Aerosol Science and Technology 36: 665–677 (2002)c° 2002 American Association for Aerosol ResearchPublished by Taylor and Francis0278-6826=02=$12.00 C .00DOI: 10.1080/02786820290038357

Analysis of Steady-State Filtration and Backpulse Processin a Hot-Gas Filter Vessel

Goodarz Ahmadi1 and Duane H. Smith2

1Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, New York2National Energy Technology Laboratory, U.S. Department of Energy, Morgantown, West Virginia

The need to develop a technology for clean and ef� cient electricpower generation has led to the development of advanced pressur-ized � uidized bed combustors (PFBC) and integrated gasi� cationcombined cycles (IGCC). The effective � ltration of hot gases forremoval of ash and sulfur sorbent, however, is the key to the suc-cess of these advanced coal energy systems. Recently, attention hasbeen given to the use of ceramic candle � lters for hot-gas cleaning.The ash cake formation on these � lters needs to be removed by thebackpusle for their successful operation. In this paper, steady-state� ltration as well as the transient gas � ow during the backpulseprocess in the integrated gasi� cation and cleanup facility (IGCF)(located at the National Energy Technology Laboratory, NETL)is studied. The steady-state � ltration condition is � rst evaluated,using a compressible heat-conducting � ow analysis. Particle trans-port patterns are studied, and the deposition patterns of 1–30 ¹mparticleson the ceramic � lters and the vessel surfacesare analyzed.

To simulate the backpulse process, the pressure at the � lter exitis increased sharply in a period of about 0.01 s pressure. The stresstransport model of the FLUENT code is used to evaluate the timeevolution of the transient gas � ow velocity, pressure and thermal� elds, as well as turbulence intensities and stresses inside the can-dle � lter and in the IGCF � lter vessel. Contour plots of the hot-gas� ow conditions from the start of the pressure buildup to its satura-tion level are presented. The results show the rapidly changing � owconditions during the initial stages of the backpulse. The pressurewave propagates along the length of the � lter until a monotonicincrease of pressure with time is achieved; that is, the pressure � eldinside the � lter at the initial stages of the backpulse is stronglynonuniform. Therefore the potential for incomplete � lter cake re-moval exists. Motions of particles that enter the vessel and/or areejected from the candle � lter during the backpulse process are alsostudied, and illustrative particle trajectoriesare presented.

Received 26 April 1999; accepted 25 January 2001.The support of the U.S. Department of Energy and NYSTAR at

different stages of this work is gratefullyacknowledged.Thanks is alsogiven to the FLUENT Corporationfor providingthe software to the au-thors for the computationsthat were performed at Clarkson University.

Address correspondenceto Goodarz Ahmadi, Clarkson University,Mechanical and AeronauticalEngineering,Potsdam, NY 13699-5725.E-mail: ahmadi@clarkson.edu

INTRODUCTIONThe abundance of coal in the U.S. makes it an attractive

alternative to imported oil for use in power generation. De-spite the gradual reduction of coal burning power plants, coal isstill the main fuel for electric power generation in the U.S. Overthe past decade, considerable efforts have been directed towarddeveloping advanced clean coal technologies for electric powergeneration with high ef� ciency and low pollutants. As a result,advanced pressurized � uidized bed combustors (PFBC) and in-tegrated gasi� cation combined cycles (IGCC) are developed.These highly ef� cient coal energy systems require effective � l-tration techniques for removal of ash and unreacted and reactedsulfur sorbent from the hot gases.

For low-temperature gas cleaning, cyclones, impact separa-tors, fabric and � ber � lters, granular beds, and electrostatic pre-cipitators have been used in many industrial applications. Someof these techniques have been extended to high-temperaturegases. Recently, however, considerable attentionhas been givento the use of ceramic candle � lters for hot-gas � ltration. Thecandle � lters are hollow cylinders (closed on one end), typicallywith a diameter of about 6 cm and a length of 1–1.5 m. Thethicknessof the ceramic walls varies between0.8 and 1.5 cm. Anindustrial � lter vessel normally contains a large number (severalhundreds) of candle � lters. Groups of candle � lters are periodi-cally cleaned by a rapid (reverse-� ow) backpulse of compressedair to remove the dust cake that builds up on � lter surfaces.

A number of hot-gas � ltration systems were developed andtested in the recent past or are currently operating. Rockey et al.(1995) described the Integrated Gasi� cation and Cleanup Facil-ity (IGCF), which is located at the National Energy TechnologyLaboratory (NETL) and can support 4 candle � lters. The test re-sults on the full-scale hot-gas PFBC � ltration system at the TiddPower Plant in Ohio were reported by Lippert et al. (1995). ThePower Systems Development Facility, which is currently oper-ating (Dahlin 1998), will eventually include � ltration systemsfor both IGCC and advanced PFBC.

Extensive reviews of gas cleanup at high temperatures, in-cluding candle � lters, were provided by Thambimuthu (1993)

665

666 G. AHMADI AND D. H. SMITH

and Clift and Seville (1993). The candle � lters generally have avery high cleaning ef� ciency, on the order of 99.8%. For somesystems and operating conditions there are, however, a num-ber of unresolved problems with occasional ash-bridging in be-tween � lters and � lter failure and breakage. The mechanismsof ash-bridging are dif� cult to determine. However, incomplete� lter cleaning is often thought to be one potential cause of ash-bridging; buildup on non� lter surfaces during the steady � ltra-tion, or � lter-cake fragments from the cleaning backpulses isanother possible cause (Smith and Ahmadi 1998). If either ofthese 2 mechanisms is operative, effective backpulse cleaningof the candle � lters is the key to successful operation of theseadvanced hot-gas cleaning systems.

For backpulse cleaning purposes normally a high pressuretank is mounted to the tube sheet of a groupof � lters in a plenum.Typically, every 20–60 min the outlets of a group of candle� lters are exposed to the high pressure air in the tank for avery short duration (about 0.2 s). As a result, a rapid pulse jetenters the tube sheet and pressurizes the inside of the candle� lters. The direction of the � ow across the � lter wall reversesduring the backpulse;the reversal of the pressure gradient acrossthe � lter cake is normally suf� cient to break the cake away.

Numerous studies on the pulse-jet cleaning of fabric � ltershave been conducted in the past. Recently, there has been a num-ber of investigationsof the backpulse cleaning of ceramic � ltersin the literature. Laux et al. (1993) and Berbner and Lof� er(1993) described the results of their experimental and compu-tational study of pulse-jet cleaning of a laboratory scale model.The effect of reservoir pressure on the ef� ciency of cleaningwas also reported in the latter work. The characteristics of thebackpulsecleaning in a pilot plant were reported by Skroch et al.(1993). The pulse jet process in a single ceramic � lter elementwas analyzed by Ito (1993). Recently, Jhon and Smith (1997)performed numerical simulations of the backpulse cleaning us-ing a steady-state analysis. Studies that emphasize the chemistryof cake strengths (Smith et al. 1997), physics of cake fragmenta-tion (Ferer and Smith 1998a,b), measurementsof cake propertiesat high temperatures and pressures (Kono et al. 1998), or fractionof cake removed (Schmidt 1998) have also been performed. Toimprove the effectiveness of the backpulsecandle � lter cleaningprocess, a fundamental understanding of the transient gas � owand cake breakup,as well as of the motionof detached fragmentsof cake and particles in the gas � ow in the � lter vessel, is needed.

Considerableeffort has been devoted to understandingthe ki-neticsofaerosoldispersion,transport,anddepositiondue to theirsigni� cance in numerous industrial processes. Reviews of parti-cle diffusion in laminar � ows were provided by Levich (1962),Rosner (1989), Fernandez de la Mora (1986), and Rosner andTassopoulos (1991). In turbulent � ows, particles are transportedby the mean motion and are dispersed by the � uctuating ve-locities. Friedlander and Johnstone (1957), Cleaver and Yates(1975), and Wood (1981a,b) provided semiempirical expres-sions for particle mass � ux from a turbulent stream to sur-faces. Extensive reviews on the turbulent deposition process

were provided by Friedlander (2000), Wood (1981a,b), Hinds(1982), Hidy (1984), and Papavergos and Hedley (1984). Li,Ahmadi, and coworkers (1993, 1994, 1995) developeda compu-tationalmodel for simulatingthe turbulentdepositionof aerosolsin complex passages. Recently, Ahmadi and Smith (1997,1998a,b) reported their analyses of particle transport and de-position during steady-state hot-gas � ltration.

The present work is concerned with a computationalmodel-ing of the steady-state � ltration and the backpulse process forthe IGCF pilot plant, located at the NETL. Operational datafrom the IGCF � lter vessel were analyzed by Smith et al. (1997,1998a,b) using simple models for interpretationof the pressure-drop time variations. Kono et al. (1998) have performed hightemperature/high pressure measurements of the tensile strengthsand other properties of � lter cakes formed from IGCF material.Simulations of steady-state gas � ow and particle deposition inthis � lter vessel during � ltrationswere discussed by Ahmadi andSmith (1997, 1998a,b), where an incompressible and isothermal� ow analysis was used. In this study the compressible � ow andthermalconditionin thevessel understeady-state� ltration is � rstanalyzed, and the particle deposition pattern is studied. Startingwith the steady � ltration condition, the pressure buildup and theevolution of gas � ow conditions inside the candle � lters andthe IGCF � lter vessel during the backpulse are then analyzed.The stress transport model of FLUENT code (FLUENT User’sGuide 1994) is used, and time variationsof gas velocityand pres-sure and temperature � elds are evaluated. It is shown that thepressure wave propagates along the � lter cavity at high speed;therefore, a spatiallynonuniformstrong pressure gradientacrossthe � lter wall is present at the initial stages of the backpulse pro-cess. Illustrative particle trajectories during the backpulse arealso presented and discussed.

EQUATIONS OF THE MOTION ANDTURBULENCE MODEL

Gas Flow ModelThe FLUENT code has options for using either the k–" (stan-

dard or renormalization group version) or the stress transportmodel, which is a simpli� ed version of the one developed byLaunder et al. (1975). In addition, the code can handle incom-pressible isothermal � ows, as well as compressible gas � owswith heat transfer. The stress transport model that accounts forthe evolution of individual turbulent stress components is usedin the simulation. The stress transport model properly handlesanisotropic turbulence � uctuations and entirely avoids the useof eddy viscosity. The effect of heat transfer and gas compress-ibility were included in the analysis. The code also used a wallfunctionboundarycondition.(Additionaldetailsof the � ow sim-ulation features and the computationalschemes may be found inthe FLUENT User’s Guide (1994).) The steady-state � ow andpressure condition in the IGCF vessel were reported by Ahmadiand Smith (1997), where an incompressible and isothermal con-dition was assumed.

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While neglectingthe gas compressibilityeffect may not intro-duce a signi� cant error into the steady-state � ltration condition,it is thekey for analyzingthebackpulseprocess.During theback-pulse, air rapidly enters the plenum and then the � lters throughtheir open ends (i.e., the “exits” of the � lters while the steady� ltration is taking place). To simulate the backpulse process, theboundary conditionat the outlet of the � lter vessel is modi� ed toa pressure boundary condition. It is assumed that the pulse pres-sure at the � lter exit increases sharply over 0.01 s to a maximumvalue. The initial buildup of backpulse pressure is assumed tobe roughly linear and is modeled numerically with a series ofstep increases in the boundary pressure.

Particle EquationTo simulate the trajectories of particles during steady-state

� ltration and/or those that are removed from the � lter as the � ltercake breaks up, the particle equation of motion, including thedrag and gravitational force as prescribed in the FLUENT code,was used in the analysis. The drag is generally the dominatinghydrodynamic force. In the regions with a strong shear � eld, thelift force may also become important. For particles of interestin this study, which are larger than 1 ¹m, the Brownian motioneffect (which is negligible) is neglected.

The particle equation of motion requires knowledge of theinstantaneous turbulent � uid velocity at every point. As notedbefore, the mean � ow � eld is evaluated by using the stress trans-port turbulence model. The gas instantaneous � uctuation ve-locities are modeled as � ltered white-noise random processes.That is, the � uctuation velocity � eld is evaluated by solving avectorLangevin equation.The resulting velocity is a continuous(anisotropic) Gaussian random vector � eld whose variances andcorrelation times equal those of the turbulent � ow � eld. Stickboundary condition for the particle-surface contact is assumed.That is, a particle that touches a wall and/or the candle � lter sur-face will stick to the surface. Additionaldetails of the theoreticalbasis of the model may be found in the FLUENT User’s Guide(1994). Ahmadi and Smith (1998a) discussed the importanceof turbulence dispersion on particle transport in the IGCF � ltervessel and made comparisons for different cases.

IGCFThe NETL has been extensively involved in hot-gas cleaning

research. In particular, the IGCF for testing the performance ofcandle � lters has been in use for more than 7 years. Recently,extensive data on candle � lter performance were collectedusingthe IGCF. A schematicdiagramof the IGCF � lter vessel is shownin Figure 1. The vessel can accommodate testingof up to 4 � lters.In a recent test, 7 gasi� er runs were performed (over an 18 monthperiod) with an accumulated 870 h of operation. The averagegas � ow to the � lter vessel was 123 lb/h (15.5 g/s), with theface velocity through the candle of about 2.5 ft/min (1.3 cm/s).The particle loading was estimated at 0.28 lb/h (0.035 g/s). Theash size distribution varies, but it is of the order of a few ¹m,

Figure 1. Schematics of the IGCF � lter vessel.

with 30 ¹m being the upper limit. The average � lter operatingpressure was 294 psig (2030 kPa), with an average differentialpressure of 5 psi (34.5 kPa) across the � lter. The average of � lterinlet and outlet temperature was 1063±F (846 K). An averagesupply tank purge pressure of 454 psig (3130 kPa) was used toclean the � lter cake buildup. The blow-back for the � lters wasroughly once every hour for a duration of 0.1–0.2 s.

STEADY-STATE FILTRATION RESULTSIn this section, simulation results for compressible gas � ow

and dispersion and deposition of particles in the IGCF � ltervessel under steady-state � ltration conditions are presented anddiscussed. The FLUENT code is used to generate the � ow � eldin the � lter vessel. Trajectories of particles of different sizes thatenter the vessel at the inlet are analyzed. In a series of tests thatwere performed by Rockey et al. (1995), two 1/2 m long � lterswere installed in the IGCF � lter vessel. The simulation resultsfor this case are described in the following section.

Gas FlowA grid of 23 £ 23 £ 24 and a high resolution grid of 45 £

45 £ 47 were used to simulate the steady gas � ow and tem-perature condition inside the candle � lters and the IGCF � ltervessel. Since there are 2 planes of symmetry, only one-quarterofthe vessel is simulated and the symmetry boundary conditionsare used. Figure 2 shows the upper part of the high resolutiongrid near the inlet including the (permeable) candle � lter. Nonoticeable differences in the simulated � ow and thermal � eldsby the 2 grids were noticed. Therefore for the computationallyintensive unsteady backpulse simulation the coarser grid was

668 G. AHMADI AND D. H. SMITH

Figure 2. Computational grid for the IGCF � lter vessel with2 candle � lters.

used. As was noted before, the Reynolds stress transport modelof the FLUENT code was used in these calculations, and the gascompressibility and temperature variations were also includedin the analysis.

The IGCF system operates at a high temperature and a highpressure. In the steady-state � ltration simulation of Ahmadi andSmith (1997), a mean velocity of V D 4 m/s, a temperature of833 K (1040±F), and a pressure of 2.06 £ 106 Pa at the inlet tothe vessel were assumed. The ideal gas law was used to relatethe gas pressure, temperature, and density. During the steady-state � ltration, the gas enters the � lter vessel as a ring wall-jetnear the top around the inlet pipe. On the basis of the earliermeasurement data (Smith et al. 1997a,b), the permeability of

Figure 3. Static pressure variations in the IGCF � lter vessel.

the � lter was assumed to be 10¡12 m2. A particle-to-gas densityratio of 1000 and a range of diameters from 1 ¹m to 30 ¹m wereused in the analyses. As noted before, particles were assumedto stick upon contact with a wall. In the experimental IGCFunit, heaters were installed around the vessel to heat the gasand compensate for the heat loss. In the simulation, a thermallyinsulated wall boundary condition is used instead.

Figure 3 shows the contour plot for variations of the relativestatic pressures at 2 sections of the � lter vessel during steady-state � ltration. It is observed that the static pressure remainsroughly constant inside the � lter vessel.The majorpressure dropoccurs at the candle � lter as the gas passes through the ceramicporous wall. There is also small pressure variation inside thecandle � lter.

In Figure 4, the contour plots for variations of the mean tem-perature in the IGCF � lter vesselare presented.This � gure showsthat the gas enters the vessel at 833 K and the temperature de-creases with distance from the inlet region. The temperaturedrops to about 760–780 K outside the ring wall-jet region. FromFigure 4, it is also observed that the gas leaves the � lter exitwith a temperature of about 780 K (940±F). The computed tem-perature range is comparable with those reported for the exper-imental setup by Rockey et al. (1995). As noted before, in theactual system electric heaters were used to heat the gas in thevessel in order to compensate for the heat loss from the ves-sel wall. In the present computation, a thermally insulated wallboundary condition was used, which appears to be a reasonableapproximation.

The results for the gas density variations in the IGCF ves-sel (not shown here) show that the gas density increases from8.3 kg/m3 at the inlet to 9 kg/m3 in the vessel. The densityvariation is mainly due to the changes of gas temperature atroughly constant gas pressure in the tank.

FILTRATION IN A HOT-GAS FILTER VESSEL 669

Figure 4. Temperature contours in the IGCF � lter vessel.

The mean velocitymagnitudecontoursare shown in Figure 5.To allow the details of the � ow � eld to be seen, the maximumcontour level is reduced from the inletvelocityof 4 m/s to 2.1 m/sin this � gure. It is observedthat thegas velocitydecreases rapidlyto <0.2 m/s in the bulk of the IGCF � lter vessel. The highvelocity region is concentrated in the ring wall jet around theupper part of the inlet pipe. Inside the � lter, the gas velocityincreases gradually and reaches its peak value of about 0.7 m/snear the outlet.

Figure 6a shows the mean velocity vector plot in 2 sectionsnear the planes of symmetry in the upper part of the IGCF vessel.

Figure 5. Mean velocity variations in the IGCF � lter vessel.

It is observed that the gas leaves the inlet as a strong ring walljet toward the bottom of the � lter vessel and moves up nearthe outer wall and through the candle � lter. Two recirculationregions are formed in the vessel: a very large one that almostcovers the entire vessel and a small one above the inlet regionnear the top. This � gure also shows that the speed of gas insidethe � lter increases toward the � lter exit region at the top of thevessel.

Mean velocity vector plot at a section across the IGCF vesselis shown in Figure 6b. It is observed that the � ow inside the IGCF� lter vessel is strongly three dimensional.Figure 6b shows that a

670 G. AHMADI AND D. H. SMITH

Figure 6. Mean velocity vector plots in the IGCF � lter vessel.

counterclockwise circulation forms in the vessel. The velocitiesare of the order of a few centimeters per second, and the gasmoves toward the inlet region. Figure 6b also shows a roughlyuniform radially inward � ow through the candle � lter in spite ofthe differences in the surrounding � ow � elds.

Particle TransportParticle transport and deposition in the IGCF vessel with 2

� lters are studied in this section. Three ring sources of particlesat the inlet to the vessel are considered. The inlet is essentiallyan annulus with an inner radius of 1.8 cm and an outer radius of2.5 cm. Ensembles of particle trajectoriesare evaluatedand theirdeposition patterns are studied. Several different particle sizesfrom 1 ¹m to 30 ¹m are used in these simulations.These choicescover the range of particle sizes of the order of one to a few ¹mobserved in the IGCF � ltration system. The gravitational effectis included in these simulations.

The combinationof the 3 ring sources of 1.9, 2.15, and 2.4 cmradii approximates a uniform distribution of particles emittedfrom a plane source at the inlet. These include 27 particle injec-tors that are apart 0.25 cm radially and 9± angularly.The uniforminlet particle source is a reasonable assumption for simulatingthe experimental condition. Thus the results could provide in-formation concerning the trend of particle size distribution inthe � lter cake during the operation of the IGCF system.

Figure 7a shows the mean trajectories of 1 ¹m particlesand their points of deposition on the candle � lter for the uni-form source at the vessel inlet. Only one-quarter of the vesselis simulated, and the re� ecting boundary condition is used onthe planes of symmetry. The mean particle paths are shown bydifferent lines in this � gure. (The lines correspond to a particlesource/injector position on the 3 uniform ring sources at the in-let.) The locationwhere a particledeposits on the � lter is markedby a small cross. Typically, particle trajectories were evaluatedfor 50,000 (variable) time steps, which corresponds to a totaltime duration of about 5–50 s. In this time duration, most in-jected particles are deposited on the � lter side wall with onlyone particle being deposited on the bottom of the � lter.

Figure 7. Trajectories for d D 1 ¹m particles. (a) mean � owtrajectories, (b) mean � ow trajectories, and (c) turbulent � owtrajectories.

As noted before, a strong circulating � ow pattern forms inthe IGCF vessel. The gas leaves as a wall jet from the inlettoward the bottom of the vessel and moves up in the outer wallof the vessel toward the candle � lters. Figure 7a indicates that theparticles are carried by the inlet circular wall-jet � ow downwardalong the IGCF � lter vessel and are moved toward the � lter bythe main circulating � ow. Figures 7a and 7b show that 1 ¹mparticles deposit roughly uniformly along the � lter, while theirangular distribution is nonuniform.There are gaps in the angulardeposition of the 1 ¹m particles. These particles are essentiallytransported by the general mean circulation of the � ow in thevessel. A careful examination of the results indicated that theparticles that are released from the sources near the inner wallof the inlet deposit on the � lter within one loop. Those thatare emanated from near the outer wall of the inlet, however,complete several loops before depositing.

The particle trajectory analysis is repeated, including the tur-bulence dispersion effects for ensembles of 270 and 2700 par-ticles. Figure 7c shows the sample trajectories for an ensembleof 270 particles and the corresponding distribution of depositedparticles on the candle � lter. When the effect of turbulence � uc-tuation is included, the deposition pattern changes with a largenumber of particles depositing on the surface of the � lter thatfaces the inlet. This result is in agreement with the earlier workof Ahmadi and Smith (1998a). The simulation results for the en-semble of 2700 particles also shows a similar trend of depositionpattern.

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Additional results for 10 and 30 ¹m particles (not shownhere due to space limitation) indicate that these larger particleshave a somewhat nonuniform distribution vertically along thecandle � lter, with more particles depositing on its lower half. Afew of these particles also deposit on the bottom surface of thecandle � ler. This nonuniformity is mainly due to gravitationalsedimentation, which shows its effect for the 10 and 30 ¹mparticles. The angular variation of the deposited particles is alsostill nonuniform, while the amount of angular nonuniformitydecreases as particle size increases. While the general trajectorypatterns of 10 and 30 ¹m particles are similar to those of 1 ¹mparticles, there are certain noticeable differences. In particular,a number of 10 and 30 ¹m particles penetrate deeper into thevessel and some deposit on the bottom of the vessel. This furthershows the importance of inertia and gravity for 10 and 30 ¹mparticles.

The presented results suggest that the micron-sized particleswill have a relativelyuniform verticaldistributionalong the � ltercake, but a rather nonuniform angular variation. The � lter cakewill thenhavea nonuniformparticledistribution,with largerpar-ticles (of the order of 10–30 ¹m) having a higher concentrationtoward the � lter bottom. Since the larger particles will generate� lter cakes with higher porosity and higher permeability, the � l-ter cake thickness will increase toward the bottom of the candle� lter, as well as being nonuniform in angular directions.

BACKPULSE RESULTSThe simulation results for the backpulse process of the IGCF

with 2 � lters are described in this section. Here, all pressures inthe � lter and the � lter vessel are reported relative to the absolutepressure in the � lter vessel before the backpulsebegins. The signconvention is chosen such that pressures that cause � ow fromthe plenum into the candle � lter are positive.

Starting from the steady-state � ltration condition, the � lter-exit boundary condition is modi� ed to simulate the backpulseprocess. It is assumed that the � lter-exit pressure increasessharply from –6 £ 103 Pa to about 2 £ 105 Pa during a timeduration of 0.01 s. The exact value of the gas pressure at the � l-ter inlet is not known, but it is expected to be lower than the tankpurge pressure (due to the loss in the line and the need to � ll theplenum connected to the � lter). In order to obtain a convergedsolution for this rapidly evolving gas � ow condition, a time stepof 10¡6 s was used at the startup of the computation.The lengthof the time step was then gradually increased as the computationprogressed.

Figure 8 shows contourplots for the time evolutionof the rel-ative static pressures at the sections near the planes of symmetryof the � lter vessel. One plane of symmetry passes through theaxes of the candle � lters. Figure 8a shows the pressure variationsin the vessel at the time of 10¡4 s after the start of the backpulseprocess. At this time, the � lter exit pressure is 2000 Pa and thepressure wave begins to enter into the candle � lter. It is observedthat the steady-state � ltration conditions still prevail in the bulk

of the vessel. The static pressure remains roughly constant andequal to its steady-state � ltration value inside the � lter vessel.The major pressure drop occurs across the wall of the candle� lter. The pressure inside the candle � lter is quite low, with theexception of a small region near the exit. In this region there is avery sharp pressure gradient near the pressure wave front suchthat the relative pressure changes from its maximum value of2000 Pa to about ¡6000 Pa.

Figures 8b and 8c show the pressure contours at times of2 £ 10¡4 s and 5 £ 10¡4 s, respectively. At these moments, thebackpulse pressure at the open end of the � lter rises to 4000 Paand 10000Pa, respectively,while the minimum relative pressureinside the � lter remains at ¡6000 Pa. These � gures illustratehow, early in the backpulse, the pressure wave approaches theclosed end of the � lter, while the size of the low-pressure regioninside the � lter shrinks.

Figure 8d indicates that 0.001 s after initiation of the back-pulse, the entire inside of the candle � lter is pressurized. Thehigh-pressure backpulse gas now begins to reverse the � owthrough the � lter wall and pulse air� ow begins to enter intothe vessel. At this moment the purge pressure at the � lter outletis 2 £104 Pa, and the pressure decreases monotonically insidethe � lter with distance from the outlet.

Figures 8e and 8f show the pressure variations in the IGCFvessel at times of 0.002 and 0.0105 s, respectively. The outletpressures in these cases are 4 £ 104 and 2 £ 105 Pa, with thelatter pressure being the estimated saturation purge pressure.It is observed that the high-pressure region expands inside theceramic � lter. In particular, Figure 8f shows that the entire insideof the candle � lter is at the saturation purge pressure of about2 £ 105 Pa. There is also a sharp pressure gradient across thecandle � lter walls, causing � ow from inside the � lter out intothe � lter vessel.

In Figures 9a–c, contour plots for variations of the tempera-ture in the IGCF � lter vessel at times of 0.002 s, 0.0075 s, and0.0105 s are shown. It is observed that the cold backpulse gasgradually penetrates deeper into the vessel with time. The tem-perature inside the vessel is not affected during the early stagesof the backpulse process. The presence of cold gas near theoutlet of the � lter leads to a sharp temperature gradient, whichexposes the ceramic candles to a thermal shock that may bedamaging.

Variations of gas density inside the candle � lter at times of0.002 s, 0.0075 s, and 0.0105 s are shown in Figure 10. At thetime of 10¡4 s after the start of the backpulseprocess, Figure 10aindicates that the gas density at the � lter exit is about 23 kg/m3

and reduces sharply at short distances as the pressure wavefrontis reached.At this time, the gas density remains roughly constantat the level of the steady-state � ltration condition in the rest ofthe candle � lter and the bulk of the vessel. Figures 10b and 10cshow the development of gas density into smooth pro� les withtime, as the pressure wave spreads inside the candle � lter.

Time evolution of the mean velocity vectors in 2 sectionsnear the planes of symmetry in the upper part of the IGCF vessel

672 G. AHMADI AND D. H. SMITH

Figure 8. Time evolution of mean static pressure contours during the backpulse process. (The contour values shown are in kPa.)(a) t D 0:0001 s, (b) t D 0:0002 s, (c) t D 0:0005 s, (d) t D 0:001 s, (e) t D 0:002 s, and (f ) t D 0:0105 s.

during the backpulseare shown in Figure 11. Figure 11a displaysthe velocity plot in the candle � lter and the top part of the vessel10¡4 s after the start of the backpulse process. At this time, the� lter exit pressure is 2000 Pa and the high pressure gas begins

to enter the candle � lter. The reversal of the velocity directionnear the top of the � lter can be clearly seen from this � gure. Asnoted before, the steady-state � ow conditions still prevail insidethe bulk of the candle � lter and the � lter vessel.

FILTRATION IN A HOT-GAS FILTER VESSEL 673

Figure 9. Time evolution of mean temperature contours during the backpulse process. (The contour values shown are in degreeK.) (a) t D 0:002 s, (b) t D 0:0075 s, and (c) t D 0:0105 s.

Figure 11b shows the velocity � eld after 2 £ 10¡4 s. At thistime, the pressure at the � lter exit rises to 4000 Pa. The pressurewave has penetrated deeper into the � lter, and the volume of the� ow-reversal region has increased. Also, the magnitude of the

Figure 10. Time evolution of mean density contours during the backpulse process. (The contour values shown are in kg/m3.)(a) t D 0:002 s, (b) t D 0:0075 s, and (c) t D 0:0105 s.

reversed � ow velocity has become comparable with the steady-state � ow rate inside the � lter during � ltration.The velocity � eldinside the � lter vessel remains almost undisturbed at this time.At t D 5 £ 10¡4 s, the exit pressure becomes 10000 Pa and the

674 G. AHMADI AND D. H. SMITH

Figure 11. Time evolution of a mean velocity vector � eld ina vertical plane during the backpulse process. (a) t D 0:0001 s,(b) t D 0:0002 s, (c) t D 0:0005 s, (d) t D 0:001 s, (e) t D0:002 s, and (f ) t D 0:0105 s.

reverse-� ow region covers one-third of the inside of the candle� lter. The magnitudeof the reversed � ow increases substantiallyand reaches about2.5 m/s. This � gure also indicates that the � owinside the bulk of the � lter vessel remains essentially unaffectedby the backpulse up to this time.

Figure 11d shows that at 0.001 s after initiation of the back-pulse, the � ow in the entire insideof the candle � lter has changeddirection.As noted before, at this time the pressure pulse reachesthe bottom of the candle � lter. At this instant, the pressure at the� lter outlet is 2 £104 Pa. The gas enters at a speed of about 5 m/sand the velocity decreases monotonically inside the � lter withdistance from the outlet.

The velocityvector plots in the IGCF vessel at times of 0.002and 0.0105s are shown, respectively,in Figures 11e and 11f. Thebackpulse purge pressure at these instances are 4 £ 104 and 2 £105 Pa. It is observed that the reverse � ow velocityinsidethe can-dle � lter increases to peaks of about 11 and 34 m/s, respectively.The � ow inside the � lter vessel also begins to be distorted by thebackpulse. The peak gas velocity in Figure 11e occurs at somedistance from the inlet, possibly because of interaction of an in-coming wave with its re� ection from the closed end of the � lter.

Figure 12 shows the velocity vector � elds across the IGCF� lter vessel at times of 0.002 and 0.0105 s after the initiationof the backpulse. The purge gas leaves the surface of the candle� lter at a radial speed of about 1 m/s.

Figure 12. Time evolution of a mean velocity vector � eldacross the � lter vessel during the backpulse process. (a) t D0:002 s and (b) t D 0:0105 s.

The time evolution of the mean-velocity magnitude contoursis shown in Figure 13. Figure 13a shows the condition of meanvelocity 10¡4 s after initiationof the backpulseprocess. The gasvelocity in the bulk of the IGCF � lter vessel remains unchanged.Inside the � lter, however, the magnitude of the velocity nearthe outlet is reduced and the peak velocity magnitude occurs atsome distance from the top of the � lter. Clearly this is due to theinitiationof � ow reversal and entrance of backpulse gas into thecavity within the candle � lter. At this moment, inside the � lterthe gas velocity increases from the outlet to its peak value ofabout 1.2 m/s and then decreases gradually toward the closedend of the � lter. Figure 13b shows that at t D 5 £ 10¡4 s, thehigh-pressure backpulse gas alters the gas velocity � eld insidethe � lter signi� cantly. The cleaning gas enters the � lter with avelocity of about 2.4 m/s, and the magnitude of the gas velocitydecreases along the � lter.

The mean-velocity contours at times of 10¡3 and 1.05£10¡2 s after the initiation of the backpulse are shown inFigures 13c and 13d. Here the peak gas velocity reaches about5.4 m/s and 33 m/s, respectively. The peak velocity at 10¡3 soccurs at the top of the candle � lter as the backpulse gas en-ters the cavity of the � lter. At time 1.05£ 10¡2 s, however, thepeak velocity region has moved downward from the � lter exit.As noted before, this is perhaps due to the interaction of in-coming and re� ected waves. Figure 13d shows that the velocity� eld inside the � lter vessel is also distorted by the backpulseprocess.

Particle TransportParticle transport during the backpulse in the IGCF vessel

with 2 � lters is described in this section.The purposeof the back-pulse is to remove the � lter cake from the candle � lter. While thedetailsof the cake breakupare not fully understood,it is expectedthat pieces of � lter cake of different sizes break away from thecandle � lter (Ferer and Smith 1998a). The larger broken pieceswill drop to the bottom of the vessel under the action of gravity.At the same time, certain amountsof the released dust cake couldbe redeposited on the candle � lter (Smith et al. 1998b). Here thetransport of 10 ¹m particles that are released from the surfaceof the candle � lter at 1.05£ 10¡2 s is studied. Only one-quarterof the vessel is simulated and the re� ecting boundary condition

FILTRATION IN A HOT-GAS FILTER VESSEL 675

Figure 13. Time evolution of mean velocity contours during the backpulse process. (The contour values shown are in m/s.)(a) t D 0:0001 s, (b) t D 0:0005 s, (c) t D 0:001 s, and (d) t D 0:0105 s.

is used on the planes of symmetry. The mean-� ow particle pathsare shown by different lines in these � gures. Eighteen particletrajectories are evaluated.Nine of the particles are released nearthe top of the candle � lter; the other 9 are released at a dis-tance of about one-third the length of the � lter. Figures 14a and14b show that the particles are ejected radially outward fromthe surface of the candle � lter. Four particles deposit on the topsurface and the side wall of the � lter vessel, while the rest dropdownward. It should be emphasized that the gas � ow � eld att D 1.05 £ 10¡2 s is used for the trajectory analysis, and thegravitationaleffect is included in these simulations.By this timethe rapid variations during the initial stages of the backpulseare over and the general trend of particle trajectories will besigni� cantly altered by the rather smooth variation of the � ow� eld.

The transportof particles thatenter thevessel duringtheback-pulse is also studied. Nine 10 ¹m particles are assumed to enterthe vessel from a ring source of particles at the inlet to the vessel.The vessel inlet is essentially an annulus with an inner radiusof 1.8 cm and an outer radius of 2.5 cm. Figures 14a and 14b

also show the mean trajectories of 10 ¹m particles. The strongcirculating � ow pattern that was formed in the IGCF vessel dur-ing the steady-state � ltration (Ahmadi and Smith 1997) is totallydistorted by the backpulse � ow. The gas enters the vessel as awall jet and from the candle � lters. The IGCF vessel behavesas a pressurized tank that is being � lled. These � gures indicate

Figure 14. Trajectories of 10 ¹m particles in the � lter vesselduring the backpulse process.

676 G. AHMADI AND D. H. SMITH

that the particles are carried by the inlet circular wall-jet � owdownward along the IGCF � lter vessel.

CONCLUSIONSIn this work, a computer simulation procedure for analyz-

ing the steady-state � ltration condition as well as the transientgas � ow in the IGCF � lter vessel during the backpulse pro-cess for cleaning the candle � lters is described. The Reynoldsstress transport model of the FLUENT code was used to simu-late the transient mean compressible turbulent � ow � eld. Whilethe walls were assumed to be thermally insulated, variations oftemperature and density of gas were included in the analysis. Tomodel the backpulse purge pressure, a rapidly increasing pres-sure boundary condition was imposed at the open end of thecandle � lter. The rapidly evolving gas � ow conditions from thebeginning of the pressure buildup were evaluated.

The particle equation of motion used includes the nonlineardrag and the gravitational force. Simulation results for transportand deposition of ash particles in the IGCF � lter vessel duringthe steady-state � ltration are reported. Motions of particles thatenter the vessel and/or are ejected from the candle � lter duringthe backpulse process were also studied, and sample particletrajectories were calculated. The gas- and particle-� ow resultselucidatedthe rapidly changing� ow conditionsduring the initialstages of the backpulse. On the basis of the results presented,the following conclusions can be drawn.

Steady-State Filtration² The mean gas � ow forms an elongated circulating � ow

pattern that penetrates deep into the IGCF � lter vessel.² Except for the inlet circular wall-jet region, the inten-

sity of gas turbulence is generally low in the vessel.² The pressure is roughly constant in the bulk of the � lter

vessel.² The main pressure drop occurs across the � lter porous

wall, and the pressure drop varies in direct proportionto the � lter permeability.

² The particles are transported by the circulating � owfrom the inlet to the candle � lter.

² The mean particle trajectories of small particles arequite similar.

² The effect of inertia and gravitational sedimentationbecomes important for particles larger than 10 ¹m.

² The deposition pattern of particles varies with size.While the smaller particles have a roughly uniformdistribution along the � lter length, the larger particlestend to deposit on the lower part of the � lter. The largeparticles have a more uniform angular deposition dis-tribution, while the smaller particles seem to mainlydeposit on the side of the � lter facing the inlet withlittle deposition on some parts of the � lter.

² The nonuniform deposition pattern of different sizeparticles suggests that the � lter dust cake compositionand porosity may vary along the � lter as well as in the

angular direction. As a result, the cake thickness mayalso become nonuniform.

Backpulse² The backpulse pressure wave propagates rapidly along

the length of the � lter cavity before a monotonic in-crease of the pressure in the cavity is achieved.

² At about 0.001 s after initiation of a backpulse, thepressure inside the � lter cavity becomes approximatelyuniform and increases with time. Before that time thereis a pressure front in the cavity with a sharp pressuredifference across the front.

² The steady-state � ltration � ow inside the � lter vesselremains essentially unaffected by the backpulse for the� rst 0.002 s; after this time, the reversed � ow throughthe candle-� lter wall begins to distort the steady-state� ow � eld.

² The transport pattern of particles that enter the vesselduring the backpulseprocess is strongly distorted fromthe steady-state � ow.

² The reverse-� ow velocity across the candle � lter wallreaches about 0.35 m/s.

² The sharp pressure gradient across the � lter and � l-ter cake, together with the high-speed reversed � ow,appears to be the main cause for breakup of the � ltercake.

² During the initial stages of the backpulse, the pressure� eld inside the � lter is strongly nonuniform; therefore,the potential for incomplete � lter-cake cleaning exists.

² Sample particle trajectories show radial ejectionof par-ticles at highspeeds from the surface of the candle � lter.

² The high-speedradial ejectionof particles suggests thatthe particles could impact and deposit on solid surfacesnear the candle � lter during the backpulse process.

² The simulated particle-transport patterns suggest thatsmall particles released during the backpulse cakebreakup could deposit on nearby solid surfaces, espe-cially on any central support column surrounded by acircle of � lters. Excessive cake buildup on the columncould become the starting point for support-� lter and,eventually, � lter-� lter ash bridging.

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