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chemical engineering research and design 8 7 ( 2 0 0 9 ) 669–676

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

journa l homepage: www.e lsev ier .com/ locate /cherd

ubble-bed structural models for hybrid flow simulation:n outlook based on a CFD generated flow image

. Staykova, M. Fialovab,∗, S.D. Vlaevc

Technical University of Sofia, Blvd. Kl. Ohridski 8, 1000 Sofia, BulgariaInstitute of Chemical Process Fundamentals of the AS CR, v.v.i., Rozvojova 135, 16502 Prague 6, Czech RepublicInstitute of Chemical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 103, 1113 Sofia, Bulgaria

a b s t r a c t

A major problem of hybrid modelling is the selection of the most realistic structural flow model to represent a reactor

equipment unit. Based on CFD simulation, the paper is considering the best version of a circulation flow model for

description of the flow pattern in bubble columns. The 3D Euler–Euler model of two-phase flow is solved to prepare

the fundamental instantaneous mixing images of bubble column. Two cases of different viscosity including water

and aqueous solution of saccharose and gas bubbles at two different diameters to mimic bimodal extremes have

been visualized. The model validity is confirmed by comparison with instantaneous gas hold-up experimental data

measured by conductometry. More than 100 flow images were examined and compared with four reference bubble-

bed structural models. The unsteady flow structures occurring naturally in the bubble column were identified. The

frequencies of the vertical structures were of the order 10−1–100 Hz. The structure composed of a macro vortex

with large single loops was found to appear alternatively in crossed planes; accordingly, the multiple cell cross-flow

circulation suggested earlier by Zehner has been found as the most appropriate.

© 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Bubble column; Hybrid modeling; Phenomenological mixing models; CFD

generalized compartmental models selected to conform best

. Introduction

luid flows play important role in various equipment androcesses in industry. Flows of gas introduced into liquideds through perforated gas distributors constitute bubbleed columns that are widespread process engineering devices.as and liquid flows in bubble columns are very complex and

nherently unsteady. In order to solve engineering problems,ne should know their flow structure that is obtained fromeasurements in experimental facilities or from visualiza-

ion studies. Visualizations can be useful if compared withhe detail generated by CFD simulation. Consequently, bubbleolumns two-phase flows have become a major goal of flowrediction based on theoretical models.

In general, CFD of multiphase flows is computer intensive.or example, a two-phase flow model involving gas bubblesf ten different sizes would require 41 equations (Ranade,

002). Consequently, effort has been made to reduce the CFDimension: In order to avoid computer intensive solutions,

∗ Corresponding author. Tel.: +420 220 390262; fax: +420 920661.E-mail address: Fialova@icpf.cas.cz (M. Fialova).Received 13 May 2008; Received in revised form 10 October 2008; Acce

263-8762/$ – see front matter © 2008 The Institution of Chemical Engioi:10.1016/j.cherd.2008.10.006

some authors employed structural models. Devanathan et al.(1995), Zahradnik et al. (2001) and Gupta et al. (2001) reportedsuccessful predictions using computer-based structural mod-els to produce quality results. Additionally, task reductionby hybrid simulation has been considered (Rigopoulos andJones, 2003; Bezzo et al., 2003, 2004). One could judge thatthe feedback to structural representation of instantaneousflow phenomena in the reactor vessels could lead to com-bined, i.e. CFD-based and structural modeling-based solutionswith significant accuracy. Indeed, a recent paper by Leib et al.(2001) summarized that CFD models can be used to establishthe flow field in bubble column reactors and to incorporatethe results further in simplified zone models. In order toavoid intensive computations, Rigopoulos and Jones (2003)proposed hybrid schemes for modeling of bubble columnswhere one may design computational grids to correspond to

pted 22 October 2008

to the CFD-generated flow fields representative for the spe-cific geometry. Bezzo et al. (2004) offered similar methodology.

neers. Published by Elsevier B.V. All rights reserved.

670 chemical engineering research and

Nomenclature

CD drag coefficientdB bubble diameter, mg gravity acceleration, m s−2

H height of aerated bed, mH0 clear liquid height, mk turbulent kinetic energy, m2 s−2

n number of phasesP pressure, Pat time, sU velocity, m s−1

u0G superficial gas velocity, m s−1

xi,j coordinates

Greek letters˛ volume fractionε rate of turbulent energy dissipation, m2 s−3

εG average gas hold-upεZ local gas hold-up� dynamic viscosity, Pa s� density, kg m−3

� shear stress, Pa

SubscriptsB bubbleG gasL liquidm mixtureq phase indext turbulentz axial coordinate

The mixture turbulence model was used with k and ε and

The approach has been demonstrated earlier by Zahradniket al. (2001) and recently by Guha et al. (2006). Zahradnik etal. (2001) based their compartmental model on Whalley andDavidson assumption of liquid circulation (Kastanek et al.,1993) while Guha et al. (2006) employed a CFD-based compart-mental concept. Both procedures have been focused on flowcompartmentalization.

Since it is flow circulation that dominates the convectiveflows in bubble columns, the compartmentalization shouldcorrespond to the most realistic circulation phenomena, e.g.the unsteady flows. However, most of the earlier work isfocused on time-averaged behaviour. In contrast with thesestudies, recent studies (Buwa and Ranade, 2003, 2004) showedthat the overall dynamics that influences the mixing andtransport processes in bubble beds bring about time-averagedvalues of mixing parameters that are different from the experi-mental ones. Consequently, the hybrid models should capturethe transient features of the circulation flow structures in bub-ble columns. These structures are found to be significantlydifferent from the gross circulation patterns observed in time-averaged flow measurements.

Thus, the discussion on circulation flow models has beenrenewed. Looking at recent literature on bubble columns,one finds a gap between existing circulation models andrecent dynamic visualization. Recalling the models of Joshiand Sharma (1979), Kastanek et al. (1993), Zehner and Schuch(1985) and Gupta et al. (2001), it would be interesting to discuss

their viability in the context of the recent advances of CFD flowvisualization.

design 8 7 ( 2 0 0 9 ) 669–676

In an attempt to promote the hybrid multi-zonal CFDapproach to dynamic reactor modeling, this study is aimed atdiscussing the reported structural flow models and point at thestructural concept that is most relevant to the CFD-generateddynamic flow field of a bubble column.

2. Circulation flow models

Fig. 1 presents a summary of the major mechanistic circulationflow models that have been reported within the former twodecades (Kastanek et al., 1993), i.e. the multiple-cell two-loopcirculation concept (a), the multiple-cell single-loop circula-tion (b) followed by Zehner’s 3D cross-flow version (c) andthe gas and liquid recirculation model (e). Schemes (d) and (f)represent two recent ‘zone’ versions of these models, i.e. the“network-of-zones” (Zahradnik et al., 2001) (d) and the “gener-alized compartmental” model concept (Rigopoulos and Jones,2003) (f). A detailed description of the authors’ argumentsbehind these mechanistic models is beyond the scope of thispaper. For more details, one could refer to the source literature.In this study, we have recalled these schemes to compare themwith evidence from numerical analyses, in order to identifythe one that is most realistic to use in industrial engineeringproblems.

3. Computational flow model andsimulations details

The Euler–Euler two-fluid model was used to simulate dis-persed gas–liquid flow in bubble columns (Ranade, 2002;Fluent Inc., 2003). The mass conservation equation andmomentum conservation equations for each phase were

∂(˛q�q)∂t

+ div(˛q�qUq) = 0, (1)

∂

∂t(˛q�qUq) + div(˛q�qUq ⊗ Uq)

= −˛q grad P + ˛q�q div (�q) + ˛q�qg + Mq, (2)

where q means gas or liquid phase (q = L or G), � is density, ˛

volume fraction, U means phase velocity, P is pressure and Mq

represents the inter-phase momentum exchange term.The stress tensor was represented by

�q = ˛q�q

(∂Uqi

∂xj+ ∂Uqj

∂xi

)− ˛q

(23

�q

) ∂Uqi

∂xiıij, (3)

where �q is effective viscosity (�q = � + �t) with � and �t indi-cating molecular and turbulent viscosity, respectively.

The Reynolds-averaged equations of flow were solved. Tur-bulent viscosity was assumed to be satisfactorily estimated bythe k − ε turbulence model (Sokolichin and Eigenberger, 1999;Pfleger et al., 1999)

�t,m = C��mk2

ε. (4)

parameters delivered from the relevant transport equationswith density and velocity for the mixture of two phases (n = 2,

chemical engineering research and design 8 7 ( 2 0 0 9 ) 669–676 671

Fig. 1 – Multiple-cell and networks-of-zones models incorporating liquid circulation: (a) the multiple-cell two-loopcirculation concept, (b) the multiple-cell single-loop circulation model, (c) Zehner’s 3D cross-flow model, (d) the“network-of-zones” model, (e) the gas and liquid recirculation model, and (f) the “generalized compartmental” modelc

n

U

W(mb

M

S

wbctf

op

oncept.

amely, q = L and G):

� = �m =n∑

q=1

˛q�q,

m =∑n

q=1˛q�qUq∑n

q=1˛q�q

as for the single-phase k − ε model.

ith reference to previous analyses of the multiphase modelTomiyama et al., 2002; Buwa and Ranade, 2003) the interfacial

omentum transfer (Mk) has been assumed to be dominatedy drag force:

L = MDG = 3

4�L˛G˛L

CD

dB|UG − UL|(UG − UL). (5)

The drag coefficient CD was calculated based onchiller–Nauman model used by default in Fluent code.

No mass transfer between the gas and the liquid phaseas considered and the dispersed phase was represented

y a single phase with effective bubble diameter (no coales-ence or break-up). For two-phase flow, the same values ofhe standard turbulence parameters were used as proposedor single-phase flows (Launder and Spalding, 1974).

The boundary conditions were as follows: (1) the bottomne was set as velocity inlet specified as inlet for the gashase with values corresponding to superficial gas velocity in

the column of 4 and 8 cm/s, thus, 21 m/s and 41m/s, respec-tively, liquid volume fraction in the openings being set to zero.(2) the top one was set as pressure outlet with gas volumefraction 1; it was assumed to coincide with the free surface ofdispersion.

Patching was used to define the boundary between the dis-persion and the gas phase. The free surface was assumed tovary, the normal liquid velocity, the tangential stress and thenormal fluxes being set to zero. The standard wall functionapproach was adopted. The gas bubbles were free to escapefrom the top or to backflow. Gravity condition was activated.

The geometry and mesh were constructed using the GAM-BIT tool of the CFD package. Referring to the conclusions ofBertola et al. (2003), a fine grid cell with mean linear dimen-sion less than 10 mm has been selected. The grid consisted of0.75 × 106 cells. There was grid refinement around the holesand the column wall. Hexahedral mesh with sizing functionvicinity was used to model the nozzles (Fig. 2).

Fluent unsteady 1st order implicit solver was used. Thedynamic reactor start-up was followed with the simulationstarting at zero gas flow initial condition, i.e. without gas atclear liquid height 0.9 m. Steady state condition was observedthroughout the analysis.

The following simulation procedure was followed: (1) com-

puter generation of the time-course of flow field images andflow patterns and (2) post-processing focused on the flowstructures-ascending flows, vortices and descending flows.

672 chemical engineering research and design 8 7 ( 2 0 0 9 ) 669–676

Fig. 2 – Bubble column computational domain, bottom and top surface boundaries: (A) overall view, (B) view of plane Y = 0,rface

Unlike previous studies analyzing the overall flows, this studywas directed to instantaneous local flow structures followingtheir origination, appearance and dying out. Altogether 147

(C) bottom plate and gas flow iso-surface, and (D) top free su

4. Laboratory experiment and validationexamples

A previous experimental background (Vlaev and Fialová, 2003)was referred to for the meshing procedure and for bench-marking the solution. The simulated reactor (Fig. 2) was ofthe same size, as the one used in validation experiments,e.g. a bubble column of ID 0.29 m, H = 1.5 m and clear liquidheight Ho = 0.9 m. Gas distributor comprised a perforated platewith 67 holes of 1.6 mm in diameter, the holes spaced uni-formly on the plate area in triangular pitch sided 3.5 cm. Thefree plate area ratio was 0.2%. The fluid phases were air andwater (case 1) or air and 30 wt % saccharose solution in water(case 2). The input liquid viscosity in the latter case was 2.7mPa·s and density was 1127 kg/m3. In the validation experi-ments, the air-flow rate was 10 m3/h and in the studies alsoflow rate 20 m3/h was examined. The initial velocity of air inthe holes was 21 m/s and 41 m/s, respectively, and bubble sizewas assumed to be 2 mm or 5 mm.

So far, adequacy of the theoretical model has been provedbefore in several studies (Ranade, 2002). Yet our simulationresults were compared with experimental data, in so far asthe computational procedure of this study involved its specificmeshing and solution practice. Model validity was tested byseveral procedures. Gas hold-up εG was measured with air atvariable feed rates and zero liquid flow. The local value at var-ious height z, i.e. εZ, was measured by two-plate conductivityprobe and the average value was determined by bed expan-sion: εG = (H − Ho)/H. Experimental details have been reportedelsewhere (Vlaev and Fialová, 2003).

5. Results and discussion

5.1. Comparison of gas hold-up values predicted byCFD with experiment

The average values of εG predicted by CFD approached theexperimental values εG = 0.12 ± 0.02, as follows: in water at

of gas–liquid dispersion.

u0G = 4.2 cm/s and dB = 5 mm, εG = 0.1, in 30 wt % saccharoseand bubbles of the same size, εG = 0.155, in water at dB = 2 mm,εG = 0.15. The differences between measured and predicteddata depended on bubble diameter and were between −26%and 15% for water and 29% for the 30 wt % saccharose solu-tion. Fig. 3 compares instantaneous gas hold-up profiles εZ inwater predicted for 2 mm bubbles at u0G = 4.2 cm/s correspond-ing to bulk levels z = 0.5 m and 0.6 m with data measured atsimilar heights. Evidently of the successful prediction of gashold-up by the simulation profiles, it has been accepted thatthe CFD model describes satisfactorily the bubble bed fluiddynamics relevant to the water and the saccharose solutionemployed.

5.2. Comparative analysis of the structural flowmodels based on similarities and differences withfundamental dynamic structures

Fig. 3 – Comparison of local gas-hold-up profiles predictedby the CFD model with measurements (� z = 0.5 m; ©z = 0.6 m). (Deviations 5% of measured values are indicated).

chemical engineering research and design 8 7 ( 2 0 0 9 ) 669–676 673

Fig. 4 – Evolution of the fluid flow field in water in the bubble column angular-crossed planes Y = 0 and Y = X correspondingt d su

iaadtttrut

fianaYflcsFb

12trev

o

(

o time segments (a) 20 s and (b) 26 s. Bubble size is 5 mm an

nstantaneous images corresponding to six major cases of aer-tion, namely, of water at u0G = 4 cm/s and 8 cm/s, dB = 2 mmnd 5 mm and of saccharose at u0G = 4 cm/s and 8 cm/s and

B = 5 mm were examined. The macroscopic flow structureshat appeared in the images were identified. Averaging relatedo gas hold-up was carried out, in order to check adherenceo steady state values. Quasi steady state in both cases waseached in the first seconds following bed expansion, the vol-me average gas hold-up remaining constant for the rest ofhe runs.

Fig. 4 illustrates the time-course of the instantaneous floweld of the bubble column reactor in water. In order to beble to discriminate between the formations in 2D (e.g. pla-ar flow) and in 3D (e.g. cross-flow), the views in two planest 45◦, namely, figure for Y = 0 (left-hand placed) and figure for= X (right-hand placed) are shown. Fig. 5 represents similarow patterns in 30 wt % saccharose. The views in the figuresorrespond to different time segments. Fig. 4(a) and (b) corre-ponds to temporary segments 20 s and 26 s, respectively, andig. 5(a) and (b), to 12 s and 14 s, respectively. Bubble size inoth cases was 5 mm and steady state was reached by 7 s.

Following previous experimental work (Kastanek et al.,993; Tzeng et al., 1993) and simulation studies (Lapin et al.,001; Lehr et al., 2002) the following macroscopic flow struc-ures have been sought: central plume of ascending flow orising curved macro-vortex of preferentially aerated liquidxpected to follow an S-shaped path, descending flows andortex-like flows.

The following characteristics of the flow patterns werebserved (Figs. 4 and 5):

1) Main liquid flow in nearly all figures followed the S-shaped path in a discontinuous way, it was ascending

(Figs. 4(a) and 5(a)) or descending (Fig. 4(b)), most oftenmixed even in one plane (Fig. 5) and not in a central posi-tion (all figures).

perficial gas velocity is 0.08 m/s.

(2) Apart from the well-defined descending flow near thewalls, the fluid was engaged in a massive down-flow inthe column centre, as appeared to be the case in Fig. 4(b).

(3) Considering the vortex-like structures in the figures, theloops in planes were indicated by “L” and loop origins orsuspected loops in angular-crossed planes were markedwith “O”. It can be seen that large-scale vortices originated,migrated and faded away changing the path of the fluidmain flow, e.g. as seen within a time step of 6 s in Fig. 4and over a time step of 2 s in Fig. 5. The frequencies of thevertical structures were of the order 10−1–100 Hz.

(4) The case of water (Fig. 4) exhibited larger vortices andstreams, whereas dissolved sugar presented more rigidstructures rather constraint in space.

(5) Important flow property seen in both figures is the alter-native appearance of loops and origins in crossed-planes.The vortices are separated by sections (O) with no vor-tices present, where vortices appear often in the oppositeangular-crossed planes, e.g. see lower Fig. 4(a), upperFig. 4(b), and Fig. 5(b).

More images representing similar behavior could be shown.Similar patterns have been observed in the case of 2 mm bub-bles in water and in other subsequent temporal steps for thecases in Figs. 4 and 5. Exceptions reduced to smaller vortex sizeand continuity of up-flow that happens at increased viscosity(in saccharose) due to the limited amplitude of the local veloc-ity pulsations corresponding to this case. These flow patternsare accompanied by gas flow patterns that exhibit no loopsand represent mostly centrally located upstream. Example isshown in Fig. 6 left.

As seen in the figures, the instantaneous velocity vec-tor plots (in planar 2D view) exhibit flow patterns that are

most close to the multiple-cell single-loop concept of Kas-tanek and Zahradnik (Fig. 1(b)) extended in a 3D version byZehner (Fig. 1(c)). Indeed, comparing the ‘real’ flow patterns in

674 chemical engineering research and design 8 7 ( 2 0 0 9 ) 669–676

Fig. 5 – Evolution of the fluid flow pattern in 30 wt % saccharose in the bubble column angular-crossed planes Y = 0 and Xsize

corresponding to time segments (a) 12 s and (b) 14 s. Bubble

2D generated by CFD with the models in Fig. 1, one observessimilarity between Fig. 1(b) and these figures. It has been foundthat instantaneous formation of two loops is rather a rare

event, e.g. in this experiment it happened once in twelve 1-ssegments observed; most often there were single loops gener-ated by the main stream with S-shaped path. Consequently,

Fig. 6 – Gas phase distribution in the bubble column in water atvolume fraction contour plot obtained for plane Y = 0; right: gas vX = 0, X = Y, Y = 0. The profiles in planes Y = 0 and Y = X correspond

is 5 mm and superficial gas velocity is 0.08 m/s.

the two-loop structures are seen rather as an outcome of thetime-averaged flow pattern.

On the other hand, considering the 3D presentation by the

extension to angular-crossed planes, one could see the shiftedrepetition of single-loops occurring transversely in the crossedplanes. Referring to the parallel views of the crossed planes in

5 mm bubbles: left: 2D air-velocity (m/s) vector plot and gasolume fraction radial profiles in different vertical planes:to the positions indicated in Fig. 4.

nd de

tsatZsst

tamlbFtetmiwi

cutFpXzvahvtmdtmtima

6

Imiaaeosbtatwmathc

chemical engineering research a

he figures, one could observe eddies in three dimensions andee the loops as planar circulations in one plane (L) to appears originating loops in the transverse plane (O). Consequently,he multiple cell cross-loop circulation model proposed byehner and Schuch (1985) seen as a three-dimensional exten-ion of the single-cell model looks like to be the most realistictructural model version that could be used in hybrid simula-ion.

Referring to the literature, one may admit that the data ofhis study resemble data reported by Devanathan et al. (1995)nd Lehr et al. (2002). Neither view of these studies neitherore recent ones (Buwa and Ranade, 2004) backed the two-

oop circulation model. On the contrary, the flow patterns inoth studies exhibit the vortices referred to as single loops.urthermore, the cells of ideal mixing at column both ends inhe gas–liquid circulation model of Fig. 1(e) suggested by Guptat al. (2001) seem realistic merely in cases of small volumes ofhe cells at the bed top and bottom boundaries. However, this

odel version is likely to be unrealistic for a deep bubble bed,n so far as it involves single up-flow and down-flow sections,

hile the occurrence of multiple up-flow and down-flow zoness obvious.

Additional evidence supporting the multiple cell cross-loopirculation vision is seen in the instantaneous gas hold-p profiles obtained at different horizontal cross sectionshat reflect peaks of local gas hold-up in the various zones.ig. 6 illustrates the typical volume fraction profiles in crossedlanes X = 0 (0◦), X = Y (45◦), Y = 0 (90◦), the profiles Y = 0 and= Y corresponding to the z-levels indicated in Fig. 4, namely= 0.3 m and 0.75 m. In parallel, the corresponding gas velocityector plots and gas volume fraction contours in plane Y = 0re illustrated. It is seen that the extremes of the local gasold-up in the various zones follow the extremes of the gaselocities in the relevant cross sections, showing high and lowo high and low gas flow velocities, respectively. But what is

ore important, the instantaneous gas hold-up distribution inifferent cross sections and instants (as seen in the XY-plots),hough closer to a parabolic shape, showed most often asym-

etric. Parabolic and flat profiles with incidental peaks werehe most frequently observed cases, as observed also exper-mentally (Vlaev and Fialová, 2003). With regard to the flow

odels illustrated in Fig. 1, it would be only possible to obtainxis-asymmetric profiles in cases 1(b) (2D) and 1(c) (3D).

. Conclusions

n an attempt to identify the most realistic structural flowodel of a bubble bed, in order to enable its use in engineer-

ng hybrid (i.e. mixed CFD and “network-of-zones”) modeling,bubble column flow field has been resolved numerically

nd its velocity vectors and gas volume fractions have beenxamined. Evidence on liquid and gas circulation has beenbtained and used in selection of structural models. Thepatial flow images revealed structures composed of com-ined curved macro-vortices and large single loops what washe case generally registered in practice, however, the loopsppeared alternatively in crossed planes. In this study, addi-ionally crossed planar views of the flow field were comparedith the reference schematics. Two facts relevant to structuralodeling could be elevated: (1) the single loops are found to

ppear in crossed planes and (2) the planar local volume frac-

ion distributions show axis-asymmetric time-dependent gasold-up behaviour conforming to multiple-cell single-loop cir-ulation modeling. Both facts fit to the multiple-cell cross-loop

sign 8 7 ( 2 0 0 9 ) 669–676 675

modeling concept. It can be inferred that the compartmentalmodel that fits best to construct a CFD grid of a bubble columnis the one suggested earlier by Zehner.

Acknowledgement

The support of grants of the Academies of Sciences of CzechRepublic and Bulgaria is acknowledged.

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