CFD Prediction of Flow and Homogenization in a Stirred Vessel: Part II Vessel with Three and Four Impellers

This article deals with CFD simulations of flow inside stirred vessels equipped with three and four radial or axial impellers mounted on the same shaft. A comparison was made between simulated data and experiments for one‐ and two‐impeller systems and was presented in Part I [1]. The effect of the lowest impeller off‐bottom clearance, number of impellers used, and impeller type on the tracer distribution was studied. The simulations were mainly focused on the grid size and type and the analysis of the concentration curves in each impeller section. The predicted velocity fields, power and pumping numbers, concentration curves, and mixing times were validated with experimental data. The simulation results show the significant influence of the grid density on the velocity profiles and power and pumping numbers in contrast to the low impact on the concentration curves. A better prediction of the concentration curves was reached when radial impellers were used; the mixing times were generally over‐predicted.     

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.     

Radial Gas Mixing in a Fluidized Bed with a Multi‐Horizontal Nozzle Distributor using Response Surface Methodology

The gas mixing in the radial direction within a fluidized bed equipped with a multi‐horizontal nozzle distributor was studied using response surface methodology (RSM), which enables the examination of parameters with a moderate number of experiments. All experiments were carried out in a circular fluidized bed of 0.29 m I.D. cold model fluidized bed. The distributor is placed beside twenty‐two horizontal nozzles that are arranged in three concentric circles with all existing discharge directed clockwise. The tracer gas (CO₂) was discharged into the bed as a tracer gas and the analysis was performed with a gas chromatograph. In order to compare the different internal circulations, the tracer gas was discharged in the center area or annular area of the bed. In RSM, the static bed height, superficial velocity and the open area ratio of the distributor are chosen as the research variables, and the standard deviation of the time averaged radial tracer concentration is used as the objection function. A mathematical model for the gas mixing as a function of the operating parameters was empirically proposed. The results show that the standard deviation of time averaged radial tracer concentration is well correlated with the operating and geometry parameters, (U – U_mf)/U_mf, H_s/D and ψ_d, and that the tracer gas injected to the center position has a better dispersion than when injected to the annular position. This model can be used for optimizing the design of fluidized bed reactors at a required performance level.     

Optimisation of vertical axis wind turbine: CFD simulations and experimental measurements

A system for the conversion of kinetic energy of wind into thermal energy has been developed which can replace relatively expensive electro‐mechanical equipment. The system consists of a vertical axis wind turbine (VAWT) which is coupled with the shaft of a stirred vessel. In the present work, computational fluid dynamic (CFD) simulations have been performed for the flow generated in a stirred tank with disc turbine (DT). The predicted values of the mean axial, radial and tangential velocities along with the turbulent kinetic energy have been compared with those measured by laser Doppler anemometry (LDA). Good agreement was found between the CFD simulations and experimental results. Such a validated model was employed for the optimisation of drag‐based VAWT. An attempt has been made to increase the efficiency of turbine by optimising the shape and the number of blades. For this purpose, the combination of CFD and experiments has been used. The flows generated in a stirred tank and that generated by a wind turbine were simulated using commercial CFD software Fluent 6.2. A comparison has been made between the different configurations of wind turbines. Results show that a provision in blade twist enhances the efficiency of wind turbine. Also, a wind turbine with two blades has higher efficiency than the turbine with three blades. Based on the detailed CFD simulations, it is proposed that two bladed turbine with 30° twist shows maximum efficiency. © 2011 Canadian Society for Chemical Engineering     

The Effects of Power Law Fluid Rheology on Coil Heat Transfer for Agitated Vessel in the Transitional Flow Regime

A CFD model of heat transfer from power‐law fluids to helical cooling coils in the transitional flow regime of a baffled tank mixed with a pitched blade turbine was developed with Fluent^TM. The model captured local temperature and velocity gradients. Simulations were run, varying Re, Pr, K and n. The results indicate that a Sieder‐Tate type correlation, with the exponent on and the coefficient in front of the Reynolds number being a function of n, is recommended for estimating ho. Also, a new two coil bank design was found to be more efficient when 450 < Re < 650.     

Experimental and Numerical Studies of the Flow Field in a Stirred Tank Equipped with Multiple Side‐Entering Agitators

The flow field and the macro‐mixing process in a stirred tank equipped with four side‐entering agitators were investigated experimentally and numerically. Experiments were conducted using two‐dimensional particle image velocimetry (PIV) measurements to characterize the flow field at different positions in the vessel. The computational fluid dynamics (CFD) simulation was performed by the software Fluent 6.3, using the standard k‐ϵ turbulent model and the multiple reference frame together with the sliding mesh technique. The macro‐mixing process was also discussed using CFD and decolorization experiments. The effects of the tracer detection positions and some mounting parameters in the mixing system were discussed. The results show that the mixing process was dominated by the flow field pattern in the stirred tank. According to the mixing times under different conditions using CFD simulation, the mounting parameters including inclination angle, plunging length and mounting height of the shaft were optimized.     

CFD and experimental studies of single phase axial dispersion coefficient in pulsed sieve plate column

This paper intends to study the single phase axial dispersion in pulsed sieve plate column using a combination of computational fluid dynamics (CFD) simulations and experimental measurements. Experiments and CFD simulations were conducted on 0.076 m diameter pilot scale column having standard geometry of 0.05 m plate spacing, 0.003 m hole diameter and 0.21 fractional free area. The effect of density of tracer solution and radial probe position on axial dispersion coefficient has been studied to ensure precision of the experimental measurement method. The effect of pulse velocity from 0.01 to 0.025 m/s and superficial velocity of water from 0.01 to 0.03 m/s has been studied. Simulations were carried out using commercial CFD software, FLUENT 6.2.16, with standard k–? model for turbulence. An unsteady state tracer injection technique was used for axial dispersion measurement. The range of velocity ratio (ψ = Re_o/Re_n) employed in this work was 1–4 which is very low. Therefore the effect of superficial velocity, V_c was found to be greater than pulse velocity. These results were critically compared with published data and it has been found that single phase axial dispersion coefficient is directly proportional to effective velocity (Af + 0.5 V_c). The presented CFD predictions and validation with experimental data will provide useful basis for further work on single phase axial dispersion with various geometrical parameters and understanding the two phase flow patterns in pulsed sieve plate column.     

Computational modelling of industrial pulp stock chests

Agitated pulp stock chests are the most widely used mixers in pulp and paper manufacture. Stock chests are used for a number of purposes, including attenuation of high‐frequency disturbances in pulp properties (such as mixture composition, fibre mass concentration, and suspension freeness) and are designed using semi‐empirical rules based largely on previous experience. Tests made on both laboratory and industrial‐scale pulp chests indicate that they are subject to non‐ideal flows, including channelling and creation of dead zones. In the present work, a commercial computational fluid dynamic (CFD) software (Fluent) is used to model two industrial pulp stock chests. The first chest is rectangular, agitated using a single side‐entering impeller, and feeds a mixture of chemical pulps at 3.5% mass concentration (C_m) to a papermachine. The second chest has rectangular geometry, with a mid‐feather wall used to direct suspension flow through a U‐shaped trajectory past four side‐entering impellers. This chest is used to remove latency from a C_m = 3.5% thermomechanical pulp suspension ahead of stock screening. For CFD computations, pulp rheology was described using a modified Hershel–Buckley model. Steady‐state simulations were made corresponding to process conditions during mill tests. The calculated steady‐state flows were then used to determine the dynamic response of the virtual chests and then compared with experimental measurements and found to agree reasonably well. The computed flow fields provided insight into mixing processes occurring within the chests, showing cavern formation around the impellers (which reduced the agitated volume available for mixing). Mass‐less particle tracking, using the steady‐state flow field, gave insight into the stagnant regions and bypassing zones created in the vessels. This paper discusses difficulties encountered in characterising the mixing (both experimentally and computationally) and the limitations of the industrial data.     

Vortex depth in mixed unbaffled vessels

An experimental investigation of vortex depth in an unbaffled cylindrical vessel with co-axial agitation was made. Five types of impellers: standard six-blade disc turbine, flat six-blade turbine, pitched six-blade turbine, pitched three-blade turbine and anchor agitator were tested. Turbine impellers were investigated in two positions (H₂ = d and H₂ = d/3). On the basis of theoretical analysis, the dimensionless vortex depth was statistically correlated as a function of Froude and Galileo numbers and a relative impeller size. Liquid viscosity and impeller size variations were reflected in the value of the Galileo number which was within the range 4 × 10⁵ – 5 × 10¹⁰. The vessel diameters used in the experiments were, D= 0.15, 0.20, 0.30, 0.40 and 0.64 m.     

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     

An integral criterion for turbulence suppression in swirling flows

A numerical study of flow in rotating pipes was conducted to elucidate the relative importance of convection and turbulence. CFD (Computational Fluid Dynamics) simulations of flow inside a rotating pipe (D = 2 cm and L/D = 20) were carried out, using the Reynolds Stress Model, for four different Reynolds numbers and a range of rotation numbers. The objective was to gain a deeper understanding of the interaction between fluid forces in swirling flows. This widely‐studied model problem was used to ascertain the conditions under which computationally cheaper turbulence models such as the k‐? model should be accurate. We identified a dimensionless rotation parameter that delineates the condition at which decreasing turbulence force equals increasing convective force as rotational speed increases. This dimensionless number establishes a criterion for knowing which forces are dominant, and thereby a rational basis for choosing turbulence models that are both cost‐effective and accurate. We found a universal, critical threshold that determines when convective forces dominate over turbulence forces. This threshold determination is based on an ‘integral measure criterion’ of local forces in the radial direction. The threshold itself is defined by a dimensionless rotation number, N, based on the ratio of the circumferential and axial flow velocities. The critical value was found to be N_cr = 0.45. Above this, convection dominates; below it, turbulence dominates. This finding will facilitate selection of CFD models to optimize cost and accuracy for modelling swirling flows. For example, k‐? models suffice when N_cr < 0.45, but more complex models are required for higher values.

     

Mixing of miscible liquids with density differences: Effect of volume and density of the tracer fluid

The effect on the mixing time of the density difference between the tracer fluid and the bulk, the type and geometry of the impeller, and the amount of the fluid added as a tracer, has been investigated in a tank with diameter of 0.31 m. The amount of tracer pulse has been varied in the range of 2 to 8% of the bulk volume and the density difference between two fluids has been varied in the range of 54 to 145 kg/m³. A generalized correlation has been developed for the prediction of dimensionless mixing time (Nθ) in terms of amount of the tracer fluid, density differences between the bulk and the tracer liquid and the pumping effectiveness of the impeller. A pitched blade downflow turbine with diameter as small as possible is the most energy efficient among the impellers studied in this work.     

CFD‐DEM Model for Simulating Solid Exchange in a Dual‐Leg Fluidized Bed

The domain coverage method (DCM) is proposed to establish a computational fluid dynamics‐discrete element method (CFD‐DEM) model based on irregular mesh. The gas field was solved by Fluent software and the DEM model was coupled with Fluent software by user‐defined functions. Gas turbulent viscosity was calculated by the coupled k‐? two‐equation model and the soft‐sphere collision model was used to get particle contact force. The CFD‐DEM model based on irregular mesh was firstly verified to be reasonable by comparing the simulated injected bubble with that simulated by Bokkers et al. The solid exchange behavior was studied numerically in a 2D dual‐leg fluidized bed (DL‐FB). The simulation results were compared with experimental results and proved that the CFD‐DEM model is established successfully based on the efficient DCM. The DEM model is expanded to be used on irregular mesh in fluidized beds with complex geometries.     

Influence of Floating Suspended Solids on the Homogenization of the Liquid Phase in a Mixing Vessel

The impact of floating suspended solids on the homogenization of the liquid phase in a stirred vessel was studied. The experiments were performed in a tank with an internal diameter of 0.32 m, equipped with a 45° pitched four-blade turbine (PTD) placed at varying positions in the vessel. Tap water was used as the liquid phase and polyethylene particles (PEHD) were used as the solid phase. The impeller speed was varied from N = 200–900 rpm. The mixing time of the suspended system was measured by a conductivity technique using a sodium chloride solution as the tracer, whereas power consumption was measured by the torque table. The influence of mean concentration of the suspended floating solids, average particle size, surface tension at the liquid/air interface and impeller diameter and its position on the mixing time and power consumption were analyzed.     

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.     

Determination of the Initiating Capability of Detonators Containing TKX‐50, MAD‐X1, PETNC,DAAF, RDX,HMX or PETN as a Base Charge,by Underwater Explosion Test

A comprehensive investigation to determine the initiation power of detonators containing as a base charge the novel explosives: dihydroxylammonium 5,5′‐bis(tetrazolate‐1N‐oxide) – TKX‐50, dihydroxylammonium 5,5′‐bis(3‐nitro‐1,2,4‐triazolate‐1N‐oxide) – MAD‐X1, pentaerythritol tetranitrocarbamate – PETNC and 3,3′‐diamino‐4,4′‐azoxyfurazan – DAAF in comparison with RDX, HMX and PETN was undertaken. In order to estimate the initiation power of the detonators, the underwater initiating capability test was used. The total energy as a sum of the primary shock wave energy and the bubble gas energy was determined for each of these explosives, by measuring the overpressure of the shock waves generated in water. Moreover, the complete synthesis for novel explosives is presented. The thermal behavior of the explosives was investigated using DSC (differential scanning calorimetry). The gas phase absolute molar enthalpies at 298 K and 10⁵ Pa were calculated theoretically using the modified complete basis set method (CBS‐4M; M referring to the use of minimal population localization) with the Gaussian 09 software. Gas phase standard molar enthalpies of formation (ΔH_f°_(g)) at 298 K were computed using the atomization energy method. Standard molar enthalpies of formation (▵H_(s)°) were calculated using ΔH_f°_(g) and the standard molar enthalpies of sublimation by applying Trouton’s rule. The Chapman‐Jouguet (CJ) characteristics based on calculated ▵H_(s)° values were computed using the EXPLO5 V6.01 thermochemical computer code. For the calculations the theoretical maximum densities and densities obtained during the experiments presented in this work were used.     

Gas‐Liquid Mass Transfer Rates and Impeller Power Consumptions for Industrial Vessel Design

Volumetric mass transfer coefficients (k_La) and power input (P) are often the key parameters in the design of gas‐liquid contactors. However, due to the limitations of most measurement methods, there is a lack of reliable data for predicting k_La for non‐coalescent batches under high energy dissipation rates. Accurate k_La and P correlations are proposed. The reliability of the correlations is ensured by using experimental data from a wide range of process conditions conducted in multiple‐impeller vessels of both laboratory scale and pilot scale, and including both non‐coalescent and coalescent batches. Applying the proposed correlations, the scale‐up and optimization of industrial vessels can be performed more accurately.     

Heat transfer and flow pattern in co‐current downward steam condensation in vertical pipes‐I: CFD simulation and experimental measurements

The condensation of pure steam flowing inside a vertical tube has been extensively studied during the last nine decades. Considerable amount of experimental and analytical efforts can be found due to the significance of this subject in practice. In the present work (Part I), experimental investigations have been performed over a range of pressure (0.1 < P < 0.35 MPa) and internal tube diameter (D_i = 10, 20 and 43 mm). A two‐dimensional computational fluid dynamic (CFD) simulations have been carried out commercial software Fluent 6.2 [Fluent 6.2, “User's Manual to FLUENT 6.2,” Fluent Inc., Lebanon, USA, 2005]. CFD results were used to predict the temperature profiles, pressure drop and the heat transfer coefficient, which was in close agreement with the experimental values. The film characteristics predicted by the CFD simulations have been compared qualitatively with the photographic images. Further, the CFD model developed in Part I extended for the analysis of all the experimental data reported in the published literature. © 2012 Canadian Society for Chemical Engineering     

半圆管曲面涡轮搅拌槽内混合特性的数值模拟

在商业化软件ANSYS CFX 10.0平台上,采用多重参考系法来解决挡板与桨叶之间的相对转动问题,由标准k-ε模型对半圆管曲面涡轮搅拌槽内流动和混合过程进行了详细的数值模拟,本模拟所得的功率准数和设计值以及相关文献值吻合良好。结果表明：当搅拌桨离底距离由搅拌槽直径的1/2处变为1/3处时,搅拌槽内的流型均为典型的“双循环流型”,而当搅拌桨离底距离由搅拌槽直径的1/3处降低至1/6处时,槽内流型由典型的“双循环流型”转变为“单循环流型”;通过对不同时刻不同桨叶离底距离下的示踪剂浓度分布图分析表明槽内的混合过程与流动场密切相关;加料点位置对于最终的流场混合效果有着显著影响,对于混合时间数据的采集应注意不同加料位置时监测点的选取。CFD模拟结果表明本文所采用的模型可以很好的预测半圆管曲面涡轮搅拌槽内的混合特性,为进一步改进和优化半圆管曲面涡轮的设计提供了一定的参考。     

Measurement and Simulation of Fluid Flow in Agitated Solid/Liquid Suspensions

Numerical and experimental investigations were carried out to improve the knowledge of the flow field in solid/liquid suspensions in agitated vessels and to examine the ability of the commercial CFD, code CFX 4.2, for this application. The numerical results were compared with our own experimental results of time resolved Laser‐Doppler‐Velocimeter (LDV) and power input measurements with particle concentrations of up to 15 percent of the volume. To perform LDV measurements within the solid/liquid flow the refractive index matching method was used. Results of the CFD simulation show the necessity to use high grid resolution, the k‐ϵ turbulence model and an advanced discretization scheme to achieve a grid‐independent solution. Simplifications of the grid geometry were shown to be an acceptable way to minimize the time required for calculation. The comparison of experimental and numerical results shows good agreement for velocities and power input in the single‐ and in all two‐phase flow cases. Good agreement with regard to the kinetic energy k is also apparent, except in the region near the stirrer blades, where local maxima are underestimated by the simulation.