ULTRAPURE WATER® DECEMBER 2002 1

HOXIDATIONMAJOR CHALLENGES IN THE DEVELOPMENT OF PHOTOCATALYTICREACTOR FOR WATER PURIFICATION

vanced oxidation technologies for air andwater purification treatment and is docu-mented in various references (1-4). It cou-ples low energy ultraviolet (UV) light withsemiconductors acting as photocatalysts,overcoming many of the drawbacks thatexist for traditional water treatment meth-ods. By using this technology in-situ, deg-radation of toxic compounds can beachieved both by oxidation (using photo-generated holes to oxidize organics, dyes,surfactants, and pesticides (5) and by re-duction (using photogenerated electrons toreduce toxic metal ions (6).

The appeal of this process technology isthe prospect of complete mineralization ofpollutants to environmentally harmlesscompounds. Besides, the process useatmospheric oxygen as oxidants, the cata-lyst titanium dioxide (TiO2) is cheap, sta-ble, non-toxic, and can be used for extend-ed periods without substantial loss of itsactivity. Moreover, it uses very low energyUV-A light (λ < 380 nanometers [nm]),resulting in energy requirement as low as 1to 5 watts per square meters (W/m2) ofcatalyst surface area, and more important-ly, can even be activated even by sunlight(7).

In spite of the potential of this promis-ing technology, development of a prac-tical water treatment system has not yetbeen successfully achieved. There areseveral factors that impede the efficientdesign of photocatalytic reactors (8). Pho-tocatalytic reactions are a complex, multi-

phase reaction system. The solid photocat-alyst is distributed within the continuousfluid phase, water and oxygen (or air), andthe UV-light electronic phase. In these typeof reactors, an additional engineering factorrelated to illumination of the catalyst be-comes relevant. This is in addition to otherconventional reactor complications suchas reactant-catalyst contacting, flow pat-terns, mixing, mass transfer, reaction kinet-ics, catalyst installation, and temperaturecontrol. The illumination factor is of utmostimportance since the amount of catalyst thatcan be activated determines the water treat-ment capacity of the reactor. The highdegree of interaction between the transportprocesses, reaction kinetics, and light ab-sorption leads to a strong coupling of thephysico-chemical phenomena and it is oneof the major hurdles in the technical devel-opment of a photocatalytic reactor.

The scale-up of fixed-bed photocatalyticreactors has been severely limited as reac-tor configurations have not been able toaddress the issue of mass transfer of pol-lutants to the catalyst surface. The new

e t e r o g e n e o u sphotocatalysis isone of the ad-

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reactor design concepts must deal with thischallenge. Earlier experimental studies byour group of catalyst-coated tube bundles(9), novel immersion type lamps (10), androtating tube bundles revealed that thephotocatalytic reaction is mainly diffusion(mass-transfer) controlled. The reactionoccurs at the fluid-catalyst interface, and inmost cases, the overall rate of reaction islimited to mass transport of the pollutant tothe catalyst surface. In our earlier studies,we have enhanced mass transfer by in-creasing mixing of fluids through turbu-lence and introduction of baffles (11). In thiswork, a new photocatalytic reactor is con-sidered that uses flow instability to increasereaction yield throughout the reactor vol-ume.

Centrifugal Instability ofRotating Taylor-Couette FlowThe laminar flow confined within the annulusregion between two co-axial cylinders withthe inner one differentially rotating withrespect to the outer suffers centrifugal insta-bility, depending on the geometry and ro-

Figure 1. Schematic diagram of the Taylor vortex reactor (left), and location of theobservation stations in the annular region to analyze flow behavior. D* = 0 (rotating innercylinder), d* = 1 (stationary outer wall), y* = 0 (bottom), y* = 1 (top).

By Ajay K. Ray, Ph.D.National University of Singapore

ULTRAPURE WATER® DECEMBER 20022

tation rates. First experimental reportingwas done by Taylor (12), although the firstcriteria of centrifugal instability was pre-sented earlier by Rayleigh (13), who showedthat an inviscid rotating flow to be unstableif the energy of rotation associated with fluidparticle decreases radially outward.

Under such an unstable configuration,one notices the appearance of circumferen-tial toroidal vortices in between the twocylinders and is known as Taylor-Couettevortices. These vortices evolve due to theadverse gradient of angular momentumthat creates potential unstable arrange-ment of flow (14). Such an unstable condi-tion arises naturally if the outer cylinder isheld stationary while the inner cylinder isrotated at a sufficiently high rotation rate – anarrangement considered in the presentstudy.

A schematic of the system is shown inFigure 1. The toroidal vortices that areformed in the annular region betweenthe cylinders for a particular combina-tion of the geometric arrangement andthe inner cylinder rotation rates areshown in Figure 2. The non-wavy vortexflow is seen to appear as a conse-quence of primary instability as given byappropriate non-dimensional numbers likeTaylor number and Reynolds (Re) number.When the Reynolds number is increased tosomewhat higher values, then one sees thewavy vortex flow, also shown in Figure 3.(Editor’s note: This article has an Appendixthat contains additional figures presented

with the original paper. Due to spaceconsiderations, not all figures could beincluded with the printed version. TheAppendix is available with the electronicversion that is available at our web site:ultrapurewater.com.)

In such an unstable condition, theannulus is filled with pair of counterrotating vortices. This can be viewed inFigures 3 and 4. Figure 4 also shows theboundary layer forming on the innersurface to have an axial periodicity. Theboundary layer oscillates periodically be-tween almost zero thickness to a maxima inbetween the counter-rotating vortex pair,where the two shear layers approachingeach other spews out a jet of fluid towardsthe outer wall. The fluid particles in theirmotion around the toroidal vortices comeperiodically in contact with the inner sur-face.

By assuming the annular gap, d = (ro

- ri), as small compared to the innercylinder radius (ri), where ro is the outercylinder radius, it has been shown byTaylor (12) that stability is dependentonly on the ratio of the rotation rate of theouter cylinder to the rotation rate of theinner cylinder, (Ωo/Ω i), and a single param-eter, called Taylor number, Ta, which can bedefined as seen in Equation 1. (Editor’snote: All equations for this article are togeth-er in a single Equations table.) From thestability theory for 0 ≤ Ω o/Ω i ≤ 1 and largeaspect ratio, it has been established thatprimary instability in the form of the appear-

ance of Taylor vortices occurs at Ta, crit ≈1,708.

A particle image velocitymetry (PIV)was used to measure the axial andradial velocities in a meridional plane fornon-wavy and wavy Taylor-Couette flowin the annulus between a rotating innercylinder and a fixed outer cylinder withfixed-end conditions by Wereley andLueptow (15). It was shown that thevortices became stronger and the out-flow between pairs of vortices was jet-like. Wavy vortex flow is characterizedby azimuthal deformation of vorticesboth axially and radially.

According to their findings, it was alsoshown that significant transfer of fluidbetween neighboring vortices occurs ina cyclic fashion at certain points alongan azimuthal wave so that while onevortex grows in size, the two adjacentvortices become smaller, and vice ver-sa. Vortex cells were not independentas the significant transfer of fluid be-tween adjacent vortices occurs in wavyflow regime. This aspect of the flow isimportant, because traditionally it is as-sumed that the vortex pair in Taylor-Couette vortices is independent of eachother and is of the same size and it iscustomary to treat this as plug flow. But, theobservation of Werely and Lueptow (15) issignificant from the point of view of presentapplication.

If indeed there is significant mass trans-fer between adjacent vortex pair, then that

Figure 2. Vortices without and with circumferential waves.Figure 3. Schematic presentation of streamlines invortical cells

ULTRAPURE WATER® DECEMBER 2002 3

adjacent vortices taking place periodical-ly, the individual vortex centers also moveboth axially and radially in a cyclic fashion.Once again, the maximum departure in theradial direction is a strong function of theReynolds number and is found to be amaximum for Re = 253.

In this work, we have considered a TaylorVortex Photocatalytic (TVR) reactor, whichis shown schematically in Figure 1, and adimension of the reactor is given in Table A.In the present reactor, it is assumed that theouter surface of the inner cylinder is coatedwith TiO2 photocatalyst and it is illuminatedwith a lamp placed inside the inner cylin-der. Sczechowski, et al. (16) have reportedtheir experimental studies related to en-hancing the photo-efficiency of a TVR. But,they have used semiconductor photocata-lyst particles as slurry in the fluid within theannulus. They have found that despite thephotocatalyst being dispersed in the fluid,the useful reaction took place only period-ically when the fluid was in contact with theilluminated inner cylinder surface. Theyreported three-fold increase in the photo-efficiency when the reactant was illuminat-ed for less than 150 ms, and it stayed in darkfor more than 1’s.

The maximum photo-efficiencyachieved by them was 30% at 300 rev-olutions per minute (rpm) of the innercylinder when 10 grams per liter (g/L)loading of TiO2 was used. The majorproblem of achieving higher photo-effi-ciency was related to the transport ofpurified fluid from the vicinity of thecatalyst. Furthermore, their configura-tion suffers from the additional problemof separation of sub-micron size cata-lyst particles after the purification stage.Moreover, the working fluid is opticallydense, and therefore, the light penetra-tion depth is restricted to a distance thatis of the order of the boundary layerthickness of the inner cylinder.

In view of all these factors we haveconsidered, a TVR of similar geometry,but instead of a slurry type reactor, thephotocatalyst was assumed to be im-mobilized (fixed) on the outer surface of theinner cylinder and a fluorescent lamp illu-minates the inner cylinder on which thecatalyst is immobilized, and in the pres-ence of light the catalyst is activated and asa result the redox reaction takes place.Thus, one can use a very low level of catalystloading, and simultaneously, eliminate theprocess of separation of catalyst particlesafter the purification stage. The enhancedpurification has been obtained by usingfluid dynamical instability associated withcentrifugal instability in the cylindrical an-

Figure 4. Radial mass transfer in Taylor-Couette flow.

can be used for additional benefit for theperformance enhancement of the presentreactor. The transfer of fluid particles be-tween adjacent vortices occurs with a cyclicfashion as a particular vortex gains fluid

from adjacent vortices. It has also beenreported that the degree of transfer of fluidis greater at a Reynolds number equal to253 than at either a higher or lower Reynoldsnumber. In addition to flow into and out of

Figure 5. A comparison of the axial velocity.

Figure 6. A comparison of the axial velocity.

ULTRAPURE WATER® DECEMBER 20024

nular geometry.It is, therefore, essential to focus on

the twin aspects, photocatalysis andcentrifugal instability, in an annular cy-lindrical geometry. The residence timein the illuminated region is a function ofthe angular velocity of the re-circulatingvortex as well as the size of the vortex. Thelatter, once again depends on the gap sizeand the number of vortices formed in a

Results and DiscussionFlow development. The performances ofthe reactor depends on the photo-efficiencyof the photocatalytic process as well as onthe mass transfer efficiency of the fluid fromthe vicinity of the rotating inner cylinder tothe stationary outer cylinder and back with-in a single Taylor-Couette vortex. The latterdepends on the primary instability of flow insetting-up of the vortical roles. This insta-bility and associated mass transfer can bemade more effective by initiating a second-ary motion when additional mass transferbetween neighboring roles through the wavyvortex flow would take place. This has beenshown to be a strong function of Reynoldsnumber by Werely and Lueptow (15) and itwas reported that inter-role mass transfer ismaximum for the chosen geometry in theirexperiment for Re = 253.

In the present set of computations, thesame geometric parameters are cho-sen, including the aspect ratio, (AR = L/d) of the reactor. However, in the exper-iment, the starting protocol of the innercylinder rotation was taken as quasi-static and the reported results wererecorded after allowing the flow to de-velop further for 10 minutes after theattainment of the final rotation rate. Inthe present computations, the flow isstarted impulsively for the practical op-eration of the reactor in a shortest pos-sible time period. For such an opera-tion, the transient mass transfer dependsstrongly upon the vortices that are formedat initial times near the fixed end-caps ofthe reactor.

Since the rotating inner cylinder drivesthe flow inside the reactor and the rota-tion rates are low, it is quite adequate toconsider the flow to be incompressibleand solve the governing Navier-Stokesequation in primitive variable form asshown in Equations 2 and 3.

Furthermore, isothermal conditionscan be assumed for both the flow evolu-tion and chemical reaction calculationssince the pollutant being oxidized intoother products is present in traceamounts, and heat of reaction in photo-catalytic reactions is usually negligible(18). The boundary conditions that areapplied on the inner and outer cylindri-cal surface correspond to no-slip condi-tions. The end caps are considered tobe a part of the outer cylinder and henceare stationary. The following boundaryconditions are used for the numericalsimulations. With reference to Figure 1,on the inner cylinder surface (Equations4 and 5).

Equations 6 and 7 show that the simula-

Figure 7. A comparison of the axial velocity.

Figure 8. The axial velocity is plotted along the dimensionless axial direction.

Figure 9. The axial velocity is plotted along the dimensionless axial direction.

given length of the reactor. The two mostimportant factors for unstable Taylor-Cou-ette flow establishment are the aspect ratio(L/D) and the Reynolds number. The effectof aspect ratio on the flow development hasbeen studied by Sengupta, et al. (17). In thepresent study we investigated the effect ofReynolds number on the formation of vorti-ces and its effect on overall degradation ofa pollutant.

ULTRAPURE WATER® DECEMBER 2002 5

tion is for the impulsive start of the rotationrate of the inner cylinder. The model pollut-ant considered in this work is benzoic acidwith an initial concentration of 100 parts permillion (ppm), while the initial mass fractionof oxygen (O2) is taken to be equal to twicethe stoichiometric requirement for the reac-tion given in Equation 8. The rate expres-sion for photocatalytic degradation for ben-zoic acid used in this study is given byEquation 9 (19).

The amount of catalyst coating is as-sumed to be 3 × 10-3 kilograms per squaremeter (kg/m2) (10). The density of thesystem is assumed to be constant andequal to that of water as the pollutant ispresent at very low concentration.

Computational details. In computing theflow, the three-dimensional Navier-Stokesequation is solved in primitive formulationby using the commercial software Fluent®.This is found adequate as the flow consid-ered is laminar, and therefore, the need forresolving large ranges of wave numbersand circular frequencies is not necessary.In solving the governing equations, no sim-plification is made regarding symmetryand reflection of the solution. The time-accurate solution was obtained instead ofassuming an a priori steady state. Thegeometric dimensions chosen for the reac-tor are identical to the value reported inWerely and Lueptow (15).

The reactor is considered to be operatingin a batch mode, purifying 1.136 liters (L) ofwater at a time. The three different rotationspeeds of the inner cylinder is considered0.655, 0.984, and 1.638 rad/s, which resultin Reynolds numbers of 253, 380, and 633,

respectively. The rotation speed is variedto obtain the Reynolds number of 1.5 and 2.5times, respectively, that in the first case theRe = 253. The present reactor provides0.116 m2 of illuminated catalyst surfacearea and an illuminated catalyst density of102 square meters per cubic meters (m2/m3).

For generating grids within the annu-lus region of the geometry, every edgein three directions is defined with certainnodes. There are high-shear regions nearthe inner cylinder wall, the outer cylinderwall, and the end-cap regions. Therefore,axial and radial derivatives of all physicalvariables across such layers would belarger than in the azimuthal direction, andconsequently, more grid points are taken inaxial and radial directions compared to theazimuthal direction. In order to incorporatethese, grid points are taken more clusteredin two ends and next to inner and outer wall.

To enhance the direct mapping of gridfrom upper wall to bottom wall, the totalgeometry is separated into two volumes bya brick. Two interior planes are created bythis process within the annular space thatwas used to analyze our results at the timeof post processing. Grid points along thethree directions are taken as follows: r × θ×h = 100 ×40 ×75. Fluent pre-processorGAMBITÒ 1.1 is used to create geometryand generate grid for both cases. There are0.3 million cells, 907,000 total quadrilateralfaces (3,000 inner wall faces, 11,000 outerwall spaces, 15,000 interior plane faces,and 878,000 rest of interior plane faces).The total numbers of nodes are 307,040. Thepresent set of computation of Navier-Stokesequation for Taylor-Couette geometry is

expensive. The one without reaction wascomputed in a 1.5-Gb RAM Windows NTworkstation and it took 78 hours of actualtime for simulation results of 10 s.

Equations 2 and 3 are solved subject tothe boundary conditions and initial condi-tions defined in Equations 4 through 7 withinthe annulus between the cylinders as shownin Figure 1. The results are shown in theradial-axial (r-y) plane and along the threesets of horizontal (H1-H3) and vertical lines(V1-V3), as indicated in Figure 1.

A brief description of the method is givenin the next section. The solver is based onsolving Equations 2 and 3 in a sequentialmanner by a control volume based tech-nique, using the following three steps. First,the computing domain was separated intodiscrete control volume, using a computa-tional grid. The governing equations weretime advanced in integral form for eachcomputational cell to yield algebraic equa-tions for the discrete dependent variables,such as velocity components, pressure,and conserved scalars. Finally, thediscrete equations were linearized intoa set of algebraic equations, which weresolved to yield updated variables.

For the separation process, the famil-iar QUICK scheme was used for themomentum and species equations, asthis is a higher-order accurate schemewith minimum numerical dissipation thatis implicit with the separation. The solv-er uses finite volume method in solvingthe Navier-Stokes equation.

Simulation results. The following non-dimension is used in order to be able tocompare results to reported results inliterature. The annulus gap, d, is usedas length scale while the speed (W ri)imposed on the inner cylinder surface isused as the velocity scale. Thus, thedimensionless time scale used is t* [≡ t (Ωri)/d]. Since the water pollutant pollutant ispresent in a trace quantity, it is expectedthat the chemical reaction will not influencethe fluid dynamic behavior of the system.To show this two sets of computations wereinitiated from t = 0, one with the chemicalreaction, while in the other only the fluid flowwas computed and the results compared.It was observed that flow field was identical.

The numbers of vortices formed in thethree configurations (see Table A andFigure A of the Appendix) are 5.75, 6.5,and 5.0 for Configuration 1, Configura-tion 2, and Configuration 3, respective-ly. It can be clearly seen that the number ofvortices formed are maximized when theReynolds number is 1.5 times the referencecase (Re = 253). Moreover, when the

Figure 10. Photocatalytic degradation of benzoic acid.

ULTRAPURE WATER® DECEMBER 20026

Reynolds number is 2.5 times that of thereference case, we see that the flow has notbeen completely established in the entireregion. The vortex at the top is degeneratedand the vortices in the middle section arealso not as compact when compared to theother cases.

We observed the following for Configura-tion 2 compared to configuration 1 (refer-ence case): 1. It reaches steady state faster;2. The number of vortices per unit length ismore; 3. The vortices move faster towardscenter from end; and 4. The intensity (i.e.,magnitude) of both axial and radial compo-nent of velocity is more than the referencecase (i.e., Re = 253). It can be observed thatfor the simulated case with impulsive start,that the optimum Re = 380 instead of 253,as was found by Werely and Lueptow (15).The deviation from the experimental resultsprobably is due to the impulsive start of thesimulated reactor as opposed to the quasi-static start in the experimental case. Sincethe Configuration 2 gives better results thanthe Configuration 3, for all subsequent re-ported results comparison are made be-tween the Configuration 1 and Configuration2.

In Figures 5 through 7, the axial veloc-ity as a function of dimensionless radialcoordinate is plotted for various timeinstants at the observation stations H1,H2, and H3. Comparing the velocityprofile of Configurations 1 and 2, thevelocity magnitudes are 1.3 times high-er for Configuration 2 than that for thereference case. The results from Figure5 also indicate that for Configuration 2 therate of change of axial velocity is almostnegligible and therefore, the flow reachessteady state faster than that of the referencecase. From Figure 6, the axial velocitiesdemonstrate that Taylor-Couette vorticesmove faster toward the middle part whenthe Reynolds number is higher. In generalfor both cases, since the middle section isat the center (y* = 0.5), there the axialvelocity is smallest in magnitude (about 4order of magnitude lower) when comparedto the other two observation stations.

The radial component of velocity is plot-ted (see Figure B in the Appendix) in theannular gap at the three different heights atthree different non-dimensional times. InConfiguration 2, an inflow of fluid movestowards the inner cylinder for all the indicat-ed times, while for Configuration 1 up to t*= 862 the fluid moves towards the innercylinder, but at t* = 1581 the fluid movestoward the outer cylinder. The rate of changeof radial velocity is much slower for Config-uration 2 than for Configuration 1, indicatingthe flow will reach steady state faster when

Re = 380.The magnitude of the radial velocities

is the smallest for both configurations(Figure B in the Appendix). The re-search also indicated that the flow doesnot show the formation of Taylor-Cou-ette vortices in the middle part of thereactor for the reference case, but forConfiguration 2 the vortices have start-ed forming in the center. Thus, higherRe is responsible for formation of vorti-ces at the middle part of the reactor.

The axial velocity (seen in AppendixFigure C) is plotted along the dimen-sionless axial direction at observationstations V1, V2 and V3. For both theconfiguration at smaller times, the Tay-lor-Couette vortices are formed at theends and as time progresses more andmore of these are formed covering themiddle part. The magnitude of bothaxial and radial velocities is on an aver-age 1.5 times larger for Configuration 2than for the reference case.

From Figures 8 and 9 (and Figures Cand D in the Appendix), it is evident thatfor at higher Reynolds numbers the vor-tices move faster to the middle part.This is of great importance as the fastermovement and formation of vortices inthe entire reactor is the basis for im-provement of performance of the photo-catalytic Taylor vortex reactor. Of spe-cific interest is the plot of the axial veloc-ities in the middle of the annulus at V2. Ifindeed the vortices formed were like aplug flow, then this velocity componentalong this line would have been zero.

The very fact that the velocity compo-nent alternates in sign is indicative of thefact that the vortex centers not onlyexecute axial waviness, but also showsignificant radial motion. Werely andLueptow (15) also observed this exper-imentally where they showed such mo-tions for all Reynolds numbers between131 to 1,221. They reported large ex-cursions of axial motions for low Rey-nolds numbers while maximum radialmotion of vortex centers were observedfor Re = 253 as opposed to at Re = 380in this present case. However, it has tobe noted that in the present investiga-tion the flow is started impulsively andnot accelerated quasi-statically.

The velocity vector plots are shown foronly the top half of the reactor (y* = 0.5- 1.0) in a given y - r plane at t* = 879 whensteady state has reached (Figure E in theAppendix). One can see weak vorticesforming near the upper part of the left seg-ment. There are regions along the heightwhere one can see a jet-like flow starting

from the inner wall moving towards the outerwall due to centrifugal action. In the seg-ment between y* = 0.7 and 0.85, significantmixing of fluid is noticeable due to theformation of coherent vortices.

Once again, one can see the jet-likeflow from inner to outer cylinder - al-though the trajectory of the fluid parti-cles are not strictly straight. Moreover,there is no visible wall shear layer form-ing on the inner wall as has been shownin Figure 4. In the segment between85% and the top of the reactor, thevelocity vectors clearly shows recircu-lating rolls, although the axial lengthsvary significantly due to end-wall ef-fects. Also in this segment, apart fromthe jet-like regions, one can as well seesmall axial regions where a flow is es-tablished from the outer to the inner wallside. However, this cannot cover theentire radial gap because of centrifugalforce acting on fluid particles near theinner wall.

For the same reasons one will not seea wall shear layer forming on the innercylinder as has been shown in Figure 4.Instead, one would notice the formationof an internal layer after some time andassociated full saddle point inside theflow domain. In retrospect, it appearsthat to resolve such internal layers, oneshould have finer grid in the interior, too.An internal band characterizes the for-mation of the internal layer where theflow is along the axis of the reactor(Figure F of the Appendix). This is seento originate at the saddle points, one ofwhich is marked in the figures with filledcircle for different times.

The flow is seen to be axial in oppositedirection across the saddle point. Suchvertical lines are nothing but the internallayer. While at t* = 383, no such innerlayers were seen, it is seen for the plotshown at t* = 575. Once this saddlepoint is seen to form, it does not seem tomove as it can be traced at the samelocation at later times. It is also interest-ing to note that between t* = 671 and t*= 767, while the saddle point remainsfixed, the velocity vectors indicate anincrease in upward velocity above thesaddle point while it decreases in down-ward direction. The velocity vectorsinside the recirculating eddies showtime dependent behavior, though it isnot so pronounced near the middle sec-tion of the reactor where the eddies areeither very weak or not formed. All ofthese unsteady events would lead to anincrease of mass exchange betweenadjacent fluid cells.

ULTRAPURE WATER® DECEMBER 2002 7

Finally, in this section we want to dis-cuss about the flow structure for thechosen parameters of this computationwith an impulsive start of the reactor.This aspect is very important in thecontext of non-unique flow evolution dueto different initial conditions referred toin Andereck, et al. (20). The flow struc-ture that we have computed is signifi-cantly different than what has been ex-perimentally visualized by Werely andLueptow (15), although the geometricparameters and Reynolds number cho-sen are identical. This is due to theimpulsive start of the present computedcase as opposed to the quasi-staticstart in Werely and Lueptow (15) wherethe inner cylinder is accelerated fromrest to its final value at the very slow rateof 0.3 Re per second.

Our research showed the flow struc-ture for the two segments for t* = 1,054(Figure G in Appendix). The time is notimportant as we have noted that the flowstructure remains invariant beyond t* =575. If one looks carefully one noticesthe jet-like flow structure between fluidcells. For example, one can notice anunidirectional jets emerging from theinner wall and approaching the outerwall. This is the expected jet structureindicated in the sketch of Figure 4.However, one can also notice the exist-ence of bi-directional jets as marked byF and H.

A longer segment originating from theouter wall and moving towards the innerwall is met with a smaller segment wherethe flow is from the inner to outer wall.Then, we have marked a line J in thefigure, which is the limiting case of thebi-directional jet when the width of thejet degenerates into a line and the merg-er line of the opposing jet becomes thesaddle point. The notation U, B, and Sin the figure indicate locations of uni-directional, bi-directional, and singularzones.

Photocatalytic reactions. To analyze theperformance of the TVR, benzoic acid isconsidered as typical pollutant present inwater with an initial concentration of 100ppm. Pollutant degradation as integratedover the full reactor volume and is shown asfunction of time in Figure 10. It is to be notedthat after 225s of operation, benzoic acid isdegraded by about 69% and 76% respec-tively for Case 1 (Re = 253) and Case 2 (Re= 380). It clearly indicates the role of Taylor-Couette vortices in enhancing the rate ofpollutant degradation.

At early times, the very rapid rate of

degradation is due to the vortices thatare form at the fixed ends where strongrecirculating zones causes rapid masstransfer from inner to outer cylinder andback. Figure 10 illustrates that photo-catalytic reaction is diffusion controlled,as the rate of degradation increaseswhen Re is increased. Since in this casethe vortices move faster towards centerfrom the end caps and the magnitude ofthe vortices are also larger compared towhen Re = 253.

A close scrutiny of Figures 5 through 9(and Figures A through G) reveals thatreaction is faster at either end wherewell-developed vortices are present,while the degradation rates are slowerwhere Taylor-Couette vortices are notwell formed (see also Appendix FigureH). The reaction takes place only in theshear layer of the inner cylinder wherethere are no Taylor-Couette vorticespresent.

Figure 10 clearly indicates the role ofTaylor-Couette vortices in enhancingthe rate of pollutant degradation. More-over, the figures also indicate the possi-bility of operating the reactor in thetransient mode by periodically switch-ing the reactor on and off since duringthe transient phases the reaction pro-ceed at a rapid rate due to the vorticesnear the end walls.

Table B compares the performance ofa slurry reactor (19) with that of the twocases of Taylor vortex reactor (TVR)considered in this work for photocatalyt-ic degradation of benzoic acid. Thetable clearly illustrates that increase inefficiency of TVR over the slurry reactor.One can observe 50.4% and 78.3%increase in efficiency for Taylor vortexreactor with Re = 253 and with Re = 380respectively over a slurry reactor.n

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17.Sengupta, T. K.; Kabir, M. F.; Ray, A. K. “ATaylor Vortex Photocatalytic Reactor forWater Purification”, Industrial Engineer-ing Chemical Research, 40, p. 5268(2001).

18.Chen, D. W.; Li, F.; Ray, A. K. “Effect ofMass Transfer and Catalyst Layer Thick-ness on Photocatalytic Reaction”, AIChEJ., 46(5), p. 1034 (2000).

19.Mehrotra, K.; Yablonsky, G.; Ray, A. K.“Effect of Various Macro-Kinetic Parame-ters on Photocatalytic Degradation ofBenzoic Acid: some further Insights”, sub-mitted to Environmental Science Technol-ogy (2002).

ULTRAPURE WATER® DECEMBER 20028

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Author Ajay K. Ray, Ph.D., is an associ-ate professor in the Department of Chem-ical and Environmental Engineering atthe National University of Singapore.Prior to joining the university in 1995, hewas with the University of Groningen, TheNetherlands for three years. His researchinterests are in chemical reaction engineer-ing, especially photocatalysis and design,development, simulation, optimization, andanalysis of chemical reactors. He holds aPh.D. in chemical engineering from theUniversity of Minnesota.

This paper was presented at ULTRAPURE WATERAsia 2002, Aug. 14-15, Singapore.

Key words: MONITORING, WATER QUAL-ITY

TABLE AGeometric Dimensions and Conditions Used for Different Simulation Runs

Specification Case 1 (Reference) Case 2 Case 3Length L, m 0.425 0.425 0.425Inner radius ri, m 0.0434 0.0434 0.0434Outer radius ro, m 0.0523 0.0523 0.0523Annular gap, d, m 0.0089 0.0089 0.0089Aspect ratio, L/d 47.70 47.70 47.70Rotation speed, ?, rad/s (rpm) 0.655 (6.25) 0.984 (9.39) 1.638 (15.65)Volume of liquid treated, VL m3 1.136 ×10-3 1.136 ×10-3 1.136 ×10-3Reynolds Number, Re 253 380 633Taylor Number, Ta 13,126 29,625 50,116

TABLE BComparison of Performance of TVR with that of a Slurry Reactor*

Slurry Reactor Taylor Vortex ReactorMehrotra et al., 2002 Case 1 Case 2

Volume of reactor, m3 6.35 × 10-5 3.65 ×10-3 3.65 × 10-3Catalyst surface area, m2 3.7 0.116 0.116‡ ICD, ?, m2/m3 6,139 102 102Volume of liquid treated, m3 2.50 ×10-4 1.136 × 10-3 1.136 ×10-3Electrical energy input, W 125 30 30Time for 50% conversion, s 210 128 108§ Efficiency, s-1 m-3 W-1 0.0762 0.1146 0.1358% increase in efficiency 0 50.4 78.3

*For photocatalytic degradation of benzoic acid.‡: Illuminated catalyst density defined as illuminated catalyst surface area (m2) per unit volume of liquid treated (m3) in the reactor (see Reference 10).§: Efficiency is defined as 50% pollutant (benzoic acid) converted per unit time (s) per unit volume of liquid treated (m3) per unit electrical energy input (W).