Two-phase Flow Measurement Research Articles

EXPERIMENTAL INVESTIGATION AND CFD SIMULATION OF THE ORIFICE FLOW METER TO MEASURE TWO-PHASE FLOW

In this study, an investigation is conducted to examine various methods for measuring the two-phase flow of water and air. The two-phase flow loop and its equipment, including the orifice flow meter, were designed and manufactured in accordance with relevant standards. By employing the orifice flow meter in the two-phase flow loop and determining the total mass flow rate of the two-phase flow passing through it, the pressure drop of the orifice flow meter was determined for different values of the flow rate and volume fractions of the water and air phases in the two-phase flow. The Reynolds number of the two-phase flow ranged from 700 to 11000, while the air volume fraction ranged from 10% to 45%. We observed that, for the orifice flow meter, the slope of the discharge coefficient variation in relation to the two-phase flow Reynolds number was higher at low Reynolds numbers, where a laminar flow pattern was established. As the two-phase flow Reynolds number increased, the flow pattern transitioned from laminar to plug flow, resulting in a decrease in the slope. The orifice flow meter under two-phase flow conditions was simulated using computational fluid dynamics (CFD) with different turbulence models. The results indicated that the k-epsilon RNG turbulence model yielded more accurate results compared to other turbulence models. This study provides a foundation for the measurement of two-phase flows in the oil and gas industries.

MRCNN: Multi-input residual convolution neural network for three-dimensional reconstruction of bubble flows from light field images

Accurate measurement of bubbles in air-water two-phase flows holds immense significance in the realm of thermal hydraulics assessments within nuclear reactors. Nevertheless, conventional bubble measurement techniques grapple with challenges encompassing system intricacy, limited real-time capabilities, and inaccuracies stemming from their inherent two-dimensional (2-D) nature. In response, we pioneered an innovative three-dimensional (3-D) analysis approach that leverages light field (LF) imaging diagnosis and deep learning algorithms. Unlike traditional 2-D reconstruction methods, our approach enables direct computation of bubble depth from LF images using digital refocusing technology. Following calibration, a seamless transformation is established between the camera coordinate system and the real-world coordinate system using a sharpness evaluation algorithm. This calibration process ensures precise alignment of refocused images with real-world positions. Subsequently, fully automated and highly accurate computations of bubble depth are realized from input images via the incorporation of a multi-input residual convolution neural network (MRCNN). The limitations of traditional two-dimensional imaging techniques are effectively addressed by this methodology, resulting in a reduction in measurement errors. The study confirms the feasibility of employing LF imaging diagnosis and deep learning algorithms for bubble measurements in an air-water two-phase flow, offering a significant improvement over traditional methods.

Percolation without trapping: How Ostwald ripening during two-phase displacement in porous media alters capillary pressure and relative permeability.

Conventional measurements of two-phase flow in porous media often use completely immiscible fluids, or are performed over timescales of days to weeks. If applied to the study of gas storage and recovery, these measurements do not properly account for Ostwald ripening, significantly overestimating the amount of trapping and hysteresis. When there is transport of dissolved species in the aqueous phase, local capillary equilibrium is achieved: this may take weeks to months on the centimeter-sized samples on which measurements are performed. However, in most subsurface applications where the two phases reside for many years, equilibrium can be achieved. We demonstrate that in this case, two-phase displacement in porous media needs to be modeled as percolation without trapping. A pore network model is used to quantify how to convert measurements of trapped saturation, capillary pressure and relative permeability made ignoring Ostwald ripening to account for this effect. We show that conventional measurements overestimate the amount of capillary trapping by 20-25%.

A modified capacitance tomography image reconstruction approach based on iterative shrinkage-thresholding algorithm combined with deep networks

Abstract Due to the ‘soft-field’ effect and the challenges posed by ill-posed and ill-conditioned inverse problems, it is difficult to obtain high quality images from an electrical capacitance tomography (ECT) system. To achieve both high-quality images and fast imaging speed with limited measurement data, an image reconstruction algorithm, which was initially proposed for compressive sensing, is adapted for ECT image reconstruction to optimize the ill-posed nature of its inverse problem. The proposed algorithm leverages deep learning networks inspired by the iterative shrinkage-thresholding algorithm (ISTA), thereby creating a model that is both mathematically interpretable and endowed with trainable parameters. Building upon this foundation, the conventional Landweber iteration is integrated with the ISTA-Net to refine the optimization process for ECT image reconstruction. In order to propose an effective model adapting to the actual multiphase flow characteristics and complex flow pattern changes, the training and test process is driven by a comprehensive dataset generated from dynamic simulations, rather than artificial samples of multiphase distributions. This numerical methodology simulates the dynamic measurement process of a virtual ECT sensor by coupling the gas–liquid two-phase flow field and the ECT electrostatic field. The results of the testing phase indicate that the proposed algorithm outperforms traditional ECT image reconstruction methods. Compared with the linear back projection algorithm, the average image error and gas fraction error have been reduced by 20.44% and 16.74%, respectively, while maintaining a computational speed comparable to that of the Landweber iteration. The accuracy of the new algorithm in reconstructing the two-phase interface and estimating the gas fraction has been validated by static experimental tests, showing its potential for practical application in online gas–liquid two-phase flow measurement scenarios.

Unveiling intricate foam behaviors and dynamic instabilities in a two-phase natural circulation loop with seawater

The use of seawater as an alternative emergency coolant in a nuclear power plant presents great potential to enhance the nuclear safety. The present study investigates the dynamic instabilities during the startup experiments of a natural circulation loop with seawater through synchronization of two-phase flow visualization and measurements of transient fluid flow parameters. The results reveal that in seawater the pressure drop oscillations (PDO) with nature of low-frequency pulse-type loop flow occurs at the modified heat flux of 531.56–654.80 kW/m2. On the other hand, the density wave oscillations (DWO) characterized by high-frequency oscillatory flow prevails at higher modified heat flux of 654.80–1844.46 kW/m2. For the loop with seawater, the flow patterns in the riser may evolve from dispersed bubbly flow, foam flow, foam and short slug flow due to the flashing effects, and foam and long slug flow periodically. The image analysis reveals that the foam fraction may decline from 75% to 52.2%, while the flow pattern transforms from the stage II (foam and cape bubbly flow) to III (foam and long slug flow). On the other hand, the flow pattern may evolve from bubbly flow, cap bubbly flow, turbulent slug flow, and long slug flow in de-ionized water. For DWO, the oscillatory frequency is found to be inlet temperature dependent. Interestingly, both fluids demonstrate identical frequencies of 0.06 Hz, 0.14 Hz, and 0.09 Hz, respectively, corresponding to the inlet temperature range of 40–52 °C, 52–65 °C, and 65–75 °C, despite significantly different evolution of two-phase flow patterns. Indeed, the density wave travels at the same speed through the loop operating at the same power for both seawater and de-ionized water, as the buoyancy force is the primary driving force for the present study. These findings contribute significantly to the better understanding of related industrial processes using seawater as the working fluid.

Quantification of two-phase flow in a microchannel heat exchanger header based on capacitance measurement

The two-phase distribution has always been one of the research focuses of microchannel heat exchangers, because the maldistribution could seriously affect the heat transfer performance. This paper developed a capacitive method to quantify the two-phase distribution of vapor-liquid flow in the aluminum header of a microchannel heat exchanger. A flexible capacitance sensor was used to quantify the two-phase distribution with R134a. The inlet mass fluxes vary from 17.47 kg m−2 s−1 to 52.42 kg m−2 s−1 and inlet vapor qualities range from 0.2 to 0.6. The normalized time-averaged capacitance signal was processed by a Gaussian function to obtain the mathematical expectation and the standard deviation. The local vapor quality in the header was solved for using a correlation derived from the pre-experiments. The distribution of local vapor quality showed that gases were concentrated upstream of the header, while liquids were concentrated in the middle and lower reaches. The local vapor quality reached a minimum and remained constant at 0.1 in the middle and lower reaches, unaffected by changes in inlet conditions. As the mass flux increased, both the local vapor quality maximum point and the minimum point in the header were shifted back toward the downstream. Additionally, the increase of mass flux caused the fluctuation of the standard deviation increased, which meant the stability of the flow decreased. The two-phase flow measurement technique based on flexible capacitance sensors proposed in this study realized the extension of the capacitive method from the experimental stage to the industrial application stage.

The development of the ultrasonic flowmeter sensors for mass flow rate measurement: A comprehensive review

A two-phase flow measuring device whose measurement system does not disturb the flow pattern, real-time measurement, and non-destructive measurement or non-intrusive model is a typical tool for an ideal situation. One measuring instrument that meets these criteria is an ultrasonic flow meter. Ultrasonic sensors can measure the velocity of fluid flow in pipelines. It has the advantage of high accuracy and reproducibility and does not make direct physical contact with the fluid in the pipe. Low fabrication costs and fast response make ultrasonic flowmeters widely used for two-phase flow measurements in both horizontal and vertical orientations. The void fraction or liquid holdup and velocity are the two most essential parameters for flow monitoring. The Time of Flight (ToF) method is mainly used for measurements in several ultrasonic flowmeter methods. In the present manuscript, the introductory section of this review explains the advantages of using the Time of Flight (ToF) method and its basic principles. This review also discusses research on measuring velocity and flow rate, differences in intrusive and non-intrusive measurement methods, parameters that affect ultrasonic measurements, and finally, measuring film thickness using non-intrusive methods.

Comparative analysis of NIR point source and surface array probes in two-phase flow measurement model

As one of the most significant parameters, phase fraction is of great importance for ensuring the accuracy of two-phase flow measurement. Although near-infrared (NIR) technology has been widely used, its accuracy remains limited. Two methods have been proposed to reduce the energy loss of near-infrared light transmission signal in two-phase flow: the point light source method, which shortens optical path and the array light source method for increasing light source area. Experiments were conducted on single phase flow and gas–liquid two-phase flow, and the results indicated that the signal transmission effect of the point source near-infrared device was better. Using the experimental results from the point source near-infrared device, phase fraction models for bubble flow, annular flow, and slug flow were established. Validation results demonstrate that the relative measurement error of the three phase fraction models is within ± 4.96 %.

Investigation of unsteady friction effects in transient two-phase pipe flow

Water hammer and transient cavitating flow may induce large pressure fluctuations in pipelines. Transient events in pipeline may cause a drop in pressure large enough to break liquid homogeneity and continuity (liquid column separation, distributed vaporous cavitation). Trapped air pockets in liquid may be a major problem in piping systems. The paper deals with mathematical tools for modelling unsteady skin friction, transient vaporous cavitation (liquid column separation) and transient gaseous cavitation (trapped air pockets). The method of characteristics transformation of the unsteady liquid pipe flow equations gives the water hammer solution procedure. A convolution-based unsteady skin friction model is explicitly incorporated into the staggered grid of the method of characteristics. Incorporating discrete cavities into the water hammer model leads to the discrete cavity model. An advanced discrete gas cavity model (DGCM) with consideration of unsteady pipe flow friction effects is presented in the paper. The DGCM is capable to simulate vaporous and gaseous cavitation at the same time. Pipeline apparatus for measurement of transient liquid flow (water hammer) and transient two-phase flow (vaporous and gaseous cavitation) is briefly described. The paper concludes with two distinct case studies showing profound effects of unsteady skin friction on pressure histories.

A numerical study on machine-learning-based ultrasound tomography of bubbly two-phase flows

Ultrasound tomography (UT) of bubbly two-phase flows using machine learning (ML) was investigated by performing two-dimensional ultrasound numerical simulations using a finite element method simulator. Studies on UT for two-phase flow measurements have been conducted only for some bubbles. However, in an actual bubbly flow, numerous bubbles are complexly distributed in the cross-section of the flow channel. This limitation of previous studies originates from the transmission characteristics of ultrasound waves through a medium. The transmission characteristics of ultrasound waves differ from those of other probe signals, such as radiation, electrical, and optical signals. This study evaluated the feasibility of combining UT with ML for predicting dense bubble distributions with up to 20 bubbles (cross-sectional average void fraction of approximately 0.29). We investigated the effects of the temporal length of the received waveform and the number of sensors to optimize the system on the prediction performance of the bubble distribution. The simultaneous driving of the installed sensors was simulated to reduce the measurement time for the entire cross-section and verify the method’s applicability. Thus, it was confirmed that UT using ML has sufficient prediction performance, even for a complex bubble distribution with many bubbles, and that the cross-sectional average void fraction can be predicted with high accuracy.

Gas–Liquid Two-Phase Flow Measurement Based on Optical Flow Method with Machine Learning Optimization Model

Gas–Liquid two-phase flows are a common flow in industrial production processes. Since these flows inherently consist of discrete phases, it is challenging to accurately measure the flow parameters. In this context, a novel approach is proposed that combines the pyramidal Lucas-Kanade (L–K) optical flow method with the Split Comparison (SC) model measurement method. In the proposed approach, videos of gas–liquid two-phase flows are captured using a camera, and optical flow data are acquired from the flow videos using the pyramid L–K optical flow detection method. To address the issue of data clutter in optical flow extraction, a dynamic median value screening method is introduced to optimize the corner point for optical flow calculations. Machine learning algorithms are employed for the prediction model, yielding high flow prediction accuracy in experimental tests. Results demonstrate that the gradient boosted regression (GBR) model is the most effective among the five preset models, and the optimized SC model significantly improves measurement accuracy compared to the GBR model, achieving an R2 value of 0.97, RMSE of 0.74 m3/h, MAE of 0.52 m3/h, and MAPE of 8.0%. This method offers a new approach for monitoring flows in industrial production processes such as oil and gas.

An experimental approach to heat loss measurement of horizontal two-phase flow boiling in low-pressure low-flow (LPLF) conditions

A crucial parameter remarkably influencing the reliability and accuracy of vapor quality measurements in flow boiling experiments is the measurement of heat loss. The latent heat loss estimation in two-phase flow boiling sounds more demanding than that of sensible heat loss in single-phase flow experiments. To accurately investigate the impact of vapor quality on the heat transfer coefficient of flow boiling, accurate estimates of heat loss and subsequent calibration of heat supplies are of a great significance. It is widely common that the single-phase flow tests are performed to estimate a fixed heat loss percentage and calibrate heat supplies for further measurements of vapor quality and heat transfer coefficient of flow boiling experiments. In the present work, an empirical methodology is first proposed to measure heat losses and calibrate latent heat supplies directly from flow boiling process. The proposed methodology is then compared and verified with the commonly applied methodology which uses single-phase flow experiments. The proposed methodology exhibited higher accuracy than the single-phase-based methodology to estimate heat losses and measure vapor quality within two-phase flow boiling under low-pressure low-flow (LPLF) operating conditions.

An experimental investigation on the fluid–structure coupling in horizontal pipes conveying two-phase intermittent flow

Two-phase flow is typically found in several industrial applications, such as in the production and transportation of oil and gas in the petrochemical industry, in the catalytic cracking and microreactors in the chemical industry, and in nuclear reactor cooling pumps. Measurement of two-phase flow features is usually necessary and has been done in several ways, including pressure probes, resistive sensors, gamma-ray, wire-mesh sensor and many others. However, these are either intrusive or invasive techniques, which might be of challenging application in industrial environments, or rely on a hazardous radioactive source. Vibration-based measurement of two-phase flow in pipes stands out as a non-invasive/non-intrusive approach and, consequently, multiphase-flow induced vibration in pipes has receiving increasing attention in recent years. In this work, the dynamic behaviour of a horizontal tube conveying an intermittent two-phase gas-liquid flow is investigated based on indirect approaches. The phenomenon of fluid–structure coupling is investigated using acceleration and pressure measurement. Moreover, the bubble size distribution is estimated from high-speed camera images and a deep learning model for image segmentation, along with its spectral content and time modulation. Focus is given at frequency bands around the cut-on frequencies of the circumferential wave modes of the pipe. An approach based on the estimation of frequency response function of the pressure and vibration at the liquid slug and elongated bubble is proposed, such that the coherence function can be used as quantitative measure of the coupling. Two experimental conditions with intermittent flow are investigated as representative cases. It is shown that there is a great vibration amplification at the cut-on frequencies of circumferential wave modes in pipes due to the corresponding structural wave and pressure coupling. Consequently, the frequency of passage of bubble can be estimated from the demodulation of vibration response filtered at the cut-on modes. The experimental results pave the way for innovative vibration-based measurement approaches.

Flow rate measurements of slug flow by pressure differences of a venturi tube with a swirler

When the elongated bubbles and liquid slugs of slug flow alternately flow through a throttling element, the strong random fluctuations of pressure difference leads to low accuracy of online measurement of gas-liquid flow rates. In this paper, slug flow is converted into an annular flow before entering a venturi tube using a swirler, and the pressure fluctuation amplitude of the gas-liquid two-phase flow is greatly reduced, and the linear correlation between the pressure difference and the gas-liquid flow rates is more significant. The effects of gas-liquid flow rates on the axial pressure difference ΔPs across the swirler, the radial pressure difference ΔPr on a cross-section downstream of the swirler and the axial pressure difference ΔPo of the venturi tube were studied under the condition of 40%–82% gas volume fraction. The square root of the pressure difference increases linearly with the liquid/gas flow rate, and the empirical correlations between the square root of the pressure differences and the gas-liquid flow rates are established. By combining the empirical correlations in pairs, three flow rates measurement models of slug flow based on double pressure differences are established. When ΔPo and ΔPs are used as the measurement parameters of flow rates, the relative errors of liquid-phase flow rate and gas-phase flow rate are below ±2% and ±15%, respectively. When ΔPo and ΔPr are used as the measurement parameters of flow rates, the relative errors of liquid-phase flow rate and gas-phase flow rate are below ±3% and ±15%, respectively. It provides high-precision, low-cost and non-radioactive two-phase flow measurement technology for oil-gas gathering and transportation.

The modulation of coherent structures by the near-wall motions of particles

Particle–wall interaction generates strong particle near-wall motion, including collision bounce and impact splashing. To distinguish the effect of particles and particle near-wall motions on the turbulent coherent structure, this study carried out three different cases of sand-laden two-phase flow measurements: a uniform sand release at the top, local-laying sand bed and global-laying sand bed (Liu et al., J. Fluid Mech., vol. 943, 2022, A8). Based on large field of view particle image velocimetry/particle tracking velocimetry measurements, we obtained the velocity field of a two-dimensional gas–solid two-phase dilute faction flow $(\varPhi _{v} \sim O(10^{-4}))$ with a friction Reynolds number $R e_{\tau }$ of 3950. Results indicate that particles weaken the high- and low-velocity iso-momentum zones and hairpin vortices, resulting in the increased length scale of the coherent structure. However, the collision bounce and impact splashing break up the inner iso-momentum zone and hairpin vortices while enhancing them in the outer region, thus reducing the structure scale. In addition, the upward-moving particles increase the large-scale structure inclination angle, while the downward-moving particles decrease it. The linear coherence spectrum analysis suggests that the particles themselves do not change the structural self-similarity, but their saltation motions disrupt the similarity of the near-wall structure, making the inclination angle decrease with the scale, and the generated ascending particles reduce the aspect ratio of the streamwise to wall-normal direction in the outer region.

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.

Soft measurement model for wet gas flow rate based on ultrasonic and differential pressure sensing

Non-separation measurement of gas–liquid two-phase flow is of great significance to industrial production and theoretical research on two-phase flow. In this paper, a soft measurement method of wet gas flow rate based on ultrasonic and differential pressure (DP) sensors is proposed. A total of 129 sets of experimental data are obtained in DN50 horizontal pipe, the superficial velocity of gas and liquid ranging from 5 m s−1 to 33 m s−1 and 0.015 m s−1 to 0.6 m s−1, respectively. Ten feature parameters of ultrasonic signals such as the time difference between two echoes and kurtosis factor are proposed from time and frequency domain. As well as the power spectral density, mean value and standard deviation value are analyzed based on DP signals. Furthermore, the Spearman correlation coefficient is introduced to evaluate these feature parameters quantitatively. And nine parameters which are highly correlated to gas–liquid flow rate are selected as the inputs of the soft measurement model. Finally, Decision Tree, least square support vector machines and artificial neural network (ANN) models are established through training with the experimental data. Comparison results show that ANN has the lowest prediction errors on the test set, with the mean absolute percentage errors of 1.49% and 3.2% for gas and liquid, respectively.

Experimental investigation on steam-water flow patterns in a vertical narrow rectangular channel utilizing conductance scanning measurement

In order to tackle the challenges in two-phase flow measurement in narrow rectangular channels, especially under pressurized conditions, a novel conductance scanning sensor, consisting of two ceramic-substrate printed circuit (CSPC) boards, has been developed based on the concept of wire mesh sensor. A leak-tight structure was also fabricated to avoid leakage at the penetrations of lead wires through the sensor housing. Measurements have been carried out in a narrow rectangular channel, with inner the cross-sectional dimension 70 mm × 2 mm, under pressure between 0.20 and 0.90 MPa. In the experiment, bubbly, churn and annular flows have been observed, except for slug flow. Flow pattern maps have been proposed for the steam-water two-phase flow. Comparing with those in the literature, it can be found that as the channel width/gap increases, the flow pattern transition boundaries shift towards the higher vapor superficial velocity direction. Additionally, the transition criteria for narrow rectangular channels were investigated by separately evaluating the critical void fraction and the superficial velocity calculation correlations. Results show that the critical void fraction of bubbly to churn flow and churn to annular flow can be approximately estimated as 0.2 and 0.75, respectively. However, the existing correlations for superficial velocity calculation are not suitable for the steam-water flows with a void fraction less than 0.5.

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.

Two-phase flow measurement through orifice-meter with regression analysis

Two-phase flow measurement through orifice-meter with regression analysis