Capacitive Void Fraction Research Articles

Development of capacitance sensor for void fraction measurement in a packed bed of spheres

A capacitance void fraction sensor (CVS) is applied to measure the volumetric averaged void fraction in a packed bed of spheres. The void fraction in the packed bed is one of the most important parameters to evaluate cooling characteristics in a porous debris bed during a severe accident of nuclear reactors, and the quantitative void fraction measuring technique for such porous flow channels should be developed. The CVS is a very simple method, and the void fraction is estimated from the electrical capacitance measured between the electrodes installed on the pipe. Generally, the linear relationship or Maxwell equation could be applied to estimate the void fraction from the capacitance measured by the CVS. However, the electrical field in the packed bed becomes complex due to the existence of spheres. Therefore, they may not be applied to the void fraction estimation in the packed bed. In this study, the CVS with a ring-type electrode configuration is used for the sphere-packed beds, and the applicability of the CVS is investigated. At first, the particle size and the pipe diameter are varied in the packed test section, and X-ray transmission imaging is used to clarify the relation between the void fraction and the capacitance in the packed bed. Then, it is found that the void fraction can be obtained by the coefficient in Maxwell's equation, depending on the packed bed properties. Finally, the measurement accuracy of the CVS for the sphere-packed bed is estimated by comparing it with a volumetric method, and the availability of the proposed method is shown.

Development of All Metal Multi-plate-type Capacitive Void Fraction Sensor for gas-liquid two-phase flow

In the aerospace field, liquid hydrogen and oxygen which are “cryogenic fluid” are used as the propellant for rockets and hypersonic engines. These fluids become easily a gas-liquid two-phase flow in pipes and fluid machines. We have developed small capacitive void fraction sensors which can measure in real time, which is used to control the flow rate of cryogenic fuel and to understand typical two-phase flow phenomena such as the cavitation. The conventional capacitive sensors have a structure in which two electrodes sandwich a pipe made of dielectric material. However, the dielectric material has problems such as insufficient strength under high pressure condition and decreasing measurement accuracy due to changes in dielectric constant with temperature change. We developed a new capacitive sensor which consists of only metal parts to solve these problems. On the other hand, it may cause a decrease in measurement accuracy due to the structural limitation. This paper presents the results of the electric field analysis and the static fluid experiment using silicon oil and air to verify the accuracy of the sensor. The mean errors obtained by the analysis and the experiment are 3.47 % and 5.32 %, respectively, which almost satisfy the required specification. However, it was found that the accuracy is poor in some void fraction ranges, and the sensor needs to be improved.

Flow regime characterization of a silicon-based vaporizing liquid microthruster

The present work discusses an experimental investigation of the flow into a silicon-based vaporizing liquid microthruster equipped with sensing capabilities and low-power on-channel secondary heaters. The sensing capabilities (resistance temperature detectors and capacitive void fraction sensors) are used to investigate the flow instability and to evaluate its performances. The device has a sandwich structure composed of a silicon substrate and a glass substrate. This last one allows optical access into the device. The main heating of the propellant is provided using a platinum resistive heater placed on the bottom of the silicon layer. By varying the electrical power supplied to the main heater at fixed mass flow rate, three flow regimes have been observed and investigated: fully liquid flow, two-phase flow, and fully vaporized flow. Their dynamics have been captured through high-speed micro-flow visualizations under rough vacuum conditions (about 29 kPa). Furthermore, the expansion of the exhaust vapor plume exiting from the micronozzle has been analyzed via Schlieren visualizations. Results highlighted the occurrence of a cyclic flow behavior during the two-phase flow regime. In contrast, the flow exhibits the presence of both liquid and vapor phases at the micronozzle exit. Once the fully vaporized flow regime is established, the two-phase flow dynamics into the inlet chamber become more stable with complete filling and more uniform distribution of the flow at the microchannels entrance. Schlieren imaging captured the increase of the exhaust plume spreading half-angle when moving from ambient condition towards rough vacuum.

Investigation of the void fraction–quality correlations for two-phase hydrogen flow based on the capacitive void fraction measurement

The void fraction and vapor quality are important parameters for characterizing the gas–liquid two-phase flow. However, neither an established void fraction measurement method nor a verified void fraction – vapor quality interconversion model is available for the two-phase hydrogen flow. The object of this study is the development of a void fraction measurement technique and the investigation of the void fraction–quality correlations. A capacitive void fraction sensor was developed using the electric field analysis (EFA) and design of experiment (DOE), and it was applied in a boiling hydrogen experimental facility. The experimental conditions were as follows: the inner diameter of the heating pipe was 15 mm, the mass flux was ranged from 50 to 110 kg/m2s, and the static pressure was ranged from 250 to 300 kPaA. Further, the correlation between the thermal equilibrium quality (χac=− 0.03–0.14) and void fraction (α = 0–70%) was compared with that obtained in previously proposed models, and the void fraction – actual quality – thermal equilibrium quality interconversion models applicable to the boiling hydrogen flow were investigated. It was observed that the combination of the Sekoguchi model for thermal equilibrium quality – actual quality conversion and the Steiner drift-flux model for actual quality – void fraction conversion agreed well with the experimental results.

Development of Quality Measurement System Using Slip Ratio Model with Homogenization System

Quality is an important parameter on the gas-liquid two phase flow for organizing its heat transfer, pressure loss properties and flow regime. However, a method to measure quality has not been established yet. A new quality measurement method has been developed by using the mixers and capacitive void fraction sensor. The method is based on the experimental results that the slip ratio of the two phase flow homogenized by the mixers correlates closely with quality. A slip ratio model is created using the mass flux and void fraction after the mixer. Helical type and cross type mixers are arranged in series to homogenize the two phase flow in wide range of the flow regime. Air and silicon oil are used as the working fluids in this experiment. Several types of the flow condition are made by changing the mass flow rates in the horizontal, vertical flow passages. As a result, quality can be measured within ±50% of the error at 92% cases of the whole experiments. Quality meter shows less or comparable errors compared with the Smith's formula which is generally used. In addition, quality meter can be used both for the developed and undeveloped flows.

Capacitive Void Fraction Sensor for Ground Test of LE-5B-3

Capacitive Void Fraction Sensor for Ground Test of LE-5B-3

Void fraction measurement in cryogenic flows. Part I: Design and validation of a void fraction capacitive sensor

This manuscript presents the design of a capacitive void fraction sensor for cryogenic LN2 two phase flows and its validation at room conditions. The capacitive void fraction sensor is first designed by means of Electric Field Analysis (EFA) simulations taking into account specific technical constraints coming from the test section in which it should be accommodated. Then it is manufactured and validated using a proper combination of fluids (Polydimethylsiloxane (PDMS) and air) having a dielectric constant ratio similar to the one encountered in LN2/GN2 two phase flows. The validation is performed through comparison with void fraction measured by means of optical visualizations and shows how the capacitive measurement technique robustness allows obtaining reasonable accurate values of void fraction also for the substitute fluid case. The sensor presented in this manuscript was used to evaluate the void fraction during LN2 chilldown of a rectangular cooling channel and the results are presented in the second part of this work.

静電容量型ボイド率計における螺旋型極板の最適化設計

静電容量型ボイド率計における螺旋型極板の最適化設計

The influence of inclination angle on void fraction and heat transfer during condensation inside a smooth tube

Most work in literature on condensation in tubes has been done for smooth tubes in the horizontal and vertical configurations. Recent experimental works with condensation at different inclination angles showed that the heat transfer characteristics were a function of inclination angle. These works were limited to heat transfer and pressure drop measurements with visual observations. However, no work has been done on measuring the void fractions during condensation at different inclination angles. The purpose of this study was to measure void fractions and heat transfer coefficients during condensation for tube inclinations ranging from vertical downwards (−90°) to vertical upwards (90°) at a saturation temperature of 40 °C. Measurements were taken in an experimental set-up in which condensation occurred on the inside of a test section. The test section was a circular tube with an inner diameter of 8.38 mm and a heat transfer length of 1.488. The refrigerant used was R134a, and the void fractions were measured using two capacitive void fraction sensors. Mass fluxes ranging from 100 to 400 kg/m2 s and vapour qualities ranging from 10–90% were considered. Heat transfer coefficients were also compared with void fractions. It was found that at combinations of low mass fluxes and vapour qualities, void fraction and heat transfer were significantly affected by changes in inclination angle. Generally, void fractions and heat transfer coefficients increased with downward inclination angles with an optimum angle between −10° and −30° (downward flow). At some intermediate mass flux and vapour quality conditions, the void fraction and heat transfer coefficients were observed to be independent of the inclination angle despite changes in the prevailing flow patterns.

Calibration of a capacitive void fraction sensor for small diameter tubes based on capacitive signal features

In this paper, calibration of a capacitive void fraction sensor for small diameter tubes based on capacitive signal features is proposed. Existing calibration methods require the mass flux and vapour quality to be known, which poses serious issues for practical applications. In this work an alternative calibration technique is proposed, based on the statistical parameters of the measurement signal.The proposed method was applied to 270 measurement points. The inner tube diameter for all these points is 8 mm, the mass flux ranges from 200 to 500 kg/m²s and the vapour quality ranges between 2.5% and 97.5%. Refrigerants R134a and R410A were used. A good agreement was found, the results were compared to the Steiner version of the Rouhani–Axelsson drift flux void fraction model. The maximum average difference between the model and the predicted value was 1.3% with a standard deviation of 4%.

Permittivity-based void fraction sensing for microfluidics

The design, fabrication and integration of capacitive void fraction sensors for microfluidic applications in silicon microchannels of 100μm wide and 500μm deep are described. Simulation data are presented and discussed and the most critical microfabrication steps involving the drilling of glass dice and the anodic bonding of glass to silicon via an intermediate sputtered Pyrex layer are elucidated.A read-out circuit was designed to convert capacitive input signals into a large-swing analog output signal. The signal-processing algorithm is explained. Measurements showing the variation of the output signal as a function of the gas content in the air/water-mixture, pumped through the microchannels, are presented.

Flow regime based calibration of a capacitive void fraction sensor for small diameter tubes

The void fraction measurement technique used in this work is based on measuring the capacity between two electrodes. The electrodes are curved so they closely fit to the tube wall; due to this the measured capacitance is influenced by the spatial distribution of the phases and not only the void fraction. Hence, the measured capacitance does not linearly vary with the void fraction. In this work a method is proposed to account for the distribution of the phases and thus determine the void fraction based on capacitive measurements. The proposed method was applied to 270 measurement points. The tube diameter D is 8 mm, the mass flux ranges from 200 to 500 kg m−2s−1 and the vapour fraction ranges between 2.5% and 97.5%. Refrigerants R134a and R410A were used. The results were compared to the Steiner version of the Rouhani–Axelsson drift flux void fraction model. A very good agreement with this model was observed.

Integrated Void Fraction Sensors for Two-phase, Microfluidic Systems

The design, fabrication and integration of capacitive void fraction sensors for microfluidic applications in silicon microchannels of 100 μm wide and 500 μm deep are described. Microfabrication steps such as electrode deposition, glass dicing and drilling and the anodic bonding process are elucidated. A read-out circuit was designed to convert capacitive input signals into a large-swing analog output signal. The signal processing algorithm is discussed. Measurements showing the variation of the output signal in function of the gas content in the air/water-mixture that was pumped through the microchannels are presented.

Mapping of horizontal refrigerant two-phase flow patterns based on clustering of capacitive sensor signals

A capacitive void fraction sensor was developed to study the objectivity in flow pattern mapping of horizontal refrigerant two-phase flow in macroscale tubes. Sensor signals were gathered with R410A and R134a in a smooth tube with an inner diameter of 8 mm at a saturation temperature of 15 °C in the mass velocity range of 200–500 kg/m 2 s and vapour quality range from 0 to 1 in steps of 0.025. A visual classification based on high speed camera images is made for comparison reasons. A statistical analysis of the sensor signals shows that the average, the variance and a high frequency contribution parameter are suitable for flow regime classification into slug flow, intermittent flow and annular flow by using the fuzzy c-means clustering algorithm. This soft-clustering algorithm predicts the slug/intermittent flow transition very well compared to our visual observations. The intermittent/annular flow transition is found at slightly higher vapour qualities for R410A compared to the prediction of Barbieri et al. (2008) [20]. An excellent agreement was obtained with R134a. This intermittent/annular flow transition is very gradual. A probability approach can therefore better describe such a transition. The membership grades of the cluster algorithm can be interpreted as flow regime probabilities. Probabilistic flow pattern maps are presented for R410A and R134a in an 8 mm ID tube.

An approximate formula for the capacitance–void fraction relationship for annular flows

A capacitance method is applied to measure the space-averaged void fraction in concentric annular flows. From the analytical solution of the governing electrical field equations, the expression for the capacitance in terms of a given void fraction is derived. Also, a closed form formula to predict the void fraction from the capacitance measurement is proposed. The relationship between the capacitance and the void fraction is successfully compared with static phantom experiments.

Microgravity flow regime data and analysis

To utilize the advantageous properties of two-phase flow in microgravity applications, the knowledge base of two-phase flow phenomena must be extended to include the effects of gravity. In the experiment described, data regarding the behavior of two-phase flow in a conduit under microgravity conditions (essentially zero gravity) are explored. Of particular interest, knowledge of the void fraction of the gas and liquid in a conduit is necessary to develop models for heat and mass transfer, pressure drop, and wall shear. An experiment was conducted under reduced gravity conditions to collect data by means of a capacitance void fraction sensor and high speed visual imagery. Independent parameters were varied to map the flow regime regions. These independent parameters include gas and liquid volumetric flow rates and saturation pressures. Void fraction measurements were taken at a rate of 100 Hz with six sensors at two locations along the conduit. Further, statistical parameters were developed from the void fraction measurements. Statistical parameters such as variance, signal-to-noise ratio, half height value, and linear area difference were calculated and found to have characteristics allowing flow regime identification.

A procedure for correcting for the effect of fluid flow temperature variation on the response of capacitive void fraction meters

In gas–liquid flows through test loops, the fluid temperature increases, causing a change in the dielectric properties, mainly of the liquid component, which interferes with the response of capacitive void fraction meters. This phenomenon causes, for example, deviations of about 4% in the meter response for each 10 ∘C variation of temperature in the air–water flow. In this work, a simple procedure is proposed for correcting for the response of capacitive void fraction meters being affected due to the flow temperature being different from the calibration temperature. Static and dynamic tests were performed on a capacitive void fraction measuring system with double-helix electrodes. The results showed the effectiveness of the proposed compensation technique, which allowed a significant reduction of the measurement deviations.

Boiling in particle beds in a two dimensional configuration

The work presented here concentrates on the boiling heat transfer from a porous bed with internal heat sources. This configuration can occur, when in the progress of a hypothetical accident the core melt relocates to the lower plenum of a nuclear reactor pressure vessel and gets partially fragmented. The coolability and the boiling heat transfer are experimentally investigated for two- dimensional particle beds. Experiments are discussed with particles of an uniform diameter of 2 mm as well as mixtures of 4 mm and 1 mm particles. The bed was placed in a glass container with an inclined bottom to represent a section of the lower plenum of a reactor pressure vessel. The refrigerant R134a was used for tests with a pressure up to 1.8 MPa. The particle bed was equipped with thermocouples and capacitive local void fraction probes to map the temperatures and the distribution of liquid and steam. In the following the basic effects and the parameters influencing the coolability of such a configuration will be discussed.

Void fraction measurements in gas-liquid flows under 1 - g and μ - g conditions using capacitance sensors

Capacitance void fraction sensors were used to obtain void fraction measurements in vertical two-phase water-air flow in a small diameter tube (9.53 mm). Measurements were obtained at 1 - g and μ - g conditions. Comparisons were made between the void fraction values obtained at both gravity conditions by matching the flow rates obtained at μ - g conditions. It was found that the average void fraction values were comparable for the bubble, transitional flow (slug-annular flow at μ - g , and churn flow at 1 - g ), and annular flow regimes. The slug flow regime showed a slightly higher overall average of about 10% at μ — g conditions. The distribution coefficient, C 0, which takes into account the flow regime and the void fraction profile was found to be 1.25 for bubble and slug flows at μ - g , and 0.61 and 1.17 for 1 - g bubble and slug flows, respectively. This suggests that a ‘flatter’ void fraction profile exists for slug flow at 1 - g as compared to μ - g . The value of 0.61 for bubble flow agrees well with the typical values obtained by averaging the ‘saddle’ shape void fraction profile typically seen at 1 - g .

Void fraction measurements in gas - liquid flows using capacitance sensors

Void fraction measurements for vertical flow in a small diameter tube (9.53 mm) were taken using two non-intrusive capacitive void fraction sensors. The sensors were needed to measure the void fraction of water - air two-phase flow under normal gravity and microgravity conditions. Void fraction data were collected with: (1) a sensor having helical wound electrodes that was used to collect data under normal gravity and microgravity conditions, (2) a sensor having concave plate electrodes, used to collect data at normal gravity. This paper covers the calibration results for both sensors and some of the problems associated with the helical wound design. Nonlinearity in the helical sensor is addressed, with improvements shown in the concave plate sensor. Comparisons are made between the capacitive sensors, quick-closing valves and a gamma densitometer.