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CFD Simulation in the Individual Channels of theParticle Filter

David Lvika, Jindich Kourek and Ji PolanskNew Technology Research CentreUniversity of West Bohemia, CZ

SYNOPSIS

A particle filter (also known as a Diesel Particle Filter DPF) can be used for cleaning sootparticles from exhaust gases. These particles pose a serious health risk, because they canbe deposited in the lungs and lung cells. In a filter, exhaust gases flow through a labyrinth ofporous walls leaving particles at the surface. After filling up a filter with particles, aregeneration process (burning particles) is started and the particle filtration can continue.The regeneration-to-regeneration time defines the working cycle of the DPF. Whencomparing to the engine life time, the life time of the DPF is much shorter depending on the

driving mode and also on the efficiency of the working cycle. The exhaust gas flowdescription through very small channels (from 1 to 2 millimetres) is the object of this article.The process of the particles deposition at the porous walls of the filter for one working cycleis presented, too, using for both cases a numerical simulation in FLUENT 6.2.

1. INTRODUCTION

Recent years have seen stiffening up of the emission limits of exhaust gases in theautomobile industry. These strict emission limits encourage application of new technologiesand new devices to decrease exhaust emissions in the automobile industry. Emissions limitsare stiffer for all components covered by the Europeans emissions limits (EURO). These areNitrogen Oxide (NOx), Carbon Monoxide (CO), Hydrocarbons (HC) and Particles.Nowadays, the attention is paid to the particle limits as you can see in the Table 1 where theparticle emission limits over the last few years is shown. European emission limit EURO5 isfive times stricter in comparison to the emission limit EURO4.

Table 1: European emission limits for soot particles for diesel engine

Emission Norm Diesel Euro 2 Euro 3 Euro 4 Euro 5

Particles [mg/km] 80-100 50 25 5

Soot particles are produced only by diesel engines and often contain remains of carbon, oiland fuel. The size of particles is in the order of several micrometers. These particles pose aserious health risk, because they can be deposited in the lungs and lung cells, where theycan invoke various respiratory infections and even lung cancer.

Strict particle emission limits are problem for diesel particle filters, which must have higherefficiency for keeping particles. This problem is connected with a pressure loss at a dieselparticle filter, because filter with higher efficiency has higher pressure loss. The increasingpressure loss is causing higher fuel consumption and also reducing the engine power. Thenumerical simulation using FLUENT 6.2.16 should help to describe the pressure loss

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dependency through the working cycle of the filter involving the particles depositionphenomena and exhaust gases flow behavior.

2. DPF IN DETAIL

Diesel particle filters consist of several segments glued together as shown at the Figure 1.

These segments are made from porous carbon silicon (SiC) material forming a system ofmany channels of the square profile of 1 to 2 millimetres, the length of these channels is thesame as the length of the whole filter.

Figure 1: Diesel particle filter and individuals segments with channels

Individual channels are divided to the clean (closed) channels and the dirty (open)

channels (see Figure 2). Clean and dirty channels are arranged in a chessboard

configuration. Exhaust gases go from the duct in front of particle filter to the individual dirtychannels. Then they pass through the porous wall of the channels leaving almost allparticles at the walls inside the dirty channels. Next, clean gases continue to the cleanchannels and leave the filter by the following duct. Output exhaust flow gases are clean andalmost without particles. Normally, these particle filters have an efficiency about 95%.

Figure 2: Flow situation in the channels

In the course of a working cycle, the filter is filling up in dirty (open) channels with settlingparticles. The engine is producing soot particles, metal particles, oil droplets and unburned

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fuel, too. Thus particles include aluminium, iron, sulphur and other materials, which originatefrom engine and exhaust ducts in front of the particle filter. The particle size is commonly atintervals from 1 micrometer to 100 micrometers, with the majority being soot particles, andonly small quantities of other particles.

Particles travel within the flow field of the exhaust duct and their positions depend on theirvolume and diameter and on the flow regime. Thus in front of the DPF particles can be

spread out in a non-uniform way. In the individual channels of the filter, particles can settledown at different positions depending upon certain conditions also in a non-uniform way.

The loss of pressure between the input and the output of the particle filter is monitored. Afterreaching the maximum permitted level, a signal is sent to the Electronic Control Unit (ECU)and the ECU starts the process of regeneration. This consists of burning the soot particleswhich have settled down in the open channels. Soot particles have self-ignition temperatureabout 550 600C, this temperature is not a common operational temperature, becausediesel engines reach this temperature only by high loads or at maximum speed; therefore theconditions have to be changed. There are two common ways to do this.

One possibility is to raise the combustion temperature by a catalytic converter and using the

injection of some extra additives to the exhaust ducts. The second way is to lower the self-ignition temperature of the soot particles using a noble metals catalyst layer directly on thesurface of the particle filter. This causes self-ignition temperature to decrease to a valuearound 350C 400C.

The driving mode (e.g. city mode, highway mode, frequent starts of cold engine) can affectthe process of filling up the DPF. These modes are important for timing the interval betweenthe individual regenerations. In general, the regeneration-to-regeneration cycle is about400km. The regeneration process must run under specified operational conditions. Theproblem is these conditions (higher loads and temperatures) are not reached in a city mode -thus leaving the filter stacked with the particles and forcing the ECU to switch the engine tothe emergency mode. This is a very unpleasant situation for the driver and the crew, too. In

the course of time, the porous channel walls of the filter become stacked with particles evenimmediately after the regenerations. Thus the filter pressure loss becomes higher andhigher, and by the end of the life time of the filter, regenerations come in very short intervals.The filter loses its functionality, in fact.

The numerical simulation of exhaust gases distribution and the deposition of the particles inthe individual channels of a particle filter may help to understand the flow phenomena indetail and hopefully to help to solve some of the marked problems or prolong the life time ofthe filter or get the functionality better.

3. NUMERICAL MODEL

The numerical model presented is based on detailed geometry, with each of the individualchannels of particle filter modelled. The particle filter generally has the shape of the circle oran oval. An example of the particle filter is showed at the Figure 1. The diameter of thisparticle filter is about 150 millimetres and its length is commonly from 150 to 250 millimetres.This particle filter is created by several segments, these segments consist of very smallchannels, about 1-2mm apart. The thickness of the porous walls between individualchannels is usually from 0.3 to 0.5 millimetres.

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3.1 Numerical model for the exhaust gases flowThe computational model of the whole particle filter would be very complex; therefore wewere modelling only one segment. This segment can be used as a testing case for varioussetups of computational models used in the simulations. The main problem was usingdifferent turbulence models and the definition of the porous walls, which vary between clean(closed) and dirty (open) channels.

The computational model geometry was prepared in the pre-processing software Gambit2.2.30. For the numerical simulation we use a standard mapped hexagonal grid. Thecomputational mesh for one segment is given by approximately 1 200 000 cells. This grid iscreated in the software Gambit 2.2.30, too. You can see the geometry and the boundaryconditions for the numerical simulation at the Figure 3 and Figure 2.

Figure 3: Numerical model for the exhaust gas or air flow

The inlet boundary condition is defined as a mass flow inlet, where the proportional part ofthe total mass flow rate is set. Mass flow rate for the whole particle filter is 80 grams per

second. The computational model is divided to five parts. Figure 3 shows the detail of theinlet part with a chessboard channel configuration, and the segment layout with the individualchannels for the particle separation from diesel engine exhaust gases. The output part issimilar, but the opposite channels are plugged vice versa according to the inlet part. Theoutput boundary condition is defined by a pressure outlet.

The porous walls separating the opened and closed channels are modelled by porous fluidcells. The porous resistance coefficients values are set up in order to match the totalpressure loss for several mass flow values with values known from the measurements andthe publications.

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3.2 Numerical model for soot particles sedimentationDuring the numerical simulation we had some problems with parallel computations on amultiprocessor cluster, (see section 5 for details). Therefore we prepared a second model,which wasnt as large as first model. This model included 16 channels, which werestaggered to the shape of 4x4 channels. The detail of the inlet part of this smallercomputational model is showed at the Figure 4. This model serves also for the numericalsimulations with the soot particles sedimentation in the individual channels of the particle

filter.

The numerical model for the soot particles sedimentation is similar to the first model for thenumerical simulation of exhaust gases flow. In this model we used similar boundaryconditions, too. The numerical model is specialized for the soot particle sedimentation, andtherefore is more detailed. This model has more cells in the cross-area of the segment andalso more cells along the height of the numerical model. The computational mesh for sootparticle sedimentation domain is given by approximately 500 000 cells. The mesh is againcreated by standard mapped hexagonal grid as in the first numerical model.

For particles behaviour in the fluid flow we used the Discrete Phase Model capabilities inFLUENT. Soot particles are treated as spherical object wit the density of carbon. Two

diameters of particle mixture were considered in this first phase of tuning the computationalprocedures: 100 um and 200 um. For particle settling, an unsteady run with time step of0.0004 s is provided in the segregated solver with RNG k-epsilon model of turbulence.

Figure 4: Numerical model for soot particles sedimentation

3.3 UDF for particle sedimentationFor the particle behaviour simulations at the DPF porous walls we use a UDF function. Thissimple function increases the resistance coefficients locally at the places where particlestouch the wall of the dirty channel.

Firstly, a UDF function (DEFINE_DPM_BC) is used for scanning the particle presence at thewall of the porous fluid. If so, an extra User Defined Memory array value is increased for thecorresponding cells. After that, the particle is aborted by returning the PATH_ABORT flag. Inthe next phase, the function of DEFINE_PROFILE type is used for increasing the resistancecoefficient C2 through the cell loop using the values in previously described UDM array. Inaddition, we use these UDFs for particle monitoring. Particle positions in the course of timeare written to an external file for further postprocessing.

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4. RESULTS

These results were computed for the mass flow rate of 80 grams per second for the exhaustgases in the whole particle filter. The mass flow rate is reduced for these numerical modelsproportionally to the cross section surface (inlet) area. A flowing medium is set as ideal-gas,which is very similar to exhaust gas from diesel engine. The numerical simulation is providedby Fluent 6.2.16, but we are ready for transition to newer version 6.3.26.

4.1 Results for flow exhaust gas through segment of particle filterFigure 5 shows the flow field of the axial velocity (z-velocity) along the height of thecomputational model in the open and closed channels. The value of the axial velocity ismonitored in different plane-cuts - shown on the left side of the Figure 5.

Plane-cutis posited near the inlet part of the segment. In the plane-cut we can see thehigher values of the axial velocity are located in the open channels and smaller in closedchannels. The flowing medium is not yet uniformly distributed in all the channels and thesituation is given by chessboard configuration of the inlet. The situation for the plane-cutissimilar but axial velocity starts to grow up slightly in the closed channels. The chessboardconfiguration of the individual channels is presented at the Figure 3.

In the next plane-cuts, andthe axial flow velocity is distributed uniformly in all the cross-section. This condition is valid for the middle flow velocity field but on the edge of thesegment we can see the higher axial velocity values. This situation is probably because ofless closed channels, which are around the open channels.

Plane-cut is posited near the output of the sedimentation part of the segment. The axialvelocity starts to have the higher values in the closed channels of the segment. The plane-cut shows the situation in the outlet part where the flowing medium goes through only theclosed channels.

Figure 5: Flow velocity field along the height of segment at size 15x15 channels

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4.2 Results for the different size of the channels cross-sectionThese results are computed with segment of the 4x4 channels geometry already describedbefore. The geometry and the shape for all variants are similar, but each model has differentsize of the cross-section of the channel. The numerical simulation is provided for sizes ofchannels 1.1, 1.5 and 1.9 millimetres. Figure 6 shows the dependence of the total-pressureand the axial velocity on the size of the cross-section of channels. In the graph on the left,we can see the pressure loss between the inlet and the outlet parts of the segment. From

this graph it is clear that the reduction of the cross-section of channels is increasing thepressure loss of the segment (or the particle filter).

Figure 6: Dependence of the total-pressure and the axial velocity on the channel size

The graph on the right side is describing the course of the axial velocity along the height ofthe computational model. Near the input part of the segment there is a higher axial velocity.This is given by fact the flowing medium isnt uniformly distributed yet in the cross-section ofthe segment as we noticed also in the previous section. Then, the inner segment axialvelocity has reduced to the value of approximately 7.7 m/s. Please note the flow goes fromright to left at the graphs.

4.3 Results for the particle settling simulationsThe graphs at the Figure 7 are showing the course of the total-pressure and the axialvelocity in dependence on the sedimentation time. The basic course for the clean particlefilter is presented by the red curve. Others curves present the pressure loss and the axialvelocity during the soot particle sedimentation process.

Figure 7: Dependence of the total-pressure and axial velocity on the sedimentation time

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In the left graph there is an increase in pressure loss in the input, because there are caughtup soot particles. The soot particle sedimentation at the porous walls creates the higherresistance, here the flowing medium is accelerated. This phenomenon is showed also byblue and orange curves in the graph on the right side of the Figure 7.

The next figure shows the trends in quantity of the soot particle sedimentation at the porouswalls of channels for 5000, 10000 and 18000 time step. The values of the resistance (i.e. the

presence of the particles) on the porous walls are presented; red colour corresponds to themost affected locations. At the Figure 8 we can see the soot particle sedimentation ishappening mostly in the top (inlet) section of the segment, which continues to the directiondown (not showed). This situation is given by accelerating the flowing medium inside thechannel as it is described at the Figure 7.

Figure 8: Particle sedimentation in the course of time

At the Figure 9 there is a visualisation of the three-dimensional flow field by the pathlines andsoot particles positions, which are contained in exhaust gases of diesel engine. Sootparticles are coloured by the particle diameter and the walls of particle filter are coloured byamount of the soot particles sedimentation. The right side of Figure 9 shows a detailed fish-eye view into one of the channels. This view is captured from the transition section betweenthe inlet and the sedimentation parts of the particle filter segment.

Figure 9: The pathlines with soot particles and detailed view into channel

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5. COMPUTATIONAL ISSUES

All the results presented are given by a single processor run in FLUENT 6.2.16 underWindows XP or Debian Linux. For future plans and estimates on how a case of this typeworks on a larger number of processors or machines we would need to use for whole DPFsimulations. For this purpose some benchmarks were done under certain conditions for theflow case of 15x15 channels segment. This case consists of 1.2 million hexagonal cells.

We used two versions of FLUENT, 6.2.16 and 6.3.26 under Linux at machines described inthe Table 2. In addition, partitioning of the case was done manually using several methods.In the next tables and graphs, paxstays for Principal Axes partitioning with 10 merge andsmooth iterations and pre-test; xaxstays for Cartesian X-coordinate partitioning and zaxforPrinciple Z-coordinate. All the cases were bandwidth-reduced except the cases marked origwith default bandwidth and default principle-axes partitioning parameters. Case markedbandwas a single partition case with bandwidth reduced. The partition cut planes are shownat the Figure 10.

Figure 10: 4 partitions for different methods xax, zax, pax

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Table 2: Machines used for benchmark

machine(hostname)

type/brand CPU per node RAM pernode

nodesused

interconnect

ajax SGI Altix 350 8x Intel Itanium21500 MHz

48 GB 1 N/A

orfeus Intel MB based

PC cluster

1x Intel Pentium

4 3200 MHz

1 GB 8 GigaEthernet

manwe SUN Fire X4600 8x dual-coreAMD Opteron885 2600 MHz

64 GB 2 GigaEthernet

skirit Intel MB basedPC cluster

2x dual-core IntelXeon 5160(Woodcrest)3000 MHz

4 GB 8 GigaEthernet

FLUENT 6.2.16 was run with -psmpi option where available. For clusters, -pnmpi or -pnetoption was used. For FLUENT 6.3.26, several MPI options were used for -pethernet option

by setting -mpi option to hp (default), intel, mpich2 and net values. For single machinecomputations, -pethernet option was used except ajax machine using -paltix instead.

In the Table 3 there are computational times in seconds for 100 iterations for used machines,types of partitioning and FLUENT versions. You can see FLUENT 6.2.16 is not suitable forparallel run for these cases at all. The original and zaxpartitioning is generally the worse.

Table 3: Computational times for 100 iterations

ajax orfeus manwe skiritCPU casetype 6.2 6.3 6.2 6.3 6.2 6.3 6.2 6.3

1 orig 3580 3115 2013 1747 1640 1415 1224 943

1 band 3220 2573 2132 1847 1717 1455 1223 951

2 pax 7775 10890 5597 1213 7691 908 3812 621

2 xax 3349 10562 3262 1035 5385 787 1838 601

2 zax 9755 10155 8032 1014 13361 802 6493 541

4 orig 56754 4257 22307 672 39819 488 19872 419

4 pax 3340 12168 4860 828 8167 548 1843 488

4 xax 4963 8553 7338 646 12602 478 2758 429

4 zax 34713 3159 20960 691 34750 493 15479 416

2x2 pax - - - - - 661 - 460

4x1 pax - - - - - - 1268 408

8 pax 2426 480 4418 743 5000 343 - -

8 xax 10087 518 17332 611 - 356 - -8 zax 49563 483 45300 465 - 316 - -

2x4 pax - - - - - 407 3028 1710

4x2 pax - - - - - - 2302 398

8x1 pax - - - - - - 1302 373

FLUENT 6.3.26 is much better than the version it replaces - even for one CPU,computational times are a bit shorter than for 6.2.16. Moreover, except ajax, the parallel runleads to speeding up of the job significantly. Note the 2x2 and 4x1 configurations mean the 2machines by 2 CPU used and 4 machines by one CPU, respectively; similarly for 2x4, 4x2and 8x1 configuration. For FLUENT 6.2.16 the -pnmpi option results are presented; for

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FLUENT 6.3.26, the -mpi=intel results are presented. Some of the results for FLUENT 6.3.26are also showed in the graph at the Figure 11. You can see in general, now the zaxpartitioning is the best - conflicting with results from FLUENT 6.2.16.

The different results for FLUENT versions are probably due to complicated cut planes ofparallel partitions. In the cut plane neighbourhood, there are cells of fluid flow, which arefragmented by cells of porous fluids representing the particle filter porous walls. In many

cases, the FLUENT 6.2.16 parallel run took only by 3% of the CPU machine power, even forcompletely free machine, thus leading to the enormous computational time.

New Intel Woodcrest processors are the most powerful for single CPU or few CPUs runs butthe shortest time (316 s, marked in red) in the benchmark was achieved by an 8 CPUs runon the Sun Fire X4600 machine. As you can see one should provide some tests for such acomplex and fragmented geometry as we use here for DPF segment simulations to achievean excepted run times and speedup.

Figure 11: Computational times for 100 iterations for FLUENT 6.3.26

6. CONCLUSIONS

In this article, we presented the fluid flow simulations in the channels of a segment of aparticle filter. For a smaller segment, we also computed the soot particle sedimentationprocess using the advanced technique of changing the porous walls resistance coefficientsthrough the UDF depending on the particle presence at the porous walls. Results areshowing that the dirty channels are filling up - starting in the inlet part and continuing to thebottom of the filter.

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We would like to continue in advancing the particle sedimentation simulations, including theeffect of the effective channel cross-section reduction due to the soot particle settlementlayers. For this, we would like to use the dynamic mesh technique in FLUENT.

Some measurements are necessary for the result validations - for this, we plan to use theexperimental capabilities of the New Technology Research Centre including the ElectronMicroscopes, element analyzers etc.

With FLUENT 6.3.26 we can also effieciently run parallel computers. This could lead us tothe simulations of the sedimentation processes in the whole DPF filter under defined flow(maybe unsteady) conditions where the non-uniform particle load could appear. We plan toinclude also the regeneration process hence simulating the whole life time of the filter.

ACKNOWLEDGEMENT

This paper is based upon work sponsored by the Ministry of Education of the CzechRepublic under research and development project 1M06031. For using computationalresources, we would like to thank the METACentrum project under the CESNET institute.

REFERENCES

[1] Lvika David : Tvarov optimalizace DPF filtru s ohledem na proudn spalin. Psemnprce ke sttn doktorsk zkouce, ZU v Plzni, prosinec 2006, Plze.

[2] Fluent 6 Users Guide, 2002.[3] Fabio Sbrizzai, Paolo Faraldi and Alfredo Soldati : Appraisal of three-dimensional

numerical simulation for sub-micron particle deposition in a micro-porous ceramic filter.In Chemical Engineering Science, Volume 60, Issue 23, December 2005, Pages 6551-6563.

[4] Guido Saracco, Nunzio Russo, Michele Ambrogio, Claudio Badini, Vito Specchia :

Diesel particulate abatement via catalytic traps. In Catalysis Today, 60, 2000, 33-41[5] Guido Saracco, Claudio Badini, Vito Specchia: Catalytic traps for diesel particulate

control,Dipartimento di Scienza dei Materiali ed Ingengeria Chimica, Politecnico diTorino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

[6] Lamacchia, S.; Pidria, M.F.; Faraldi, P.; Corrias, S.: Detection of ash and particulatedistribution in diesel particulate filters through X-ray computed tomography. In CentroRicerche FIAT S.C.p.A., Italy.

[7] METACentrum project home page http://meta.cesnet.cz[8] New Technologies Research Centre home page http://www.ntc.zcu.cz

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