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Abstract: Particle deposition in fully developed turbulent square duct flows is simulated using large eddy simulation for Reynolds numbers, based on the bulk velocity and duct width, equal to 250k, 83k and 10,320. A particle equation of motion including Stokes drag, lift, buoyancy and gravitational forces is used for particle trajectory analysis. Results obtained for the fluid phase show good agreement with experimental data and the predictions of direct numerical simulations. Predictions for particles show that the secondary flow established in the duct cross-section plays an important role in the particle deposition process. Under the influence of this flow, high-inertia particles (particle Stokes number, St>12.38) tend to deposit close to the corners of the duct floor, while low-inertia particles (St<6.43) deposit near the floor centre. It is shown that the flow Reynolds number, particle size, drag force, shear-induced lift force and gravity all affect the particle deposition process. Particle deposition in the vertical direction increases with flow Reynolds number but simultaneously decreases in the horizontal direction. The particle deposition velocity is found to increase with both the particle size and the flow Reynolds number, with the tendency for deposition at the duct corners increasing with both variables. From a dynamic analysis, gravity most significantly affects particle deposition in the vertical direction, while in the horizontal direction the drag force dominates. The influence of the lift force increases with particle size, and its effect becomes significant as particles approach the duct floor; hence, it can act as another important factor causing particles to accumulate at the corners of the duct. Generally, and for all particle populations in the three flows considered, the particle deposition process can be described by the free-flight model. [Copyright &y& Elsevier]

Abstract: Large Eddy Simulations (LESs) were performed for a confined rectangular liquid jet with a co-flow and compared in detail with particle image velocimetry (PIV) measurements. A finite-volume CFD library, OpenFOAM, was used to discretize and solve the filtered Navier–Stokes equation. The effects of grid resolution, numerical schemes and subgrid models on the LES results were investigated. The second and fourth order schemes gave similar performance, while the fourth order scheme costs much more computationally. Subgrid model comparison showed that the locally dynamic procedure is necessary for complex flow simulation. Model validation was performed by comparing LES data for the point-wise velocity statistics such as the mean and the root-mean-square velocity, shear stress, correlation coefficient, velocity skewness and flatness with the PIV data. In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data. Good agreement was observed leading to the conclusion that the LES velocity field accurately captures the important characteristics of all the turbulent length scales present in the flow, from the fully resolved energy-containing eddies to the subgrid-scale dissipative eddies. [Copyright &y& Elsevier]

Abstract: Three-compartment model was used to study non-homogeneity of mixing in a fully baffled stirred tank. Multiple reference frame (MRF) technique was used for calculations. Calculations were performed to study the effects of agitator speed, impeller diameter, baffle width and distance of impeller from bottom of the tank on turbulent flow field. Three different zones of the vessel, that were a small zone near the impeller, another zone around the baffles, and a relatively large zone far from the impeller and baffles, named circulation zone, were investigated. Boundaries of these zones were determined using two different methods. The first method used gradient of energy dissipation rate while the other method used cumulative energy dissipation rate to determine the zone boundaries. Zone boundaries determined by both methods were comparable. The turbulent kinetic energy dissipation rate gradient was the preferred method due to its simplicity. Turbulent kinetic energy dissipation rate increased with agitator speed in all zones. Both turbulent kinetic energy dissipation rate and turbulent kinetic energy showed considerable change with impeller diameter at impeller zone, while no remarkable change was observed at baffle and circulation zones. Three-compartment model parameters, impeller and baffle energy dissipation ratios λ i, λ b, impeller and baffle volume ratios μ i, μ b and impeller and baffle exchange flow rates Q i, Q b were obtained from CFD simulations. Impeller energy dissipation ratio, impeller exchange flow rate and baffle exchange flow rate increased while baffle volume ratio decreased with agitation rate and impeller diameter. Baffle energy dissipation ratio and impeller volume ratio showed no considerable change with agitation rate and impeller diameter. [Copyright &y& Elsevier]

Abstract: A three-dimensional Eulerian–Eulerian two-phase approach has been used for the simulation of a cross-flow gas–liquid wastewater treatment reactor. Two different turbulence models have been tested: the and Reynolds Stress Model (RSM) models. Bubble induced turbulence source terms have been added to these models. Numerical results have been validated using Laser Doppler Velocimetry (LDV) measurements. Simulations with both turbulence models successfully predicted the hydrodynamics of the reactor. Then particle tracking with a stochastic approach has been used to calculate residence time distributions (RTD) with the flow previously simulated. It has been shown that dispersion in the reactor is primarily due to turbulence. Results have been compared with experimental RTD for various liquid and gas flowrates both on a bench scale and full scale plant. The RSM model accurately predicted the dispersion whereas the standard model slightly underestimated the dispersion. [Copyright &y& Elsevier]

Abstract: This paper discusses the simulation of bubbling gas–solid flows by using the Eulerian two-fluid approach. Predictions of particle motion, bed expansion, bubble size and bubble velocity in bubbling beds containing Geldart B particles are compared with experimental results and correlations found in the literature. In addition, gas mixing in a bed of Geldart A particles is investigated. An in-house code has been developed based on the finite-volume method and the time-splitting approach using a staggered grid arrangement. The velocities in both phases are obtained by solving the 2D Reynolds-averaged Navier/Stokes equations using a partial elimination algorithm (PEA) and a coupled solver. The turbulence model is used to describe the turbulent quantities in the continuous phase. In general, the model predictions are in good agreement with experimental data found in the literature. Most important observations are: the level of the restitution coefficient was found to be crucial in order to obtain successful results from 2D axisymmetric simulations of a system containing Geldart B particles. Bubble size and bubble rise velocities are not as sensitive to the restitution coefficient. The turbulence model is of outmost importance concerning gas mixing in a fluidized bed of Geldart A particles. From these numerical analyzes an optimized granular flow two-fluid model can be designed for the purpose of simulating reactive systems in fluidized bed reactors. [Copyright &y& Elsevier]

An analysis of a sequencing batch reactor (SBR) from a fluid mechanical point of view, used in the cultivation of granular activated sludge (GAS), is carried out by experimental, computational fluid dynamics (CFD) and artificial neuronal networks (ANN) methods. Due to the complexity of the three-phase problem, new hybrid methods are developed in order to shorten the calculation time and to improve the numerical prediction. In the numeroexperimental hybrid, experimentally obtained velocities from particle image velocimetry (PIV) method are implemented as initial conditions for the numerical simulation. This operation causes improvement of multiphase flow results and save CPU time of about 40% in comparison with the standard calculation. In the neuronumerical hybrid, numerically obtained results and process parameters are employed for training of an ANN. With the trained ANN, several geometrical and physical entities are calculated for a range of SBRs. In this case, the acceleration, in the prediction of several process parameters, reaches the factor . [Copyright &y& Elsevier]

Two commercial CFD codes were used to simulate the strongly swirling single-phase flow with core recirculation within an axial hydrocyclone. Both packages used a Differential Reynolds Stress Model with default constants for the turbulence closure. The effect of omitting wall reflection terms was also investigated and it was generally found that this lead to better agreement with experiment. Interestingly, the predicted velocity profiles from the two CFD codes did not agree with each other. Possible reasons for this are different turbulence modelling approaches with different terms for the turbulent diffusion and rapid pressure–strain terms. [Copyright &y& Elsevier]

Abstract: A CFD (computational fluid dynamics) model of a solvent extraction pulsed column has been developed and run with a single water phase. The results are compared with experimental measurements taken on a pilot scale column using PIV (particle image velocimetry). The pulsed column investigated had disk–doughnut internals and was operated under pulsing intensities ranging from 10 to 32.5mm/s. PIV measurements of velocity were used to validate the CFD model and to characterise the pulsing flow of a single phase through the column. The CFD modelling was performed for the same geometry and operating conditions using a 2D computational grid and a low Reynolds Number – turbulence model. An improved velocity prediction was achieved by adding a gap between the doughnut internal and the pulsed column wall. The combined measurements and predictions give insight into the effect of the geometry internals on the flow hydrodynamics in the pulsed column. [Copyright &y& Elsevier]

Abstract: Many mixing applications involve viscous fluids and laminar flows where the detailed as well as overall flow structures are important. In order to understand the fluid dynamic characteristics of low Re laminar flows in mixing vessels, the flow induced by a Rushton impeller for three Re namely, 1, 10 and 28, was studied both experimentally and computationally. It was found that for the highest Re, the flow exhibited the familiar outward pumping action associated with radial impellers under turbulent flow conditions. However, as the Re decreases, the net radial flow during one impeller revolution was reduced and for the lowest Re a reciprocating motion with negligible net pumping was observed. This behaviour has not been reported in the literature in the past and represents a highly undesirable flow pattern from the standpoint of effective mixing. The CFD results successfully reproduced this behaviour. In order to elucidate the physical mechanism responsible for the observed flow pattern, the forces acting on a fluid element in the radial direction were analysed. The analysis indicated that for the lowest Re, the material derivative of radial velocity near the blade tip is small thus a balance exists between pressure and viscous forces; the defining characteristic of creeping flow. The velocity and pressure forces are in phase because the velocity is driven by the pressure field generated by the rotation of the impeller. Based on these findings, a simplified analytic model of the flow was developed that gives a good qualitative as well as quantitative representation of the flow. [Copyright &y& Elsevier]

Abstract: In this work, we employ direct numerical simulation of turbulence one-way coupled to Lagrangian tracking to investigate microbubble distribution in upward and downward channel flow. We consider a closed channel flow at and a dispersion of microbubbles characterized by a diameter of . Bubbles are assumed contaminated by surfactants (i.e., no-slip condition at bubble surface) and are subject to drag, gravity, pressure gradient forces, Basset history force and aerodynamic lift. Our results confirm previous findings and show that microbubble dispersion in the wall region is dominated by the action of gravity combined with the lift force. Specifically, in upward flow, bubble rising velocity in the wall region generates a lift force which pushes bubbles to the wall. In downward flow, bubble rising velocity against the fluid generates a lift force which prevents microbubbles from reaching the viscous sublayer. In the wall region, we observe bubble preferential segregation in high-speed regions in the downflow case, and non-preferential distribution in the upflow case. This phenomenon is related to the effect of the lift force. Compared to experiments, the current lift force model produces larger consequences, this effect being overemphasized in the upflow case in which a large number of bubbles is segregated near the wall. In this case, the resulting bubble wall-peak of concentration outranges experimental results. These results, so deeply related to the lift force, underline the crucial role of current understanding of the fluid forces acting on bubbles and help to formulate questions about available force models, bubble–bubble interactions and two-way coupling which can be crucial for accurate predictions in the region very near the wall. [Copyright &y& Elsevier]

Abstract: The present paper demonstrates how 2D, dynamic simulations of a flat bubble column are feasible, applying state-of-the-art dynamic turbulence models, when an appropriate turbulent dispersion term is applied in the conservation equation for the gas volume fraction. The turbulence model yielded a better qualitative prediction of the bubble plume than the model, due to the low-Reynolds number treatment of the former model. The simple mixing length turbulence model gave the best prediction of the meandering plume, without any dispersion term. The mixing length model is, however, almost identical to a Large-Eddy simulation when run time-dependent on a fine mesh, and should be applied with care due to the use of a constant turbulence length scale and the inherent 3D nature of turbulence. By refining the mesh to the extreme end, it was shown that an apparently grid independent numerical solution was really grid-dependent, even when dynamic turbulence models were applied. The apparently grid independent solution was computed with an increment in the computational mesh that was of the same size as an equilibrium Kolmogorov length scale. [Copyright &y& Elsevier]

The study of the hydrodynamics of bubble column reactors reveals that three main flow regimes can be distinguished. The present study is an original application of standard numerical multiphase models aiming at a better prediction of the transitions and a better description of these regimes. This approach consists of a two-step calculation with, in a first time, the determination of bubble size distributions using coalescence and break-up laws, and in a second time, the implementation of this distribution in a multiple gas phase Euler–Euler model. Calculations are compared with experimental data: liquid velocities and global gas hold-ups. They were obtained in a cylindrical bubble column in which local or uniform aerations were performed. The comparison shows that our approach allows a good prediction of both flow regime transitions and flow characteristics such as hydrodynamics or turbulence. Furthermore, two bubble-induced turbulence models consisting, respectively, of an added viscosity and of two turbulence source terms added in the k–&epsiv; transport equations have been compared. [Copyright &y& Elsevier]