Void Fraction Measurements Research Articles

Experimental void fraction measurement approach of small channel two-phase flow

This investigation presents a novel experimental approach for assessing void fraction parameters in two-phase flows within microchannels. The study critiques the conventional impedance methods that utilize alternating current (AC) for void fraction measurements, highlighting the inherent drawbacks such as ground capacitance interference and non-uniform current distribution. To circumvent these issues, the research introduces the use of direct current (DC), which ensures a homogeneous distribution across the conductor's cross-section, as a more reliable alternative. Termed the "Direct Impedance Method," this technique employs DC to enhance the accuracy of void fraction measurements. The study explores various geometric configurations of full-ring and half-ring electrodes, both vertical and horizontal, within a microchannel of 500 μm diameter. An empirical formula is derived to calculate the void fraction from the electrical data obtained. High-speed imaging at 4000 frames per second supplements the method by providing visual confirmation of the flow patterns. The comparative analysis of the direct impedance method and image processing using the homogeneous theoretical model reveals a deviation of approximately 2 %–10 % for the slug and annular flow pattern. In contrast, the deviation is more for the bubble pattern. The results affirm that the Direct Impedance Method is a cost-effective and reasonably precise technique for small-channel applications. Its accuracy is inversely proportional to the channel diameter, rendering it unsuitable for channels larger than 2 mm. The method's low construction cost further enhances its practical appeal.

Void fraction measurement of slug flow using electromagnetic wave phase sensor based on optimized hybrid dielectric constant

The void fraction is one of the basic parameters to study the gas-liquid two-phase flow, which has great significance to the transportation of oil pipelines and the design of nuclear reactor cooling towers. However, due to the complex and variable nature of gas-liquid two-phase flow, accurately measurement of the void fraction has remained a challenging task in both scientific research and industrial applications. According to the principle of electromagnetic wave propagation, a coaxial line phase sensor was designed, a hybrid dielectric constant model based on the homogeneous flow was established and a void fraction based on hybrid dielectric constant model was proposed. The experiments were carried out on the high-precision gas-liquid two-phase flow simulation experimental setup at Hebei University, China (70 data points), and the void fraction model was inspected and verified. Five typical hybrid dielectric constant correlations were compared. Introducing the frequency weight, optimizing the hybrid dielectric constant model based on the Series – Parallel correlation, a new void fraction prediction correlation of slug flow was proposed and evaluated. The results indicated that the mean absolute percentage error (MAPE) of the new void fraction correlation is 1.02 % and the all of the relative errors are within ±5 % error band.

On the analysis of static thermal instabilities occurring in two-phase flow systems

In this study, we investigate a novel type of static thermal instability that occurs in two-phase flow systems. The instability is theoretically and experimentally confirmed to occur for flow boiling micro-channel scenarios and flow condensing scenarios. The theory presented is independent of the evaporator geometry as well as flow boiling/condensing situations. A stability criteria is derived using a Reynolds Transport approach applied to the evaporator of a two-phase pumped loop (TPPL) system. The theory is then validated experimentally using a TPPL containing a parallel micro-channel evaporator. The instability is confirmed with pressure, temperature, and void fraction measurements acquired at the exit of the evaporator. The findings reveal that static thermal instabilities can arise when simultaneous heat addition and reduction in system saturation temperature occurs (or vice versa). The implications of the thermal instability result in dramatic changes in evaporator heat flux, as well as a flow transition from stratified laminar flow to vigorous turbulent flow with high void fractions. By identifying the additional instability mechanisms, this work contributes to enhancing system reliability and predictability of TPPL systems.

Measurement and prediction of void fraction and pressure drop during air drying process of wet particle packed bed

This study aimed at development of a pressure drop prediction method at a drying process by flowing air through a wet particle packed bed saturated with distilled water. At first, the pressure drop measurement during the drying process of the wet particle packed bead of glass sphere was carried out, and a method for predicting the pressure difference of the bed was proposed by investigating the effect of liquid saturation on the bed void fraction. It was clarified that the effect could be predicted by a simple model by considering liquid bridges formed between particles. Next, the liquid saturation when the measured pressure difference suddenly decreased was investigated as the residual saturation. The value was like that of past research. Finally, considering the effect of liquid saturation on the bed void fraction and the influence of the residual saturation on the relative permeability of liquid phase, more than 90 % of all pressure drop data could be predicted with an error of less than ±15 %. Furthermore, in the range where the gas-phase velocity was large, it was important to predict the pressure difference considering the change of the bed void fraction and the residual saturation.

Measurement of void fraction of zeotropic refrigerant R454C using capacitance-based sensor in horizontal flow configuration

This study measures and analyzes the void fraction of R454C, a zeotropic refrigerant, using a capacitance-based sensor. Capacitance-based sensors offer an attractive method for real-time void fraction measurement. Given that zeotropic refrigerants undergo compositional changes in their gas and liquid phases during phase change, it is essential to account for variations in relative permittivity due to these compositional changes when using a capacitance-based sensor for void fraction measurement. In this study, Landau and Lifshitz’s mixing rule is employed to predict the relative permittivity based on compositional variations of a bi-component refrigerant, along with a calibration strategy for the capacitance-based sensor based on flow pattern transitions. The void fraction measurement results obtained from the capacitance-based sensor for R454C are validated by comparison with results obtained using the quick-closing valve-based (QCV) method under identical conditions. The measurement uncertainty of the developed sensor is 4.13 %, and compared to the measurement results from the QCV method, it is found to have a relative error of −0.955 % over the entire range of experimental conditions. The measurements are conducted in a smooth tube with an inner diameter of 7.1 mm, mass flow rates ranging from 100 to 400 kg m−2 s−1, pressures from 0.789 to 1.724 MPa, and inlet vapor quality from 0.025 to 0.900. The measurement results are then compared with existing prediction correlations, and those correlations offering acceptable predictions of the void fraction of R454C are presented.

Integrating machine learning and image processing for void fraction estimation in two-phase flow through corrugated channels

There is a substantial amount of information embedded in images of two-phase flow captured through high-speed video (HSV) or high-resolution photography. However, accurate image segmentation is necessary to unlock a meaningful analysis of the data. In this study, we discuss how to estimate the flow void fraction in chevron-type corrugated channels typical of compact plate heat exchangers (CPHE) from back-lit front-view HSV images, using machine learning (ML) algorithms and data processing techniques. A U-Net neural network was employed for image segmentation, demonstrating robust performance with evaluation metrics consistently exceeding 0.9. The binary masks (indicating gas or liquid phases) derived from segmentation were processed in MATLAB® to estimate void fraction through a 3D reconstruction algorithm of the gas cluster’s volume. In contrast to conventional void fraction estimates based on the area ratio of binary masks, this algorithm models the curvature of the liquid-vapor interface through the corrugated channel. When compared to other methods, our algorithm predicts very similar void fraction contour maps. However, the average discrepancy between our algorithm and the area-ratio approach can be as high as 80%, underscoring the importance of the processing method in analyzing the data and developing correlations. Finally, a drift flux model was introduced to predict the void fraction distribution using a two-part equation accommodating the dependency of the distribution coefficient C0 on the liquid flow rate for a corrugation Froude number Fr∼ larger than 1. The proposed model can predict the void fraction dataset with a mean average percentage error of 8.17%. In summary, U-Net’s pixel-level accuracy facilitates deep and precise post-processing of HSV images, enabling meaningful void fraction measurements. Thanks to its generality and minimal training effort requirements, the discussed methodology can be applied to estimate void fractions in various two-phase flow experiments and operating conditions.

An experimental study of dynamic flashing in a square tube using tap water

Flashing is a pressure driven phase change phenomenon. It is widely studied due to its richness in physics and applications such as in desalination, in nuclear industry to name a few. Dynamic flashing is a situation wherein the pressure drop for flashing is initiated through the flow of liquid. A recently developed novel desalination system [1] utilizes combined dynamic flashing and vapor separation through tangential injection for producing potable water. An understanding of dynamic flashing in a tube with reference to the novel desalination system could help with its optimization. In this work, dynamic flashing of tap water occurring in a clear quartz square tube was studied. The pressure and temperature measurements along the tube were made and analyzed for different inlet flowrates and initial liquid temperatures. The pressure and temperature values showed increasing gradients along the tube indicating increased vapor production or flashing for increasing flowrates and initial liquid temperatures. The vapor production from flashing and the resulting flow regimes along the tube were tracked and identified through high-speed imaging. Visual observations showed complex flow regimes with bubbles nucleating and growing throughout the tube due to flashing. Most of the bubble formation was observed in the bulk with little nucleation on the glass tube wall. Void fraction measurements along the tube based on capacitance impedance technique were performed to supplement the visual observations which showed increasing void fraction along the tube matching the observed flow regimes from vapor production.

Influence of a restriction on flow patterns, void fraction, and pressure drop in gas–liquid pipe flow

Subsurface safety valves play an important role in the hydrocarbon production process. The Brazilian industry is suffering significant losses due to the reduction of the useful life of this device, not to mention the risks associated with the operation and the environment. One possible reason for the failure of the subsurface safety valve’s reliability prediction may be the occurrence of two-phase flow in the well. For this reason, a set of twenty horizontal two-phase flow experiments was carefully designed to evaluate the influence of a simplified internal reduction in a steel pipe. Superficial velocities were considered in the range of 0.1 m/s and 2.0 m/s for water and, 0.33 m/s and 7.47 m/s for compressed air. The experiments were carried out in 2″-i.d. and 2-m-long steel pipes, being a tube with restriction and another without restriction. Both tubes have an upstream development length of 126 pipe diameters. Gamma-ray densitometry and a differential pressure transducer were used to measure void fraction and pressure drop, and a visualization window was used to observe the flow patterns. Among the main findings are the effects of void fraction and mixture velocity on pressure gradient, with different impacts on the restricted pipe (RP) compared to the unrestricted pipe (UP). The presence of the restriction generated significant changes in the upstream flow: the lengths of the liquid slugs were increased, appeased by the increase in local pressure necessary to overcome the resistance produced by the restriction. Downstream, the change was reflected in the rise of void fraction and decrease of slip ratio between the phases.

Measurement and analysis of void fraction in horizontal plug flow based on electromagnetic wave sensor

Void fraction measurement is a crucial challenge in two-phase flow, which is related to the measurement of phase flow and the calculation of pressure drop. In this study, a coaxial line phase sensor is designed for void fraction acquisition and the void fraction of the plug measured has a well time-domain and Probability Density Functions (PDF) distribution characteristics. Four typical correlations were selected to compare with the measured values of the sensors, the mean absolute errors (MAPE) are 19.88 %, 18.94 %, 18.25 %, and 17.19 %, respectively. Considering the nonlinear and strong coupling between the flow characteristic parameters and the void fraction, the flow parameters were analyzed and selected by Pearson correlation coefficient. The Kernel ridge regression methods were employed to select effective variables for model training, and the Extreme gradient boosting (XGboost) machine learning model was proposed. The prediction accuracy of the model is 1.65 % (current data) and 4.18 % (literature data), respectively.

CO2 capture using gas-lift pumps operating under two-phase flow conditions

CO2 capture through dissolution in water offers environmental benefits and industry applications. However, current studies mostly focus on CO2 extraction into solvents, overlooking its direct solubility in water. Alternatively, gas-lift pumps may hold significant potential for capturing and storing CO2 in water; but this ability remains unexplored. Therefore, this study experimentally delves into the CO2 capture capacity and hydraulic performance of a dual injection gas-lift pump with a 25.4 mm riser diameter. Operating at a constant submergence ratio of 70 %, the pump is fed with simulated flue gas with flow rates within 5–30 LPM at volumetric CO2 concentrations of 10 %, 15 %, and 25 %, and temperatures of 22 °C (isothermal operation) and 110 °C (non-isothermal operation). Two-phase flow hydrodynamics is also evaluated using high-speed imaging in conjunction with time-series void fraction measurements. Within the riser pipe, three distinct two-phase flow patterns — slug, intermittent, and churn flows — are identified. The results reveal that under both isothermal and non-isothermal operations and across all volumetric CO2 concentration levels, churn flow demonstrates superior mass transfer coefficient and lifted liquid flow rate, while slug flow achieves minimum energy consumption per ton of captured CO2, highest CO2 capture degree, and maximum lifting efficiency. Also, the highest degrees of sensitivity to inlet gas flow rate for volumetric mass transfer coefficient, delivered liquid flow rate, and void fraction were observed in slug flow regime. Both gas temperature and volumetric CO2 concentration positively impacted the mass transfer performance. However, the pump showed remarkably higher lifting efficiencies under isothermal operation conditions. Moreover, compared to four established CO2 capture methods (absorption, adsorption, cryogenic distillation, and membrane diffusion), the gas-lift pump exhibits moderately lower energy consumption, at 38-266 kWh/tonCO2, but with lower CO2 capture degree of 2.3 % to 6.7 %.

Experimental investigation on local flow structures of upward cap-bubbly flows in a vertical large-size square channel

Gas–liquid two-phase flows are typical in engineering systems involving heat and mass transfers. The cross-sectional geometries and sizes of these flow channels vary, exerting a notable impact on the thermofluid behavior. To develop thermofluid models, it is imperative to obtain local measurements of two-phase flows and gain insights into their characteristics from these measurements. Numerous experimental studies have investigated the local flow characteristics in circular pipes and rectangular channels; however, few studies on square channels have been conducted, particularly for flow regimes beyond bubbly flows, such as cap-bubbly flows. Given the importance of two-phase flows in large square channels for advanced nuclear reactors, such as the economic simplified boiling water reactor (ESBWR), we experimented with upward cap-bubbly flows in a large square channel. Detailed cross-sectional distributions of the void fractions, axial gas velocities, and interfacial area concentrations for two bubble-size groups were obtained at three axial locations using local measurements of a four-sensor optical probe. Based on the database, the cap-bubbly flow characteristics were understood, including flow development in a large square channel. In addition, the existing drift-flux correlations for large circular pipes predicted the measured void fraction with an accuracy of approximately ± 10 %, whereas the existing interfacial area concentration correlations reasonably correlated with the measured interfacial area concentration with an accuracy of approximately ± 30 %. Furthermore, the database was used to calculate the covariances of the void fractions. The correlations for large circular pipes significantly underestimated the void fraction covariance of the larger bubble group, probably because of the peculiar void fraction distribution of the group in a large square channel. The other covariances were well predicted.

An optimised and novel capacitance-based sensor design for measuring void fraction in gas–oil two-phase flow systems

ABSTRACT This study explores a new electrode configuration for measuring the void fraction of two-phase flows using capacitance-based sensors. The proposed method is considered ‘skewed’ because of its unique geometric shape, and the performance of the proposed sensor was evaluated and improved via multiple simulations using the COMSOL Multiphysics software. The simulations encompass three different flow patterns, stratified, annular and homogeneous, whose performance themselves were verified in a previous study. The influences of geometric properties and parameters on the sensitivity of the proposed sensor were evaluated to determine an optimal configuration. Furthermore, the sensitivity distribution on different void fractions of the sensor was analysed for various void fractions in different flow patterns. Additionally, the proposed configuration was also compared alongside double-ring and concave sensors to determine the overall sensitivity. At 2.11 pF, the overall sensitivity of the proposed sensor was significantly higher than that of the other sensors. It is worth mentioning that the measurement precision of multiphase flow meters is of high importance, particularly in petroleum industry because of the oil price and also the high amount of transported products.

Measurement of void fraction in gas-water bubbly flow using a derived multi-eigenvalue sequence from normalized EIT impedance matrix

Void fraction is one of the dominant parameters of gas-water two-phase flow. Its accurate measurement plays an important role in achieving parameter control and reliable operation in industrial processes. This article proposes a more practical method for the measurement of void fraction in gas-water bubbly flow using a derived multi-eigenvalue sequence from a normalized electrical impedance tomography impedance matrix. The relations between eigenvalues and void fraction, bubble radius, number of bubbles are investigated by numerical simulations, which illustrates the superiority of using multi-eigenvalue rather than the largest eigenvalue for void fraction prediction. The nonlinear mapping between the multi-eigenvalue sequence and void fraction is established by applying the XGBoost model with a sliding window of time series. This proposed method is verified by static and dynamic experiments using a self-developed setup in our laboratory, generating stable gas-water bubbly flow with void fraction of less than 0.12. It is shown that the proposed method can predict void fraction with a relative deviation of 10%. Compared with the conventional method based on the largest eigenvalue, the proposed method efficiently improves the measurement accuracy of void fraction in gas-water bubbly flow and applicability in actual measurement of two-phase flow, which can be further extended to other flow regimes.

Void Fraction Measurement of Gas-Liquid Two-Phase Flow Based on Capacitance Sensor

Void Fraction Measurement of Gas-Liquid Two-Phase Flow Based on Capacitance Sensor

Vertically downward gas-liquid flow: Void fraction and pressure drop

Using an air-water mixture and 34 mm ID pipe, a series of pressure drop and void fraction measurements were collected. The observed flow regimes were falling film, annular, bubbly, cap bubble, slug, and churn flows. The temporal fluctuations of void fraction and pressure drop measurements were firstly studied using signals visualization and PDF. It was revealed that both signals can be used to identify the flow regimes. A new flow pattern map is proposed based on the Froude number, calculated using the mixture velocity of the two phases, and the ratio of gas-to-liquid superficial velocities. The behaviors of the total and frictional pressure drops were studied and the influence of the superficial velocities as well as the flow regimes were identified. The experimental results were compared to four existing vertically downward frictional pressure drop models, none of which provided accurate predictions.

Numerical Analysis of the Boiling Heat Transfer Coefficient in the Flow in Mini-Channels

Abstract This paper deals with boiling heat transfer in the flow of water through an asymmetrically heated horizontal rectangular mini-channel. The mini-channel was made by gluing three transparent glass plates and a copper block. Through the glass window, the variable along the length of the mini-channel two-phase flow structures were recorded to determine local values of the void fraction. Four resistance heaters were attached to the copper block, powered by direct current, generating the heat initiating the flow boiling inside the channel. During the experiment, the following were measured: water volumetric flow rate, inlet pressure with pressure drop, inlet and outlet water temperature, copper block temperatures at three points inside its body, voltage and current supplied to the heaters. Stationary and laminar fluid flow with low Reynolds numbers were assumed in the mathematical model of heat transfer in selected elements of the measuring module. The temperature distributions in the copper block and flowing water were described by the appropriate energy equations: the Laplace equation for the copper block and the Fourier–Kirchhoff equation with parabolic fluid velocity for the flowing water. These equations were supplemented with a set of boundary conditions based on measurement data; moreover, data from experimental studies were the basis for numerical calculations and their verification. Two-dimensional temperature distributions of the copper block and water were calculated with the Trefftz method (TM). The main objective of this study was to determine the heat transfer coefficient on the contact surface of the copper block and water, which was calculated from the Robin boundary condition. The results of the calculations were compared with the results of numerical simulations performed using the Simcenter STAR-CCM+ software, obtaining consistent values. Computational fluid dynamics (CFD) simulations were verified based on experimental data including void fraction and temperature measurements of the copper block and flowing water.

Experimental investigation of the void fractions of refrigerants R32 and R1234yf in a 1 mm diameter horizontal channel using a capacitance-based method

The void fraction of two-phase flow in the 1 mm of channel is investigated in this study. The small channels, including micro to mini-channel, are widely used for developing miniaturized air conditioning systems. In terms of carbon emission reduction, optimizing the refrigerant charging amount based on sufficient information and understanding of the characteristics of the two-phase flow is a noteworthy challenge. The void fraction is a parameter of the two-phase flow that is essential for determining the heat transfer coefficient, modeling the pressure drop, and predicting the refrigerant charging amount. Therefore, the precise measurement and prediction of void fraction in small channels for various refrigerants are required. However, thus far, the void fraction characteristics of small channels have not been actively investigated because of the limited volume inside a single small channel and the relatively high error of the quick-closing valve (QCV) method for small channels. This study proposes a capacitance-based sensor as an alternative method for void fraction measurement of small channels. The newly designed void fraction sensor was fabricated with 7.8 % uncertainty under compensation for manufacturing limitations. The void fractions of refrigerants R32 and R1234yf flowing through smooth small horizontal channels under adiabatic conditions (inner diameter: 1 mm, mass flux: 300–600 kg m−2s−1, saturation temperature: 20–30 °C, vapor quality: 0.025–0.900) were measured. The measurement results were compared with ten existing prediction correlations of five classifications, and the correlations that optimally predicted the void fractions of R32 and R1234yf in the small horizontal channel were presented.

Simulation of droplet entrainment in annular flow with a morphology adaptive multifield two-fluid model

Modeling of annular flow with the computational fluid dynamics (CFD) is challenging as one has to consider several, rather different, phenomena simultaneously: the continuous liquid film, continuous gas core, and dispersed droplets. A morphology-adaptive multifield two-fluid model (MultiMorph) developed by Meller et al. [“Basic verification of a numerical framework applied to a morphology adaptive multifield two-fluid model considering bubble motions,” Int. J. Numer. Methods Fluids 93(3), 748–773 (2021)], with three numerical phase fields, is well suited to simulate such multiple flow structures. Droplet formation plays an important role in annular flow, and a new droplet entrainment model is proposed, expressed as a phase morphology transfer term from the continuous liquid film to dispersed droplets phase field. The new model is developed based on the shear-off entrainment mechanism on the interfacial wave, implying that the droplet formation is dominated by the balance between the shear forces and the surface tension forces at the gas–liquid interface. In contrast to the existing entrainment models, the new model considers the flow parameters locally at the interface, and it is suitable for phase-resolving CFD frameworks without input of global parameters such as a pipe diameter. The proposed model is implemented in the MultiMorph framework based on the OpenFOAM Foundation release open-source CFD library. The performance of the new model is evaluated by conducting own annular flow experiments with void fraction measurements using electrical resistance tomography, as well as with comparison to published models from the literature. Qualitatively, the model can adequately resolve the formation of interfacial waves on the liquid film downstream from the inlet. The simulated droplets are primarily generated at the tip of such waves, which is consistent with the physical understanding and experimental observations of droplet entrainment. Quantitatively, the modeled entrained droplet fraction matches well the experimental observation in the developing entrainment region. The liquid film fraction obtained with the new model is analyzed and compared with the experimental data. Good agreement between measured and simulated statistics of the liquid film fraction, i.e., the mean, standard deviation, probability density function, and power spectral density, is demonstrated.

COMPARISON OF FLOW DYNAMICS AND AIR ENTRAINMENT UNDER LABORATORY PLUNGING AND SPILLING BREAKING WAVES

Wave breaking plays a vital role in enhancing transfer of mass, momentum, and energy across the air-sea interface. Even though wave breaking has been intensively studied, a vast part of the air entrainment process is still poorly understood. One major reason is that multiphase approaches considering air-water mixture density variation have rarely been used. To quantify certain flow properties that involve air entrainment and fluid density variation, such as the mean and turbulent kinetic energy as well as potential energy under breaking waves, void fraction measurements are essential. In the present study, through combined velocity and void fraction measurements, flow kinematics, turbulence, void fraction, and the effects of void fraction to energy dissipation were investigated. The data uniquely characterize and compare kinematic and dynamic properties of the multiphase flow, including flow structure in the highly aerated region, under plunging and spilling breaking waves.

Measurements of gas-liquid two-phase flow dynamics using high-speed neutron imaging

Gas-liquid two-phase flow appears in many heat-exchanging devices. The two-phase flow dynamics should be clarified to understand the phenomena in such devices. Although many measurement techniques have been applied to two-phase flow experiments, measuring the gas-liquid interfacial structure is difficult, which changes temporally and spatially. In this study, high-speed neutron imaging is used to measure two-phase flow dynamics, and the accuracy of the void fraction measurement is investigated. In high-speed neutron imaging, image blurring and distortion occur due to light and object motion intensifying. As a result, the quantitative accuracy might decrease. So, the rotating stainless-steel calibration disk, which simulates the bubble behavior in water, is observed by high-speed neutron imaging. Several noise reduction filters are tested to remove the blur and noise in the acquired images. Finally, the air-water two-phase flow is visualized by high-speed neutron imaging, and noise filtering is applied.