Simulations of Vapor / Ice Dynamics in a Freeze-Dryer Condenser

Freeze-drying is a low-pressure, low-temperature condensation pumping process widely used in the manufacture of pharmaceuticals for removal of solvents by sublimation. Key performance characteristics of a freezedryer condenser are largely dependent on the vapor and ice dynamics in the low-pressure environment. The main objective of this work is to develop a modeling and computational framework for analysis of vapor and ice dynamics in such freeze-dryer condensers. The direct Simulation Monte Carlo (DSMC) technique is applied to model the relevant physical processes that accompany the vapor flow in the condenser chamber. Low-temperature water vapor molecular model is applied in the DSMC solver SMILE to simulate the flowfield structure. The developing ice front is tracked based on the mass flux computed at the nodes of the DSMC surface mesh. Verification of ice accretion simulations has been done by comparison with analytical free-molecular solutions. Simulations of ice buildup on the coils of a laboratory-scale dryer have been compared with experiments. The comparison shows that unsteady simulations are necessary to reproduce experimentally observed icing structures. The DSMC simulations demonstrate that by tailoring the condenser topology to the flow-field structure of the water vapor jet expanding into a low-pressure reservoir, it is possible to significantly increase water vapor removal rates and improve the overall efficiency of freeze-drying process.

Thus,i ti sc lear that thereisalarge seto f variablesthatg overn theperformance of af reeze-drying condenser.An improved understandingo ft he flow physicsisneeded to develop optimal designs.Thec urrent work uses the DSMC technique to solvethe flow field structureint he condenser.In thefollowing subsection adescription of the modeling approach andthe procedureadopted to predictthe performanceofacondenser is discussed.

IceAccretion on theCoils
Af reeze-drying cyclec an lastf or 3 days.F or ac ycle with 100 vials, drying at 0.5g /hr, this leadst ot he formation of 3.6 kg of ice.This corresponds to atotal volume of 3871 cm 3 foradensity of 930 kg/m 3 of ice.If the iceb uild-up is assumed to be uniformo nt he coils of theL yostar condenser, al ayer of icea bout 1 cm thick is formed.In reality, thecoils closesttothe duct exit receive abouttwice as much iceasthose farthest away from it.
Then on-uniformi ce growth canl ead to as igni Kobayashi [15] showed that thedecreaseinperformanceofacondenserw ithice formationinthe coilsissigni and increaseswithreducing condenser temperatures.In ordertopredict theice accretiono neachcoilduring acycle, aG aussian weighted approach is used.Eachnodei nt he surfacemeshi sapart of 1 or more panels.I ft he distance betweent he node whoseinitial positionisP n t and thecentroid of thepanel of whichitisapart of is d, to predictthe positiono fthe node after time

PerformanceMetrics
In view of therequirementso facondenser discussed earlier, itsp erformancec an be evaluated based on a) the energy requirementsf or ac ycle or thed rying rate and b) then on-uniformity of icef ormationo nt he coils.Condensers used todayare bulkyand thelarge volumeso ccupied by thecondensing surfaces require an appropriate quantity of heat transfer fluid to condense thevapor completely.Itiscritical that thecondenser efficiently trapsthe vaport hate xits from theductand prevents increase in thevapor pressure.Thus, it is desirabletohaveahigher area averaged mass m on thec ondensing surfaces.I ti se qually importantt oe valuate thec ompactness of the condenser.Thus,t he measureo fe fficiencyf or ac ondenser is thea reaa veraged mass v m occupied by thec ondensings urfaces.O ncet he mass simulations, each of thep anelsa re assigned a it is composed of.T he area averaged mass wherem i is themass i ,Ais thetotal surfaceareaexposed forcondensationand Visthe volumeoccupied by thecondensing surfaces.

Mass Flux in theCondenser Chamber: Conical Design
In theconical design,the jet remainsconfined closetothe ducte xita nd thepresenceofthe condensing surfaces in thepatho fthe vapori ncreases themass reduces moving away from theduct, bothradiallyand longitudinally.Figure3showso ne half of thegeometryalong with thec ontourso fmass ux on thec oils with thes treamtraces superimposed.T he mass away from theducte xitreduces to at hird of thev aluec lose to theducte xit.Thec onical design trapsasigni portiono ft he ec hamber housingc lose to thed ucte xiti nt he Lyostar design.Thus,a3times increase in theareaaveragedmass Thepressure in theconical chamber is higher than that in theLyostar design.T hus, even though theconical design is efficientb ecauseitt raps ahighero nc oming mass ap ressure as lowasthatm aintained by theL yostar.F igure5represents thecontourso faverage velocity in theY Z planef or thet wo designs.Thej et expandsa si te ntersi ntot he chambera nd reachesavelocity of ˜450 m/s.However, theregiono fhigherv elocityfor theconical condenserisconfined to theregionabove thefirst setofcoils.Thec oils being directly in thep ath of thev apor,o bstructs it, leading to ah ighm ass inlet.However, moving radiallyoutwardsor in theshadowofthe firstset of coils,the

PerformanceComparison
As ummaryo ft he performanceo ft he twod esigns is showni nt he Table1 .I tw as found that the m on the conicald esign was~3.2timest hato n theL yostar condenser.Moreover, the v m of thec onical condenseri ncreases by 8.5 times.H owever,f romt he pressure contoursitw as found that theleast pressure that could be maintained in thec onical condenserw as twicet hati nt he Lyostar chamber.This provest hatw hile thec onical design could be a useful,c ompact condenserd esignd ue to thel arge m and v m ,i tm ay notb ea blet om aintain thes amep ressure levels as is maintained by theL yostar dryer.In thec onical design, thep resenceo ft he coils in thes hadowo ft he firstr ow increasest he non-uniformity as thesec oils receive as ignificantly lowerm ass row.Thus,w esee a40% increase in thenon-uniformity over theLyostar design.

Verification of IceAccretion Simulations
Ac omparisonw as made with thea nalytical solutionf or cm and with thefollowing parameters fort he analyticalsolution, theice growth for aperiod of 1hourw as compared to that predicted using thealgorithm.Density of ice:930 kg/m 3 ,f ree-stream velocity:400 m/s, free-stream temperature: 213 K, pressure:6mTorr, speed ratio:0.9,stickingcoefficient:1 Figure 6 showsthe comparison betweent he analytical solutiona nd thepredicted icegrowth.It is clear that the predicted profile matches thea nalytical solutionq uite well and theo bserved deviation can be attributed to theg rid resolution used.

Prediction of IceAccretion on theCoils of theLyostarCondenser
With thepredicted mass to be higher than that on thec oils away from it.Figure 7 represents thes teadyand unsteady predictiono ft he ice accumulated on thec oils in theY Zplane overaperiod of 75 hours.In thes teadysimulation,t he coils closetothe ductexithaveamaximum iceaccumulationo f2.2 cm overaperiod of 75 hourswhile that on thecoils farthest away from theductexithaveathickness of 0.5 cm. Figure 8illustratesthe steady state 3D predictiono fthe icegrowth.

CONCLUSIONS
Thec urrentw ork focuseso nu sing DSMC techniques to modelt he vapor of a pharmaceutical freeze-dryer.Relevant metricsf or comparing condenser performancea re defined.Thesem etrics were used to comparethe performance of two condenserdesigns,the Lyostar II and theconical design.It wasfound that while thel east pressure that could be maintained in thec onical condenserw as twicet hati nt he Lyostar,t he m was3.2 times higher and the m v was8 .5 times higher.T hus, while thec onical design could be au seful, compactc ondenser design,i tmay notb eabletomaintain thes amep ressure levels as is maintained by theLyostar dryer.Moreover,the presence of thecoils in thes hadowofthe firstrow increased thenon-uniformity as thesecoils received al ower mass -uniformity over the Lyostar design.T he steadys tate mass thec ondenser coils.T ov erifyt he algorithmu sed for thep rediction, ac omparisonw as madew itha n analyticals olutionf or the condensation of vapord uring free molecular inletw eresubjected to thelargest mass icef ormed on thecoilc losest to theducte xitw as 2.2 cm while that on thecoilf arthestf romi tw as 0.5 cm over 75 hours.Then on-uniformity wasu nder predicted compared to thee xperimental measurements discussed in the introduction.This wasattributed to theunsteadyice accretion.For unsteady icebuild-up calculations,anewsurface mesh wasused afterice thicknessreached 15% of theinitial coil diameter.Theunsteadysimulationspredict amuch higher non-uniformity in icegrowthw ith thec oils closesttothe ducte xithaving about2 0 times largeri ce growth rate than thecoils at thefar end.
From thee xperimental observations,i tw as noticed that therem ay be an on negligible differenceb etween the inletand exit temperatureso fthe coil.H owever,s ince this temperature variation wasnot known, in themodeling, it wasassumed that all thec oils were at au niformt emperature and hencew erep rescribed au nits ticking coefficient.Then on-uniformity of ice buildup can be attributed to twoa spects, a) the variationi nt he coils betweent he inleta nd outlet.Whilethe current technique captures thenon-uniformity due to thef ormer, future efforts will focuso np rescribing ak nown mass measurements and capturet he icef ormationb ased on thet emperature dependents ticking coefficienta sw ellt o accurately representice formation based on multipleupdates of thecoilgeometry.

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thenumbero fpanelsconnected to thepoint m, thesteadystate mass n is theo utward surfacenormalf romt he panela nd Wrepresentst he Gaussian weight givent ot he panelb ased on the distance of thepoint d from thecentroidofthe panel.Theweightiscalculated as represented by no rder to representt he iceb uildup, each node is displaced throughadistance proportionalt ot he mass normal of thepanel thenodeisapart of.