin et al., 1957), optical (Wojtan et al., 2005), wire mesh probe (Da Silva et al., 2010), quick-closing valves (QCV) (Beggs, 1973; Pabon et al., 2019; Qian and Hrnjak, 2019) and capacitive method (Abouelwafa and Kendall, 1980; De Kerpel et al., 2013, Olivier et al., 2016). However, some of the methods are not widely used because of inherent limitations. X-ray/γ -ray absorption method is relatively expensive and may cause safety issues. Transparent tubes are required for optical method, but it is
∗ Corresponding author at: Air Conditioning and Refrigeration Center, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA. E-mail address: [email protected] (P. Hrnjak).
https://doi.org/10.1016/j.ijrefrig.2019.10.019 0140-7007/© 2019 Elsevier Ltd and IIR. All rights reserved.
somewhat difficult to measure vapor volume by visualization results. Wire mesh probe is an intrusive method, and the sensor affects original flow patterns and void fraction. QCV is a relatively easy and straightforward experimental method to measure void fraction. By closing two valves simultaneously at both ends of a test section and measure the weight of fluid inside, the average void fraction is calculated. This method has a low uncertainty and can be used as a calibration standard when calibrating other void fraction sensors (Rocha and SimõesMoreira, 2008). The capacitive method utilizes different electrical properties between the liquid and vapor phases to measure void fraction and detect flow regimes in two-phase flow. The electrical impedance is defined as in Eq. (1), where R is the resistive term, and ωC is the capacitive term. If the working media has very high resistance and/or it is measured by a high-frequency circuit, the influence of resistivity can be neglected (Canière, 2010; Jaworek and Krupa, 2004). The signals mainly depend on the capacitance component within the sensor. Capacitive method can be used in this
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two concave electrodes to characterize two-phase flow in horizontal tubes also on charge/discharge principle. Jaworek and Krupa (2004) used two concave electrodes with a circuit measuring changes of frequency to measure gas/liquid ratio. The frequency changes were generated by a reference oscillator and the sensor. Later, Jaworek and Krupa (2010) proposed a new circuit measuring phase shift between a reference signal and a sinusoidal signal passing the sensors to measure void fraction. Most of the previous studies focused on measuring volumetric void fraction. Some studies on measuring semi-cross-sectional void fraction were proposed recently. Cross-sectional void fraction is essential to local heat transfer coefficient and pressure drop calculation. This kind of sensor can also be used in more compact applications thanks to its smaller size. Table 1 gives a brief review of experiments on void fraction measurements with capacitive sensors. Two-concave-plate configuration (Fig. 1a) is often used in the literature. In comparison to other configurations, it has the following advantages:
Nomenclature cross-sectional area (m2 ) capacitive signal (pF) inner diameter (m) mass flux (kg m−2 s−1 ) length (m) refrigerant recycling weight (g) pressure (Pa) shield inner diameter (m) temperature (°C) electrical impedance () mass flow rate (g s−1 ) dielectric layer thickness (m) vapor quality electric potential (V) void fraction electrode angle (o ) permittivity (F m−1 ) density (kg m−3 )
A C D G L M P R T Z m t x
α β ε ρ Subscripts r w Vapor Liquid measured norm
1) relatively easy to be built, especially for sensors on smaller tubes or complicated geometries. 2) higher sensitivity compared to double-helix configuration (Abouelwafa and Kendall, 1980). 3) possibility to measure semi-cross-sectional void fraction by reducing sensor axial length.
refrigerant water vapor phase liquid phase measured value normalized value
way.
Z=R+
1 jω C
169
(1)
The capacitive method is a nonintrusive method with lower cost. This method usually does not involve safety issues and is easy to implement. Abouelwafa and Kendall (1980) applied the capacitive sensors to measure phase percentage and compared different electrodes configurations. Later on, various sensor designs (electrodes configurations, Fig. 1) and electrical measuring circuits (transmitter/transducer) were proposed. Some (Ahmed and Ismail, 2008) directly measured the capacitance within the sensors with different electrode configurations to determine void fraction and/or flow regimes. Elkow and Rezkallah (1996) used concave and helical wound electrodes to measure void fraction on charge/discharge principle. Canière et al. (20 07, 20 08) used
The electrical field within some sensors (such as two concave plates) is not uniform. The signals obtained from capacitive sensors depend on both void fraction and flow patterns within the sensor. The relation between capacitive signals and void fraction is thus not linear. Hence, to measure void fraction of two-phase flow, the capacitive sensors must be calibrated first. Kerpel et al. (2014, 2013) calibrated the sensor developed by Canière et al. (2007) based on flow regimes or signal features for horizontal flow. In these two calibration methods, void fraction predicted by correlations from Rouhani and Axelsson (1970) was set to be calibration standard void fraction. Finite element method (FEM) was used to obtain capacitance and void fraction relations of different flow regimes. Olivier et al. (2016) used the calibrated sensor to measure void fraction in a smooth tube with different inclination angles during condensation. However, the difference between predicted void fraction from correlations and real values cannot be neglected for a calibration procedure. It is more reasonable to use mass measurement based method to calibrate the capacitive sensor. We selected Quick-closing valve method (QCV). FEM may also not provide the precise capacitance and void fraction relations due to the difference between the real flow regime and simulated models. Besides, both horizontal and vertical flow are encountered in HVAC systems. It is necessary to calibrate the capacitive sensor for both orientations. 2. Design of capacitive sensor 2.1. Capacitance governing equations and relative permittivity Volume resistivity and relative permittivity for different working media are shown in Table 2. The working fluid in this paper is R134a, whose resistivity is very high. Hence, capacitive methods that neglect conductivity effects are used. Canière (2010) proposed a general governing equation of capacitance between two electrodes:
C = −ε0 Fig. 1. Some typical electrode configurations (Jaworek and Krupa, 2004). (a) Two concave plates. (b) Four concave plates. (c) Six concave plates. (d) Rings. (e) Double helix.
S
εr (r )∇ · dA S − d
(2)
where S is source electrodes electric potential, d is detector electrodes electric potentials, is spatial potential distribution, ɛr is relative permittivity and ɛ0 is vacuum permittivity. Eq. (2) must
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Table 1 Review of experiments on void fraction measurements with capacitive sensors. Authors
Electrodes configuration
Pipe ID and orientation
Working media
Approach
Abouelwafa and Kendall (1980) Geraets and Borst (1988)
6 configurations Helical
12.7 – 50 mm 5 and 50 mm
Volumetric Volumetric
Kendoush and Sarkis (1995) K. J. Elkow and Rezkallah (1997) Jaworek and Krupa (2004) Ahmed and Ismail (2008) De Kerpel et al. (2014, 2013)
5 configurations Helical and concave 5 configurations Ring, concave (up and down) Concave
26–49 mm 9.53 mm, vertical 32 mm (ID), vertical 12.7 mm, horizontal 8 mm, horizontal
Air, water, and oil Air, water, glycerin and acrylate mock-ups Air and nonflow mock-ups Air–water Air–watter Air–oil R134a, R410A
De Kerpel (2015) Olivier et al. (2016) Sakamoto et al. (2019) This paper
Concave Concave Asymmetric Concave
8 mm, horizontal 8 mm (8.38 mm tube) 15 mm, horizontal 7 mm, horizontal and vertical upward
R134a, R410A R134a Hydrogen R134a
Volumetric Volumetric Semi-cross-sectional Volumetric/Semi-cross-sectional Calibration procedure for Semi-cross-sectional Semi-cross-sectional Semi-cross-sectional Semi-cross-sectional Semi-cross-sectional
Table 2 Conductivity and relative permittivity for some working media (ASHRAE, 2013). Volume resistivity (M m)
Working media Air (0 °C) Pure water (25 °C) (Haynes, 2014) R134a liquid between 23 and 26 °C (Meurer et al., 2001) R134a liquid at 25 °C R134a vapor at 25 °C R410A liquid between 23 and 26 °C (Meurer et al., 2001) R410A liquid at 25 °C R410A vapor at 25 °C
0.182 10,890
3920
be solved to get analytical solutions of capacitance for different void fraction and flow regimes. However, precise analytical solutions to some flow regimes are difficult to obtain. Experimental measurement is thus preferred. Eq. (2) also shows the overall capacitance is dependent on relative permittivity. It is important to examine relative permittivities of different working media before utilizing the capacitive method. Relative permittivity (ɛr ) is also called dielectric constant, which is a material property and temperature dependent. The permittivity is defined as ε = ε0 εr , the product of vacuum permittivity (ε0 = 8.854 × 10−12 F m−1 ) and relative permittivity. The relative permittivity of water at 25 °C is much larger than that of liquid R134a at the same temperature (Table 2). The absolute capacitive signals measured from R134a two-phase mixture are thus smaller than that from the air-water mixture. In addition, the relative permittivity difference between water and air is much bigger than that between R134a liquid phase and vapor phase. As a result, overall capacitance signal difference measured between full liquid phase and full vapor phase of R134a is smaller (Eq. (3)). Whether the sensor has the capability to measure small capacitive signals (signals of R134a mixture are typically in the order of pF and CR134a is about 1 pF) is a limitation to the sensor and transducer/transmitter design. Hence, to utilize capacitive sensors to refrigerant flow, some designs aimed to other working media from literature must be modified first.
CR134a = Cfull liquid − Cfull vapor < CWater−Air = Cfull water − Cfull air (3) The relative permittivity is a temperature dependent property. For R134a, researches (Feja, 2012) reported it decreased as temperature increased. Measured capacitance would be affected if the temperature of R134a changes. However, if the temperature is kept constant, this effect can be eliminated. This situation can be achieved when refrigerant is evaporating/condensing in the twophase zone or refrigerant flow in an adiabatic part, such as headers of microchannel heat exchangers. If the temperature varies and
Relative permittivity (domensionless) 1.00059 79.55 9.24 9.87 1.0125 7.78 5.37 1.0078
Fig. 2. Cross-sectional view of the capacitive sensor.
cannot be kept constant, dos Reis and Goldstein (2005) developed a procedure to correct the effect. 2.2. Determination of key parameters The capacitive sensor used in this paper is similar to Canière et al. (2007). To make the sensor suitable for more configurations other than only for horizontal tubes, some modifications and further developments are made. Figs. 2 and 3 show the cross-sectional and side view of the capacitive sensor. Two-phase refrigerant flows in a thin tube (diameter of D) made up with a dielectric layer. Sensors (two concave electrodes, each with central angle of β ) are outside the dielectric layer, connecting to copper wires. Outermost layer is a grounded metal shield. Some key parameters are necessary to be determined during the sensor design: dielectric layer thickness t, electrodes angle β , shield diameter R, orientation of the electrodes for horizontal configuration and electrode axial length L. To obtain a higher homogeneity for the electric filed within the sensor and larger overall capacitance difference between full liquid phase and full vapor phase, Canière (2010) suggested smaller shield radius, thinner dielectric layer thickness, larger electrode angle
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Fig. 3. Side view of the capacitive sensor.
Table 3 Dimensions of key parameters. Key parameter
Dimension
Inner tube diameter, D Electrode axial length, L Electrode angle, β Dielectric layer thickness, t Shield inner diameter, R
7 mm D, 2D/3, D/2 160° 0.05 mm 42.8 mm
for the sensor and perpendicular towards gravity as the orientation of electrodes for horizontal configuration should be applied. Similar FEM simulations to the work from Canière (2010) are made, and the results agree well to his. Canière (2010) selected the axial length of electrode (L) equal to one inner diameter (D) and claimed it could be further reduced if the transducer could be improved. Many researches (Elkow and Rezkallah, 1996; Jaworek and Krupa, 2010) used two-concave-plate configuration sensors with axial length more than one diameter. No open literature used sensors with this configuration with axial length shorter than tube diameter and compared the signals from sensors with different lengths, to our best knowledge. If shorter sensors can work as functionally as ones with longer electrodes, the sensor will be more capable to measure cross-sectional void fraction in different situations. Three sensors with axial length of one inner diameter (D), 2D/3 and D/2 are studied in this paper. From the discussion above, Table 3 lists the most important parameters of the capacitive sensor. 3. Building of the capacitive sensor The dielectric layer and electrodes are made up with the lamR inate circuit material Ultralam 3850. It is has three layers: the dielectric layer is in the middle with two copper layers on both sides. Following properties are desirable for the dielectric layer: 1) extremely low moisture absorption. 2) high electrical volume resistivity. 3) very thin thickness (0.05 mm) and excellent thickness uniformity.
Fig. 4. Configuration of the electrodes.
Precise shape and location of electrodes on dielectric layer is achieved by the etching technique. A photomask with the desired pattern of electrodes is made first. After the circuit material is attached to a silicon wafer, photoresistive material is spun onto the surface with a programmable spinner. Then ABM Flood Exposure Model 60 is used to apply UV light onto the mask and the circuit material. After photoresistive pattern is developed onto the circuit material surface, etching is applied to eliminate other parts of copper. Seven pairs of electrodes (1–7) with three different axial lengths are located in a row (Fig. 4). The gap between each pair of electrodes is half diameter (D/2, D = 7 mm). First three pairs from the left (1–3) have the axial length of one diameter (D). The axial length of the two pairs of electrodes in the middle (4 and 5) is 2D/3 and the last two pairs (6 and 7) is D/2. The dielectric layer with electrodes is made into a tube with a diameter (D) of 7 mm. Copper wires are then soldered onto the electrodes. Four pairs of electrodes (1, 3, 5 and 7) are connected to the ground as guarding electrodes. The other three pairs with
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Fig. 5. Capacitive sensor.
Fig. 6. Void fraction measured by the uncalibrated sensor (assuming linear relation between capacitance and void fraction) compared with experimentally measured void fraction by QCV, correlation by Dix (1971), and homogeneous correlation.
different axial lengths measure the capacitance signal within the electric field. 3D printed parts are mounted outside of this tube to support the structure. Outside of the inner design of the sensor, a piece of aluminum tube which is connected to the ground is used as a shield. This shield is used to reduce outside influence. The gap between the 3D printed parts and the aluminum tube is filled with resin. The resin acts also as a shield and helps the sensor withstand higher pressure. Fig. 5 shows the final schematic of the capacitive sensor. The capacitive signals measured by the sensors are in the order of pF. Hence, the transmitter/transducer must be capable to measure such small signals with reasonable high resolutions. Many researchers designed and built their own transducers/transmitters based on several techniques: charge/discharge (Canière, 2010; Canière et al., 2007, 2008; Elkow and Rezkallah, 1996), frequency deviation (Jaworek and Krupa, 2004) and phase shift (Jaworek and Krupa, 2010). Some were designed to measure air-water two-phase mixtures and may not be suitable for refrigerant flow due to the electric property difference mentioned above. Canière (2010) developed a transducer for refrigerant flow that can measure capac-
Fig. 7. Uncalibrated sensor failed to measure void fraction in the test condition explored (horizontal).
itive signals in 0–10 pF range. However, this design is not open in the literature. This transducer is hard to be duplicated in other research groups. We have used a commercially available transmitter which can directly measure capacitive signals from custom sensors. It is capable to read such small capacitive signals and provide relatively good resolutions (approx. 0.001 pF). 4. Calibration method The signals measured by the capacitive sensor depends on both void fraction and phase distribution. The capacitive signals do not vary linearly with void fraction. If the sensor measures void fraction directly without any calibration procedure (assuming a linear relation between capacitance and void fraction), the error is significant and cannot be neglected (Fig. 6). Uncalibrated results are lower compared to experimental data, and void fraction correlations (Dix, 1971) recommended in the previous work (Qian and Hrnjak, 2019) especially in the high vapor quality region. Homogeneous correlation, which is the upper limit of void fraction in horizontal and vertical upward flow, is shown for comparison. Other mass flux and flow orientation conditions have similar results.
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conditions, void fraction measured by the uncalibrated sensor is lower than those measured by QCV. The error is over 20%. Hence, a calibration procedure is necessary before utilizing this sensor to measure void fraction. In this paper, the capacitive sensor is calibrated by mass measurement based method (i.e. QCV). For each quality, time-averaged capacitive signals from all three sensors (D, 2D/3, and D/2) are related to void fraction obtained by QCV. Signals from three sensors are compared first to study the possibility of utilizing smaller sensor. The relation (polynomial equations) between experimentally measured void fraction and time-averaged signals will then be obtained by curve fitting for each flow orientation. If the test conditions are similar in the further studies, void fraction will be measured directly by reading capacitive signals. Detailed facility and test condition will be shown in the following section. 5. Facility
Fig. 8. Uncalibrated sensor failed to measure void fraction in the test condition explored (vertical).
Figs. 7 and 8 show the comparison between uncalibrated void fraction measurement from the sensor and experimental measured values by QCV. For both flow directions and all the mass flux
The schematic drawing of the calibration facility is shown in Fig. 9. The facility is similar to that in the previous study (Qian and Hrnjak, 2019) except the test section. Basically, it is a gear pump facility without oil. Refrigerant is first heated into superheat vapor and then condensed to the desired quality. In the test section, two quick-closing valves A and B are used to measured void fraction. A high-speed camera is used to capture high-speed video of flow regimes. The capacitive sensor is located right after the visualization part (Fig. 10). Flow regime characterization with the capacitive signals will be reported in the further study. Before the
Test secon bypass loop Capacitive sensor
P
Pre-cooler
Visualizaon part
T
C
QCV A
High-speed camera
C Vacuum
QCV B
T
T
T
Transmier
T P
Refrigerant removal tank (cooled in liquid nitrogen)
P Aer-cooler
Chilled water
T
AC
Pre-heater
Chilled water
Glycol (-2°C) Pressure and temperature transducers Bypass Filter valve
Mass flow meter
Sub-cooler
Charge port (in a water bath)
High/low temp refrigerant Water Chilled water (7°C)
Mixer
Glycol Pump bypass valve
Gear pump Fig. 9. Schematic drawing of calibration facility, test section in red box. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 10. Schematic drawing of the test section, horizontal and vertical. Table 4 Experimental conditions. Working media
R134a
Refrigerant saturation temperature Test section orientation Test section length Mass flux Quality
33 °C Horizontal and vertical Horizontal: 1500 mm (∼214 diameters)Vertical: 750 mm (∼107 diameters) Horizontal: 40, 80 and 115 kg/m2 sVertical: 65, 80 and 115 kg/m2 s 0.05–0.9
visualization section, 600 mm (∼86D) of the same PVC tube for the horizontal configuration and 170 mm (∼25D) for the vertical configuration is utilized to ensure the flow is fully developed. In addition, for the vertical configuration, 460 mm (∼66D) of the tube is maintained before the lower quick-closing valve to eliminate liquid pools within the test section. Hence, void fraction and flow regime in the test section are assumed to be constant. The experimental conditions are listed in Table 4. The mass flux is adjusted by the gear pump. After the system becomes stable (temperature, pressure, and refrigerant vapor quality do not change in the test section), capacitive signals are recorded by the sensor for a period of time. The time-averaged signal is obtained for each tested vapor quality. Then QCV technique is utilized to measure average void fraction in the test section. For the QCV technique, refrigerant in the test section is first sucked (or recovered) into a vacuumed tank that is cooled with liquid nitrogen. Thanks to liquid nitrogen’s extremely low temperature, it keeps the pressure in the tank very low. Once all the refrigerant from the test section is transferred into the tank, the weight of the
refrigerant in the tank is measured, and the average void fraction in the test section between valves A and B as shown in Fig. 9 can then be calculated. The time-averaged signals and measured void fraction for each test condition are then related. The detailed procedure of QCV to obtain void fraction can be found in Qian and Hrnjak (2019). 6. Data reduction and uncertainty Data reduction and uncertainty analysis of void fraction measurement can be found in the previous study (Qian and Hrnjak, 2019). The measurement uncertainties are shown in Table 5. Error propagation rule is given in Eq. (4). It estimates overall uncertainty based on measured values.
uc =
N i=1
∂y ∂ xi
2
u2 ( xi )
(4)
where uc is combined standard uncertainty, y is calculated values, xi are measured values and u(xi ) is the uncertainty of xi . This
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Table 5 Measurement uncertainties. Measurement point
Variable
Instrument
Uncertainty
Refrigerant and water temperature Absolute pressure in the mixer and after the test section Refrigerant mass flow rate Refrigerant recycling weight
Tr , Tw P mr M
Sheathed T-type thermocouple Absolute pressure transducer Coriolis mass flow meter Scale (calibrated)
±0.05 K ±0.073% FS ±0.1 g s−1 ±0.1 g
Table 6 Range of CL-V for different sets of experiments for horizontal and vertical configurations with R134a, axial length of L = D/2, 2D/3 and D, pF.
Horizontal Vertical
D/2
2D/3
D
1.119±0.057 1.319±0.011
1.224±0.05 1.363±0.017
1.797±0.069 1.853±0.01
equation is built in EES, following the procedure outlined in where the results are obtained. The median value of uncertainties of measured void fraction for horizontal flow is 1.7% and 5.5% for vertical upward flow. The maximum of uncertainties of void fraction measurement (α ±0.0405) happens at the lowest tested vapor quality condition (x = 0.05) for vertical upward flow. For each test condition, the time-averaged capacitive signals are read in pF. Before each set of experiments is conducted, capacitive signals for two base points are measured: capacitive signals for full vapor phase (CVapor ) and full liquid phase (CLiquid ). CLiquid is obtained at °C. Some researches (dos Reis and Goldstein, 2005; Olivier et al., 2015) indicated the effect of temperature on relative permittivity of refrigerant vapor phase could be neglected. Hence, CVapor is measured at room temperature. After signals of the two base points are determined, the capacitive signals for other test conditions (Cmeasured ) are measured. Time-averaged CVapor , CLiquid and Cmeasured are then calculated: CVapor , CLiquid and Cmeasured . Normalized capacitance Cnorm is defined as follows:
Cnorm =
Cmeasured − CVapor CLiquid − CVapor
(5)
The denominator shows the entire range of signal difference (quality from 0 to 1 for each mass flux). It is assumed constant for the duration of the one set of experiments. The numerator shows how much larger the measured signal is than the full vapor condition. Hence, the normalized signals are typically from 0 (fully vapor) to 1 (fully liquid). As the quality increases, the normalized signals decrease. Though the absolute values of CLiquid and CVapor may shift among different sets of experiments, the difference between CLiquid and CVapor ( CL−V ) keeps quite constant with little fluctuations as the temperature keeps constant in this study (Table 6). De Kerpel et al. (2013) proposed that normalized calibration curves would not be affected if CL−V remained the same. 7. Results 7.1. Signal analysis among sensors with different axial lengths Fig. 11 shows the comparison of normalized signals obtained from sensors with different axial lengths corresponding to the measured void fraction for horizontal flow (G = 40 kg m−2 s−1 ). All the three mass flux conditions of both orientations are compared. The results are similar and not shown here due to the space limitation. Three series of signals have the same trend: as the void fraction increases, the normalized signals decrease. When the sensors with different axial lengths measure the same void fraction, the values of normalized signals are nearly the same. The signal
Fig. 11. Comparison of signals from electrodes with different widths: D/2, 2D/3, D (Horizontal, G = 40 kg m−2 s−1 ).
values from electrodes with axial length of D/2 are close to those of D. However, the signal values of electrodes with length of 2D/3 are slightly lower than those from the other two. This may due to the configuration of the electrodes or instrumentation errors. The pair of electrodes with 2D/3 axial length is located in the middle, where more grounded guarding electrodes are on both sides. This configuration may have resulted in lower values of signals. Nevertheless, the normalized signals obtained from all three sensors have the capability to measure void fraction of both horizontal and vertical upward flow. Hence, narrower electrodes (D/2) can be used and is calibrated to measure void fraction in the next section.
7.2. Calibrated relationship between signal and void fraction As mentioned in the former sections, the capacitive sensors are calibrated by experimentally measured void fraction (Quick-closing valves). QCV technique has a low uncertainty and is often used as a calibration standard. Void fraction measured by QCV technique has definitely higher fidelity than those predicted by correlations. When calibrating a new sensor, this method is thus much more preferred. The calibration curve shows the relation between normalized capacitive signal (from D/2 sensor) and void fraction for horizontal flow (Fig. 12) and vertical upward flow (Fig. 13) in this mass flux range. Results from all three mass flux conditions of either orientation are put together to obtain a general curve. This is because mass flux has a small influence on the relation between void fraction and normalized signals in this mass flux range. Besides, the calibrated curve can be used as a mass flux independent equation in future studies if used within this mass flux range. With these two calibrated curves, the capacitive sensor can be used to measure void fraction in horizontal and vertical upward flow with R134a in similar test conditions.
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Fig. 12. Calibrated relationship for horizontal flow at low mass flux, R134a.
Fig. 15. Measurements by sensor vs. QVC for vertical upward flow at low mass flux.
Figs. 14 and 15 show comparisons between void fraction measured by the calibrated sensor and QCV technique. Compared to results obtained from the uncalibrated sensor (Figs. 7 and 8), the error is reduced significantly. After the calibration procedure, most void fraction data measured by the sensor falls into the ±15% deviations of the experimental results by ACV for horizontal flow and ±10% for vertical upward flow. 8. Conclusions
Fig. 13. Calibrated relationship for vertical upward flow at low mass flux, R134a.
A capacitive sensor based on the work from Canière (2010) is designed, built and further developed. To evaluate the influence of the axial length of the sensor and the possibility of utilizing shorter sensors in applications with space limitation, three sensors with different axial lengths are set in a row. Relations between measured void fraction and normalized signals from each sensor are compared (Fig. 11). Results show that signals are independent of the sensor axial length (D, 2D/3 and D/2) in the test conditions explored. This justifies the use of the shorter sensors in many applications, such as to measure void fraction along the headers of microchannel heat exchangers. The mass measurement based calibrated curves of void fraction and normalized signal for both horizontal and vertical flow are proposed (Figs. 12 and 13). Calibrated sensors provide more accurate void fraction measurement compared to the uncalibrated (Figs. 14 and 15). With these two calibrated relationships, the sensor can be utilized directly to measure void fraction in the smooth circular tubes with similar test conditions in the future studies. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References
Fig. 14. Measurements by sensor vs. QVC for horizontal flow at low mass flux.
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