Three Phase flow

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Chemical Engineering Science 62 (2007) 71847195www.elsevier.com/locate/ces

CFD simulations of gasliquidsolid stirred reactor: Prediction of criticalimpeller speed for solid suspension

B.N. Murthy, R.S. Ghadge, J.B. Joshi

Department of Chemical Engineering, Institute of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India

Received 19 April 2007; received in revised form 27 June 2007; accepted 9 July 2007Available online 13 July 2007

AbstractIn this work, simulations have been performed for three phase stirred dispersions using computational uid dynamics model (CFD). The

effects of tank diameter, impeller diameter, impeller design, impeller location, impeller speed, particle size, solid loading and supercial gasvelocity have been investigated over a wide range. The Eulerian multi-uid model has been employed along with the standard k turbulencemodel to simulate the gasliquid, solidliquid and gasliquidsolid ows in a stirred tank. A multiple reference frame (MRF) approach was usedto model the impeller rotation and for this purpose a commercial CFD code, FLUENT 6.2. Prior to the simulation of three phase dispersions,simulations were performed for the two extreme cases of gasliquid and solidliquid dispersions and the predictions have been compared withthe experimental velocity and hold-up proles. The three phase CFD predictions have been compared with the experimental data of Chapmanet al. [1983. Particlegasliquid mixing in stirred vessels, part III: three phase mixing. Chemical Engineering Research and Design 60, 167181],Rewatkar et al. [1991. Critical impeller speed for solid suspension in mechanical agitated three-phase reactors. 1. Experimental part. Industrialand Engineering Chemistry Research 30, 17701784] and Zhu and Wu [2002. Critical impeller speed for suspending solids in aerated agitationtanks. The Canadian Journal of Chemical Engineering 80, 16] to understand the distribution of solids over a wide range of solid loading(0.3415 wt%), for different impeller designs (Rushton turbine (RT), pitched blade down and upow turbines (PBT45)), solid particle sizes

(1201000 m) and for various supercial gas velocities (010mm/s). It has been observed that the CFD model could well predict the criticalimpeller speed over these design and operating conditions.2007 Elsevier Ltd. All rights reserved.

Keywords: Stirred tank; CFD; EulerianEulerian; Three phase ows; Gasliquidsolid

1. Introduction

Stirred reactors involving three phases, gas, liquid and solid,are very common in the chemical and allied industries. Thesolid phase may act as a catalyst or undergo a chemical re-action. Typical applications include catalytic hydrogenation,FischerTropsch synthesis, oxidation of p-xylene to tereph-thalic acid, production of polymers using suspension polymer-ization, oxidative leaching of ores and many other economicallyimportant reactions. Various examples of industrial importancehave been compiled by Nigam and Schumpe (1996) .

In some of these applications, the reaction occurs between adissolved gas and a liquid-phase reactant in the presence of asolid catalyst. In some other cases, the liquid is an inert medium

Corresponding author. Tel.: + 91222414 5616; fax: + 912224145614. E-mail address: [email protected] (J.B. Joshi).

0009-2509/$- see front matter 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2007.07.005

and the reaction takes place between the dissolved gas and thesolids. The performance of these reactor types depends uponefcient and simultaneous dispersion of gas and suspensionof solid particles. The complexity of the ow generated in thesystem (3D, recirculating and often turbulent) has compelledthe researchers, designers and the practicing engineers to resortto empirical approach to tackle the problems associated withthe design, scale-up and optimization of three phase stirred re-actors. In order to reduce existing state of empiricism, duringthe past 30 years, an attempt is being made to understand theunderlying uid mechanics and its relationship with the designparameters. In particular, the computational uid dynamics(CFD) and the experimental uid dynamics (EFD) have led tobetter understanding of the detailed hydrodynamics in singlephase ow systems. However, in the case of gasliquid andliquidsolid ows, relatively scanty work has been publishedusing both the EFD and CFD techniques. Further, because of
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B.N. Murthy et al. / Chemical Engineering Science 62 (2007) 7184 7195 7185

even additional complexities associated with the three phasesystems, practically no published information is available onthe CFD simulations of three phase systems. In addition, ex-perimental data for the local velocities and the local gas andsolid phase hold-ups are also not available which are useful forthe validation of CFD models.

In the case of a three-phase stirred tank system, the solidsuspension process depends upon the quality of gasliquid dis-persion in the absence of solids and the quality of solidliquiddispersion in the absence of gas. The objective of this studywas to undertake CFD simulations for the prediction of criti-cal impeller speed for the solid suspension. For this purpose,simulations have been performed for gasliquid, liquidsolidand gasliquidsolid dispersions under different design (mainlyimpeller design and sparger design) and operating conditions(such as solid loading, particle size, supercial gas velocity andthe impeller speed).

2. CFD modeling

In the present work, an Eulerian multi-uid model has beenadopted to describe the ow behavior of each phase, where thegas, liquid and solid phases are all treated as different continua,interpenetrating and interacting with each other everywhere inthe computational domain. In FLUENT, the derivation of theconservation equations for mass and momentum for each of thethree phases is done by phase weighted Favre-averaging ( Violletand Simonin, 1994 ) the local instantaneous balances for eachof the phases, and then no additional turbulent dispersion termis introduced into the continuity equation. The pressure eldwas assumed to be shared by the three phases, in proportion to

their volume fraction. The motion of each phase is governedby respective mass and momentum conservation equations.

The continuity equation for each phase is

j ( GG )j t

+ .( GG uG ) = 0, (1)

j ( LL )j t

+ .( LL u L ) = 0, (2)

j ( S S )j t

+ .( S S u S ) = 0, (3)

where is the density, is the volume fraction, and u is the

velocity vector of each phase.The momentum balance equation for each phase is

j ( GG uG )j t

+ .( GG u G u G )

= G p + .(G eff ,G ( u G + ( uG )T))

+ GG g M I,LG , (4)

j ( LL u L )j t

+ .( LL u L u L )

= L p + .(L eff ,L ( u L + ( u L )T))

+ LL g + M I,LG + M I,LS , (5)

j ( S S u S )j t

+ .( S S u S u S )

= S p + .(S eff ,S ( uS + ( u S )T))

+ S S g M I,LS , (6)

where p is the pressure, eff is the effective viscosity, g is thegravitational acceleration, and M I is the interphase transferforce. The volume fractions satisfy the compatibility conditions

G + L + S = 1. (7)

2.1. Interphase momentum transfer

Interactions between the phases involve various momentumexchange mechanisms such as the drag, the lift, the added massforce, etc. However, the contribution of drag force has beenconsidered while the effect of the other forces has been ignored.It has been reported that the other forces have no considerableeffect on both the gasliquid and solidliquid hydrodynamicsin stirred tanks ( Ljungqvist and Rasmuson, 2001; Montanteet al., 2001 and Khopkar et al., 2005 ).

The drag force exerted by the dispersed phase on the contin-uous phase is calculated as

M D,LG =34

CD,LGd B

LG |u G u L | (u G uL ), (8)

M D,LS =34

CD,LS d p

LS | u S u L | (u S u L ) , (9)

where CD is the drag coefcient and d is the diameter of a

bubble ( d B ) or a particle ( dp ).The drag coefcient exerted by the gas phase on the liquidphase is obtained by the modied Brucato drag model (Khopkaret al., 2006 ), which is as follows:

CD,LG CDOCDO

= 6.5 10 6d p

3. (10)

The drag coefcient exerted by the solid phase on the liq-uid phase is calculated using the drag law proposed by Pinelliet al. (2001) , which is as follows:

CDOC

D,LS

= [ 0.4tanh16d

p

1 + 0.6]2 . (11)

2.2. Turbulence closure

In the present work the standard k model for single phaseows has been extended for the three phase ows with ex-tra terms that include interphase turbulent momentum trans-fer (Elgobashi and Abou-arab, 1983 ) to take into account theeffects of turbulence. The modeling of multiphase turbulentows is much more complex and computationally expensivefor three phase ows mainly because the inuence of the dis-persed phases on turbulence of the continuous phase. There-fore, in the present three phase CFD turbulence modeling, it hasbeen assumed that the turbulence in multiphase stirred tanks is


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restricted within the continuous phase. Further, it is apparentfrom the literature that both the gasliquid and liquidsolid twophase ows have been successfully simulated by the standardk turbulence model with some modications.

The turbulence viscosity of the continuous phase is obtainedby the k model:

t,L = C Lk2L

L. (12)

The equations of change for the turbulent kinetic energy ( k)and the energy dissipation rate for the liquid phase are given by

DL L kLDt

= L +t,L

kL kL

+ L L (P kL L ) + L L kL , (13)

DL L LDt

= L +t,L

L L

+ L LL

kL(C 1P kL C 2 L ) + L L L . (14)

Here kL and L represent the inuence of the dispersedphase on the continuous phase and the predictions for turbu-lence quantities for the dispersed phases are obtained using theTchen theory of dispersion of discrete particles by homoge-neous turbulence ( Hinze, 1975 ). The standard values were usedfor the turbulence parameters: C 1 = 1.44, C 2 = 1.92, C = 0.09,

k = 1.0, = 1.3. The value of the molecular viscosity of solidphase is set to be the same as that of water, since its variationdoes not bring obvious changes to the simulation results.

3. Method of solution

Steady state simulations were performed for the differenttypes of impeller, agitation speeds, particle diameter, solidconcentration and supercial gas velocity. The details of thereactor geometry and the operating parameters are given inTables 1 and 2. In this work, all the simulations have beenperformed using the commercially available CFD softwareFLUENT 6.2. The set of governing equations are solved bya nite control volume technique, where the entire vesselhas been considered for the simulation. A multiple reference

frame (MRF) approach has been used for the simulation of

Table 1Geometrical details of the gasliquid and liquidsolid system

References Reactor geometry Impeller Solids details Operating variables

Barresi and Baldi (1987) T = 0.39m,H = 1.19T , C = T / 3

4-PBTD, D = T / 3 Glass particles: S = 2660 kg / m3,

d p = 0.15, 0.225, 0.45mmSolid conc . = 0.5 kg/ 100kg, N = N js

Mishra and Joshi (1991) T = 0.50m, H = T ,C = T / 3

6-PBTD, D = T / 3 N = 210rpm, ring sparger = 0.116,sparger location = 0.1 m V G = 0.15 l / s

Aubin et al. (2004) T = 0.19m, H = T ,C = T / 3

6-PBTD, D = T / 2 N = 300rpm, ring sparger = 0.8D ,sparger location = 0.6C , V G = 0.042 l / s

Angst et al. (2004) T = 0.20m, H = T ,

C = T / 3

4-PBTD, D = T / 3 Glass particles: S = 2520 kg / m3,

d p = 327 m

Solid conc . = 1, 2, 3 vol%, N = 1000rpm

impeller rotation. In this method, computational domain isdivided into impeller zone (rotating reference frame) andstationary zone (stationary reference frame). For all the sim-ulations, the boundary of the rotating domain was positionedat r = 0.16 and 0 .10 m z 0.24 m. For the case of Zhu andWu (2002) , the rotating domain was positioned at r = 0.12

and 0 .08 m z 0.18 m. Tetrahedral elements were used formeshing the geometry and a good quality of mesh was en-sured throughout the computational domain using the GAM-BIT mesh generation tool. As regards the particular meshquality, we have been restricted to use tetra mesh elementsdue to more number of case studies and complex geom-etry. However, in this study a very high quality of mesh(skewness < 0.7) has been ensured throughout the computa-tional domain. The number of grid elements in all the threedirections in both the impeller and the outer zone were sys-tematically increased. When rening the mesh, care was takento put most additional mesh elements in the regions of highgradient around the blades and the discharge regions. In orderto check the sensitivity of the simulation result on the grid size,the grid spacing was reduced by a factor of 2 till the compari-son of the two consecutive cases showed that the reduction of the grid size did not generate a noticeable difference in simula-tion results. Therefore, grid elements of 600,000700,800 havebeen used in all the studies. Regarding boundary conditions,tank walls, the impeller surfaces and bafes have been treatedas no-slip boundary surfaces with standard wall functions. Thebubble size distribution in the stirred tank reactor depends onthe design and operating parameters. Unfortunately, exper-imental data of bubble size distribution in the present caseis not available in the published literature. Hence, the mean

bubble size of 3 mm has been used for all the simulations.At a liquid surface, a small gas zone was added at the freesurface of water, a method that has been reported to dampeninstabilities ( FLUENT 6.2, 2005 ) and only gas is allowed toescape using pressure outlet boundary condition which meanstop surface being exposed to atmospheric pressure. It was ini-tially assumed that the particles were uniformly distributed inthe liquid. All terms of the governing equations are discretizedusing the QUICK scheme. The SIMPLE algorithm has beenemployed for the pressurevelocity coupling. The convergencecriterion (sum of normalized residuals) was set at 10 4 for allthe equations. All the simulations have been carried on the

16 node, 32 processor AMD64 cluster with a clock speed of


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Table 2Summary of experimental details

References Reactor geometry Impeller Solids details Sparger details Operating variables

Chapman et al. (1983) T = 0.56m,H = T , C = T / 4

DT, D/T = 1/ 3 Glass particles: S = 2660kg / m3 ,

d p = 150, 225, 450 mRing type (SR) Solid conc . = 3wt%,

N = 8 . 12rps, V G = 5 . 20mm / sRewatkar et al. (1991) T = 0.57m,

H = T , C = T / 3

DT, PBTD45,

PBTD45,D/T = 1/ 3

Quartz particles: S = 2520kg / m3 ,

d p = 180, 340, 460, 700 m

Pipe (SP) and

ring type (SR)

Solid conc . = 3.4, 6.6, 12.7wt%,N = 6 . 15rps, V G = 2, 4.8, 8 and15mm/s

Zhu and Wu (2002) T = 0.39m,H = T , C = T / 3

Rushton turbine,D/T = 0.3 . 41

Glass particles: S = 2520kg / m3 ,

d p = 10 . 425 mPipe (SP), ringtype (SR)

Solid conc . = 1.8, 5.5, 15 wt%,V G = 10 . 30mm / s, N = 6 . 15rps

2.4 GH and 2 GB memory with each node. Total simulationtime for each case was around 120h.

4. Results and discussions

4.1. Two phase ows

It was thought desirable to conrm the validity of the modelfor the two extreme cases of gasliquid and solidliquid dis-persions. For a gasliquid system, particle image velocime-try (PIV) data of Aubin et al. (2004) (see Table 1 ) have beenused for the comparison of radial proles of the mean axialvelocity at various axial locations generated by PBTD45 withD/T = 0.5. Further, experimental data of Mishra and Joshi(1991) have been used for the comparison of radial gas hold-upproles at various axial locations. Fig. 1 shows the schematicrepresentation of stirred system with stream lines and particlestrajectories. The above simulations have been carried out us-

ing the modied Brucato drag model ( Khopkar et al., 2006 )with an appropriate grid resolution. Fig. 2 (z/T = 0.19 (A),0.31 (B), 0.49 (C) and 0.65 (D)) shows an excellent agreementbetween the predictions and experimental data. In case of gashold-up proles, the present model is quite successful in pre-dicting the local gas hold-up values at various axial locationsof z/T = 0.19, 0.31 and 0.49 (Fig. 3).

For solidliquid systems, Pinelli et al. (2001) drag modelwas used. From Fig. 4 it can be seen that the CFD predic-tions of the axial solid concentration proles are in good agree-ment with the experimental measurements of Barresi and Baldi(1987) . The impeller geometry and reactor details are given inTable 1 . The inuence of solid particle concentration on themean liquid velocity has been studied using CFD and com-pared with the experimental data of Angst et al. (2004) . It canbe seen in Figs. 4 BD that the present model has predicted thedecrease in the mean liquid velocity (at z/T = 0.40) with anincrease in the solid concentration (1, 2 and 3 vol%) which is ingood agreement with the experimentally measured velocities.

4.2. Three phase ows

In Section 4.1, the validity of the CFD model was shownfor gasliquid and solidliquid systems. However, for the caseof three phase systems, experimental data on gas and solidhold-up proles are not available in the published literature.

Fig. 1. Schematic set-up: (A) streamlines; (B) particle trajectories.

Therefore, the present simulations have been focused on thebulk ow properties such as the critical impeller speed for solidsuspension and qualitative features of liquid circulation. Simu-lations have been performed over a wide range of experimentalconditions as summarized in Table 2 .


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0

0.05

0.1

0 0.2 0.4 0.6 0.8 1

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NORMALISED RADIAL COORDINATE, r/R (-)

D I M E N S I O N A L M E A N A X I A L V E L O C I T Y , W

/ U t i p , ( - )

Fig. 2. Comparison between the simulated and experimental proles of the dimensionless mean axial velocity for PBTD45 at various axial levels.(A) z/T = 0.19m; (B) z/T = 0.31m; (C) z/T = 0.49m; (D) z/T = 0.65m: experimental; CFD predictions.

4.2.1. Gross ow eld The gasliquidsolid ows generated by DT, PBTD45 and

PBTU45 impellers have been computed for a supercial gasvelocity of 2 mm/s, a solid loading of 3.4 wt% and for the im-peller speeds ( N) above the respective critical speeds for gasdispersion (7.5, 6.5 and 8 rps). The predicted liquidvelocityvectors have been depicted in Figs. 5 AC, for all the threeimpellers. It can be observed that the present CFD model isable to capture all the qualitative ow features generated byvarious impellers. Fig. 5A shows that, in the case of DT im-peller, the liquid ow leaving the impeller travels in the ra-dial direction and near the wall splits into two streams. Each

stream creates a circulation loop, one below and one abovethe impeller. Only a part of the energy supplied by the im-peller, which is associated with lower loop, is available in thebottom region for performing various functions such as solidsuspension. PBTD impeller (Fig. 5B) generates one circula-tion loop where the ow leaving the impeller is downward to-ward the bottom of the tank, and is directly available for thesuspension. PBTU impeller generates one circulation loop andthe liquid ow moves upwards toward the surface of liquidand turns down to the bottom. The length of the liquid pathand the number of direction changes are greater in the case of PBTU and DT as compared that for PBTD ow. As a result,the energy associated with the PBTD ow (in the bottom re-gion) is much higher than the DT and PBTU ows and hence

the turbulence intensity for the PBTD impeller is also rela-tively high. Therefore, a PBTD impeller is relatively more ef-cient under otherwise identical design and operating parameters(T,D,C ,H,P /V,V G , etc.).

The CFD predictions of the overall gas hold-up have beencompared with the experimental data of Chapman et al. (1983)in Table 3 . A satisfactory agreement can be seen betweenthe CFD predictions and the experimental measurements. Thesimulated gas hold-up distribution in the mid-plane betweenthe two bafes shows gas accumulation in the low-pressureregion behind the impeller blades forming the so-called gascavities.

4.2.2. Solid suspension studiesThe suspension of solid particles in a three phase

gasliquidsolid system has been studied by Zlokarnik andJudat (1969) , Queneau et al. (1975) , Subbarao and Taneja(1979) , Wiedmann and Efferding (1980) , Chapman et al.(1983) , Wong et al. (1987) , Rewatkar et al. (1991) , Zhu andWu (2002) , and Dohi et al. (2004) . These studies have beencritically reviewed by Kasat and Pandit (2005) . It was thoughtdesirable to undertake systematic CFD simulation of threephase stirred dispersions. The simulations have been validatedby comparing the CFD predictions and the experimental mea-surements of critical impeller speed for solid suspension over awide range of design and operating conditions (Table 1). In the


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0

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0

0.1

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0.4

0 0.2 0.4 0.6 0.8 1NORMALISED RADIAL COORDINATE, r/R (-)

F R A C T I O N A L G A S H O L D - U P ,

( - )

G

Fig. 3. Comparison between the simulated and experimental proles of thefractional gas hold-up for PBTD45 at various axial levels. (A) z/T = 0.19m;(B) z/T = 0.31m; (C) z/T = 0.49m: experimental; CFD predictions.

EulerianEulerian approach as used in this work, it is difcultto incorporate Zwieterings criterion in the CFD simulation of critical impeller speed for solid suspension. Therefore, we haveextended the method proposed by Bohnet and Niesmak (1980)for solidliquid system, which has been based on the value of standard deviation of solid concentration. The same methodol-ogy has successfully been employed by Oshinowo and Bakker(2002) and Khopkar et al. (2006) . Bohnet and Niesmak (1980)quantied the suspension quality using the standard deviation

dened as

=1n

n

1

S

S 1

2, (15)

where n is the number of sampling locations used for measur-

ing the solid phase hold-up. The increase in the degree of ho-mogenization (better suspension quality) is manifested as thereduction of the value of standard deviation. On the basis of the quality of the suspension, the range of the standard devi-ation has been broadly divided into three ranges ( Oshinowoand Bakker, 2002 ). For uniform (homogeneous) suspensions,the value of the standard deviation is found to be smaller than0.2 ( < 0.2). However, for the just suspension condition,the value of the standard deviation lies between 0.2 and 0.8(0.2 < < 0.8), and for an incomplete suspension, > 0.8.

The CFD simulations were performed to calculate the val-ues of the standard deviation using Eq. (15) for all the threeimpeller designs ( V G = 4 mm / s, 3.4 wt% solid loading, 180 mand pipe sparger). In the present study, the standard deviationwas calculated using the values of S stored at all computa-tional cells. Fig. 6 shows the variation of the standard devia-tion with respect to impeller speed. It can be noted that thereis a sharp reduction in the standard deviation as the impellerspeed approaches N CS . It can be noted that, at the experimen-tally measured values of N CS (6.75rps (PBTD), 10.25rps (DT)and 9.3 rps (PBTU)), the corresponding predicted values of are 0.76, 0.76 and 0.78, respectively. Therefore, the critical im-peller speed for suspension was considered to be achieved whenthe predicted value of was 0.75. Further, with an increase inthe impeller speed, the value of decreases rather slowly. This

means, at a constant loading of solid particles and supercialgas velocity, when the impeller speed is gradually increased,beyond N CS , more particles get suspended. The position of solids on the tank bottom (N > N CS ) depends on the impellerdesign. It can be clearly seen from Fig. 7 that in the case of DT and PBTU impellers, the particles are suspended from anannular space around the center of the tank bottom, whereasfor a PBTD impeller suspension occurs from the periphery of tank bottom. It is evident that the impeller speed required forsuspension by a PBTD impeller (in fact P /V ) is much lowerthan required by PBTU and DT impellers. Further, for DT andPBTU impellers the present CFD model predicts a signicant

quantity of unsuspended particles present on the tank bottom.This further shows that, at N CS , PBTD45 is more efcient thanthe DT and PBTU impellers.

4.2.2.1. Effect of impeller design. Earlier it has been shownthat DT, PBTD and PBTU impellers generate different owpatterns, and hence, offer different efciencies for the suspen-sion operation. In order to understand the quantitative role of the impeller design, CFD simulations have been carried outfor the three impeller designs and at different impeller speeds.For brevity, qualitative results are shown in Figs. 7 AC at thecritical impeller speeds. Figs. 7 DF show the axial concentra-tion proles with respect to impeller rotational speed for allthe three impeller designs, where the axial solid concentrations


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D I M E N S I O N L E S S M E A N

A X I A L V E L O C I T Y , W

/ U t i p ( - )



/ U t i p ( - )



/ U t i p ( - )

NORMALISED RADIALCOORDINATE, r/R (-)

z / T

C/Cavg



Fig. 4. (A) Comparison of experimental and predicted axial solid concentration proles at N js of different particle sizes ( : d p = 100 . 177 m; :d p = 208 . 250 m; : d p = 417 . 500 m) for 4-PBTD. (B) Comparison of experimental and predicted dimensional mean axial proles with mean dispersedphase volume fractions of (B) 1 vol%, (C) 2 vol%, (D) 3 vol%, stirrer speed 1000 s 1 : experimental, CFD predictions.

Fig. 5. Axial velocity (mm/s) vectors for liquid in presence of gas and solid in the mid-plane between two bafes: (A) DT; (B) PBTD45; (C) PBTU45.


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Table 3Experimental and predicted values of overall gas hold-up

S. no. Impellerspeed (s 1)

Gas spargingrate (m3 / s)

% Gas hold-up ( G )

Experimental Predicted

1 3.3 0.57 1.7 1.5

2 4 1.14 2.8 2.53 5 2.32 5.6 5

0

0.4

0.8

1.2

1.6

2

2.4

4 5 6 7 8 9 10 11 12 13

S T A N D A R D D E V I A T I O N , j

( - )

1 PBTD (CFD)2 DT (CFD)3 PBTU (CFD)2

3

1

IMPELLER ROTATIONAL SPEED, N (1/s)

Fig. 6. CFD predicted values of the standard deviation with respect to impellerrotational speed: (1) PBTD; (2) DT; (3) PBTU ( V G = 4 mm / s, 3.4 wt% solidloading, 180 m and pipe sparger).

are made dimensionless by dividing local solid concentrationby the average solid concentration. It can be noted that with anincrease in the impeller rotational speed the amount of solidparticles present at the bottom of the reactors has decreased.However, the increased impeller speed has not much inuenceon the solids distribution in top 14 th of the reactor. The values of the standard deviation have been calculated using Eq. (17). Pre-dictions of critical impeller speeds using CFD (when = 0.75)for all the impeller designs are compared with the experimen-tally measured critical impeller speed. Table 4 shows an excel-lent agreement between the values of N CS for PBTD, DT andPBTU for given reactor geometry (pipe sparger), solid loading

(3.4 wt%) and particle diameter(180 m

)at 6.5, 9, and 11 rps.

4.2.2.2. Effect of particle size. The critical impeller speed forsolid suspension also depends upon the particle size. Therefore,it was thought desirable to study the predictive capabilities of the present CFD model for various particle sizes. The simu-lations have been carried out for the three particle diameters,i.e., 180, 340 and 700 m with PBTD45, DT and PBTU45 im-pellers, pipe sparger, 6.6wt%, V G = 4.8 mm / s and at variousimpeller speeds. Fig. 8 shows a good agreement between theCFD predictions and the experimentally measured data for allthe impeller designs. Further, it conrms the fact that, for agiven tank and impeller conguration and for xed set of oper-ating conditions, uniformity of solids increases with a decrease

in the particle size. With increasing particle size the settlingvelocity increases and there is a decrease in the homogeneityof the suspension. Therefore, higher average liquid velocity isrequired to suspend the particles.

4.2.2.3. Effect of solid loading. CFD simulations were per-

formed to investigate the effect of solid loading on the criti-cal impeller speed for solid suspension. For this, particles of diameter 180 m particles with solid loadings of 3.4, 6.6 and12.7 wt%, respectively, have been considered (with a PBTD45impeller, pipe sparger, V G = 8 mm / s and at various impeller ro-tational speeds). Fig. 9 shows a fairly good agreement betweenthe CFD predicted and the experimentally measured values of N CS . The present model is able to simulate (results are notgiven for brevity but for two phase ows see Figs. 4 BD) thedecrease in liquid ow with an increase in the solid loading.This is because some of the impeller energy dissipates at thesolidliquid interface.

4.2.2.4. Effect of supercial gas velocity. In order to study thecapability of the present CFD model to simulate the effect of supercial gas velocity on the distribution of solids, CFD sim-ulations have been performed over a wide range of super-cial gas velocity. Fig. 10 shows a good agreement between theCFD predictions and the experimental data on N CS for all theimpeller designs and at V G = 2, 4 and 8 mm/s (pipe sparger60 mm).

The qualitative distribution of solids in the absence of gas atthe critical impeller speed of 6.5 rps ( Rewatkar et al., 1991 ) isshown by the contours of S in Fig. 11 A. On the introductionof gas ( V G = 2 mm / s) experimentally it has been reported that

the solid particles settle down due to a decrease in the circula-tion velocity as well as the liquid turbulence. As a result thereis a reduction in the solids cloud height. The same behaviorhas been qualitatively well predicted by the present CFD modelas shown in Fig. 11 B. Further, the predicted axial dimension-less concentration proles with respect to increasing impellerspeed are shown in Fig. 11 C. It shows that with increasing im-peller speed the amount of particles present at the bottom of the reactors has decreased which has been in agreement withexperimentally reported observations. However, the increasedimpeller speed has marginal inuence on the solid distributionin the top zone of the reactor. In order to model the suspension

capabilities of all the three impellers at N CS , the simulations of solid suspension were performed using the present model at su-percial gas velocities of 2,4,6,8 and 10 mm/s. The predictedvalues of standard deviation are shown in Fig. 12 . Experimen-tally it was observed that the effect of V G on the amount of solids suspended depends upon the type of impeller becausethe reduction in power with increasing V G varied with the typeof impeller. It can be seen that the present CFD model was ableto predict a gradual increase in with an increase in V G forPBTD impeller and hence relatively less particles tend to settledown at the bottom of the reactor. Whereas with DT and PBTUimpellers there is a remarkable rise in on the introduction of gas and more and more solid particles start getting settled withincreasing V G . This essentially means that PBTD impeller is


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0

0.2

0.4

0.6

0.8

1

0 1 2 3

0

0.2

0.4

0.6

0.8

1

600 rpm

550 rpm

500 rpm

360 rpm

420 rpm

480rpm

620 rpm

580 rpm

680 rpm

0.025

0.018

0.0125

0.06

0.00

0 0.4 0.8 1.2 1.6 20

0.2

0.4

0.6

0.8

1

0 0.4 0.8 1.2 1.6 2

Fig. 7. Effect of impeller type on solid concentration distribution for (A) DT; (B) PBTD; (C) PBTU at N CS (Rewatkar et al., 1991 ) by CFD simulations

(d p = 180 m, p = 2520kg / m3 , 6.6 wt%, V G = 2 mm / s (pipe sparger)).

Table 4Effect of impeller type on solid concentration distribution for (d p = 180 m,

p = 2520 kg / m3 , 6.6wt%, V G = 2 mm / s (pipe sparger))

S. no. Impeller type Critical impeller speed for off-bottomsuspension ( N CS ) (1/s)

Experimental Simulated

1 PBTD 6.5 6.52 DT 9.2 9.53 PBTU 11.1 11.3

still efcient than DT and PBTU on the introduction V G at agiven impeller speed.

4.2.2.5. Design of sparger. The ow generated by all the im-peller types get modied by the presence of gas and also theway in which the gas is sparged into tank, i.e., the spargerdesign. Therefore, in order to model the effects of spargerdesign on N CS the present CFD model is used. The simula-tions of solid suspension were performed for the pipe spargerand ring spargers of different diameter (with a PBTD45,

0

2

4

6

8

10

12

14

16

0 200 400 600 800AVERAGE PARTICLE SIZE, dp (micron)

CFD

PBTD (Exp)DT (Exp)PBTU (Exp)

C R I T I C A L I M P E L L E R S P E E D F O R S O L I D

S U S P E N S I O N , N C S

( 1 / s )

Fig. 8. Comparison of experimental and predicted critical impeller speedsfor different impeller designs. PBTD; DT; PBTU (experimental), CFD predictions ( d p = 180 m, p = 2520kg / m3 , 6.6wt%, V G = 4.8 mm / s(pipe sparger)).

V G = 8 mm / s, d p = 180 m, sparger is located at 100 mm fromthe bottom and solid loading of 3.4 wt%). It is evident fromTable 5 that the predicted N CS values agree fairly well with the


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0

2

4

6

8

10

0 5 10 15

CFDPBTD (Exp)

C R I T I C A L I M P E L L E R

S P E E D F O R S O L I D

S U S P E N S I O N , N C S

( 1 / s )

SOLID LOADING, X (%, wt.)

Fig. 9. Effect of solid loading on the critical impeller speed for PBTD(d p = 180 m, p = 2520 kg / m

3 , V G = 8 mm / s (pipe sparger)): experimental, CFD predictions.

6

7

8

9

10

11

0 2 4 6 8 10 C R I T I C A L I M P E L L E R S P E E D F O R S O L I D S U

S P E N S I O N , N C S

( 1 / s )

CFDPBTD (Exp)DT (Exp)

PBTU (Exp)

SUPERFICIAL GAS VELOCITY, V G (mm/s)

Fig. 10. Comparison of experimental and predicted critical impeller speeds forvarious supercial gas velocities. PBTD; DT; PBTU (experimental), CFD predictions ( d p = 180 m, p = 2520 kg / m3 , 6.6 wt%, V G = 2, 4and 8 mm/s (pipe sparger)).

0

390rpm

450rpm

z / T

5.20e-02

4.00e-02

2.95e-02

1.85e-02

0.00e-00

5.20e-02

4.00e-02

2.95e-02

1.85e-02

0.00e-00

1

0.8

0.6

0.4

0.2

C/Cavg0 0.4 0.8 1.2 1.6 2

550rpm

Fig. 11. Effect of supercial gas velocity on solid concentration distribution for PBTD by CFD simulations at 6.5 rps ( Rewatkar et al., 1991 ) (d p = 180 m,

p = 2520 kg / m3 , 6.6 wt%, (ring sparger, 0.095mm o.d.)). (A) V G = 0 mm / s; (B) V G = 2 mm / s; (C) dimensionless axial concentration proles at 390, 450and 550rpm.

experimental values for all the sparger designs. It can be notedthat the ring sparger provides lower value of N CS comparedto that for the pipe sparger. Further, sparger having large ringdiameter is found to give the lowest value of N CS compared to

0

0.4

0.8

1.2

1.6

2

2.4

2.8

0 2 4 6 8 10 12

1 2

3

S T A N D A R D D E V I A T I O N , ( -

)1 PBTD (CFD)2 DT (CFD)3 PBTU (CFD)

SUPERFICIAL GAS VELOCITY, V G (mm/s)

Fig. 12. CFD predicted values of the standard deviation at N CS with respectto supercial gas velocity: (1) PBTD; (2) DT; (3) PBTU (3.4wt%, 180 mand pipe sparger).

Table 5Design of sparger on solid concentration distribution for PBTD (d p = 180 m,

p = 2520 kg / m3 , 6.6wt%, V G = 8 mm / s)

S. no. Sparger type Critical impeller speed for off-bottomsuspension ( N CS ) (1/s)

Experimental Simulated

1 SP60 7.8 82 SR95 7.5 7.753 SR190 7.25 7.54 SR152 7 7.25 SR420 6.5 6.5


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Fig. 13. Effect of sparger on solid concentration distribution for PBTD at N CS (Rewatkar et al., 1991 ) by CFD simulations ( d p = 180 m, p = 2520kg / m3 ,6.6wt%, V G = 10mm / s): (A) pipe sparger (0.06m); (B) ring sparger (0.095 m o.d.); (C) ring sparger (0.42 m o.d.).

the smaller one which are in good agreement with the experi-mental ndings.

Experimentally it has been observed that the ring spargerwith diameter 2D (SR420) sparges the gas along the peripheryand generates the ow pattern in the same direction as thatgenerated by the impeller action of PBTD. Therefore, it helpsto maintain better suspension of the solid particles throughoutthe reactor. Figs. 13 AC show the contour plots of S at N CS inthe mid-bafe plane for the three sparger designs (for brevity,SP60, SR95 andSR420). The concentration distribution is moreuniform with SR420 compared to SP60 and SR95.

5. Conclusions

(1) In the present work, three phase stirred suspension has beensimulated using FLUENT 6.2 CFD software. The Eulerianmulti-uid model along with the standard k turbulencemodel has been used to simulate gasliquid, solidliquidand gasliquidsolid dispersions.

(2) A very good agreement was found between the predictedand the experimental velocity and G proles in gasliquid

dispersions.(3) A very good agreement was also found between the pre-dicted and experimental proles of S over a wide rangeof impeller speed and the impeller design.

(4) By using the concept proposed by Oshinowo and Bakker(2002) a value of standard deviation ( = 0.75) has beensuggested for the prediction of critical impeller speed forsolid suspension. The suggested value of holds for dif-ferent impeller designs and over a wide range of particlesize, solid loading and supercial gas velocity.

(5) For three phase dispersions, the predicted critical impellerspeeds have been compared with the experimental resultsof Chapman et al. (1983) , Rewatkar et al. (1991) andZhu and Wu (2002) over a wide range of solid loading

(0.3415 wt%), for different impeller designs (Rushtonturbine (RT), pitched blade down and upow turbines(PBT45)), solid particle sizes (1801000 m) and for var-ious supercial gas velocities (010mm/s). A very goodagreement was observed in all these cases.

Notation

C , C 1, C 2 turbulence model constantsC solid concentration, kg / m3

Cavg average solid concentration, kg / m3

CD drag coefcient in turbulent liquidCDO drag coefcient in still liquidd B bubble diameter, md p particle diameter, mD impeller diameter, mg acceleration due to gravity, 9 .8 m / s2

H liquid height, mk turbulent kinetic energy, m 2/ s2

M D drag force per unit area, N / m3

N impeller rotation speed, s 1

N CS critical impeller speed for solid suspensionin gasliquidsolid system, rps

N j s critical impeller speed for just suspension, rpsp pressure, PaP power consumption, WP K turbulence production, kg / m1 s3

t time, sT tank diameter, mu average velocity, m/sV volume of the reactor, m 3

V G supercial gas velocity, m/sw width of the impeller blade, mz axial co-ordinate direction, m


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Greek letters

Kolomogoroff eddy size, mturbulent energy dissipated per unit mass, m 2/ s3

volume fractionviscosity, kg/ms

density of uid, kg / m3

turbulent Prandtl number for the dissipation ratek turbulent Prandtl number for the turbulent ki-

netic energy

Subscripts

eff effectiveG gas phase

L liquid phase LG liquidgas LS liquidsolidS solid phaser radial co-ordinate directiont turbulenttip at the tip of the impeller blade

Acknowledgment

Mr. B.N. Murthy and Dr. R.S. Ghadge gratefully acknowl-edge the nancial support during this work by Department of Atomic Energy (DAE), Government of India.

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