simulation of flows in stirred vessels agitated by dual rushton impellers using computational...

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Simulation of flows in stirredvessels agitated by dualrushton impellers usingcomputational snapshotapproachVaibhav R. Deshpande a & Vivek V. Ranade ba Swiss Centre for Scientific Computing , Manno,Switzerlandb Industrial Flow Modeling Group , National ChemicalLaboratory , Pune, IndiaPublished online: 09 Sep 2010.

To cite this article: Vaibhav R. Deshpande & Vivek V. Ranade (2003) Simulationof flows in stirred vessels agitated by dual rushton impellers using computationalsnapshot approach, Chemical Engineering Communications, 190:2, 236-253, DOI:10.1080/00986440302144

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SIMULATIONOFFLOWS INSTIRREDVESSELSAGITATEDBYDUALRUSHTON IMPELLERSUSINGCOMPUTATIONAL SNAPSHOTAPPROACH

VAIBHAVR. DESHPANDE

Swiss Centre for Scientific Computing, Manno, Switzerland

VIVEKV. RANADE

Industrial FlowModeling Group,National Chemical Laboratory, Pune, India

Flow in baffled stirred vessels involves interactions between flow around ro-

tating impeller blades and stationary baffles. When more than one impeller is

used (which is quite common in practice), the flow complexity is greatly in-

creased, especially when there is an interaction between two impellers. The

extent of interaction depends on relative distances between the two impellers

and clearance from the vessel bottom. In this paper we have simulated flow

generated by two Rushton (disc) impellers. A computational snapshot ap-

proach was used to simulate single-phase flow experiments carried out by

Rutherford et al. (1996). The computational model was mapped on the

commercial CFD code FLUENT (Fluent Inc., USA). The simulated results

were analyzed in detail to understand flow around impellers and interaction

between impellers. The model predictions were verified using the data of

Rutherford et al. (1996). The results presented in this paper have significant

implications for applications of computational fluid mixing tools for design-

ing multiple impeller stirred reactors.

Keywords: Stirred vessels; Dual Rushton turbines; CFD; Snapshot approach

Received 16 February 2001; in final form 2 December 2001.

Address correspondence to Vivek V. Ranade, Industrial Flow Modeling Group,

National Chemical Laboratory, Pune 411 008, India. E-mail: [email protected]

Chem. Eng. Comm.,190: 236�253, 2003

Copyright# 2003 Taylor & Francis

0098-6445/03 $12.00+ .00

DOI: 10.1080=00986440390179217

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INTRODUCTION

Stirred reactors, in which one or more impellers are used to generatedesired flow and mixing within the reactor, are among the most widelyused reactors in chemical and allied industries. A number of industrialstirred tank reactors make use of two or more impellers mounted on thesame shaft. When more than one impeller is used, the flow complexity isgreatly increased, especially when there is an interaction between flowgenerated by two impellers. The extent of interaction depends on relativedistances between the two impellers (and clearance from the vessel bot-tom). The flow structure in vessels agitated by dual impellers is deter-mined mainly by flow characteristics of both impellers and interactionoccurring between them. When clearance between the two impellers issufficiently high, impellers are likely to act independently of each other.However, for smaller clearances, two impeller streams may interact,resulting in complicated and often unstable flow patterns.

Recently Rutherford et al. (1996) have experimentally studied flowgenerated by dual Rushton turbines in cylindrical baffled vessels. Theyreport three stable flow patterns observed with different lower impellerclearance (C1), impeller separation (C2), and upper impeller submergence(C3) values. These three patterns are qualitatively shown in Figure 1. Theparallel flow pattern shown in Figure 1(a) was observed when twoimpellers are sufficiently separated (C1¼C3¼ 0.25T, C2¼ 0.5T). In thispattern, each impeller generated its own characteristic upper and lowerring vortex, leading to the formation of four stable ring vortices. Whenimpeller separation was decreased (C1¼C2¼C3¼T=3), the flow patternshown in Figure 1(b) was observed. It was termed ‘‘merging flow’’ sincetwo impeller streams merge and form two large ring vortices. The thirdstable flow pattern was named ‘‘diverging flow’’ (Figure 1(c)), and it wasobserved for smaller clearance for the lower impeller (C1¼ 0.15T,C2¼ 0.5T, C3¼ 0.35T). In this case, the lower impeller stream is directedtowards the vessel bottom. This results in the lower impeller producingone large ring vortex while the upper impeller generates the usual well-defined two ring vortices.

For simulating flow in a baffled stirred vessel, several approaches,namely, black box approach, inner-outer approach, multiple referenceframe approach, computational snapshot approach, and sliding meshapproach, were used in the past. Brucato et al. (1998) and Ranade andTayalia (2000) among others have compared predictions of differentapproaches. In a recent book, Ranade (2001) has discussed the advan-tages and disadvantages of various modeling approaches used forrepresenting rotating impellers in a baffled vessel. It is obvious that forsimulating angle-resolved flow characteristics within and near theimpeller region, the black box approach is not useful. It is necessary to

SIMULATION OF FLOW GENERATED BY DUAL IMPELLERS 237

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Figure

1.Schem

aticofstable

flow

patternsobserved

withdualRushtonturbines

(from

Rutherford

etal.(1996)).

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fully model the geometry of individual blades and to use either the slidingmesh approach or an approximation of it (like multiple reference frame,inner-outer, or snapshot approach).

Recently Micale et al. (1999) have simulated flow generated by dualRushton turbines using inner-outer and sliding mesh approaches. Theyreport reasonably good agreement between model predictions andexperimental data. Recently Ranade et al. (2001, 2002) used thecomputational snapshot approach to simulate flow generated by a discturbine and a pitched blade turbine. They report good agreementbetween experimental data and model predictions for the flow generatedby a single impeller of different shapes. The computational snapshotapproach can be easily implemented with the stationary grid CFD(computional fluid dynamics) code. It is, therefore, easier to use higherorder differencing schemes (which are necessary for capturing trailingvortices accurately: see Ranade et al. (2002)) and easier to extend tomultiphase flows. Considering its promise as a mixer design tool, in thispaper we examine whether this computational snapshot approach can beused to make a priori simulations of interaction between impellers. A caseof a dual Rushton turbine, studied by Rutherford et al. (1996), wasconsidered here for this purpose. Predicted results obtained using thesnapshot approach were compared with the results obtained using othermodeling approaches reported by Micale et al. (1999) and with theexperimental data of Rutherford et al. (1996).

COMPUTATIONALMODELING

In the computational snapshot approach, impeller blades are consideredas fixed at one particular position (similar to taking a snapshot of arotating impeller). The flow generated by an impeller of any shape ismainly governed by pressure and centrifugal forces generated because ofthe impeller rotation and the corresponding rotating flows. The shape ofthe impeller blades controls the direction and characteristics of theimpeller discharge stream via generated pressure and centrifugal forces.The blade rotation causes suction of fluid at the backside of the bladesand equivalent ejection of fluid from the front side of the blades. Thisphenomenon of ejection and suction needs to be modeled correctly tosimulate impeller rotation in a steady framework proposed in a compu-tational snapshot approach. Recently Ranade et al. (2002) discussed thedevelopment of the snapshot approach in detail and can be referred to forfurther information. Extension of this snapshot approach for the simu-lation of the dual impeller case is straightforward and will not be dis-cussed here. While implementing a computational snapshot approach,several issues such as extent and position of the inner region, location ofimpeller blades, number of computational cells, discretization schemes,


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and turbulence model need appropriate selection. The basis for suchselection is discussed below.

Geometry of the vessel used by Rutherford et al. (1996) was con-sidered in the present simulations. All the other dimensions of impellerdiameter, vessel diameter, and so on were the same as used by Rutherfordet al. (1996). Impellers used in the experiments of Rutherford et al. (1996)were standard Rushton turbines with six blades. The vessel was fullybaffled (four baffles). Making use of the symmetry, the solution domainfor the computational model was considered as only half of the vessel(180�). It is very important to use an adequate number of computationalcells while numerically solving governing equations over the solutiondomain. Prediction of turbulence quantities is especially sensitive to thenumber of grids and grid distribution within the solution domain. Ourprevious work (Ranade et al., 2002) as well as other published work (forexample, Ng et al., 1998; Wechsler et al., 1999) gives adequate infor-mation to understand the influence of grids on predicted results. It wasdemonstrated that in order to capture trailing vortices accurately, it isnecessary to use at least 300 grids to resolve the blade surface. Based onprevious experience and some preliminary numerical experiments, about700,000 computational cells (68 in the radial direction, 116 in the axialdirection, and 88 in the tangential direction) were used. The solutiondomain and typical grid used in the r-z plane are shown in Figure 2. Asdemonstrated in earlier studies (Ranade et al. 2001, 2002), it is alsonecessary to use higher order discretization schemes. In the present work,the QUICK discretization scheme (with limiter functions to avoid non-physical oscillations) was used. The results (discussed in the followingsection) seem to indicate that the number of grids used is sufficient tocapture most of the important features of the flow generated by dualRushton impellers.

For any specific computational snapshot simulation, a specificangular position of blades is used (see Ranade et al. (2002)). The choiceof blade positions with respect to baffle positions is rather arbitrary.Ranade and van den Akker (1994) have studied the sensitivity of simu-lated results with the exact position of blades relative to baffles bycomparing the predicted results of five snapshots. Their results clearlyindicate that though local values may differ for different relative posi-tions, angle-averaged results are not sensitive to the actual positioning ofimpeller blades. They also compared ensemble-averaged results (over fivesnapshots) for the mid-baffle plane with angle-averaged results. For theregion away from the impeller, both averaging methods yield almost thesame results. Predicted values of overall characteristics like pumpingnumber and power number are also not sensitive to relative positions ofimpeller blades and baffles. Since the objective of the present work is toevaluate whether the snapshot approach can capture possible interaction

240 V. R. DESHPANDE AND V. V. RANADE

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Figure

2.Solutiondomain

andcomputationalgrid.Solutiondomain:180�portion(halfofthevessel);grids:68�116�88::r�z�y.

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between multiple impellers, only one snapshot was carried in the presentwork. The baffles were considered at angles of 46� and 136�. The impellerwas positioned in such a way that three blades were located at angles of21�, 81�, and 141�.

As discussed by Ranade et al. (2001, 2002), the computationalsnapshot approach divides the solution domain into an inner region, inwhich time-derivative terms are approximated using spatial derivatives,and an outer region, in which time-derivative terms are neglected. Theboundary between the inner and outer region needs to be selected in sucha way that the predicted results are not sensitive to its actual location.Fortunately, for the standard impellers with an impeller diameter ofabout one-third of vessel diameter, the predicted results are not sensitiveto the actual location of the boundary between the inner and outer region(Ranade and Tayalia, 2000; Ranade et al., 2001a). In the present work,for all the simulations, the boundary of the inner region was positioned toinclude both impellers. The inner region considered in simulations isshown as a shaded region in Figure 2.

An appropriate turbulence model needs to be selected to simulateturbulent flow generated in a baffled stirred vessel. Most of the otherresearchers in the field have used the standard k-e model for simu-lating flow in stirred vessels (Ng et al., 1998; Brucato et al., 1998;Wechsler et al., 1999). Moreover, recent studies (see, for example,Jenne and Reuss (1999)) indicate that different time scales and ani-sotropy considerations are of minor importance and do not lead tosignificant improvements over the standard k-e model. More oftenthan not, the number and quality of the computational grid influencepredicted results more than the underlying turbulence model. It isimportant to evaluate the model based on its usefulness rather thandebating whether it is theoretically appropriate to use such a model fora given situation. If the results are useful, that is enough justification.Considering these points, we have used the standard k-e model in thepresent work to evaluate the snapshot approach for simulations offlow generated by dual Rushton turbines. Wall functions were used tospecify wall boundary conditions. The top surface of the dispersionwas assumed to be flat and was modeled as a wall. The computationalsnapshot approach was implemented using a commercial CFD code,FLUENT (Fluent Inc., USA). User-defined subroutines were used forthis purpose. All the computations were carried out for the impeller tipspeed of 1.28m=s. The fluid properties were set as: viscosity ofliquid¼ 0.0009 kg=m�s and density of liquid¼ 1000.0 kg=m3. For initi-ating computations, all variables except k and e were set to zero. Theinitial values of k and e were set to 0.0001 with appropriate units.Converged results were not found to be affected by initial conditions.The computational results are discussed in the following section.


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RESULTSANDDISCUSSION

As discussed above, three stable flow patterns are possible for differentconfigurations of dual Rushton impellers (shown qualitatively inFigure 1). A suitable grid was generated to map the three configurationscorresponding to these three stable flow patterns:

Parallel flow: C1¼C3¼ 0.25T, C2¼ 0.5TMerging flow: C1¼C2¼C3¼T=3Diverging flow: C1¼ 0.15T, C2¼ 0.5T, C3¼ 0.35T

The computational snapshot approach was used to simulate flow gen-erated in these three impeller configurations. Vector plots based onexperimental measurements of Rutherford et al. (1996) at the mid-baffleplanes for these three configurations are shown in Figures 3�5.Experimental results include averaging over different relative positionsbetween impeller blades and baffles. For a strict correspondence with

Figure 3. Comparison of predicted and experimental results observed with dual Rushton

turbines (parallel flow regime). (a) Experimental data of Rutherford et al. (1996);

(b) predicted results (angle-averaged).


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such conditions, it is necessary to carry out multiple snapshots andemploy ensemble averaging over these different snapshots. However, asRanade and van den Akker (1994) demonstrated, the ensemble averageover multiple snapshots may be closely approximated by angle-averagedresults of a single snapshot. In this work, we have therefore comparedangle-averaged results with the experimental results of Rutherford et al.(1996) for the considered three configurations. The predicted angle-averaged mean velocity field for the parallel, merging, and the divergingflow configurations are shown in Figures 3�5.

For parallel flow configuration, it can be seen that predicted resultsshow a slight upward inclination of the impeller stream emanating fromthe bottom impeller (see Figure 3). Predicted results, in accordance withthe experimental data, show little interaction between the two impellers.When spacing between the two impellers is reduced, predicted resultsshow significant interaction between the two impeller streams and resultin a merging flow pattern. It can be seen from Figure 4 that the com-putational snapshot approach is able to capture, not only qualitativelybut also quantitatively, the change in the directions of the emergingimpeller streams from both impellers. For reduced clearance of the bot-tom impeller, the computational snapshot approach captures the diver-ging flow pattern correctly (see Figure 5). The impeller stream of theupper impeller remains almost unaffected and retains the usual char-acteristics of a single impeller. The impeller stream emerging from thebottom impeller makes a significant deviation towards the vessel bottom.It can be seen from Figure 5 that the computational snapshot approachcorrectly predicts such downward inclination. The downward inclinationbecomes even steeper as flow moves away from the center, which was alsocorrectly captured by the snapshot approach.

Contours of simulated turbulent kinetic energy for the three config-urations are shown in Figure 6. These contours clearly show the differentextents of interaction between impellers for three configurations. Theresults predicted with the snapshot approach are quite similar to thosereported by Micale et al. (1999) using inner-outer and sliding meshapproaches. In general, it can be said that the computational snapshotapproach captures the interaction between impellers reasonably well. Inaddition to these qualitative comparisons, the quantitative comparison ofpredicted mean radial velocity and experimental data is shown inFigures 7 and 8 for two different values of radial positions. Simulatedresults of Micale et al. (1999) using the sliding mesh and inner-outerapproach are also shown in these figures. For the parallel flow regime,results of the computational snapshot approach show good agreementwith the results obtained with two approaches used by Micale et al.(1999) and experimental data. For the merging flow and diverging flowcases, the maximum value of radial velocity was underpredicted by all the


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approaches. Predicted results of all three approaches are, however,comparable. For both impellers in the merging flow configuration and forthe bottom impeller in the diverging flow configuration, predictions ofthe snapshot approach show an additional peak of smaller magnitude. Asignificantly finer grid and higher-order discretization scheme was used inthe present work, and simulations could therefore capture trailing vorticesbehind impeller blades. None of the simulations of Micale et al. (1999)were able to capture such trailing vortices. These vortices may cause asecond, smaller peak in the velocity profile as seen in Figure 7. As onemoves away from the impeller, this second peak disappears. In the regionaway from the impeller, predicted results with the snapshot approachshow reasonably good agreement with experimental data (see Figure 8).The computational snapshot approach, thus, appears to be useful tosimulate mean flow patterns for multiple impeller configurations.

The quantitative comparison of simulated turbulent kinetic energywith experimental data is shown in Figure 9. The simulated results of


turbines (merging flow regime). (a) Experimental data of Rutherford et al. (1996); (b) pre-

dicted results (angle-averaged).


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Micale et al. (1999) are also shown in this figure. The simulated values ofturbulent kinetic energy by the snapshot approach are the lowest amongthe three approaches. One of the possible reasons for observed differencesin predictions of the different approaches is the difference in the numberof grids used while carrying out these simulations. Prediction of turbu-lence quantities is very sensitive to number of grids and grid distributionwithin the solution domain. When one moves from a coarse grid to a finergrid, initially predicted values of turbulence quantities (kinetic energy, k,and energy dissipation rates, e) increase with grid refinement. As onestarts resolving small-scale flow and trailing vortices behind impellerblades with further grid refinement, the predicted values of k and edecrease with further refinement until they become grid independent (seeRanade and Tayalia, (2000) and Ranade et al. (2002)). The predictedvalues of turbulent kinetic energy using the snapshot approach are muchlower than the predicted values of other approaches because these valueswere obtained with a much finer grid (� 700,000 as against fewer than


turbines (diverging flow regime). (a) Experimental data of Rutherford et al. (1996);

(b) predicted results (angle-averaged).


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Figure 6. Contours of predicted turbulent kinetic energy (k=U2tip). (a) Parallel flow, (b) mer-

ging flow, (c) diverging flow.


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Figure 7. Comparison of predicted and experimental results for dual Rushton turbines:

radial velocity.


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radial velocity.


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turbulent kinetic energy.


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100,000 used by Micale et al., (1999)). Finer grids used in the presentwork resolve trailing vortices behind the impeller blades (as can be seen invector plots as well as the profiles shown in Figures 7 and 9). None of theother approaches use such a fine grid and therefore do not resolve trailingvortices. Predicted results of turbulent kinetic energy using the snapshotapproach are therefore lower than those of the other approaches.

One other reason for the observed discrepancy in the predicted tur-bulent kinetic energy and the experimental data is that the experimentalvalues include the contributions of periodic variation in velocity due toblade passage, whereas the simulated results comprise purely randomcomponents. In the case of a single impeller vessel, our earlier work hasshown good agreement between predicted turbulent kinetic energy andangle-resolved experimental data of turbulent kinetic energy (see Ranadeet al., (2001, 2002)).

Despite some discrepancies, the simulated results indicate that thecomputational snapshot approach may be used to simulate all threedifferent flow patterns with varying degrees of interaction between twoimpellers without requiring excessive computations like the sliding meshapproach or the inner-outer approach. The required computationalresources for the computational snapshot approach are an order ofmagnitude smaller (for the same number of computational cells) than theother two approaches used by Micale et al. (1999) without significantlyjeopardizing the accuracy of the simulated results. The absence of arotating framework or moving grids makes the computational snapshotapproach easier to implement, especially with higher order discretizationschemes and multiphase flows. Recently, Deshpande and Ranade (2001)have extended the snapshot approach to simulate gas-liquid flow gener-ated by dual impellers. These results indicate the promise of using thecomputational snapshot approach as a computational fluid-mixing toolfor engineering of stirred reactors.

CONCLUSIONS

The computational snapshot approach was used to simulate flow gen-erated by dual Rushton turbines. The approach was mapped onto acommercial CFD code, FLUENT (Fluent Inc., USA). Computationalresults were examined to evaluate the differences and similarities of flowstructures around lower and upper Rushton turbines. The comparison ofthree flow patterns, namely, parallel, merging, and diverging flow, showinteresting results. When significant interaction was present between thetwo impellers, as in the merging flow pattern, the flow structure aroundthe impellers was entirely different than the usual noninteracting case.The approach was found to be adequately successful in a priori predicting


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varying degrees of interaction between two impellers. Reasonably goodagreement was observed between experimental and predicted results ofmean velocity for the three stable flow patterns reported by Rutherfordet al. (1996). Simulated values of turbulent kinetic energy were con-sistently lower than the experimental values. The experimental values,however, include the periodic contributions, unlike the simulations of thesnapshot approach. Considering an order of magnitude lower compu-tational requirement of the snapshot approach, the results lookencouraging. The results and approach will be useful for extending thescope of computational models to study multiphase flows generated bydual or multiple impellers.

NOMENCLATURE

k turbulent kinetic energy, m2=s2

r radial coordinate

T tank diameter, m

Vtip impeller tip speed, m=s

V mean radial velocity, m=sz,Z axial coordinate (with origin located at impeller center)

Greek Lettersr density, kg=m3

y tangential coordinate

m viscosity, Pa�s

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simulation of flows in stirred vessels agitated by dual rushton impellers using computational...

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