Diesel particulate filter pressure drop Part 1: modelling and experimental validation

http://jer.sagepub.com/International Journal of Engine Research

http://jer.sagepub.com/content/5/2/149The online version of this article can be found at:

DOI: 10.1243/146808704773564550

2004 5: 149International Journal of Engine ResearchO. A. Haralampous, I. P. Kandylas, G. C. Koltsakis and Z. C. Samaras

Diesel particulate filter pressure drop Part 1: Modelling and experimental validation

Published by:

http://www.sagepublications.com

On behalf of:

Institution of Mechanical Engineers

can be found at:International Journal of Engine ResearchAdditional services and information for

http://jer.sagepub.com/cgi/alertsEmail Alerts:

http://jer.sagepub.com/subscriptionsSubscriptions:

http://www.sagepub.com/journalsReprints.navReprints:

http://www.sagepub.com/journalsPermissions.navPermissions:

http://jer.sagepub.com/content/5/2/149.refs.htmlCitations:

What is This?

- Apr 1, 2004Version of Record >>

by guest on September 6, 2012jer.sagepub.comDownloaded from

http://jer.sagepub.com/

http://jer.sagepub.com/content/5/2/149

http://www.sagepublications.com

http://www.imeche.org/home

http://jer.sagepub.com/cgi/alerts

http://jer.sagepub.com/subscriptions

http://www.sagepub.com/journalsReprints.nav

http://www.sagepub.com/journalsPermissions.nav

http://jer.sagepub.com/content/5/2/149.refs.html

http://jer.sagepub.com/content/5/2/149.full.pdf

http://online.sagepub.com/site/sphelp/vorhelp.xhtml


Diesel particulate filter pressure dropPart 1: modelling and experimentalvalidation

O A Haralampous, I P Kandylas, G C Koltsakis

and Z C Samaras

Laboratory of Applied Thermodynamics,

Aristotle University Thessaloniki, Greece

Accepted 29 September 2003

Abstract: Pressure drop modelling is a subject of special Due to the fuel penalty resulting from the increased

backpressure of the loaded filter, it is necessaryinterest for the design and control of diesel particulate

for the filter to be regenerated. This regenerationfilters. Based on previous experience, an improved pressure

involves oxidation of the accumulated particulate,drop model is presented. Special emphasis is given on the

which may be periodical or continuous, duringsoot permeability properties and its dependence on tem-

regular engine operation. The initiation and controlperature and pressure. With the assumption of uniform

of the regeneration process is the main issue in dieselwall flow distribution throughout the channel length, it

filter technology, as regeneration should be as safeis possible to derive an analytic expression for pressure

as possible to avoid excessive thermal stresses anddrop calculation. The main difference with previously pro-

failure of the filter material. Regeneration systemsposed analytic expressions lies in the inclusion of gas

are based on the use of catalysts (catalytic coatingsdensity dependence on local pressure, which necessitates

or fuel-borne catalysts) to lower the reaction tem-an iterative calculation procedure. The importance of this

perature and/or engine measures (e.g. post-injection)improvement is illustrated parametrically. The new model

or electrical heating to increase the exhaust gasis validated against experimental data on an engine bench,

temperature.using a double filter configuration to ensure constant filter

Understanding the flow phenomena contributingsoot loading throughout the test.to the pressure drop in particulate filters is of great

importance for the emissions engineer. On the oneKey words: diesel engine, after-treatment technology,hand, filter design should target the minimization ofexhaust emissions, mathematical modelling, pressure droppressure drop in real-world conditions by careful

selection of filter geometry (volume, cell density,

wall thickness, porosity). On the other hand, the1. Introductioninitiation and control of the regeneration process by

Particulate filtration in the exhaust system of the engine management should take into account

diesel engines is increasingly gaining in importance the mass of accumulated soot in the filter, which is

for both light-duty and heavy-duty applications. commonly assessed by interpreting the pressure drop

Passenger cars equipped with diesel particulate measurement on-board. Furthermore, pressure drop

filters (DPFs) appeared in the market as a means to measurements are expected to support the task of

achieve the low particulate emission standards on-board diagnosis of a filter structural failure [1].

required in Europe [1]. The particulate filter tech- Mathematical models have been widely employed

nology is also considered the most promising to describe the filter pressure drop as a function of

solution towards attaining the emission standards of filter geometry (volume, cell density, wall thickness),

heavy-duty vehicles [2 ± 5]. operating conditions (flowrate, temperature) and the

Diesel filters show close to 100 per cent filtration accumulated soot mass. These models are either

based on analytical functions [6, 7] or on the solutionefficiencies for the solid part of emitted particulates.

149Int. J. Engine Res. ä Vol. 5 ä No. 2JER 02202 ä © 2004 ä IMechE



O A Haralampous, I P Kandylas, G C Koltsakis and Z C Samaras

of mass and momentum balances in the filter channel non-reacting conditions. Therefore, only the balance

equations for mass and momentum of the one-[8, 9]. The former approach is definitely simpler and

allows straightforward application for on-board esti- dimensional model will be employed. The con-

servation of energy and the reaction rate equationsmation of the accumulated soot. The latter approach

requires a computationally demanding solution of a will not be included.

The mass balance equation for gas flowing in thesingle-channel model. The possible advantages of

employing such a complicated model are discussed inlet and outlet channels is given as

in this paper.

Validation of pressure drop models is not an qqz

(rivi)=( 1)iA 4

DiB rwvw (1)obvious task, mainly due to the difficulty of measuring

exactly the mass of accumulated soot in the filter.

Since the diesel engine continuously emits soot, it is where the subscript i identifies regions 1 (inletnot possible to measure the pressure drop under channel) and 2 (outlet channel). The momentumdifferent flowrate and temperature conditions with balance of exhaust gas in the inlet and outleta constant soot mass. A common approach used to channels can be formulated as below, taking intoevaluate the pressure drop of particulate filters is account the mass loss/gain through the porous wallcold flow testing using air at constant temperature and the flow friction in the axial direction z:(usually room temperature) as the flowing gas

[10 ± 12]. qpi

qz+

qqz

(riv2i )=

a 1mvi

D2(2)In the present work, the problem is overcome by

using two particulate filters in series. The first is

responsible for collecting practically all soot emittedThe right-hand side of this expression is based on

during the test. The second filter is used for pressurethe assumption of laminar flow conditions for the

drop measurements under variable flowrates andchannel flow, which is actually the case in usual

temperatures. The accumulated soot mass is measuredoperating conditions.

by dismantling and weighing the second filter.To solve the velocity and pressure distribution in

the inlet and outlet channels, it is necessary to know

the pressure drop law for the flow through the soot

layer deposit and the porous filter wall. In the

original model of Bissett [13], the soot porosity was2. One-dimensional Pressure Drop Modelconsidered negligible and thus the soot layer thick-

The prediction of filter pressure drop requires ness was assumed to be negligible compared to the

a mathematical description of flow phenomena wall thickness and the channel diameter. This allowed

including flow distribution in the channels, through the use of a constant velocity through the wall.the soot layer and filter walls, as well as flow Moreover, the soot permeability was considered to

entrance and exit effects. A one-dimensional model, be constant. The pressure drop calculation was based

which could sufficiently describe the velocity and on the Darcy law, neglecting the inertial terms

pressure variations inside a single-filter channel, was and applying a correction for initial pressure drop

originally presented by Bissett [13]. The model relies build-up due to initial blocking of the open wall

on the transient solution of the mass, momentum pores.

and energy balances in a single channel, with the Since then, numerous studies have shown that soot

following major assumptions: porosity in actual conditions may be of the order of

90 per cent and therefore the soot layer thickness is

1. All filter channels behave in the same way. This large enough to cause variations in wall velocities in

presumes adiabatic conditions and uniform flow the flow direction (Fig. 1). On the other hand, the

distribution at the filter entrance. soot permeability dependence on temperature has

2. Laminar axial flow inside channels. proven to be far from being negligible in real-world

3. Pressure drop according to Darcy’s law for flow conditions [8, 10, 14]. The contribution of inertial

across the soot layer and substrate. pressure drop terms for the soot layer has also

been questionable. Taking the above into account, a

comprehensive approach to model the soot layerFor the purpose of pressure drop modelling, the

focus here will be on steady state, isothermal and pressure drop is now described.

150 Int. J. Engine Res. ä Vol. 5 ä No. 2JER 02202 ä © 2004 ä IMechE



Diesel particulate filter pressure drop. Part 1

dependence. In the present study, the following

expression proposed in reference [15] is used:

kp=k0A1+C4

p0

pmS T

MgB (8)

This formula expresses the dependency of soot

permeability on local temperature and pressure.

Two parameters, namely k0 and C4 , present in this

expression have to be estimated by experimental

data on soot properties. This procedure is discussed

in the next chapter.

Equation (5) can be integrated over x to provide

the pressure drop over the soot layer thickness,Fig. 1 Schematic of gas flow through the soot layer and filter

taking into account equations (6) to (8):wall.

Dpsoot=T

MgpÅ CmDrwvw

2kp(pÅ )lnA D

D 2wB+bDw(rwvw)2

D 2w DWith the definitions shown in Fig. 1, the soot layer

deposit shape is trapezoidal. Its width is given by(9)

b(x)=D 2(w x) (3)According to equation (8), kp is a function of local

pressure. Considering that the pressure is reducedThe particulate layer thickness w can be calculated

in the flow direction x through the soot layer,from

the soot permeability should be a function of x.

Introducing this dependence in the analytic solutionw=

1

2AD SD2 2mp

rpVtrap ×1550 cpsiB (4)would extremely complicate the solution. Instead, it

is possible to calculate the soot permeability at awhere Vtrap is the `effective’ volume of the trap,

pressure equal to the mean value of the inlet andexcluding any cement volume and the plug length

outlet pressures:at the inlet and outlet of the filter. Starting from the

elementary Darcy pressure drop law, including thepÅ =

p1+p2

2(10)

inertial (Forchheimer) term, the differential pressure

drop over dx will beThe authors found that the error due to this simpli-

fication is less than 1 per cent over a wide range ofdp

dx=

mv(x)

kp

+br(x)v2(x) (5)typical filter configurations and flowrates.

The pressure loss through the porous filter wallAlthough the mass flowrate is steady throughout the

for typical filters and operating conditions is com-soot layer, the gas velocity varies along the soot layer

paratively small. This allows the assumption of con-due to changes in gas density and flow area, as

stant flow velocity through the wall. Moreover, theshown by the continuity equation

inertial (Forchheimer) term can be neglected without

significant error [16] and the pressure drop can bev(x)=

rwvwD

r(x)b(x)(6)

described by the Darcy law:

Moreover, the gas density along the soot layer is aDpwall=

mvw

ks

ws (11)function of the local pressure. With the realistic

assumption of ideal gas, the density can be expressedTherefore the pressure drop between the inlet and

asoutlet channels is

r(x)=p(x)Mg

T(7) p1 p2=Dpsoot+Dpwall (12)

2.1 Contraction/expension pressure lossesThe permeability of the particulate deposit is

dependent on the gas mean free path due to slip The chequered face of the filter causes a sudden

contraction of the flow at the inlet and a suddenphenomena [8]. Few experimental works are avail-

able in the literature to provide information on this expansion at the outlet. These pressure losses can be





assessed using the following formulae respectively able to flow. On the other hand, in the case of the

clean filter, the channel velocity profiles deviate sub-[17]:

stantially from linear, while the flow through the

wall is far from being uniform. Thus, the assumptionDpcontraction = C1.1 0.4(D 2w)2

2(D+ww)2DMg(p1v21)z=0

2 Tof uniform wall velocity is realistic for moderately

and heavily loaded filters.(13)

The pressure variation inside the inlet and outlet

channels was also studied for the same conditions.Dpexpansion =C1 D2

2(D+ww )2D2 Mg(p2v22)z=L

2 T(14)

Figure 3a depicts the absolute pressure inside the

inlet channel for several soot loadings. The pressureThe mass and momentum balance equations canin the outlet channel is shown in Fig. 3b. When uni-be solved to compute the velocity v1(z), v2(z), theform wall flow conditions prevail (moderately andpressure field p1 (z), p2(z) in the inlet and outletheavily loaded filters), the pressure field in the outletchannels, as well as the velocity through the wallchannel is almost independent of the soot loading.vw (z) with given gas flowrate and temperature. The

pressure at the exit of the outlet channel is set equal

to ambient. The axial gas velocity is set to zero for

the last node of the inlet channel and at the first node 3. One-dimensional Pressure Drop Modelof the outlet channel. An iterative solution procedure Validationis employed to calculate the velocity and pressure

field, as described in reference [18]. This solution3.1 Experimental set-up

method offers very low computational time. The experiments were carried out on a direct injectionThe model was applied for the case of an SiC filter diesel engine installed on an engine dynamometer

with a 200 cpsi cell density. More details about test bench. The engine displacement is 1.9 l andthe geometrical properties of the filter are given in the maximum power output is 66 kW. The engineTable 1. The exhaust gas flowrate selected for this is turbocharged, intercooled and uses exhaust gasanalysis is 0.1 kg/s and the temperature is 200 °C. recirculation (EGR). The original oxidation catalyst

Figures 2a and b present the computed axial velocity was removed from the exhaust system of the engineprofiles in the inlet and outlet filter channels at and two particulate filters were installed in series, asvarious soot loadings. Figure 2c presents the com- shown in Fig. 4. The geometric and thermophysicalputed velocity of the gas through the filter wall. It is properties of the two particulate filters are given inclear that for the case of a heavily loaded filter (8 g/l) Table 1.the gas velocity decreases and increases almost The first filter in series is used to filter out thelinearly in the inlet and outlet channels respectively, particulates emitted during a single test. In this way,while the wall velocity remains uniform throughout it is possible to carry out measurements in the secondthe whole length of the trap. In a moderately loaded filter at steady soot loading. The second filter, intrap (2 g/l), the channel velocity profiles are very addition to the standard canning material, was alsoclose to linear, while the wall velocity is close to uni- heavily insulated externally in order to approximateform. Near the entrance of the loaded channels, the adiabatic operating conditions. Dedicated measure-flow accelerates slightly in the beginning of the inlet ments showed that the maximum temperaturechannel during the transition from the clear region difference in the radial direction during the tests did(due to the plugs of the outlet channel) to the loaded not exceed 5 °C.region, where a smaller cross-sectional area is avail- The intake air flow was measured by a hot-wire

anemometer. This measurement along with the air±

fuel ratio measured by a wide-range sensor installedFilter material Silicon carbide in the exhaust pipe was used to calculate the exhaustCell density 200 cpsi

mass flowrate. The pressure drop was continuouslyWall thickness 0.38 mmDiameter 144 mm monitored by pressure transducers installed upstreamLength 152 mm

and downstream of the filter while 1 mm thick thermo-Plug length 5 mmWall density 1800 kg/m3

couples measured the exhaust gas temperature atWall permeability 1.2×10 12 m2

different positions in the exhaust system, as shown

in Fig. 4. All the measured data were recorded at aTable 1 Geometrical data and properties of thefilter used in this study. 1 Hz acquisition rate.





Fig. 2 Computed velocity profiles for different soot loadings: (a) inlet channel, (b) outlet channel, (c) wall.

3.2 Model validation measurements After completion of the loading protocol the filter

is weighed and the first filter is installed. The engineTo load the second filter with a prescribed amount

of soot, the first filter was removed and the engine operates at various steady state operating points,

varying the engine speed and torque in such a wayoperated steady state at 4000 r/min and 40 N m

torque. The filter temperature during the loading as to ensure that the filter temperature remains con-

stant while the flowrate varies between differentexperiment was between 320 and 350 °C.





Fig. 3 Computed pressure profiles for different soot loadings: (a) inlet channel, (b) outlet channel.

Fig. 4 Experimental set-up.

steady state points. Figure 5 presents the gas flow- 200 °C exhaust gas temperature and 0.024 kg/s mass

flowrate. As soon as stabilized engine and gas con-rate, the temperature and the filter pressure drop

recordings during a typical experiment with 9.2 g/l ditions are attained, the engine is set to a different

point with the same exhaust gas temperature andsoot mass. Initially an engine point is selected with





Fig. 5 Temperature, flowrate and pressure drop recordings during a typical pressure drop experiment with 9.2 g/l soot mass.

different mass flowrates. The same procedure is 4. Analytical Approximationrepeated with operating points that result in filter

As mentioned in section 1, analytical solutions fortemperatures of 300 and 400 °C. The above protocolthe pressure drop in the case of an isothermal, cleanwas repeated four times using soot loadings from 0.2filter with constant gas density and a negligibleto 9.2 g/l. The soot loading in each case was esti-inertial term contribution have been derived [19].mated by dismantling and weighing the filters beforeEven with the assumption of constant gas density,and after each test.the analytical expression is particularly cumbersome.The results obtained for each soot loading are pre-Simplified analytical formulae have also been pro-sented in Fig. 6 in the form of measured pressureposed. The validity of the simplified formula wasdrop versus mass flowrate, using the filter temper-established by showing that the fit to the originalature as a parameter. The lines in these plots presentanalytical expression is generally good [19].the pressure drop for the respective conditions as

The above studies claimed that an analyticalcomputed by the one-dimensional model presentedpressure drop formula could be extended to includeabove. The computed results were obtained afterthe effect of accumulated soot by adding thefitting the following parameters: soot permeabilityrespective pressure drop term. The soot permeabilityk0 , soot slip correction factor C4 and soot inertialwas expressed as a function of the mean free pathpressure drop coefficient b, which were kept thelength and the Peclet number during the soot loadingsame for all simulations. From these results it ismode [7]. The analytical expression derived con-shown that the one-dimensional model is able tosiders uniform gas properties throughout the filter.predict the dependence of the pressure drop as aHowever, in the case of heavily soot-loaded filters,function of soot loading, mass flowrate and temper-the absolute pressure in the inlet channel couldature for the filter tested, after fitting the relatedbe substantially different compared to the outletpressure drop parameters.channel pressure. This will in turn affect the gasAn additional type of experiment was conducteddensity and the mean free path length, which willto validate the pressure drop model at room tem-also vary. In the following, an improved analyticalperature conditions. The filter was mounted in theexpression will be developed, which is able toinlet air duct of the engine. The engine was operatedaccount for the pressure-dependent gas propertiesat various steady state operating points to obtain avariation. The importance of this improvement willlarge range of intake flow rates and the pressurebe discussed with comparative results.drop was measured along the filter. The results are

presented in Fig. 7 for two soot loadings. The com-

parison with the computed pressure drop validates the 4.1 Soot layer pressure drop

accuracy of the model, even at ambient temperature With the assumption of uniform wall velocity and

using the index w for the conditions at the wall-outletconditions.





Fig. 6 (continued over)

channel interface, the mass balance gives In equation (17), the mean pressure pÅ is not known

beforehand. This means that an iterative procedure

is necessary when applying this equation.rwvw=

mÇ g

Af

(15)

4.2 Wall pressure dropThe filtration area Af appearing in the above The overall contribution of the porous wall on theequations is defined as pressure drop for uniform wall velocity is given by

Af=2Vtrap D×1550 cpsi (16)Dpwall=

T

Mgp2AmwwmÇ

ksAf B (18)

The soot layer pressure drop contribution can be

calculated from equations (9) and (15):4.3 Channel flow pressure drop

With the assumption of uniform wall velocity,

Dpsoot=T

MgpÅ C mDmÇ

2kp(pÅ )Af

lnA D

D 2wB+bDwmÇ 2

A2f (D 2w)D the axial velocities in the inlet and outlet channels

are readily computed from simple mass balances.

Therefore, it is possible to compute the pressure drop(17)





Fig. 6 Measured and one-dimensional model computed pressure drop versus flowrate at different temperatures. Soot loadings:

(a) 0.2g/l, (b) 5.5 g/l, (c) 8.0 g/l and (d) 9.2g/l.

Fig. 7 Measured and one-dimensional model computed pressure drop versus flowrate at room temperature. Soot loadings: 0.5

and 8.6 g/l.





due to the flow friction in the channels: To assess the importance of accounting for pressure-

dependent gas properties, the same figure presents

the results of the analytical expression in the case ofDpchannel=a1m TLmÇ

3MgN C 1

p2D4+

1

p1(D 2w)4D (19)assuming uniform gas properties throughout the

filter, corresponding to ambient pressure. In this casewhere N denotes the total number of open channels the deviation compared to the one-dimensionaland can be assessed with the following formula: model can be quite significant, especially for heavily

loaded filters.

To illustrate the significance of the analyticalN=Vtrap ×1550 cpsi

2L(20)

expression improvement, Fig. 9 presents the measured

pressure drop versus flowrate compared with theAgain, this equation requires an iterative procedure

respective calculations based on the analyticalsince the unknown pressure is included in the

expression. The same calculations with the assump-expression.

tion of uniform gas properties are also included in

the same graph. Neglecting the dependence of the gas

properties on pressure, the error could be obvious,4.4 Contraction/expansion pressure losses

especially at high flowrates and temperatures.With a simple manipulation of equations (13) and

(14), the contraction and expansion losses can be

expressed using the exhaust mass flowrate as a4.6 Pressure drop contributions

parameter:It is interesting to study the relative contribution of

each of the pressure drop mechanisms describedDpcontractionabove, based on the analytical expressions derived.

Figure 10a shows the computed dependence of these=C1.1 0.4(D 2w)2

2(D+ww)2D TmÇ 2

2p1MgN2(D 2w)2 contributions on soot loading for the filter described

in Table 1. The results refer to a temperature of 300 °C(21)

and a mass flowrate of 0.05 kg/s.

In the case of a completely clean filter, the pressureDpexpansion =C1

D2

2(D+ww )2D2 TmÇ 2

2p2MgN2D2(22) drop due to friction losses in the channel axial

flow are more than 50 per cent of the total. The

wall flow pressure drop accounts for about 30 perThe total trap pressure drop is the sum of thecent. The contraction end expansion pressure lossindividual terms previously explained:contributions are of minor importance.

For soot loadings exceeding 1 g/l, the contributionDp=Dpcontraction +Dpchannel+Dpsoot+Dpwall

of the soot layer becomes dominant. The channel+Dpexpansion (23)

flow still accounts for about 10 per cent at soot load-

ings up to 20 g/l. At unusually high soot loadings

(>20 g/l) the free-flow channel diameter becomes4.5 Comparisons between the one-dimensional model and

very small and the channel flow pressure loss contri-analytic solutions

bution starts to increase significantly. The wall flowThe accuracy of the analytical expression was

pressure drop is of course independent of soot load-initially evaluated by comparing its results with the

ing; therefore, its percentile contribution steadilymore comprehensive one-dimensional model as a

decreases with soot loading. The contraction pressurefunction of soot loading. The calculation was done

losses increase with soot loading as absolutefor the filter described in Table 1, assuming a flow-

magnitude due to the open frontal area decrease.rate of 0.1 kg/s and a temperature of 200 °C. It is

Figure 10b presents the same results obtained withapparent from Fig. 8a that the analytical approxi-

a lower cell density filter (100 cpsi/0.43mm wallmation [equation (23)] yields almost identical results

thickness), keeping all other parameters the same.with the one-dimensional model. A small deviation

Interestingly, compared to the 200 cpsi filter theof the order of 3 per cent occurs in the case of the

channel flow pressure loss is much less importantclean filter, as shown in Fig. 8b. This deviation is

in both clean and loaded filters. The wall flow isapparently due to the fact that the assumption of

responsible for more than 60 per cent of the totaluniform wall velocity is not accurate in this case, as

discussed above. pressure drop in the clean filter. However, the soot





Fig. 8 Comparison between one dimensional model and approximate analytical expression. (a) Pressure drop versus soot mass,

(b) percentile deviation of analytical expression. Temperature, 200 °C; flowrate, 0.1 kg/s.

Fig. 9 Pressure drop versus flowrate at different temperatures for a soot loading of 9.2 g/l. Markers represent measured data; thick

line, analytical expression; dotted line, analytical expression with uniform gas properties.





Fig. 10 Computed pressure drop contributions as a function of soot loading: (a) 200 cpsi/0.38 mm, (b) 100 cpsi/0.43 mm.

layer contribution accounts for more than 90 per cent the full range of engine operating conditions. The

innovative dual-filter configuration employed wasof the total pressure loss when the soot loading is

larger than 3 g/l. necessary to ensure constant filter soot loading

throughout the test procedure.

Finally, the possibility of deriving a more practical

analytical expression for the pressure drop was5 Conclusionsexamined. Indeed, with the assumption of uniform

In this first part of the present paper, the mass and wall velocity, it is relatively simple to derive such an

momentum balance governing the flow phenomena analytical expression, which correlates excellently

in the inlet and outlet channels of a particulate with the experimental and the one-dimensional

filter were solved. Special focus was given on the model results. It was shown that the assumption of

dependence of soot permeability on temperature and a uniform wall velocity is very close to reality for

pressure. For the first time, the effect of non-uniform moderately and heavily loaded filters. The inclusion

gas properties due to significant pressure variations of pressure-dependent gas properties in the present

in the filter was addressed. analytical expression was proven to be necessary.

The independent parameters of the improved Neglect of this effect could yield an error of the order

pressure drop model referring to the permeability of of 10 per cent in terms of pressure drop predictions.

the soot layer and wall were determined based on In the second part of this work, pressure drop

an extensive set of experimental data. The experi- modelling and the analytical expression derived

mental set-up designed especially for this validation here will be applied to solve the so-called inverse’

problem, namely that of calculating the soot mass infacilitated the pressure drop measurement under





the filter based on the flowrate, temperature and s solid, ceramic substrate

w wall-outlet channel interfacepressure drop recordings. This approach could be

very valuable for a number of applications, including

regeneration control and on-board diagnostics.Acknowledgements

The authors gratefully acknowledge the financial

support and useful contributions to this work ofNotation

NGK Insulators Limited. Special thanks also go to

Dr P. Pistikopoulos and Mr A. Tzilvelis for theirAf filtration area (m2 )

valuable assistance in carrying out the experi-b particulate layer width (m)

mental work. The financial assistance of the Greekcpsi cells per square inch=cell density

Scholarship Foundation (IKY) is also acknowledged.C4 slip correction factor

[ms/(kg mole T)1/2 ]

D hydraulic diameter of the clean channel (m) Referenceskp apparent permeability of the particulate

layer (m2) 1 Salvat, O., Marez, P. and Belot, G. Passenger carserial application of a particulate filter system on aks permeability of the ceramic substrate (m2)common rail direct injection diesel engine. SAE Paperk0 permeability of the particulate layer (m2)2000-01-0473, 2000.

L filter length (m)2 Khair, M., Lemair, J. and Fischer, S. Achieving

m mass (kg) heavy-duty diesel NOx/PM levels below the EPA2002 standardsÐ an integrated solution. SAE PaperM molecular weight (kg/mole)2000-01-0187, 2000.N total number of open channels (cells)

3 Chandler, G. R., Cooper, B. J., Harris, J. P., Thoss, J. E.,p pressure (Pa) UusimaÈ ki, A., Walker, A. P. and Warren, J. P. An

integrated SCR and continuously regenerating trappÅ mean pressure of the inlet and outletsystem to meet future NOx and PM legislation. SAEchannels (Pa)Paper 2000-01-0188, 2000.

p0 reference pressure for apparent4 LuÈ ders, H., Stommel, P. and Geckler, S. Diesel exhaust

permeability calculations (103 250 Pa) treatmentÐ new approaches to ultra low emissiondiesel vehicles. SAE Paper 1999-01-0108, 1999.Dp backpressure (Pa)

5 Zelenka, P., Egert, M. and Cartellieri, W. Ways to meetuniversal gas constant (J/mole K)future emission standards with diesel engine powered

t time (s) sport utility vehicles. SAE Paper 2000-01-0181, 2000.6 Ohno, K., Shimato, K., Taoka, N., Santae, H.,T temperature (K)

Ninomiya, T. and Komori, T. Characterization ofv velocity (m/s)SiC± DPF for passenger car. SAE Paper 2000-01-0185,

Vtrap effective trap volume (m3 ) 2000.w particulate layer thickness (m) 7 Konstandopoulos, A. G., Skaperdas, E. and Masoudi, M.

Microstructural properties of soot deposits in dieselws channel wall thickness (m)particulate traps. SAE Paper 2002-01-1015, 2002.

z axial distance (m)8 Versaevel, P., Colas, H., Rigaudeau, C., Noirot, R.,

Koltsakis, G. C. and Stamatelos, A. M. Some empiricala 1 constant in channel pressure drop observations on diesel particulate filter modeling and

comparison between simulations and experiments. SAEcorrelationPaper 2000-01-0477, 2000.b Forchheimer term coefficient (m 1)

9 Opris, C. N. and Johnson, J. H. A 2-D computationall thermal conductivity (W/m K) model describing the flow and filtration characteristics

of a ceramic diesel particulate trap. SAE Paper 980545,m exhaust gas viscosity (kg/ms)1998.r exhaust gas density (kg/m3)

10 Mogaka, Z., Wong, V. and Shaded, S. Performance andregeneration characteristics of a cellular ceramic dieselparticulate trap. SAE Paper 820272, 1982.

11 Sorenson, S., Hoj, J. and Stobbe, P. Flow characteristicsSubscripts

of SiC diesel particulate filter materials. SAE Paperc carbon 940236, 1994.

12 Hashimoto, S., Miyairi, Y., Hamanaka, T., Matsubara,R.,g exhaust gasHarada, T. and Miwa, S. SiC and cordierite dieseli space node index (1= inlet channel,particulate filters designed for low pressure drop and

2=outlet channel) catalyzed, uncatalyzed systems. SAE Paper 2002-01-0322, 2002.p particulate layer





13 Bissett, E. J. Mathematical model of the thermal 16 Konstandopoulos, A. G., Skaperdas, E. and Masoudi, M.Inertial contributions to the pressure drop of dieselregeneration of a wall-flow monolith diesel particulate

filter. Chem. Engng Sci., 1984, 39, 1233± 1244. particulate filters. SAE Paper 2001-01-0909, 2001.17 VDI-Waermeatlas, Vol. 6, 1992 (VDI-Verlag, Duesseldorf,14 Pattas, K. N., Stamatelos, A. M., Koltsakis, G. C.,

Kandylas, I. P. and Mustel, W. Computer aided Germany).18 Koltsakis, G. C. and Stamatelos, A. M. Modes ofengineering in the design of catalytically assisted trap

systems. SAE Paper 970472, 1997. catalytic regeneration in diesel particulate filters. Ind.Engng Chem. Res., 1997, 36, 4255± 4265.15 Pulkrabek, W. W. and Ibele, W. E. The effect

of temperature on the permeability of a porous 19 Konstandopoulos, A. G. and Johnson, H. J. Wall-flowparticulate filters Ð their pressure drop and collectionmaterial. Int. J. Heat and Mass Transfer, 1987, 30(6),

1103± 1109. efficiency. SAE Paper 890405, 1989.




Diesel particulate filter pressure drop Part 1: modelling and experimental validation

Documents

Transcript of Diesel particulate filter pressure drop Part 1: modelling and experimental validation