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Abstract: This work presents a comprehensive study of different turbulence models, including the k–ε, SST, SSG–RSM and the SAS–SST models, for simulating turbulent flow in a baffled tank stirred with a Rushton turbine. All the turbulence models tested predict the mean axial and tangential velocities reasonably well, but under-predict the decay of mean radial velocity away from the impeller. The k–ε model predicts poorly the generation and dissipation of turbulence in the vicinity of the impeller. This contrasts with the SST model, which properly predicts the appearance of maxima in the turbulence kinetic energy and turbulence energy dissipation rate just off the impeller blades. Curvature correction improves the SST model by allowing a more accurate prediction of the magnitude and location of these maxima. However, neither the k–ε nor the SST model is able to properly capture the chaotic and three-dimensional nature of the trailing vortices that form downstream of the blades of the impeller. In this sense, the SAS–SST model produces more physical predictions. However, this model has some drawbacks for modelling stirred tanks, such as the large number of modelled revolutions required to obtain good statistical averaging for calculating turbulence quantities. Taking into consideration both accuracy and solution time, the SSG–RSM model is the least satisfactory model tested for predicting turbulent flow in a baffled stirred tank with a Rushton turbine. [Copyright &y& Elsevier]

Abstract: An experimental study and numerical investigation of thermal mixing are carried out on tandem twin jets in cross flow. Experiments were carried out for velocity ratios 1, 2 and 4 for 15°C temperature difference between main pipe and jet fluid. Velocity and temperature fields are measured using Hot Film Anemometer (HFA). Three dimensional steady state Computational Fluid Dynamics (CFD) simulations have been carried out to predict the velocity and temperature fields. The predicted velocity and temperature fields are in good agreement with the experimental measurements. Temperature fluctuations have been predicted using temperature variance model. The effect of jet spacing for different velocity ratios is studied. For jet spacing equal to twice the jet diameter, both the jets influence each other. Increase in the jet spacing decreases the effect of jets on each other. [Copyright &y& Elsevier]

Abstract: Turbulent fluid flow and related solid particle behaviour in the direct vicinity of the heat exchanging (HE) surface of a scraped heat exchanger crystallizer was studied. The liquid flow is visualized by dye injection and the particles are monitored directly for two types of commonly used scraper geometries. In conjunction with this experimental work, we performed direct numerical simulations of the two-phase (solid–liquid) flow system. Our main goal is the design of scraper geometries that enhance heat transfer by perturbing the thermal boundary layer, and effectively scrape off particles that nucleate, grow and adhere onto the HE surface. Also the turbulent flow generated by the moving scrapers should direct the particles into the bulk of the tank. The experiments and simulations show good qualitative resemblance which enables the design of scrapers based primarily on numerical predictions. [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 computational fluid dynamics (CFD)-code has been developed using finite volume method in Eulerian framework for the simulation of axisymmetric steady state flows in bubble columns. The population balance equation for bubble number density has been included in the CFD code. The fixed pivot method of Kumar and Ramkrishna [1996. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332] has been used to discretize the population balance equation. The turbulence in the liquid phase has been modeled by a model. The novel feature of the framework is that it includes the size-specific bubble velocities obtained by assuming mechanical equilibrium for each bubble and hence it is a generalized multi-fluid model. With appropriate closures for the drag and lift forces, it allows for different velocities for bubbles of different sizes and hence the proper spatial distributions of bubbles are predicted. Accordingly the proper distributions of gas hold-up, liquid circulation velocities and turbulence intensities in the column are predicted. A survey of the literature shows that the algebraic manipulations of either bubble coalescence or break-up rate were mainly guided by the need to obtain the equilibrium bubble size distributions in the column. The model of Prince and Blanch [1990. Bubble coalescence and break-up in air-sparged bubble columns. A.I.Ch.E. Journal 36, 1485–1499] is known to overpredict the bubble collision frequencies in bubble columns. It has been modified to incorporate the effect of gas phase dispersion number. The predictions of the model are in good agreement with the experimental data of Bhole et al. [2006. Laser Doppler anemometer measurements in bubble column: effect of sparger. Industrial & Engineering Chemistry Research 45, 9201–9207] obtained using Laser Doppler anemometry. Comparison of simulation results with the experimental measurements of Sanyal et al. [1999. Numerical simulation of gas–liquid dynamics in cylindrical bubble column reactors. Chemical Engineering Science 54, 5071–5083] and Olmos et al. [2001. Numerical simulation of multiphase flow in bubble column reactors: influence of bubble coalescence and breakup. Chemical Engineering Science 56, 6359–6365] also show a good agreement for liquid velocity and gas hold-up profiles. [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: A computational fluid dynamics model is used to calculate a three-phase (air–water–solid particles) flow in a bubble column. The calculation of multi-phase flows is significantly influenced by the formulation of the inter-phase drag and the modelling of the turbulence. Both are influenced by the dispersed phases. The – turbulence model extended with terms accounting for the bubble-induced turbulence is used to calculate the eddy viscosity of the liquid phase. Bubble–bubble and particle–particle interactions are considered as well as a direct momentum transfer between the two dispersed phases bubbles and solid particles. The local volume fractions of the dispersed phases are considered for the calculation of the drag coefficients between the dispersed phases and the continuous phase. Measured local gas and solid hold-ups as well as measured liquid velocities are compared with the corresponding calculated results. The measured and the calculated results show good agreement. [Copyright &y& Elsevier]

Abstract: A hybrid (deterministic/stochastic) fundamental model is proposed for the major physico-chemical processes involved in an industrial HVOF thermal spray process (Diamond Jet hybrid gun, Sulzer Metco, Westbury, NY, USA). The model includes continuum type differential equations that describe the evolution of gas and particle temperature and velocity, and a rule-based stochastic simulator that predicts the evolution of the coating microstructure. Regarding gas/particle dynamics, the Reynolds- and Favre-averaged Navier–Stokes equations and the energy balance equations are solved with the renormalization group (RNG) k– turbulence model, and the particle trajectories, temperature histories and melting degrees are determined using the fourth-order Runge–Kutta method. On the microscopic particle deposition process, the formation of coating microstructure is captured by the Madejski deformation model and several rules that govern splat formation, solidification and coating growth. Based on the proposed model, a detailed comprehensive parametric analysis is carried out to study the relationship between the key process parameters and the particle in-flight behavior as well as the resulting coating properties. [Copyright &y& Elsevier]

Abstract: Particle breakage due to fluid flow through various geometries can have a major influence on the performance of particle/fluid processes and on the product quality characteristics of particle/fluid products. In this study, whey protein precipitate dispersions were used as a case study to investigate the effect of flow intensity and exposure time on the breakage of these precipitate particles. Computational fluid dynamic (CFD) simulations were performed to evaluate the turbulent eddy dissipation rate (TED) and associated exposure time along various flow geometries. The focus of this work is on the predictive modelling of particle breakage in particle/fluid systems. A number of breakage models were developed to relate TED and exposure time to particle breakage. The suitability of these breakage models was evaluated for their ability to predict the experimentally determined breakage of the whey protein precipitate particles. A “power-law threshold” breakage model was found to provide a satisfactory capability for predicting the breakage of the whey protein precipitate particles. The whey protein precipitate dispersions were propelled through a number of different geometries such as bends, tees and elbows, and the model accurately predicted the mean particle size attained after flow through these geometries. [Copyright &y& Elsevier]

An implementation of the conditional moment closure (CMC) of Bilger (Phy. Fluids A 5 (1993) 436) and Klimenko (Fluid Dyn. 25 (1990) 327) has been carried out in the commercial CFD software FLUENT. A new implementation method is suggested that uses the CMC-equations to calculate an unconditional reaction rate that is subsequently inserted in a Reynolds averaged species equation. The objectives are to ensure conservation of reacting species by elimination of the spurious term that usually contaminates a CMC solution and to obtain convergence on a coarser grid than is usually required in CMC. The implementation has been successfully carried out for two sets of well-known mixing sensitive reaction pairs (parallel competitive and competitive consecutive) that both have one instantaneous and one fast irreversible reaction. Calculations with different discretizations of the CMC-equations in mixture fraction space have been performed and compared to experiments, full/finite-mode PDF models and the interpolation model of Baldyga. It is shown that the suggested implementation can achieve sufficient numerical accuracy with a much coarser mixture fraction space discretization than standard CMC implementations, which allows for more efficient CFD calculations. [Copyright &y& Elsevier]