Measurements of void fraction by an improved multi-channel conductance void meter

An improved multi-channel conductance void meter (CVM) was developed to measure a void fraction. Its measuring principle is based upon the differences in electrical conductance of a two-phase mixture due to the variation of void fraction around a sensor. The sensor is designed to be flush-mounted to the inner wall of the test section to avoid flow disturbances. The signal processor with three channels is specially designed so as to minimize inherent bias error due to the phase difference between channels. It is emphasized that the guard electrodes are electrically shielded in order not to affect the measurement of two-phase mixture conductance, but to ensure that the electrical fields are evenly distributed in the measuring volume. Void fraction is measured for bubbly and slug flow regimes in a vertical air–water flow and statistical signal processing techniques are applied to show that CVM has good dynamic resolution which is required to investigate the structural developments of bubbly flow and the propagation of void waves in a flow channel.     

Heat transport and void fraction in granulated debris

The paper discusses the boiling heat transfer from a porous bed with internal heat sources and refers to the configuration in a nuclear reactor after a partial core melt. The flow of coolant, the temperature and the local liquid/vapor distribution were investigated in a two-dimensional configuration. Experiments were conducted using monodisperse beds as well as a mixture of two different particle sizes with a total porosity below 20%. In some tests the bed was supported by a shell of porous material to create a gap along the bottom of the test container. Water was used for tests up to 9% of the critical pressure, while other tests were made with R134a up to 44% of the critical pressure. The maximum heating rate realized inductively was 730 kW/m². The experiments have been compared to analytical results with a one-dimensional approach.It is shown that in contrary to the situation in small cylindrical configurations the heat transfer was increased by large buoyancy driven convective flows. If there was a gap along the container bottom an additional flow of liquid improved the coolability of the bottom region even if the upper part of the particle bed was already overheated. In case of high density ratios (water at low pressure), the measurements indicated a strong enhancement of the coolant flow above a certain minimum heating rate resulting in decreasing vapor fraction values which were nearly independent of the system pressure. This was assumed to be caused by the appearance of vertical channels through which the vapor could flow through the particle bed.     

Vapour void fraction in subcooled flow boiling

Experimental data on steam void fraction and axial temperature distribution in an annular boiling channel for low mass-flux forced and natural circulation flow of water with inlet subcooling have been obtained. The ranges of variables covered are: mass flux = 1.4 × 10⁴−1.0 × 10⁵ kg/hr m²; heat flux = 4.5 × 10³−7.5 × 10⁴ kcal/hr m²; and inlet subcooling = 10–70°C. The present and literature data match well with the theoretical void predictions using a four-step method similar to that suggested by Zuber and co-workers.     

An assessment of eight void fraction models

This paper provides an assessment of eight well known models and correlations for predicting the void fraction. The void fraction predictions are compared using steady-state steam–water test data for vertical configurations that included almost 1500 data points representing several areas of interest to nuclear analysts such as: (1) high-pressure–high-flows, (2) high-pressure–low-flows, (3) low-pressure–low-flows, (4) countercurrent flooding limitation, (5) natural circulation flows, and (6) co-current downflows. The data were representative of PWR and BWR fuel assemblies and pipes up to 18 inches in diameter.     

A void fraction correlation for generalized applications

A void fraction correlation has been developed to cover the full range of pressures, flows, void fractions, and fluid types (steamwater, air-water, hydrocarbons, and oxygen). The correlation, referred to here as the Chexal-Lellouche correlation, has been qualified against several sets of steady-state two-phase/two-component flow test data that cover a wide range of thermodynamic conditions and geometries typical of PWR and BWR fuel assemblies as well as for pipes up to 450 mm in diameter. The correlation is based on a drift flux model and determines the drift flux parameters, C_o and V_gj both cocurrent and countercurrent two-phase flows for the full range of pressures, flows and void fractions. The correlation is available as a source code module for inclusion into any thermal-hydraulic computer program, and as an interactive personal computer program. The correlation is continuous and does not depend on flow regime maps or spline fitting.     

Experimental study on void fraction in a simulated BWR fuel assembly (evaluation of cross-sectional averaged void fraction)

Void fraction measurement of a vertical (4 x 4) rod bundle has been conducted in a steam-water two phase flow, using an advanced X-ray CT scanner. A large amount of rod bundle data was obtained. It was found from the results that the cross-sectional averaged void fraction data for a rod bundle can be correlated by the Drift-Flux model and that the Zuber-Findlay correlation underestimates the data in a void fraction area of 80% or more. This is because the data range over which this correlation was developed, does not cover this experimental range. Therefore, a modified correlation was developed based on the authors' data.     

Creep crack initiation and creep crack growth assessments in welded structures

In this study, creep crack initiation and creep crack growth in welded structure are analysed. An interaction phenomenon between base metal and weld metal in a cross weld plate is highlighted with a finite element model. A simplified method based on the reference stress approach is proposed to evaluate C* in welded structures. This simplified method is applied for creep crack initiation and creep crack growth assessments in the case of a double edge notched tension cross-welded plate. Correlations between crack initiation time and C* on the one hand, and between creep crack growth rate and C* on the other hand are used. Creep crack initiation time estimation for the full size welded plate is very conservative when crack initiation properties of CT specimen are used. Concerning creep crack growth evaluation, simplified estimation is in good agreement with experimental results when CT specimen crack propagation properties are used.     

Gas–liquid phase distribution and void fraction measurements using MRI

We used a permanent-magnet magnetic resonance imaging (MRI) system to estimate the integral, spatially- and temporally-resolved void fraction distributions and flow patterns in vertical gas–liquid two-phase flow. Air was introduced at the bottom of the stagnant liquid column using an accurate and programmable syringe pump. The air flow rate was in upward vertical direction against the gravity vector. Air flow rates were varied between 1 and 200 ml/min. Bubble formation and detachment at the inlet of the vertical column was non-uniform. The cylindrical non-conducting test tube in which two-phase flow is characterized was placed in a 0.26 T permanent-magnet MRI unit. A roughly linear relationship has been observed for the integral void fraction versus volume flow rate of air through vertical stagnant liquid column. Integral or sample-averaged void fraction was obtained by volume-averaging of the spatially-resolved signals. Spatial averaging was performed in a radial or longitudinal axis of the column. The time-averaged spatially-resolved void fraction has also been obtained for the quasi-steady flow of air in a stagnant liquid column. No great accuracy is claimed as this was an exploratory proof-of-concept type of experiment. Preliminary results show that MRI can indeed provide qualitative and quantitative data and is especially well suited for characterization of averaged transport processes in adiabatic and diabatic multi-phase and/or multi-component flows. Better and faster MRI sequences could improve spatial and temporal resolutions significantly.     

Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors.This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX.The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions.     

Energy transformation during dynamic crack initiation and arrest

This contribution deals with the experimental determination of fracture mechanics parameters concerning dynamic crack initiation, crack propagation and crack arrest demonstrated on reactor pressure vessel steels 20 MnMoNi 5 5 and 22 NiMoCr 3 7. Appropriate measuring methods are available to determine the impact fracture toughness K_Id for CT specimens and CCP specimens. However, for small scale specimens there are still experimental and theoretical problems to be met with when determining the fracture heat of a propagating crack and ascertaining the parameters of arrest.     

Measurement and modeling of average void fraction, bubble size and interfacial area

The local void fraction, bubble size and interfacial area concentration for co-current air-water bubbly flow through a horizontal pipe of 50.3 mm internal diameter were investigated experimentally using the double-sensor resistivity probe method. The local and area-averaged void fractions and interfacial area concentrations were analyzed as a function of liquid and gas flow rates. These parameters were found to increase systematically with decreasing liquid flow and increasing gas flow. However, variations with the liquid flow were not as significant as with the gas flow. A consistent variation of the gas phase drift velocity and distribution parameter with the liquid flow rate was observed. It was demonstrated that presentation of the average void fraction in terms of flowing volumetric concentration was more appropriate for horizontal bubbly flow. Several bubble break-up mechanisms were discussed. It was concluded that average pressure fluctuations generated by the turbulent liquid fluctuations acting across a bubble diameter are the only mechanism which causes distortion of a bubble. Based on this force and the competing surface tension force, a theoretical model was developed for mean bubble size and interfacial area concentration. The theoretically predicted mean bubble size and interfacial area concentration were found to agree reasonably well with those measured by the double-sensor resistivity method.     

Improvement on the two-phase-flow void fraction determination using Monte Carlo calculations

In this paper, a modified one-shot photon-attenuation method is presented for the determination of the average void fraction in a two-phase-flow system. The modification over the conventional one-shot method is established by a series of Monte Carlo Calculations. Through a benchmark test, it is validated that the accuracies of the void-fraction prediction can be significantly improved. The application of this new technique is demonstrated using a mixed air-water flow channel. Results show that, the improvement gained using this modified method is essential at low void fractions where the conventional one-shot method suffers high uncertainty. Another important correction made in this work is on the condition of the variation of void distribution with time. It is found that this correction can be significant when the void fractions in the flow channel are large.     

A cohesive plastic/damage-zone model for ductile crack analysis

A cohesive plastic/damage-zone model of the Dugdale-Barenblatt type (G.I. Barenblatt, Adv. Appl. Mech. 7 (1962) 55–129; D.S. Dugdale, J. Mech. Phys. Solids 8 (1960) 100–104) is presented for analyzing crack growth in ductile materials with damage evolution. A semi-infinite Mode I crack in plane stress or plane strain is considered. The damage is assumed to be present in form of dispersed microvoids which are localized into a narrow strip ahead of the crack-tip. A simple damage model of the Gurson model type (A.L. Gurson, J. Eng. Mater. Technol. 99 (1977) 2–15; V. Tvergaard, Advances in Applied Mechanics, Vol. 27, Academic Press, 1990, pp. 83–151) is developed for uniaxial tension to describe the macroscopic properties of the cohesive plastic/damage-zone. Under small-scale yielding and small-scale damage conditions, a system of nonlinear integral equations for the plastic strain and the length of the cohesive plastic/damage-zone is derived. Numerical results are presented and discussed to reveal the effect of damage evolution on the ductile crack growth.     

高冲聚苯乙烯-低密度聚乙烯的自由体积特征与其相溶性的关系

不同组成的高冲聚苯乙烯(HIPS)和低密度聚乙烯(LDPE)共混物的正电子湮没寿命谱被测量，结果表明HIPS和LDPE是不相溶共混物。在界面处，二组分的不相溶主要归因与一个组分没有足够大的自由体积孔穴尺寸容纳另一组分的侧基和分子链端基。另外，测量的自由体积分数产生的负偏差被认为主要由最长寿命强度I3所引起。     

Simultaneous measurement of void fraction and fundamental bubble parameters in subcooled flow boiling

Visualization was performed for the vapor bubbles in water subcooled flow boiling in a vertical heated tube to measure simultaneously the void fraction and the four fundamental bubble parameters: nucleation site density, bubble release frequency, bubble lifetime and bubble size. Using the mass flowrate and liquid subcooling as the experimental parameters, the changes of void fraction and bubble parameters with the wall heat flux were measured. The results of image analysis showed that the vapor void fraction could be approximated by the function of nucleation site density and bubble lift-off diameter; the bubble lift-off diameter was more influential than the nucleation site density. It was hence concluded that the bubble lift-off diameter could be regarded as the key parameter to determine the vapor void fraction under the present experimental conditions. The strong relation of bubble lift-off diameter to superheated liquid layer thickness was indicated for the future model development studies of bubble lift-off diameter.     

A problem in the COBRA-EN code related to the void fraction calculation

When a certain void fraction value is reached in the two-phase flow regime, a problem occurs in the COBRA-EN code. This problem was observed in the drift-flux model option and interrupts code execution. Two solutions are proposed to solve the problem.     

Development of one-dimensional two-fluid model with consideration of void fraction covariance effect

Accurate evaluation of gas-liquid two-phase flow behavior within rod bundle geometry is crucial for the safety assessment of the nuclear power plants. In safety assessment codes, two-phase flow in rod bundle geometry has been treated as a one-dimensional flow. In order to obtain the reliable one-dimensional two-fluid model, it is essential to utilize proper area-averaged models for governing equations and constitutive relations. The area-averaged interfacial drag term utilized to evaluate two-phase interfacial drag force is typically given by the drift-flux parameters which consider the velocity profile in two-phase flow fields. However, in a rigorous sense, the covariance due to void fraction profile is ignored in traditional formulations. In this paper, the rigorous formulation of one-dimensional momentum equation was derived by taking consideration of void fraction covariance, and a new set of one-dimensional momentum equation and constitutive relations for interfacial drag was proposed. The newly obtained set of formulations was embedded into TRAC-BF1 code and numerical simulation was performed to compare against the traditional model without covariance. It was found that effect of covariance was almost negligible for steady-state adiabatic conditions, but for high void fraction condition with added perturbation, the traditional model underpredicted the damping ratio at around 8%.     

Gamma-ray attenuation technique for measuring void fraction in horizontal gas-liquid two-phase flow

The measurement of void fraction is of importance to the oil industry and chemical industry. In this article, the principle and mathematical method of determining the void fraction of horizontal gas-liquid flow by using a single-energy γ-ray system is described. The γ-ray source is the radioactive isotope of 241Am with γ-ray energy of 59.5 keV. The time-averaged value of the void fraction in a 50.0-mm i.d. transparent horizontal pipeline is measured under various combinations of the liquid flow and gas flow. It is found that increasing the gas flow rate at a fixed liquid flow rate would increase the void fraction. Test data are compared with the predictions of the correlations and a good agreement is found. The result shows that the designed γ-ray system can be used for measuring the void fraction in a horizontal gas-liquid two-phase flow with high accuracy.     

Distribution of void fraction for gas-liquid slug flow in an inclined pipe

In order to investigate the effect of inclination angle on the spatial distribution of phases,experiments on gas-liquid two-phase slug flow in an inclined pipe were carried out by using the optical probe and an EKTAPRO 1000 high speed motion analyzer.It has been demonstrated that the inclination angle and the mixture velocity are important parameters to influence the distribution of void fraction for upward slug flow in the inclined pipe.At high mixture velocity,the gas phase profile is axial symmetry in the cross-section of the pipe.This is similar to that for vertical slug flow.In contrast.most of the gas phase is located near the upper pipe wall at low mixture velocity.By measuring the axial variation of void fraction along the liquid slug.it can be concluded that there is a high void fraction wake region with length of 3-4D in the front of liquid slug.In the fully developed zone of liquid slug.the peak value of the void fraction is near the upper wall.     

Prediction of void fraction for PWR and BWR conditions with the sub-channel code F-COBRA-TF

The present paper discusses a comprehensive extension of the already substantial validation of the sub-channel code F-COBRA-TF with respect to void fraction prediction. In contrast to many established sub-channel codes, F-COBRA-TF allows a two-fluid/three-field representation of two-phase flow. Due to this modeling F-COBRA-TF, does not need to apply classical void correlations predicting void fraction according to quality. Instead, void fraction is a direct result of the basic transport equations for mass, momentum, and energy by using flow regime dependent interfacial friction correlations.Experimental data from open literature (tube boiling measurements in the sub-cooled region), from the OECD/NRC PSBT benchmark, and from in-house tests in AREVA's KATHY loop were used for validating F-COBRA-TF. In summary, it can be stated that all measurements could be recalculated with F-COBRA-TF with overall good agreement. Especially having in mind that no special code tuning concerning certain flow geometries or ranges of flow conditions had been performed, the obtained results look very convincing. Both, BWR and PWR conditions were simulated with exactly the same model set.