Void Fraction Prediction Research Articles

04/03082 A modified sequential approach for solvinginverse heat conduction problems: Lin, S.-M. et al. International Journal of Heat and Mass Transfer, 2004, 47, (12–13), 2669–2680

This paper presents a numerical solution of one-dimensional transient two-phase flow in a vertical channel using the Drift Flux Model (DFM). The DFM treats the two phases as a mixture, but allows slippage between the gas and the liquid phase. The DFM was used for the calculation of velocity and fraction of each phase, combined with the most relevant closure relationships models for condensation, wall evaporation, and phasic velocities. The solution of the three conservation equations for the mixture and a continuity equation for the gas phases is obtained by a semi-implicit numerical method. A finite volume method is used to discretize the governing equations on a staggered grid in the computational domain. Satisfactory agreement is shown between predicted void fraction, RELAP5 code and available experimental data under both transient and steady state conditions. Numerical solution was also obtained for a wide two-phase flow conditions: system pressure, surface heat flux, mass flow rate and inlet sub-cooling to check the model ability to predict void fraction accurately. It is concluded, therefore, that the DFM is able to predict void fraction in subcooled flow boiling with sufficient accuracy. For pressures lower than 30 bars, the DFM overestimated the void fraction in comparison with the experimental data by about 15%. The model requires less computational power to simulate than other approaches and has no limitations on the nodalization process for numerical stability. It is therefore expected that development of presented model will be useful for the assessment of experimental data, as well as performing pre-test numerical experimentation.

Void fraction predictions in forced convective subcooled boiling of water between 10 and 18 MPa

Forced convective subcooled boiling is of interest for many industrial applications, especially as a possible heat transfer regime in the core of pressurized water reactors (PWR). Due to practical interest, R12 was used as a testing fluid to simulate water between 10 and 18 MPa. This article presents a study of the forced convective subcooled boiling of R12 based on previous models and new physical considerations. The axial void fraction profile is determined and compared to R12 experimental data obtained on the DEBORA loop at CEA/Grenoble. The research yielded a void fraction model, shown to be valid for R12 as well as water, and based on a new correlation for the distribution parameter and on a continuous actual quality versus equilibrium quality function extended to the partially developed boiling region. Results showed good agreement with the DEBORA R12 experimental data as well as the experimental data obtained by Bartolomei et al. [Thermal Engng. 29(3) 132] in water at high pressure.

Modelling of gas entrainment from Taylor bubbles. Part A: Slug flow

A model that attributes the aeration of the liquid slug to a recurrent bubble entrainment from the Taylor bubble (TB) tail is introduced. The bubble fragmentation is related to the rate of turbulent kinetic energy produced in the wall jet and shear layer, which are formed in the TB wake as the liquid film plunges into the slug front. The bubble fragmentation model has been incorporated into a complete model, which suggests a unified method for the prediction of the slug void fraction and other slug characteristics in horizontal, inclined and vertical slug flow. The model has been tested against experimental data available from the literature and was found to predict the effects of liquid and gas flow rates and their physical properties, as well as tube diameter and inclination.

An investigation on void fraction of vapor–liquid two-phase flow for smooth and microfin tubes with R134a at adiabatic condition

The present paper deals with experiments and a prediction method for the void fraction of R134a vapor–liquid two-phase flow in horizontal smooth and microfin tubes in adiabatic condition. The void fraction is measured by the quick closing valve method. The smooth tube tested is 1024 mm in length and 7.52 mm in inside diameter. The microfin tube tested is 1015 mm in length and 8.86 mm in mean inside diameter; the fin height is 0.18 mm, the helix angle of fins is 25° and the total number of fins are 70. The experiments were carried out in the range of vapor quality from 1% to 96%, where the pressure was kept at 1.2 and 0.8 MPa and the mass flow rate was kept at 20 and 40 kg h −1. It is confirmed that the void fraction for smooth tube is well correlated by the Smith or the Baroczy correlations. It is also shown that the void fraction in the microfin tube is lower than that of smooth tube in any quality and the prediction results using previous correlations for smooth tube are higher than the present experimental data of microfin tube. The void fraction prediction method consisting of a stratified-annular flow model and an annular flow model is proposed. In the stratified-annular flow model, it is assumed that most of liquid flows at the bottom of the tube and all grooves are filled with additional liquid. The momentum equations are constructed for regions of vapor, main liquid flow at the bottom and additional liquid flow in grooves, respectively. These coupled equations are solved numerically. In the case of annular flow model, it is assumed that all grooves are filled with liquid uniformly. The momentum equations in the vapor and liquid flows in grooves are also solved numerically. The values of the predicted void fraction are in good agreement with experimental data in high vapor quality region, while the predicted values are slightly smaller than experimental ones in low vapor quality region.

Void Fraction and Critical Power Assessment of CORETRAN-01/VIPRE-02

CORETRAN-01 is the Electric Power Research Institute core analysis computer program that couples the neutronic code ARROTTA to the thermal-hydraulic code VIPRE-02 to achieve an integrated three-dimensional representation of the core for both steady-state and transient applications. The thermal-hydraulic module VIPRE-02, the two-fluid version of the one-fluid code VIPRE-01, has been the object of relatively few assessment studies, and the work presented seeks to reduce this lacuna. The priority has been given to the assessment of the void fraction prediction due to the importance of the void feedback on the core power generation. The assessment data are experimental void fractions obtained from X- and gamma-ray attenuation techniques applied at assembly-averaged as well as subchannel level for both steady-state and transient conditions. These experiments are part of the NUPEC (Japan) program where full-scale boiling water reactor (BWR) assemblies of different types, including assemblies with part-length rods, and pressurized water reactor subassemblies were tested at nominal reactor operating conditions, as well as for a range of flow rates and pressures. Generally, the code performance ranged from adequate to good, except for configurations exhibiting a strong gradient in power-to-flow ratio. Critical power predictions have also been assessed and code limitations identified, based on measurements on full-scale BWR 8 × 8 and high-burnup assemblies operated over a range of thermal-hydraulic conditions.

Structure of vertical downward bubbly flow

In view of the great importance to two-fluid model, structure of downward bubbly flows in vertical pipes has been discussed intensively based on available data sets of local flow parameters including extensive air–water data sets recently measured by the authors. In this study, an approximate radial phase distribution pattern map has been proposed based on available data sets, and radial profiles of local flow parameters such as void fraction, interfacial area concentration, interfacial velocity, and bubble Sauter mean diameter have been discussed in detail. The one-dimensional drift-flux model for a downward two-phase flow and the correlation of the interfacial area concentration have been compared with the downward flow data. The correlations applicable to the predictions of one-dimensional void fraction and interfacial area concentration for a downward bubbly flow have been recommended by the comparison.

Interfacial heat transfer during subcooled flow boiling

In order to develop a mechanistic model for the subcooled flow boiling process, the key issues which must be addressed are wall heat flux partitioning and interfacial (condensation) heat transfer. The sink term in the two-fluid models for void fraction prediction is provided by the condensation rate at the vapor–liquid interface. Low pressure subcooled flow boiling experiments, using water, were performed using a vertical flat plate heater to investigate the bubble collapse process. A high-speed CCD camera was used to record the bubble collapse in the bulk subcooled liquid. Based on the analyses of these digitized images, bubble collapse rates and the associated heat transfer rate were determined. The experimental data were in turn used to correlate the bubble collapse rate and the interfacial heat transfer rate. These correlations are functions of bubble Reynolds number, liquid Prandtl number, Jacob number, and Fourier number. The correlations account for both the effect of forced convection heat transfer and thickening of the thermal boundary layer as the vapor bubble condenses which in turn makes the condensation heat transfer time dependent. Comparison of the measured experimental data with those predicted from the correlations show that predictions are well within ±25% of the experimentally measured values. These correlations have also been compared with those available in the literature.

Void fraction prevision in LCM parts

The formation of defects during the LCM processing of composite parts depends on various injection parameters. Industrial users need to realize pieces with good physical and mechanical properties and appearance. This requires to predict what is named a “processability window”. This term defines a range of parameters which will ensure a nearly absence of defects. Knowing that most of the defects created during an injection are voids, a bibliographical background about the formation and removal of these voids is presented. An original model of void fraction prediction is developed. This model is based on an empirical analysis of void formation and of the flow behaviour. An experimental qualitative validation of the model is presented.The proposed model can be used as an effective prediction tool at the design stage of a composite part.

Assessment of the ATHENA Code for Calculating the Void Fraction of a Lead-Bismuth/Steam Mixture in Vertical Upflow

Lead-bismuth is currently being considered as a coolant for fast reactors designed to produce low-cost electricity as well as burn actinides. Lead-bismuth fluid properties have been added to the ATHENA code so that it can be used in the thermal-hydraulic analysis of lead-bismuth-cooled reactors. The capability of ATHENA to calculate the void fraction of a two-component, two-phase mixture of liquid lead-bismuth and steam in cocurrent upflow was assessed using the El-Boher and Lesin void correlation. The assessment showed that the drift flux correlations currently available in the code predicted trends that were in reasonable agreement with the El-Boher and Lesin void correlation, but the predicted void fractions were significantly too high. For example, the Kataoka-Ishii correlation, which was the best of the available correlations, predicted void fractions that were up to 30% greater than the values from the El-Boher and Lesin correlation. Consequently, the El-Boher and Lesin correlation was implemented in a modified version of ATHENA. The implementation was complicated by the fact that the El-Boher and Lesin correlation was an explicit correlation for void fraction rather than a drift flux correlation. An approach was developed so that the code’s basic drift flux formulation could be used to easily implement an explicit void correlation. The predictions of the modified code were in excellent agreement with the El-Boher and Lesin void correlation.

902 様々な流路における沸騰二相流の乱流構造とボイド率分布の解析(GS-6 熱工学)

Analyses were carried out on turbulence structure and void fraction distribution in boiling two-phase flow for various channel geometries. Basic conservation equations of mass, mometum and energy and turbulence in boiling two-phase flow were solved couppled with basic equation of void fraction distribution. Turbulence source terms of two phase flow were considered and fully two-way coupling model between gas and liquid chases used. The results show that bubble number density and void fraction distributions in boiling two-phase flow in rectangular channel has sharp wall peak in the central region of the channel whereas it has flattened distribution near wall region which reasonably agree with experimental observation. It is indicated that multi-dimensional turbulence structure is quite important in predicting void fraction distribution in boiling two-phase flow.

Prediction of Gas Phase Volumetric Variations In Diphasic Reservoir Oils

Abstract The gas and liquid phases present in diphasic mixtures often have distinctly different physical properties. Hence, the ability to predict the changes in their relative saturation as the conditionsvary during their flow in a conduit or in the porous media is highly desirable. This work presents analytical expressions relating the gas phase volume variations with physical properties of the reservoiroils. It was established that the gas phase volume variations, as pressure changes, can be correlated with the saturation pressure of the fluid and the dimensionless pressure regardless of thetemperature and the kind of fluid at conditions far from the critical state. These equations proved to provide the volume variations with remarkable accuracy and can be applied to surface separation processes, surface multiphasic pumping and flowmetering and e prediction of variations in the phase saturation in the reservoir. Introduction In several petroleum engineering applications gas and oil coexist, having established equilibrium either in the pores of the reservoir or as they flow in the production tubing or t1rrough the pipes and the surface separation unit. As a result of the reservoir depletion or of the fluid flow, the pressure of the system varies with time and distance. Hence, it is considered useful to be able to estimate the influence that the pressure change bears on the gas phase volume, acting both with the compressibility of the gas and with the incremental volume of the condensed liberated gas. This piece of information helps to evaluate variations of the fluid saturationsn the reservoir and the possible displacement of fluid interfaces, under certain conditions, during depletion or prolonged testing. For the applications concerning the flow at the surface, it can be used to determine the variations of the flowrates of each phase and consequently, the phase cuts as the stream passes through valves and restrictions and is subjected to subsequent pressure drops. The prediction of the gas void fraction (GVF) at operating pressure is reported as a key parameter in the design of the recently developed subsea multiphase pumping systems (1). The change of the gas phase volume can be quantified in two ways:as the fractional change that the fraction Vfg of the total volume of a mixture occupied by the gas phase undergoes as the pressure drops:Equation (1) Available In Full Paper.as the fractional change of the gas volume Vg of a mixture as the pressure changes: Equation (2) Available In Full Paper. The first expression relates the change of the gas volume to the total volume of the mixture and is used to express the change in the gas phase cut. The second expression, however, deals exclusively with the changes in the volume of the gas phase and is used to express the incremental volume of gas available in the system. Obviously the fractional changes of Vfgand Vg obtain the same values when a given mass of a mixture continues to occupy practically the same volume (Vt1, Vt2 even after it was subjected to a pressure change Δp.

Pressurized Water Reactor Fuel Assembly Subchannel Void Fraction Measurement

The void fraction measurement experiment of pressurized water reactor (PWR) fuel assemblies has been conducted since 1987 under the sponsorship of the Ministry of International Trade and Industry as a Japanese national project. Two types of test sections are used in this experiment. One is a 5 x 5 array rod bundle geometry, and the other is a single-channel geometry simulating one of the subchannels in the rod bundle. Wide gamma-ray beam scanners and narrow gamma-ray beam computed tomography scanners are used to measure the subchannel void fractions under various steady-state and transient conditions. The experimental data are expected to be used to develop a void fraction prediction model relevant to PWR fuel assemblies and also to verify or improve the subchannel analysis method. The first series of experiments was conducted in 1992, and a preliminary evaluation of the data has been performed. The preliminary results of these experiments are described.

Predictions of Void Fraction in Convective Subcooled Boiling Channels Using a One-Dimensional Two-Fluid Model

Subcooled nucleate boiling under forced convective conditions is of considerable interest for many disciplines, such as nuclear reactor technology and other energy conversion systems, due to its high heat transfer capability. For such applications, the liquid entering the heating channel is usually in a subcooled state and nucleate boiling is initiated at some distance from the entrance. Further downstream from the boiling incipient point, the bubbles may depart from the heating wall. The point of first bubble departure is called the net vapor generation (NVG) point, because after this point, significant void is present in the subcooled liquid and the void fraction rises very rapidly even though the bulk liquid may still be in a highly subcooled state. The presence of vapor bubbles, which are at a temperature near the saturation temperature, in a subcooled liquid shows the existence of thermal nonequilibrium, which complicates the analysis of this boiling regime. 13 refs., 4 figs.

Void Fraction Distribution in BWR Fuel Assembly and Evaluation of Subchannel Code

Void fraction measurement tests for BWR fuel assemblies have been conducted as part of a Japanese national project. The aim was to verify the current BWR void fraction prediction method. Void fraction was measured using an X-ray CT scanner. This paper describes typical results of void fraction distribution measurements and compares subchannel-averaged void fraction data with current subchannel analysis codes. The subchannel analysis codes COBRA/BWR and THERMIT-2 were used in this comparison. The agreement between data for an actual BWR fuel assembly with two unheated rods was good, but in the case of many unheated rods, the codes were unable to predict well large void fraction gradient in the radial direction observed in the measured data over the unheated rod region. The prediction errors of COBRA/BWR and THERMIT-2 for the subchannel-averaged void fraction were (A) (average of difference between measurement and calculation)=-1.1%. σ (standard deviation)=5.3% and <A>=-2.2%, σ=6.3 %, respectively.

Level swell in pool boiling with liquid circulation

Level swell in pool boiling is overestimated by drift-flux equations for forced convection boiling. This is attributed to the presence in pool boiling of large slug-like bubbles and of bubble induced liquid circulation. These phenomena are analysed and a new drift-flux equation is presented which is specifically aimed at predicting void fraction in pool boiling. The correlation is compared to a set of experimental data and proves to be more accurate than other existing correlations.

Phenomenological model for dispersed bubbly flow in pipes

AbstractAn analytical approach to the problem of steady‐state, axisymmetrically disperesed, bubbly flow in pipes based on a zero equation turbulence model is discussed. The formulation incorporates recent experimental observations and introduces the effect of bubble size in a rudimentary way. The two‐phase mixture is modeled as a variabledensity single fluid assuming an empirical void distribution family. The turbulent shear stress is formed from the contributions of both the velocity and density variation, and the solution of the resulting Reynolds‐type equation yields the velocity profile of the flow. Predicted void fraction and velocity distributions agree well with experimental measurements. The main objective of the model is to predict the friction multiplier with minimal computational effort. The velocity profiles of this model agree reasonably well with experiments. Predictions for the friction multiplier are compared to six known and widely used correlations, as well as to experimental data. All the correlations severely underpredict the friction multiplier in the disperesed bubbly flow regime, while the results of our model agree well with the measurements, within the range of its validity.

Void Fraction Distribution in BWR Fuel Assembly and Evaluation of Subchannel Code.

Void fraction measurement tests for BWR fuel assemblies have been conducted as part of a Japanese national project. The aim was to verify the current BWR void fraction prediction method. Void fraction was measured using an X-ray CT scanner. This paper describes typical results of void fraction distribution measurements and compares subchannel-averaged void fraction data with current subchannel analysis codes. The subchannel analysis codes COBRA/BWR and THERMIT-2 were used in this comparison. The agreement between data for an actual BWR fuel assembly with two unheated rods was good, but in the case of many unheated rods, the codes were unable to predict well large void fraction gradient in the radial direction observed in the measured data over the unheated rod region. The prediction errors of COBRA/BWR and THERMIT-2 for the subchannel-averaged void fraction were (A) (average of difference between measurement and calculation)=-1.1%. σ (standard deviation)=5.3% and <A>=-2.2%, σ=6.3 %, respectively.

Prediction of liquid level distribution in horizontal gas-liquid stratified flows with interfacial level gradient

A one-dimensional momentum equation has been derived based on a two-fluid model and used to predict the axial distribution of liquid level or void fraction in steady, cocurrent, gas-liquid stratified flows in horizontal circular pipes and rectangular channels. The equation is carefully formulated to incorporate the effect of interfacial level gradient. Two different critical liquid levels are found from the momentum equation and are adopted as a boundary condition to calculate the liquid level or void fraction distribution upstream of the channel exit. The predicted void fraction distributions are compared with the experimental data obtained in a rectangular channel in this work and other data reported for large-diameter pipes. Good agreement is shown for air-kerosene, air-water and stream-water stratified flows with a smooth gas-liquid interface.

An improved method for void-fraction measurement using gamma-transmission gauge

On the basis of gamma-transmission measurements, an iterative method has been established previously to better determine the void fraction in two-phase flow. In order to further improve the accuracy of the experimental results, a simple ring model is proposed to correct for the void-distribution effect. This method is tested by a series of benchmark experiments designed according to two fundamental void-distribution types. The results show that the accuracies of void-fraction predictions can be significantly improved by this modified method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A phenomenological model of the thermal hydraulics of convective boiling during the quenching of hot rod bundles. Part III: Model assessment using Winfrith steady-state, post-CHF, void-fraction and heat-transfer measurements and Berkeley transient-reflood test data

Alter completion and assessment of the thermal-hydraulic model developed in companion papers, we performed further independent assessment calculations using recently available Winfrith steady-state, post-CHF, void-fraction and heat-transfer data, and Berkeley transient-reflood test data. This paper discusses the results of those calculations. The thermal-hydraulic model in the Transient Reactor Analysis Code, Modification 2 (TRAC/PF1-MOD2, or simply TRAC), was used to predict the axial variation of void fraction as measured in Winfrith post-CHF tests. The predictions for reflood calculations were reasonable. The model correctly predicted the trends in void fraction due to the effect of pressure and power, with the effect of pressure being more apparent than that of heat flux. The effects of pressure, test-section power, and flow rate on the axial variation of tube wall temperature are predicted reasonably well for a large range of operating parameters. The predicted precursory cooling rates in Berkeley transient-reflood tests were in reasonably good agreement with the measured data. For high-test section input powers, oscillations associated with the void-fraction predictions observed. The predicted quench-front velocities (rewetting velocities) and their variations along the test tube were also found to be in reasonably good agreement with measured data.