Cross-sectional Averaged Void Fraction Research Articles

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.

Modeling of distribution parameters for upward steam-water boiling flows in subchannels of a vertical rod bundle

ABSTRACT In simulations of two-phase flow behavior in nuclear reactors, subchannel analysis codes are often used to evaluate the void fraction within a BWR fuel bundle in detail. When solving the momentum conservation equation averaged over a subchannel cross-section for upward two-phase flows, the distribution parameter is required to consider the void fraction and velocity distributions in the subchannel cross-section. In this paper, constitutive equations were developed for the distribution parameters for dispersed two-phase flows applicable to the inner, edge, and corner subchannels, which are typical subchannels in a fuel bundle. The distribution parameters could be calculated by giving the void fraction and the velocity distribution. Therefore, the distribution parameters were evaluated and modeled as a function of the geometrical parameters by assuming the void fraction and velocity distributions with bulk and subcooled boiling for each subchannel type. The developed constitutive equations were evaluated by comparing them with the distribution parameters estimated based on the NUPEC rod bundle void fraction test data. The developed distribution parameter model was implemented into the subchannel analysis code NASCA and compared with the measured cross-sectional average void fraction of the NUPEC rod bundle void fraction test data. In comparison with the original NASCA code, which assumed the distribution parameter to be unity, the improved NASCA with the distribution parameter model decreased the mean error of the measured cross-sectional average void fraction to less than half of the result of the original NASCA code, both in absolute and relative differences.

An experimental study of boiling two-phase flow in a vertical rod bundle with a spacer grid-Part 2: Effects of vane angle

We performed boiling flow experiments and measured the void fraction in a 3 × 3 rod bundle including a spacer grid with split type vanes using X-ray computed tomography, which provides high-resolution time-averaged void data without disturbing the flow. We studied the effects of mixing vanes with different vane angles, namely, 20°, 29° and 40°, for a mass flux between 535 and 1950 kg/m2 s and the central rod being heated giving a heat flux of 85.7 kW/m2. The experiments were conducted using octafluorocyclobutane (RC318) as the working fluid. The presence of vanes leads to an increase of the cross-sectional averaged void fraction up to an axial position of Z≈0.8Dh. After that, the void fraction decreases until 3Dh<Z<4Dh due to the induced swirl flow, before it increases again. It was further found that the vanes cause a high local void fraction near the spacer, which increases the possibility of DNB occurrence. From this study, it can be concluded that a vane angle of 29° is optimal for two-phase flow, which is consistent with the findings in the literature for single-phase flow.

Void fraction measurement and calculation model of vertical upward co-current air–water slug flow

The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air–water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s −1 and gas superficial velocity ranging from 0.049 to 0.65 m·s −1 . A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness C δ and nose shape C Z* were proposed to calculate α TB . In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate α LS , by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al. , indicating that the new model was effective and applicable under the slug flow conditions.

Identification of Oil-Gas Two Phase Flow in a Vertical Pipe using Advanced Measurement Techniques

The characteristics of flow configuration in pipes are very important in the oil industry due to its role in governing equipment design. In vertical risers, many flow configurations could be observed such as bubbly, slug, churn, and annular flow. In this project, two tomographic techniques have been applied simultaneously to the flow in a vertical riser: the Electrical Capacitance Tomography (ECT) technique and the Capacitance Wire Mesh Sensor (WMS) technique. The employed pipe diameter was 50mm and the superficial studied velocities were 0.06-3.0m/s for gas and 0.06-0.4m/s for oil. Several techniques have been used to analyze the output data of the two tomography techniques such as time series of cross-sectional averaged void fraction, Probability Density Function (PDF), image reconstruction, and liquid hold-up profile. The averaged void fractions were calculated from the output signal of the two measurement techniques and plotted as functions of the superficial velocity of the gas. The flow patterns were identified from the PDF of the averaged void fraction. In addition, it was found that both tomographic techniques are reliable in identifying the flow regimes in pipes.

Vertical upward and downward churn flow: Similarities and differences

Investigation of downward two-phase flows received less attention compared to the vertical upward flows. Downward flows are found in many industries and facilities including; oil/gas production, nuclear industry and petroleum refinery/production facilities such as evaporators, chemical reactors and distillation towers. A thorough understanding of the flow dynamic characteristics occur in such transportation lines, process plants and units is very crucial in terms of design, operation, production and safety.In the current work, air-water two-phase churn flow in a 34 mm I.D. pipe was investigated for two configurations of vertical upward (51 cases) and downward (48 cases). Several conductance probes and pressure transducers were used to measure cross-sectional averaged void fraction time series, and pressure drop along the pipe, respectively.The main objectives of the work were to investigate the similarities and dissimilarities between vertically upward and downward churn flow and specifically understand how gravity could affect the behavior of liquid structures present within the flow. To quantify this, different parameters such as Probability Density Function, distribution coefficient in the drift-flux model, structural velocity, slippage number, dimensionless pressure gradient etc. were used.It was noticed that in both configurations, dimensionless pressure gradient and slippage number demonstrated a strong correlation with the mixture Froude number. There were, however, discrepancies in Probability Density Functions (PDFs) and structural velocities of flow in the two orientations.

Void fraction characteristics of adiabatic one-component vertically upward two-phase flows in circular and non-circular small diameter tubes.

Evaporating and condensing heat transfer and pressure loss characteristics strongly depend on interfacial structure of gas-liquid two-phase flows. Cross-sectional average void fraction is important parameter on the one-dimensional analysis. Recently, since channel diameter becomes smaller, the effect of surface tension on the flow behaviors would become stronger. This study deals with void fraction characteristics of adiabatic two-phase flows using FC-72 as the working fluid. Crosssectional average void fraction was measured by capacitance sensor. Circular, square and triangular tubes with the hydraulic diameter of 2 mm were used. Vertically upward flow was selected to evaluate for axially symmetric phase distribution. From the results, it was confirmed that for the square and triangular tube, void fraction became lower than the circular tube because liquid was accumulated in the corner by surface tension. Although the lower void fraction leads to larger slip velocity, the gas-liquid interface of liquid film became smoother.

Experimental investigation of a vertically downward two-phase air-water slug flow

The present experimental work investigates the vertical downward two-phase slug flow in a transparent vertical pipe of 34 mm internal diameter. The gas and liquid superficial velocities are in the range of 0–3.27 m/s and 0.015–1.4 m/s respectively. The cross-sectional averaged void fraction has been measured at seven positions along the test section by the intermediary of the conductance probe technique.The results of the development of the void fraction time-series and Probability Density Function along the tube are presented. A good accordance was found between the experimental data and the line transitions of the flow pattern map proposed by (Usui, 1989). We also present results of the structure velocity of the slug flow, where the distribution parameter is found to be lower than unity. A new correlation for the prediction of slug frequencies is also proposed. It agrees well with the data collected in this study with ±10% error.

Visualization of gas-liquid multiphase pseudo-slug flow using Wire-Mesh Sensor

Intermittent two-phase flows are commonly encountered in the petroleum industry. Much attention has been focused by several researchers on intermittent flows existing at low superficial gas velocities (<10 m/s). There is limited work performed on intermittent structures persisting at higher superficial gas velocities (pseudo-slug flows). In the present experimental study, a conductivity-based Wire-Mesh Sensor (WMS) was used to visualize and characterize pseudo-slug flow. Experiments were performed in a 76.2 mm horizontal pipe with air and water as the working fluids at atmospheric conditions. The superficial gas and liquid velocities ranged from 9 m/s to 35 m/s and 0.45 m/s to 0.76 m/s, respectively. A 16 × 16 WMS was placed 17 m away from the pipe inlet to measure spatio-temporal void-fraction distribution. The WMS data acquisition frequency was set to 10 kHz.From the void-fraction time series data, the periodic pseudo-slug structures were visualized. The visualization suggested that unlike slug flow where the liquid structures fill the pipe cross-section, the pseudo-slugs were extremely aerated structures (high gas-liquid mixing) formed due to the gas penetration into the liquid slug body. This paper also presents the measurements of important hydrodynamic characteristics such as cross-sectional averaged void-fraction time series and mean void fraction. The effect of liquid viscosity on the visualized structures is also presented.

Validation of NEPTUNE CFD two-phase flow models against OECD/NRC PSBT subchannel experiments

This paper deals with the validation of the multifield computational fluid dynamics code NEPTUNE_CFD v2.0.1 against experimental data available from the OECD/NRC NUPEC PWR subchannel and bundle tests (PSBT) international benchmark. The present work is performed in the framework of the NURESAFE European collaborative project and focuses on the steady-state single subchannel void fraction tests.From overall 126 PSBT experiments covering wide range of test conditions and 4 different geometrical configurations of PWR subchannel, 42 tests have been selected and simulated using NEPTUNE_CFD. Following the NEA/CSNI (Nuclear Energy Agency/Committee on the Safety of Nuclear Installations) best practice guidelines about computational grid design and grid quality, mesh sensitivity analysis has been performed using axial and radial grid refinement. Both axial and radial mesh sensitivity studies do not exhibit any significant change in the predicted results, which thus result to be grid-converged. Besides, a series of sensitivity calculations have been performed in order to investigate the influence of uncertainties of the experimental boundary conditions on the code predictions.The influence of code physical and closure models on the void fraction prediction has been studied and discussed in detail. Generally, the calculated cross-sectional averaged void fraction at the measurement plane differs from the measured one by maximum of ±8%. This discrepancy is comparable to the 2σ experimental uncertainty range on void fraction measurement. The performed investigations have shown the ability of NEPTUNE_CFD to predict reasonably the void fraction in PSBT subchannel using appropriate modeling.

Inverse uncertainty quantification of trace physical model parameters using BFBT benchmark data

Forward quantification of simulation (code) response uncertainties requires knowledge of physical model parameter uncertainties. Nuclear thermal-hydraulics codes, such as RELAP5 and TRACE, do not provide any information on uncertainties of physical model parameters. A framework is developed to quantify uncertainties of physical model parameters using Maximum Likelihood Estimation (MLE), Bayesian Maximum A Priori (MAP), and Markov Chain Monte Carlo (MCMC) algorithms.The objective of the present work is to perform the sensitivity analysis of the physical model parameters in code TRACE and calculate their uncertainties using MLE, MAP, and MCMC algorithms. The OECD/NEA BWR Full-size fine-mesh Bundle Test (BFBT) data is used to quantify uncertainty of selected physical models of TRACE code. The BFBT is based on a multi-rod assembly with measured data available for single or two-phase pressure drop, axial and radial void fraction distributions, and critical power for a wide range of system conditions. In this work, the steady-state cross-sectional averaged void fraction distribution is used as the input data for inverse uncertainty quantification (IUQ) algorithms, and the selected physical model’s probability distribution function (PDF) is the desired output quantity.

Experimental characterization of vertical downward two-phase annular flows using Wire-Mesh Sensor

Annular two-phase flow has been vastly investigated because of its large and deep involvement in industrial processes, particularly in nuclear engineering and petroleum production facilities. Much effort has been devoted to investigating upward flows involving the flow patterns, void fraction, as well as local interfacial characteristics. However, research for vertical downward two-phase flow, especially of the interfacial characteristics, are comparatively scarce. In order to gain insight on void fraction, interfacial structures and characteristics frequencies, experimental work was performed in downward annular two-phase flow with water and air as process fluids at low pressure conditions. A flow loop, including a 76mm ID, 16.5m long vertical pipe, has been instrumented. A state-of-the-art instrument for two-phase flow measurements based on the fluid conductivity, namely dual Wire-Mesh Sensor (WMS) has been utilized to acquire the experimental data. A total of 43 data points have been acquired at superficial liquid velocities that ranged from 0.005m/s to 0.10m/s and superficial gas velocities that varied from 10m/s to 31m/s. The effects of liquid viscosity on the measured parameters are also investigated using two different viscosities of 1 and 10cP. Analysis of time series void fraction data from the dual Wire-Mesh Sensors allows the determination of cross-sectional averaged void fraction, local time averaged void fraction distribution, liquid phase distribution around the tube periphery, interfacial structure frequencies, pseudo 3D reconstruction as well as Probability Density Function (PDF) and Power Spectral Density (PSD). The experimental results indicate that the interfacial shape and frequencies are significantly altered by the superficial gas velocity. Comparisons between mechanistic model predictions and the acquired experimental data show a maximum absolute average relative error of approximately 7% for the cross-section void fraction.

Uncertainty and sensitivity analyses as a validation tool for BWR bundle thermal–hydraulic predictions

In recent years, more realistic safety analyses of nuclear reactors have been based on best estimate (BE) computer codes. The need to validate and refine BE codes that are used in the predictions of relevant reactor safety parameters, led to the organization of international benchmarks based on high quality experimental data. The OECD/NRC BWR full-size fine-mesh bundle test (BFBT) benchmark offers a good opportunity to assess the accuracy of thermal–hydraulic codes in predicting, among other parameters, single and two phase bundle pressure drop, cross-sectional averaged void fraction distributions and critical powers under a wide range of system conditions. The BFBT is based on a multi-rod assembly integral test facility which is able to simulate the high pressure, high temperature fluid conditions found in BWRs through electrically heated rod bundles. Since code accuracy is unavoidably affected by models and experimental uncertainties, an uncertainty analysis is fundamental in order to have a complete validation study. In this paper, statistical uncertainty and sensitivity analyses are used to validate the thermal–hydraulic features of the POLCA-T code, based on a one dimensional model of the following macroscopic BFBT exercises: (1) single and two phase bundle pressure drop, (2) steady-state cross-sectional averaged void fraction, (3) transient cross-sectional averaged void fraction and (4) steady-state critical power tests. The Latin hypercube sampling (LHS) strategy was chosen since it densely stratifies across the range of each uncertain input probability distribution, allowing a much better coverage of the input uncertainties than simple random sampling (SRS). The results show that POLCA-T predictions on pressure drop and void fractions under a wide range of conditions are within the validation limits imposed by the uncertainty analysis, while the accuracy of critical power predictions depends much on the boundary and input conditions.

Separated two-phase flow regime parameter measurement by a high speed ultrasonic pulse-echo system

In this work, a high speed ultrasonic multitransducer pulse-echo system using a four transducer method was used for the dynamic characterization of gas-liquid two-phase separated flow regimes. The ultrasonic system consists of an ultrasonic pulse signal generator, multiplexer, 10 MHz (0.64 cm) ultrasonic transducers, and a data acquisition system. Four transducers are mounted on a horizontal 2.1 cm inner diameter circular pipe. The system uses a pulse-echo method sampled every 0.5 ms for a 1 s duration. A peak detection algorithm (the C-scan mode) is developed to extract the location of the gas-liquid interface after signal processing. Using the measured instantaneous location of the gas/liquid interface, two-phase flow interfacial parameters in separated flow regimes are determined such as liquid level and void fraction for stratified wavy and annular flow. The shape of the gas-liquid interface and, hence, the instantaneous and cross-sectional averaged void fraction is also determined. The results show that the high speed ultrasonic pulse-echo system provides accurate results for the determination of the liquid level within +/-1.5%, and the time averaged liquid level measurements performed in the present work agree within +/-10% with the theoretical models. The results also show that the time averaged void fraction measurements for a stratified smooth flow, stratified wavy flow, and annular flow qualitatively agree with the theoretical predictions.

PSEUDO-LAMINARIZATION OF MICRO-BUBBLE CONTAINING MILKY BUBBLY FLOW IN A PIPE

Micro bubble technology has become to attract people's concerns due to its wide potential in practical applications to a variety of advanced and conventional science and technologies. However, our knowledge of micro bubbles containing bubbly two-phase flow is almost nothing. We developed a specially designed nozzle which generates micro air bubbles with high bubble number density (mean diameter ≈ 40microns, number density higher than 2×105/cc). Using this micro-bubble generator, we carried out a measurement of two-phase frictional pressure drop, cross-sectional average void fraction, local void fraction profiles and liquid velocity profiles. The range of cross-sectional average void fraction covered was up to 0.6 % which is high enough to realize milky bubbly flow. The most exciting result we found is that the two-phase flow becomes pseudo-laminarized by injecting such ultra small bubbles into the water flow. For 0.3 ≈ 0.5% void fractions, pseudo-laminar-to-turbulent transition occurred at Re= 10,000 ≈ 20,000, showing a significant reduction in wall friction. The radial liquid velocity profiles show typical turbulent 1/7 th power law profile. However, the liquid velocity profiles in milky bubbly flow obviously shifted from von Karman's universal velocity profile towards lower values of the non-dimensional distance from the wall. The cross sectional averaged void fraction correlates well with a homogeneous flow model, which is verified by uniform profiles of the local void fraction distribution over the whole channel cross section. The mechanisms of pseudo-laminarization and flow structures have been discussed.

PSEUDO-LAMINARIZATION OF MICRO-BUBBLE CONTAINING MILKY BUBBLY FLOW IN A PIPE

Micro bubble technology has become to attract people's concerns due to its wide potential in practical applications to a variety of advanced and conventional science and technologies. However, our knowledge of micro bubbles containing bubbly two-phase flow is almost nothing. We developed a specially designed nozzle which generates micro air bubbles with high bubble number density (mean diameter ≈ 40microns, number density higher than 2×105/cc). Using this micro-bubble generator, we carried out a measurement of two-phase frictional pressure drop, cross-sectional average void fraction, local void fraction profiles and liquid velocity profiles. The range of cross-sectional average void fraction covered was up to 0.6 % which is high enough to realize milky bubbly flow. The most exciting result we found is that the two-phase flow becomes pseudo-laminarized by injecting such ultra small bubbles into the water flow. For 0.3 ≈ 0.5% void fractions, pseudo-laminar-to-turbulent transition occurred at Re= 10,000 ≈ 20,000, showing a significant reduction in wall friction. The radial liquid velocity profiles show typical turbulent 1/7 th power law profile. However, the liquid velocity profiles in milky bubbly flow obviously shifted from von Karman's universal velocity profile towards lower values of the non-dimensional distance from the wall. The cross sectional averaged void fraction correlates well with a homogeneous flow model, which is verified by uniform profiles of the local void fraction distribution over the whole channel cross section. The mechanisms of pseudo-laminarization and flow structures have been discussed.

Void Fraction Distribution of Upward Bubbly Flow in a Vertical Pipe with Sudden Expansion

Experimental study was made on the multi-dimensional behavior of upward gas-liquid two-phase flow through a vertical pipe with an axisymmetric sudden expansion. In this study, the measurement on the void fraction distribution was carried out for the sudden expansion channel. The void fraction distributions below and above the sudden expansion point were measured at the different axial and radial positions using a point-electrode resistivity probe for various gas and liquid flow conditions. The results of measured void fraction distributions showed that how the two-phase flow develops along the direction of the downstream of the sudden expansion. Furthermore, the development of the void fraction distribution also revealed quite complicated behaviors depending upon flow rates of gas and liquid phases and bubble size. Based on the measured void fraction distribution in the sudden expansion, cross-sectional averaged void fraction and phase distribution parameter were evaluated at the different tube cross sections in the sudden expansion. As a result, it revealed that the void fraction along the flow direction in the sudden expansion might be predicted by using the appropriate distribution parameter representing the void fraction distributions in the sudden expansion.

The structure of gas–liquid flow in a horizontal pipe with abrupt area contraction

Single fiber optical probes were used to measure the cross-sectional void fraction distribution for air–water flow in a horizontal test section with sudden area contraction. The local void fraction was plotted as a function of its two spatial co-ordinates, so that a representation of the time average gas distribution over the cross-section could be obtained. The cross-sectional average void fraction was obtained by numerical integration of the local values; the contraction was shown to considerably alter the distribution of the phases, so that the correlations for straight pipes appear no longer suitable.

Intermittent flow parameters from void fraction analysis

Two-phase horizontal intermittent flow in straight pipes is experimentally investigated. A new procedure is proposed to characterize the flow through the statistical analysis of the instantaneous cross-sectional averaged void fraction obtained by means of ring impedance probes. The algorithm, based on the statistical analysis of the void fraction records, allows the main intermittent flow parameters, such as slug frequency and length, time average void fraction, minimum and average liquid film height to be evaluated. The procedure is validated through flow visualizations, as obtained from a fast digital video camera. Experiments on air-water horizontal flows in 40 and 60 mm inner diameter pipes are performed. The operating conditions cover the 0.3–4.0 and 0.6-3.0 m/s gas and liquid superficial velocity ranges, respectively. An extensive comparison with literature data shows a general agreement with present measurement. The reliability of both the instrumentation and the signal analysis procedures allows new correlations for minimum and average liquid film height in stratified regions to be proposed. Finally proper dimensionless numbers were applied to correlate frequency data in a wide range of superficial velocity values.

Effect of Pressure With Wall Heating in Annular Two-Phase Flow

The local distributions of void fraction, interfacial frequency, and velocity have been measured in annular flow of R-134a through a wall-heated, high aspect ratio duct. High aspect ratio ducts provide superior optical access to tubes or irregular geometries. This work expands upon earlier experiments conducted with adiabatic flows in the same test section. Use of thin, transparent heater films on quartz windows provided sufficient electrical power capacity to produce the full range of two-phase conditions of interest. With wall vapor generation, the system pressure was varied from 0.9 to 2.4 MPa, thus allowing the investigation of flows with liquid-to-vapor density ratios covering the range of about 7 to 27, far less than studied in air-water and similar systems. There is evidence that for a given cross-sectional average void fraction, the local phase distributions can be different depending on whether the vapor phase is generated at the wall, or upstream of the test section inlet. In wall-heated flows, local void fraction profiles measured across both the wide and narrow test section dimensions illustrate the profound effect that pressure has on the local flow structure; notably, increasing pressure appears to thin the wall-bounded liquid films and redistribute liquid toward the edges of the test section. This general trend is also manifested in the distributions of mean droplet diameter and interfacial area density, which are inferred from local measurements of void fraction, droplet frequency and velocity. At high pressure, the interfacial area density is increased due to the significant enhancement in droplet concentration.