An assessment of different turbulence models for predicting flow in a baffled tank stirred with a Rushton turbine

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.     

NUMERICAL SIMULATION OF TURBULENT FLOW OF AGITATED LIQUID WITH PITCHED BLADE IMPELLER

The turbulent flow field in an agitated system with baffles was solved numerically using the standard k-e model, an algebraic Reynolds stress model (ASM) and a differential Reynolds stress model (RSM). The commercial software FLOW3D (CFDS, Harwell Laboratories, 1991) was used for this purpose. The aim of the study was to investigate the influence of the impeller boundary conditions and turbulence models to the agreement with experimentally obtained laser-Doppler anemometry data. The boundary conditions for the impeller discharge used in the numerical calculations were obtained as whole-cycle-ensemble averages from experimental LDA-measurements (Fort et al., 1992). Since measurements of the rate of dissipation of turbulent kinetic energy ( ε) was not available the dissipation rate per unit mass in the impeller discharge was estimated from the expression:

where k is the turbulent kinetic energy per unit mass and L the macroscale of turbulence in the pitched blade impeller discharge. The macroscale of turbulence (L) in the impeller boundary condition for e was varied in order to optimize the fit of theoretically obtained profiles of turbulent kinetic energy with experimental data. The constant A was fixed to 0.85 according to Wu and Patterson (1989). The optimal values of L for the different turbulence models were compared with the projected height of the impeller blade (h). All three components of the mean velocity were compared with experimental data for the optimal ratio of L/h for six radial cross-sections in the tank.

The mean velocity field obtained from simulations showed good agreement with experimental data for all models, with somewhat better agreement for the k — e model. An optimal value of the ratio L/h was found to be equal to 2.0 for the k — ε model and 1.3 for the ASM. However, no such optimal value for the RSM could be determined in this study.     

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.     

Turbulent mixing in a confined rectangular wake

Liquid-phase turbulent transport in a confined rectangular wake was investigated for a Reynolds number of 37,500 based on bulk velocity and the hydraulic diameter of the test section and a Schmidt number of 1250 using particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF). The velocity and concentration field data were analyzed for flow statistics such as the mean velocity, Reynolds stresses, turbulent kinetic energy, turbulent dissipation rate, mixture-fraction mean, mixture-fraction variance and one-point composition probability density functions (PDF). Computational fluid dynamics (CFD) models, including a two-layer k-ε turbulence model, a scalar gradient-diffusion model and a scalar dissipation rate model were validated against PIV and PLIF data collected at six downstream locations. Low-Reynolds-number effects on turbulent transport were taken into consideration through the mechanical-to-scalar time-scale ratio. The experimental and computational results were found to be in satisfactory agreement.     

Numerical simulation of turbulent flow in a baffled stirred tank with an explicit algebraic stress model

An explicit algebraic stress model (EASM) was used to simulate anisotropic turbulent flows in baffled stirred tanks equipped with a standard Rushton turbine. The quantitative predictions of velocity components, turbulence kinetic energy, Reynolds stresses and turbulence energy dissipation rate in the context of anisotropic turbulence were conducted to assess the comprehensive performance of the EASM. A lot of efforts have been made to ensure numerical stability during the calculations such as using a good initial flow field, manipulating source terms and adjusting under-relaxation factors. The predicted results were also compared with experimental data and other simulation results obtained using the standard k–ε model, algebraic stress model (ASM), Reynolds stress model (RSM) and large eddy simulation (LES). All the simulations were run with in-house codes. The simulation results show that agreement between the EASM predictions and experimental values is satisfactory. The EASM is consistently superior to the standard k–ε model when predicting both peak values and trend of variation in velocities and turbulence quantities. In comparison to the RSM, the EASM has almost the same predictive accuracy. The EASM is inferior to the LES on the prediction of turbulence kinetic energy. Nevertheless, the computational cost of the EASM is significantly lower than that of the LES, which is an obvious advantage in practical applications.     

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.     

CFD modeling of pilot-scale pump-mixer: Single-phase head and power characteristics

The present work involves single-phase computational fluid dynamics (CFD) simulations of continuous flow pump-mixer employing top-shrouded Rushton turbines with trapezoidal blades. Baffle—impeller interaction has been modeled using sliding mesh and multiple reference frame approaches. Standard k-ε model has been used for turbulence modeling. Several CFD runs representing different combinations of geometric and process parameters have been carried out. Results of CFD simulations have been used to find out two macroscopic performance parameters of pump-mixer—power consumption and head generated by the impeller. The simulation results have been compared with the experimental data obtained on a pilot-scale setup. Good agreement between CFD predictions and experimental results is observed. In most cases, sliding mesh approach is found to perform better than multiple reference frame approach. Details from CFD simulations have been used to have an insight into the pumping action of the impeller.     

Detached eddy simulation on the turbulent flow in a stirred tank

A detached eddy simulation (DES), a large‐eddy simulation (LES), and a k‐ε‐based Reynolds averaged Navier‐Stokes (RANS) calculation on the single phase turbulent flow in a fully baffled stirred tank, agitated by a Rushton turbine is presented. The DES used here is based on the Spalart‐Allmaras turbulence model solved on a grid containing about a million control volumes. The standard k‐ε and LES were considered here for comparison purposes. Predictions of the impeller‐angle‐resolved and time‐averaged turbulent flow have been evaluated and compared with data from laser doppler anemometry measurements. The effects of the turbulence model on the predictions of the mean velocity components and the turbulent kinetic energy are most pronounced in the (highly anisotropic) trailing vortex core region, with specifically DES performing well. The LES—that was performed on the same grid as the DES—appears to lack resolution in the boundary layers on the surface of the impeller. The findings suggest that DES provides a more accurate prediction of the features of the turbulent flows in a stirred tank compared with RANS‐based models and at the same time alleviates resolution requirements of LES close to walls. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3224–3241, 2012     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

CFD Modeling of Turbulent Jacket Heat Transfer in a Rushton Turbine Stirred Vessel

CFD modelling of the turbulent heat transfer was performed for a stirred tank equipped with a Rushton turbine impeller and four standard baffles. Eight different turbulence models, i.e. the standard k‐?, RNG k‐?, realizable k‐?, Chen‐Kim k‐?, optimized Chen‐Kim k‐?, standard k‐ω, k‐ω SST and Reynolds stress models, were used during the modelling. In all investigated cases, the boundary flow at the vessel wall was described by the standard logarithmic wall functions. The CFD modelling values of the local heat transfer coefficient were compared with the corresponding experimental data. The best agreement was obtained for the standard k‐?, optimized Chen‐Kim k‐? and k‐ω SST models.     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

CFD simulation of hydrodynamics of gas–solid multiphase flow in downer reactors: revisited

In the present work, a k₁–ε₁–k₂–k₁₂ two-fluid model based on the kinetic theory of granular flow (KTGF) was employed to predict the flow behavior of gas and solids in downers, where the particles of small size as 70 μm in diameter apparently interact with the gas turbulence. The turbulence energy interaction between gas and solids was described by different k₁₂ transport equations, while the particle dissipation by the large-scale gas turbulent motion was taken into account through a drift velocity. Johnson–Jackson boundary condition was adopted to describe the influence of the wall on the hydrodynamics. The simulation results by current CFD model were compared with the experimental data and simulation results reported by Cheng et al. (1999. Chem. Eng. Sci. 54, 2019) and Zhang and Zhu (1999. Chem. Eng. Sci. 54, 5461). Good agreement was obtained based on the PDE-type k₁₂ transport equation. The results demonstrated that the proposed model could provide good physical understanding on the hydrodynamics of gas–solid multiphase flow in downers. Using the current model, the mechanism for formation and disappearance of the dense-ring flow structure and the scale-up characteristics of downers were discussed.     

CFD simulations of gas-liquid-solid stirred reactor: Prediction of critical impeller speed for solid suspension

In this work, simulations have been performed for three phase stirred dispersions using computational fluid dynamics model (CFD). The effects of tank diameter, impeller diameter, impeller design, impeller location, impeller speed, particle size, solid loading and superficial gas velocity have been investigated over a wide range. The Eulerian multi-fluid model has been employed along with the standard k-ε turbulence model to simulate the gas-liquid, solid-liquid and gas-liquid-solid flows in a stirred tank. A multiple reference frame (MRF) approach was used to model the impeller rotation and for this purpose a commercial CFD code, FLUENT 6.2. Prior to the simulation of three phase dispersions, simulations were performed for the two extreme cases of gas-liquid and solid-liquid dispersions and the predictions have been compared with the experimental velocity and hold-up profiles. The three phase CFD predictions have been compared with the experimental data of Chapman et al. [1983. Particle-gas-liquid mixing in stirred vessels, part III: three phase mixing. Chemical Engineering Research and Design 60, 167-181], Rewatkar et al. [1991. Critical impeller speed for solid suspension in mechanical agitated three-phase reactors. 1. Experimental part. Industrial and Engineering Chemistry Research 30, 1770-1784] and Zhu and Wu [2002. Critical impeller speed for suspending solids in aerated agitation tanks. The Canadian Journal of Chemical Engineering 80, 1-6] to understand the distribution of solids over a wide range of solid loading (0.34-15 wt%), for different impeller designs (Rushton turbine (RT), pitched blade down and upflow turbines (PBT45)), solid particle sizes (120-) and for various superficial gas velocities (0-10 mm/s). It has been observed that the CFD model could well predict the critical impeller speed over these design and operating conditions.     

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.     

CFD analysis of turbulence in a baffled stirred tank, a three-compartment model

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.     

三种湍流模型下搅拌釜内气含率特性的模拟

采用计算流体力学（CFD）方法,应用Euler-Euler双流体模型,桨叶采用多重参考系法（MFR）,与考虑气泡聚并与破碎对气泡尺寸影响的群体平衡模型（PBM）相结合,比较了标准k-ε、Realizable k-ε和RNG k-ε3种湍流模型对双层涡轮搅拌釜内气-液两相液相流场、局部气含率及气泡尺寸分布的影响。结果表明：3种湍流模型预测的液相流场流型相似,总体气含率预测值相差不大,均与实验值吻合较好。对于局部气含率,标准k-ε和RNG k-ε模型在桨叶区的预测值偏大,在接近自由液面处三者预测值均偏低,Realizable k-ε模型预测结果与实验值符合最好;对于气泡尺寸,3种湍流模型预测结果均与实验值较吻合,在靠近自由液面处预测值均偏小,气泡尺寸分布与湍流长度分布相吻合。     

CFD simulation of mixing in tall gas-liquid stirred vessel: Role of local flow patterns

In this work, we have used the computational fluid dynamics (CFD)-based models to investigate the gas-liquid flows generated by three down-pumping pitched blade turbines. A two-fluid model along with the standard k-ε turbulence model was used to simulate the dispersed gas-liquid flow in a stirred vessel. Appropriate drag corrections to account for bulk turbulence [Khopkar and Ranade, 2005. CFD simulation of gas-liquid flow in a stirred vessel: VC, S33 and L33 flow regimes. A.I.Ch.E. Journal, accepted for publication] were developed to correctly simulate different flow regimes. The computational snapshot approach was used to simulate impeller rotation and was implemented in the commercial CFD code, FLUENT4.5 (of Fluent. Inc., USA). The computational model has successfully captured the flow regimes as observed during experiments. The particle trajectory simulations were then carried out to examine the influence of the different flow regimes on the circulation time distribution. The model predictions were verified by comparing the predicted results with the experimental data of [Shewale and Pandit, 2006. Studies in multiple impeller agitated gas-liquid contactors. Chemical Engineering Science 61, 489-504]. The computational model and results discussed in this study would be useful for explaining the implications local flow patterns on the mixing process and extending the applications of CFD models for simulating large multiphase stirred reactors.     

Numerical optimization for blades of Intermig impeller in solid–liquid stirred tank

The multiphase flow in the solid-liquid tank stirred with a new structure of Intermig impeller was analyzed by computational fluid dynamics(CFD).The Eulerian multiphase model and standard k-ε turbulence model were adopted to simulate the fluid flow,turbulent kinetic energy distribution,mixing performance and power consumption in a stirred tank.The simulation results were also verified by the water model experiments,and good agreement was achieved.The solid-liquid mixing performances of Intermig impeller with different blade structures were compared in detail.The results show that the improved Intermig impeller not only enhances the solid mixing and suspension,but also saves more than 20% power compared with the standard one.The inner blades have relatively little influence on power and the best angle of inner blades is 45°,while the outer blades affect greatly the power consumption and the optimized value is 45°.     

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.