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.     

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.     

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.     

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.     

Relationship between ductile crack initiation and void volume fraction

An investigation on ductile crack initiation in structural steel has been made, based on the concept of Gurson's yield function for porous material. First, the condition of ductile crack initiation in the uniform stress field has been investigated. The condition of ductile crack initiation under various stress triaxiality obtained from the tests on axisymmetric notched tensile specimens is well expressed by the condition of constant void volume fraction analytically obtained from Gurson's model. This result means that the condition of constant void volume fraction may be used as the criterion of ductile crack initiation. Secondly, the behavior of void growth and ductile crack initiation in the area near the notch tip under mode I and mode II loading has been investigated. Under mode I loading, the increase in void volume fraction around the notch with an increase in applied load agrees well with the behavior of porous material predicted by the finite element analysis based on Gurson's yield function, and the ductile crack initiation can be predicted by the concept of critical void volume fraction as in the case of uniform stress-strain field given above. The same criterion is not applicable to the crack initiation under mode II loading and further study is needed.     

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.     

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.     

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.     

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.     

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.     

低质量流速绝热管内截面平均空泡率实验研究

汽液两相流空泡率实验与计算方法研究对于反应堆自然循环及事故分析具有重要意义,然而现有研究主要以高质量流速工况为主,已有的空泡率公式预测结果在低质量流速条件下也存在较大差异。为此,本文以单探头光学探针为主要测量手段,进行了低质量流速绝热工况空泡率实验研究,截面平均空泡率根据探针测量得出的局部空泡率在流道截面上积分计算得出。实验数据与已有空泡率计算公式进行了比较,表明低质量流速工况下多数公式预测结果偏高,而Chexal et al．、GE—Ramp以及Dix公式可得出非常满意的预测结果。综合Vijayan的研究结果,本文建议低质量流速空泡率计算中采用Chexal et al．的公式。     

Measurement of void fraction in bubbly-slug flow with a constant electric current method

In several void fraction measurement methods, a constant electric current method which is one of conductance methods is focused in the present study. By using this method, void fraction can be measured with higher temporal resolution. However, it has been mainly applied to annular flow in previous studies. In the present study, Maxwell's estimation, Bruggemann's estimation, low void fraction approximation and new estimations which consider the bubble shape are applied in order to measure more accurately void fraction of dispersed bubbly flow and slug flow. To understand the effect of bubble shapes and flow patterns, void fraction was measured by the constant electric current method for a rising single spherical bubble and a rising single slug bubble without a forced convection. In addition, void fraction was also measured in bubbly flow and bubbly-slug flow with a forced convection. Then, effects of flow patterns on the proposed estimations of void fraction and the accuracy of their estimations were discussed with the measurement results. From the result, the new estimations which consider a bubble shape are more accurate than the previous estimation in a slug bubble and bubbly-slug flow.     

A dual photon source method for void fraction measurements in dynamic fluid systems

A dual source method of void fraction measurements in flowing media is described. The method is compared with the commonly used single source as a means of making measurements of dynamic fluid systems. The dual source method is shown to be less severe when the static void assumption is made. Also, it is shown that the mean void fraction determined by this method is independent of the thickness of flowing fluid. Both the single and the dual source methods are compared for an assumed case of Poisson-distributed voids passing the detector location.     

Simulation of a neutron scattering method for measuring void fraction in two-phase flow

Experiments have indicated that fast/epithermal neutron scattering techniques are attractive for void fraction measurement in two-phase flow. Some of these experiments have been simulated by Monte Carlo neutron transport calculations. The simulations predict results in agreement with the measurements. This suggests that the experimental technique has a sound theoretical basis, and that numerical simulations may be used to design experimental setups for different applications.     

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%.