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Multiphase computational fluid dynamics (CFD) simulation is a useful tool to study the hydrodynamics in a bubble column, if appropriate closure models are known. Systematic assessment of different models is an ongoing venture that benefits from improved validation data. The present study accumulates a database on three-phase flow experiments in a bubble column. This is achieved by using a combination of Particle Image Velocimetry and Shadowgraphy to measure the liquid velocity, solid velocity, solid concentration and gas dispersion properties simultaneously. This methodology is applied for different needle diameters, gas flow rates and particle concentrations. A detailed description of the experimental setup can be found in XXX. The experimental data (Table 1) described in this repository is structured into different folders and files as follows: Level 1: Folders classified by measurement configuration: TW_Jg_X_Di_YYY_C_ZZZ as outlined in Table 1 TW = Identifier Jg_X = Superficial gas velocity in mm/s Di_YYY = Inner diameter of the needle in µm C_ZZZ = Particle concentration * 100 in % Level 2: Folders classified by measurement height: Z_XXX Z_XXX = Measurement height in mm Level 3: csv files classified by their analysis parameter: Gas_Eg_ub_over_x.csv: Each csv file consists of five columns, namely the x-coordinate (in m), the gas holdup, the uncertainty of the gas holdup, the averaged bubble rising velocity (in m/s) and the corresponding uncertainty (in m/s). Liquid_v_z_over_x.csv: Each csv file consists of three columns, namely the x-coordinate (in m), the averaged liquid velocity (in m/s) and the corresponding uncertainty (in m/s). Solid_alpha_over_z.csv: Each csv file consists of three columns, namely t

This study investigates homogeneous flow in a bubble column up to 50% gas-holdup. For low to medium gas-holdup, the good performance of an established baseline model is confirmed. In this range, the mixture pressure gradient is decisive in determining the relative velocity, resulting in good predictions without considering swarm effects. However, beyond a gas-holdup of ~20%, a swarm corrector to the drag-force becomes necessary, for which several proposals from the literature are evaluated. In addition, the lift-force influences the shape of the gas-fraction profile depending on the bubble size, which has a significant impact on the liquid flow inside the column. For wall-peaked profiles, the liquid flow remains moderate, while center-peaked profiles strongly boost the liquid velocity. Finally, several mechanisms proposed in the literature for inducing unstable flow based on the lift-force, bubble-induced turbulence or flooding are investigated. Of these only the first gave qualitative agreement with the observed gas-holdup.

Turbulent multiphase jets appear in machines used for enhanced flotation processes like the Concorde Cell™ and the REFLUX™ Flotation Cell. Likewise, flows generated in conventional mechanically stirred rotor–stator cells bear strong resemblance to jets. In contrast to their single-phase counterparts however, they have not been extensively studied yet. The present contribution summarizes experimental and numerical methods that are available for this purpose, specifically shadowgraphy on the experimental side and the Eulerian multi-fluid framework for multiphase CFD simulations. Some specific questions that arose from preliminary application of these methods are highlighted which have not been addressed adequately so far. These concern bubbly twophase jets in the experiments,and simulations of both bubbly and particulate two-phase jets as well a three-phase jets in which both bubble and particles are presented.

This study investigates homogeneous flow in a bubble column up to a 50% gas holdup. For low to medium gas holdup the good performance of an established baseline model is confirmed. In this range, the mixture pressure gradient is decisive in determining the relative velocity, resulting in good predictions without considering the swarm effect. However, beyond a gas holdup of ~20%, a swarm corrector becomes necessary, for which several proposals from the literature are evaluated. In addition, the lift force influences the gas fraction profile depending on the bubble size. The resulting profile shape has a significant impact on the liquid flow inside the column. If the profile is wall-peaked, the liquid flow remains moderate, while a center-peaked profile strongly boosts the liquid velocity.

The prediction of solid-liquid flow in a pipe is of significance for a variety of industrial processes. Since the physical phenomena in such processes appear on widely differing length- and time-scales, many CFD methods are not quite cost-effective. The Euler-Euler multiphase approach makes it feasible to simulate such flows with reasonable computation time. The main challenge of this approach lies in the modeling of the interfacial momentum exchange between the phases, since the interface is not resolved. In this paper, a baseline model is validated that describes the interfacial forces (drag, virtual mass, (shear-) lift, wall (-lift), and turbulent dispersion) between solid particles and a liquid. This model is validated against experimental data of positively and negatively buoyant particles in a vertical pipe flow from the literature. The results show a reasonable agreement with the experimental data, except for the solid volume fraction distribution in the negatively buoyant particle cases. Possible reasons for this are discussed.

Bubble column reactors are one of the simplest and most representative system for multiphase flows. Regardless of its simple geometry, complex hydrodynamics and its effect on transport properties requires better understanding in order to accomplish a reliable design and scale-up of bubble column reactors. Although with many other parameters, co- or counter-current liquid flow is often used to adjust the residence-time of the bubbles, which is especially important when mass transfer is present in the system. The present study comprises of the initial stage numerical effort to study the hydrodynamics and also the parametric effect in counter current bubble column. For this purpose, simulations are performed within the Eulerian two-fluid framework using OpenFOAM as a CFD software and later the results are being compared with the experimental data.

The recovery of mineral ores greatly depends on the hydrodynamics in a froth flotation process. Turbulent jets are created inside a froth flotation cell to enhance mixing, and thus improve recovery of mineral particles. Computational Fluid Dynamics (CFD) simulations provide a means to study such two- or three-phase turbulent jet flows by using mathematical models. The purpose of the current work is to validate the Euler-Euler CFD simulations in OpenFOAM using a set of interfacial closure models to predict the behavior of multiphase turbulent jet flows. Previously, simulations using this framework and validations were carried out for bubble columns by Rzehak and Kriebitzsch (2015) and for stirred tanks with solid-liquid flows by Shi and Rzehak (2020). The baseline closure models employed include drag, shear lift, virtual mass, wall forces, and turbulent dispersion forces for the gas-liquid as well as the solid-liquid interactions. In the present contribution, new CFD simulations using this framework are reported and validated with experimental results from Sun and Faeth (1986) for bubbly jets pointing in upward direction, and from Parthasarathy and Faeth (1987) for particulate jets pointing in downward direction. Along the axial and radial direction of the jet, a reasonable agreement is observed between the experimental and simulation results. Extending the scope of the topic, an attempt is made to simulate also three-phase premixed turbulent jets using the individually validated combination of closure models for both gas-liquid and solid-liquid jets jointly in the same simulations. Suitable data to validate the overall closure models for premixed gas-solid-liquid three-phase turbulent jet flows are not available in the literature. Thus, the simulations for three-phase turbulent jets are carried out in the same setup as used previously for the gas-liquid and the solid-liquid turbulent jets. A parametric study is carried out for the interfacial forces and an attempt t

Bubble size and deformation are important factors for the closure models required in Euler-Euler simulations of bubbly flows. To properly simulate polydisperse bubbly flows where the bubble size spectrum may cover a range of several millimeters, several velocity groups with different sizes have to be considered. To this end, the theory for the particlecenter-averaged Euler-Euler model is generalized for the simulation with multiple bubble velocity groups. Furthermore, bubble deformation effects have been included in appropriate bubble force models. The particle-center-averaged Euler-Euler model provides additional freedom to consider the bubble shape during the conversion between the bubble number density and the gas volume fraction. Therefore, the theory is also generalized to consider an oblate ellipsoidal bubble shape in simulations. A bubbly pipe flow is used to validate the theory and to demonstrate the improvements of the proposed generalizations.

The Euler-Euler model is widely used in bubbly flow simulations up to industrial dimensions. The standard Euler-Euler model is based on the phase-averaging method. After averaging, the bubble forces in the field equations are functions of the local gas volume fraction. In simulations, when the bubble diameter is larger than the computational cell spacing, the forces can transport the gas belonging to the same bubble in different directions. By contrast, a closure model for the bubble force is typically developed based on the assumption that the force is a resultant force that acts on the bubble's center-of-mass. This inconsistency can lead to a nonphysical gas concentration in the center of a channel or near the channel wall if the bubble diameter is larger than the cell spacing. The purpose of the present contribution is to developed an Euler-Euler model where the bubble force consistency is recovered for two-phase flow simulations where the diameter of the disperse phase can be larger than the cell spacing. Such an Euler-Euler model is developed by combining an existing particle-center-averaged Euler-Euler framework with a Gaussian convolution method. To validate this Euler-Euler approach, a comparison is made with experimental data for the bubbly flows in two different vertical pipes. The results show that the proposed Euler-Euler model recovers the bubble force consistency and alleviates the over-prediction of the gas volume fraction peak near the wall, while its simulation results in the axial gas and liquid velocity and the liquid turbulence kinetic energy are similar to the results of the standard Euler-Euler model.

Turbulent multiphase jets appear in machines used for enhanced flotation processes like the Concorde Cell and the REFLUX Flotation Cell. Likewise, flow structures generated in conventional mechanically stirred rotor-stator cells bear strong resemblance to jets. In contrast to their single-phase counterparts however, they have not been extensively studied yet. In the invited talk we present experimental and numerical methods that are available for this purpose, specifically shadowgraphy and particle image velocimetry on the experimental side and the Eulerian multi-fluid framework for multiphase CFD simulations. The corresponding numerical approach pursued at HZDR is presented. First preliminary results of both bubbly and particulate two-phase jets as well a three-phase jets are presented.

Bubble columns are gas-liquid contactors that are used in many process-engineering applications. A counter-current liquid flow is frequently imposed to adjust the bubbles’ residence-time and thus optimize mixing and mass-transfer. The present work describes measurements in such a device together with corresponding computational fluid dynamics simulations based on the Eulerian two-fluid framework. Bubble-size and -velocity are measured by shadow-imaging for a large range of gas and counter-current liquid flow rates, as well as different nozzle sizes. The corresponding liquid flow-fields are characterized by Particle Image Velocimetry. From the large experimental database, a few cases are selected to analyze the flow structure and effects of the bubble-size. In the simulations, different models for the drag- and lift-force acting on the bubbles are evaluated. While good agreement between experiments and simulations could be achieved for the gas-fraction and gas-velocity, differences are found for the liquid-velocity, which is generally overestimated in the calculations.

Multiphase computational fluid dynamics (CFD) simulation is a useful tool to study the hydrodynamics in a bubble column if appropriate closure models are known. Systematic assessment of different models is an ongoing venture that benefits from improved validation data. The present study accumulates a database on two-phase flow experiments in a bubble column. This is achieved by using a combination of particle image velocimetry and shadowgraphy to measure the liquid velocity field and gas dispersion properties simultaneously. This methodology is applied for different needle diameters and gas flow rates. The experimental data are compared with CFD simulations which show good predictions. A systematic investigation of the three-phase flow in the bubble column will appear as a sequel.

The dynamics of a sub-millimeter air bubble rising at a bubble Reynolds number of about 100 in water in an inclined, laminar channel flow is investigated experimentally. In this configuration which is relevant in modern separation technologies for valuable particles, the bubble is undergoing a cross-stream motion, as the buoyancy force is not aligned with the undisturbed liquid flow. From measurements of bubble velocities and trajectories we estimate the drag and lift forces on the bubble at two different channel Reynolds numbers. The results are compared with their streamwise counterparts, i.e. in the configuration where the bubble rises largely along a streamline of the undisturbed liquid flow. For the lower channel Reynolds number, the cross-stream effects are only small. For the larger channel Reynolds number however, the drag coefficient is found to be notably larger than its streamwise counterpart. The lift coefficient may be either larger or smaller than its streamwise counterpart depending on the detailed local flow conditions. In particular, its value is non-zero when the bubble crosses the channel centerline where the shear rate is zero. These deviations are found to be closely connected with the bending of the bubble wake as well as the finite value of the angle formed between the bubble slip velocity and the velocity of the liquid flow.

Mass transfer in bubbly flows is important in many engineering applications. Simulation of such processes on technical scales is feasible by the Euler-Euler two-fluid model, which relies on suitable closure relations describing interfacial exchange processes. In comparison with the pure fluid dynamics of bubbly flows however, modeling and simulation of bubbly flows including mass transfer is significantly less developed. In particular, previous studies have focused entirely on absorption in upward vertical flows, whereas the present study considers a larger variety of conditions including desorption and counter-current (downward) flow. Suitable experimental data for comparison are available from the classic work of Deckwer et al. [Canadian Journal of Chemical Engineering 56 (1978) 43-55]. In line with previous studies on the co-current absorption cases from that work, a monodisperse approximation is made. In addition, a class method to treat bubble shrinkage and growth is implemented in the OpenFOAM code and tested by showing the crossover between two monodisperse cases.

This package contains the software and the trained models described in the publication "Hydrodynamics in a bubble column – Part 1: Two-phase flow". Please refer to the readme.md for installation instructions and to the Prediction_demo.ipynb for usage demonstration.

supplementary material for bubble trajectories

Results on modeling and simulation of flotation processes obtained by groups of Helmholtz-Zentrum Dresden-Rossendorf and Helmholtz Institute Freiberg for Resource Technologygroups are shown. These comprise a flotation kinetic model based on the multilayer structure and van der Waals interactions, and a hydrodynamic model using the Eularian multiphase framework. Unfortunately, a full validation of the combined model for data from a real flotation system was not possible yet due to numerical stability issues.

An inconsistency exists in bubble force models used in the standard Euler-Euler simulations. The bubble force models are typically developed by assuming that the forces act on the bubbles' centers of mass. However, in the standard Euler-Euler model, each bubble force is a function of the local gas volume fraction because the phase-averaging method is used. This inconsistency can lead to gas over-concentration in the center or near the wall of a channel when the bubble diameter is larger than the computational cell size. Besides, a mesh-independent solution may not exist in such cases. In addition, the bubble dimension is not fully considered in the standard Euler-Euler model. In the present study, a particle-center-averaging method is used to represent the bubble forces as forces that act on the bubbles' centers of mass. A particle-center-averaged Euler-Euler approach for bubbly flow simulations is developed by combining the particle-center-averaged Euler-Euler framework with a Gaussian convolution method. The convolution method is used to convert the phase-averaged and the particle-center-averaged quantities. The test results illustrate that the particle-center-averaging method alleviates the over-prediction of the gas volume fraction peak in the channel center and provides a mesh-independent solution. In the particle-center-averaged Euler-Euler model, the bubble dimension is fully considered and bubble deformation can be considered by using anisotropic diffusion in quantities conversion.

The standard Euler-Euler two-fluid modelling is based on the phase averaging method and the bubble forces are functions of the gas volume fraction. Therefore, it is not guaranteed that all the gas belonging to the same bubble experiences the same force and moves with the same velocity. However, closure models for interfacial forces are typically developed based on the assumption that the bubbles’ motion can be represented by their center-of-mass on which the forces act. This inconsistency can lead to a nonphysical gas concentration in the center of a pipe or near its wall if the mesh size is smaller than the bubble diameter. In addition, a mesh independent solution may not exist in such simulations. In the present contribution, a particle-center-averaged method is used to average quantities related to the disperse phase such that the bubble forces act on the bubble centers. A systematic approach for the simulation of bubbly flows using the particle-center-averaged method is developed by combining the HZDR baseline closure models, a diffusion-based method for the field coupling and the Euler-Euler framework using the particle-center-averaged method. A physically motivated model for the wall-contact force is introduced to ensure that the bubble centers cannot come arbitrarily close to the walls. To validate this approach, a comparison is made with experimental data for monodisperse and fixed polydisperse bubbly flows in two different pipes. The results show that the particle-center-averaged method can alleviate the over-prediction of the peaks in the gas volume fraction profiles in the near wall region.

Bubble column reactors are extensively used in a variety of industrial processes involving gas-liquid mass transfer along with chemical reactions. Despite intensive research, knowledge on the mass transfer is still limited in comparison with that on the fluid dynamics, which provides an open field of research. In this study, mass transfer of CO2 between air bubbles and water in a bubble column is investigated using Euler-Euler simulations in OpenFOAM. Previously validated fluid dynamics models are applied and focus is put on the description of the mass transfer. Experimental data to validate the results are taken from the study of Deckwer providing axial profiles of gas fraction, and carbon dioxide concentration in both phases. Previous work considering only cases with co-current absorption is extended to also include the cases with counter-current flow and desorption. Some simplifications are made in accordance with the previous work, i.e. taking the bubble diameter to be constant and using the experimentally determined values for the mass transfer coefficient. Despite these simplifications, the simulation results show a quite good agreement with the experimental data. As a second step, the change in bubble size due to the mass transfer is included in the simulations by means of a population balance equation discretized using the class method. The well-known model of Brauer is implemented as an example of a bubble size dependent mass transfer coefficient. Since experimental data including the development of bubble size are not available for comparison, an initial validation is provided by comparison of the polydisperse calculation with two monodisperse calculations corresponding to initial and final size in the former.

The dependence of froth flotation performance on various inter-related chemical, operational and instrumental components, makes optimizing a flotation system a very complex task. Computational Fluid Dynamics tools provide the means to study the flow inside a flotation cell by employing mathematical models that describe the interaction between the different phases of the system. The purpose of this work is to use Euler-Euler-Euler CFD simulations in OpenFOAM to validate a set of interfacial models to determine the hydrodynamics of a gas-solid-liquid flow. The combination of previously well validated baseline models for gas-liquid flows and solid-liquid flows is used for this purpose. The baseline combination includes drag, lift, wall, turbulent dispersion and virtual mass forces as well as bubble induced turbulence for gas-liquid interaction, and drag, lift, turbulent dispersion and virtual mass forces for solid-liquid interaction. Based on an extensive literature review of gas-solid-liquid experiments, the bubble column data of Rampure et al. are chosen for the numerical validation. Preliminary results show that the bubble diameter, which was not measured precisely, plays a significant role for the gas volume fraction distribution. Bubble diameter of 7 mm yields gas volume fraction profiles in agreement with the experimental data. The baseline combination yields higher particle suspension than indicated by the experimental data. This leads to a systematic study of the closure models. Choosing a model set similar to that of Rampure et al. improves the agreement of the solid distribution but deteriorates that of the gas distribution. It must be noted that, the high gas flow rate and high solid concentration likely require consideration of further aspects that are expected to have a significant effect on the flow. These may include a PIT model, a swarm corrector for the bubble and particle drag force, modifying the bubble drag force due to the existence of particles an

The understanding of gas-solid-liquid three-phase flow is very importnant for the development of Reflux Flotation Cell. CFD simulations of such flows are feasible even on industrial scales within the Eulerian framework of interpenetrating continua. The performance of the framework, however, relies on the suitability of the closure models to account for phenomena on the scale of individual particles or bubbles, which are not resolved in this approach. To this end, the present work attempts to combine closure relations that were previously established for two-phase gas-liquid and solid-liquid flows. Due to the complexity of the RFC system, CFD-grade data to evaluate the overall closure model for three-phase gas-solid-liquid flows are not available yet. Therefore, comparison is made with a dataset from Rampure et al. [Can. J. Chem. Eng. 81 (2003), 692-706] for a slurry bubble column. Agreement of the combined model with the data is not entirely satisfactory yet. Possible reasons concerning both modeling and experiment are discussed and directions for further research identified.

The standard Euler-Euler model is based on the phase-averaging method. Each bubble force is a function of the local gas volume fraction. As a result, the coherent motion of each bubble as a whole is not enforced when the bubble diameter is larger than the mesh size. However, the bubble force models are typically developed by tracking the bubbles' centers of mass and assuming that the forces act on these locations. In simulations, this inconsistency can lead to a nonphysical gas concentration in the center or near the wall of a pipe when the bubble diameter is larger than the mesh size. Besides, a mesh independent solution may not exist in such cases. In the present contribution, a particle-center-averaging method is used to average the solution variables for the disperse phase, which allows to represent the bubble forces as forces that act on the bubbles' centers of mass. An approach to simulate bubbly flows is formed by combining the Euler-Euler model framework using the particle-center-averaging method and a diffusion-based method that relates phase-averaged and particle-center-averaged quantities. The remediation of the inconsistency with the standard Euler-Euler model based on phase-averaging method is demonstrated using a simplified two-dimensional test case. The test results illustrate that the particle-center-averaging method can alleviate the over-prediction of the gas volume fraction peak in the channel center and provide mesh independent solutions. Furthermore, a comparison of both approaches is shown for several bubbly pipe flow cases where experimental data are available. The results show that the particle-center-averaging method can alleviate the over-prediction of the gas volume fraction peaks in the wall peaking cases as well.

Mass transfer in bubbly flows is a field of obvious technological importance. On industrially relevant scales it may be studied by simulations based on the Euler-Euler two-fluid model, which however requires closure models for the interfacial exchange processes. Despite recently increased efforts, modelling of the exchange of mass between the phases is still much less developed than the corresponding exchange of momentum. The present study compares several proposed models for the mass transfer coefficient using a previously established set of closure relations for the purely fluid dynamical part of the problem. A set of experimental data for the absorption of O2 into water in a bubbly mixing layer from the literature is used to assess their relative merits. A model for the pertinent material properties of this system has been assembled from available measurements. A rather sensitive dependence of the amount of absorbed O2 is found on the pressure, which varies with the hydrostatic head above the test section.

Simulations of solid-liquid flow on industrial scales are feasible within the Euler-Euler / RANS approach. The reliability of this approach depends largely on the closure models applied to describe the unresolved phenomena at the particle scale, in particular the interfacial forces. In this work, a set of closure models assembled previously for this kind of application (Shi and Rzehak 2020) is further validated by comparing the predictions to a recent experiment on stirred-tank flows (Sommer et al. 2021), which focuses on dilute suspensions. The dataset used for validation comprises 14 different experimental cases, covering a wide range of particle slip Reynolds number, impeller Reynolds number, and particle Stokes number. For each case, simulation results on the solid velocity and volume fraction as well as liquid velocity and turbulence are compared with the experimental data. It turns out that by and large the experimental data are reasonably well reproduced. However, the measurements show a small but clear effect of modulation of the liquid phase turbulence by the particles. Therefore, several particle-induced turbulence (PIT) models based on the available literature are assessed as well. Our results indicate a reduction in the predicted fluctuations by all PIT models, which improves the results in cases with turbulence suppression but deteriorates those with turbulence augmentation.

Current Euler-Euler modeling based on phase-averages shows inconsistencies since the finite size of the bubbles is not properly accounted for. As a result, nonphysical gas concentration can appear in the center or the near wall region of a pipe if the bubble diameter is larger than the mesh size (Tomiyama, Shimada et al. 2003). In addition, mesh independent solutions may not exist in these cases. By employing particle-center-averages (Prosperetti 1998), these inconsistencies can be remedied and mesh independent solutions are obtained. In this approach, the number density of bubble centers is the primary variable. This requires an additional wall-contact force to ensure that bubble centers cannot come arbitrarily close to walls (Lucas, Krepper et al. 2007). The gas volume fraction can be calculated from the number density by a convolution (Kitagawa, Murai et al. 2001) with a kernel that has a support corresponding to the extent of a bubble. In addition, the derivation shows explicitly that bubbles respond to pressure and stress of the continuous liquid phase such that no additional closure models for the gas phase pressure or stress are required. In the present contribution, the convolution method is replaced by a diffusion-based method (Sun and Xiao 2015), which is much easier to implement in CFD codes using unstructured meshes like OpenFOAM. A physically motivated model for the wall-contact force is introduced. The remedy of the issues with the conventional phase-averaged two-fluid model is demonstrated using a simplified two-dimensional test case. Furthermore, comparison is made for real pipe flow cases where experimental data are available. References Kitagawa, A., Y. Murai and F. Yamamoto (2001). "Two-way coupling of Eulerian–Lagrangian model for dispersed multiphase flows using filtering functions." International journal of multiphase flow 27(12): 2129-2153. Lucas, D., E. Krepper and H.-M. Prasser (2007). "Use of models for lift, wall and turbulent dispersion f

We report on a series of fully resolved simulations of the flow around a rigid sphere translating steadily near a wall, either in a fluid at rest or in the presence of a uniform shear. Non-rotating and freely rotating spheres subject to a torque-free condition are both considered to evaluate the importance of spin-induced effects. The separation distance between the sphere and wall is varied from values at which the wall influence is weak down to gaps of half the sphere radius. The Reynolds number based on the sphere diameter and relative velocity with respect to the ambient fluid spans the range 0.1 - 250, and the relative shear rate defined as the ratio of the shear-induced velocity variation across the sphere to the relative velocity is varied from -0.5 to +0.5, so that the sphere either leads the fluid or lags behind it. The wall-induced interaction mechanisms at play in the various flow regimes are analyzed qualitatively by examining the flow structure, especially the spanwise and streamwise vorticity distributions. Variations of the drag and lift forces at low-but-finite and moderate Reynolds number are compared with available analytical and semiempirical expressions, respectively. In more inertial regimes, empirical expressions for the two force components are derived based on the numerical data, yielding accurate fits valid over a wide range of Reynolds number and wall-sphere separations for both non-rotating and torque-free spheres.

Two-equation turbulence models based on the Boussinesq eddy viscosity hypothesis that have been used in the vast majority of previous simulation studies on bubbly pipe flows contain a term which renders the radial pressure distribution non-constant. In single phase simulations this effect is invariably absorbed in the definition of a modified pressure, from which the real pressure may be recovered if necessary. For bubbly multiphase flows however, this is not possible since the bubbles experience a force which depends, of course, on the real pressure rather than the modified one. As it turns out, most software codes by default rely on the approximation of neglecting the difference between modified and real pressure for bubbly flows. The purpose of the present study is to assess the influence of this approximation on the final simulations results. Fortunately it turns out that at least for the conditions considered in this study, the error is small.

Eulerian-Eulerian computational fluid dynamic (CFD) models allow the prediction of complex and large-scale industrial multiphase gas-liquid bubbly flows with a relatively limited computational load. However, the interfacial transfer processes are entirely modelled, with closure relations that often dictate the accuracy of the entire model. Numerous sets of closures have been developed, often optimized over few experimental data sets and achieving remarkable accuracy that, however, becomes difficult to replicate outside of the range of the selected data. This makes a reliable comparison of available model capabilities difficult and obstructs their further development. In this paper, the CFD models developed at the University of Leeds and the Helmholtz-Zentrum Dresden-Rossendorf are benchmarked against a large database of bubbly flows in vertical pipes. The research groups adopt a similar modelling strategy, aimed at identifying a single universal set of widely applicable closures. The main focus of the paper is interfacial momentum transfer, which essentially governs the void fraction distribution in the flow, and turbulence modelling closures. To focus on these aspects, the validation database is limited to experiments with a monodispersed bubble diameter distribution. Overall, the models prove to be reliable and robust and can be applied with confidence over the range of parameters tested. Areas are identified where further development is needed, such as the modelling of bubble-induced turbulence and the near-wall region. A benchmark is also established and is available for the testing of other models. Similar exercises are encouraged to support the confident application of multiphase CFD models, together with the definition of a set of experiments accepted community-wide for model benchmarking.

For the simulation of bubbly flows, knowledge of the lift force as an interaction between gas bubbles and a surrounding shear field is of great importance. The sign of the lift coefficient Cᴸ changes with increasing bubble size, i.e. with more pronounced bubble deformation. Beside this, impurities in terms of surface-active components are well-known to change the complete hydrodynamic behavior of a bubble even if the amount is very small. In the present work, the lift coefficient of single ellipsoidal bubbles is determined with a recently developed method, which is suitable to overcome difficulties connected to low viscous systems. In order to investigate the influence of impurities on the lift force, we conducted experiments with single bubbles of different sizes in purified, deionized and tap water. Overall, the determined lift coefficients show no difference between deionized and tap water but reveal differences to results obtained with purified water. As no significant differences in shape and velocity are found between the different water qualities, it remains unclear how the impurities cause the observed differences. For the deionized and tap water results that are more relevant in practice, a new correlation is proposed to account for the observed differences in comparison to data from the literature. It can be used to calculate Cᴸ of ellipsoidal bubbles in the investigated size range.