Numerical investigation of bend and torus flows—Part II : Flow simulation in torus reactor

Flow in a torus reactor with straight parts fitted with a marine impeller is investigated. The laser Doppler anemometry (LDA) is first employed to achieve experimental measurements of mean velocity profiles. Next, a numerical resolution of the steady-state flow is performed using a multiple reference frames (MRF) approach to represent the particular flow induced by the marine impeller in the geometry. A comparison of predictions using different turbulence models to LDA measurements is made, and a k-ω model is assessed.The numerical tool is used to investigate in more details the particular flow induced in the torus geometry. Evolution of the axial and rotating motions when moving away from the impeller is especially investigated, showing the complex hydrodynamical interaction between the main rotating swirl motion involved downstream the impeller, and bend curvature effects. Two different flow conditions can be considered in the torus geometry, with a main swirling motion close to the impeller, which freely decays and vanishes when Dean vortices appear in bends. Simulations for two rotation velocities of the impeller and comparison with the study with simple bends (first part) reveal pertinence of the swirl number Sn to describe the change of flow conditions along the reactor axis. When this parameter decreases below a threshold value around 0.2 in a bend entry, centrifugal effects due to bend curvature are more important than the swirl motion, and Dean vortices appear in bend outlet. One main consequence is the axial distance of the swirl motion persistence, which is found to be smaller for the higher impeller rotation velocity, due to the dual effect of the marine impeller that generates simultaneously both axial and rotating motions.     

Modelling of non-premixed swirl burner flows using a Reynolds-stress turbulence closure

In this computational study, the performance of a differential Reynolds-stress turbulence model has been assessed in predicting a turbulent, non-premixed combusting swirling flow of the type frequently found in practical combustion systems. Calculations are also performed using the widely employed eddy-viscosity based k-ε turbulence model in order to examine the relative performances of these two closure models. The predictions are compared against the experimental data of mean axial and tangential velocities, turbulence quantities, gas temperatures and oxygen concentration collected in a 400 kW semi-industrial scale combustor fired with coke-oven gas using an industry-type swirl burner at the International Flame Research Foundation [17]. Computations of a corresponding non-combusting flow are also carried out and the predictions are compared with limited data available. The overall agreement between the measurements and the predictions obtained with both the k-ε and Reynolds-stress turbulence models are reasonably good, in particular, the flame properties. However, some features of the isothermal and combusting flow fields, and the flame are better predicted by the Reynolds-stress model. The subcritical nature of the isothermal flow and the effects of combustion on the size and shape of the swirl-induced internal recirculation zone in the corresponding combusting flow are well simulated by this model. The k-ε model fails to reproduce the subcritical nature of the isothermal flow. The predictions of this model erroneously show a general trend of the mean tangential velocity distribution to assume a forced-vortex profile. The levels of gas temperature and oxygen concentration in the internal recirculation zone and the enveloping shear region are on the whole better predicted by the Reynolds-stress model.     

Effect of the shaft eccentricity on the hydrodynamics of unbaffled stirred tanks

The aim of this work is to investigate the effect of the shaft eccentricity on the hydrodynamics of unbaffled stirred vessels. The difference between coaxial and eccentric agitation is studied using a combination of experiments carried out by particle image velocimetry, that provide an accurate representation of the time-averaged velocity, and computational fluid dynamics simulations, that offer a complete, transient volumetric representation of the three-dimensional flow field, once a proper modelling strategy is devised. The comparison of the experimental and simulated mean flow fields has demonstrated that calculations based on Reynolds-averaged Navier-Stokes equations are suitable for obtaining accurate results. Depending on the position of the shaft, steady-state or transient calculations have to be chosen for predicting the correct flow patterns. Care must be exerted in the choice of turbulence models, as for the unbaffled configurations the results obtained with the Reynolds stress model are superior to that of the k-ε model.     

Numerical simulation of pulverized coal combustion and NO formation

A pure two-fluid model, instead of the Eulerian gas-Lagrangian particle models (particle trajectory models), is used for simulating three-dimensional (3-D) turbulent reactive gas–particle flows and coal combustion. To improve the simulation of the flow field and NO_X formation, a modified k–ε–k_p two-phase turbulence model and a second-order-moment (SOM) reactive rate model are proposed. The proposed models are used to simulate NO formation (fuel NO produced by NH₃) of methane–air combustion, and the prediction results are compared with those using the pure presumed PDF-finite-reaction-rate model and experimental data. The modified k–ε model and SOM model are more reasonable than the standard k–ε model and the pure presumed PDF-finite-reaction-rate model. The proposed models are also used to predict the coal combustion and NO formation at the exit of a double air register swirl pulverized-coal burner. The predicted results indicate that a pulverized-coal concentrator installed in the primary-air tube of burner has a strong effect on the coal combustion and NO_X formation.     

CFD modeling of gas-solid flow and cracking reaction in two-stage riser FCC reactors

The Eulerian-Eulerian approach was applied to simulate the flow behavior and catalytic cracking reactions in the riser reactors of two-stage riser fluid catalytic cracking (TSRFCC) technology. A k-ε-k_p-ε_p-Θ gas-solid turbulent flow model was used, which took account of the particle turbulence and the interaction of turbulence between gas and particle phases. A 14-lump kinetics model was used for simulating cracking reactions. The approach and model were validated with both experimental results and commercial data. The distributions of particle fraction volume and velocity, as well as product yields in the TSRFCC riser reactors were first analyzed. The simulations were then carried out for optimization studies to understand the influence of the operating conditions on the performance of commercial TSRFCC riser reactors. The model and results presented here are valuable for the design and optimization of TSRFCC technology.     

Simulation of swirling gas–particle flows using USM and k–ε–kp two-phase turbulence models

The turbulent swirling gas–particle flows with swirl numbers 0.47 and 1.5 are simulated using a unified second-order moment (USM) (two-phase Reynolds stress equations) and a k–ε–kp two-phase turbulence models. The results are compared with experiments. Both two models can well predict the axial time-averaged two-phase velocities in case of s=0.47, but the USM model is better than the k–ε–kp model in predicting the tangential time-averaged two-phase velocities of strongly swirling flows (S=1.5). The anisotropic two-phase turbulence can well be described only using the USM model. The results give the difference in flow behavior between weakly swirling and strongly swirling gas–particle flows.     

Flow field and residence time distribution simulation of a cross-flow gas-liquid wastewater treatment reactor using CFD

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 k-ε 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 k-ε model slightly underestimated the dispersion.     

Large eddy simulation of the Gas–Liquid flow in a square cross-sectioned bubble column

In this work the use of large eddy simulations (LES) in numerical simulations of the gas–liquid flow in bubble columns is studied. The Euler–Euler approach is used to describe the equations of motion of the two-phase flow. It is found that, when the drag, lift and virtual mass forces are used, the transient behaviour that was observed in experiments can be captured. Good quantitative agreement with experimental data is obtained both for the mean velocities and the fluctuating velocities. The LES shows better agreement with the experimental data than simulations using the k–ε model.     

A two-scale second-order moment particle turbulence model and simulation of dense gas-particle flows in a riser

A two-scale second-order moment particle turbulence model is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. It is then used to simulate dense gas-particle flows in a riser. The predicted results are in reasonable agreement with the experimental results and show the core-annulus flow structure observed in experiments. It is seen that the two-scale model is somewhat better than k_f-ε_f-k_p-ε_p-θ two-phase turbulence model and the single-scale second-order moment two-phase turbulence model (USM-θ model).     

DEM simulation of gas-solid flow behaviors in spout-fluid bed

Three-dimensional gas and particle turbulent motions in a rectangular spout-fluid bed were simulated. The particle motion was modeled by discrete element method and the gas motion was modeled by k-ε two-equation turbulent model. Shear induced Saffman lift force, rotation induced Magnus lift force as well as drag force, contract force and gravitational force acting on individual particles were considered when establishing the mathematics models. A two-way coupling numerical iterative scheme was used to incorporate the effects of gas-particle interactions in volume fraction, momentum and kinetic energy. The gas-solid flow patterns, forces acting on particles, the particles mean velocities, jet penetration depths, gas turbulent intensities and particle turbulent intensities were discussed. Selected stimulation results were compared to some published experimental and simulation results.     

CFD models of jet mixing and their validation by tracer experiments

The classical theory of RTD was applied to characterize a flow in a laboratory jet mixer using both numerical and experimental approaches. Detailed information about flow field in the reactor was obtained through computational fluid dynamics (CFD) simulations. Three different turbulence models have been tested: the standard k-?, RNG k-? and Reynolds Stress Model (RSM). The CFD models predicted slight yet relevant differences in flow patterns. The experimental RTD can be used to identify erroneous numerical results. This paper points out differences in the predicted flow velocities. Such discrepancy may have significant impact on the assessment of the reactor's performance. Thus, the role of experimental verification is emphasized. A dedicated experiment is proposed to resolve the potential validation problem.     

CFD simulations of bubble column reactors: 1D, 2D and 3D approach

CFD simulations have been carried out for the predictions of flow pattern in bubble column reactors using 1D, 2D and 3D k-ε models. An attempt has been made to develop a complete correspondence between the operation of a real column and the simulation. Attention has been focused on the cylindrical bubble columns because of their widespread applications in the industry. All the models showed good agreement with the experimental data for axial liquid velocity and the fractional gas hold-up profiles. However, as regards to eddy diffusivity, only the 3D model predictions agree closely with the experimental data.The CFD model has been extended for the estimation of an axial dispersion coefficient (D_L) using 1D, 2D and 3D models. Excellent agreement was found only between the experimental values and the 3D predictions. The 1D and 2D simulations, however, yielded D_L values, which were lower by 25-50%. For this, a mechanistic explanation has been provided.     

Evaluation of pseudohomogeneous models for heat transfer in packed beds with gas flow and gas-liquid cocurrent downflow and upflow

Several pseudohomogeneous models are used by researchers in the study of heat transfer in packed beds. In this work, five of the most used pseudohomogeneous models (to one, two and three parameters) are analyzed, for gas and gas-liquid flow configurations. The models were evaluated concerning the following aspects: (a) the fitting between calculated and measured temperatures, (b) the values of thermal parameters, (c) their confidence intervals, (d) the quality of the estimation of the thermal parameters by analysis of their Box biases, and (e) the nonlinear dependence of the calculated temperatures on the thermal parameters (using the curvature measures of Bates and Watts). It was observed, particularly in gas-liquid flow, that the fittings between calculated and measured temperature profiles are better for models in which a wall heat transfer coefficient is incorporated to consider the convective resistance at the bed wall. It was also noted that the values of the thermal parameters fitted from the pseudohomogeneous models may be very different at identical operational conditions. The effective axial thermal conductivity may be neglected in the modeling because its estimation does not affect the residual functions. Besides, the estimation of k_a is tricky because it depends on the initial guess and also because the parameter is extremely sensitive to changes in the operational conditions. The confidence intervals for the parameters depend on the model and are also affected by the experimental conditions. The estimation of the parameters was adequate for the k_r-h_W and k_r-k_a models and the curvatures measures were satisfactory only for models in which h_W was not incorporated.     

Time-dependent flow structures and Lagrangian mixing in Rushton-impeller baffled-tank reactor

The object of this work is to investigate the role of large-scale convective structures in promoting mixing in a stirred tank. We focus on a standard geometry (flat bottom, four-baffle reactor stirred by a six-blade Rusthon impeller) and we use an Eulerian-Lagrangian approach to investigate numerically the dispersion of fluid particles. The three-dimensional, time-dependent, fully developed flow field is calculated with a computationally efficient procedure using a RANS solver with k-ε turbulence modeling and the flow field is assessed precisely against experimental data. Then, fluid parcels are tracked in the calculated flow field. Analyzing the trajectory of fluid parcels, the segregated regions within the flow are identified and mixing indicators are calculated (mixing time, circulation length and sojour time distribution). A physical explanation is thus proposed to establish a link between large-scale mixing and complex fluid dynamics generated by the interactions of radial-discharge jet, ring vortices, and upper counter rotating vortex.     

Modelling of a RDC using a combined CFD-population balance approach

In the present study we propose an extension of the Euler/Lagrangian approach for liquid-liquid two phase flows when the volume fraction of the dispersed phase is not small. The continuous phase velocity is obtained by solving the Reynolds-averaged Navier-Stokes equations augmented with the k-ε turbulence model. The motion of the dispersed phase is calculated by solving the equations of motion taking into account inertia, drag and buoyancy forces. The coupling between the phases is described by momentum source terms and the terms that account for turbulence generation by the droplets’ motion. Collision and breakage of the droplets are treated by a single particle Monte-Carlo stochastic simulation method. This method is based on a mass flow formulation and operator splitting technique. For validation of the numerical procedure the droplet size distribution and flow fields in a rotating disc contactor are calculated and compared with the existing experimental results.     

Axial mixing in pipe flows: turbulent and transition regions

In the present work, the flow pattern in pipe flow has been simulated using low Reynolds number k-ε model. The CFD model has been extended to simulate the axial dispersion phenomena in both the transition and turbulent regions. An extensive comparison of the predicted axial dispersion coefficient with the experimental data has been presented along with the predictions of various models published in the literature. The proposed CFD model for axial mixing was found to give an excellent agreement with the experimental measurements.     

Near field characteristics of swirling flow past a sudden expansion

The effect of swirl on the flow characteristics of an axisymmetric sudden expansion chamber with an expansion ratio of 2.5 was examined experimentally. Particle image velocimetry (PIV) was employed to capture the instantaneous flow field. The experiments were carried out for three swirl numbers of 0, 0.17 and 0.65 and a Reynolds number of 10,000. The measured time-mean and fluctuating velocities downstream of the expansion showed that the introduction of weak swirl does not affect the flow significantly whereas stronger swirl (S=0.65) results in the formation of a central recirculation region, a typical manifestation of vortex breakdown, which alters the character of the flow. Proper orthogonal decomposition (POD) was employed to further characterise the flow by decomposing it into eigenmodes and identifying dominant structures and their spatial distribution. Both velocity-based and vorticity-based POD were implemented. The analysis indicated that the first two eigenmodes are the most energetic ones and are associated with the instability of the jet, whereas higher modes are associated with rolling vortices along the shear layer and smaller scale motion. Phase portraits of the time-dependent amplitude coefficients also indicated the existence of low-dimensional dynamics in the swirling flow for swirl numbers well below the critical ones for vortex breakdown. This low dimensionality at low swirl numbers might be due to a precessing motion of the flow.     

Measurements and modelling of free-surface turbulent flows induced by a magnetic stirrer in an unbaffled stirred tank reactor

Measurements and numerical simulations of turbulent flows with free-surface vortex in an unbaffled reactor agitated by a cylindrical magnetic stirrer are presented. Measurements of the three mean and fluctuating components of the velocity vector are made using a laser Doppler velocimetry in order to characterise the flow field at different speeds of the stirrer. A homogeneous Eulerian-Eulerian multiphase flow model coupled with a volume-of-fluid method for interface capturing is applied to determine the vortex shape and to compute the turbulent flow field in the reactor. Turbulence is modelled using a second-moment differential Reynolds-stress transport (RST) model, but for some cases the k-ε/k-ω based shear-stress transport (SST) model is also used. The predictions obtained using the ANSYS CFX-5.7 computational fluid dynamics code are compared with the images of the vortex and the measured distributions of mean axial, radial and tangential velocities and turbulent kinetic energy. The predicted general shape of the liquid free-surface is in good agreement with measurements, but the vortex depth is underpredicted. The overall agreement between the measured and the predicted axial and tangential velocities obtained with the RST model is good. However, the radial velocity is significantly underpredicted. Predictions of the turbulent kinetic energy yield reasonably good agreement with measurements in the bulk flow region, but discrepancy exists near the reactor wall where this quantity is underpredicted. The SST model predictions are generally of the same quality as those of the RST model, with the latter model providing better predictions of the tangential velocity distribution.     

CFD simulation of gas-liquid flows in stirred vessel equipped with dual rushton turbines: influence of parallel, merging and diverging flow configurations

Computational fluid dynamics (CFD) was used to investigate the influence of parallel, merging and diverging flow configurations on the gas dispersion operation in stirred vessel. The simulation was based on the two-fluid model along with the standard k-ε turbulence model along with an appropriate drag correction to account for bulk turbulence [Khopkar, A.R., Ranade, V.V., 2006. CFD simulation of gas-liquid stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal 52, 1654-1671]. The model predictions were compared with the published experimental data of Bombac, Zun [2000. Gas-filled cavity structures and local void fraction distribution in vessel with dual-impellers. Chemical Engineering Science 55, 2995-3001] for parallel flow configuration. The predicted results show reasonably good agreement with the experimental data. The computational model was then used to simulate the gas-liquid flows for the other two flow configurations. The results of this work provide ‘a priory’ information on the implications of flow configuration on the vessel performance.