A Study of the Mixing Performance of Different Impeller Designs in Stirred Vessels Using Computational Fluid Dynamics

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Article A Study of the Mixing Performance of Different Impeller Designs in Stirred Vessels Using Computational Fluid Dynamics

Ian Torotwa and Changying Ji *

College of Engineering, Nanjing Agricultural University Jiangsu Province, Nanjing 210031, China; [email protected] * Correspondence: [email protected]

Received: 8 January 2018; Accepted: 6 March 2018; Published: 8 March 2018

Abstract: Design and operation of mixing systems using agitated vessels is a difficult task due to the challenge of obtaining accurate information on impeller-induced turbulence. The use of Computational Fluid Dynamics (CFD) can provide detailed understanding of such systems. In this study, experimental tests and computational fluid dynamics simulations were performed to examine the flow characteristics of four impeller designs (anchor, saw-tooth, counter-flow and Rushton turbine), in achieving solution homogeneity. The impellers were used to mix potassium sulfate granules, from which values of electrical conductivity of the solution were measured and used to estimate the distribution pattern of dissolved solid concentrations within the vessel. CFD models were developed for similar mixing arrangement using commercial software, ANSYS Fluent 18.1 solver and the standard k-epsilon (ε) turbulence model. The Multiple Reference Frame (MRF) approach was used to simulate the impeller rotation. Velocity profiles generated from the simulations were in good agreement with the experimental predictions, as well as with results from previous studies. It was concluded that, through CFD analysis, detailed information can be obtained for optimal design of mixing apparatus. These findings are relevant in choosing the best mixing equipment and provides a basis for scaling up mixing operations in larger systems.

Keywords: impeller design; turbulent mixing; homogeneity; computational fluid dynamics; ANSYS fluent; multiple reference frame; velocity profile

1. Introduction Mixing is an essential operation in many engineering fields. It has central significance in food processing, pharmaceutical production, chemical engineering, biotechnology, agri-chemical preparations, paint manufacturing, water purification among countless other applications [1]. Many mixing schemes using stirred tanks have been developed to meet various production and processing goals [2]. In agricultural systems, mixing set-ups have been used in a number of processes, such as preparing farm chemical concentrations, balancing nutrient amounts in fertilizer tanks, blending different substances and processing farm products. One of the main aims of agitation systems using stirred vessels is to maintain balanced quantities of substances in different phases based on concentration levels [3]. In cases where soluble solids are mixed, stirrers are used to increase interaction between the particles and avoid uneven accumulation at one point [4]. Flow streams in stirred vessels are known to be turbulent, chaotic and difficult to determine; therefore attaining homogeneity in such mixing processes is a demanding task. Achieving uniform concentrations of mixing products is paramount for efficient and economical use of the expensive chemicals, fertilizers and other mixing agents in agricultural applications. A careful choice of equipment that generates sufficient turbulence and flow in the mixing vessel is therefore necessary.

Designs 2018, 2, 10; doi:10.3390/designs2010010 www.mdpi.com/journal/designs Designs 2018, 2, 10 2 of 16

The inconsistencies in mixing quality can be attributed to the lack of a clear understanding of the mixing processes due to the complex nature of impeller-induced turbulence in agitated vessels [5,6]. There is a need for in-depth studies to determine mixing efficiency and accurately predict the overall performance of these systems. It has been established that the performance of mixing processes is a product of the mixing time, the type of impeller used, number of impeller blades, blade size, working angular speeds, and vessel configurations [7]. In large-scale mixing plants, stirrers and the entire agitation set-up should be able to create faster movement of substances and high turbulence. This makes the entire mixing process in large containers complicated and impractical to study through experiments [8]. There is therefore a need to provide a more workable method that will simplify the process. Computational fluid dynamics (CFD) is instrumental in analyzing fluid flow systems using numerical methods and simulations in computer-controlled programs [9]. With CFD, engineers can easily study new and complex models in virtual environments, determine the design details, predict possible sources of failure and optimize system operations. Simulations have been used to investigate the hydrodynamics of many industrial processes and aeronautics among other numerous fields [10]. Furthermore, many researchers and industrialists have found the use of CFD helpful in reducing the cost and time spent in creating large and complicated prototypes of trial systems. Using CFD technique, satisfactory and crucial information can be obtained within a small working area and with less effort. In order to achieve excellent mixing results, CFD can be employed as a tool for gaining in-depth knowledge of the turbulent dynamics of mixing operations in stirred vessels. Through numerical simulations, the effects of diverse and irregular configurations of mixing tanks, impeller designs and baffles can be modelled. The expected performance of using atypically large vessels [11] and under extreme working conditions can also be projected. Some of the mixing parameters that have been investigated using numerical methods in CFD include mixing times, power requirements, flow types, and velocity patterns [12]. Since impeller design is the most important component for determining the performance of mechanically agitated mixers [13], its design features and operational characteristics can be described theoretically using CFD. Several researchers have performed CFD tests to examine the effects of impeller type in mixing vessels. Cokljat et al. [14–16] did simulations of impeller flow behavior in stirred tanks using CFD in order to study flow velocities and mixing time. Tatterson [17] emphasized the importance of numerically modelling precise impeller flow characteristics. The objective of this work was to use CFD technique alongside experimental tests to study the mixing behavior of different impeller designs. This will add to the knowledge necessary for choosing the best mixing designs. It was also expected that this work would give a justifiable basis for accurate scale-up of mixing systems in industrial, field, and agricultural mixing operations. In this study, four different types of impellers: anchor, counter-flow, saw-tooth, and Rushton turbine impellers were designed and studied to determine how their distinct design features affected flow characteristics in a stirred vessel. Experimental tests were performed to provide a comparative reference to the simulation results. Velocity profiles generated in CFD were interpreted as the impeller flow characteristics. Simulations were done using commercial software, ANSYS Fluent 18.1 solver. The standard k-epsilon (ε) model was used to set up the turbulent flow process and the multiple reference frames (MRF) approach used to model the impeller motion in a baffled tank.

2. Materials and Methods Experiments were conducted in the engineering laboratory of Nanjing Agricultural University in the month of August 2017, at room temperature and pressure. Four distinct, top-entering agitation impeller designs were used to dissolve solid granules of potassium sulfate (K2SO4) in water. Electrical Conductivity (EC) measurements of the mixed solutions from different locations in the liquid volume were used to predict the individual impeller performance. Designs 2018, 2, 10 3 of 16

DesignsDesigns 2018 2018, 2, ,x 2 FOR, x FOR PEER PEER REVIEW REVIEW 3 of3 16of 16 2.1. Experimental Set-Up 2.1.2.1 Experimental. Experimental Set Set-Up-Up A cylindrical tank with four bafﬂes arranged symmetrically on the tank’s inner walls was designed A cylindricalA cylindrical tank tank with with four four baffles baffles arranged arranged symmetrically on on the the tank’s tank’s inner inner walls walls was was for the experiment. Figure1 below shows the experimental tank, with one bafﬂe cut off to show the designeddesigned for for the the experiment. experiment. Figure Figure 1 1 below below showsshows the experimental tank, tank, with with one one baffle baffle cut cut off off to to inner apparatus.showshow the the inner inner apparatus. apparatus.

Figure 1. FigureExperimental 1. Experimental apparatus apparatus set-up set-up showing showing the assembly the assembly that was thatused to was perform used the tomixing perform the mixing experiment.Figureexperiment. 1. Experimental apparatus set-up showing the assembly that was used to perform the mixing experiment. The shaft holding the impellers had a diameter of 0.012 m and were positioned concentric to the The shaftaxis of holding the tank. the Baffles impellers were included had a in diameter the set-up of to 0.012prevent m the and liquid were from positioned spinning as concentric a single to the The shaft holding the impellers had a diameter of 0.012 m and were positioned concentric to the body. The outline of the experimental tank and the dimensions of the agitation components are axis of theaxis tank. of the Bafﬂestank. Baffles were were included included in in the the set-up set-up to prevent prevent the the liquid liquid from from spinning spinning as a single as a single shown in Figure 2 and Table 1 respectively. body. Thebody. outline The outlineof the experimental of the experimental tank andtank the and dimensions the dimensions of the of the agitation agitation components components are are shown in Figureshown2 and in Table Figure1 respectively.2 and Table 1 respectively.

Figure 2. Diagram representing the experimental set-up dimensions.

FigureFigure 2. Diagram 2. Diagram representing representing the the experimentalexperimental set set-up-up dimensions dimensions..

Table 1. Dimensions of the agitation apparatus.

Parameter Symbol Value (mm)

Tank diameter T 360 Tank height H 500 Impeller diameter D = T/2 180 Impeller blade height h 10 Bafﬂe length L 440 Bafﬂe width B = D/12 15 Impeller clearance C = D/3 60 Designs 2018, 2, x FOR PEER REVIEW 4 of 16

Table 1. Dimensions of the agitation apparatus.

Parameter Symbol Value (mm) Tank diameter T 360 Tank height H 500 Impeller diameter D = T/2 180 Impeller blade height h 10 Baffle length L 440 Baffle width B = D/12 15 Designs 2018, 2, 10 4 of 16 Impeller clearance C = D/3 60

AnAn electric electric mixer mixer (M12 (M12 + + 70 70 cm, cm, Wuyi Wuyi Mingcheng Mingcheng Co. Co.,, Hengshui Hengshui City, City, China China)) with with a a capacity capacity of of 220220 V, V, 50 50 Hz, Hz, 1050 1050 W W and and six six adj adjustableustable speeds speeds of of between between 100 100–600–600 rpm rpm was was used used to to run run the the impellers. impellers. WaterWater was filled ﬁlled into the tank up to the 500 mm mark so that all bafﬂesbaffles werewere submerged.submerged. TheThe four four distinct distinct designs designs of of impellers impellers used used for for the the experiment experiment were were designed designed in in Solid Solid-works-works 20162016 computercomputer aided aided design design (CAD) (CAD) software software and manufacturedand manufactured using Computer using Computer Numerical Numerical Machines Machines(CNC). They (CNC). were They all open were left-hand all open (LH) left types-hand and (LH) made types of SUS304 and made steel. of The SUS304 blade steel thickness. The blade of the thicknessimpellers of was the 2.5 impellers mm with was a diameter 2.5 mm with of 0.180 a diameter m (T/D of = 0.180 0.5). m (T/D = 0.5). TheThe impellers were were placed placed 60 60 mm mm above above the tangential the tangential line of line the of liquid the bottom liquid bottom surface. surface. A working A workingangular velocityangular ofvelocity 100 rpm of 100 was rpm used was for allused the for designs. all the designs. FigureFigure 33 belowbelow shows shows the thedesign design details details of the ofimpellers the impellers and the manufactured and the manufactured experimental designsexperimental. designs.

FigureFigure 3 3.. ExperimentalExperimental impeller impeller designs designs and and the the actual actual impellers impellers tested: tested: (a) saw (a) saw-tooth-tooth impeller impeller (b) Rushton(b) Rushton turbine turbine (c) counter (c) counter-ﬂow-flow impeller impeller and and (d.) (anchord) anchor impeller impeller.

ThreeThree hundred hundred grams grams of of p potassiumotassium sulfate sulfate granules granules were were dissolved dissolved for for a a period period of of two two minutes minutes forfor e eachach impeller impeller construction. construction. Eleven Eleven samples samples of of the the resultant resultant solution solution were were collected collected at at different different pointspoints as as the the solution solution was was drained drained through through the the valve valve at at the the bottom bottom of of the the tank. tank. The The points points of of sample sample collectioncollection were were identified identiﬁed when when the the solution solution was was at at an an inte intervalrval of of 50 50 mm mm (5 (5 cm) cm) apart apart along along the the verticalvertical cross cross-section-section (i.e. (i.e.,, 0 0 mm, 50 mm, 100 mm ...… 500500 mm). mm). EC EC values values of of the the resultant resultant sampled sampled solutionssolutions were were measured measured using an EC EC-meter.-meter. K 2SOSO44 waswas used used as as the the tracer tracer element element in in this this experiment experiment becausebecause it it dissolves dissolves and and ionize ionize readily readily in in water water [18 [18]. ].Figure Figure 4 4below below shows shows the the laboratory laboratory set set-up-up of of the experimental apparatus and the Electrical conductivity meter used to measure the electrical conductivity values. Designs 2018, 2, x FOR PEER REVIEW 5 of 16

the experimental apparatus and the Electrical conductivity meter used to measure the electrical Designs 2018, 2, 10 5 of 16 conductivity values.

Figure 4.4. ((aa)) TheThe laboratorylaboratory apparatusapparatus set-upset-up showing the mixer connected to a power source, tank ﬁlledfilled withwith water,water, standstand andand aa shaftshaft connectingconnecting thethe motormotor toto the impeller insideinside thethe tank. (b) Measuring electricalelectrical conductivityconductivity (EC)(EC) usingusing anan EC-meter.EC-meter.

The samples tested represented the solution from the different specific regions of the tank and The samples tested represented the solution from the different speciﬁc regions of the tank and would be used to predict the concentration variability of the dissolved solids in the entire container. would be used to predict the concentration variability of the dissolved solids in the entire container.

2.2.2.2. Numerical Modeling Simulations of of the the mixing mixing process process were were done done in inCFD CFD using using an ANSYS an ANSYS Fluent Fluent 18.1 18.1solver. solver. The Thedesign design model model used usedwas an was agitated an agitated baffled baffled-cylindrical-cylindrical vessel of vessel identical of identical dimensions dimensions to the one to used the onein the used experimental in the experimental tests. tests. The aim aim of of turbulence turbulence simulation simulation is to ispredict to predict the physical the physical behavior behavior of turbulent of turbulentflow generated flow generatedin a system in using a system numerical using numerical methods. Turbulentmethods. Turbulentmotions in motions engineering in engineering applications applications are three- aredimensional, three-dimensional, non-homogenous non-homogenous and non-isotropic. and non-isotropic. The various The methods various methodsof simulating of simulating this behavior this behaviorallows for allows the statisticalfor the statistical description description of variable of variable flow flow fields fields using using the the post post-process.-process. A A modeling method usedused shouldshould ensureensure accuracy,accuracy, simplicitysimplicity andand computationalcomputational efficiencyefficiency [ 19[19].]. A numbernumber ofof approachesapproaches have have been been employed employed for for turbulent turbulent flow flow simulation simulation in stirredin stirred tanks. tanks. In the In casethe case of CFD, of CFD, the the Reynolds-averaged Reynolds-averaged Navier–Stokes Navier–Stokes (RANS) (RANS) equations, equations, the the Large Large Eddy Eddy SimulationSimulation (LES)(LES) andand thethe DirectDirect NumericalNumerical SimulationSimulation (DNS)(DNS) areare thethe threethree mainmain methodsmethods commonlycommonly used. used. InIn the RANS technique, technique, the the equations equations are are averaged averaged over over a atime time interval interval or or across across a collection a collection of ofequivalent equivalent fields. fields. RANS RANS computations computations are extensively are extensively used in practical used in computations practical computations for predicting for predictingsteady-state steady-state solutions. solutions. Anisotropy Anisotropy in the nature in the of nature flow introduces of flow introduces a key uncertainty a key uncertainty in the incomputation. the computation. The Navier-StokesNavier-Stokes equationsequations areare usedused toto represent thethe characteristicscharacteristics ofof turbulenceturbulence andand formform the basis ofof describingdescribing thethe flowflow phenomena. phenomena. The The chaotic chaotic nature nature of of turbulent turbulent fluxes fluxes act act as as a directa direct result result of non-linearof non-linear terms terms in thein the N-S N equations.-S equations. These These equations equations are are based based on theon the conservation conservation laws laws namely namely the continuity,the continuity, momentum momentum and and energy energy conservation conservation laws laws as respectively as respectively given given below below [20]. [20]. 휕𝜌 ∂ρ + 훻. (𝜌푢) = 표 (1) 휕푡 + ∇·(ρu) = o (1) ∂t ∂ρu + ∇·(ρuu) = −∇·P (2) ∂t Designs 2018, 2, 10 6 of 16

∂ρe + ∇·(eu) = −∇(u·P) − ∇·q (3) ∂t where u, ρ, e and q are the velocity components, density, total energy per unit volume, and heat flux, respectively. The stress tensor, P for a Newtonian fluid is defined by:

2 h i P = p(ρ, T)I + µ(∇·u)I − µ (∇u) + (∇v)T (4) 3 where, p(ρ, T) is the scalar pressure, I, is a unit diagonal tensor, T is the temperature, and µ is the dynamic viscosity coefﬁcient. Thus, the Navier-Stokes equation [21,22] can be given by:

! ∂Ui ∂Ui ∂ P ∂ ∂Ui + Uj = − + v (5) ∂t ∂xj ∂xi ρ ∂xj ∂xj

The k-ε model is a two-equation method under the RANS approach, where, the turbulent kinetic energy (TKE) and its dissipation rate (ε) are used to describe the unsteady fields. These two parameters are obtained in the flow field by solving their modeled partial differential transport equations. The standard k-ε model solves for high Reynolds number scenarios. This model is formulated on the assumption that the Reynolds stress is proportional to the mean velocity gradient [23,24]. The constant of proportionality is taken to be the eddy viscosity, given as:

k2 v = C · (6) t µ ε where k is the kinetic energy, ε is the dissipation rate, and Cµ is a parameter that depends on the k-ε turbulence model. The equation showing the TKE for three-dimensional ﬂows can be represented as:

1 k = · u2 + v2 + w2 (7) 2 The governing transport equations (k-equation and ε-equation) for the Standard k-ε model are given below by Equations (8) and (9) respectively,

∂(ρk) ∂(ρu k) ∂(ρu k) µ ∂k + i = i t · + ρ·(P − ε) (8) ∂t ∂xi ∂xi σk ∂xi ∂(ρε) ∂(ρuiε) ∂(ρuik) µt ∂ε 1 + = · + ρ· ·(C1,εP − C2,εε) (9) ∂t ∂xi ∂xi σε ∂xi τd where τd is the dissipation rate time scale that characterizes the dynamic process in the energy spectrum and P is the evolution of turbulence, represented respectively as,

k τ = (10) d ε ! ∂ui ∂uj ∂uj P = vt + (11) ∂xj ∂xi ∂xi

The values of empirical constants of the Standard k-ε model are Cµ = 0.09, σk = 1, σε = 1.314, C1,ε = 1.44, and C2,ε = 1.92. The standard k-ε model combines reasonable accuracy, time economy, and robustness for a wide range of turbulent flows [25,26]. To improve the predictive accuracy of k-ε models, more transport Designs 2018, 2, 10 7 of 16 equations have been derived. These include the realizable k-ε and the k-ε RNG (renormalization group) methods. The realizable k-ε model contains an additional state of eddy viscosity and a transport equation for the dissipation derived from an exact equation for the transport of the mean square vorticity variations. A disadvantage of this model is that it produces non-physical turbulent viscosities in the turbulent viscosity equation. Thus, the use of this model is limited. The k-ε RNG model is a method where the smallest eddies are first resolved in the inertial range and then represented in terms of the next smallest eddies. This process continues until a modified set of the Navier Stokes equations is obtained which can then be solved. This approach still poses modeling problems of imperfectly solved eddies. Generally, the main weakness associated with the RANS models is that it fails to predict satisfactorily the explicit characteristics of complex flows, since the k-ε model assumes the isotropy of turbulence. Anisotropic models such as Reynolds Stress Model (RSM), DNS and the LES model have been applied in the simulation of complex three-dimensional flows. RSM presents good accuracy in predicting flows with swirl, rotation and high strain rates. It consists of six transport equations for the Reynolds stresses and an equation for the dissipation rate, making it computationally cumbersome. This model also lacks universality in its parameters and it does not adequately capture the time dependent nature of flow. The DNS is based on a three-dimensional and unsteady solution of the Navier-Stokes equations. However, the drawback of this model is its Reynolds number limitations, since the resolution of all the fine scales of a high Reynolds number flow requires enormous computing capability. In addition, it is hard to prove if it yields fully resolved eddies, because it would be impractical with inadequate computing ability. LES has arisen as a possible choice for modeling, where the time-dependent behavior of the flow is resolved. It is based on the idea that the big eddies produced in the mean flow are anisotropic and have a lengthy lifespan. On the other hand, the small eddies produced from inertial transfer have more universal properties and are isotropic with a short life span hence relatively easy to model. Equations describing this model are derived by filtering the Navier–Stokes equation [27]. This effectively separates the eddies whose scales are smaller than the filter size used in meshing. The resulting equations have the structure of the original equation and resultant subgrid scale stresses (SGS). The large eddies are resolved directly, while the small eddies are modelled using available subgrid-scale models. The filtered Navier–Stokes and conservation equation of LES for incompressible flows are as shown below: 2 ∂u ∂u u 1 ∂p ∂ u ∂τij i + i i = − + v i − (12) ∂t ∂xj ρ ∂xi ∂xj∂xj ∂xj ∂u i = 0 (13) ∂xi where the items with bars indicate the large scales obtained from grid filtering. The effects of the SGS are reflected in the subgrid scale stress tensor represented as:

τij = uiuj − uiuj (14)

The LES model can solve all eddying scales in a complex flow: however, the challenge of limited computing power still prevails, and thus not suitable for practical industrial applications. Moreover, there is excessive dissipation in flows produced by growth of initially small agitation to fully turbulent flow which ought to be resolved [28]. For these reasons, it is deemed that the RANS equations for turbulence modeling are the most fitting CFD tool to use for realistic and economical study of turbulent mixing schemes. The results obtained from the simulations using this model were an estimate prediction of the expected behavior Designs 2018, 2, 10 8 of 16 of the impellers under study and were not fully validated in the experiments due to the scale of the computations and inadequacy of apparatus. To this effect, future work should employ reliable experimental procedures such as the laser Doppler velocimetry (LDV) or particle image velocimetryDesigns 2018, 2, (PIV).x FOR PEER REVIEW 8 of 16

2.2.1.2.2.1. M Meshingeshing and Pre Pre-Processing-Processing The different impeller configurations,configurations, fluid fluid volume,volume, and the bafflesbaffles were modelled as separate regions in SolidSolid WorksWorks 20162016 software,software, beforebefore beingbeing importedimported into ANSYS Fluent for pre-processingpre-processing and meshing. meshing. Elaborate Elaborate interfaces interfaces between between the the contacting contacting fluid fluid regions regions and and boundary boundary conditions conditions were createdwere created in ANSYS in ANSYS workbench workbench design desi modeler.gn modeler. A mesh was generated to discretize the domains into small control volumes, where the conservation equations equations were were to to be be approximated approximated by by computer computer numerical numerical calculations. calculations. The The mesh mesh for forthe the mixing mixing simulation simulation set set-up-up contained contained two two main main zones, zones, tank tank-fluid-fluid region region,, and and impeller impeller region, modelled as separate interacting fluid fluid domains. A fine fine mesh was used to enhance the stability and accuracy of the computation [9].]. Figure 55 below below shows shows the the boundary boundary interfaces interfaces created created and and meshed meshed regions regions of of the the agitation agitation assembly.assembly. A compactcompact meshmesh cancan bebe seenseen atat thethe impellerimpeller andand shaftshaft region.region.

(a) (b) (c)

Figure 5. (a) Boundary conditions between impeller and fluid interfaces set in ANSYS workbench Figure 5. (a) Boundary conditions between impeller and ﬂuid interfaces set in ANSYS workbench design modeler;modeler; (b) Sectional view of the meshed model showing the impeller and shaft region at the center;center; and (c) Meshing the ﬂuidfluid volume.volume.

2.2.2. Simulation Set up and Computation 2.2.2. Simulation Set up and Computation The simulations were prepared in fluent solver, using the pressure-based steady state and The simulations were prepared in fluent solver, using the pressure-based steady state and absolute absolute velocity conditions with gravity acting in the negative y-axis direction. The created fluid velocity conditions with gravity acting in the negative y-axis direction. The created fluid regions were regions were then set to viscous type in the k-ε standard model with standard wall functions. The then set to viscous type in the k-ε standard model with standard wall functions. The material was material was chosen as water-liquid with a density, ρ, of 998.2 kg/m3 and constant viscosity, µ, of chosen as water-liquid with a density, ρ, of 998.2 kg/m3 and constant viscosity, µ, of 0.001 kg/m.s. 0.001 kg/m.s. Cell zone conditions entailed the impeller-fluid interface, which consisted of the Cell zone conditions entailed the impeller-fluid interface, which consisted of the impeller surface and impeller surface and the fluid regions around the impeller. Mesh interfaces and contact regions were the fluid regions around the impeller. Mesh interfaces and contact regions were confirmed to be the confirmed to be the exact points where interactions occurred. exact points where interactions occurred. The movement of the impeller zone in the tank-fluid region was modeled using a Multiple The movement of the impeller zone in the tank-fluid region was modeled using a Multiple Reference Frame (MRF) approach that combines the computation of both stationary and moving Reference Frame (MRF) approach that combines the computation of both stationary and moving frames. The two zones consists of well-defined boundaries. The moving zone comprised of the frames. The two zones consists of well-defined boundaries. The moving zone comprised of the impeller and the shaft domains, rotating with an angular velocity of 600 rpm along the y-axis [29]. impeller and the shaft domains, rotating with an angular velocity of 600 rpm along the y-axis [29]. The tank-fluid zone together with the baffles and tank walls were set to the stationary frame [30]. The tank-fluid zone together with the baffles and tank walls were set to the stationary frame [30]. The simulation was configured using Hybrid initialization technique before running the The simulation was configured using Hybrid initialization technique before running the calculations with 200 iterations at a reporting interval of six and profile update of four cycles. The calculations with 200 iterations at a reporting interval of six and profile update of four cycles. calculations were ascertained to have converged for all the computations within 1–3 h of computational time. Velocity profiles (contours, velocity streamlines and velocity vectors) were finally generated in CFD-post process to represent the effects of each impeller type. The simulations were executed using a 2.30 GHz, 4 GB RAM, (Lenovo TianYi 300-15ISK, Intel core i5) laptop computer (Lenovo Group Ltd., Beijing, China).

Designs 2018, 2, 10 9 of 16

The calculations were ascertained to have converged for all the computations within 1–3 h of computational time. Velocity proﬁles (contours, velocity streamlines and velocity vectors) were ﬁnally generated in CFD-post process to represent the effects of each impeller type. The simulations were executed using a 2.30 GHz, 4 GB RAM, (Lenovo TianYi 300-15ISK, Intel core i5) laptop computer (LenovoDesigns 2018 Group, 2, x FOR Ltd., PEER Beijing, REVIEW China). 9 of 16

3. Results and Discussion The values of electrical conductivity obtained through experiments were used to predict the mixing performance of the different impellers. CFD results were compared to the experimental data obtained on the distribution of the granules concentration inin thethe tank.tank.

3.1.3.1. Analysis of the Experimental Concentration Distribution Figure 66 below below showsshows aa graphicalgraphical representationrepresentation ofof thethe distributiondistribution patternpattern ofof thethe ECEC valuesvalues ofof dissolveddissolved K22SO4 inin the the solution. solution. These These values values were were assumed assumed to to be be the the amounts amounts of of solids solids at at the the specific speciﬁc regions. The horizontal axis represents the sample point in the tank from which the solution sample was collected. The vertical scale shows the values of the measured EC at the speciﬁcspecific points. The lines show the trend of concentrations in the tank fromfrom bottombottom toto top.top.

Figure 6. Graph comparing the performance of the different impellers under study (Anchor, Rushton Figure 6. Graph comparing the performance of the different impellers under study (Anchor, Rushton turbine, Saw Saw-tooth-tooth and and Counter Counter-ﬂow-flow impellers). impellers). The The lines lines show show the the trend trend of the of thedissolved dissolved solids solids (EC (ECvalues) values) within within the vessel. the vessel. This Thisrepresents represents the amounts the amounts of solid of solid granules granules that were that were broken broken down down into intosolution solution and distributed and distributed by the by turbulence the turbulence generated generated by the by impeller the impeller action. action.

From the graph, it can be observed that the saw-tooth impeller and the counter flow impellers From the graph, it can be observed that the saw-tooth impeller and the counter ﬂow impellers performed better than the anchor and the Rushton turbine in breaking down the solids into solution. performed better than the anchor and the Rushton turbine in breaking down the solids into solution. The counter-flow and Rushton turbine impellers attained more uniform solution concentrations, The counter-ﬂow and Rushton turbine impellers attained more uniform solution concentrations, though the mixing ability of the latter ranked lower than the former impeller. though the mixing ability of the latter ranked lower than the former impeller. The saw-tooth impeller was able to dissolve more granules and distribute them evenly within The saw-tooth impeller was able to dissolve more granules and distribute them evenly within the the solution as shown by the high values in the averages derived from the experiment (Table 2). The solution as shown by the high values in the averages derived from the experiment (Table2). The anchor anchor impeller performed the least, both in the total amount of solids it dissolved and in level of homogeneity, it attained.

Table 2. Mean values of the measured Electrical Conductivity (EC).

Type of Impeller Mean EC saw tooth impeller 4113.5 Rushton turbine 3571.4 Anchor impeller 3119.0 counter flow impeller 4101.9

Designs 2018, 2, 10 10 of 16 impeller performed the least, both in the total amount of solids it dissolved and in level of homogeneity, it attained.

Table 2. Mean values of the measured Electrical Conductivity (EC).

Type of Impeller Mean EC saw tooth impeller 4113.5 Rushton turbine 3571.4 Anchor impeller 3119.0 counter ﬂow impeller 4101.9 Designs 2018, 2, x FOR PEER REVIEW 10 of 16

TheseThese results results clearly clearly point to a possibility of of combining combining different different flow ﬂow patterns patterns such such as as the the counter-axialcounter-axial ﬂow flow and and the the slots slots effects effects of the of saw-tooth the saw- impellers.tooth impellers. This will This increase will mixing increase turbulence mixing andturbulence provide and more provide particle more interaction, particle interaction, which will which improve will the improve mixing the performance mixing performance of the impellers. of the Commonlyimpellers. Commonly used impeller used types impeller can thustypes be can redesigned thus be redesigned to attain better to attain standards. better standards.

3.2.3.2. CFDCFD Post-ProcessPost-Process AnalysisAnalysis FromFrom thethe numericalnumerical simulationsimulation procedures, velocity contours, contours, streamlines streamlines and and velocity velocity vector vector representationsrepresentations werewere generatedgenerated inin CFDCFD post process. The The results results represented represented the the flow flow behavior behavior of of the the differentdifferent mixingmixing impellersimpellers andand helpedhelped in explaining the experimental outcome. outcome. ForFor thethe anchoranchor impeller, the performance around around the the impeller impeller regions regions was was as as in in Figure Figure 77 below. below. ThereThere was was more more contact contact between between the the fluid fluid and and the the impeller impeller as as the the impeller impeller cut cut through through the the fluid. fluid. In In the velocitythe velocity vector vector diagram diagram it was it observedwas observed that therethat there was awa zero-flows a zero- regionflow region generated generated behind behind the blades the dueblades to thedue relatively to the relatively wide blade wide cross-sectional blade cross-sec areational of area this impeller.of this impeller.

FigureFigure 7.7. Diagrams showing the ( a)) velocity velocity vectors vectors and and ( (bb)) contours contours generated generated by by anchor anchor impeller impeller..

The velocity streamlines of this impeller in (Figure 8), shows that the blades drove the fluid to The velocity streamlines of this impeller in (Figure8), shows that the blades drove the fluid to the walls, which then splashed back and was directed vertically and in opposite directions toward the walls, which then splashed back and was directed vertically and in opposite directions toward the center of the tank. There was more turbulence experienced at the impeller region, due to the large the center of the tank. There was more turbulence experienced at the impeller region, due to the blade area. This type of impeller was not very efficient in distributing the fluid all over the tank. The large blade area. This type of impeller was not very efficient in distributing the fluid all over the tank. generated flow is expected to cause higher concentrations of the solution in the lower parts of the The generated flow is expected to cause higher concentrations of the solution in the lower parts of the tank as compared to the upper regions. This observation clearly concurs with the experimental results tank as compared to the upper regions. This observation clearly concurs with the experimental results performed in this work as well as conclusion of Akiti, and Bai [31], who earlier proved that the anchor performed in this work as well as conclusion of Akiti, and Bai [31], who earlier proved that the anchor impeller produces less flow and turbulence regardless of the configuration of the mixing vessel. impeller produces less flow and turbulence regardless of the configuration of the mixing vessel. The counter-flow impeller design is based on the idea that the blades can be modeled to produce axial flow in opposite directions. This is with the view that the counter flows generated will increase turbulence and mixing performance. From the CFD post process results, it was observed that the design was able to distribute the fluid towards the lower and upper parts of the tank efficiently.

Figure 8. Velocity streamlines generated by the anchor impeller. More turbulence can be observed at the lower regions than the upper regions of the tank.

Designs 2018, 2, x FOR PEER REVIEW 10 of 16

These results clearly point to a possibility of combining different flow patterns such as the counter-axial flow and the slots effects of the saw-tooth impellers. This will increase mixing turbulence and provide more particle interaction, which will improve the mixing performance of the impellers. Commonly used impeller types can thus be redesigned to attain better standards.

3.2. CFD Post-Process Analysis From the numerical simulation procedures, velocity contours, streamlines and velocity vector representations were generated in CFD post process. The results represented the flow behavior of the different mixing impellers and helped in explaining the experimental outcome. For the anchor impeller, the performance around the impeller regions was as in Figure 7 below. There was more contact between the fluid and the impeller as the impeller cut through the fluid. In the velocity vector diagram it was observed that there was a zero-flow region generated behind the blades due to the relatively wide blade cross-sectional area of this impeller.

Figure 7. Diagrams showing the (a) velocity vectors and (b) contours generated by anchor impeller.

The velocity streamlines of this impeller in (Figure 8), shows that the blades drove the fluid to the walls, which then splashed back and was directed vertically and in opposite directions toward the center of the tank. There was more turbulence experienced at the impeller region, due to the large blade area. This type of impeller was not very efficient in distributing the fluid all over the tank. The Designs 2018, 2, 10 11 of 16 generated flow is expected to cause higher concentrations of the solution in the lower parts of the tank as compared to the upper regions. This observation clearly concurs with the experimental results Fromperformed the velocity in this vector work contouras well as (Figure conclusion9), it canof Akiti, be seen and that Bai the[31] ﬂuid, who isearlier well projectedproved that axially the anchor in both directions.impeller produces The vector less diagram flow and shows turbulence a relatively regardless even of distribution the configuration around of the the impeller mixing vessel. region.

Designs 2018, 2, x FOR PEER REVIEW 11 of 16

DesignsThe 2018counter, 2, x FOR-flow PEER impeller REVIEW design is based on the idea that the blades can be modeled to11 produce of 16 axial flow in opposite directions. This is with the view that the counter flows generated will increase turbulenceThe counterand mixing-flow impellerperformance. design From is based the on CFD the ideapost that process the blades results, can it be was modeled observed to produce that the

designaxial was flow able in o ppositeto distribute directions. the fluid This towards is with the the view lower that and the upper counter part flowss of the generated tank efficiently. will increase From turbulence and mixing performance. From the CFD post process results, it was observed that the theFigure velocityFigure 8. 8Velocity .vector Velocity contour streamlines streamlines (Figure generated generated 9), it bycanby thethe be anchoranchor seen that impeller. the fluid More More isturbulence turbulence well projected can can be be observedaxially observed in at both at design was able to distribute the fluid towards the lower and upper parts of the tank efficiently. From directions.thethe lower lower The regions regions vector than than diagram the the upper upper shows regions regions a relatively of of thethe tank.tank. even distribution around the impeller region. the velocity vector contour (Figure 9), it can be seen that the fluid is well projected axially in both directions. The vector diagram shows a relatively even distribution around the impeller region.

FigureFigure 9. 9(a. )(a Velocity) Velocity vectors vectors and and ( b(b)) velocity velocity contourscontours of counter counter-ﬂow-flow impeller. impeller. More More particles particles are are Figure 9. (a) Velocity vectors and (b) velocity contours of counter-flow impeller. More particles are seenseen on on the the axial axial blade blade surface surface as as they they are are projectedprojected vertically.vertically. seen on the axial blade surface as they are projected vertically. The velocity streamlines (Figure 10), are observed to have dispersed to further regions of the The velocityThe velocity streamlines streamlines (Figure (Figure 10), 10 are), are observed observed to to have have dispersed dispersed to to further further regions regions ofof thethe tank. tank. When mixing substances, this type of impeller will be able to efficiently distribute the particles tank. When mixing substances, this type of impeller will be able to efficiently distribute the particles Whenand mixingcreate a substances,more homogenous this type solution. of impeller will be able to efﬁciently distribute the particles and createand a more create homogenous a more homogenous solution. solution.

Figure 10. Flow streamlines of counter-ﬂow impeller. Figure 10. Flow streamlines of counter-flow impeller. Figure 10. Flow streamlines of counter-flow impeller. The counter flow impeller was, thus expected to increase mixing performance due to the The counter flow impeller was, thus expected to increase mixing performance due to the counter-axial flow, which improved turbulence in the vessel. This outcome agrees well with the counterexperimental-axial flow, findings which as well improved as the explanation turbulence given in the by vessel. McDonough This outcome [32] on the agrees characteristics well with of the experimentalthe axial flow findings impellers. as well as the explanation given by McDonough [32] on the characteristics of the axialFewer flow studiesimpellers. have been done to study the saw tooth impeller. This type of impeller uses a circularFewer disc studies with protrudinghave been slotsdone on to its study edges, the modified saw tooth to act impeller. like saw Thisblades type that of cut impeller through uses the a circularfluid. discThrough with experiments,protruding slots this impelleron its edges, was seenmodified to have to actperformed like saw well blades in dissolving that cut through the solid the fluid.granules. Through This experiments, is also proven this in CFD impeller simulation was asseen observed to have in performedFigure 11 below. well Thein dissolving velocity contours the solid granules.and vectors This indicateis also proven that this in impeller CFD simulation produced as a observeduniform mixing in Figure result 11 aroundbelow. theThe impeller velocity regions contours and vectors indicate that this impeller produced a uniform mixing result around the impeller regions

Designs 2018, 2, 10 12 of 16

The counter flow impeller was, thus expected to increase mixing performance due to the counter-axial flow, which improved turbulence in the vessel. This outcome agrees well with the experimental findings as well as the explanation given by McDonough [32] on the characteristics of the axial flow impellers. Fewer studies have been done to study the saw tooth impeller. This type of impeller uses a circular disc with protruding slots on its edges, modified to act like saw blades that cut through the fluid. Through experiments, this impeller was seen to have performed well in dissolving the solid Designsgranules. 2018 This,, 2,, xx FORFOR is also PEERPEER proven REVIEWREVIEW in CFD simulation as observed in Figure 11 below. The velocity contours12 of 16 and vectors indicate that this impeller produced a uniform mixing result around the impeller regions as seen by the evenly distributeddistributed patterns. The The slots in this disc are accredited to increasing contact area and inducing circular flow in the fluid. area and inducinginducing circular flowflow inin thethe fluid.fluid. The velocity streamlines (Figure 12) shows that there was great turbulence generated as the fluid The velocity streamlines (Figure 12) shows that there was great turbulence generated as the fluid fluid was caused to swirl in the vessel. This type of impeller was, thus expected to distribute the fluid more was caused to swirl in the vessel. Thi Thiss type of impeller was, thus expected to distribute the fluid fluid more evenly throughout the entire volume. This validates the excellent performance of such a construction evenly throughout the entire volume. This validates the excellent performance of such a construction as established through experiments. as established through experiments.

Figure 11. (a) Velocity vectors and (b) velocity contours of saw-tooth impeller. Uniform patterns can Figure 11.11. (a) Velocity vectors and (b)) velocityvelocity contourscontours of saw-toothsaw-tooth impeller. Uniform patterns can be seen around the impeller. be seen around the impeller.

Figure 12 12... VelocityVelocity streamlines of the saw saw-tooth-tooth impeller impeller showing showing the the swirling swirling motion motion of of the the impeller, impeller, which is spread throughout thethe vessel.vessel.

The Rushton turbine is one of the most studied agitation impellers. It has provided the basis for comparative studies studies for for many researchers [ 33]. The The flow ﬂow patterns around the impeller region were generally well distributed due due to to its radial action on the fl ﬂuiduid (Figure(Figure 13). This impeller was able to thrust the fluid from the center towards the walls of the tank and as the flow approached the wall regions, the velocity was observed to steadily drop.

Designs 2018, 2, 10 13 of 16

thrust the ﬂuid from the center towards the walls of the tank and as the ﬂow approached the wall DesignsDesignsregions, 2018 2018 the, ,2 2, , velocityxx FOR FOR PEER PEER was REVIEW REVIEW observed to steadily drop. 1313 ofof 1616

FigureFigure 13 13.13.. ((aa)) Velocity Velocity vectors vectorsvectors and and ( (bb))) velocity velocityvelocity contours contourscontours of of Rushton Rushton turbine. turbine. TheThe radialradial actionaction ofof thethe impellerimpeller onon the the fluid ﬂuidfluid can can be be observed observed at at the thethe blades. blades.blades.

The streamlines were observed (Figure 14) to move towards the wall of the stirred tank and then The streamlines were observed (Figure(Figure 14)) to move towards the wall of the stirred tank and then split into upward and downward directions. The mixing was better distributed at the central parts of split into upward upward and and downward downward direction directions.s. The The mixing mixing was was bet betterter distributed distributed at atthe the central central parts parts of the vessel as compared to the outer regions as seen from the vector diagram. The intensity of the theof the vessel vessel as ascompared compared to tothe the outer outer regions regions as as seen seen from from the the vector vector diagram. diagram. The The intensity intensity of of the velocity currents in the regions below the impeller was stronger than that above the impeller [34]. velocity currents in the regions belowbelow thethe impellerimpeller waswas strongerstronger thanthan thatthat aboveabove thethe impellerimpeller [[3434].].

Figure 14. Velocity streamlines of Rushton turbine. FigureFigure 1414.. VelocityVelocity streamlinesstreamlines ofof RushtonRushton turbineturbine..

FromFrom the the obtainedobtained results,results, it it was was evidentevident thatthat thethe unconventionalunconventional impellerimpeller typestypes (saw(saw toothtooth andand countercounter flowflow flow impellers)impellers) exhibitedexhibited betterbetter mixingmixing results,results, which which isis essentialessential inin achievingachieving concentrationconcentration homogeneityhomogeneity in in in agitation agitation agitation tanks. tanks. tanks. Therefore, Therefore, Therefore, t too realize realize to realize the the best best the results results best from from results mixing mixing from processes, processes, mixing processes,impellersimpellers needneedimpellers toto bebe need modifiedmodified to be toto modified generategenerate to adequateadequate generate energyenergy adequate forfor energycreatingcreating for turbulenceturbulence creating turbulenceinin thethe vessel.vessel. in Optimum theOptimum vessel. designsdesignsOptimum of of mixing mixing designs impellers impellers of mixing can can impellers be be established established can be by by established methods methods such such by methods as as turbul turbul suchentent diffusivity. diffusivity. as turbulent This This diffusivity. method method allowsThisallows method forfor numericalnumerical allows for calculationscalculations numerical ofof calculations turbulentturbulent mixingmixing of turbulent scenarios.scenarios. mixing TurbulentTurbulent scenarios. diffusiondiffusion Turbulent isis defineddefined diffusion byby aisa t ct turbulentturbulentdefined by mass mass a turbulent diffusion diffusion mass coefficient coefficient diffusion,, coefficient, DD,t, which which D is ist, awhich a factor factor is a of of factor the the turbulent ofturbulent the turbulent Schmidt Schmidt Schmidt number, number, number, SSct,, representedSrepresentedct, represented asas:: as: 휇µt Sct = 휇푡푡 (15) 푆푐푡 = ρD (15) 푆푐푡 =𝜌퐷 t (15) 𝜌퐷푡푡 where, µt is the turbulent viscosity. t wwhere,here, μμ t isis thethe turbulentturbulent viscosity.viscosity. TheThe SchmidtSchmidt numbernumber determinesdetermines thethe relativerelative distributiondistribution ofof impellerimpeller--inducedinduced motionmotion andand massmass causedcaused byby turbulence.turbulence. ForFor efficient efficient mixing mixing processes, processes, precise precise prediction prediction of of mixing mixing behavior behavior of of impellers impellers in in stirred stirred vesselsvessels isis necessary.necessary. ThisThis willwill bebe beneficialbeneficial whenwhen designingdesigning oror selectingselecting thethe mostmost suitablesuitable apparatus.apparatus. TheThe useuse ofof thethe turbulenceturbulence modelsmodels cancan provideprovide aa goodgood basisbasis fforor detaileddetailed understandingunderstanding ofof generatedgenerated

Designs 2018, 2, 10 14 of 16

The Schmidt number determines the relative distribution of impeller-induced motion and mass caused by turbulence. For efficient mixing processes, precise prediction of mixing behavior of impellers in stirred vessels is necessary. This will be beneficial when designing or selecting the most suitable apparatus. The use of the turbulence models can provide a good basis for detailed understanding of generated flow in mixing vessels. Nonetheless, the RANS, k-ε model used in this work is characterized by unsteadiness because it assumes that the flow is statistically steady [35]. This assumption leads to poor estimates for swirling and rotational flows. RANS model is valid only for fully turbulent flows, requires wall function implementation, and leads to over-prediction of turbulence in highly strained flows. More advanced methods such as DNS model can provide better simulation results. However, they are expensive and demand immense computer capability in regards to both processor speed and capacity for storing intermediate results than in RANS methods. A more realistic alternative would be the large eddies simulation model, which has higher accuracy. It is much more economical in terms of computational power requirements than DNS. It is applicable in resolving time-dependent behavior of turbulent flow and allows computation of large and complex vortexes [36]. Like in DNS, LES have high computational cost as compared to RANS model, and is affected by viscous near-wall features. The performance of the four impeller designs in this experiment were clearly captured by the CFD simulation model and was in good agreement with all the experimental results and prior studies conducted on the same. The good concurrence demonstrated in both the simulation and experimental procedures is an evidence that CFD is a reliable tool for explaining turbulence in mixing systems. It was also noted that numerical aspects play an important role in turbulent-flow computations in terms of both accuracy and efficiency. The future significance of CFD turbulent mixing systems will be guided by how accurate complex flows can be estimated. For successful simulation and prediction of flow characteristics in turbulent systems, a compromise between accuracy and computing demands ought to be made. Although it was acknowledged that complex flow may not be predicted adequately with RANS models, the emphasis on simplicity, practicality, computational speed and robustness in an industrial setting influences against the adoption of more advanced models. The ANSYS solver and numerical approach used in this work can therefore aid in the development of optimal mixing schemes in regards to the equipment geometry and related parameters. It is expected that improving the impeller designs from the conventional types will offer cheaper modes of agitation, while minimizing costs and improving on the quality of the resultant products in agricultural chemical preparations and many other fields.

4. Conclusions The approach used in this study clearly depicted the mixing dynamics in mechanically stirred tanks, which are often difficult to predict. This technique provided relevant information about the turbulent flow characteristics. The flow patterns of the different impeller designs used in this work were satisfactorily described through experiments and CFD analysis. The results obtained from CFD simulations were confirmed to be in good agreement with experimental values. It was proven that the impeller-blade configuration significantly affected the performance of a mechanically agitated mixer. Achieving the best mixing designs will improve the quality of mixing and establish a good degree of homogeneity, as a function of the design. This work will be useful in selecting the right type of impellers that will guarantee optimum results and economical use of expensive chemicals and other mixing agents. It will also provide a basis on which large mixing systems can be designed and controlled using minimal costs, time and space.

Acknowledgments: Support from the Department of Agricultural Mechanization Engineering of Nanjing Agricultural University facilitated the successful completion of this work. Designs 2018, 2, 10 15 of 16

Author Contributions: Ian Torotwa conceived and designed the experiments. Changying Ji supervised the work and facilitated the acquisition and installation of the apparatus. Ian Torotwa performed and analyzed the data with extensive input from Changying Ji. Ian Torotwa wrote the paper and Changying Ji verified and approved it. Conflicts of Interest: The authors declares no conflict of interest.

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