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A numerical model for gas flow and droplet motion in wave-plate mist eliminators with drainage channels

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A numerical model for gas flow and droplet motion in wave-plate mist eliminators with drainage channels
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  Chemical Engineering Science 63 (2008) 5639--5652 Contents lists available at ScienceDirect ChemicalEngineeringScience  journal homepage: www.elsevier.com/locate/ces Anumericalmodelforgasflowanddropletmotioninwave-platemisteliminatorswithdrainagechannels Chiara Galletti ∗ , Elisabetta Brunazzi, Leonardo Tognotti Department of Chemical Engineering, Industrial Chemistry and Materials Science, University of Pisa, via Diotisalvi 2, 56126 Pisa, Italy A R T I C L E I N F O A B S T R A C T  Article history: Received 5 February 2008Received in revised form 10 June 2008Accepted 17 August 2008Available online 22 August 2008 Keywords: ComputationDispersionSeparationsDropWave-plate mist eliminatorDemisterCollection efficiency Computational fluid dynamics (CFD) is used to develop Eulerian/Lagrangian models of two wave-platemist eliminators, both equipped with drainage channels. The models are assessed through comparisonwith comprehensive experimental data on removal efficiencies and pressure drops.For the range of droplets sizes of interest for demisting operation, the turbulent dispersion model is foundto play a fundamental role in determining the droplet motion. However, classical dispersion models, asthe eddy interaction model, often available in commercial CFD codes are unsuited, resulting in errors onthe removal efficiency larger than 100% for the investigated cases. Therefore, a simple procedure for themodification of the code in order to replace the dispersion model with alternative models by using theexisting Lagrangian algorithm is proposed. Predictions with a varied eddy interaction model are observedto match closely experimental data on removal efficiencies. An analysis of the turbulence models is alsocarried out, those for low  Re  resulting in a better description of the gas flow field and droplet motion.© 2008 Elsevier Ltd. All rights reserved. 1. Introduction Wave-plate mist eliminators (also called vane or blade type sep-arators) are widely used in the chemical, oil and gas industries toremove liquid droplets from a gas or vapour flow (see Holmes andChen, 1984; Monat et al., 1986; B ¨ urkholz, 1989; Fabian et al., 1993; Ziebold, 2000 among others). Mist removal is necessary for a num-ber of reasons, such as to restrict pollutant emission into the envi-ronment, to prevent damage to downstream equipment caused bycorrosive or scaling liquid, to recover valuable products dispersedin a process gas stream, to remove hazardous liquid mists from re-active gases, to increase purity of gases or vapours for successivetreatments and to increase the global operation economy.Wave-plate mist eliminators basically consist of a number of nar-rowly spaced bended layers oriented as the direction of the gas flow.Thedropletsladengasstreamisforcedtotravelthroughthetortuouschannels between the layers and to change repeatedly flow direc-tion. The entrained droplets that are not able to follow these changesin directions because of their inertia, deviate from the main gas flowand impact on the channel walls, where they coalesce and form liq-uid rivulets that are continuously drained out from the separatorby gravity. Wave-plate mist eliminators can be operated with eithervertical (upward) or horizontal gas flows. In the vertical operational ∗ Corresponding author. Tel.: +390502217897; fax: +390502217866. E-mail address:  chiara.galletti@ing.unipi.it (C. Galletti).0009-2509/$-see front matter  ©  2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2008.08.013 mode,thecollectedliquiddrainsdownwardcounter-currentlytotherising gas. In the horizontal flow, the liquid drainage is accomplishedin a cross-flow fashion. It is generally agreed that the removal of liquid droplets occurs predominantly by inertial impaction for bothconfigurations.Thus,separationperformanceimproveswithincreas-ing gas velocity. But as reported in the literature by Houghton andRadford (1939), the maximal gas velocity is limited due to eitherflooding or re-entrainment of the collected liquid. To overcome thisproblem, the introduction of drainage channels (hooks) in industrialdevices has shown to increase both separation efficiency and capac-ity (McNulty et al., 1987; James et al., 2003; Brunazzi et al., 2004). The different types of wave-plate separators commercially availablenowadays differ mainly on the plate profile (e.g. zig-zag, sinusoidal,etc.)andthedrainagechannels'design(e.g.unshieldedsingle-pocketdesign or double-pocket hook channels).Typically, wave-plate mist eliminators are less efficient in remov-ing very small droplets compared with other types of impingementbased separators, such as wire mesh. Depending on the design pa-rameters, wave-plate mist eliminators provide low pressure dropsand collect 100% of all droplets greater than 10–40  m in diameter.This type of separator is preferred in applications involving high gasvelocities, low available pressure drops, viscous or foaming liquids,dirty streams (for example liquids with high salt concentration,Paglianti et al., 1996) and in general in those applications that wouldrapidly plug wire mesh type mist eliminators. Moreover, both pres-sure drops and separation efficiency are relatively insensitive to inletmist loadings(HolmesandChen,1984),hencethistypeofseparators  5640  C. Galletti et al. / Chemical Engineering Science 63 (2008) 5639--5652  Table 1 Some literature on the use of computational fluid dynamics for vane-type demistersReference DrainagechannelsDroplet size  d  p  (  m) Numerical model Comparison withexperiments?CFD code LagrangiansolverTurbulence model Turbulent disper-sionVerlaan (1991) Yes 10–90 Phoenics Phoenics STD  k –   No YesWang and Davies (1996) No/yes Normal distribution( D m  =  10, 15, 20  m)Phoenics Phoenics STD  k –   No NoGillandt et al. (1996) No 100–1000 Fluent Fluent STD  k –  , low  Rek –  No YesWang and James (1998) No 1–30 CFX Self STD  k –  , low  Rek –  No Yes, Phillips andDeakin (1990)Wang and James (1999) No 1–50 CFX Self STD  k –  , low  Rek –  Const. EIM, variedEIM, GQ EIMYes, Phillips andDeakin (1990) James et al. (2003) Yes Rosin Rammler( D 32  =  15, 20, 25  m)CFX Self STD  k –   Varied EIM No James et al. (2005) No Rosin Rammler D 32  =  15, 20, 25, 40  m)CFX Self STD  k –   Varied EIM NoZhao et al. (2007) No 10–40 Fluent Fluent STD  k –   No Yes, Lang et al.(2003) is usually employed with liquid mass flow rate up about to onetenth of the gas flow rate. In complex separation units, wave-platemisteliminatorsaresometimesusedincombinationwithmeshpadsor cyclonic devices for optimum performance in special situations(Brunazzi and Paglianti, 2001).Aspects of the gas flow and droplet motion in wave-plate misteliminators have been studied experimentally and/or numerically byseveral authors. Early experimental studies provided performanceparameters such as pressure drops, capacity, resistance to pluggingor fouling and only overall collection efficiency. Subsequently, withthe development of methods for measuring the size of the liquiddroplets, such as cascade impactors, gelatine covered slides, andmore recently optical techniques, works provided also fractionalcollection efficiency data, i.e. separation efficiency data as a functionof droplet size (B ¨ urkholz, 1989; Calvert et al., 1974; Ushiki et al., 1982; Monat et al., 1986; Verlaan, 1991; Phillips and Deakin, 1990; Brunazzi et al., 2004). Experimental studies investigated the effectof geometrical parameters such as number of bends, bend angle,distance between parallel plates and length between two successivebends on the performance. In particular, these studies showed thatthe droplet motion through the separator and hence its capture iscontrolled by the droplet inertia and drag force of the gas stream.Due to the small size of the droplets the influence of gravity is usu-ally not considered. Therefore, many theoretical studies to predictthe collection efficiency of wave-plate mist eliminators formulatethe equations of droplets motion using the Newton's first law inconjunction with an equation for the drag force. The equations aresolved using simplifying assumptions. For example, the fractionalefficiency of a single bend (  B ) is related to the Stokes number, inwhich the characteristic length depends on both separator geomet-rical parameters (bend angle, distance between the plates) and em-pirical factors. Prediction of the overall efficiency is then obtained byconsidering the cumulative effect of all bends as   = 1 − (1 −  B ) m · n B ,where  m  is a mixing factor, generally varied between 0.5 and 1.For instance, B ¨ urkholz (1989) and Calvert et al. (1974) assume complete mixing of both the gas and liquid phases after each bend( m  =  1), Gardner (1977) instead assumes incomplete mixing andsuggests values of   m  between 0.5 and 0.63. Other workers, suchas Ushiki et al. (1982) suggest to assume  m  =  1 and to reducethe efficiency of the 1st bend considering that it contributes onlyat 50%.Recently some attempts to use computational fluid dynamics(CFD) to predict wave-plate mist eliminator performance can befound.ForinstanceVerlaan(1991)usedthecommercialsoftwarePhoen-ics to predict the flow and collection efficiency on a wave-platemist eliminator. The author used an RANS formulation with stan-dard  k –   (STD  k –  ) turbulence model for the continuous phase. Thedroplet trajectories were solved in a Lagrangian framework, takinginto account only drag force and neglecting turbulent dispersioneffects.Wang and Davies (1996) used the same commercial code to carryout a comprehensive numerical investigation on the effect of inletgas velocity, bend angle and rear pockets on removal efficiency andpressure drops of wave-plate mist eliminators. A STD  k –   turbulencemodel was used to simulate the gaseous phase; turbulent disper-sion effects on droplet trajectories were not taken into account. Nocomparison with experimental data was provided.Gillandt et al. (1996) used the commercial software Fluent tosimulate the flow in a zig-zag classifier, comparing experimentaland predicted data. The droplet size investigated was 0.1–1mm. Theauthors pointed out that the use of low  Re k –   turbulence modelgives better results than the standard version of the model.Wang and James (1998) simulated a wave-plate mist eliminator(without drainage channel), which was previously experimentallycharacterised by Phillips and Deakin (1990), through the softwareCFX. The authors compared the performance of low  Re  and STD  k –  models. They observed that  D 95 , i.e. the droplet diameter at whichthe separation efficiency is 95%, was predicted better by the low Re  turbulence model. However, a great discrepancy between experi-mental and numerical collection efficiency curves was reported; thisdiscrepancy was attributed by the authors to the lack of a disper-sion model. This point was addressed in a later work from the sameresearch group (Wang and James, 1999), where different turbulent dispersion models were compared in the prediction of the samewave-plate demister of  Phillips and Deakin (1990). The commer-cial code CFX was used to simulate the continuous phase behaviour,whereas an algorithm was developed on purpose to perform the La-grangian particle tracking. The authors found that a version of theeddy interaction model (EIM) based on suggestion of  Sommerfeldet al. (1993) and Kallio and Reeks (1989) gave better results that the standard version of the model. The authors also found a fairly goodagreement between low  Re  and STD  k –   models in the prediction of collection efficiency curves for the range of gas speeds and dropletdiameters investigated.Using the same computational approach, the effect of drainagechannels on collection efficiency of wave-plate mist eliminators wasanalysed numerically ( James et al., 2003).  C. Galletti et al. / Chemical Engineering Science 63 (2008) 5639--5652  5641  Table 2 Geometrical details of the wave-mist eliminatorsWave-mist eliminator  n B    (deg)  s  (mm)    (mm) Drainage channelsA 4 45 25 118.5 YesB 4 45 50 118.5 Yes More recently James et al. (2005) showed how CFD can be cou-pled to other mathematical models as for instance to predict filmdeposition and separation in wave-plate mist eliminators, in orderto improve understanding of the phenomena.Recently Zhao et al. (2007) used the commercial CFD code Fluentto relate the separation efficiency with structural parameters of ademister vane. The authors investigated droplet sizes in the range of 10–40  m,forwhichtheyconsideredonlythedragforceintheequa-tion of motion, the effect of turbulent dispersion being neglected.The overall collection efficiency for gaseous speeds in the range of 3–5m/s were compared with measurements by Lang et al. (2003),indicating that predicted values were always smaller than experi-mental data by approximately 5%.Table 1 summarises main features of the available literature onCFD applied to wave-plate type mist eliminators, in order to gain aglobal view. It can be noticed that, to our knowledge, experimentalassessments of the numerical models have been carried out only forwave-plate mist eliminators without drainage channels. Neverthe-less, the extensive use of drainage channels in the industrial prac-tice makes it worth assessing the CFD model directly for drainagechannels configurations. The present work aims partly at filling this“gap”, carrying out a comparison between CFD and experimentaldata taken in wave-plate mist eliminators equipped with drainagechannels. To this purpose, numerical models of two different wave-plate mist eliminators were developed with the commercial codeCFX and the predictions were compared with the measurements of Ghetti (2003).The choice of the turbulence model for the gaseous phase calcu-lation is discussed. Attention is also paid to the dispersion model. Asimple modification of the commercial code is suggested in order totake into account the findings of  Wang and James (1999). 2. Experimental apparatus Two types of commercial wave-plate mist eliminators with zig-zag plate profiles have been investigated and will be denoted as typeAandtypeB.Bothtypesofeliminators,constructedinstainlesssteel,are equipped with drainage channels and differ mainly for the widthof the channel, as the number of bends, bend angle and drainagechannel size are the same.Geometrical details of both eliminators are listed in Table 2.The experimental apparatus has been described extensively byBrunazzi et al. (1998, 2003) and consists mainly of a spray-generation circuit and an air carrier circuit. The test section is a4m-long stainless steel duct with a rectangular cross section anda housing for the separator under test. A Malvern Particle Sizerinstrument (Mastersizer S) is used to measure accurately andnonintrusively the total concentration and the volumetric dropletdistribution.Experimental data used in the present work are provided byGhetti (2003), who investigated the performance of different typesof commercial wave-plate mist eliminators operated at atmosphericworkingconditionswithhorizontalgasflow.Theaforementionedau-thor measured droplet size distribution upstream and downstreamof the wave-plate mist eliminator and determined the collection ef-ficiencies as a function of droplet size and gas velocity. The accuracyof the measured efficiency is reported to be quite high with a max-imum uncertainty below 5%.For clarity of representation it is worth recalling that an array of the zig-zag channels is fitted into the test rig apparatus. For wave-plate mist eliminator A exactly five channels were fitted into the testduct. Conversely for wave-plate mist eliminators B, only the centralchannel is completely fitted into the duct, other two channels beingonly partly fitted in the test duct.Gas superficial velocities were in the range of 2–5m/s, corre-spondingtoReynoldsnumber of3300–16,700.Theupper limitofgasvelocity was below the re-entrainment velocity for the tested sepa-rators observed experimentally by Ghetti (2003). The droplet size inthe inlet stream, generated by the two-fluid ultrasonic nozzle, wasfrom 2 to 70  m and showed a Sauter mean diameter  D 32  =  7.9  m.Air and water were used as working fluids. The liquid to gas massflow ratio was up to 0.1, which is the typical value in the industrialpractice. 3. Numerical method The numerical model was developed with the commercialsoftware CFX 5.7 by Ansys Inc. An Eulerian–Lagrangian approachwas used to simulate the two-phase flow. Reynolds-averagedNavier–Stokes equations were solved to predict the continuousphase, whereas the equation of motion was solved for the droplets.  3.1. Computational domain and grid Since industrial wave-plate mist eliminators show a depth muchlarger than the other two dimensions, it was assumed the flow tobe two-dimensional. The computational domains for the two typesof wave-plate mist eliminators are shown in Fig. 1.For wave-plate mist eliminator A (Fig. 1a) it was chosen to modela single channel, as in the experimental rig, five channels were fittedinto the test duct.For wave-plate mist eliminator B (Fig. 1b), three channels had tobe modelled as the inlet effects are expected to be considerable. Asmentioned earlier three channels are not fitted exactly into the testsection, thus the presence of recirculation regions near the inlet sec-tion has to be investigated. Logically this is not the industrial case,but such a refinement is needed for interpreting correctly experi-mental data.Thegrid was structured and generated with the softwareICEM byAnsys. The grids for wave-plate mist eliminators A and B contained34,000 and 80,000 elements, respectively, and are shown in Fig. 2.A grid sensitivity analysis was carried out by halving and doublingthe number of elements.  3.2. Physical models for the gaseous phase Two turbulence models were tested to describe the continuousphase: the STD  k –   turbulence model of  Jones and Launder (1972)with constants of  Launder and Sharma (1974) and the shear stresstransport (SST) model of  Menter (1994).Despite Reynolds numbers used in the present work refer to anot fully turbulent flow, it was chosen to use a STD  k –   turbulencemodel.Although,as pointedoutby Wangand James (1998)theweakrecirculation zones need a low  Re  turbulence model to be accuratelypredicted,theSTD k –  modelisableofcorrectlydescribingtheregionoutside the recirculation zone as well the extent of the recirculationzone. Consequently, effects on droplet trajectories and removal effi-ciency should be minimised. This was assessed for wave-plate misteliminators without drainage channels (Wang and James, 1999). Actually the presence of drainage channels may change the rele-vanceofweakregions,whichoccurnotonlyneartheconvexcorners,but also at the drainage channels location. Therefore, it was chosento investigate the performance of an alternative turbulence model,  5642  C. Galletti et al. / Chemical Engineering Science 63 (2008) 5639--5652 Fig. 1.  Computational domain for (a) wave-plate mist eliminator A and (b) wave-plate mist eliminator B. the SST model. This model is conceptually more correct for boundedflows as those present in wave-plate mist eliminators. Such a modelcombines the  k –   model of  Wilkox (1993) in the near wall regionand  k –   in the free stream, to account for deficiency of the STD  k –   inthe treatment of the viscous near-wall region. With the SST model,the solver automatically integrates to the wall where the grid reso-lution is enough to solve the boundary layer appropriately, and useswall functions otherwise. Hence the SST  k –   model can be used asa low  Re  turbulence model without any extra damping functions.  3.3. Lagrangian tracking for droplets Once the primary gas flow is calculated, the droplet motion anddepositionarecomputed.Effectsofthedropletsonthegaseousphase(i.e.transferofmomentumandturbulencemodulation)arenottakeninto account. Such one-way coupling approaches is justified by thedilute characteristic of the flow: for the largest loading of the presentexperimentation, a dilute flow occurs for droplet sizes smaller than100  m (see Fig. 2.4 of  Crowe et al., 1998), which is well satisfied by the inlet size distribution.The droplet motion is calculated through the Lagrangian solveravailable in the commercial CFX code; however, in some cases a sim-ple modification of the code is easily implemented by coupling thesolver with a subroutine written in Fortran language. Indeed, most of the CFD codes available commercially allow modifying submodels'theory by deactivating the available submodels and inserting alter-native ones through user define subroutines.A number of 1000 droplets were injected randomly from the inletsection for each droplet size and runs were repeated at least twice.Droplets were assumed to enter the separator with zero slip velocitywith respect to the gaseous phase.In order to solve the equation of motion of the dispersed phase,it was assumed that: •  the droplet–droplet interaction is negligible, •  the droplet–film interaction at the walls is negligible, •  droplets behave as hard spheres, •  unsteady forces (virtual mass and Basset history), pressure gradi-ent and lift forces are negligible.Consequently, the only force acting on the droplets is drag.The droplet–droplet interaction (and hence coalescence) was ne-glected because a preliminary analysis indicated that the droplet col-lision time is much larger that the relaxation time for the loading,droplet size and gas velocity investigated.Since the horizontal arrangement of the wave-plate mist elimi-nator and the drainage channels lead to a removal of the liquid filmwhich is drained downwards the droplet–film interaction and thusphenomena like splashing are not considered. It was also assumedthat once the droplets collide with the walls, they do not reboundbut are removed immediately from the walls. Re-entrainment wasalso not taken into account. This was motivated by the experimen-tal observations that the working gas inlet velocity was below thosefor which re-entrainment occurred (see Brunazzi et al., 2004).The equation which governs the droplet motion isd  u d d t   = u  g   −  u d  d , (1)  C. Galletti et al. / Chemical Engineering Science 63 (2008) 5639--5652  5643 Fig. 2.  Computational grids for (a) wave-plate mist eliminator A and (b) wave-platemist eliminator B. where   u  g   is the instantaneous gas velocity, whereas   d  is the dropletrelaxation time.  d  =  4  d d  p 3   g  C  D | u  g   −  u d | . (2)The drag coefficient  C  D  is calculated as a function of the dropletReynolds number  Re d  through the Schiller–Naumann equation: C  D  =  24 Re d (1 + 0.15 Re 0.687 d  ). (3)The instantaneous gas velocity   u  g   is the sum of the mean and fluc-tuating velocity:  u  g   =  U   g   +  u ′′  g  . (4)The continuous phase simulation provides the mean velocity   U   g  across the domain as well as turbulence levels and eddy dissipationrates. Such characteristics have to be used to reconstruct a fictitiousturbulent flow field seen by the droplets and responsible for the tur-bulent dispersion.Three different approaches were used in the present work: •  u  g   =  U   g  , i.e. no turbulent dispersion model is used; •  turbulentdispersionistakenintoaccountthroughtheEIMasavail-able in the commercial code, •  turbulent dispersion is taken into account through a modified ver-sion of the EIM (called “varied EIM” in the following text) as sug-gested by Wang and James (1999).In the EIM it is assumed that the droplets encounter discrete eddiescharacterised by a lengthscale L e  =  C  1 k 3  /  2   (5)and a timescale t  e  =  C  2 k  . (6)The constant  C  1  and  C  2  are usually 0.164 and 0.201, respectively.The eddy lengthscale and timescale vary with location, and arecomputed from the continuous phase calculation.It is assumed that a droplet sees a gas velocity  u  g   =  U   g   +  N  r   u ′  g   (7)during the time it needs to cross the eddy.Thus, the fluctuating velocity of the reconstructed turbulent flowfield seen by the droplet is  u ′′  g   =  N  r   u ′  g  , (8)where   u ′  g   is derived from the assumption of turbulence isotropy:  u ′  g   = ( 23 k ) 1  /  2  I  . (9) N  r   is a random number taken from a Gaussian (normal) distributionwith zero mean and standard deviation equal to 1, in order to ensurethe root mean square velocity of the reconstructed flow field to beequal to that of the srcinal.During the droplet–eddy interaction   U   g   is usually updated when-ever the droplet crosses a grid element, whereas   u ′  g   and  N  r   are com-puted at the end of the eddy interaction. This is the model availablealso in CFX by Ansys Inc. and will be called “constant EIM” in thefollowing text.However, according to Wang and James (1999) better results maybe achieved by updating   u ′  g   each time the droplet crosses a grid ele-ment, but keeping  N  r   constant until the end of the eddy interaction.This method has been suggested also by Kallio and Reeks (1989) andSommerfeld et al. (1993) and will be called “varied EIM”.  3.4. Implementation of the varied EIM in the CFD code In the present work the numerical Lagrangian solver of CFX isused and a simple subroutine is written in order to account for theturbulent dispersion through the modified version of the EIM, i.e.varied EIM.Simple steps of the implementation are illustrated in Fig. 3. Basi-cally, the submodels (drag, dispersion, etc.) available in the softwareare deactivated and a subroutine is created in Fortran language tocalculate the right hand member of Eq. (1). The subroutine needssome input variables from the solver: gas density, turbulent kineticenergy and dissipation, mean gas velocity, droplet diameter, dropletReynoldsnumber,dropletpositionandvelocity.Thegasflowcharac-teristics are used to determine timescale and lengthscale of discreteeddies, whereas the droplet position is used to establish whetherthe droplet enters a new eddy or is still within the old eddy. If thedroplet is within the same eddy as the previous integration steps,then the random number  N  r   to evaluate the instantaneous gas ve-locity from Eq. (7) is taken from the previous step. Conversely if the droplet enters a new eddy, then a new  N  r   is chosen to computethe instantaneous gas velocity. Subsequently, the right hand term of Eq. (5) is evaluated and transferred to the main solver.The subroutine is rather simple, the only difficult arises from thefact that CFX allows only one variable, i.e. the source term whichrepresents the right hand member of Eq. (1), to be transferred to
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