Radial Void Fraction Distribution Research Articles

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.

Computational Fluid Dynamics Modeling of the Pressure Drop of an Iso-Thermal and Turbulent Upward Bubbly Flow Through a Vertical Pipeline Using Population Balance Modeling Approach

Abstract A computational fluid dynamics (CFD) model of the two-phase flow is presented to simulate isothermal, turbulent, upward bubbly flow in a pipeline for the purpose of forecasting a mean pressure reduction along the pipe (a three-dimensional (3D) multiphase flow, by Eulerian–Eulerian strategy combined with population balance model (PBM)). A set of experimental data from the literature for water (liquid) and air (gas) in an isothermal pipe is used where the internal diameter of which is 200 mm; it tends to analyze radial void fraction and bubble diameter distributions as well as the axial pressure distribution of fluid flow. The CFD model is applied to grids of minimum control volumes. The interfacial forces, including nondrag and drag forces, where the former can be categorized into turbulent scattering, lift, and wall lubrication, have been noticed in simulations. The comparison between CFD forecasts with experimental data demonstrates that the coring phenomena plus observed wall peaking could be predicted with this CFD-PBM modeling approach. The primary aim of this study was to anticipate the axial pressure distribution of bubbly flow in the pipe by CFD modeling in a large vertical pipe. Acceptable agreement between models predictions and experimental data indicates that CFD can be a beneficial method for investigating pressure drop of an upward and multiphase flow.

Experimentally investigating bubble dynamics and pressure drop for bubbly upflow in a vertical annular channel

This paper experimentally investigates the bubble characteristics for a bubbly upflow in an annular channel using two-sensor probes and the high-speed camera. The measured parameters include the radial distributions of void fraction, interfacial area concentration, and bubble size. The present measured results are also compared with those from the previous work, confirming the reasonability of present data for the bubbly flow. A simplified two-phase frictional pressure-drop model is proposed to estimate the frictional pressure-drop across the annular channel for the bubbly upflow. Based on comparison with the measured data, the deviation in the two-phase frictional pressure-drop predicted by this simplified model is within 40%. In addition to providing the understanding of bubble dynamics in an annular geometry, the present measured data can also help develop and assess the CFD two-phase model.

Measurement of forced convection subcooled boiling flow and rod surface temperature distribution

In order to obtain high-resolution data for modelling of boiling two-phase flow and its validation, we designed and constructed a test loop with a vertical annulus flow path and conducted subcooled boiling experiments to investigate subcooled bubble incipience and its development process under atmospheric condition. Three kinds of the state-of-the art measurement techniques were applied to quantify key parameters such as radial and vertical distributions of void fraction, bubble velocity, interfacial area concentration (IAC), Sauter mean diameters, high-resolution temperature distribution on rod surface, bubble transport behavior, and turbulent velocity components as well as onset of nucleate boiling (ONB), and onset of significant void (OSV).

Influence of Interphase Forces on Onset of Fully Developed Subcooled Flow Boiling at High Pressure

Accurate prediction of the onset point of fully developed boiling (FDB) in subcooled flow boiling is crucial for the design of industrial equipment. In this work, Eulerian−Eulerian two fluid model incorporated with the Rensselaer Polytechnic Institute (RPI) wall boiling model was used to investigate high-pressure subcooled boiling flow, with particular attention to the model’s capability of objectively predicting the onset of FDB. After using the experimental data to verify the model, the present work covered a working range of P=6.81−15.5MPa, G=966−2123 kg/m2s, q=750−1500 kW/m2. Results show that the onset of FDB coincided with the inflection point on the axial distribution of boundary void fraction. Lift force had no obvious effect on axial distribution of mean void fraction but had a significant influence on radially local void fraction and determination of the onset of FDB. The turbulent dispersion force, wall lubrication force had a great influence on both axial and radial distribution of void fraction, directly affecting the onset of FDB. Performance of interphase force models in boiling flow was found to be different from that in adiabatic flow, and the underlying mechanism was further revealed. At last, the most feasible interphase force models for predicting onset of FDB were recommended.

Influence of Macroscopic Wall Structures on the Fluid Flow and Heat Transfer in Fixed Bed Reactors with Small Tube to Particle Diameter Ratio

Fixed bed reactors are widely used in the chemical, nuclear and process industry. Due to the solid particle arrangement and its resulting non-homogeneous radial void fraction distribution, the heat transfer of this reactor type is inhibited, especially for fixed bed reactors with a small tube to particle diameter ratio. This work shows that, based on three-dimensional particle-resolved discrete element method (DEM) computational fluid dynamics (CFD) simulations, it is possible to reduce the maldistribution of mono-dispersed spherical particles near the reactor wall by the use of macroscopic wall structures. As a result, the lateral convection is significantly increased leading to a better radial heat transfer. This is investigated for different macroscopic wall structures, different air flow rates (Reynolds number Re = 16 ...16,000) and a variation of tube to particle diameter ratios (2.8, 4.8, 6.8, 8.8). An increase of the radial velocity of up to 40%, a reduction of the thermal entry length of 66% and an overall heat transfer increase of up to 120% are found.

ON THE EFFECT OF FINE-SCALE RADIAL VOID DISTRIBUTIONS ON ASSEMBLY CRITICALITY AND PIN POWER DISTRIBUTION

The assumption that void fraction, and by extension coolant density, is uniform in the radial direction is a common approximation used in lattice physics simulations. In this study, models without uniform radial void fraction are used and lattice criticality and pin powers are investigated in two ways. One way uses hypothetical models that reflect extreme radial void distributions; modifications such as uniform radial pin enrichment and the removal of gadolinium rods are included in these models as well. Experimentally-determined boiling water reactor radial void distributions are also replicated in neutronics models using Serpent 2. It is found in the hypothetical models that the presence of gadolinium rods has a large effect on the interaction between lattice criticality and radial void distribution. It was also found that considering experimental radial void fraction distributions had the largest effect on the pin power of the rods containing gadolinium. Furthermore, it is observed that considering realistic radial void distributions, in general, decreased lattice criticality. The reason can be attributed that to the passive negative-feedback design of light water reactors. These are useful findings because calculation of more accurate peaking factors can lead to efficient and yet safer reactor operation.

Uncertainty Analysis on k-ε Turbulence Model in the Prediction of Subcooled Boiling in Vertical Pipes

Computational fluid dynamics (CFD) has become an effective method for researching two-phase flow in reactor systems. However, the uncertainty analysis of Computational fluid dynamics simulation is still immature. The effects of uncertainties from two-phase models and boundary conditions have been analyzed in our previous work. In this work, the uncertainties from a turbulence model on the prediction of subcooled boiling flow were analyzed with the DEBORA benchmark experiments by a deterministic sampling method. Seven parameters in the standard k-ε model, which interrelated momentum, energy, turbulent kinetic energy, and dissipation rate, were studied as uncertainty sources, including Cμ, Cμ,g, C1ε, C2ε, σk, σε, and Prt. Radial parameters were calculated to study the effects of uncertainties from the turbulence model. The contributions of each uncertainty source on void fraction and liquid temperature were also analyzed. It was found that the models can simulate subcooled boiling flow accurately and uncertainty analysis by deterministic sampling can give a reference interval to increase the reliability of results. The C2ε and C1ε, parameters in the production term and dissipation term of transport equations, dominate the radial distributions of void fraction and liquid temperature.

A multiscale approach to analyze the effect of radial void fraction distributions on BWR neutronic lattice parameters

The aim of this study is to analyze the effect of radial void fraction distribution, considered at three degrees of fidelity, on lattice k∞ and 2-group homogenized cross sections. The novelty of this work lies in its use of experimentally-determined radial void fraction distributions which allows for fine-scale coolant density data with no predictive uncertainty and which could be prohibitively expensive to simulate over the range of operational parameters used in the experiments. The experimentally-determined radial void fraction distributions are also characterized using a statistical tool called a semi-variogram in order to determine the scale of continuity. Void fraction distributions are averaged at the lattice and subchannel level for comparison with the fine-scale model. Models averaged at the subchannel and lattice level show a difference in k∞ about 68% of the time. Also, by comparing 2-group homogenized cross-sections, the differences between the subchannel and homogeneous cases are measurable.

Analysis of the effect of hydrodynamics over the activity and selectivity of the oxidative dehydrogenation of propane process in a packed bed reactor through CFD techniques

A study of the effect of hydrodynamics on the activity and selectivity of the oxidative dehydrogenation of propane (ODHP) of a non-isothermal Packed Bed Reactor (PBR) was implemented. 2D and 3D CFD models were employed, considering the mass, energy and momentum transport, and a 5-step oxidation Eley-Rideal kinetic model. The effect of the inclusion of porosity function was also carried out in order to capture non-homogeneities in the radial void fraction distribution on the predictive quality. The CFD model was validated against experimental and theoretical data reported in the literature. The validated model was used to perform a parametric sweep in order to determine the process inlet temperature which maximizes the conversion, selectivity and yield. The CFD model that considers the multiphysics in the ODHP led to an increase from 30% to 33% and from 20% to 24% in the conversion and the selectivity, respectively, which represents an increase of 22% and 20% with respect to the plug flow model. The 3D model exhibited a higher activity and reactivity respect to the plug flow model, similar to that reported for the membrane reactor. This reveals that incorporating hydrodynamics in all coordinates, results similar to dose one reactant, which emphasize the low predictive quality by using the plug flow model.

Liquid-phase turbulence measurements in air-water two-phase flows using particle image velocimetry

Liquid-phase turbulence plays a vital role in determining various gas-liquid two-phase flow parameters, such as void fraction distribution, bubble morphology, bubble-bubble interactions, and interfacial area concentration. In this study, a two-phase flow database including both the gas- and liquid-phases measurements was developed focusing on three bubbly flow conditions in an air-water two-phase flow loop with a vertical one-inch diameter circular pipe test section. A particle image velocimetry (PIV) system integrating an optical phase separation method, i.e., the planar laser-induced fluorescence (PLIF) technique using fluorescent particles and optical filtration, was applied to measure the liquid-phase turbulence information, including the time-averaged velocity, Reynolds stress, and turbulent kinetic energy for the liquid phase. The PIV measurements were taken at three ports along the test section at 14.5, 51.5, and 88.5 pipe inner diameters downstream of a bubble injector. In addition, a double-sensor conductivity probe was used to measure radial distributions of the local time-averaged void fraction and gas velocity. The measured liquid-phase turbulence was used to benchmark Sato's turbulence model considering the bubble-induced shear stress for the three tested bubbly flows. The benchmark results showed good agreement between the PIV measurements and model predictions. In the two bubbly flows tested that have low void fractions being less than 3%, the effect of the bubble-induced turbulence was found not significant. However, the bubble-induced shear stress becomes important with the increase of the void fraction.

Experimental study on local interfacial parameters in upward air-water bubbly flow in a vertical 6 × 6 rod bundle

This paper presents a complete database of the local two-phase flow parameters for upward adiabatic air-water two-phase flows in a vertical 6 × 6 rod bundle flow channel. A total of 16 flow conditions were selected and investigated at 16 measuring points in the octant triangular measuring region of a cross section at the position with height-to-diameter ratio of 149 (z/DH = 149) in the rod bundle experiment. The local void fraction, interfacial area concentration (IAC), bubble diameter and bubble velocity vector were measured by using the four-sensor optical probe measuring technique. In the measured cross-sectional distributions of local void fraction and IAC, both core-peaking and wall-peaking distribution shapes were observed and the distribution pattern trended to change from the core-peaking shape to the wall-peaking shape with the increase of superficial liquid velocity (〈jf〉) and the decrease of superficial gas velocity (〈jg〉). The radial distributions of local bubble diameter are nearly flat, which explains the similarity of the radial local void fraction and IAC distributions. The measured local bubble diameters increase with the increase of 〈jg〉 and the decrease of 〈jf〉. The bubbles move along the rod bundle flow channel with their velocity component in the main flow direction (vgz) showing a typical radial core-peaking profile and their velocity components in the cross section showing a significant movement from the central region to the channel box wall region especially under high superficial liquid velocities. The cross-sectional area-averaged results of the local parameters were obtained by a measuring-point-based graphical integration. The obtained area-averaged void fraction and IAC are compared with the predictions of the drift-flux model with its available 2 frequently-used distribution parameter and drift velocity correlations and the 2 recently-developed IAC correlations respectively. The applicability of the 2 drift-flux correlations and the 2 IAC correlations to the rod bundle flow channel is evaluated and analyzed.

110th Anniversary: Numerical Simulations of Gas–Liquid Two-Phase Flow in Vertical Pipe Implementing Population Balance Modeling

Population balance modeling in a gas–liquid two-phase bubbly flow allows us to predict the bubble size distribution. The prediction of bubble size distribution is of utmost importance as it prevails the heat, mass, and momentum transport mechanisms. In the present work, numerical simulations of gas–liquid two-phase flow in a vertical pipe have been performed using population balance modeling. The effects of different coalescence and breakage models have been studied. The wall peak and core peak case in the bubbly flow regime is considered for the prediction of the radial distribution of the gas void fraction, interfacial area concentration, bubble size distribution, Sauter mean diameter, and gas and liquid velocities. Numerical simulations were performed with the Euler–Euler two-fluid model and the k–ω SST turbulence model. The population balance equation is solved using the traditional class method. The combination of Brownian coalescence and Ghadiri breakage model is recommended for the prediction of th...

Neutronics modeling of bubbles in bubbly flow regime in boiling water reactors

Abstract This study mainly focused on the neutronics modeling of bubbles in bubbly flow in boiling water reactors. The bubble, ring and homogenous models were used for radial void fraction distribution. Effect of the bubble and ring models on the infinite multiplication factor and two-group flux distribution was investigated by comparing with the homogenous model. Square pitch unit cell geometry was used in the calculations. In the bubble model, spherical and non-spherical bubbles at random positions, sizes and shapes were produced by Monte Carlo method. The results show that there are significant differences among the proposed models from the viewpoint of physical interaction mechanism. For the fully-developed bubbly flow, k inf is overestimated in the ring model by about 720 ± 6 pcm with respect to homogeneous model whereas underestimated in the bubble model by about −65 ± 9 pcm with a standard deviation of 15 pcm. In addition, the ring model shows that the coolant must be separated into regions to properly represent the radial void distribution. Deviations in flux distributions principally occur in certain regions, such as corners. As a result, the bubble model in modeling the void fraction can be used in nuclear engineering calculations.

Rigid Body Dynamics Algorithm for Modeling Random Packing Structures of Nonspherical and Nonconvex Pellets.

Despite the common use of nonspherical catalyst pellets in chemical engineering applications, the packing structures of such pellets have not been as systematically studied and characterized as spherical packings. We propose a packing algorithm based on rigid body dynamics to simulate packing of nonspherical and possibly nonconvex pellets. The algorithm exerts a hard-body approach to model collision phenomena. The novelty is that the transition between moving and resting particles is controlled by a cutoff on the relative contact velocities, instead of artificially damping linear and angular velocities to stabilize the algorithm. The algorithm is used to synthesize packings of spheres, cylinders, and Raschig rings with tube-to-pellet diameter ratios 3–9.16. The packings are validated in terms of bulk porosity and radial void fraction distribution, finding satisfactory agreement with literature data. Denser packing structures are generated with high restitution coefficients and low friction coefficients. The confining tube walls play an important role, with highly fluctuating bulk porosities in narrow tubes.

Void fraction, bubble size and interfacial area measurements in co-current downflow bubble column reactor with microbubble dispersion

Microbubbles dispersed in bubble column reactors have received great interest in recent years, due to their small size, stability, high gas-liquid interfacial area concentrations and longer residence times. The high gas-liquid interfacial area concentrations lead to high mass transfer rates compared to conventional bubble column reactors. In the present work, experiments have been performed in a downflow bubble column reactor with microbubbles generated and dispersed by a novel mechanism to determine the gas-liquid interfacial area concentrations by measuring the void fraction and bubble size distributions. Gamma-ray densitometry has been employed to determine the axial and radial distributions of void fraction and a high speed camera equipped with a borescope is used to measure the axial and radial variations of bubble sizes. Also, the effects of superficial gas and liquid velocities on the two-phase flow characteristics have been investigated. Further, reconstruction techniques of the radial void fraction profiles from the gamma densitometry's chordal void fraction measurements are discussed and compared for a bubble column reactor with dispersed microbubbles. Empirical correlations are also proposed to predict the Sauter mean bubble diameter. The results demonstrate that the new bubble generation technique offers high interfacial area concentrations (1000–4500 m2/m3) with sub-millimeter bubbles (500–900µm) and high overall void fractions (10–60%) in comparison with previous bubble column reactor designs.

Void Fraction Measurement of Two Phase Flow in an External Air-Lift Loop with Middle Riser

Background/Objectives: The key objective of the present investigation is to study the void fraction distribution of two phase flow in a riser of an External Air-Lift Loop with middle riser and two downcomers on either side. Methods/ Statistical Analysis: Experimentation is performed to measure void fraction by using conductivity probe technique with the appropriate electrical processing circuit. The operating fluids considered were air and water. Air flow rate is varied from 0.00017 m3/s to 0.00116 m3/s with step interval of 0.0001 m3/s. The conductivity probe data obtained consists of qualitative change of voidage and radial distribution of void fraction. Findings: From the present investigation it is evident that the increase of air flow rate brings the more increase of void fraction. At all air flow rates void fraction got increased from centre of tube to the wall. Cubic profile is obtained at the high airflow rates, which is dependent again upon air flow rate. Different flow patterns were obtained from radial distribution of void fraction graph. Application/Improvements: By introducing the two downcomers to External Air-Lift loop, loop flow rate got increased and as a result the amount of water coming into the riser increased which resulted in lower averaged void fraction.

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.

Axial and radial void fraction measurements in convective boiling flows

This work is inspired by the need to have measurements and predictive capability on vertical saturated boiling flows, which are of importance in boiling water nuclear reactors. In these systems, sub-cooled water flows upwards in vertical tubes which contain a multiplicity of nuclear fuel rods, and the heat is taken away from these rods by natural convection boiling. A close analog of this situation exists when the liquid is in forced flow, and the heat flux from the vertical rods is quenched by forced convection boiling of the upward liquid water flux.In this work, we present experimental data has for axial, and radial vapor void fraction distributions in an annular boiling channel for low mass-flux forced the flow of water at high inlet sub-cooling. A single centrally placed electrical rod, designed to mimic the nuclear fuel rod has been used. The void fraction measurement is made using gamma ray densitometry technique. Axial and radial vapor void fractions have been reported, as a function of inlet liquid flux and inlet liquid temperature. The experimental data has been rationalized using a simple one-dimensional drift flux model adapted to the conditions of the experiment.

3D CFD simulation of flashing flows in a converging-diverging nozzle

Flashing of initially sub-cooled water in a vertical circular converging-diverging nozzle is simulated with two-fluid model incorporating drag and non-drag forces. Phase change is assumed to be induced only by interphase heat transfer while pressure jump across the interface is ignored. The reliability of CFD simulations is confirmed by comparison with experimental data and one-dimensional results basing on a drift-flux model. Satisfactory prediction of mass flow rate and cross-section averaged parameters is achieved. The predicted radial distribution of void fraction is however much more flat than the measured one. The discrepancy is found to be caused by the effect of lift force and the reversal of relative velocity. Cases characterised with large pressure-undershoot exhibit significant pressure non-equilibrium effect in form of a pressure recovery process. Sensitivity tests on bubble number density, heat transfer coefficient as well as nucleation are performed.