Radial Void Fraction Profiles Research Articles

Understanding two‐phase flow behaviour: CFD Assessment of silicone oil–air and water–air in an intermediate vertical pipe

AbstractThe study utilized computational fluid dynamics (CFD) simulations employing the volume of fluid (VOF) model to analyze silicone oil–air flows in a vertical pipe with a diameter of 67 mm. Various structured meshes ensured grid independence, and the k‐ε realizable model addressed turbulence. The analysis characterized bubbly to annular flows, involving the evaluation of flow patterns, radial void fractions, void fraction time series, probability density functions (PDFs), power spectral densities (PSDs), and mean void fractions. Results indicated a transition from bubbly to annular flow with increasing gas velocities and notable changes in radial void fraction profiles. Void fraction exhibited significant variations with distinct flow patterns at constant liquid velocity. PDFs identified flow regimes, and PSDs revealed frequency patterns. CFD results were validated against experiments, demonstrating good agreement. The validated CFD model was utilized to investigate radial gas velocities and pressure drops, revealing a shift from uniform velocity distributions to irregular patterns and a decrease in total pressure drop with an increase in gas superficial velocity. The model was also applied to a water‐air system to explore two‐phase flow behaviour. The impact of superficial gas velocity on flow patterns and radial void fractions was studied through numerical analysis and compared with the silicone oil‐air system. Results showed that at extreme gas velocities (0.06 and 5.53 m/s), silicone oil exhibited bubbly and annular flows, while water displayed cap bubbly and churn flows. The significant variation in radial void fraction at these velocities emphasized the impact of fluid properties.

Assessment of State-of-the-art multiphase CFD modeling for subcooled flow boiling in reactor applications

Multiphase Computational Fluid Dynamics (M-CFD) has the potential to provide high fidelity simulation of complex boiling phenomena in Light Water Reactors (LWRs), thereby accelerating the development cycle and reducing the need for expensive large-scale experiments. M-CFD relies on two-phase closure models to consistently represent the relevant physical phenomena in flow boiling. However, the still incomplete understanding of the ability of these closures to accurately capture the underlying physics, limits the adoption of M-CFD in reactor development and design optimization. Due to the interaction of complex physical phenomena present in subcooled flow boiling, local measurements are necessary to assess the performance of existing closures. Furthermore, because previous validation was performed mostly on low pressure data, measurements at high pressure are needed to understand the performance of multiphase closures at PWR conditions. In this work, benchmarking was conducted using measured radial profiles of void fraction from subcooled flow boiling experiments of R12 refrigerant that reproduced density ratios and scaled flow conditions corresponding to PWR operation, called the DEBORA experiments. This work leverages recent advancements in momentum closures to perform a systematic assessment of the wall boiling representation by evaluating heat flux partitioning formulations and the associated closure relations. The influence and sensitivity of bulk boiling and condensation models were also evaluated. Using separate effect assessments and recent advancements in experimental understanding, this work presents a closure representation that demonstrates consistent predictions and is applicable to prototypical PWR conditions, while identifying areas for future improvement.

Investigation of bubble parameters and interfacial heat transfer correlations based on radial void fraction profiles of R-134a subcooled boiling flows

Investigation of bubble parameters and interfacial heat transfer correlations based on radial void fraction profiles of R-134a subcooled boiling flows

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.

CFD modelling and validation of upward bubbly flow in an adiabatic vertical pipe using the quadrature method of moments

An Eulerian–Eulerian approach was investigated to model adiabatic bubbly flow with CFD techniques. In the framework of the OpenFOAM® software, a two-fluid model solver was modified to include a population balance equation, solved with the quadrature method of moments approximation to predict upward bubbly flow in vertical pipes considering the polydisperse nature of two-phase flow. Some progress have been made recently solving population balance equations in OpenFOAM® and this research aims to extend its application to the case of vertical pipes under different conditions of liquid and gas velocities. In order to test the solver for nuclear applications, interfacial forces and bubble induced turbulence models were included to provide to this solver the capability to correctly predict the behavior of the continuous and disperse phases. Two-phase flow experiments with different superficial velocities of gas and liquid are used to validate the model and its implementation. Radial profiles of void fraction, gas and liquid velocities, Sauter mean diameter and turbulence intensity are compared to the computational results. These results are in satisfactory agreement with the experiments, showing the capability of the solver to predict two-phase flow characteristics.

Detailed analysis of phase distributions in a vertical riser using wire mesh sensor (WMS)

This paper looks into the results of an experimental study concerned with the phase distributions of gas–liquid multiphase flows experienced in a vertical riser. Scale experiments were carried out using a mixture of air and silicone oil in a 6m long riser pipe with an internal diameter pipe of 67mm. A series of pipe flow experiments were performed for a range of injected air superficial velocities over the range 0.05–4.73m/s, whilst the liquid superficial velocities ranged from 0.05 to 0.38m/s. Measurements of cross-sectional void fraction and radial time averaged void fraction across a pipe section located 4.92m from the pipe flow injection were obtained using a capacitance wire mesh sensor (WMS). The data were recorded at a frequency of 1000Hz over an interval of 60s. For the range of flow conditions studied, the average void fraction was observed to vary between 0.1 and 0.83. An analysis of the data collected concluded that the observed void fraction was strongly affected by the gas superficial velocity, whereby the higher the gas superficial velocity, the higher was the observed average void fraction. The average void fraction distributions observed were in good agreement with the results obtained by other researchers. The accuracy and performance of void fraction correlations were carried out in terms of percentage error and Root Mean Square (RMS) error. Reasonably symmetric radial void fraction profiles were obtained when the air–silicone oil was fully developed, and the shape of the symmetry profile was strongly dependent on the gas superficial velocity. The data for air/water and air/silicone oil systems showed reasonably good agreement except at gas superficial velocity of 0.05m/s. A comparison of the experimental data was performed against a published model to investigate the flow structure of air–water mixtures in a bubble column. A satisfactory report was observed for radial void fraction profile (mean relative error is within 5.7%) at the higher gas superficial velocities.

Reprint of "CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations

Two-dimensional (2D) numerical simulations have been widely reported in the literature for qualitative, even quantitative, study of the complex gas–solids flow behavior in circulating fluidized bed (CFB) risers. It is generally acknowledged that there exist quantitative differences between 2D and three-dimensional (3D) numerical simulations. However, no detailed study evaluating such differences can be found for simulations of CFB risers. This paper presents 2D and 3D numerical simulations of three different CFB risers. Axial pressure gradients from both 2D and 3D simulations are compared with the experimental data. It has been clearly demonstrated that the 2D simulation cannot satisfactorily reproduce the 3D simulation results. A further comparison of radial profiles of void fraction and solids velocity for an axi-symmetric riser configuration is reported and the quantitative differences between 2D and 3D simulations are analyzed. In conclusion, 2D simulation is only recommended for qualitative evaluation and 3D modeling is recommended for predictive simulations.

CFD simulations of circulating fluidized bed risers, part II, evaluation of differences between 2D and 3D simulations

Two-dimensional (2D) numerical simulations have been widely reported in the literature for qualitative, even quantitative, study of the complex gas–solids flow behavior in circulating fluidized bed (CFB) risers. It is generally acknowledged that there exist quantitative differences between 2D and three-dimensional (3D) numerical simulations. However, no detailed study evaluating such differences can be found for simulations of CFB risers. This paper presents 2D and 3D numerical simulations of three different CFB risers. Axial pressure gradients from both 2D and 3D simulations are compared with the experimental data. It has been clearly demonstrated that the 2D simulation cannot satisfactorily reproduce the 3D simulation results. A further comparison of radial profiles of void fraction and solids velocity for an axi-symmetric riser configuration is reported and the quantitative differences between 2D and 3D simulations are analyzed. In conclusion, 2D simulation is only recommended for qualitative evaluation and 3D modeling is recommended for predictive simulations.

The dependence of wall lubrication force on liquid velocity in turbulent bubbly two-phase flows

Based on the significance of a computational fluid dynamics (CFD) simulation of dispersed two-phase flow systems in many engineering fields, especially in nuclear energy systems, extensive analytical and numerical studies of wall lubrication force for vertical upward turbulent bubbly two-phase flow are presented. An analytical expression of the wall lubrication force considering the effect of liquid velocity is developed and analyzed. A numerical methodology for evaluating the wall lubrication force coefficients is proposed, which is based on the assumption that the balance of the forces acting on a bubble perpendicularly to the flow direction determines the establishment of radial void fraction profiles. Wall lubrication force coefficients are determined based on a reasonable agreement in radial void fraction profiles between numerical results predicted by the CFD EAGLE (elaborated analysis of gas–liquid flows evolution) code and extensive experimental database in the open literature as well as experiments performed at the Korea Atomic Energy Research Institute-vertical air–water loop test facility. Liquid velocity dependence of wall lubrication force is clearly shown in both analytical and numerical ways in the present study, and new correlations are then proposed for the wall lubrication force coefficients.

Modeling Vertical Subcooled Boiling Flows at Low Pressures

Abstract An improved wall heat flux partitioning model at the heated surface was developed by Yeoh et al. This model, coupled with a three-dimensional two-fluid model and Multiple Size Group model, has led to satisfactory agreement being achieved between the model predictions and experimental measurements. Nevertheless, one shortcoming is the reliance on empirical correlations for the active nucleation site density in the wall heat flux partitioning model. This discrepancy brings about uncertainties, especially in appropriately evaluating the vapor generation rate, which greatly influences the model prediction on the axial and radial void fraction profiles within the bulk fluid flow. By considering the fractal model with the aforementioned subcooled boiling flow model in the absence of empirical correlations for the active nucleation site density, a comprehensive mechanistic model to predict vertically oriented subcooled boiling flows is developed. The proposed model is assessed against the experimental data of axial measurements of Zeitoun and Shoukri and the radial measurements of Yun et al. and Lee et al. for vertical subcooled boiling flows within annular channels. Improved model predictions are obtained when the model is compared against typically applied empirical correlations for active nucleation site density. Discussions on the agreement of other two-phase flow parameters are also presented.

Characterization of two phase flows in chemical engineering reactors

Most industrial processes like fermentation, hydrogenation, oxidation, water treatment, petrochemical, nuclear and aerospace involve intimate contact between continuous phase and dispersed phase. Bubble columns and external loop airlifts are commonly used in these operations. Although these reactors are widely used, and extensive research has been carried out there exists no perfect model to characterize the local hydrodynamics and mass transfer. Computational fluid dynamics has also evolved recently trying to model the flow and transfer within these reactors but a lot of results are conflicting. Besides, there is a need to validate these results with experimental work. This work is dedicated to the experimental methods of measuring the local parameters such as the gas hold-up, the bubble velocities, the liquid velocity, bubble sizes. Two intrusive methods are used in this study, hot film anemometry for measurements of liquid phase and bi-optic probe for the gas phase. Although intrusive methods may interfere with fluid flow, presently they are the most adapted for real industrial processes with opaque equipment walls and high gas hold-ups compared to non-intrusive methods such as imagery. In this study, an external loop airlift of 16.5 l capacity is used. Local variables are measured in the riser of an external loop airlift reactor in air/water medium. The results are presented in the form of the radial profiles of void fraction, bubble diameter, liquid velocities at superficial gas velocities ranging from 0.03 to 0.11 m/s. The axial variations of the same parameters are also investigated. The results suggest that the bi-optical probe and hot film anemometer can reliably predict flow characteristics in high gas hold up contactors.

Three-dimensional void space structure of activated carbon packed beds

The three-dimensional void space structure generated by piling active carbon grains has a large impact on the filter operation, through the modification of the transport properties inside the bed. To gain insight into the relation between morphology and transport properties, the three-dimensional void space structure of activated carbon packed beds was studied by X-ray microtomography coupled with image analysis. Image analysis algorithms allowing the determination of the total void fraction, the void size distribution and the radial void fraction profiles were developed. This methodology was used to characterize the void space structure of two filters with the same length but different diameters, 15 and 28 mm. Commercial granular activated carbon with average particle size close to 1 mm was used. The comparison of the void size distributions indicated that void sizes are almost normally distributed around only one maximum for the large filter, while the distribution has a more complex shape in the small filter. The radial void fraction profiles showed an increase of the void fraction from the center of the filter to the wall accompanied with an oscillatory behaviour at the small scale. Power spectrum of radial profiles of the large filter shows a characteristic length matching well with the carbon particle size, indicating that the carbon grains are uniformly packed in the bed. In the small filter, power spectrum suggests an uneven packing of grains. For both filters, the total void fraction measured by image analysis was very close to the value determined ‘physically’ knowing the carbon mass, bulk density and filter dimension.

High-resolution gas–oil two-phase flow visualization with a capacitance wire-mesh sensor

The application of a novel wire-mesh sensor based on electrical capacitance (permittivity) measurements for the investigation of gas–oil two-phase flow in a vertical pipe of 67 mm diameter under industrial operating conditions is reported in this article. The wire-mesh sensor employed can be operated at up to 5000 frames per second acquisition speed and at a spatial resolution of 2.8 mm. By varying the gas and liquid flow rates, different flow patterns, such as bubbly, slug and churn flow, were produced and investigated. From the images of gas void fraction distribution, quantitative flow structure information, such as time series of cross-sectional void fraction, radial void fraction profiles and bubble size distributions, was extracted by special image-processing algorithms.

CFD simulation of convective flow boiling of refrigerant in a vertical annulus

In this paper a convective flow boiling of refrigerant R-113 in a vertical annular channel has been simulated by a CFD (Computational Fluid Dynamics) code CFX. The Arizona State University (ASU) boiling flow experiments [Roy, R.P., Kang, S., Zarate, J.A., Laporta, A., 2002. Turbulent subcooled boiling flow—experiments and simulations. J. Heat Transfer 124, 73–93] in annular channel were used to check the simulation capability of the code CFX. In general a good qualitative agreement with experimental data was obtained. Radial profiles of void fraction, phase velocities, turbulent kinetic energy and temperature at one axial location were compared. The employed subcooled boiling model uses a special treatment of the wall boiling boundary, which assures the grid independent solution. A sensitivity analysis of several modelling parameters on the radial distribution of flow quantities has been performed. The sensitivity analysis highlighted the importance of correct description of the boiling boundary layer. To correctly predict the phase velocities in the near-wall region a new two-phase wall law has been used.

Application of high frame-rate neutron radiography to liquid-metal two-phase flow research

Liquid metal two-phase flows in metallic vessels were studied by using high frame-rate neutron radiography. Both a bubble column and a gas-lift loop arrangement have been considered. Liquid velocity field of two-phase flow in a flat bubble column with rectangular cross-section was measured precisely by the particle tracking velocimetry. In a gas-lift loop, simultaneous measurements of void fraction by using high frame-rate neutron radiography and four-sensor probe were also performed to observe the bubble-probe interaction. Asymmetric Abel inversion was applied to compare the radial void fraction profiles. Measured radial void fraction profiles obtained by neutron radiography and electrical conductivity probe agreed well with each other. From these measurements, the measurement error and basic characteristics of gas–liquid metal two-phase flow were clarified.

Measurements of liquid–metal two-phase flow by using neutron radiography and electrical conductivity probe

Neutron radiography and electrical four-sensor conductivity probe method were applied to measurement of liquid–metal two-phase flow. Visualization and measurements of nitrogen gas–molten lead bismuth two-phase flow were performed by using neutron radiography technique. Simultaneous measurements of void fraction by using high-frame-rate neutron radiography and four-sensor probe were also performed to observe the bubble–probe interaction. At the same experimental conditions, four-sensor probe was applied to the measurements of interfacial area concentration in radial direction. From the visualization of the two-phase flow, it turned out that cap bubbles or elongated slug bubbles were dominant at the superficial gas velocity of 1.1–38.3 cm/s and no stable Taylor bubbles were detected in this experiment. Measured radial void fraction profiles obtained by neutron radiography and electrical conductivity probe agreed well with each other. From these measurements, the measurement error and basic characteristics of gas–liquid–metal two-phase flow were clarified.

Bubble size effect on low liquid input drift–flux parameters

We investigated the effect of bubble size on the drift–flux parameters at low liquid flow conditions by measuring the radial profiles of void fraction and phase velocities in a vertical bubbly pipe flow of diameter D p=72 mm and height H=18 m . To study the effect of the bubble size we used two different types of bubble inlets. We measured the local bubble fraction and velocity U g by using single and four-point-optical fibre probes, and we used Laser Doppler Anemometry to determine the liquid velocity U l . The distribution parameter C 0 and the weighted mean drift velocity | U drift| were directly computed from the local measurements at a height h=5 m on our experimental set-up. Both parameters were influenced by the bubble size. Provided no liquid flow reversal occurred at the near wall region, the distribution parameter reached a below unity minimum plateau value of C 0=0.95 for wall peaking void fraction profiles. At low liquid input conditions both the liquid input and bubble size had an influence on the distribution parameter. Extreme values such as C 0>2 were measured. From these measurements we developed models for the drift–flux parameters to take into account the effect of bubble size and input-flow conditions for our intermediate pipe diameter value. These models were tested and validated with separately collected experimental data.

Measurements of local interfacial area: application of bi-optical fibre technique

Local mean interfacial area in gas–liquid bubbly flow is experimentally investigated; data is obtained from the experiments carried out with a double optical sensor intrusive probe and analysed by statistical methods. Local variables are measured in the riser of an external loop airlift reactor in air/water medium. The results are presented in the form of the radial profiles of void fraction, bubble diameter and local average interfacial area at superficial gas velocities ranging from 0.003 to 0.11 m/ s . The axial variations of the same parameters are also investigated. The values of local interfacial area obtained from the classical equation ( a i t=6ε g/ d 32 ) and from bubble velocity statistical treatment methods agree reasonably well. This shows that the double optical probe is a reliable method for local measurements of interfacial area. Eventually, the maximum angle α 0 between the probe vertical direction and bubble velocity vector at the piercing point is evaluated and the influence of gas superficial velocity on α 0 is demonstrated.

Gas flow and heat transfer through catalyst filled tubes

A detailed knowledge of the fluid flow profile and of the radial heat transfer parameters is essential for a proper design of fixed-bed processes. For different sphere, ring and cylinder catalysts radial velocity profiles were measured below the fixed-bed at empty tube velocities of air between 0.5 m·s −1< v 0<1.5 m·s −1 and tube to particle diameter ratios 3.3< d t/ d P<11. As a consequence of the statistical behaviour of packings, it was necessary to average velocity measurements after repacking in order to obtain representative flow profiles. All profiles show a velocity maximum in the vicinity of the wall. In order to relate the measured profiles below the packing to the velocity profiles inside the packing, model simulations have been performed. The model is based on the extended Brinkman equation and the independently determined radial void fraction profiles. It considers an “effective viscosity” for which correlations have been derived for spheres, cylinders and rings. Radial heat transfer parameters were obtained experimentally from packings between two parallel plates of different temperatures. The determined heat transfer parameters can be transformed to the round cross section of a tube by considering the respective radial velocity profiles. The transformed values of the effective heat conductivity could be well described by literature correlations. For the heat transfer coefficient at the wall a new correlation was developed.

Fluid flow through catalyst filled tubes

A detailed knowledge of the fluid flow profile is essential for a proper design of fixed-bed processes. For different sphere, ring and cylinder sizes, radial velocity profiles were measured below the bed at empty tube velocities of air of 0.5 m/s < v 0 < 1.5 m/s and the tube-to-particle diameter ratios 3.3 < d t d P < 11 . The profiles show a velocity maximum in the vicinity of the wall. As a consequence of the statistical behaviour of packings, it was necessary to average velocity measurements after repacking in order to obtain representative flow profiles. These averaged profiles were the basis for a model through which the flow profile inside the packing can be calculated for spheres, cylinders and rings. The model is based upon the extended Brinkman equation and the independently determined radial void fraction profiles. It considers an ‘effective viscosity’ for which correlations have been derived. Comparison of simulated velocity profiles with exemplary liquid flow measurements inside the packed bed of Vortmeyer and co-workers shows reasonable agreement.