Numerical Simulation of Gas‐Liquid Flow in a Stirred Tank with Swirl Modification

Although the standard k‐? model is most frequently used for turbulence modeling, it often leads to poor results for strongly swirling flows involved in stirred tanks and other processing devices. In this work, a swirling number, R_S, is introduced to modify the standard k‐? model. A Eulerian‐Eulerian model is employed to describe the gas‐liquid, two‐phase flow in a baffled stirred tank with a Rushton impeller. The momentum and the continuity equations are discretized using the finite difference method and solved by the SIMPLE algorithm. The inner‐outer iterative algorithm is used to account for the interaction between the rotating impeller and the static baffles. The predictions, both with and without R_S corrections, are compared with the literature data, which illustrates that the swirling modification could improve the numerical simulation of gas‐liquid turbulent flow in stirred tanks.     

Simulation of a Spray Dryer Fitted with a Rotary Disk Atomizer Using a Three-Dimensional Computional Fluid Dynamic Model

Abstract

Spray dryers fitted with a rotary disk atomizer are widely used in many industries requiring high throughputs to produce powders from liquid streams. The interaction between droplets or particles and the drying medium within the drying chamber is still not well understood and hence difficult to model reliably. In this article CFD results are presented to describe the behavior of the performance of a spray dryer fitted with a rotary disk atomizer in a cylinder-on-cone chamber geometry. Four different turbulence models, i.e., standard k ? ε, RNG k ? ε, Realizable k ? ε, and Reynolds stress models were tested and compared to simulate the swirling two-phase flow with heat and mass transfer in the chamber. The results of this investigation can provide further insight into turbulent swirling flow modeling. The predicted results, such as, air flow patterns, air velocity and temperature, distributions, particle/droplet trajectories, drying performance etc., are obtained using the CFD code FLUENT6.1. Comparison with available limited experimental data shows that CFD results display reasonable agreement. Predicted results also show that the RNG k ? ε model performs better in this specific case.     

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.     

Fine particle turbulence modulation

Streamwise turbulence intensities of fine particulate suspensions were studied in a 26 mm N.B. horizontal pipe loop. Colloidal silica spheres were prepared in 10^?4M and 1M KNO₃ solutions to control the degree of aggregate formation in the suspension. Using an ultrasonic Doppler velocity profiling sensor, the turbulence intensities of the fine particle suspensions were compared with those of a particle‐free flow over a range of Reynolds numbers. At low electrolyte concentration, the silica particles remain dispersed, with the turbulence intensity of the suspension flow comparable with that of the particle‐free flow. At high electrolyte concentration, increased particle‐particle interaction leads to the formation of particle aggregates which support turbulence augmentation over a critical Reynolds number range. The range of Reynolds numbers over which this turbulence enhancement is observed is limited by both fluid dynamic effects at low Reynolds numbers (Re ≈ 5500) and aggregate breakup at high Reynolds numbers (Re ≈ 8000). © 2010 American Institute of Chemical Engineers AIChE J, 2011     

CFD simulation of stirred tanks: Comparison of turbulence models. Part I: Radial flow impellers

A critical review of the published literature regarding the computational fluid dynamics (CFD) modelling of single‐phase turbulent flow in stirred tank reactors is presented. In this part of review, CFD simulations of radial flow impellers (mainly disc turbine (DT)) in a fully baffled vessel operating in a turbulent regime have been presented. Simulated results obtained with different impeller modelling approaches (impeller boundary condition, multiple reference frame, computational snap shot and the sliding mesh approaches) and different turbulence models (standard k ? ε model, RNG k ? ε model, the Reynolds stress model (RSM) and large eddy simulation) have been compared with the in‐house laser Doppler anemometry (LDA) experimental data. In addition, recently proposed modifications to the standard k ? ε models were also evaluated. The model predictions (of all the mean velocities, turbulent kinetic energy and its dissipation rate) have been compared with the experimental measurements at various locations in the tank. A discussion is presented to highlight strengths and weaknesses of currently used CFD models. A preliminary analysis of sensitivity of modelling assumptions in the k ? ε models and RSM has been carried out using LES database. The quantitative comparison of exact and modelled turbulence production, transport and dissipation terms has highlighted the reasons behind the partial success of various modifications of standard k ? ε model as well as RSM. The volume integral of predicted energy dissipation rate is compared with the energy input rate. Based on these results, suggestions have been made for the future work in this area.     

Experimental Study and CFD Simulation of Hydrodynamic Behaviours in an External Loop Airlift Slurry Reactor

The local hydrodynamic behaviours in an external loop airlift slurry reactor, including the gas holdup, bubble rise velocity, bubble size, were measured with a fibre optic probe. The liquid circulation velocity was measured with an ultrasound Doppler velocimetry. Two‐dimensional simulations were carried out in the framework of Two‐Fluid formulation coupled with a k‐? turbulence model. The lateral forces and interphase turbulence were taken into account and good agreement between the experimental and simulation results was obtained. The simulations show that the lateral forces and interphase turbulence have noticeable influence and should be included in the CFD model.     

Particle capture by a rotating disk in a kitchen exhaust hood

Abstract

Chinese cooking produces large numbers of particles that can cause both indoor and outdoor air quality problems. To reduce the extraction of particles to the outdoor air, this investigation studied capture efficiency of a rotating disk in an exhaust hood. The studies were performed experimentally in a wind tunnel and numerically by computational fluid dynamics (CFD) models with the Lagrangian method for tracking particle trajectories. The experimental data were used to identify the best turbulence model among the three tested in the CFD simulations. The results show that the capture efficiency increased with disk rotation speed and particle size but decreased with exhaust airflow rate. The CFD simulations provided detailed information about the mechanisms by which particles of different sizes were captured by the rotating disk. CFD was then used to explore two methods for improving the capture efficiency: adding more wires to the middle and outer zones of the disk, and using two layers of disks. Both methods can increase the capture efficiency of the rotating disk at an acceptable pressure loss.

Copyright © 2020 American Association for Aerosol Research     

Mass transfer modeling and simulation at a rotating cylinder electrode (RCE) reactor under turbulent flow for copper recovery

This work presents the numerical simulation of a laboratory reactor with rotating cylinder electrode (RCE) and a six-plate counter electrode that is used in studies on heavy metal recovery. The rate of electrode rotation and the potential applied are of such magnitude that the electrochemical reactor works in conditions of mass transport control under turbulent flow to obtain high recovery rates and formation of dendritic metal deposits. For hydrodynamics, the Reynolds averaged Navier–Stokes (RANS) equations were solved using the standard k–ε turbulence model, as well as wall functions based on the universal velocity distribution in the near-wall region. Results of 3-D simulations of the velocity field show clearly the formation of the turbulence Taylor vortex flow. For mass transfer, convection–diffusion equation was solved using the Kays–Crawford model for turbulent Schmidt number and Launder–Spalding wall functions adapted for mass transfer. Kinetics of copper recovery from aqueous solutions containing 0.019 M CuSO₄ and 1 M H₂SO₄, in the range of rotation speed of 400–1100 rpm, was adequately fit (error <8%) during the electrolysis time to achieve a final recovery of 85% for potentiostatic and 60% for galvanostatic experiments. The fitting parameter of the concentration wall function used in all experiments was A=2.9.     

CFD Prediction of the Critical Agitation Speed for Complete Dispersion in Liquid‐Liquid Stirred Reactors

A computational fluid dynamics (CFD) model is adopted to simulate the turbulent immiscible liquid‐liquid flow in a stirred vessel based on a two‐fluid model with a k‐ϵ‐A_P turbulence model. An improved inner‐outer iterative procedure is adopted to deal with the impeller rotation in a fully baffled stirred tank. Different drag formulations are examined, and the effect of the droplet size on both the dispersed phase holdup distribution and the velocity field is analyzed. Two different numerical criteria are tested for determining the critical impeller speed for complete dispersion. The simulated critical impeller speeds are generally in good agreement with the correlations in the literature when the fixed droplet size is properly selected. This demonstrates that the modeling approach and the numerical criteria proposed in this work are promising for predicting the dispersion characteristics in liquid‐liquid stirred tanks.     

CFD Prediction of Flow and Homogenization in a Stirred Vessel: Part I Vessel with One and Two Impellers

A simulation of flow field and tracer homogenization was performed using the commercial CFD software FLUENT 6.1. The aim is to investigate the potential of CFD software to predict concentration distribution of added tracer in cylindrical vessels. The calculated results – dimensionless velocity profiles, power and pumping numbers, dimensionless concentration curves, and mixing times – were compared with experiments in stirred vessels. In Part I, the study was performed for vessels agitated by one or two impellers on a centric shaft. Two different impellers were used – a 6‐bladed 45° pitched blade turbine and a standard Rushton turbine. The standard k‐? turbulence model and multiple reference frames method were used for the simulations. The influence of the grid type was also investigated; three types of grid – a structured, unstructured and a special user‐defined grid – were studied.     

Hydrodynamic and heat transfer characteristics of a centrally heated cylindrical enclosure: CFD simulations and experimental measurements

Natural convection in enclosures is of importance in many engineering applications. The stratification arising out of natural convection may be desirable/undesirable depending on applications. In order to control the degree of stratification, understanding of flow pattern and temperature profiles is required. In the present work, transient natural convection in a cylindrical enclosure has been investigated for water with CFD simulations and flow visualization [using particle image velocimetry (PIV) and hot film anemometry (HFA)] over a wide range of parameters namely Rayleigh number (1.08 × 10¹¹ ≤ Ra ≤ 3.76 × 10¹³) and aspect ratio (1 ≤ H/R ≤ 2). The effect of various parameters like pressure, tube diameter and aspect ratio on the extent of stratification has been studied. PIV measurements have been performed to understand the transient flow behavior. Multiple thermocouples were used to measure the temperature profiles. CFD simulations have been performed using SST k–ω model and the results have been compared with the PIV measurements. The CFD simulations have been carried out for 2D axi-symmetric cases and the effect of boundary conditions (free-slip and no-slip) has been investigated. An excellent agreement was found between the CFD predictions and the experimental measurements of flow and temperature patterns. The extent of stratification has been quantified using dimensionless parameters like stratification number and stratification time. The kinetic energy profiles and kinetic energy dissipation profiles show that almost 75% of the enclosure is stratified (after different times depending on Ra number and the aspect ratio). The turbulence parameters were found to weaken with time in the stratified region and these predictions are corroborated with HFA measurements.     

Study of an Annular Photoreactor with Tangential Inlet and Outlet: I. Fluid Dynamics

Photochemical reactors tend to exhibit turbulent flow even with low Reynolds numbers. The k‐? model is not always appropriate in this situation. An annular photoreactor was designed with tangential inlet and outlet tubes to investigate this. The fluid flow was characterized by residence time distribution (RTD) experiments, which were reproduced by computational fluid dynamics considering four relevant turbulence models: the k‐?, the k‐ω, the shear stress transport, and the Reynolds stress models. Inlet effects induced helical flow throughout the reactor, switching to plug flow depending on the flow rate and the turbulence model. The k‐ω model properly deals with viscous effects and reproduces the experimental RTD curves with correlation coefficients greater than 0.9566, against 0.8705 from the k‐? model.     

Onset of solutal convection in liquid phase epitaxy system

The onset of convective instability in the liquid phase epitaxy system is analyzed with linear stability theory. New stability equations are derived under the propagation theory, and the dimensionless critical time τ _c to mark the onset of the buoyancy-driven convection is obtained numerically. It is here found that the critical Rayleigh number Ra _c is 8000, below which the flow is unconditionally stable. For Ra>Ra _c the dimensionless critical time τ _c to mark the onset of a fastest growing instability is presented as a function of the Rayleigh number and the Schmidt number. Available numerical simulation results and theoretical predictions show that the manifest convection occurs starting from a certain time τ _o (> τ _c ). It seems that during τ _c ≤τ≤τ _o secondary motion is relatively very weak. This article is dedicated to Professor Chang Kyun Choi for celebrating his retirement from the School of Chemical and Biological Engineering, Seoul National University.     

Prediction of strongly swirling flow within an axial hydrocyclone using two commercial CFD codes

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.     

Coaxial Mixer Hydrodynamics with Newtonian and non‐Newtonian Fluids

The performance of several combinations of a wall scraping impeller and dispersing impellers in a coaxial mixer operated in counter‐ and co‐rotating mode were assessed with Newtonian and non‐Newtonian fluids. Using the power consumption and the mixing time as the efficiency criteria, impellers in co‐rotating mode were found to be a better choice for Newtonian and non‐Newtonian fluids. The hybrid impeller‐anchor combination was found to be the most efficient for mixing in counter‐rotating or co‐rotating mode regardless of the fluid rheology. For both rotating modes, it was shown that the anchor speed does not have any effect on the power draw of the dispersing turbines. However, the impeller speed was shown to affect the anchor power consumption. The determination of the minimum agitation conditions to achieve the just suspended state of solid particles (N_js) was also determined. It was found that N_js had lower values with the impellers having the best axial pumping capabilities.     

LIMITATIONS AND EMPIRICAL EXTENSIONS OF THE k-ε MODEL AS APPLIED TO TURBULENT CONFINED SWIRLING FLOWS

Shortcomings and recommended corrections to the standard two-equation k-ε turbulence model suggested by previous investigators are presented. They are assessed regarding their applicability to turbulent swirling recirculating flow. Recent experimental data on swirling confined flows, obtained with a five-hole pilot probe and a six-orientation hot-wire probe, are used to obtain optimum values of the turbulence parameters C_μ, C₂, and σ_ε, for swirling flows. General predictions of moderately and strongly swirling flows with these values are more accurate than predictions with the standard or previous simple extensions of the k-ε turbulence model.     

Axial dispersion in gases flowing through small bore helical column

The results of an experimental study on the axial dispersion of gases flowing in helical columns under laminar flow conditions are reported. The ranges of variables covered are 26.6 < λ < 98; 10 < N_Re < 100; 0.176 < N_Sc < 1.359. The measured dispersion coefficients are correlated with Reynolds, Schmidt and Dean groups. A single dimensionless parameter, N_Dc (N_Se^0,5, was found to correlate the data well. Up to N_De (N_Sc)^0,5 =10, dispersions in straight and coiled tubes exhibit very similar axial dispersion behavior.     

Turbulence modelling of multiphase flow in high-pressure trickle-bed reactors

Computational fluid dynamics (CFD) has been used as a successful tool for single-phase reactors. However, fixed-bed reactors design depends overly in empirical correlations for the prediction of heat and mass transfer phenomena. Therefore, the aim of this work is to present the application of CFD to the simulation of three-dimensional interstitial flow in a multiphase reactor. A case study comprising a high-pressure trickle-bed reactor (30 bar) was modelled by means of an Euler-Euler CFD model. The numerical simulations were evaluated quantitatively by experimental data from the literature. During grid optimization and validation, the effects of mesh size, time step and convergence criteria were evaluated plotting the hydrodynamic predictions as a function of liquid flow rate. Among the discretization methods for the momentum equation, a monotonic upwind scheme for conservation laws was found to give better computed results for either liquid holdup or two-phase pressure drop since it reduces effectively the numerical dispersion in convective terms of transport equation.After the parametric optimization of numerical solution parameters, four RANS multiphase turbulence models were investigated in the whole range of simulated gas and liquid flow rates. During RANS turbulence modelling, standard k-ε dispersed turbulence model gave the better compromise between computer expense and numerical accuracy in comparison with both realizable, renormalization group and Reynolds stress based models. Finally, several computational runs were performed at different temperatures for the evaluation of either axial averaged velocity and turbulent kinetic energy profiles for gas and liquid phases. Flow disequilibrium and strong heterogeneities detected along the packed bed demonstrated liquid distribution issues with slighter impact at high temperatures.