Axial Void Fraction Profile Research Articles

Experimental validation of the mechanism and condition for the onset of significant void in subcooled flow boiling

In evaluating the axial void fraction profile in the subcooled boiling region in heated channels, accurate determination of the point of onset of significant void (POSV) is of critical importance. Recently, it has been reported that the POSV can be predicted with high accuracy if the onset of significant void (OSV) is assumed to be caused by a sudden decrease in the interfacial area due to global bubble coalescence (GBC) leading to the formation of large bubbles. Therefore, in this work, experimental investigations were carried out to measure the void fraction, bubble size and bubble number density. The experimental results were utilized to validate the mechanism causing the OSV in subcooled flow boiling. The experimental results were in qualitative and quantitative agreement with the model based on the GBC concept. Thus, it was validated that the sudden decrease in condensation rate due to large bubble formation is the main cause of OSV. It was also confirmed that the GBC occurs when the local void fraction near the heated wall reaches about 0.3, analogous to the flow regime transition from bubbly flow to slug flow in adiabatic gas-liquid two-phase flows.

Void fraction thermo-kinematics for subcooled flow boiling

This work presents some preliminary results about a new void fraction model in subcooled flow boiling based on brand new mass and energy balances developed by the author over the past years. As main novelties, the new mass balance is based on the liquid velocity and the mixture specific volume, whereas the new heat balance is a function of the mixture enthalpy, based on the thermodynamic quality, and explicitly includes the mean vapor–liquid velocity ratio, or the slip ratio. The core of the model is to predict the slip ratio profile and then to calculate the mixture enthalpy from the new heat balance and, finally, to derive the void fraction. In this work, it is shown that the continuity of the first derivative of the mixture specific volume just at saturation establishes a first equation to obtain the slip evolution. A second kinematic equation between the onset of nuclear boiling (ONB) and the vapor velocity is also found. Three additional parameters, related to the ONB and the point of net vapor generation, are needed for void fraction profiles predictions, which have been found by trial and error, searching the best fitting to the measured void fraction. The new model is compared to eight full axial void fraction profiles data for upward subcooled flow of water at high pressure.

Direct numerical simulation study of end effects and D/d ratio on mass transfer in packed beds

Direct Numerical Simulation (DNS) was performed to investigate the end effects on mass transfer in a packed bed for Reynolds number (Re) ≤ 100. The system considered in this study was naphthalene-air with a Schmidt number (Sc) ∼ 2.52. The location of the spheres’ centers in a randomly packed bed were obtained from Discrete Element Method – Computational Fluid Dynamics (DEM-CFD) simulations. The influence of the confining wall on how packed bed ends affect mass transfer was studied by examining the axial void fraction profile with varying ratio of the column diameter to the particle sphere diameter (D/d). Overall, it was found that the confining wall has a significant impact. The ‘local’ mass transfer coefficient was calculated based on the obtained DNS results and the probability distribution curve and the spatial distribution of the computed ‘local’ Sherwood numbers as function of the ratio X/L (ratio of the height of the active part of the bed to the total height of the bed) were developed to quantify the end effects on mass transfer within packed beds. For a packed bed with no wall effects (D/d = 11), it was found that the end effects can be eliminated by replacing the active particles located at ∼2 sphere diameters from the entrance and ∼1 sphere diameter from the exit by inert particles.

3D DEM simulation and analysis of void fraction distribution in a pebble bed high temperature reactor

The current work analyzes the radial and axial distributions of void fraction of a pebble bed high temperature reactor. A three-dimensional pebble bed corresponding to our test facility of pebble bed type gas-cooled high temperature reactor (HTR-10) in Tsinghua University is simulated via discrete element method, and the radial and axial void fraction profiles are calculated. It validates the oscillating characteristics of radial void fraction near the wall. Detailed calculations show the differences of void fraction profiles between the stationary packing bed and the dynamically discharging bed. Based on the vertically and circumferentially averaged radial distribution and horizontally averaged axial distribution of void fraction, a fully three-dimensional analytical distribution of void fraction throughout the bed is established. The results show the combined effects of gravity and void variation in the pebble bed caused by the pebble discharging. It indicates the linearly increased packing effect caused by gravity in the vertical (axial) direction and the normal distribution of void in the horizontal (radial) direction by pebble drainage. These two effects coexist in the conical base of the bed whereas only the former effect exists in the cylindrical volume of the bed.

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.

Implementation of a Two-Phase Boiling Model into the RELAP5/MOD2 Computer Code to Predict Void Distribution in Low-Pressure Subcooled Boiling Flows

This paper demonstrates that the empirical models developed for subcooled flow boiling in RELAP5/MOD2 at high pressures are not valid for applications at low pressures. Modifications carried out in RELAP5/MOD2 to include better correlations of the interphase heat transfer and mean bubble diameter, and the wall heat flux partition model are shown to yield substantial improvements in the predictions of the axial void fraction distribution. When compared against experimental data covering a wide range of heat fluxes and flow rates, predicted axial void fraction profiles follow closely the measured data. Predictions made by the default subcooled boiling model show, however, an unacceptable margin of error with the experimental data.

Axial void fraction profile in low pressure subcooled flow boiling

Axial void fraction profiles in subcooled flow boiling in a vertical annulus were obtained using gamma attenuation techniques for different levels of mass flux, wall heat flux and inlet subcooling. A mechanistic model was developed to predict the axial void fraction profile. Various closure relationships were used and a new model, for dividing the wall heat flux between vapour generation and heating the subcooled liquid, was incorporated. The predictions of the proposed model were found to be in good agreement with the present experimental data, as well as other available data, on axial void fraction distribution in low pressure subcooled flow boiling. The proposed mechanistic model does not require prior identification of the location of the onset of significant voids.

Fluidized bed nuclear fission reactor

For the further development of nuclear fission reactors, the feasibility of a new concept is evaluated. It concerns a fluidized bed reactor in which carbon particles with a uranium core are fluidized and cooled by a high velocity pressurized helium flow. Nuclear reaction takes place if the bed is in fluidized conditions at a void fraction above 80% and it stops as soon as the bed is unfluidized, i.e. when no coolant flow is available. The feasibility has been evaluated by design calculations of the nuclear reactor physics and heat transfer, and by an experimental study of an appropriate large particle high velocity fluidized bed. During the experimental study, pressure measurements and γ-ray transmission measurements have been performed along the height of a Geldart D powder fluidized bed in a 38 cm diameter column. From these measurements, axial void fraction profiles have been calculated, the regimes have been analysed and the frequencies of the major bed fluctuations have been determined.

Drift-flux correlation disengagement models: Part II — Shape-based correlations for disengagement prediction via churn-turbulent drift-flux correlation

In Part I of this work the theoretical foundation was laid for predicting disengagement via volumetric gas production and an axial void fraction profile. Earlier work indicated for non-foaming systems one of the two drift-flux correlations can be chosen on the basis of viscosity. Herein, for the churn-turbulent drift-flux correlation (low-viscosity system), the dependence average void fraction and dimensionless superficial vapor velocity [1] on vessel shape (e.g., vertical cylinder, horizontal cylinder, or sphere) is explored. There is very little shape dependence and it is quantified below. A simple two-constant correlation is suggested, which satisfies the conditions at low and high dimensionless superficial vapor velocity conditions. Constants are given for vertical cylinders, horizontal cylinders, and spheres for the churnturbulent drift-flux correlation. The disengagement model is based on a constant energy generation per unit mass of liquid. Thus, the application to runaway reaction with vaporization is straightforward. The application of the correlation to reactive systems producing gas (i.e., gassy systems) and to those both producing gas and involving vaporization (i.e., hybrid systems) in non-constant cross-sectional area vessels is clarified here. Rating calculation equations are developed, and the calculations are illustrated. For a rating calculation, the maximum gas rate (based on vent capacity) is known. The calculation of maximum average void fraction (i.e., 1-fill ratio) and gas generation per unit of liquid is straightforward. Thus, the rate of reaction (i.e., gas generation) must be found to assure that the vent capacity is sufficient

Drift-flux correlation disengagement models: Part I — Theory: Analytic and numeric integration details

In the design of pressure relief systems for vessels containing liquid, the phase of the flow through the vent line is very important. Mounting the line on the top of the vessel does not necessarily guarantee all vapor flow. One must calculate whether vapor bubbles formed in the liquid will disengage before they reach the vent entrance. Disengagement can be predicted via an axial void fraction profile that is calculated based upon volumetric gas production. It is assumed that the liquid phase is continuous and that pseudo-steady state is reached. The disengagement model is based on a constant energy generation per unit mass of liquid. For non-foaming systems, one of two drift-flux correlations can be chosen on the basis of viscosity. The churn-turbulent drift-flux correlation is for low-viscosity systems, and the DIERS' viscous-bubbly drift-flux correlation is for high-viscosity system [1, 2]. This model reduces to a single ordinary differential equation (ode). Analytic integration results for this model are possible for constant cross-sectional area vessels (e.g., vertical cylinder) and non-unity distribution parameters Co [3–5]. If this calculation shows the bubbles do not disengage, either a partial differential equation model must be solved or the coupling equation must be used. The coupling equation uses the maximum void fraction (calculated from the ode) and ties together the vessel and vent models. The ode solutions relate the local and average void fractions to the dimensionless superficial vapor velocity. For the churn-turbulent drift-flux correlation, explicit relationships are presented for the first time. They validate the earlier approximation of Fauske et al. [6] (see also Ref. [3]). For the DIERS' viscous-bubbly drift-flux correlation, implicit relationships are presented for the first time in the open literature. The earlier approximation of Fauske et al. [6] (see also Ref. [7]) fit the data, but is different than these integration results. Further work is in progress to refit the data [8] and to clarify the best model to use. For non-constant cross-sectional area vessels (e.g., horizontal cylinders and spheres), the analytic integration is difficult, but numeric results have been presented [3, 7]. The details of the numeric integration are presented and discussed here. As the cross-sectional area converges (toward the top of the vessel), the vapor concentration (i.e., the void fraction) and velocity increase. The maximum local void fraction occurs at the top of the vessel. Numerical difficulties are encountered as a result of the cross-sectional area going to zero at the bottom and top of the vessel. The pseudo-steady-state model imposes void fractions of minimum and maximum at these extremes (i.e., 0 and 1/Co).

Determination of Time-Dependent Void Fraction Distribution in Bubbly Two-Phase Flow by A Real-Time Neutron Radiography Technique

Radiographic images generated by the real-time neutron radiography system (RTNR) are analyzed by customized image processing software of the determination of instantaneous void fraction distribution. The cross-sectional averaged axial void fraction profiles and the two-dimensional void fraction profiles are determined simultaneously for each image. Various flow regimes are generated to determine if the RTNR system can accurately predict the void distribution in the radial, axial, and temporal coordinates. The results show the RTNR system correctly determines the void fraction distribution for each flow regime; however, accuracy decreases with decreasing void fraction. For net water thicknesses > 1.0 cm, the accuracy decreases with increasing water thickness due to the extreme sensitivity of thermal neutron interactions with light water. Heavy water is a more suitable fluid than light water for void fraction measurements in large-diameter flow systems.

DIERS bubbly disengagement correlation extended to horizontal cylinders and spheres

Abstract Numeric solutions are given for the DIERS (Design Institute for Emergency Relief Systems) bubbly disengagement model (i.e. the axial void fraction profile under volumetric heating model). Vertical cylinders, horizontal cylinders, and spheres with a non-unity distribution parameter (C0) were investigated. Disengagement in horizontal cylinders and spheres is predicted at the same or lower void fractions than for vertical cylinders (i.e. the solution for the vertical cylinder is conservative). These solutions do not agree well with the earlier vertical cylinder approximation of Fauske et al. Significantly lower void fractions at disengagement are predicted with this model than with the approximation. Since the approximation is a fit to experimental data, it should continue to be used. These results contrast with the early results for the churn-turbulent correlation where little dependence on vessel shape and good agreement with the DIERS approximation were found.

DIERS churn—turbulent disengagement correlation extended to horizontal cylinders and spheres

For a vertical cylinder and non-unity distribution parameter ( C 0 ), an analytical solution is given for the DIERS (Design Institute for Emergency Relief Systems) churn—turbulent disengagement model (i.e. axial void fraction profile under volumetric heating model). This solution validates the earlier approximation of Fauske et al. 1 . Horizontal cylinders and spheres were investigated using numerical integration and the results plotted against a generalized dimensionless superficial vapour velocity. Thus, the analytical solution is shown to hold for varying cross-sectional vessels. Therefore, this correlation predicts liquid disengagement regardless of vessel shape. An alternative correlation form is introduced, and examples for design and for rating are included.