Modeling and Interpreting the Observed Effects of Ash on
Diesel Particulate Filter Performance and Regeneration
By
Yujun Wang
1,MASSACHUSETTS INS
OF TECHNOLOGy
B.S., Automotive Engineering
Tsinghua University, 2005
MAY 0 8 201
S.M., Mechanical Engineering
LIBRARIES
Beijing Jiaotong University, 2008
Submitted to the Department of Mechanical Engineering in Partial Fulfillment of the
Requirements for the Degree of
DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2014
© 2014 Massachusetts Institute of Technology
All rights reserved.
Signature of Author:
V
Departmen of Mechanical Engineering
January 15, 2014
Certified by:
/
Wai K. Cheng
Professor of Mechanical Engineering
Committee Chair
Certified by:
Principal Re arch Scientist and I
Victor W. Wong
turer in Mechanical Engineering
Thesis Supervisor
Accepted by:
David Hardt
Chairman, Department Committee on Graduate Students
I
E.
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2
Modeling and Interpreting the Observed Effects of Ash on
Diesel Particulate Filter Performance and Regeneration
by
Yujun Wang
Submitted to the Department of Mechanical Engineering on January 15, 2014 in Partial
Fulfillment of the Requirements for the Degree of
DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING
ABSTRACT
Diesel particulate filters (DPF) are devices that physically capture diesel particulates to
prevent their release to the atmosphere. Diesel particulate filters have seen widespread
use in on- and off-road applications as an effective means for meeting increasingly
stringent particle emissions regulations. Although the soot deposit can be removed by
regeneration, the incombustible material - ash, primarily derived from metallic additives
in the engine lubricant, accumulates in the DPF channels with the increasing vehicle
mileage or equivalent running hours. Ash accumulation inside filter increases the flow
restriction and reduces the filter soot storage capacity, which results in higher filter
regeneration frequencies and larger engine fuel penalty.
Combined with experimental observations, DPF models are built to investigate the
fundamental mechanisms of DPF aging process. The DPF soot and ash loading model,
based on porous media filtration theory, is applied to understand the soot deposition
across the substrate wall with soot and ash cake layer formation. DPF models are also
used to investigate the process of ash transport and catalyst deactivation with increasing
ash load level. DPF ash aging is found to have negative effect on passive regeneration
due to the catalyst deactivation and diffusion resistance of ash cake layer. Besides, at
given amount of ash load, the effects of ash spatial distribution on DPF performance are
studied via simulation. It is found that the ash end plug has significant influences on DPF
pressure drop while ash radial and axial distributions have minor effects. At known ash
and substrate property, DPF performance can be optimized according the sensitivity map
developed from this study.
DPF model is beneficial to interpret the experimental observations and it is applied to
predict the effects of certain factors, like flow rate and deposit level, on DPF performance.
At the same time, modeling results are useful in optimizing the design of the combined
engine-aftertreatment-lubricant system for future diesel engines and in understanding the
requirements for robust aftertreatment systems.
Thesis Supervisor: Victor W. Wong
Title: Principal Research Scientist and Lecturer in Mechanical Engineering
3
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4
ACKNOWLEDGEMENTS
My time at MIT has afforded me a multitude of opportunities to grow and develop on a
number of levels. I am extremely grateful for having such a memorable and rewarding
experience.
I would like to extend my sincerest thanks to my thesis advisor, Dr. Victor Wong, for his
guidance in my research and for his patience, motivation, and knowledge. Aside from
learning to conduct scientific research, Dr. Wong has helped me to develop the ability to
critically analyze the final results and effectively present them. Additionally, I would also
like to acknowledge Prof. Wai K. Cheng and Prof. Bill Green for their advice as members
of my thesis committee.
This project would not have been possible without the support of the MIT Consortium to
Optimize Lubricant and Diesel Engines for Robust Emission Aftertreatment Systems. I
would like to thank all of the current and past consortium members for not only funding
this work, but for providing stimulating discussions and for their helpful advice during
our consortium meetings.
Many thanks also go to the experimental group working for the consortium. Dr. Alex
Sappok and Dr. Carl Justin Kamp provide me a lot of fundamental experimental data and
give me many important suggestions in DPF modeling. I would also like to thank all of
the students in the laboratory who have made my time enjoyable.
Most of all I would like to thank my family for all of their support and the inspiration
they have provided me with every step of the way. I am especially grateful to my parents
for the immerse love they giving to me. I am also extremely blessed to have the loving
support of my wife, Ting, whose patience, encouragement, and support has made my
time here at MIT that much happier. I also would like to thank my little son for the joys
he brings to me every day.
5
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6
TABLE OF CONTENTS
ABSTRACT........................................................................................................................................
3
ACKNOW LEDGEM ENTS ...................................................................................................................
5
TABLE OF CONTENTS .......................................................................................................................
7
LIST OF FIGURES ............................................................................................................................
10
LIST OF TABLES ..............................................................................................................................
13
NOM ENCLATURE ...........................................................................................................................
14
1 Introduction ..............................................................................................................................
17
1.1 Diesel Engine
i
.......................................................................................................................
17
1.2 Em ission Regulations ...........................................................................................................
19
1.3 Diesel Particulate Filter ..................................................................................................
20
1.3.1 Filter Operation Principle .........................................................................................
20
1.3.2 Porous M edia Filtration M echanism s........................................................................
21
1.3.3 Regeneration ................................................................................................................
22
1.4 Ash Effects on DPF perform ance .....................................................................................
23
1.4.1 Ash Source ....................................................................................................................
23
1.4.2 Ash Effects on DPF Performance
23
.....................................
1.5 Research Objectives ............................................................................................................
25
2 DPF Soot and Ash Loading M odel............................................................................................
27
2.1 M odel Form ulation..............................................................................................................
27
2.1.1 Flow M odel ...................................................................................................................
28
2.1.2 Substrate W all M odel ................................................................................................
29
2.1.3 Particle Deposition Partition Ratio ............................................................................
32
2.1.4 Cake Layer and Regeneration...................................................................................
34
2.1.5 Particle Size Distribution ...........................................................................................
34
2.1.6 M odel Overall Structure ............................................................................................
36
2.2 M odel Validation and Application...................................................................................
38
2.2.1 DPF Soot/Ash Loading ..............................................................................................
38
2.2.2 Depth Filtration and Cake Layer Filtration ..............................................................
43
7
2.2.3 Ash Distribution am ong Substrate Slabs ...................................................................
44
2.2.4 Substrate Layer Optim al Arrangem ent .....................................................................
46
2.3 Sum m ary..............................................................................................................................
48
3 Ash Spatial Distribution Effects ..............................................................................................
50
3.1 Ash Deposit Accum ulation ...............................................................................................
50
3.2 Ash Perm eability..................................................................................................................
51
3.2.1 Perm eability Estim ation from Experimental Data...................................................
51
3.2.2 Perm eability from Literature .....................................................................................
55
3.3 Radial Distribution Effects ................................................................................................
56
3.3.1 M odel Form ulation...................................................................................................
56
3.3.2 Results Discussion.....................................................................................................
57
3.4 Ash Cake Layer Profile Effects .........................................................................................
60
3.4.1 M odel Form ulation...................................................................................................
60
3.4.2 Results Discussion.....................................................................................................
63
3.5 Ash End-plug Effects ............................................................................................................
66
3.5.1 Ash Distributed as Layer and End-plug......................................................................
66
3.5.2 Param eter Analysis ..................................................................................................
67
3.5.3 Sensitivity M ap .............................................................................................................
68
3.5.4 Sensitivity M ap w ith Actual DPFs ..............................................................................
70
3.6 Sum m ary..............................................................................................................................
72
4 Ash Transport M odeling .............................................................................................................
74
4.1 Experim ental Observation and Analysis..........................................................................
74
4.1.1 Ash Distribution inside DPF Channels........................................................................
74
4.1.2 Ash Transport Observation........................................................................................
76
4.1.3 Force Analysis of Particle Transport ..........................................................................
79
4.2 Transport M odel ..................................................................................................................
80
4.2.1 M odeling Assum ptions ..............................................................................................
80
4.2.2 Flow M odel...................................................................................................................
81
4.2.3 M odeling Approach ..................................................................................................
82
4.2.4 Sim ulation Condition ................................................................................................
83
4.2.5 Results and Discussion..............................................................................................
84
4.3 Sum m ary..............................................................................................................................
87
8
5 Passive Regeneration M odel..................................................................................................
89
5.1 Passive Regeneration ..........................................................................................................
89
5.2 CDPF Aging Experim ent Observation ..............................................................................
91
5.2.1 Focused Ion Beam (FIB) Observation .......................................................................
93
5.3 CDPF Catalyst Deactivation .................................................................................................
94
5.3.1 Catalyst Deactivation M echanism s ...........................................................................
95
5.3.2 CDPF Catalyst Deactivation M echanism ...................................................................
95
5.4 M odel Form ulation..............................................................................................................
96
5.4.1 Catalyst Deactivation M odel .....................................................................................
97
5.4.2 Passive Regeneration M odel.....................................................................................
99
5.4.3 NO and NO 2 Equilibrium .............................................................................................
103
5.5 Results and Discussion.......................................................................................................
105
5.5.1 N0
2
Generation Test...................................................................................................
105
5.5.2 Ash Effects on Soot Oxidation ....................................................................................
112
5.6 Sum m ary............................................................................................................................
117
6 Conclusions...............................................................................................................................
119
6.1 DPF Study Sum m aries........................................................................................................
119
6.2 Possible Applications of M odeling Understandings ..........................................................
121
6.2.1 Ash M em brane ...........................................................................................................
122
6.2.2 Sensitivity M ap ...........................................................................................................
122
REFERENCES ................................................................................................................................
123
Appendix 1...................................................................................................................................131
Appendix 2 ...................................................................................................................................
134
Appendix 3...................................................................................................................................137
9
LIST OF FIGURES
20
Figure 1.1. EPA emission standards for heavy duty diesel engines ...............................
flow
filtration
Figure 1.2. Actual ceramic DPF image and schematic presentation of wall
................................... ................................... ................................... ................................... ..2 1
21
Figure 1.3. Porous media filtration mechanisms ............................................................
24
Figure 1.4. Ash and soot distribution in a DPF channel [10] .........................................
on-road
equivalent
loading
and
filter
ash
of
as
a
function
Figure 1.5. DPF pressure drop
24
...............................................................
ex po su re [1 1 ] ..........................................................
28
Figure 2.1. Diesel particulate filter with soot and ash deposit .......................................
Figure 2.2. SEM picture of polished cordierite samples from RC 200/19 diesel particulate
........................................ 3 0
...........................................
filters[17 ] ...........................................
Figure 2.3. Schematic representation of filter wall discretization into slabs composed of
. 30
"unit cell/collectors" .......................................................................................................
31
Figure 2.4. Unit-cell filtration model [19] ......................................................................
32
Figure 2.5. Soot Particle deposition with soot and ash cake layer ................................
diesel
inside
ash
load
level
Figure 2.6. Ash end plug mass fraction with increasing
34
particulate filter ...................................................................................
35
......................
Phase
Compounds[29]
and
Vapor
Figure. 2.7. Diesel emitted Particles
Figure. 2.8. Measured Diesel emitted particle agglomerate size distribution from
. . 36
literature .........................................................................................
36
Figure 2.9. Soot particle distribution and its filtration across the substrate wall ......
Figure 2.10. The overall structure of DPF soot and ash loading model ........................ 37
Figure 2.11. Experimental DPF pressure drop with soot loading level at different ash
. 39
deposit load .........................................................................................
40
..........................
DPF
for
clean
Figure 2.12. Model simulation and experiment results
Figure 2.13. Substrate wall is discretized into slabs in the numerical simulation
........................................... .............. 4 0
...........................................
...........................................
Figure 2.14. Simulation results and experiment results for DPF at 3 g/L ash load
41
..........................................................
...........................................
...........................................
Figure 2.15. Simulation results and experiment results for DPF at 10.7 g/L ash load 42
Figure 2.16. DPF pressure drop with soot loading ........................................... ................. 43
44
Figure 2.17. DPF pressure drop caused the soot deposited in DPF ..............................
Figure 2.18. Substrate wall is discretized into three slabs in soot distribution analysis
45
.........................................................................................................
Figure 2.19. DPF pressure drop with soot mass deposited inside substrate wall under four
45
assumed mass distribution patterns ..............................................................
Figure 2.20. Two slab arrangement for a substrate wall ....................................... 46
Figure 2.21. The soot mass deposited in each slab in the two slab arrangements ......... 47
Figure 2.22. The DPF pressure drop in the two slab arrangements ....................... 47
Figure 2.23. A substrate wall with n slabs and each slab property can be independently
48
con tro lled ............................................................................................
10
Figure 3.1. Ash fraction of the total accumulated material in the DPF as a function of
total mileage prior to ash cleaning assuming a maximum DPF soot load of 6 g/l for
regeneration [2 5] ....................................................................................
50
Figure 3.2. Experimental DPF pressure drop with ash loading for all lubricant
formulations at a constant space velocity 20,000 1/Hour [26] ............................. 52
Figure 3.3. Linear fitting in ash/wall permeability estimation ...........................
53
Figure 3.4. Assumed ash distribution inside inlet channel at permeability estimation
.........................................................................................................
53
Figure 3.5. DPF ash radial distribution model ..................................................
57
Figure 3.6. Two distribution patterns considered in the radial distribution analysis
.........................................................................................................
58
Figure 3.7. Ash radial distribution considered in the simulation ......................... 58
Figure 3.8. Ash distribution inside one DPF inlet channel ................................
60
Figure 3.9. Four types of investigated ash layer profiles ...................................... 64
Figure 3.10. Mg ash pressure change ratio of three cake layer profiles .................. 65
Figure 3.11. Ca ash pressure change ratio of three cake layer profiles .................... 65
Figure 3.12. Ash distributions inside DPF channel under two ash plug ratios ............ 66
Figure 3.13. DPF sensitivity contour map at 20g/L ash load ..............................
69
Figure 3.14. DPF sensitivity contour map at 40g/L ash load ..............................
69
Figure 3.15. DPF sensitivity contour map at 20g/L ash load with real DPF and ash data
....................................................................................................
. . 71
Figure 3.16. DPF sensitivity contour map at 40g/L ash load with real DPF and ash data
....................................................................................................
. . 71
Figure 3.17. DPF sensitivity contour map at 20g/L ash load with DPF and ash data from
literatu re .............................................................................................
72
Figure 4.1. Ash distribution inside DPF inlet channels as cake layer or as end plug
....................................................................................................
. . 74
Figure 4.2. Ash deposit inside DPF inlet channels from accelerating ash loading system
using CJ-4 lubricant oil .........................................................................
75
Figure 4.3. Comparison of ash packing density for DPFs containing 12.5 g/l ash and 42
g/l ash generated in the laboratory using CJ-4 oil and periodic regeneration [26]
....................................................................................................
. . 76
Figure 4.4. (a) DPF core sample fixture with optical access. (b) detail showing field of
view into single channel [28] ..................................................................
77
Figure 4.5. Step-wise increase in flow through optical DPF samples following full- or
partial-regeneration [28] .......................................................................
77
Figure 4.6. Image sequence showing transport of ash particles formed following filter
regeneration with increasing channel flow [28] ............................................
78
Figure 4.7. Flow field inside DPF inlet channel from a CFD model ...................... 79
Figure 4.8. Forces acting on particle accumulated on filter surface, Schematic adapted
from [30] ......................................................................................
. . .. 80
Figure 4.9. Lift force acting on particle near deposited surface ...........................
80
Figure 4.10. Ash deposit and flow inside one dimensional flow model .................. 81
Figure 4.11. Flow chart of the whole transport model .....................................
82
Figure 4.12. Ash cake layer and end-plug density with ash loading level .................. 83
11
Figure 4.13. Predicted ash layer profile and experimental measurement at two ash loading
. . .. 85
lev els ...........................................................................................
Figure 4.14. predicted ash layer profile at 20 g/L and 30 g/L ash load ...................... 86
Figure 4.15. Evolution of ash accumulation in channel end-plug predicted by the 1 -D
87
mo del .................................................................................................
89
Figure 5.1. Catalyzed Diesel Particulate Filter ..............................................
Figure 5.2. Reaction-diffusion phenomena across the soot layer and the catalyzed filter
90
w all ...................................................................................................
Figure 5.3. Reaction and diffusion across wall with ash cake layer ....................... 91
Figure 5.4. N02 formation efficiency at aged CDPFs [46] ................................ 92
Figure 5.5. Clean and ash aged CDPFs' downstream N02 concentration 20,000 1/Hour
. . 93
....................................................................................................
Figure 5.6. Focus Ion Beam Technique and its observation[50] ........................... 94
95
Figure 5.7. Five mechanisms of catalyst deactivation .....................................
..........
96
catalyst
Figure 5.8. Fouling/surface masking deactivation mechanism of CDPF
Figure 5.9. Three dimensional ash particle packing on the catalyzed surface .............. 98
Figure 5.10. Catalyst coverage ratio with increasing ash load ............................... 98
Figure 5.11. Three dimensional ash particle packing on the catalyzed surface considering
99
ash size distribution between 0.1 to 3.9 micron ................................................
Figure 5.12. Chemical reaction across the cake layer and wash coat.......................103
Figure 5.13. NO and N02 concentration at equilibrium state...............................104
Figure 5.14. Experimental Setup for catalyzed DPF N02 generation test.................106
Figure 5.15. Model predicted and experimental measured downstream N02 concentration
for clean catalyzed diesel particulate filter.....................................................107
Figure 5.16 Model predicted and experimental measured downstream N02 concentration
for 42 g/L ash aged catalyzed diesel particulate filter........................................107
Figure 5.17. Clean CDPF inlet channel N02 concentration.................................109
Figure 5.18. 42 g/L ash aged CDPF inlet channel N02 concentration.....................109
Figure 5.19. N02 concentration distribution inside wash coat region for clean catalyzed
diesel particulate filter............................................................................110
Figure 5.20. N02 concentration distribution inside wash coat region for 42g/L ash aged
catalyzed diesel particulate filter................................................................111
Figure 5.21. Two cases simulated in ash effects on passive regeneration..................112
Figure 5.22. Inlet channel N02 concentrations at two simulated cases....................113
Figure 5.23. Prous media region N02 cocnentrations in two smiluated cases at three
positions: channel starting point, channel middle point, and channel rear end
1 14
........................................................................................................
Figure 5.24. N02 concentration in the porous media region at 0 g/L ash and 3 g/L soot
115
loadin g lev el .......................................................................................
Figure 5.25. N02 concentration in the porous media region at 15 g/L ash and 3 g/L soot
1 16
load in g lev el .......................................................................................
Figure 5.26. Passive Regeneration (soot oxidation) rate at three simulated conditions
1 17
........................................................................................................
12
LIST OF TABLES
Table 2.1. DPF specifications and flow condition...........................................38
Table 2.2. Simulation condition in depth/cake filtration comparisons.......................44
Table 2.3. Simulation condition in ash distribution among substrate slabs..................45
Table 3.1. Six lubricant formulations tested in experiments...............................51
Table 3.2. Estimated permeability of ash generated from six lubricant formulations
..................................................................................................
. . .. 5 5
Table 3.3. Published ash and substrate wall permeability from literature..................55
Table 3.4. DPF specifications and flow condition used in simulation.......................58
Table 3.5. DPF Pressure change ratio with ash radial distribution when ash deposits as
cak e lay er ............................................................................................
59
Table 3.6. DPF Pressure change ratio with ash radial distribution when ash deposits as
en d plug ........................................................................................
. ... 60
Table 3.7. Maximum value of 2xSash/bk for four ash cake layer profiles
at 2 ash load levels .................................................................................
64
Table 3.8. Target Function for real DPF and ash at two ash loading level .................. 70
Table 4.1. Simulation conditions of transport model .......................................
84
Table 5.1. DPF passive regeneration global reaction parameters...........................102
Table 5.2. Experiment conditions in CDPF N02 generation test ........................... 106
Table 5.3. Simulation condition in ash effects on DPF passive regeneration ............. 112
13
NOMENCLATURE
a
A
b
cj,k
cm
bk
bio
Ca
CI
CPSI
CDPF
CO
CO 2
D
DPF
E
EDX
EGR
f
F
Lash plug
LDPF
Leff
Lpiug
ka
kw
kij
Mg
Nchannel
NMHC
NO
NO 2
P
P1
P2
Pe
PM
PPM
91
R
Re
Sa
line slope at least square fitting
pre-exponential factor
factor at least square fitting
stoichiometric coefficient of species j in reaction k
molecular density, mole/m 3
clean DPF channel open width
loaded DPF inlet channel open width
calcium
compression ignition
cell density per square inch
catalyzed diesel particulate filter
Carbon Monoxide
Carbon Dioxide
mass diffusivity, m2/s
diesel particulate filter
reaction activation energy
Energy Dispersive X-ray Spectrometry
exhaust has recirculation
target function
laminar channel flow friction factor
channel ash plug length
total DPF length
DPF effective filtration length
DPF plug length
ash cake layer permeability
substrate wall permeability
mass transfer coefficient of species j in channel i, m/s
magnesium
number of total DPF total channels
Non-Methane Hydro Carbon
Nitrogen Oxide
Nitrogen Dioxide
Phosphorous
inlet channel pressure
outlet channel pressure
Peclet number
particulate matter
Parts per Million
universal gas constant, J/mole K
reaction rate, mole/(m 3s)
Reynolds Number
ash cake layer thickness
14
SEM
Sh
SI
Ss
SW
t
T
TDC
U1
U2
uin
uw
Vash
VDPF
w_deposit
wS
x
XRD
Scanning Electron Microscope
Sherwood number
spark ignition
soot cake layer thickness
substrate wall thickness
time
temperature
top dead center
inlet channel velocity
outlet channel velocity
entrance velocity in inlet channel
filtration velocity across the wall
ash volume for each inlet channel
DPF total volume
deposit thickness
substrate wall thickness
axial coordinate in DPF length direction
APDPF
X-Ray Diffraction
DPF ash load level, g/L
Mole fraction of species j
DPF length direction
Zinc Dialkyl-Dithio-Phosphate
Zinc
DPF pressure drop
AP.all
substrate wall pressure drop
APsh
ash cake layer pressure drop
APiction
channel friction pressure drop
11
Forchheimer coefficient
porosity
Yash
yi
z
ZDDP
Zn
gas viscosity
P
p
Is
2s
Partition coefficient constant
density
inlet channel- soot surface interface
outlet channel- wall surface interface
15
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16
1 Introduction
Diesel engines are widely used in on- and off-road applications around the world because
of its advantages such as low cost, good durability and high torque at low speed. Diesel
engines have a dominant market share in the area of freight transport since the diesel
engines with high fuel efficiency help to reduce the cost of long distance transport. At the
same time, nearly 50% of personal vehicles in the Europe use diesel engines due to the
fuel taxing policy. However, the diesel engine suffers from the problems of high soot and
NOx emissions. As the emission regulations become more stringent than before,
additional technologies and devices are needed to apply to continuously reduce the
engine emission level.
Diesel particulate filter (DPF), which is one of key components of diesel after-treatment
system, is designed to reduce diesel engine soot particulate emission. The recent
catalyzed diesel particulate filter also can reduce CO and HC emissions. From 2007, all
the on road heavy duty diesel engines operated in United States are required to install the
particulate filter in the after-treatment system to satisfy the new soot emission regulation.
Thus fundamental study is needed to understand diesel particulate filter aging process and
resulting influences on diesel engine performance.
1.1 Diesel Engine
The diesel engine was first patented by Rudolph Diesel in 1892 and successfully operated
in 1897 in Germany. It was originally used as a more efficient replacement for stationary
steam engines. Since the 1910s they have been used in submarines and ships. Use in
locomotives, trucks, heavy equipment and electric generating plants followed later. In the
1930s, they slowly began to be used in a few automobiles.
The fundamental operating principles of diesel engine have remained same, although new
technologies and improvements are continuously implemented like electronic control of
fuel injection, EGR and turbo-charging. The fundamental difference between spark
ignition (SI) engines and Diesel's compression ignition (CI) cycle is the ignition's
operating principle. Diesel engines (also known as a compression-ignition engines) use
the heat of compression to initiate ignition and burn the fuel that has been injected into
the combustion chamber. Spark ignition (SI) engines use external source like spark plug
to start the combustion. This fundamental difference in combustion organizing yields a
substantial improvement in fuel efficiency.
In its most basic form, diesel engine can be described as a reciprocating piston, internal
combustion engine which relies on high pressure air compression paired with accurately
timed fuel injection to produce in-cylinder combustion. During the intake stroke, clean air,
usually near atmosphere pressure in non-turbo-charging engine, is introduced into the
combustion chamber. Diesel engines have typical compression ratios in the 12-24 range
which is substantially higher than those seen in SI engines which generally fall within 817
12. Due to this high compression ratio, diesel engines can reach a rather high in-cylinder
pressures of about 30-55 bar and temperatures around 527-827 'C during the
compression stroke [1]. Before the piston's top dead center (TDC) position liquid fuel is
either injected directly into the cylinder or into an adjacent pre-combustion chamber. Due
to the high injection pressure in modern diesel engines, the fuel is atomized into small
droplets and entrained into the cylinder air creating a fuel-air mixture of combustible
proportions. The high pressure and temperature of the compressed air are above the
mixture's auto ignition point which causes spontaneous combustion. The rapid expansion
of the burning mixture generates the power stroke and initiates the exhaust process for the
cycle to start again.
The diesel engines have a much higher compression ratio than spark ignition engine. The
reason is that spark ignition engine's compression ratio is constrained by knock
phenomenon, which could damage the engine body or incur other dangers. For diesel
engines, during most of time of compression stroke there is no fuel inside engine cylinder.
Thus knock is not a problem to be considered in diesel engines and the compression can
be increased to an ideal level. Another major difference between diesel engine and spark
ignition engine is the engine load control method. Diesel engine load is controlled by the
amount of fuel injected per cycle and intake air is always redundant. Since in spark
ignition engine the fuel to air ratio is always kept stoichiometric, the spark ignition
engine load is controlled by restricting the intake air through the usage of a throttle plate,
which causes the extra loss of useful work out of engine.
Generally speaking, diesel engines have higher fuel efficiency than spark ignition engines
for several reasons. Diesel engines have higher compression ratio, as described above,
which means more useful work can be extracted from the thermal cycle in diesel engine.
Meanwhile, diesel engines do not use throttle plate to control engine load which could
cause throttling loss in spark ignition engine. High fuel efficiency for diesel engine means
low operating cost and low CO 2 emission.
Due to the advantages described in the previous sections diesel engines are attractive to a
variety of applications including agriculture, construction, engine and equipment
manufacturing, fuel production, freight (trucking, railroads, ships and marine vessels),
and mining equipment. A study conducted in the year 2000 determined a variety of
percentages that the diesel market controls within certain applications [2]. The study
showed that based on fraction of fuel energy consumed by vehicle type in the United
States, diesel engines power nearly 85% of commercial trucks, 100% of marine and
railway freight transport, 75% of inner-city rail transit, 62% of school buses and 100% of
inner city buses. One should note that the percentage of bus applications may be outdated
with the surge of natural gas / hybrid powered buses. The study also determined that 83%
of construction equipment, 66% of agriculture equipment and 22% of mining equipment
are diesel powered [2]. Although diesel powered vehicles only make up a very small
percentage of the personal passenger market in the United States, this is not the case for
both Europe and Asia in which the majority of personally owned passenger vehicles are
diesel powered. As previously mentioned this is primarily due to that fuel price volatility
in those specific economies.
18
1.2 Emission Regulations
Although the hydrocarbon and carbon monoxide emissions are relatively low in diesel engine,
the heterogeneous nature of diesel fuel combustion leads to high levels of NOx and soot
emissions from diesel engines. With increasing public concerns of environment protection, a
number of relevant rese4rches have been conducted to investigate the environmental and
health effects of diesel emission.
In recent years, emission of diesel particulate matter (PM) has become one of the major
health concerns among all diesel emissions. Diesel engines accounted for nearly 75% of all
mobile source PM2.5 emissions in the U.S. in 2000 [3]. PM2.5 is defined as all particulate
matter smaller than 2.5 pim. Medical research on health effects of PM is still in the initial
phase of exploring this new area of human knowledge. The preliminary study shows that soot
particles originated from diesel combustion can be transported deep to human lungs, which
could be extremely dangerous to pregnant women and children. At the same time, Diesel
particle emissions are a recognized carcinogen and are associated with respiratory illness,
heart attacks, and premature death [4].
Because of the growing concerns of engine emissions, United Stats Environmental Protection
Agency (EPA) imposed more and more stringent emission standard. Over the years, these
emissions control mandates have brought vehicle emissions to near-zero levels as shown in
Figure 1.1. While the mandates were spaced out to provide time for the development and
commercialization of emissions control improvements, they have created unique and
complex challenges to communications, research and development cycle and purchase
planning.
Specific to heavy-duty commercial vehicles, the new 2010 regulations introduce very
stringent emission standards, as follows:
.
.
0
PM-0.01 g/bhp-hr
NOx-0.20 g/bhp-hr
NMHC (Non-Methane Hydro Carbon) -0.14
g/bhp-hr
In conjunction with the tighter emissions limits, the EPA also limited the sulfur content of
diesel fuel for highway and off highway engines. Beginning June 1, 2006, refiners began
producing ultra-low sulfur diesel fuel with sulfur levels at or below 15 parts per million (ppm)
for use in heavy duty highway diesel engines. Non-road diesel engines were required to use
low sulfur (500 ppm) diesel fuel beginning in 2007 and ultra-low sulfur diesel fuel beginning
in 2010. Locomotives and smaller marine engines required low sulfur (500 ppm) diesel fuel
beginning in 2007 and ultra-low sulfur diesel fuel beginning in 2012.
The ultra-low sulfur level in diesel fuel is essential to keep the catalyst of after-treatment
system active. For example, the platinum catalyst in catalyzed DPF is very sensitive to sulfur
deposit. The catalyst can be easily deactivated by little amount of sulfur through the
poisoning mechanism and soot will be continuously accumulated in the filter channels ending
up with device plugging.
19
Figure 1.1. EPA emission standards for heavy duty diesel engines.
1.3 Diesel Particulate Filter
1.3.1 Filter Operation Principle
Diesel particulate filters (DPF) are devices that physically capture diesel particulates to
prevent their release to the atmosphere. Diesel particulate filter materials have been
developed that show impressive filtration efficiencies, in excess of 90%, as well as good
mechanical and thermal durability. Diesel particulate filters have become the most
effective technology for the control of diesel particulate emissions-including particle
mass and numbers-with high efficiencies.
Cellular ceramic wall-flow particulate filters are widely used today due to their relatively low
cost and high trapping efficiency. The wall-flow filter consists of a larger number of
rectangle porous channel walls and the cell density is about 200 or 300 CPSI (cell density per
square inch). As shown in Figure 1.2, the channels are alternately blocked by small ceramic
plugs at each end. As particulate-laden exhaust enters the upstream open end of the channels
it must pass through the porous walls before exiting the filter. As the exhaust passes through
the walls, the particles are trapped inside the porous material and along the channels walls as
depicted in the schematic. The trapped particles act as an added filtering medium in cellular
ceramic traps further increasing trapping efficiency as the traps are loaded [5].
20
CLE
EiXt^i5T
IN
W
W_
*SOOT PARTICU
*ASHPARTICE
Figure 1.2. Actual ceramic DPF image and schematic presentation of
wall flow filtration.
1.3.2 Porous Media Filtration Mechanisms
Diesel particulate filter substrate captures particle emissions through a combination of
filtration mechanisms, such as diffusion deposition, inertial impaction, or flow-line
interception [6].
Inertial impaction
Flow stream
~~'1
Particle
r fiber
Partici
Flow stream
Diffusion
Filter fiber
Partide
Flow stream
Interception
Filter fiber
Figure 1.3. Porous media filtration mechanisms.
Inertial deposition is applicable to particles larger than 1 ui m in diameter. The inertia of
the large heavy particles in the flow stream causes the particles to continue on a straight
path as the flow stream moves around an obstacle. The particulate then impacts and is
21
attached to the solid part of porous media and held in place as shown in the top picture of
Figure 1.3. This type of filtration mechanism is effective in high-velocity filtration
systems.
Diffusion deposition is effective for very small particles typically less than 0.5 11 m in
size. Effectiveness increases with lower flow velocities. Small particles interact with
nearby particles and gas molecules. Especially in turbulent flow, the path of small
particles fluctuates randomly about the main stream flow. As shown in the middle of
Figure 1.3, aerosol particles may deviate from their line of flow due to Brown's diffusion
movement, and are collected by coming into contact with the filter material. The smaller
a particle and the lower the flow rate through the filter media leads to a higher probability
that the particle will be captured.
Interception occurs with medium-sized particles that are not large enough to leave the
flow path due to inertia or not small enough to diffuse. The interception collection
mechanism is defined as particles that follow along the flow line and are collected by
coming into contact with the filter material. The larger the aerosol particles, the easier
they are to be collected.
1.3.3 Regeneration
Due to the low bulk density of diesel particulates, diesel particulate filters can quickly
accumulate considerable volumes of soot. For example, 6 g/L soot loading in the filter
may occupy approximately 20% of the volume inside inlet channel. Several liters of soot
per day may be collected from an older generation heavy-duty truck or bus engine. The
collected particulates would eventually cause excessively high exhaust gas pressure drop
in the filter, which would negatively affect the engine fuel efficiency. Therefore, diesel
particulate filter systems have to provide a way of removing particulates from the filter to
restore its soot collection capacity. This removal of particulates, known as the filter
regeneration, can be performed either continuously, during regular operation of the filter,
or periodically, after a pre-determined quantity of soot has been accumulated.
Active/Periodic regeneration of diesel particulate filters is typically employed, where the
collected particulates are oxidized-by oxygen-to gaseous products, primarily to carbon
dioxide. This reaction is only able to happen in the temperature higher than 600 0C. Thus,
late fuel injection or other methods are used to elevate the exhaust temperature to initiate
the soot combustion.
A recent developed technology is catalyzed diesel particulate filter with deposited
platinum to facilitate the reaction of carbon with nitrogen dioxide. The working principle
is that catalyst helps to convert NO to NO 2 since NO 2 can react with carbon at low
temperature like 300 0C. At most of suitable engine loads, the soot accumulated in diesel
particulate filter can be continuously regenerated.
22
1.4 Ash Effects on DPF performance
1.4.1 Ash Source
The accumulated soot is removed after diesel particulate filter regeneration. However, the
incombustible material-ash remains in the inlet channels and it continues increase with
vehicle mileage or equivalent running hours. The increasing ash deposit adversely affects
the diesel particulate filter performance and limits the filter's service life. Although
considerable work has been done in understanding DPF performance for soot
accumulation alone, the reality is quite different. In fact, more often than not, the amount
of ash in the filter can significantly exceed the amount of soot the DPF was initially
designed to trap.
Ash accumulated in the filter originates from several sources including lubricant
additives, engine wear and corrosion particles, and trace metals found in diesel fuel.
Generally, the majority of ash in the filter comes from lubricant additives [7-9]. Ash
accumulation in the DPF increases with oil consumption and lubricant ash content, as
lubricant additives are generally the largest source of ash. Ash derived from lubricant
additives is composed primarily of zinc, calcium, and magnesium in the form of sulfates,
phosphates, and oxides.
When the fuel borne catalyst is used to facilitate the soot oxidation during regeneration,
the fuel catalyst can be another major source of ash formation. Since the fuel borne
catalyst is contained in the soot captured inside filter, it will remain in filter after
regeneration and generally increase linearly with running time or vehicle mileage.
1.4.2 Ash Effects on DPF Performance
When significant amount of ash is deposited inside diesel particulate filter channels, it
will occupy a relative larger portion of channel volume. As shown in Figure 1.4, the ash
accumulation inside DPF changes the filter geometry, forming ash end plug and ash cake
layer. The soot loading with significant amount of ash deposit is quite different with soot
loading inside clean filter for two reasons. Firstly, the ash end plug reduces the effective
filtration length of filter and soot will form a much thicker layer at same soot loading
level. Secondly, the ash cake layer decreases the open width of inlet channel and the soot
cake layer needs to have larger thickness to occupy the same space compared with soot
cake layer formation in a clean filter channel.
Due to the long time scales over which the ash builds up in diesel particulate filter,
several thousand hours and tens-to-hundreds of thousands of miles, much of the research
into ash effects utilized various approaches to accelerate filter aging and ash build up in
an effort to identify the various ash sources and means by which ash may affect diesel
after-treatment system performance.
23
Figure 1.4. Ash and soot distribution in a DPF channel [10].
Generally, the ash accumulation inside DPF increases the flow pressure drop across the
filter. A recent study shows lubricant-derived ash from CJ-4 specification oils, containing
no more than 1.0% sulfated ash, resulting in an approximately doubling of the DPF
pressure drop after 4,680 hours or 188,000 miles (303,000 km) of equivalent on-road use
[11].
30
CJ-4(2)
~20
12
10
CJ-4 (1)
2
/
00
40
35
15
20
25
30
Cummumlative Ash Load [g/L]
5,960 hrs
Equivalent Hours
240k mi.
I Equivalent Miles
0
5
10
45
Figure 1.5. DPF pressure drop as a function of filter ash loading and
equivalent on-road exposure [111].
24
At the same time, ash aged DPF adversely affects the fuel efficiency of diesel engine.
The engine fuel economy is reduced because of two main reasons. Firstly, ash
accumulation in filter increases exhaust flow restriction and backpressure, which reduces
the work extracted from thermal cycle. Secondly, ash aged DPF decreased filter
regeneration intervals (increased regeneration frequency) through a reduction in filter
soot storage capacity, in which engine fuel is needed in higher frequency to raise the
exhaust temperature. Furthermore, the ash may also reduce the regeneration efficiency in
catalyzed systems, requiring an increased reliance on active regeneration or higher
temperature operation for successful passive soot oxidation.
1.5 Research Objectives
While previous studies have investigated the soot loading effects on DPF performance
via experiment or model, little DPF modeling work has been done to study the ash effects
on filtration, DPF pressure drop and filter catalyst deactivation. And there is limited
understanding of the underlying fundamental mechanisms responsible for the observed DPF
performance degradation. For example, the mechanism how ash loading deactivates the filter
catalyst is not well understood and further optimization strategy is difficult to develop.
Combined with the observations and measurement provided by the experimental group, the
modeling effort attempts to fill the knowledge gap as listed before. Through careful analysis
of the experimental results, several new understandings of ash aging mechanism are applied
in the DPF model. The computer model is used to not only help interpret the experimental
observation but also develop possible optimization strategies. At the same time, certain
mechanisms or understandings are tested in the model to see whether the predicted results
based on these mechanisms can fit the experimental observations.
The modeling work aimed to understand the ash effects on DPF performance including
following targeted areas.
(1) DPF pressure drop with increasing soot and ash loading and the effects of ash deposit
on soot filtration.
(2) Optimization of ash spatial distribution in DPF channels at given amount of ash
loading level
(3) Ash particle transport inside filter channels and ash end-plug/ ash cake layer increase
with ash loading level
(4) Mechanism of catalyst deactivation due to DPF ash aging and the effects of ash
deposit on following continuous regenerations
An enhanced understanding of these fundamental processes should provide useful
information to minimize the deleterious effects of lubricant-derived ash on diesel
aftertreatment systems. For example, if the DPF is found to have lower pressure drop at
25
certain spatial distribution pattern, relevant technology may worth developing to facilitate the
formation of preferred ash distribution pattern. The modeling results and experimental
observation combined together could obtain a deeper understanding of the fundamental
underlying mechanisms governing the effects of lubricant-derived ash on aftertreatment
system pressure drop performance. These new understanding will be useful in optimizing the
design of the combined engine aftertreatment-lubricant system for future diesel engines,
balancing the requirements of good filtration performance with the requirements for robust
aftertreatment systems.
26
2 DPF Soot and Ash Loading Model
The prediction of the pressure drop of DPF is essential in developing new product. The
complexity arises from the need of predicting not only the new or slightly loaded state
but also the behavior after a long mileage. A number of DPF pressure drop models have
been developed over the last three decades. Due to the special geometry character of DPF
channels, a long channel with relative small channel width, one dimensional model is
suitable to describe the DPF performance. The underlying theory of one dimensional
model is same, based on largely on mass and momentum conservation and considering
Darcy equation across the porous media. While most of the previous models have
focused on predicting pressure drop in clean and soot loaded filter, very few have
accounted for ash accumulation. Since pressure drop prediction has to be done during the
design phase of new particulate filter, a model which allows a quick evaluation of DPF
pressure drop at varied ash and soot loading level is needed.
2.1 Model Formulation
The built DPF soot and ash loading model is a one dimensional model and it includes
several sub-models like flow model, substrate wall model and particle partition model.
The sub-models are introduced respectively in following sections. The objective of
developing DPF soot and ash loading model is to evaluate DPF pressure drop at varied
soot and ash load, to study DPF filtration behavior with increasing soot and ash load, and
to develop suitable strategy to optimize DPF performance.
A typical diesel particulate filter has more than 5,000 channels, which make it unrealistic
to model each of them. To simplify the problem, following assumptions are applied in the
DPF soot and ash loading model.
1)
Assuming all the inlet channels in the filter have the same deposit loading level
and same deposit distribution.
2) Assuming all the inlet channels in DPF have the same inlet flow velocity.
3) Ash deposit is assumed to be composed of a flat cake layer and end-plug while
soot deposit is assumed to only have a cake layer part.
The assumptions used above are supported by experimental observations and are widely
used in diesel particulate filter modeling [17-21]. Since all the inlet channels behave same
according to the assumptions, only a representative inlet and outlet channel of the filter
need to be solved in the model.
27
2.1.1 Flow Model
The flow model describing the performance of clean DPFs was developed by Bisset,
Konstandopoulos and Johnson in the late 1980s [17-20]. And this basic model was
extended to consider ash and soot deposit with flat cake layer by Gaiser [21], which is
shown in Figure 2.1. In the analysis of ash spatial distribution effects, this basic model is
upgraded to include ash cake layer variation in the axial direction. Due to the need, the
basic model considering deposit flat cake layer is applied here to model the soot and ash
loading effects on DPF performance.
The flow model here is one dimensional and it applies the governing equations of mass
and momentum conservation of exhaust gas and utilized Darcy's Law to describe the
flow through porous media. The mass conservation equations for exhaust gas inside inlet
and outlet channels are:
Inlet channel:
d(u1 )
dz
4bku
b2
Outlet channel: d(u2
(2.1)
4u,
dz
(2.2)
bk
Where ui and u 2 is exhaust gas flow velocity inside inlet and outlet channel respectively,
bk is the clean filter open width and blo is loaded filter open width. u, is the flow velocity
across the wall, z is the position in the filter length direction.
LashVUg
LPiug
substrate
SS001ash
layer
Sas,
soot layer
swan
52!d\swak
shn
Figure 2.1 Diesel particulate filter with soot and ash deposit.
Similarly, the momentum conservation equations of exhaust gas inside inlet and outlet
channel are described as:
d(u2)
Inlet channel: p d
dz
=
dP
Jdz
Fri
b1
1
(2.3)
28
Outlet channel: p d(u2 =
dz
dP2
dz
F7U22 (2.4)
b
(2
Where p is the exhaust gas density, q is the viscosity of exhaust gas, P1 is inlet channel
gas pressure and P2 is the outlet channel gas pressure. F is the rectangle channel friction
factor which is a constant of 28.454.
Darcy equation evaluates the pressure drop across the porous media. Here, the pressure
drop caused by soot/ash cake layer and substrate wall is determined as:
s
Ji-Pi,
=r7'
k,
s +saU2
+
k,
+ "
ka
++ p(/Js,+ ss,+asa)u2
(2.5)
Where s., ss, and sa is the substrate wall, soot cake layer and ash cake layer thickness
respectively, kw, ks, ka is the substrate wall, soot cake layer and ash cake layer
permeability,
s,,
P,,
Pa
is the coefficient of Darcy quadratic effects, which is usually
negligible in the common DPF flow rate. The boundary conditions for these equations are
following:
u()= U
(2.6)
u 2(0)=0
(2.7)
0
(2.8)
= Partn
(2.9)
U,(Lfj)=
P2 (L)
Where L is the DPF total length, Leff is the DPF effective filtration length. Combined
with the boundary conditions listed here, the system of governing equations from Eq. (2.1)
to Eq. (2.5) can be used to solve the flow and pressure in DPF channels. The system of
governing equations can be reduced to one equation through mathematical manipulation
and the normalized form is used in the numerical simulation. Besides, there is one
approximate analytical solution for these equations, which has an error less than 2% in
most of cases. These detailed discussions can be founded in Appendix 1.
2.1.2 Substrate Wall Model
Soot particles penetrate into substrate wall of diesel particulate filter during depth
filtration and deposit inside the pores of porous media. The particle deposit occupies
certain fraction of void volume of porous media and changes the porosity of substrate
wall. Thus the permeability of the substrate decreases and the pressure drop across the
substrate wall increases rapidly. The transient behavior of substrate wall during depth
filtration is described by "unit collector" filtration theory in a self-consistent manner.
29
The scanning electron microscope (SEM) picture of diesel particulate filter substrate wall
is shown in Figure 2.2. The void space geometry structure inside porous media is
irregular and complex in three dimensional spaces. Thus, the direct simulation of flow
and particle deposition inside porous media is a rather challenging and computationally
expensive. In the unit-cell theory, the porous filter wall is approximately as a collection
of cells which has simple geometry. For cordierite and silicon carbon filter, the cell
usually assumed as a sphere.
Figure 2.2. SEM picture of polished cordierite samples from RC 200/19
diesel particulate filters [171.
Min
. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mout=(-En) xmn
Figure 2.3. Schematic representation of filter wall discretization into
slabs composed of "unit cell/collectors".
30
Clean unt cell
Partially loaded
unit cell
Completely loaded
unt cell
Uit
'enpt 1'envelope
on0
Figure 2.4. Unit-cell filtration model. [191.
As shown in Figure 2.4, the unit cell is a sphere with centered solid core-collector, which
represents the solid part of the filter wall, and with surrounding space that represents the
void space inside filter wall. The collector diameter increases with particle deposition in
the unit-cell. The substrate wall is discretized into slabs as shown in Figure 2.3. During
depth filtration, the porous media property (porosity, permeability etc.) is updated by
tracking the amount of particulate mass deposited in each slab. The filtration efficiency
across porous media is
E = I-exp -1D
I-c
2e -d
S
(2.10)
Where r1DR is the collector filtration efficiency, P is the porosity, w is the thickness of
porous media, d, is the collector diameter. The unit collector diameter for a clean filter is
related to substrate wall porosity and pore size.
do =
2
-
dpoe (2.11)
co
The "unit cell" size b is given by:
=1 - CO
(2.12)
de'O
Where so is the porosity of clean filter, dco is the collector diameter for clean filter.
Accordingly, as shown in Figure 2.3, the particulate mass captured in slab is:
mdeposit(it) =
mi x E(i,t) (2.13)
31
The mass deposited on each collector is given by:
M,
0m=
Mdeposit(it)
~cells
nceil is the total number of unit cell inside respective slab. And the collector diameter and
cell porosity is updated by:
d, (i,t)= 2 3 m (i,t)
41r psot,
dco
2
d-
____)=
-
(2.15)
)
The local permeability of the filter wall changes as the particles deposit on each "unit
collector". k(i,t) is the permeability of slab i at time t. The local permeability k(i,t) of the
loaded filter is related to the permeability of the clean filter ko by:
k(it)r
ko
d(i,)2
dco
f(e(it)) (2
16)
f (-VO )
The calculation of unit cell collection efficiency is not included here. More details about
unit cell theory used porous media modeling can be founded in many filter wall model
publications [18].
2.1.3 Particle Deposition Partition Ratio
For a new diesel particulate filter, soot particles in exhaust gas initially penetrate into the
substrate wall during the depth filtration phase. With substrate surface pore shrinking and
cake layer building up, fewer and fewer soot particles can enter into the porous media and
eventually the deposition transits into cake filtration phase, in which no particle could
deposit inside porous media.
soot
ash
substrate
Figure 2.5. Soot Particle deposition with soot and ash cake layer.
32
In the substrate wall filtration modeling, the fraction of mass collected on the substrate,
which is called partition coefficient, needs to be determined. For a clean filter, the widely
used expression for partition coefficient is defined in Eq. (2.17). The physical
interpretation of this partition coefficient is that it depends on the dimensionless blockedarea fraction at the scale of the unit "collector". D is assumed to be given by Eq. (2.17),
where y is a dimensionless "percolation" control constant (O<Y<l), that determines the
onset of pore bridging, which has to be estimated from experimental data or detailed
discrete particle dynamics simulations using the methods of digital material[4].
(t)= d, (1,
(2.17)
(T -b) - d,20
This concept of partition coefficient is extended in DPF soot ash loading model by taking
the soot and ash cake layer into consideration. Physically speaking, the soot and ash cake
layer acts like membrane which reduces the percentage of soot particles penetrate into
substrate wall. According to our experimental observation, once the cake layer is thick
enough to from a continuous porous media, almost no soot particles can enter into
substrate wall.
The soot or ash cake layer, by its nature, is medium of porous media. Thus, according to
classical porous media filtration theory, its filtration efficiency can be described by Eq.
(2.18) and (2.19). Where T1DR is the collector filtration efficiency, F is the porosity, w is
the thickness of porous media, dc is the collector diameter.
expFI
1- L
E,=
1-
exp
3
1DR _soot( 1 2
soot
-3DR3
2RshO
ash
soot
s
dSOOt
*d
Aash
2.18)
1(18
Wsl(
as
2
.1)
The overall filtration efficiency of both soot cake layer and ash cake layer is given by Eq.
(2.20). When the filtration efficiency of either the ash cake layer or soot cake layer is
lower than 1, it corresponds to the physical scenario that the cake layer has certain
thickness but not yet to build a continuous filtration membrane. When filter has a
continuous cake layer on the substrate wall, this cake layer will block all the soot
particles and make it form soot cake layer.
hayer =1
-(1
- qSoot)(1-
1ash)
(2.20)
The final partition ratio, which is the percentage of soot particles deposit on the substrate
wall, is given by Eq. (2.21). The partition ratio is the maximum value of layer deposition
ratio calculated in Eq. (2.17) and Eq. (2.20). The physical meaning of Eq. (2.21) is that
33
the percentage of soot particles penetrates into substrate wall depends on the minimum
value of soot penetration percentage constrained by cake layer filtration, 1 -l1ayer, and soot
penetration percentage constrained by substrate surface pore blocking, 1- (D.
partitionratio = max(q,.er, 'D(t)) (2.21)
2.1.4 Cake Layer and Regeneration
As shown in Figure 2.1, the soot cake layer is assumed as flat and its thickness is tracked
in the model by considering soot loading rate and partition ratio. The regeneration setup
here is simplified by neglecting the thermal history of regeneration. After regeneration,
the deposited soot transforms to ash deposit. The generated ash mass is about 1% of
burned soot mass. Here, complete soot regeneration is assumed in the model.
0.9-0.8
>0 0.7 -C
0
y = 0.0003x2 + 0.0068x - 2E-15
R 11 1
0-6
0-5-
0.3 - 0-1T
0
0
10
20
30
40
50
Ash Load [g/L]
Figure 2.6. Ash end plug mass fraction with increasing ash load level
inside diesel particulate filter.
Besides, in the DPF soot and ash loading model, the mass fraction of ash end plug with
increasing ash load is also considered. The ash end plug mass fraction used in model is
the interpolation of obtained experimental data as shown in Figure 2.6.
2.1.5 Particle Size Distribution
Diesel exhaust is a complex mixture of organic and inorganic compounds and gas, liquid
and solid phase materials. As shown in Figure 2.7, diesel emitted particle agglomerate is
a chain of solid carbon spheres and absorbed hydrocarbon and organic compounds.
34
U
0.
Solid Carbon Spheres (0.01
0.08 pm diameter) form to
make Solid Particle
Agglomerates (0.05 -1.0 prm
diameter) With Adsorbed
Hydrocarbons
-
S
Vapor Phase
Hydrocarbons
Soluble Organic Fraction
Adsorbed
Hydrocarbons
(SOF)/Particle Phase
Hydrocarbons
I
I
Adsorbed
Hydrocarbons
o
t e(0
Liquid Condensed
Hydrocarbon Particles
Sulfate with Hydration
Sulfate (S04)
Figure. 2.7. Diesel emitted Particles and Vapor Phase Compounds[29].
The soot agglomerate size is widely investigated via experiments in diesel after-treatment
community. As shown in Figure 2.8, the reported soot agglomerate has mean size of
about 80 nm and is approximately normally distributed. According the literature, soot
agglomerate size may change with temperature or vapor concentration.
As shown in Figure 2.9, a normal distribution of soot particle is used in the model. And
the particle reduction at each size is tracked after going through each substrate slab. Thus,
the particle deposition inside each slab is updated and the overall filtration efficiency of
substrate wall is calculated in this way.
2500 rpm - 70% load
60
Avg. R =85.5 nm
50
(D
M
40
30
0
E
20
z3
10
0
0
1) 1511
250
R (nm)
(a) Experiment data from reference [23]
35
250
(nm
R
EPI
200
-P2
80.3
71.7
*P4
005
150
100
50
0
0
40
80
120 160
R, (nm)
200
240
(b) Experiment data from reference [24]
Figure. 2.8. Measured Diesel emitted particle agglomerate size
distribution from literature.
0.2
E
E
-1Slab
------------ -----
/
015
U)
0A1ui'
r
I'
p,,
0
/
01
02
0.3
particle size, micron
0. 4
(a) Soot Particle Distribution in Model
(b) Substrate wall is discretized into slabs
Figure 2.9. Soot particle distribution and its filtration across the
substrate wall.
2.1.6 Model Overall Structure
The overall structure of DPF soot and ash loading model is presented in Figure 2.10. As
shown, the model includes several sub-models that share the filter transient information.
During the simulation, the flow, substrate wall and cake layer are numerically updated at
each time step.
36
Model structure
One dimensional Flow Model
Inlet and outlet channel velocity, wall velocity and pressure drop
soot layer pressure drop
and filtration efficiency
Soot layer model
41
CCParticle
Partition Ratio Model
Layer deposition
Particle goes into the substrate
Ashlayer model
Ash layer pressure drop
and filtration efficiency
Substrate pressure drop,
filtration efficiency
Figure 2.10. The overall structure of DPF soot and ash loading model.
At any time step of simulation, the model first solves the flow inside filter. Based on the
information of substrate surface pore and cake layer thickness, the particle partition
coefficient is calculated, which determines the fraction of soot particles that penetrates
into substrate wall or deposits as cake layer. Then, certain portion of soot particles with
exhaust gas enters into substrate wall. According to the substrate filtration model, the
particle deposition inside each slab is calculated and porous media properties are updated
at each time step. The substrate wall overall filtration efficiency is obtained from
substrate wall model. The soot deposited on the substrate is assumed to form soot cake
layer and the thickness of soot cake layer is updated.
After certain long time of soot loading, usually 6 hours, the regeneration will be initiated.
The accumulated soot deposit is assumed to be become ash deposit after complete DPF
regeneration. Based on previous experimental observation, about one percentage of
deposit mass will be remained after active or passive regeneration. The remained
incombustible material, called ash, majorly comes from engine lubricant oil, fuel and
engine wear.
The DPF soot and ash loading model continuously simulates the soot loading and
regeneration of filter operations. The model is computationally efficient and it can
simulate the diesel particle filter operation up to 15,000 miles in a rather short time,
37
which is usually less than 30 minutes. It could provide the information of diesel
particulate filter like pressure drop, filtration efficiency, ash and soot layer thickness at
increasing load level.
Diesel particulate filter model helps to interpret the experimental data and to understand
the physical process undergoing inside filter. Besides, modeling also offers the useful
information which is hard to obtain from experiment. For example, it can provide the
amount of mass deposited inside porous media, porosity reduction, and pressure drop
caused by particle deposition. And the model is able to evaluate how the cake layer
affects the particle partition ration and the effect of cake layer on filter pressure drop.
These understandings from experiment observation and modeling could be useful
information for future optimization of filter performance.
2.2 Model Validation and Application
The developed DPF soot and ash loading model is validated with available experiment
data and applied in the DPF performance analysis. The model shows a great agreement
with experimental observations and provides analysis about the effects of ash distribution
on DPF performance.
2.2.1 DPF Soot/Ash Loading
One major objective of DPF soot and ash loading model is to simulate how DPF
performance, primary pressure drop and filtration efficiency, changes with soot and ash
loading level. The model, considering flow, substrate wall filtration and cake layer
formation, can predict how inlet flow rate, substrate wall property or deposit loading
level affect DPF pressure drop. In this section, the DPF pressure drop predicted by model
is compared with experimental results at varied soot or ash load under active regeneration
mode. The experimental condition and DPF specifications are listed in Table 2.1.
Table 2.1 DPF specifications and flow condition
DPF Length
6 inch
DPF plug length
DPF Diameter
5.66 inch
DPF cell density
DPF wall thickness
0.012 inch
Flow velocity
0.3 inch
300 CPSI
55,000 1/Hour
38
-.- 0 g/L ash
8
-u-3.0 g/L ash
-- 10.7 g/L ash
-- 6.9 g/L ash
7
3
CA
IA
I-2
U_
I--
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Soot Load g/L
Figure 2.11. Experimental DPF pressure drop with soot loading level at
different ash deposit load.
The measured DPF pressure drop data is shown in Figure 2.11. Generally, the DPF
pressure drop increases with soot loading level at any ash deposit load. However, the
DPF pressure drop increasing pattern has a sharp change from clean DPF to loaded DPF
at about 10 g/L of ash. As shown in Figure 2.11, under 1 Og/L of ash, the DPF pressure
drop firstly increases rapidly with initial soot loading then transits to cake filtration, under
which the pressure drop increases linearly with soot loading level. With the ash deposit
load increases, the non-linear DPF pressure drop growth during initial soot loading is
reduced. And at 10.7 g/L of ash load, the non-linear pressure drop phase disappears and
DPF pressure drop increases with soot loading from 0 g/L to 4 g/L.
39
@ ash load =Og/L
E
soot
4
Inlet channel
3
soot on the layer
E
0
/
Outlet Channel
-------
----
------ ----------------
0.5
0
(a)
1.5
1
soot load g/L
2
2.5
A5~I
(C)
@ ash load=OgIL
8
soot in the subsrate
0.6g
-A
.0
Ca
-
0. 6
U)
simulation
-eexpediment
IT
1
3
2
soot load g/L
4
5
S0.3
0
0ao0P2
II
slab
o0.35
A
4
F
slab 4
i
0.5
2
lb
1.5
1
soct load gL
2
2.5
(d)
(b)
Figure 2.12. Model simulation and experiment results for clean DPF.
(a) schematic picture of soot deposit inside wall and inlet channel. (b)
experimental and predicted DPF pressure drop data. (c) predicted soot
mass in wall and cake layer. (d) porosity of top four wall slabs.
SlabI
Slab n-1
Slab n
Substrate Wall
Figure 2.13. Substrate wall is discretized into slabs in the numerical
simulation.
40
*
M
soot
2.5
ash
2
Inlet channel
soot on the layer
1.5
E
1
soot in the substrate
0.5
Outlet Channel
/1
n
0
0.2
0.4
0.llg
0.6
soot load g/L
(a)
0.8
1
2
2.5
(c)
7
A,3R8
S.0
CL
6
U
eseriment @ ash load=
0.37
2
slab4
10
IL
4
CL
3
slab3
o0.36
SIb S2
0.35
simulation @ ash load=2.91g/L
1
2
soot load g/L
(b)
3
4
0
L-0
o..0.34
slabi1
i
0.5
1
1.5
soct boad g1L
(d)
Figure 2.14. Simulation results and experiment results for DPF at 3 g/L
ash load. (a) schematic picture of soot deposit inside wall and inlet
channel. (b) experimental and predicted DPF pressure drop data. (c)
predicted soot mass in wall and cake layer. (d) porosity of top four wall
slabs.
The model is useful in terms of providing hidden process information and interpreting the
physical process. The DPF soot and ash loading model is firstly applied in the case of
clean filter. As shown in Figure 2.12 (b), the predicted DPF pressure has a good
agreement with experimental data. The soot mass deposited inside substrate wall after
depth filtration is about 0.6 gram as show in Figure 2.12 (c). The porosity of top four
slabs of substrate with increasing soot load is shown in Figure 2.12 (d). In the numerical
simulation, the wall is usually discretized in to about 20 slabs as shown in Figure 2.13.
The physical interpretation of the simulation result for clean DPF is that significant
amount of soot penetrates into the substrate wall and causes larger non-linear DPF
pressure drop increase during depth filtration.
41
*
soot
*
2. J
6
2
ash
Inlet channel
:1.5
soot on the layer
E
0
(0
0.5
Outlet Channel
0(
soot in the substrate
/0.01g
0.2
(a)
slab 4
0.365
experiment @ ash load=10.7g/L
0.
slab 3
0.36
e
0.355
5
2
3
CI
soot load g/L
(b)
slab 2
0.35
0 0.345
simnulation @ ash load=10.67/L
4
2
3
1
1
I
0.37
4
0.8
(c)
-7I
6
0.6
0.4
soot load g/L
"76
slab
05
1
1.5
1
soot load g/L
2
2.5
(d)
Figure 2.15. Simulation results and experiment results for DPF at 10.7
g/L ash load. (a) schematic picture of soot deposit inside wall and inlet
channel. (b) experimental and predicted DPF pressure drop data. (c)
predicted soot mass in wall and cake layer. (d) porosity of top four wall
slabs.
For the case of 3 g/L ash load, the predicted DPF pressure drop from model is slightly
lower than the experimental observation. However, the difference is under the acceptable
level and predicted data shows the right trend of pressure drop curve as shown in Figure
2.14 (b). The soot mass deposited inside substrate wall is much lower than that in the
clean filter case. The mass deposited inside substrate wall in this case is 0.11 gram as
shown in Figure 2.14 (c), which is approximately one sixth of clean filter case. Thus the
physical scenario in this case is that because of existence of ash layer, the soot mass
penetrates into the substrate is much lower and respective pressure drop during depth
filtration is much smaller than that in the case of clean DPF.
For the case of 10.7 g/L ash load, the DPF pressure drop from both model and experiment
increases linearly with soot loading level. The difference between model prediction and
experimental data may arise from the difference in the estimation of cake layer thickness
42
or deposit permeability. As shown in Figure 2.15 (c), the mass of soot deposited inside
substrate wall is negligible. The physical situation is that almost no soot particle could
penetrate into the substrate wall since a rather thick layer of ash deposited on the DPF
channel. Thus, almost all the soot particles are collected on the substrate wall and form
the soot cake layer.
2.2.2 Depth Filtration and Cake Layer Filtration
For a new diesel particulate filter, the particle filtration eventually transits from depth
filtration to cake filtration. During the depth filtration, the soot particles penetrate into
substrate wall and plug the pores inside porous media. This will cause the pressure drop
across the porous media increase significantly in initial loading phase as shown in Figure
2.16. In the cake filtration phase, almost no particle goes into substrate wall and cake
layer thickness increases linearly with soot loading level. And DPF pressure drop also
increases linearly with soot loading level.
L oaded
APT
AP after initial
loading phase
-0
API
Initial loading
ph ase
Soot Loading
Figure 2.16. DPF pressure drop with soot loading.
One question discussed here is to compare the DPF pressure drop caused by depth
filtration and by cake filtration. The DPF soot and ash loading model is applied to
compute the DPF performance under two filtration modes. The simulation conditions are
typical DPF specifications and flow rate as shown in Table 2.2.
In depth filtration, all the particles are assumed to deposit inside substrate wall. And
respectively, all the particles are assumed to deposit on the substrate wall in cake
filtration. The DPF pressure drop results under two deposition phases are shown in Figure
2.17. The DPF pressure drop under depth filtration is an exponential-like curve which
increases rapidly with soot deposit mass. Respectively, DPF pressure drop under cake
43
filtration is linear curve with soot loading. The pressure drop caused by cake filtration is
much lower than that caused by depth filtration under the same soot deposit level. This
agrees with the experimental observations that DPF pressure drop increase rapidly during
initial depth filtration. This simulation results imply that during DPF filtration, if
possible, the depth filtration should be avoided.
Table 2.2 Simulation condition in depth/cake filtration comparisons
DPF Length
6 inch
DPF plug length
0.3 inch
DPF Diameter
5.66 inch
DPF cell density
300 CPSI
DPF wall thickness
0.012 inch
Flow velocity
20,000 1/Hour
Clean wall
1.5x10-' m2
Soot permeability
1x 10~ m2
permeability
X10
cake filtration-Good
6
800-
a.
5
0
s-
4
750-
3
0a
0
700a.
0.
exponential-ike curve
2
650
1
0
0.2
0.4
0.6
0.8
1.0
10
soot mass inside wall, g
(a)
0.2
0.4
0.6
0.8
soot mass on the wall,
1
1.2
g
(b)
Figure 2.17. DPF pressure drop caused the soot deposited in DPF.
(a) depth filtration. (b) cake filtration.
2.2.3 Ash Distribution among Substrate Slabs
In depth filtration one interesting issue is how the mass distribution inside substrate wall
affects the DPF pressure drop. In this section four types of soot distributions inside wall
are compared via model. The simulation conditions are stated in Table 2.3.
44
Table 2.3 Simulation condition in ash distribution among substrate slabs
DPF Length
6 inch
DPF plug length
0.3 inch
DPF Diameter
5.66 inch
DPF cell density
200 CPSI
DPF wall thickness
0.012 inch
Flow velocity
20,000 1/Hour
5x10~" m2
Clean wall permeability
Slab
1
Slab 2
Sl ab 3
Substrate Wall
Figure 2.18. Substrate wall is discretized into three slabs in soot
distribution analysis.
260
240220'U
2/3 : 1/3 : 0
180 14-
160
02/3
:1/6: 1/6
1/3 : 1/3 : 1/3
120
S0.1
0.2
0.4
0.8
soot ma S deposited inside substrate waU
Figure 2.19. DPF pressure drop with soot mass deposited inside
substrate wall under four assumed mass distribution patterns.
To simplify the problem, the substrate wall is discretized into three slabs as shown in
Figure 2.18. Four types of mass distributions are discussed. The mass distribution ratios
from slab I to slab 3 are respectively 1:0:0, 2/3: 1/3:0, 2/3: 1/6: 1/6, and 1/3: 1/3: 1/3.
The simulation results are shown in Figure 2.19. As can be seen, the uniform mass
distribution between slabs has the lowest DPF pressure drop and the most concentrated
distribution, which is 1:0:0, has the highest DPF pressure drop. Mathematically, this
45
behavior comes from the DPF pressure drop with soot loading during depth filtration is
soot
exponential-like curve as shown in Figure 2.17 (a). If the DPF pressure drop with
loading during depth filtration is a linear curve, the DPF pressure drop will not be
affected by mass distribution between substrate slabs.
2.2.4 Substrate Layer Optimal Arrangement
For certain particulate filter, the substrate wall is composed of several slabs (or layers).
Each slab has independent property that can be controlled during manufacture process. In
the design of this type of filter, there is a practical issue how to arrange the slabs to obtain
the optimal DPF performance.
A filter substrate wall has three slabs, which arises from a practical design problem, is
presented here. As shown in Figure 2.20, two arrangement methods are discussed in this
analysis. In this analysis all the slabs have the same porosity of 50%. The top slabs in
these two cases are same. Thus, the particles can penetrate into the porous media is same
in these two cases.
Case 2
Case 1
Slab 1
Slab 1
15
Slab 2
Slab 2
20
Slab 3
Slab 3
10 um, 50%
substrate
substrate
Figure 2.20. Two slab arrangement for a substrate wall.
The simulation results are presented in Figure 2.21 and Figure 2.22. As expected, the top
slabs in these two cases have the same amount of soot mass as shown in Figure 2.21. In
the case 1, since the slab 2 has a lower pore size than slab 3, the mass deposited in slab 2
is much higher than that in slab 3. Conversely in the case 2, because the slab has higher
pore size and lower filtration efficiency, the mass deposited in the slab 2 is lower than
that in slab 3. To sum up, the mass distribution between slabs in case 2 is more uniform
than that in case 1. According to the conclusion in the mass distribution inside porous
media, the DPF pressure in case should be lower than that in case.
The DPF pressure drop results for the discussed two cases are shown in Figure 2.22. As
expected, the DPF pressure drop for case 2 is lower than that in case 1. After depth
filtration, the DPF pressure drop difference can be as larger as 15%. Thus, the pressure
drop reduction by choosing the optimal arrangement is not trivial. An implication from
46
this study is that the pore size from slab 2 to slab n should decrease in the depth direction
with the top slab fixed.
Ca
5-
case 2 case 1
4-
cas e 1
-6 30
C
case 2
0
C
2-
case 2
1-
case
0
1
3
2
Slab Number
Figure 2.21. The soot mass deposited in each slab in the two slab
arrangements.
12001
case
(U
1000
cue2ijliliilll
2
0(I) 800
600
400
200
C
0.5
1
1.5
2
soot load g/L
Figure 2.22. The DPF pressure drop in the two slab arrangements.
47
The conclusion made above can be extended to the case of n slabs as shown in Figure
2.23. If all the slabs have the same porosity of 50% and the top slab property is fixed, the
optimal arrangement for slab 2 to slab n is letting the pore size decrease in the depth
direction. Under this arrangement, the soot distribution between slabs can be more
uniform than any other case. Thus the DPF pressure drop of this arrangement has the
lowest value.
The extended conclusion stated above has been validated by dozens of tested cases in
numerical simulation. The detailed results of these simulations are not presented here.
Once the substrate wall is composed of many slabs whose property can be independently
controlled, there is an issue about slab arrangement to achieve the best filter performance.
The DPF soot and ash loading model can be a useful tool to do the initial analysis and the
optimal plans suggested by model can be validated in experiments.
Substrate wall
Figure 2.23. A substrate wall with n slabs and each slab property can be
independently controlled.
2.3 Summary
In this chapter, a DPF model which considers exhaust flow, substrate filtration and cake
layer formation is built to simulate the DPF soot and ash loading process. The model also
takes soot particle size distribution and particle partition ratio into account, which make it
closer to the real physical process. Some useful and interesting summaries from this study
are following.
During DPF soot and ash loading process, the ash cake layer acts like membrane. Once
the ash cake layer is thick enough, it will block all the particles out of substrate wall and
make the DPF pressure drop increases linearly with soot loading level. Compared with
48
clean filter, the lightly ash loaded DPF (under 1 Og/ L ash) has lower pressure drop during
soot loading. Thus, a suitable amount of ash loading is helpful to reduce DPF pressure
drop. And this could be a new direction in the future DPF performance optimization.
It is founded that depth filtration has significant effects on DPF pressure drop compared
with cake filtration. The depth filtration is the reason of DPF pressure rapid growth in
initial loading phase. So, if possible, depth filtration should be avoided to reduce DPF
pressure drop.
For mass distribution between slabs inside substrate wall, it is concluded that the uniform
mass distribution has lowest pressure drop and most the concentrated mass distribution
has the highest pressure drop. Mathematically this arise from the substrate pressure drop
with deposited mass is an exponential like curve, which is a concave function. If the
substrate pressure drop with deposited mass is a linear curve, the mass distribution
between slabs should have no effect on DPF pressure drop.
For a substrate with n slabs, if the property of each slab can be independently controlled
in the manufacture process, there is optimization problem to arrange the slab in the right
order to achieve the lowest pressure drop. If all the slabs have the same porosity and the
top slab is fixed, the optimal arrangement from slab 2 to slab n is letting the pore size of
the slab decrease in the substrate wall depth direction.
49
3 Ash Spatial Distribution Effects
A small quantity of ash does deposit inside the porous filter wall, primarily in the surface
pores, during the so-called deep-bed filtration phase. However, most of the ash deposits
on top of the filter wall in the inlet channels. This analysis focuses on the effects of ash
distribution in the inlet channels, where conceptually there are three modes of ash
distribution. At given ash load, ash can accumulate either as a cake layer along the
channel or as an end-plug at the back of the channel, or has a certain radial distribution
among inlet channels. In reality, there is a combination of these distributions. This
section discusses the potential of DPF pressure drop reduction by optimizing the
distribution of ash inside DPF inlet channels. If certain kinds of ash distribution could
significantly reduce the DPF pressure drop, relevant technologies such as ash mobility
control would be worth developing to facilitate the preferred ash distribution.
3.1 Ash Deposit Accumulation
C)
Ca
Ca
0
-c
)
S +
100%
40
80%
35
30
-'
25
.0 60%
0
25_
20 .C
.
10 *
~U
LL 40%
MC1
20%
5
0%
-0
0
50
100
150
200
Service Interval [miles x 1,000]
250
Figure 3.1. Ash fraction of the total accumulated material in the DPF as
a function of total mileage prior to ash cleaning assuming a maximum
DPF soot load of 6 g/l for regeneration. [25]
The diesel particulate filter (DPF) is the key component of diesel after-treatment system
to meet stringent particle emission standards. The filter physically captures the diesel
exhaust particles by forcing the exhaust to flow through the porous filter walls. The
accumulated soot is oxidized either by regeneration with catalyst-assisted ignition at
lower temperatures, or regeneration by normal thermal ignition at higher temperatures.
However, in any case, incombustible material - ash - always remains after regeneration.
The majority of ash accumulated in the DPF originates from lubricant oil additives, fuel
50
additives, and engine wear. The DPF ash loading level is approximately linearly related
to the mileage of filter operation.
During most of the DPF's useful life, especially at moderate-to-high mileage (or
equivalent hours), there is more ash than soot present in the DPF at any time [25]. For
example, as shown in Figure 3.1, at 150,000 miles of mileage, there is more than 25g/L
of ash in the filter and the ash mass fraction at 6 g/L soot loading is more than 60%. Thus,
a good understanding of ash and its effects on DPF performance is crucial in optimizing
DPF performance.
3.2 Ash Permeability
Ash permeability is the key property of ash deposit, which determines the pressure drop
across the ash cake layer. In the ash spatial distribution analysis, ash permeability is the
input property that has significant influences on the simulation results. In this section, a
permeability estimation method based on DPF model is applied to calculate ash
permeability from DPF pressure drop data. At the same time, a collection of ash/substrate
wall permeability data from literature is presented and discussed.
3.2.1 Permeability Estimation from Experimental Data
The ash and substrate wall properties are essential to obtain reasonable projections of
distribution sensitivity using DPF model. Material properties data, such as ash density,
are provided by recent experiments at laboratory. Incidentally those studies addressed the
effects of lubricant formulation on DPF performance. The lubricant formulations tested in
the experiment are shown in Table 3.1. The DPF pressure drop due to ash accumulation
is shown in Figure 3.2. Ash packing density is directly measured in the experiments.
However, key information such as ash permeability and substrate wall permeability
cannot be directly measured from the experiments, but can be derived from carefully
analyzing the results in conjunction with basic DPF flow models.
Table 3.1 Six lubricant formulations tested in experiments.
Zn
P
5
2070
<1
<1
<1
<1
2612
1280
2
<1
2530
1180
<1
1730
1280
1180
1388
355
1226
985
Lubricant Formulation
Ca
Mg
Base+Ca
Base+Mg
Base+ZDDP
Base+Ca+ZDDP
2928
<1
<1
2480
Base+Mg+ZDDP
CJ-4
ppm
51
Ash permeability, as used in this context, means ash cake layer permeability and wall
permeability refers to the wall permeability after depth filtration, and is assumed to be
constant. The permeabilities of the ash and substrate wall are crucial parameters which
will determine the effects of ash distribution inside the inlet channel on DPF performance.
From some preliminary analysis, it is found that moving ash to the end of the channel is
beneficial to reduce DPF pressure drop under some combinations of ash and wall
permeabilities. However, for a different set of ash and wall permeability values, moving
ash to the end forming an end-plug may increase the DPF pressure drop, which totally
reverses the conclusion. Thus, the key issue is to know the real permeability of the ash
and wall under real DPF operating conditions.
3.5-3.0--
Ca + ZDDP
'ir
Ca
CJ-4
XC 2.5 -Oa2.0 --
leeMg + ZODDP
P__
1.0
3
Mg
ZDDP
0.5
0.0
0
5
10
15
20
25
30
35
40
45
Ash Load [g/L]
Figure 3.2. Experimental DPF pressure drop with ash loading for all
lubricant formulations at a constant space velocity 20,000 1/Hour [26].
Up to now, few publications have discussed the ash and substrate permeability at real
DPF running conditions. More often, the DPF total pressure drop, which couples the
substrate wall, ash cake layer and flow friction effects, is described in the literature.
Further, it is very difficult to directly measure the pressure drop of the ash cake layer or
substrate wall in a real DPF without disturbing the ash cake layer and substrate wall
properties.
As shown in Figure 3.2, there is a linear increase region in the DPF pressure drop curve,
which is generally between 3g/L to 15 g/L ash load. This section of the curve should
contain the information for the ash permeability and substrate wall permeability. The
approach of the analysis is outlined as below. To estimate the ash and wall permeability
after depth filtration, the following assumptions are essential. These assumptions are
supported by the experiments conducted in the lab.
52
1) Cake filtration dominates after 3 g/L ash load.
2) Before 15 g/L ash load, the ash cake layer has uniform thickness and no ash plug
is formed at the end of inlet channel.
3) Ash and wall properties do not change from 3g/L to 15 g/L ash load.
DPF Pressure Drop Experiment Data
3.0
y = 0.0398x + 1.3342
R2 = 0.9843
2.5 12.0 0.
01.5
a
"=1.0 -
--- +--- Experirnent data
Data used in analysis
Data linear fitting
It'
20.5 0.0
0.0
5.0
10.0
20.0
15.0
Ash Load g/L
25.0
30.0
35.0
Figure 3.3. Linear fitting in ash/wall permeability estimation.
M
Ash cake layer
0
Ash end plug
Inlet channel
Figure 3.4. Assumed ash distribution inside inlet channel at
permeability estimation.
The DPF pressure drop data between 3g/L and 15 g/L ash load, shown in Figure 3.3, is
approximately linear. Physically this corresponds to a scenario, as shown in Figure 3.4, in
which the ash cake layer has uniformly increasing thickness without ash penetrating into
the substrate wall or being swept to the end of the channel to form ash end-plug. The total
DPF pressure drop has three components as shown in Eq. (3.1). From 3g/L to 15 g/L of
ash load, the substrate wall pressure drop is a constant, the flow friction pressure drop can
be estimated from Eq. (3.2), and the ash cake layer pressure drop increases linearly with
53
ash loading as shown in Eq. (3.3). Here, the pressure loss caused by gas contraction and
expansion is ignored, since its contribution is relatively small in this analysis.
A
APDPF
all
(
pp ,LFUL
3
APwai+ APash
Sa =
Yash
.2-
±ash friction
(3.1)
1
(3.2)
2
(b - 2sa )2
/-- S. +
kw
+
bk
(3.3)
S
ka
(3.4)
VDPF
PashNchanneLef b
In Eq. (3.4) the ash layer thickness is calculated based on ash load Yas (unit is g/L) and
DPF geometry (including filter length Leff, channel width bk, channel number Nel
and DPF total volume VDPF). Combining Eq. (3.3) and Eq. (3.4) results in Eq. (3.5). Once
the linear curve from the data fitting is determined, as shown in Figure 3.3, a and b in Eq.
(3.5) can be obtained. As shown in Eq. (3.6), ash permeability is related to slope of the
linear fitting, a, and wall permeability is related to its intercept with the vertical axis.
'a ± APash =ADPF - (Apfriction)
madel
=
pu,
2.VDpF
k,
4
. ash
PashNann LeffbkY
+P"1W
(3.5)
k,
a -Yasi+b
VDPF
ka = pu,
a PashNchanne2 Leffbk
(3.6)
k = puWS.
b
Using the linear-fitting method mentioned above, the wall and ash permeabilities from
estimates are shown in Table 3.2. However, the three assumptions used in this analysis
may idealize the situation for real DPF operation. For example, ash packing density may
slightly change from 3g/L to 15g/L ash load since regenerations keep heating the ash
during this process. Thus, the estimated permeability will have an error proportional to
the change in ash packing density. Meanwhile, for each type of ash, usually only about 4
to 6 experimental data points are available for the least square fitting from 3 g/L to 15 g/L.
Thus, the experimental measurement error may affect the final estimation results.
Therefore, the data shown in Table 3.2 may need further validation in the future.
54
Table 3.2. Estimated permeability of ash generated from six lubricant formulations.
Lubricant
Ash Permeability
Wall Permeability
m2
2
Ca
1.67 x10-
4
4.56 x10-14
Zn
8.56 x10- 4
10.5 x10- 14
Mg
57.4
4
xIO-~
5.82 x10-14
Ca + Zn
4.46 x10-
4
3.75 x10-14
Mg + Zn
4.80 x10
4
9.35 x104
11.1 x10- 4
4.98 x104
CJ-4
*Note: Ash permeability here means ash cake layer permeability, and wall permeability
means the permeability of wall after depth filtration phase.
3.2.2 Permeability from Literature
Table 3.3 Published ash and substrate wall permeability from literature
Source (SAE)
Ash Permeability (in 2 )
2011-01-2091
2.8x10-4 to 7.4x10-14
Wall Permeability
Notes
(M2 )
SAE2000-01-1016
19x10' 4
2013-01-0837
0.95-5.
2000-01-1016
5.3x10-13
_
ash particle size 0.5 ~ 2 micron
2.77 to 7.4 x 10-14
(clean)
2004-01-0948
Ksoot=3.2~3.3 x 104
Kash
10 kwai
8.9x 10-12
2009-01-0630
2009-01-1272
1.8x10- 4 and 2.3x10 4
3.3 x 10-13
3.2x 10~12 (clean wall)
2006-01-3256
89-04-05
5.8-9.6x10- 4
1.8-2.2 x 10-14
8.5x10- 14 to 7.9x10-13
1.8-3.5 x10- 3
2007-01-0045
2003-01-0846
2002-01-2786
4.1-4.4x10- 3
1-8x10- 3
1.2-3.3x10- 3
55
A significant amount of effort was devoted to the search of ash permeability reported in
the literature. However, no directly measured DPF ash permeability was founded in the
publications. This is probably because of the high difficulty in obtaining ash sample and
measuring it without disturbing. But there is still some published ash permeability data
which is estimation from experiences or calibrated data in model fitting.
From the literature, the ash permeability range is 1.8 - 9.6 xIO-14 m 2 and wall
permeability range is 0.95x10-14 to 8.5x 10-1 M2 . The ash and substrate wall permeability
range generally agrees with the estimation from experimental data.
3.3 Radial Distribution Effects
From the DPF experiments, the ash non-uniform distribution between inlet channels has
been observed in both active and passive regeneration. This phenomenon may come from
the non-uniform porous media property from manufacture or non-uniform flow
distribution because of tube and filter geometry. The sensitivity of DPF pressure drop to
ash radial distribution is discussed using modeling approach.
3.3.1 Model Formulation
The cylindrical filter is equally discretized in the radial direction into annuluses as shown
in Figure 3.2. Each annulus is treated as a separate zone. Assuming that all the inlet
channels in the same zone behave the same, a representative channel for each radial zone
has to be solved.
The model for the representative channel is the typical ID, 2 channels model, as shown in
Figure 3.5, which is introduced in Appendix 1. The solution of the representative channel
depends on the respective flow condition at the entrance of the zone. The flow velocity
entering each zone depends on the pressure drop of each zone, in other words it depends
on channel ash loading level. For example, if the channels in the center have lower ash
layer thickness than that in the peripheral part and no plug is formed in any channel, the
flow rate in the centered channel should be higher than that in the periphery to achieve
same pressure drop.
The flow distribution for each zone is computed by an iterative procedure. Initially, a
guessed flow distribution is assigned to the zones and the ID, 2 channels model is applied
in each zone to calculate the pressure drop. If the pressure drop from each zone is not
same, the guessed flow distribution is corrected base on individual zone pressure drop.
This trial-error method continues until the pressure drop calculated in each zone becomes
same. The detailed procedure is presented following.
56
Step 1: assume a uniform flow distribution. You can also use other flow distribution in
this step. Q is the given DPF entrance flow rate. Q, is the initial flow rate for zone i.
(3.7)
Q =Q
Step 2: calculate APi based on ID, 2 channels model based on the assigned flow
distribution. Here, APi is the calculated pressure drop for zone i.
Step 3: correct the flow distribution. Si here is the area of each zone in the entrance.
n+1
Oin
_
(3.8)
Q"S, AP
APj
Step 4: go back to Step 2 if APi difference is higher than the tolerance.
E
IrnuIaS.a
Ash cake layer
M Ash end plug
naaI
I
(a)
1D, 2 Channels Model
(b)
Figure 3.5. DPF ash radial distribution model. (a) discretized zones in
radial direction. (b) one dimensional, two channels model.
3.3.2 Results Discussion
Two patterns of ash distribution inside channels are considered in this study, which is
shown in Figure 3.6. The first pattern is that all the ash in the inlet channel is to form the
ash cake layer. The second pattern assumes that all the ash in the inlet channel deposits as
end-plug. In the simulation, the diesel particulate filter is discretized into 20 zones and
discretization positions are equally distributed in the radial direction. The zone in the
center has the lowest ash loading level, which is lOg/L. The zone in the periphery has the
57
highest ash loading level which is 40g/L. As shown in Figure 3.7, the ash loading of the
respective zone linearly increases in the radial direction.
Ash cake layer
*
Ash end plug
Ash
cake layer
Inlet channel
Inlet channel
(a)
M Ash end plug
plugd)
(b)
Figure 3.6. Two distribution patterns considered in the radial
distribution analysis. (a) all the ash forms the cake layer. (b) all the ash
forms the end-plug.
40 g/L ash
40
tI~-I~ij
0
I
"Cj
---------------- ---------
10
0
Radial Position, r
R
10 g/L ash
Figure 3.7. Ash radial distribution considered in the simulation.
(a) Discretized zones in radial direction. (b) increased ash loading
level in radial direction.
Table 3.4 DPF specifications and flow condition used in simulation
DPF Length
DPF Diameter
DPF wall thickness
6 inch
5.66 inch
0.012 inch
DPF plug length
DPF cell density
Flow velocity
0.3 inch
300 CPSI
50,000 1/Hour
58
The simulation conditions are presented in Table 3.4. The DPF geometry is common
commercialized DPF specifications. The flow velocity of 50,000 1/Hour is used here.
One thing worth noting is that flow velocity has minor effects in the ash radial
distribution analysis. And this is also validated by the simulation results.
The simulation results of the first distribution pattern, presented in Figure 3.6(a), are
shown in Table 3.5. The DPF pressure drop is investigated at different combinations of
ash layer permeability and wall permeability as listed in Table 3.5. Generally, the
pressure change ratio caused by ash radial distribution is rather small at these wall/ash
layer permeability conditions. Here, the pressure change ratio is defined as following.
pressurechange ratio =
A
"oneven
Apeven
(3.9)
Aeven
The simulation results from the second ash distribution pattern are shown in Table 3.6.
The simulation conditions (ash layer/substrate wall permeability) are same with that in
the first case. However, as shown in Table 3.6, the pressure change ratio is much smaller,
which is all below 0.2%. That suggests that ash radial distribution as end-plug as minor
effects on DPF pressure drop.
Table 3.5. DPF Pressure change ratio with ash radial distribution when ash deposits as
cake layer.
Ash Layer Permeability (m 2
Wall
Permeability
2
1.00E-12
1.00E-13
1.00E-14
1.00E-12
0.18%
-2.05%
-6.98%
I.OOE-13
1.07%
0.22%
-4.51%
1.00E-14
0.31%
0.30%
-0.28%
11.00E-15
0.04%
0.04%
0.07%
59
Table 3.6. DPF Pressure change ratio with ash radial distribution when ash deposits as
end plug.
Ash Layer Permeability (m2)
1.00E-12
1.00E-13
1.00E-14
0.12%
0.12%
0.12%
1.OOE-13
0.20%
0.20%
0.20%
L.OOE-14
0.03%
0.03%
0.03%
l.OOE-15
0.00%
0.00%
0.00%
Wall
Permeability l.OOE-12
(m2)
3.4 Ash Cake Layer Profile Effects
3.4.1 Model Formulation
The model has the capability to consider the DPF with both soot and ash deposits.
However, the study in this section mainly focuses on the issues - relating to ash
deposition. As shown in Figure 3.8, the ash within the particulate filter can be divided
into two categories. The ash of the first category distributes in the rear part of the
channels resulting in a form of plug clogging the rear part of the inlet channels. The ash
of the second category deposits as a layer with varying thickness along the filter walls.
Both types of ash deposits are considered in the model. From ash loading experiments, it
is found that ash inside DPF channel has significant ash end-plug formation and nonnegligible cake layer variation in the axial direction [27].
Ash wall layer
Ash end plug
1l
Figure 3.8. Ash distribution inside one DPF inlet channel.
60
This section focuses on discussing DPF pressure drop within the effective filtration
length (assuming impermeable end-plugs), since variable layer thickness is considered in
this region. DPF pressure drop outside the effective filtration length, such as entrance
effects, has been well studied by others in previous publications [4].
Once the DPF channel accumulates an ash cake layer of variable thickness, the open
width of the inlet channel is no longer a constant, but changes in the DPF axial direction.
Thus, the governing equations in the inlet channel should be different from those
considering a constant channel width. The detailed derivation of the equations is given in
Appendix 2. This equation is valid for the effective filtration length Leff, meaning the
length in which the exhaust flows through the filter wall from an inlet to an outlet channel.
The flow through the end-plugs has been estimated to be small and is negligible.
Effective filtration length is calculated through Eq. (3.10). LPI., is the DPF plug length
and Lash-ptug is the ash deposit end plug length.
(3.10)
Leff = LDPF - 2 x Lplu, - Lash-plug
Considering the normalized velocity in channel 2 (outlet channel) results in:
0=
d
d2
B 2+
dL
d
(d
Amod1
"'
b2
A
3 L
d
+k
B
B
d
di
L
)
k
b,
+Id(G^2)
b
-2AA
d
2A
b
bl.
bk
2
b
Y
d
b,
2
dub
2AA
A 2 (+
2
b, d
k
)a2
(3.11)
b,
dbI
d2
dui
du2
2Amod
+
d)
d2
- Ab
bl, dz
du
A
2
9
bA
+A
bk4
1
bZ
A -2A -b_
b A
u
d2
2
d2
(3.12)
y db0
d2
Since the shooting method always fails to converge in solving Eq. (3.11), a pseudo time
loop is used to find the solution with an initial condition. Thus, the simulation solves the
one dimensional transient flow problem inside the DPF, which results in Eq. (3.12),
which is essentially Eq. (3.11) with one time derivative term on the left hand side.
The following parameters are defined:
Re = pui"bk
(3.13)
77
61
4 Leff
A =
bAs-
Re
2
L _
A
22= 4F k,
(3.15)
L
bks,
bk
Re 4 Lffk
A3
(3.16)
bk 2s1
B,
2
(3.14)
bk
AOd
, L+s kw
k, sw
(3.17)
sa k
k,
)
±,ss k + Pasa kw
= 4Re kP+
Lff
s
s
(3.18)
A = bj 0(2 =0)2
(3.19)
The boundary conditions of Eq. (3.12) are as follows:
6 2 (^Z=O)=O
(3.20)
u 2 (z=1)= b 1 (2-0)2
(3.21)
The initial conditions of Eq. (3.12) are:
u 2 z = 1) =
bi(2= 0)2
bk
(3.22)
else where, U2 (zz # 1)= 0;
Eq.(3. 11) is an ordinary differential equation and Eq.(3.12) is a partial differential
equation. Numerically it is much easier to solve Eq.(3.12) than Eq.(3.1 1) because
Eq.(3.1 1) is difficult to converge. Using a pseudo time loop to solve Eq. (3.12) turns out
to be rather robust and efficient. Actually, Eq. (3.12) can use any initial condition besides
Eq. (3.22) once it satisfies the boundary condition. When the pseudo time loop reaches
62
the equilibrium state, the velocity obtained is the solution of Eq.(3. 11). The normalized
filtration velocity profile results from Eq. (3.12) as:
dui2
d2
dU(3.23)
Thereby, the pressure drop along the effective filtration length can be calculated as
follows:
=
A1 (i|(2 =1) - 6i(2 = 0))+ A2 U2d
0
Bza,(O)+
mO
di(0)
(3.24)
The final step involves calculating the real pressure drop from the normalized pressure
drop. It is rather easy to recover the normalized term to its original form. The solution of
the differential equation and the calculation of the pressure drop are performed using a
programmed MATLAB code. The calculation is very fast and usually less than 2 seconds.
3.4.2 Results Discussion
Based on the ash/wall permeability estimated in the previous section, the reformulated
one dimensional model is applied to study the ash cake layer profile effects. Four types
of ash cake layer profiles, shown in Figure 3.9, are investigated in this study. For the
same ash loading level, the DPF pressure drop of four investigated ash layer profiles are
compared. The flat ash cake layer is the baseline of the comparison. The pressure change
ratio defined in Eq. (3.25) is used to quantify the pressure change caused by different ash
layer profiles.
pressurechange ratio = AP(nonflat layer) - AP(flat layer)
AP(flat layer)
(3.25)
The sine wave profile in Figure 3.9 has a minimum thickness of zero and a maximum
thickness of two times the average thickness. It has three complete sine wave cycles
along the whole DPF length. The linearly decreasing ash layer has a thickness of about
two times the average thickness at the channel entrance, and zero thickness at the end of
channel. The linearly increasing ash layer has the reversed profile of the linearly
decreasing ash layer. Table 3.7 shows the maximum ratio of ash cake layer thickness to
half of the channel width for four ash layer profiles. At 20 g/L ash load, the ash cake
layer generally occupies 11% of the clean channel open width for a flat ash cake profile.
For non-flat ash layer profiles, at the narrowest channel position, the ash occupies 22% of
the clean channel open width.
63
Ash cake layer
(a) Flat ash cake layer
(c) Sine wave ash layer
*
Substrate Wal
(b) Linearly decreasing ash layer thickness
(d)Linearly increasing ash layer thickness
Figure 3.9. Four types of investigated ash layer profiles.
Ash generated from six lubricant formulations were studied in the analysis. From the
simulation, in most of the cases, DPF pressure drop is not very sensitive to the ash layer
profile from 0 to 20g/L ash. As shown in figure 3.10, up to 20g/L ash load, the DPF with
the Mg ash layer does not have much difference in pressure drop between a flat and nonflat ash layer. The maximum difference in pressure change ratio is about 2%.
Table 3.7. Maximum value of 2xSash/bk for four ash cake layer profiles
at 2 ash load levels
load
Layer pr
flat
Sine wave
Linear increase
Linear decrease
10g/L
20g/L
5.2%
10.6%
10.6%
10.6%
10.8%
22.2%
22.0%
22.0%
Among the six types of ash, Ca ash is most sensitive to the ash cake layer profile, which
is shown in Figure 3.11. The maximum difference in pressure change ratio is
approximately 10% at 20 g/L ash load. In the real ash loading process, ash end plug starts
to form at about 15 g/L ash load. Thus, the practical ash layer profile effect is less than
64
8% as shown in Figure 3.11. In this case, the ash permeability is rather low and the nonflat ash layer helps to reduce the DPF pressure drop.
Mg Ash Layer Profile Effect
2
a,
sine wave
linear increase
linear decrease
1.5
a)
1
0)
0.5
C.
0-0.5-1
5
10
15
ash load g/L
-
20
Figure 3.10. Mg ash pressure change ratio of three cake layer profiles.
Ca Ash Layer Profile Effect
0)
.4-0
C:
-21-
aD
0.
40
(U
C/)
C,
-6 -8
-10
-12
-
5
sine wave
linear increase
linear decrease
10
15
20
ash load g/L
Figure 3.11. Ca ash pressure change ratio of three cake layer profiles.
65
3.5 Ash End-plug Effects
3.5.1 Ash Distributed as Layer and End-plug
This section considers the effects of ash end-plug length at a given amount of ash deposit
inside DPF channel. Ash is assumed to accumulate as a combination of deposits on the
channel walls as flat layers, and at the end of channels as end-plugs, which is shown in
Figure 3.12. The ash distribution in the inlet channels can be described by the ash plug
ratio defined at Eq. (3.26).
Ash Plug Ratio : z= AshPlug Mass
Total Ash Mass
M Ash cake layer
(nl)
(a)
sh lg R
M Ash end plug
(3.26)
Ash cake layer
Ash end plug
layer
Ash Plug Ratio=O
(b) Ash Plug Ratio=0.5
Figure 3.12. Ash distributions inside DPF channel under two ash plug
ratios. (a) ash plug ratio=O. (b) ash plug ratio=0.5.
One way to quantify the ash plug length effect on DPF pressure drop is to introduce the
target function, f, defined in Eq. (3.27). It provides a measure of DPF pressure drop
change for two extreme cases of ash distribution (one is all the ash forming the end-plug,
and the other is all the ash forming the cake layer). When the target function is negative,
it means that moving more ash to form an end-plug is beneficial to reduce DPF pressure
drop. When the target function is positive, moving more ash to the end of the channels
will increase the DPF pressure drop.
Target Function:
f-
AP(z = 0)
(3.27)
66
3.5.2 Parameter Analysis
One key objective of this analysis is to determine the parameters affect the target function,
f. In the following analysis, all the relevant parameters are listed. The parameters include
the flow rate, DPF geometry, ash load level, ash/wall properties, etc.
flow:
u
Length/Vol ume:
bk
permeability:
ka
Pair
L
Vash
Sw
kw
From the simulations, it is found that the target function is weakly related to the flow
velocity, u. This is due to the fact that the three major parts of DPF pressure drop, as
shown in Eq. (3.1), are nearly proportional to flow velocity, since flow inside DPF
channel is laminar in most cases. For the commercial DPF, the parameters such as length,
diameter and substrate wall thickness are standardized and can be treated as constants.
Thus, the unknown parameters in this analysis which remain are ash volume V,,h , ash
permeability k. and substrate wall permeability k,.
The three unknown variables can be rewritten in non-dimensional form in Eq. (3.28-3.30).
M is the material restriction ratio, which is the ash cake layer pressure drop divided by
wall pressure drop. C is the channel friction ratio, which is flow friction pressure drop
divided by the wall pressure drop. G is the ratio of ash deposit volume relative to the DPF
channel volume. These three variables are non-dimensional and have clear physical
meaning.
ash
M
-
_ APash layer
4Lbkk
k.
G
Vh
bk2 L
ash volume
channel volume
F 4L2
3 bkb
2
V
L
C
Ws
+
bk
APtlowfiction
(3.30)
wPall
67
One way to validate the variable reduction is to write the target function as a function of
M, G and C. Based on the work of Konstandopulous [22], the DPF pressure drop can be
decoupled as three components. The target function can be expressed by M, G and C.
AP(z =1)-AP(z
AP(z=0)
friction,z
fictio/X~flcto-o
n,z=0
=0)
a
=1
-1
wall,z=s
o +=AP ash,z=O
+ 1
C(_G ),G)
2-G
2
1-G
C+M+1
(3.31)
3.5.3 Sensitivity Map
To understand ash plug length effect from a broader perspective, the contours of the
target function are plotted in the plane of (M, C) at a given G (which specifies the ash
loading level). These plots are shown in Figure 3.13 and Figure 3.14. These figures
condense the information and facilitate identification of the regions suitable for moving
ash back to the end of channel.
For example, in Figure 3.13, where G equals 0.27 (the ash load is 20g/L), the upper
region shows a negative target function. This means moving more ash to the end of
channel helps to reduce DPF pressure drop. In this case the material restriction ratio is
very large, which means the ash cake layer pressure drop is dominant. Moving ash to the
end of the DPF to reduce the cake layer thickness is beneficial to reduce the total DPF
pressure drop.
In the lower region of Figure 3.13, the target function is positive. In this region, moving
ash back to form an end-plug will increase DPF pressure drop. In this scenario, the
material restriction ratio is very low, which means the ash cake layer pressure drop is
trivial, but the substrate wall pressure drop is the dominant contributor to the total DPF
pressure drop. Thus, moving ash to the end of channel will not reduce the ash cake layer
pressure drop much, but will increase the wall pressure drop significantly since flow
velocity increases as the ash end-plug length increases. Increasing the ash plug ratio in
this case will increase the total DPF pressure drop.
68
G=0.27 (Geometry Ratio)
0.2
-36%
-83%
10
0
1
-0.2
-12%
-0.4
0.2%
0.1
-0.6
24%
0.01
F
12%
,__,,_
0.001
,
0.1
0.01
-0.8
1
C, Channel Friction Loss Ratio
Figure 3.13. DPF sensitivity contour map at 20g/L ash load.
(DPF:6"L, .66"D)
[Sensitivity, Eq.(3.27): Positive values increase pressure drop in moving ash towards
channel end]
G=0.54 (Geometry Ratio)
-78%
-40%
0.8
-21%
0.6
10
0
0.4
IU
0.2
1
-25
0
-0.2
17%
0.1
-0.4
54% 36%
0.001
0.01
.0.6
0.1
1
C, Channel Friction Loss Ratio
Figure3.14. DPF sensitivity contour map at 40g/L ash load.
(DPF:6"L, 5.66"D)
[Sensitivity, Eqn. (3.27): Positive values increase pressure drop in moving ash towards
channel end]
69
Figure 3.14 shows another example, in which G equals 0.54, which indicates an ash load
of 40g/L. The general pattern of the contour is similar to the case of 20 g/L ash load
(when G equals 0.27). However, it seems more regions exhibit a positive target function
The reason for this is that, at larger ash loads, the DPF will have longer ash end-plugs
when the ash plug ratio equals zero, which increase the wall velocity to a larger extent.
This will increase the DPF pressure drop.
3.5.4 Sensitivity Map with Actual DPFs
A more interesting question would be where the experimental data for the DPF and
lubricant formulation tests stand on this sensitivity map. From the previous section, the
permeability of the DPF wall and ash generated from the six lubricant formulations were
estimated using the experimental data. Using the wall/ash permeability, three nondimensional numbers can be calculated and plotted on the sensitivity map.
Figure 3.15 shows the sensitivity map with real DPFs at an ash load of 20g/L. These data
points lie in the regions which have both positive and negative target functions. This
means that moving the ash to the end of channel does not necessarily reduce the pressure
drop for all of cases. The pressure change ratio result for this case is shown in the Table
3.8.
Figure 3.16 shows the sensitivity map with real DPFs and an ash load of 40g/L. It
exhibits a similar pattern as in Figure 3.15, and the real DPF/material data points still lie
in both the negative and positive regions. The target function for each kind of ash is
shown at Table 3.8. From 20g/L to 40 g/L ash load, the sign of the target function does
not change, but the absolute values increase. This behavior suggests that increasing the
ash load will amplify the effects of the ash plug ratio on DPF pressure drop.
Table 3.8. Target Function for real DPF and ash at two ash loading level
Target Function
Lubricant Additive Target Function
20 g/L ash
40 g/L ash
Ca
-24%
-31%
-9%
-5%
Zn
48%
22%
Mg
Ca + Zn
6%
18%
-22%
-15%
Mg + Zn
CJ-4
14%
32%
70
.~~1
G=0.27 (Geometry Ratio)
0.2
'U
IV
0
I
-0.2
Mg4.b
-12%
-0.4
12%
0.1
02%
24%
-0.6
*Mg
-0.8
0.011
0.001
0.01
1
0.1
C, Channel Friction Loss Ratio
Figure 3.15. DPF sensitivity contour map at 20g/L ash load with real
DPF and ash data. (DPF:6"L, 5.66"D)
[Sensitivity, Eq. (3.27): Positive values increase pressure drop in moving ash towards
channel end]
G=0.54 (Geometry Ratio)
0.8
-40%
-0
0.6
10
0.4
a:
0,2
-2%
1
0
-02
0.1
92%
0.001
4 7%'C-
-44
'Mg4
0.01
0.1
46
1
C, Channel Friction Loss Ratio
Figure 3.16. DPF sensitivity contour map at 40g/L ash load with real
DPF and ash data. (DPF:6"L, 5.66"D)
[Sensitivity, Eq. (3.27): Positive values increase pressure drop in moving ash towards
channel end]
71
Figure 3.17 shows the sensitivity map with reported ash/substrate wall permeability range
from literature at an ash load of 20g/L. Again, the possible ash/substrate wall range
shown in the sensitivity map lies in the regions that have both positive and negative target
functions. This means that moving the ash to the end of channel does not necessarily
reduce the pressure drop for all of cases. Thus, whether moving ash to the end of the
channel is a good strategy really depends on what combination of ash/substrate
permeability in the analysis. Thus, once given these needed permeabilities, a better
distribution pattern can be specified.
I0
N2=0 2684
0.2
-83%
10
0.1
0
(U
-W
-0.4
12%2
'
.1
-0.5
-06
24%-
-0.7
0
-
0.01
-0.8
0.001
0.01
0.1
1
C, Channel Friction Ratio
Figure 3.17. DPF sensitivity contour map at 20g/L ash load with DPF
and ash data from literature. (DPF:6"L, 5.66"D)
[Sensitivity, Eq. (3.27):
Positive values increase pressure drop in moving ash towards
channel end]
3.6 Summary
A reformulated DPF model combined with experimental data was applied to analyze the
effects of ash spatial distribution inside DPF channels on the total DPF pressure drop.
The key conclusions are as follows:
In the normal region of ash/substrate permeability, ash radial distribution, no matter
deposits as cake layer or end plug, has minor effect on DPF pressure drop.
72
During most of the ash loading process, the average ash layer thickness is less than or
equal to 11% of the clean DPF channel open width, the precise shape of the ash
distribution profile along the channel has a small and insignificant effect on DPF
pressure drop.
The ash end plug length has relatively large effect on DPF performance. For example, at
20g/L ash load, the ash distributed as end plug or as cake layer could introduce a 20%
difference in terms of DPF pressure drop. However, the optimal distribution pattern
depends on the ash permeability and wall permeability. At known ash/wall permeability,
the optimal distribution can be determined according to the sensitivity map developed in
this study.
73
4 Ash Transport Modeling
Ash accumulation inside diesel particulate filter causes filter pressure drop rise and
reduces its useful life span. The ash distribution pattern in the channels of filter is an
important question since it determines the DPF performance. Thus, the formation of
distribution pattern, ash transport, needs to be studied. During active regeneration, ash
transport is a rather complex process since flow dynamics across a small particle,
cohesion forces between particles, particle sintering and soot oxidation are couples in this
process. Based on experiment observations, a one dimensional model considering local
flow velocity is built to help understand the dynamic process.
4.1 Experimental Observation and Analysis
Since most of our experimental observations are obtained under active regeneration mode,
the discussion will focus on the active regenerative transport.
4.1.1 Ash Distribution inside DPF Channels
The major function of diesel particulate filter is to capture the soot particles of exhaust
gas and the accumulated soot in the channel is burned during active regeneration.
However, the incombustible material - ash remains after each regeneration and keeps
increasing with running hours. After vehicle reaches certain mileage, there will be
significant amount of ash inside DPF inlet channels. As shown in Figure 4.1, there is a
rather long ash plug at the rear end of filter inlet channels and it has many fractures due to
high temperature during active regeneration. At the same time, there is a significant ash
cake layer deposited on substrate wall. The dark material on the white ash cake layer is
soot deposit that comes from soot filtration.
Figure 4.1. Ash distribution inside DPF inlet channels as cake layer or
as end plug.
The diesel particulate filter ash aging process is very slow in reality. For example, to
observe the significant amount of ash in the filter, the vehicle may need to run about
74
100,000 miles or equivalent time of several years. To simulate the filter ash aging process,
an ash accelerating system is built by the experimental group [25]. The lubricant oil is
burned in a specially designed burner and the exhaust gas is directed to flow through the
diesel particulate filter. It only takes a few hours in the accelerating experiments to
simulate the vehicle aging process of multiples years.
Since the open width of diesel particulate filter channel is rather small (usually 1.5mm), it
is very difficult to observe the ash distribution inside inlet channels. The common
approach is to carefully cut the channels and take pictures of deposit and channel under
microscope. The ash distribution inside inlet channels under two ash load level is show in
Figure 4.2. The observed samples come from the accelerated ash loading experiment
using CJ-4 lubricant oil [25-27].
1.5
E
1.3
1.0
In
~d
0.8
-j
- ------------------ I ---------- ------
-- ------- ------------------------------------------- ----------------
---------------- -- '- ---------------------------
-------- -------
--------------------- -------- ----------- ------------------------ ---------
0.5
0.3
---------------- ---
0.0 0
0
...... --
--------------
--------------------
--------*-----------------------------------I------------------7 25
50
Axial Distance
75
100
125
150
125
150
(a) At 12.5 g/L ash load
----=noun
1.5
E1.3
E
t 1.0
.00
0.8
-i
(0.5
0.3
(0.0
U
-J
0
25
50
75
100
Axial Distance [mm
(b) At 42 g/L ash load
Figure 4.2. Ash deposit inside DPF inlet channels from
accelerating ash loading system using CJ-4 lubricant oil.
(a) at 12.5 g/L ash load. (b) at 42 gIL ash load.
As show in figure 4.2 (b), there is a significant amount of ash end plug inside channels
which suggests that a larger amount of ash is transported to the rear end of channel. From
75
figure 4.2(a) and 4.2(b), it is clear that the ash cake layer thickness linearly increases in
the front part of inlet channel. Without ash transport, the ash cake layer should have
uniform thickness everywhere. Thus, at 12.5 g/L and 42 g/L ash load, there is strong
evident to indicate that the ash initially deposited at the front part of the channel is
transported to the rear end of the channel.
Another thing worth mentioning is that ash density differs in the cake layer part and end
plug part. From the experimental measurement, as shown in Figure 4.3, the ash plug
density is lower than ash cake layer density under two ash load level. Physically this may
arise from two major reasons. Since the flow velocity at the rear end of inlet channel is
near zero, it is possible that ash will pack loosely in this region. Another reason is that the
deposit temperature during active regeneration is probably lower at the rear end of inlet
channel since little amount of soot can deposit inside the ash plug part. And this density
difference of ash deposited is included in the ash transport model.
N CJ-4 42 gil Ash
E
0.35
-
M CJ4 12.5 g/] Ash
0.30
0.30 0.25 -
0.20 C
0.17
0 15 0.100.05
0.00
-
I
-
Ash layer
I
Ash plug
Figure 4.3. Comparison of ash packing density for DPFs
containing 12.5 g/l ash and 42 g/l ash generated in the laboratory
using CJ-4 oil and periodic regeneration [26].
4.1.2 Ash Transport Observation
The optical observations of ash transport are conducted by the experimental group in
Sloan Automotive Lab [28]. As shown in Figure 4.4, an optically-accessible filter core
sample fixture enables optical access to a small portion of the outermost filter channel.
Figure 4.4(b) shows how a segment of the top filter wall of the channel has been removed
76
to expose the channel surface below. A stereo microscope in conjunction with this fixture
is used to do the real-time imaging of the particle transport process on channel surface.
(b)
View
(a)
Single
Channel
Figure 4.4. (a) DPF core sample fixture with optical access. (b)
detail showing field of view into single channel. [281
During ash transport experiment, the flow velocity inside diesel particulate filter is
increased gradually. The test procedure is schematically shown in Figure 4.5. The testing
system is cooled down to room temperature before conducting a controlled step increase
in flow velocity. The flow velocity starts from a value about 20,000 1/Hour and increases
up to 160,000 1/Hour. The step size of flow augment is about 10,000 or 20,000 1/Hour
and the time maintained in each flow velocity is approximately 30 seconds. This
experiment provides the useful data to quantify the impact of elevated flow on the ash
particle transport.
U--
Time
Figure 4.5. Step-wise increase in flow through optical DPF
samples following full- or partial-regeneration.[281
77
Figure 4.6 shows the ash particle transport at increasing flow velocity after a complete
active regeneration. One thing needs to specify is that the ash content of soot
accumulated before regeneration is increased by using the ash accelerated loading system
to help visualize the ash particle in this experiment.
104,00 GHSV
65,000 GHSV
168,000 GHSV
Figure 4.6 Image sequence showing transport of ash particles
formed following filter regeneration with increasing channel flow
[28].
As show in Figure 4.6, the ash particles formed by previous active regeneration can be
seen on the DPF surface. The ash particle is observed to detach from the DPF surface
from the space velocity of 42,000 1/Hour. With increasing flow velocity, more and more
particles are sheared off the DPF surface and transported to the rear part of inlet channel.
The arrows in the Figure 4.6 indicate the ash particles detached from the DPF surface in
the elevated flow rate of next step. The experimental observations presented in Figure 4.6
clearly indicate that ash particles or agglomerates can be detached from the original
78
deposited position with increasing flow rate. And it also suggests that more ash will be
transport to the rear part of channel at higher flow velocity.
4.1.3 Force Analysis of Particle Transport
Considerable research about microscopic particle transport with flow has been conducted
outside the engine and after-treatment communities. However, most of these studies are
concentrated on glass or stainless steel particles entrainment with parallel flow. Much
more complexity is added in case of particle transport inside diesel particulate filter. The
flow field inside DPF channel is presented in Figure 4.7. As the streamlines show, the
flow in the inlet channel has an axial direction component and a vertical (down)
component. Meanwhile, during DPF regeneration the soot deposit is burned and
remained incombustible material re-organizes itself to form ash particle. And the formed
ash particles begin sintering in the heat treatment initiated by following regenerations.
Additional complexity comes from multiple chemical components keep changing during
heat treatment and it may change the ash morphology and cohesion forces.
Figure 4.7. Flow field inside DPF inlet channel from a CFD model.
Figure 4.8 presents the major forces acting on a particle at rest on the DPF surface.
FD-H is
the horizontal fluid drag force upon the particle. FD-v is the vertical fluid drag force due to
the wall flow in the vertical direction. And mg is the gravitational force which can be
neglected in most of cases. FL is the aerodynamic lift due to the Bernoulli effect on a
spherical particle in a shear flow as show in figure 4.9. The pressure is higher on the
lower side of the particle where the fluid velocity is smaller, while the pressure is lower
on the upper side, where the fluid velocity is higher.
is the adhesive force between particle and substrate surface which is not easy to
measure or quantify. For the ash or soot particles deposited on the filter surface, the
governing adhesive force is believed to be Van Der Waals forces. But electrostatic or
electromagnetic force may play a role in certain cases.
FA
However, when the particle deposits near the wall, the flow velocity near wall generally
is small and drag force caused horizontal flow possibly is negligible. In this case, the
horizontal forces exerted by flow shear stress maybe is dominant and friction force or
adhesive force from the wall provides the balanced force.
79
FL
FD-H
Fshear
FR
Figure 4.8 Forces acting on particle accumulated on filter surface,
Schematic adapted from [30].
--------------
F'
F,
Figure 4.9 Lift force acting on particle near deposited surface.
4.2 Transport Model
4.2.1 Modeling Assumptions
As the 1-D model represented an initial approach to estimating the flow-induced shear
required to induce particle transport form the channel walls to the back of the channel, the
following simplifying assumptions were made:
80
1. Ash particles transport was only considered following complete soot oxidation, and the
transport of soot along with the ash was not included in this initial model.
2. The local shear stress was estimated from the local mean channel flow velocity, which
was calculated from the one dimensional flow model.
3. Once the local flow shear stress exceeds the particle's critical detachment stress, the
particle begins to move.
4. Particle re-deposition was accounted for by assuming the particle will redeposit in a
position where the local flow shear stress equals the particle critical re-deposition stress.
4.2.2 Flow Model
The one dimensional flow model used here is same the flow model used in the ash cake
layer profile effect analysis. As show in Figure 4.10, the flow model considers variable
cake layer thickness in DPF length direction and ash plug at the rear end of the inlet
channel. The channel flow velocity (U and U2) and wall velocity Uw have the one
dimensional variation in the DPF length direction.
Channel
US
b
Uw
>,Wall Flow
U2
Figure 4.10 Ash deposit and flow inside one dimensional flow model.
The one dimensional flow model ends up solving a partial differential equation shown in
Eq. (4.1). The detailed derivation of this equation and the definition of the terms can be
founded in Appendix 2. This partial differential equation can be solved by the pseudo
time loop method and the simulation code is written in MATLAB. The computation time
needed for one flow field calculation is approximately two seconds, which is much faster
the solving time in 2D or 3D model.
A,
2
b,
2AA1
+1
bAd
d-2 = d1)
dB
_
dt
di
da2
__
2 +mo
d)
dy
(
9 +.,
k
b
-2
2
(4.1)
d
b__di
b2
2A
2vdb
- A(1+ ---)Q^
=(A--bku
2 + A 2A-!2db
2
bl, dz
b,
bZ b,
d2
81
4.2.3 Modeling Approach
The one dimensional flow model is used to solve the flow flied inside DPF channel with
ash deposit. To predict the ash particle movement, the shear stress exerted by exhaust
needs to be considered. The local flow shear stress is calculated from one dimensional
flow model. This method is generally applied in DPF ID model to account the local flow
shear stress.
F-u
4b 0
(4.2)
Here, F is laminar channel flow friction factor. q is the gas viscosity. u is local mean axial
velocity of inlet channel and it is a function of axial position. And b10 is the loaded DPF
inlet channel open width.
LNext Cycle
Flow calculation
Soot
Loading
Soot particle deposition
Regeneration
Ash
Transport
K
Flow calculation
Particle Moving
Particle re-deposit
Figure 4.11 Flow chart of the whole transport model.
The flow chart of the transport model is shown in Figure 4.11. The soot deposition is
simulated based on one dimensional flow model. Then a regeneration model considers
the increase of ash layer thickness after each cycle of regeneration. The ash transport is
calculated through a trial and error process. At each cycle, the flow flied and shear stress
is calculated and compared with the particle detachment criteria at every discretized
position along the channel length. If the flow shear stress is larger than the critical detach
force, the particle leaves its original position and begins transport. If the particle moves,
its new redeposit position will be the position where flow shear stress equals particle
critical redeposit stress. This cycle repeats until the particles cease to move and an
equilibrium layer profile is found. Here, the particle critical moving stress and critical
82
redeposit stress are two different constants. And these two numbers are calculated from
the experimental measured ash deposit profiles to fit the experimental observations.
Another important issue in the model is to consider the ash density change during the
active regeneration process. The ash cake layer and end plug density are measured at 12.5
g/L and 42 g/L ash load. The assumed ash density change from 0 -50g/L ash is shown in
figure 4. This data is implemented in the ash transport model and ash volume shrinking
effect is considered based on density increase.
350
300
E 250
200
5, 150
,100
--50
Ash Layer Density
-U-Ash Plug Density
0
0
10
20
30
40
50
60
Ash Load, g/L
Figure 4.12. Ash cake layer and end-plug density with ash loading level.
4.2.4 Simulation Condition
To interpret the experimental observation presented in Figure 4.2, simulations are
conducted based on the one dimensional model described before. The simulation
conditions are listed in Table 4.1. And the ash density difference between cake layer and
end plug is considered in the model. The detailed implementation of density change is
that once the cake layer ash leaves its original position and deposits as the end plug, its
density increases to ash end plug density.
The ash critical moving and redeposit stress are also listed in table 4.1. One thing worth
mentioning is that the actual force needed to detach an ash particle probably is much
larger than the presented shear force. As presented in Figure 4.8, the horizontal drag force
may also play a role there and the lift force acting on ash particle also can facilitate the
ash detachment. In a fully developed flow inside inlet channel, when is flow Reynolds
number is low (usually less than 200 in the characteristic length of channel open width),
the flow shear stress, flow drag force and lift force are all proportional to the local mean
83
flow velocity in the channel length direction. The drag force and lift force are difficult to
estimate in this one dimensional model. However, since all the concerned forces are
proportional, the flow shear force itself can also serve as criteria to determine ash stay or
move.
Table 4.1 Simulation conditions of transport model
6 inch
Substrate
5x10'4 m 2
permeability
DPF diameter
5.66 inch
Ash permeability
4x10-4 m2
Space velocity
20, 000 1/Hour
Critical moving
0.35 N/m 2
stress
Cell density
200 cpsi
Critical redeposit
0.05 N/m 2
stress
Substrate thickness
0.0 12 inch
DPF length
4.2.5 Results and Discussion
Based on the simulation conditions listed in Table 4.1, the simulations using one
dimensional transport model are conducted. The simulation results are presented in
Figure 4.13 and the predicted ash distribution profiles for two ash loading levels are
plotted with DPF inlet channel. The data points in the figures correspond to experimental
measurements of the ash layer thickness and end plug length following post-mortem
analysis of two identical DPFs, each loaded to 12.5 g/L and 42 g/L ash, respectively,
using a commercial CJ-4 oil. Relative to the experimental measurements, the model
shows good agreement with the overall ash distribution profiles.
As show in Figure 4.13, there is a linear increase region of ash cake layer in the front part
of filter inlet channel, which suggest some of particles originally deposited here are
detached by the flow. This is mainly due to the relative larger flow velocity in the front
part of inlet channel. The majority of transported ash in the rear end of channel comes
from the cake layer thickness linearly increase region in the front part of the channel. The
middle part of channel which has rather flat cake layer has little amount of particles
transported to the end. One reason the layer thickness of the middle part doesn't increase
proportionally to ash loading level is that the layer density increasing with ash load.
Often enough, the ash cake layer is expected to shrink a little bit with increasing ash layer
density.
84
x 10
-4
E
XU
C
0
0.05
0.1
DPF Length, m
(a) Ash load =12 g/L
Cx 10
E
1C
.C
K
0
-O
0.05
CH
0.1
DPF Length, m
o Experment Measurement
(b) Ash load = 42 g/L
Figure 4.13. Predicted ash layer profile and experimental measurement
at two ash loading levels.
The model predicted ash distributions inside inlet channel are presented in Figure 4.14 (a)
and (b), for 20 g/L and 30 g/L ash load respectively. As shown in Figure 4.14, from
20g/L to 30 g/L ash load, the ash end plug length increases significantly. At the same
time, the ash cake layer thickness in the flat region, which is the middle part of inlet
channel, also increases due to dozens of soot regeneration. The ash cake layer thickness
linear increasing region, which is in the front part of the channel, also increases in the
channel length direction. The reason accounting for ash layer linear increase region
expanding is that the flow shear increases with shrinking loaded channel width, which
means more ash can be detached at the same diesel particulate filter space velocity.
85
x 104
15
E
10
C:
Ca,
5
0
0.05
0
0.1
DPF Length, m
(a) Ash load = 20 g/L
x 10
15
E
U)
U)
C
1C
(.)
-c
U)
C
I
0
I
I
0.1
0.05
DPF Length, m
(b) Ash load = 30 g/L
Figure 4.14 predicted ash layer profile at 20 g/L and 30 g/L ash load.
One important result from the ash transport modeling is to evaluate how ash end plug
length increases with increasing ash load, which is also rather important in the diesel
particulate filter pressure drop prediction. Figure 4.15 presents the evolution of the ash
build-up in the channel end plugs. Each data point in the figure corresponds to the
predicted ash plug mass fraction following a single regeneration event. The slight
deviations observed in the ash end plug mass fraction at low ash loads correspond to the
plug length changes due to the ash density change and it causes mass included in the plug
part deviate with ash load.
As shown in Figure 4.15, the predicted ash end plug start to form at the ash load of
approximately 1Og/L. In the following filter regenerations, the ash end plug fraction
86
increases with ash load. After the ash load of 30g/L, the majority of ash mass,
over 60%,
is deposited in the rear end of filter inlet channel. After 30 g/L ash load, the ash end plug
mass fraction still increases with ash load, which means the percentage of ash transported
to the channel end in all new formed ash after generation is more than 60%.
1
--
0
2 0.8
'a 0.4
0.2
0
10
20
30
Ash Load [gL]
40
50
Figure 4.15 Evolution of ash accumulation in channel end-plug
predicted by the 1-D model.
4.3 Summary
In this section, combined with experimental observations, the modeling approach is
applied to understand the ash transport inside DPF inlet channels. In this one dimensional
model, the flow and ash distribution only has variations in the DPF length direction. After
applying critical moving and redeposit conditions, the model predicted rather good ash
distribution compared with experimental observation. The practical ash transport inside
DPF inlet channel is rather complicated since the soot oxidation, heat treatment, particle
sintering and adhesion forces between micron size particles play a role in this process.
There is plenty of room to improve this model if more mechanisms of ash transport
process are understood.
1, From the experimental observation, it is found that ash has a cake layer part and end
plug part in the inlet channel. And the cake layer part has certain profile which reflects
the flow effects on particle transport. Those observations indicate the need of study the
ash transport inside DPF channels.
87
2, From the ash transport optical study, it is found that ash particle start to detach from
the substrate wall from some critical flow velocity. With increasing DPF flow velocity,
more and more ash particles leaves the original deposition position, which clearly shows
flow is the major reason of particle transport.
3, In the transport model, the flow shear stress is used as the moving condition of ash
particles. In the real particle transport, probably flow drag force and lift force also play a
role in the transport process. Since all the forces listed here are proportional to the mean
local flow velocity in a fully developed flow, the flow shear stress itself can serves as
condition to determine the ash particle transport.
4, The model predicted ash distribution has a good agreement with experimental
measurements, which may imply that the model can be useful tool in understanding and
visualizing the ash transport in DPF channels.
88
5 Passive Regeneration Model
Diesel Particulate Filter (DPF) technology is recognized as a technically feasible solution
for the emission control of diesel engines. The main issue associated with their
application is the accumulation of soot in the filter channels, which may increase the
exhaust backpressure to unacceptable levels. Active regeneration is to increase exhaust
temperature to initiate soot reaction with carbon. The problems with this method are high
fuel penalty and possible filter melting down. The catalyzed diesel particulate filter
(CDPF) enable soot reaction happen in a relatively low temperature and continuously
oxidize soot when the exhaust temperature is higher than 3000 C. The passive
regeneration in CDPF has the advantages of low fuel penalty and low regeneration peak
temperature. However, there are growing concerns about the catalyst deactivation with
ash aging. Especially with the formation of ash, the catalyst NO generation ability may
2
decrease. Thus, the soot oxidation rate in passive regeneration may decrease with ash
aging, which causes the passive regeneration unsustainable.
5.1 Passive Regeneration
Catalyzed ceramic filters were developed in the early 1980s. Their first applications
included diesel powered cars and, later, underground mining machinery. In the catalyzed
diesel particulate filter (CDPF), a catalyst (usually platinum) is applied onto the filter
media to promote chemical reactions of the soot (carbon) collected in the filter. In the
most common design, the CDPF utilizes a ceramic wall-flow monolith made of either
cordierite or silicon carbide, packaged into a steel housing, as shown in Figure 5.1. The
porous walls or wash coat are coated with the catalyst. As the diesel exhaust aerosol
permeates through the walls, the soot particles are deposited within the wall pores, as
well as over the inlet channel surface. The catalyst facilitates PM oxidation under the lean
conditions in the diesel exhaust.
Porous walls (catalyzed)
Packaging mat
Plugs
Steel housing
Figure 5.1. Catalyzed Diesel Particulate Filter.
89
The major mechanism of passive regeneration is soot oxidation by NO 2. These CDPFs
are coated or impregnated with Pt-based catalysts, which are very effective in promoting
the oxidation reaction of NO, which is present in the raw diesel exhaust, to NO . The
2
latter is a strong oxidizing agent and is able to react with deposited soot at temperatures
as low as 300'C. As shown in Figure 5.2, the NO 2 is formed on the catalytic region-wash
coat, which is downstream the soot layer deposit. The reaction with soot would not be
possible, unless NO 2 is able to diffuse back to the soot layer, driven by the concentration
gradient. Moreover, one has to take into account that in typical filter wall structures, the
pores are partially filled with soot during filter loading. Therefore, a certain amount of
soot will actually be downstream the catalytic sites, on which the NO 2 is formed.
C(lifSss of NOS)
Nlon-catafytic soot oxidation
with 02, 140
soot
I
6- wash coat
Solution of
Concentration
frld N0(X)
taking Into account
reactions/diffuslon
0
0
0
9
0
i
0
W"bu oW)
(DWOMMte of 90J
Figure 5.2. Reaction-diffusion phenomena across the soot layer and the
catalyzed filter wall.
Another possible mechanism of passive regeneration is soot catalytic reaction by oxygen.
Some researchers claim that carbon reaction pathway possible is different when the
carbon has a direct contact with catalyst. Carbon particles could be oxidized by oxygen
absorbed on catalyst sites. This mechanism is limited to the special region where the soot
deposits directly on catalyzed surface. However, this mechanism is often neglected in
many DPF catalyst study.
The main purpose of the catalyst is to facilitate passive regeneration of the filter by
enabling the oxidation of diesel particulate matter under exhaust temperatures
experienced during regular operation of the engine/vehicle, typically in the 300-400'C
90
range. In the absence of the catalyst, particulates can be oxidized at appreciable rates only
at temperatures around 550-650'C, which can occur only at full load conditions in the
diesel engine and in most cases are rarely seen during real-life operation.
In these filter systems, the role of the catalyst-in addition to lowering the soot ignition
temperature-is to regenerate soot continuously to minimize the fuel economy penalty. It
reduces the fuel penalty in two ways. Firstly, it reduces the soot deposit level in most of
engine states, which can significantly lower the CDPF pressure drop and reduce the fuel
penalty. Secondly, it reduces the needs of raising the exhaust temperature to initiate the
active regeneration, which also helps to lower the fuel consumption. Meanwhile, in
passive regeneration, the filter temperature is much lower than that in active regeneration.
Thus, it prevents the filter cracking from thermal stress in high temperature.
5.2 CDPF Aging Experiment Observation
ve
u
s
Low N02
Concentration
A
High N02
DPF Washcoat
Ca alyst
Ash
Soot
Concentration
Figure 5.3 Reaction and diffusion across wall with ash cake layer.
After CDPF regeneration, the soot particles are oxidized and the incombustible material ash remains in the filter channel. With increasing vehicle mileage or equivalent running
hours, the ash loading level continues to increase and the ash cake layer gradually builds
up. As shown in Figure 5.3, when an ash cake layer is formed, the catalyst particles are
covered by ash and the soot layer and catalyst are separated by ash cake layer. The
catalyst particles are possibly deactivated by ash coverage since the active sites may be
blocked by ash deposits. Meanwhile, the ash layer acts like a diffusion barrier which
91
could reduce the NO 2 concentration available to soot oxidation. Thus, there are growing
concerns that CDPF may become less effective at high level of ash loading.
From the literature, filter catalyst aging is discussed from several different perspectives.
Nicola Soeger et.al concludes that aged CDPFs show significant loss in catalyst activity
[46]. In Figure 5.4, the NO2 formation efficiency is defined as the ratio of generated NO
2
in total thermodynamically-allowed quantity. It is clearly shown that aged CDPFs have
much lower NO 2 formation efficiency. However, after removing the ash, the CDPF of
75,000 miles filed aging sample has same NO 2 generation ability with clean CDPF, which
shows some implications on catalyst deactivation mechanism. Research conducted in
Hyundai-Motor shows that aged CDPF in simulated cycles has lower CO or HC
conversion efficiency [47]. Other studies also find that thermal aging and phosphorus ash
have adverse effects on catalyst activity [48] [49].
53
42
C
30
CDPF iAJ
conditioned
CDPF (A) 32k CDPF (A 300h CDPF (A: 75k
miles flekd aged engne aged miles field aged
CDPF (A) 161
hydrvthem-al
CDPF (A)75k
mites field aged
aged
+ cleaned
Figure 5.4. NO 2 formation efficiency at aged CDPFs [461.
Similar results are observed in the experiments conducted in MIT - Sloan Automotive
Lab. In the NO 2 generation ability experiments, clean and ash aged CDPF samples are
tested in the flow bench. The filter sample is maintained in a well-controlled temperature
and monitored by temperature sensors. In this experiment, the upstream gas feeding the
flow bench has the following components: 10% oxygen, 500 ppm nitrogen oxide, and the
rest is inert nitrogen gas. All the concentrations listed here is based on gas mole fraction.
From the Figure 5.5, we can see that ash aged DPF, no matter the ash loading level or
flow bench temperature, show a much lower downstream NO 2 concentration. This is to
say that ash aged catalyst has a reduced activity and a lower NO 2 generation ability.
92
---
Clean
--
12.5 g/1-
---
42 g/L
350 300
250
S
200
150
100
50
0
0
100
200
300
400
Temperature (C)
500
600
Figure 5.5 Clean and ash aged CDPFs' downstream NO 2 concentration
20,000 1/Hour.
5.2.1 Focused Ion Beam (FIB) Observation
In order to enhance the fundamental understanding, this experimental group utilized a
novel apparatus, that of a dual beam scanning electron microscope (SEM) and focused
ion beam (FIB), to investigate microscopic details of soot and ash accumulation in the
CDPF. Specifically, FIB provides a minimally invasive technique to analyze the
interactions between the soot, ash, catalyst/washcoat, and DPF substrate with a high
degree of measurement resolution. The FIB utilizes a gallium liquid metal ion source
which produces Ga+ ions of sufficient momentum to directionally mill away material
from the soot, ash, and substrate layers on a nm-pm scale. As the FIB cuts into the
sample, uncovering intra-layer details, the coupled high resolution SEM imaging
provides both morphological and chemical data.
The Focus Ion Beam technique is applied to observe interface between ash cake layer and
catalyzed surface. As shown in Figure 5.6 (a), it presents milling process where a stairstep volume of the sample material is removed in order to expose an otherwise hidden
sample surface. The FIB apparatus uses a dual beam system where the beam of energetic
ions is accelerated normal to the surface and the SEM and EDX approach the milled
sample surface at 52*.
93
From Figure 5.6 (b), it is clear that the catalyst particles on the substrate wall are covered
by ash deposit. This picture provides a direct observation about ash interaction with
catalyst after CDPF ageing. And this observation provides critical information to
understand the catalyst deactivation in the following part.
(a) Schematic figure of Focus Ion Beam Milling and Observation
Masked catalyst particles
(b) Ash deposition near catalyst surface after Focus Ion Beam Milling
Figure 5.6 Focus Ion Beam Technique and its observation [50].
5.3 CDPF Catalyst Deactivation
94
5.3.1 Catalyst Deactivation Mechanisms
Catalyst deactivation is a complex phenomenon. There are a few of common mechanism
of catalyst deactivation as shown in Figure 5.7. Poisoning is defined as deactivation by
strong adsorption of certain chemical component including the reactants and products of
catalytic reaction. The most strongly adsorbing components hinder the adsorption of less
strongly adsorbing components. One example of this mechanism is that platinum can be
poisoned by sulfur compounds like SO 2 or H2 S.
Sintering mechanism is the loss of catalyst active surface due to crystallite growth of
either the support material or the active phase. Attrition deactivation mechanism is
catalytic particle mechanically breaks up due to friction or crushing. Leaching
deactivation mechanism is loss of active sites due to corrosion at a high or low pH level.
Fouling covers all phenomena where a surface is covered with a deposit. Its origin is not
always related to processes on the catalyst. An example is the deposition of dust, e.g.
from combustion residues like ash or soot or from mechanical wear of upstream
equipment. For instance, in high temperature processes large molecules can be formed by
free radical mechanisms and subsequently deposit on the catalyst particles.
Selective poisoning
S
Catalys
Sintering
Carti~
Fine
Pore plugging
Attrition
Non-selective poisoning
Fouling
*
= active site
o = support
0 = species in reaction medium
Leaching
Figure 5.7 Five mechanisms of catalyst deactivation.
5.3.2 CDPF Catalyst Deactivation Mechanism
Combined with CDPF's experimental observations, possible filter catalyst deactivation
mechanisms are discussed here. Sintering or Attrition mechanism can be neglected since
95
extremely high temperature and catalyst mechanical breakup are not expected during
passive regeneration. Catalyst poisoning is not a major mechanism because sulfur level is
rather low in current fuel and no sign of catalyst poisoning is observed in the experiment.
Leaching can also be excluded because the reaction medium is rather stable.
The most possible deactivation mechanism is fouling or surface masking. This is
supported by the optical observation shown in Figure 5.6 (b). From that picture, it shows
that the catalyst particles deposited on wash coat are covered by ash cake layer. This
surface masking reduces the active sites available to catalytic reaction.
In the catalyzed diesel particulate filter, wash coat is deposited on the filter substrate wall.
The function of wash coat is to retain catalyst particles and provide a reaction bed for
NO/ NO 2 catalytic conversion. Wash coat is porous media and has high surface area. It
has many meso-pores which are in the nanometer scale. The main chemical component of
wash coat in most of catalyzed diesel particulate filters is A1 0 .
2 3
The surface masking reduces active sites in the following way. The ash particle or deposit
may deactivate the catalyst particles via coverage. More importantly, as shown in Figure
5.8, the ash particles may also block the certain pores inside the wash coat, which may
cause all the catalyst particles deposited in this pore become ineffective.
Ash
Particles
A'Pt
meso-poresA
Figure 5.8 Fouling/surface masking deactivation mechanism of CDPF
catalyst.
5.4 Model Formulation
96
5.4.1 Catalyst Deactivation Model
In this section, the model is applied to illustrate the ash masking effects on CDPF catalyst
deactivation. A model using Monte-Carlo method is built to simulate how ash particles
pack up on the catalyzed surface. The model also tracks the ratio of covered area by ash
particles with increasing ash loading level.
Following assumptions are used in this model.
a. The catalyzed surface is assumed as perfect flat, denoted by X-Y plane. And it is
usually simulated by a rectangle region.
b. The ash particle is simulated as a sphere. If the sphere center position is (x, y, z),
(x,y) are random variables that have uniform distribution inside the given
catalyzed region. And z has an initial height h. z will continues decrease until this
sphere reaches the catalyzed surface or other existing spheres.
c. Once an ash particle reaches the catalyzed surface, the covered catalyzed area by
this ash particle is
ir2
.
In the first case, the ash particles have uniform diameter - 2 micron, which is the mean
ash particle diameter. The catalyzed surface is set as 100 micron x 100 micron rectangle
and initial height (h) of each particle is 100 micron.
The simulation results are shown in Figure 5.9. Generally, the ash layer thickness
increase with more ash particle deposition. From Figure 5.9 (a), some ash particles don't
reach the catalyzed surface because some existing particles have direct contact with them.
As shown in Figure 5.10, initially the catalyst coverage ratio increases with ash loading
level or deposited ash particle number. However, after approximately 2 g/L, the coverage
reaches the value of 26% and it doesn't increase with growing ash load. This is because
less and less percentage of ash particles can reach the catalyzed surface with growing ash
cake layer thickness. Once the ash loading level reaches 2 g/L, almost no ash particles
can deposit on the catalyzed surface since most of the surface is already blocked by
existed ash particles.
A similar study is conducted at the same setting except considering an assumed ash
particle size distribution. The particle size has a uniform distribution between 0.1 and 3.9
micron. Similar ash packing pattern is observed. And the stable coverage ratio is 22%,
which is slightly lower than the uniform ash diameter case.
97
07
(a) Total ash particle number N=500.
(b) Total ash particle number N=4000.
Figure 5.9 Three dimensional ash particle packing on the
catalyzed surface.
0
+.J
26.31%
30%
(U
20%
0
10%
(U
)
2
4
6
8
10
Ash load level, g/L
Figure 5.10 Catalyst coverage ratio with increasing ash load.
98
(a) Total ash particle number N=500.
(b)Total ash particle number N=3000.
Figure 5.11 Three dimensional ash particle packing on the
catalyzed surface considering ash size distribution between 0.1 to
3.9 micron.
5.4.2 Passive Regeneration Model
5.4.2.1 Flow Model
99
The one dimensional flow model considers the open width variation in the axial direction.
At the same time, it also takes the temperature variation in the axial direction into account.
This model is essential in solving flow inside DPF channel. And it is needed in
simulating species transport inside DPF channel and substrate wall. Since gas density is a
function of local temperature, it may have variation in the axial direction. In the stable
state, the temperature in the axial direction can be assumed as uniform.
Mass balance:
Inlet channel:
d(b,u
dP
dz
= -4bbpu
Outlet channel:
d(p 2u 2 ) b2
dz
= 4 bkpu
Momentum balance
Introducing the friction factors to express the shear stresses leads to the momentum
balances. F = 28.454.
Inlet channel:
d(b,2 p,u,2 =
dz
dI2
p b2 - Ftqu,
dz
Outlet channel:
d(p2 u2 )-2
dP
b= -2bk2-
dz
dz
Fr7U2
Darcy Equation
Pressure drop of substrate, soot layer and ash layer
S
P1 -
P2=
S
SS
w(s s + a )uw + P(
k, ks k,
+±,sw
pAss + /a,u
U
This set of differential equations doesn't have an analytical solution. Thus, numerical
method is used in solving these governing equations.
5.4.2.2 Species Transport Model
The species transport governing equations extended the previous work [81] by
considering ash cake layer and open width variation in the axial direction.
100
The governing equation for the conservation of species
layer and wall is:
j (02, NO,
ayj
a fayj
fX
ax
&
ax
c,
d
ax
,
NO 2 ) in the soot/ash
'
Where x is the position in the depth direction, yj is the species j concentration inside
porous media region, v, is the wall flow velocity, Rk is the chemical reaction rate.
The effective diffusivities are calculated based on the mixed diffusion model:
D
E,
_
D
with the Knudsen diffusivity:
d,
3
891T
r77M.
The values of porosity e,, tortuosity T and mean pore size, dp are based on the
microstructure properties of the soot layer and the filter wall. Usually, Knudsen diffusion
coefficient is 10 times larger than the gas molecular diffusion coefficient.
The geometrical parameter fx is defined as:
rd + 2x
-wwdeposit < x < 0
d
fX d
Where w_ deposit is the deposit thickness, w _ s is the substrate wall thickness, d is
channel initial open width.
The boundary conditions should "couple" the phenomena in the wall with the gas
conditions in the inlet and outlet channels. In these boundaries, one should consider the
convective mass transfer from the bulk gas to the wall surface, which can be computed as
usual based on the "film" approach with mass transfer coefficients kij, corresponding to
laminar flow of both inlet and outlet channel:
Inlet channel species transport:
a(v yj)
az
+ 4vy
df7
_-deposit
+ 4k 1 (y1, - YIs,)
0
fw_deposit
101
Outlet channel species transport:
a(v2
2,j)
4
vy
2 s,j
az
+ 4k2 ,y
df
2,
- Y2s,j )=0
d,
Where y , andy 2 , are species j concentration in inlet channel and outlet channel
respectively, yis, and Y2s,j are porous media region species j concentration near inlet
and outlet channel boundary respectively.
Boundary condition at inlet/outlet channel
a(v y 1,' 1)
d -d2
s
- 4
ay
Dfdeposit ax
a(v 2 y2 )}
-
2
_s
-d
+
z
'
= -4v~ys
w
2j
+ 4Djf,_s a |2S
-ax
Combined all the equation listed above, the flow, chemical reaction and species transport
can solved inside catalyzed DPF.
5.4.2.3 Chemical Reaction
Although multiple-step chemical reactions are used in a few of publications in passive
DPF regeneration modeling, the reaction mechanisms and kinetic parameters are not well
defined. In diesel after-treatment research community global reactions are widely used to
investigate the chemical process. To make this model manageable, well established
global reactions are applied to model DPF passive regeneration.
Table 5.1. DPF passive regeneration global reaction parameters
Global Reaction
Activation Energy
Pre-exponential Factor
E, J/mole
A
80
48000
2NO2 +C->2NO+CO 2
02 + C -> CO2
1
NO+-O2 ++ NO
0.7x10'
0.1
1.58x 105
25
2
The primary understanding of chemical reactions inside DPF is presented in Figure 5.12.
As shown, NO is converted into NO 2 in the catalyzed region - wash coat. Since the NO 2
102
concentration in the wash coat region is relatively high, it can diffuse back to soot cake
layer. In the soot cake layer, the available NO 2 is consumed to oxidize the carbon. At the
temperature above 600 0C, the carbon can directly reacts with oxygen, which is usually
used in active regenerations.
In the ash cake layer, no chemical reaction happen since no soot or catalyst deposits in
this region. It separates the soot cake layer and wash coat and acts like diffusion barrier in
the NO 2 back diffusion. At the same time, the ash cake layer increases the flow restriction
across the whole DPF.
N&u~dw
wish hs* *as EIsw
(DE6sI .1 NG~)
4
C +0
S
S
S
S
S
0
S
-+CO,
V
soot
C +2NO, -> CO, + 2NO
... ash
NO+ 211 0NO-+ NO
0
.. wash
coat
solution of
fold N03 x )
takng into accounty
reacthomu/dIffuslon
"M 01. fNO
(Danimof
a8DI
Figure 5.12. Chemical reaction across the cake layer and wash coat.
5.4.3 NO and NO 2 Equilibrium
For the NO 2 formation the catalyzed region, the NO and NO2 equilibrium should be
considered in the model. For the conversion reaction near platinum catalyst, the NO
formation rate is determined by chemical kinetics and upper bound of NO 2 concentration2
is limited by the reaction equilibrium.
NO and NO 2 reaction equilibrium is a common problem and it can be calculated based on
the information provided in NIST-JANAF Thermochemical Tables. The equilibrium
constant in the NIST-JANAF Thermochemical Table is defined in Eq. (5.1). From the
NIST-JANAF Thermochemical Table, the equilibrium constant of each reactant and
103
product can be found. Through the equation listed as Eq. (5.2), the whole reaction's
equilibrium constant can be determined.
The NO 2 forward reaction rate constant can be calculated through the parameters listed in
Table 5.1. However, there is no direct way to determine the NO 2 back reaction rate
constant. The backward reaction constants can be determined in following way. When the
reaction reaches the equilibrium, the forward reaction rate equals backward reaction rate
and the relation between forward/backward reaction rate constants and equilibrium
constants can be determined. As show in Eq. (5.3), the equilibrium constant can be used
to calculate the backward reaction rate constants. Here, the total molecule concentration,
Ctotal can be estimated by ideal gas law as shown in Eq. (5.4).
P
1
K(T)
-0.5
(5.1 )
n=
PO
x,o!
K(T) = Log 0(Kf )product - Log 1 0(Kt )reactant (5.2)
k
K(T)=- 1 .C
kb
Col-=
96T
5
(5.3)
ta
(5.4)
600
500
400
Species
mole fraction 300
ppm
200
100
n
0
200
---
400
600
Temperature, Celsius
800
1000
no -U-no2
Figure 5.13. NO and NO 2 concentration at equilibrium state.
A tested case is calculated at given condition of 500 ppm NOx, 10% oxygen and other
inert gas components (all based on mole fraction), which is very close to the gas
composition in diesel engine exhaust. The NO and NO 2 concentration at equilibrium state
104
is evaluated in the temperature range of 0 to 850 Celsius. The simulation result is
presented in Figure 5.13. When the temperature is lower than 200 Celsius, the primary
composition of NOx is NO 2 and little amount of NO is formed. When the temperature is
higher than 600 Celsius, the dominant component is NO and little amount of NO 2 is
formed. This agrees with the general observation that high temperature favors the NO
formation while low temperature favors the NO 2 formation.
5.5 Results and Discussion
In this section, the regeneration model is validated against the experiment data on
catalyzed diesel particulate filter NO 2 generation test. The model predictions have a great
agreement with experimental data, which suggests it is a valid tool to investigate the ash
aged diesel particulate filter performance.
5.5.1 NO 2 Generation Test
The objective of this experiment is to investigate the ash effects on catalyzed DPF NO 2
generation ability. In passive regeneration, deposited soot can react with nitrogen dioxide
at relatively low temperature like 300 0C. One mechanism that ash effects passive
regeneration is that ash aged catalyst has much lower ability in converting NO to NO 2 .
Thus the NO 2 generated inside aged diesel particulate filter is significant reduced, which
could cause the soot oxidation rate decreased.
In this experiment, to simplify the problem, no soot is loaded in the diesel particulate
filter. Only the clean and ash aged diesel particulate filters are tested according to the
plan. The gas composition in the upstream, as presented in Figure 5.14, is 10% oxygen,
500 ppm nitrogen oxide (NO), 0 ppm nitrogen dioxide (NO 2) and the rest of gas is inert
nitrogen (N2). All the species concentration numbers listed are based on mole fraction.
As shown in Figure 5.14, the increased NO 2 concentration due to the catalytic conversion
is measured by Fourier Transform Infrared Spectroscopy (FTIR) in the downstream of
diesel particulate filter. The measured NO2 centration is not the NO 2 concentration in the
substrate or ash cake layer. However, it is still a reflection of NO 2 generation ability of
both clean and ash aged diesel particulate filter. The experimental temperature is
increased from 100 0C to 600 'C at the speed of 10 0 C/min. The other experiment
conditions such DPF specifications and flow rate are presented in Table 5.2.
105
Fks Chamber - Plainum Subtiate
Given
N02/NO/02
condition
-
-4
N02 Measurement
--
Odaeon f NO to NM via Pkuium Catalst
Figure 5.14. Experimental Setup for catalyzed DPF N02 generation test.
DPF length
Table 5.2 Experiment conditions in CDPF N02 generation test
6 inch
Substrate
5x 10-14 m 2
permeability
DPF diameter
Space velocity
5.66 inch
40, 000 1/Hour
Cell density
200 CPSI
Ash permeability
Substrate thickness
4x 10-14 m 2
0.012 inch
The regeneration model described above is applied to understand the advection-diffusionreaction process inside diesel particulate filter. Since soot deposit is not included here,
soot oxidation rate is not a major concern. The downstream NO 2 concentration from
experiment is used to validate the model results. Using the same condition as the
experiment, the predicted results from the model are presented in Figure 5.15 and Figure
5.16, combined with the experiment measure data (shown as dots).
Generally speaking, the model predicted downstream NO 2 concentrations have a good
agreement with experiment measured data. The model predictions between 250 C and
400 0 C, as presented in Figure 5.15 and Figure 5.16, are lower than the experiment
measurements. The specific reason accounting for this difference is not quite clear.
However, the model results reflect the right trend of downstream NO 2 concentration
changing with temperature. And at most of the comparison points, the model predicts the
downstream NO 2 concentration with a good accuracy.
106
250
1
200
N02
A,
I-
150
mole fraction
ppm
100
50
0
0
100
200
300
400
500
600
Temperature, Celsius
+ Experiment, clean
clean
-Model,
Figure 5.15 Model predicted and experimental measured downstream
NO 2 concentration for clean catalyzed diesel particulate filter.
160
140
- -- -
120
- -- - -
-
-
-
100
N02
80
mole fraction
60
PPM
40
20
I
0
0
100
200
300
400
500
600
Temperature, Celsius
I
Experiment, 42 g/L ash
-
Model, 42 g/L ash
Figure 5.16 Model predicted and experimental measured downstream
NO 2 concentration for 42 g/L ash aged catalyzed diesel particulate filter.
As shown in Figure 5.15 or Figure 5.16, the downstream NO 2 concentration in both clean
and ash aged diesel particulate filter first increases with elevated exhaust temperature up
to 400 0C. Then, after 400 0C, the downstream NO 2 concentration decreases with
continuous elevating temperature. The reason behind this trend is that, when the
temperature is below 400 C, the catalyst activity increases with temperature and more
NO 2 is generated because of the faster NO 2 conversion rate. When the temperature is
above 400 0C, the NO2 concentration is limited by the NO-NO 2 equilibrium. As discussed
107
before, high temperature favors NO instead of NO 2. This is the reason why NO 2
concentration decreases with temperature after 400 0C.
This mechanism becomes much easier to understand if the simulation results about NO 2
concentration in diesel particulate filter length direction and wall depth direction are
presented. The inlet channel NO 2 concentrations in the length direction are presented in
Figure 5.17 and 5.18, for the clean and 42 g/L ash aged diesel particulate filter
respectively. The NO 2 concentrations in the wash coat region (a two dimensional region)
are presented in Figure 5.19 and 5.20, for the clean and 42 g/L ash aged diesel particulate
filter respectively.
In Figure 5.17, clean DPF inlet channel NO 2 concentrations are shown in three different
temperatures. As shown in Figure 5.17, at the temperature of 200 0C, the inlet channel
NO 2 concentration continuously increases in the length direction. The respective NO 2
concentration in wash coat region can be found in Figure 5.19 (a). Since the temperature
here is rather low and catalyst activity is limited, the NO 2 concentration increases
relatively slow in the length direction.
When the temperature reaches 350 0C, the inlet channel NO 2 concentrations also increase
in the length direction and have a much larger value than that in the case of 200 0C. In the
clean filter (T=350 C), the inlet channel NO 2 concentration can reach about 200 ppm at
the end of channel as shown in Figure 5.17. However, in the 42 g/L ash aged filter
(T=350 0C), the inlet channel NO 2 concentration gets its maximum value of
approximately 140 ppm at the end of channel, which is much lower than that in the clean
filter, T=350 0C case. This difference between clean and ash aged DPF is true all over the
observed temperature range of 100 0C to 600 0C. This evidence clearly shows that ash
deposit has a negative effect on catalyst NO 2 conversion ability, which may also affect
the diesel particulate filter passive regeneration process.
At the temperature of 350 0C, the wash coat region NO 2 concentrations are shown in
Figure 5.19(b) and Figure 5.20(b), for clean and 42 g/L ash aged filter respectively. The
NO 2 concentrations in both figures increase in the length direction.
The NO 2
concentration in the ash loaded filter has much lower value compared with that in the
clean filter, which also suggests ash may decrease the catalyst NO 2 generation ability.
When the temperature reaches 500 0C, a different phenomenon is observed. As shown in
Figure 5.17, the inlet NO 2 concentrations almost cease to increase at the half of channel
length. This is because starting from the channel middle point the NO 2 concentration is
limited by NO and NO 2 equilibrium, which can be validated by the results presented in
Figure 5.19(c). For the 42 g/L ash loaded case, the inlet channel NO 2 concentrations
increase very slowly in the rear part of channel, which also a sign of equilibrium
constrain, which can be verified by wash coat region NO 2 concentration presented in
Figure 5.20(c). At the temperature of 500 0C, the generated downstream NO 2
concentrations for both clean and ash aged case are very close. To sum up, in the high
temperature like 500 0C or above, the NO 2 generation is no longer governed by chemical
kinetics or ash aging but the NO-NO 2 species equilibrium.
108
250
200
Inlet
N02 150
mole
fraction 100
ppm
~t
-
--
.O*
50
000.-
0
0
0.05
0.1
0.15
DPF Length m
-
T=200 C ....... T=350 C
-
-
T=500 C
Figure 5.17. Clean CDPF inlet channel NO 2 concentration.
160
, -
140
120
inlet
N02
mole
fraction
ppm
100
80
-
-
60
-
-
40
--
20
0
0
0.02
0.04
0.06
0.08
0.1
DPF Length m
-
T=200 C .......
T=350C
----
T=500C
Figure 5.18. 42 g/L ash aged CDPF inlet channel NO 2 concentration.
109
N02
x 10
.5
10
wash
coat
1.5.5
DPF Length Direction
(a) T=200 C
N02
wash
coat
X 10
1.5
1
DPF Length Direction
(b) T=350 C
N02
x 10
11
10.5
wash
coat
10
.5
DPF Length Direction
(c) T=500 C
Figure 5.19. NO 2 concentration distribution inside wash coat
region for clean catalyzed diesel particulate filter.
110
x 10
16
wash
coat
10
DPF Channel Direction
(a) T=200 C
N02
x 05
14
12
wash
coat
DPF Length Direction
(b) T=350 C
N02
x 10
11
10
wash
coat
DPF Length Direction
(c) T=500 C
Figure 5.20. NO 2 concentration distribution inside wash coat
region for 42g/L ash aged catalyzed diesel particulate filter.
111
5.5.2 Ash Effects on Soot Oxidation
The passive regeneration model is applied in this section to investigate the ash aging
effects on CDPF soot oxidation. Two CDPF soot and ash loading cases are simulated in
this study. One case is CDPF loading with Og/L ash and 3g/L soot and the other case is
CDPF loading with 15g/L ash and 3g/L soot. The schematic pictures of CDPF inlet
channel with deposit under these two conditions are shown in Figure 5.21.
inlet channel
e
a
soot layer
4--.-
7
otlet channel
inlet channel
soot layer aSh layei
Ioutlet channel
(a) 0 g/L ash 3 g/L soot
(b) 15
g/L ash 3g/L soot
Figure 5.21. Two cases simulated in ash effects on passive regeneration.
The ash load of 15g/L is chosen here because in this scenario ash cake layer is thick
enough to having masking effects and no significant amount of ash end plug is formed.
The soot load of 3g/L is chosen since in passive regeneration the soot accumulation level
rate is expected to be lower than that in active regeneration. In this analysis, the ash cake
layer thickness of 15g/L loading level is about 60 micron and soot cake layer thickness of
3g/L is approximately 40 micron.
The exhaust gas feeding the diesel particulate filter has 10% oxygen, 500 ppm NO, 0
ppm N02, and other inert gas. The feeding gas temperature is 350 0 C. The tortuosity uses
the value of 3, as suggested by many relevant references. The gas diffusion coefficient in
porous media region is about 0.3 times the gas molecular diffusion coefficient. The ash
effect on catalyst activity is 26% reduction according to the ash masking model described
before. The other simulation conditions are presented in Table 5.3.
Table 5.3 Simulation condition in ash effects on DPF passive regeneration
DPF length
6 inch
Substrate
5x 10- 4 m 2
DPF diameter
Space velocity
Cell density
Ash layer thickness
5.66 inch
40, 000 1/Hour
200 CPSI
60 micron
permeability
Ash permeability
Substrate thickness
Wash coat thickness
Soot layer thickness
4x10-1 m2
0.012 inch
20 micron
40 micron
112
The model described before is applied to study the ash effects on passive regeneration
rate. Two cases are discussed here as shown in Figure 5.21. Case (a) is DPF loaded with
3 g/L of soot and case (b) is DPF loading with 15 g/L ash and 3g/L soot.
The inlet channel NO 2 concentrations in these two cases are presented in Figure 5.22(a)
and Figure 5.22(b). Since NO 2 concentration in the upstream is 0 ppm, it is expected that
inlet channel NO 2 concentration increases in the DPF length direction. However, the
maximum inlet channel NO 2 concentration in these two cases are relatively small
compared the results shown in Figure 5.18. Since the soot cake layer, which is about 40
microns, consumes most of NO 2 generated in the catalyzed region, few amount of NO
2
can be diffused to inlet channel. Generally speaking, the ash loaded channel has lower
NO 2 concentration since the ash cake layer acts like diffusion barrier in this case.
25
20
.0.
DPF
length direction, m
(a) Og/L ash, 3 g/L soot
01
15
E
.5-10
0
0.05
0.1
0.15
0.2
DPF length direction, m
(b) 15g/L ash, 3 g/L soot
Figure 5.22. Inlet channel NO 2 concentrations at two simulated
cases.
113
The porous media region NO 2 concentrations in the depth direction are shown in Figure
5.23 (a) and (b), for the case (a) and case (b) respectively. The results presented are from
three pre-determined channel position that are the channel starting point, channel middle
length point and channel rear ending point. From Figure 5.23 (a), it is clear than NO
2
concentration increases in the depth direction in any of three pre-determined positions.
The reason is that NO 2 is produced in the catalyzed region and NO 2 is consumed in the
soot layer region. Similar trend is observed in Figure 5.23(b). One noticeable difference
in Figure 5.23 (b) is that there is one region of NO 2 concentration linear changing due to
the diffusion through the ash cake layer. Here, ash cake layer acts like a diffusion barrier,
which reduces the NO 2 concentration reaching the soot layer and cause the passive
regeneration rate deteriorate.
--
-
35
30.0
.25-
25
.--'-''--
-52
0
15
0
10
- .....
.....-.-.--.--
20
f ront
m iddle
------ -end
30
50
40
60
DPF wall depth direction, micron
(a) Og/L ash, 3 g/L soot
E
0.
50
-
40
F
-
C)
.2
5-4
E
0
--
front
2....::....-middle
Z
----- end
10
0
-------
20
40
---
60
80
100
1 20
DPF wall depth direction, micron
(b) 15g/L ash, 3 g/L soot
Figure 5.23. Prous media region NO 2 cocnentrations in two smiluated
cases at three positions: channel starting point, channel middle point,
and channel rear end.
114
The two dimensional distributions of NO 2 concentration in the porous media region are
presented in the Figure 5.24 and Figure 5.25 for the case (a) and case (b) respectively. In
Figure 5.24, it is shown that oxygen cocentration doesn't change so much in the porous
media region. This is because the reaction rate of carbon and oxygen is relatively low at
the tempearature of 350 0C. It is widely believed that carbon can't effectively react with
oxygen under the temperature of 600 0C. As shown in Figure 5.25, the NO 2 concentration
is rather high in the wash coat region, where NO2 is generated and NO 2 concentration is
quite low in the soot region, where NO 2 is consumed to oxidize carbon.
In Figure 5.25, it is also observed that oxygen concentration dosen't change much in the
porous media region. The NO 2 concentration is quite high in the wash coat region and
relatively low in the soot layer region. It is observed that NO 2 concentration decrease a
lot in the ash layer region, which suggests ash cake layer reduce the NO 2 accessible to
soot cake layer. This observation in Figure 5.25 is in good agreement with that in Figure
5.24. Both simulations suggest that ash cake layer has negative effects on NO 2 diffusion
to soot cake layer.
02
0997
0996
.
.0995
soot
0992
0991
wash
coat
099
DPF Length Dkrvction
N02
X 10
soot
18
12
A
.2
wash
coat
DPF Length DIrection
Figure 5.24. NO 2 concentration in the porous media region
at 0 g/L ash and 3 g/L soot loading level.
115
02
0997
soot
.0995
0994
ash
.0993
0992
D991
wash
cot099
DPF Length Direction
N02
X 10
soot
ash
wash
coat
.
_
fl.
.1
DPF Length Direction
Figure 5.25. NO 2 concentration in the porous media region
at 15 g/L ash and 3 g/L soot loading level.
The soot regeneration rates in case (a) and case (b) are compared in Figure 5.26. The soot
regeneration rate in case (b) without ash diffusion effect is also presented in Figure 5.26.
From the simulation result, it is found that soot regeneration rate in case (a) is 26.2 g/L-h
and in case (b) is 18.1 g/L-h. From case (a) to case (b), the regeneration rate is reduced by
approximately 30%.
The case (b) without ash diffusion effect, called case (ai), is same with case (b) except the
ash layer diffusion barrier effect is not included. The regeneration rate difference between
case (a) and case (ai) can be considered as catalyst deactivation effect. The regeneration
rate in case (ai) is 22.1 g/L-h, which is 16% lower than that in case (a).
From the discussion above, the ash cake layer has negative effects on passive
regeneration. For the cases simulated, it is found that catalyst deactivation causes 16%
regeneration rate decrease and ash diffusion barrier causes approximately 14%
regeneration rate reduction.
116
30
I
S25 -
20
15 -
10
10
50
(a) Og/L ash, 3 g/L soot
15 g/L ash, 3 g/L soot
ash diffusion barrier
not included
(b) 15 g/L ash, 3 g/L
Figure 5.26 Passive Regeneration (soot oxidation) rate at three
simulated conditions.
5.6 Summary
In this chapter, DPF passive regeneration model combined with experimental data is
applied to investigate the ash effects on passive regeneration rate. Since the published
research results are rare in this area, this study focuses on the fundamental mechanisms of
CDPF catalyst deactivation. With the assistance of regeneration model, following
conclusions are obtained.
1. Ash deposit has negative effects on DPF passive regeneration. The research from
both our study (experimental and theoretical) and elsewhere shows that ash aged
CDPF have deactivated catalyst, which has lower NO 2 generation ability and
lower passive regeneration rate.
2. The CDPF catalyst deactivation mechanism due to ash aging is fouling/masking.
This is the mechanism that ash particles block certain routes in the
wash coat,
which make the catalyst particle in these routes inaccessible to catalytic reaction.
This understanding is supported by FIB observation and model simulation.
3. In the catalyst deactivation model, Monte Carlo method is used to understand how
ash particles packing up on the catalyst surface. From the simulation, it is found
that approximately 26% of catalyst surface is covered by ash particles, which
means the pre-exponential factor of NO 2 formation reaction is reduced by 26%.
117
4. A passive regeneration model is built to simulate the complex diffusion-reactionadvection problem in DPF. The flow model is one dimensional which only
considers key variables change in the DPF length direction. However, the species
concentration in the porous media region is two dimensional since it considers
species variation both in length direction and in depth direction.
5. NO and NO 2 equilibrium is needed to considered in this model. Since at the
temperature above 400 C, the NO 2 formation is limited by NO and NO 2
equilibrium.
6. Through the passive regeneration model, it is found that ash has negative effects
on passive regeneration. From the model, at the soot loading of 3 g/L, with or
without ash loading of 15 g/L, the regeneration rate can have a 30% difference.
The extended study shows that catalyst deactivation causes 16% reduction and
diffusion barrier effects of ash cake layer causes a reduction of 14%.
118
6 Conclusions
Computer models are developed to study the ash effects on diesel particulate filter
performance, including the areas if porous media filtration, ash spatial distribution, ash
transport and passive regeneration. Based on experimental observations, several new
understandings of ash deposit effects on particulate filtration and catalytic reaction are
implemented in the models. Generally speaking, the model predictions have a good
agreement with experimental results, which suggests that models could be a useful tool to
interpret experimental observations. At the same time, the model provides a lot of
information that is difficult to measure in experiment, like the particle mass deposited
inside porous media, which is rather important to understand the underlying mechanisms
of DPF complex physical and chemical process. Moreover, the models are also applied in
the analysis of the effects of certain factors on DPF performance. For example, computer
model is used to study the effects of ash spatial distribution on DPF pressure drop. The
computer models combined experimental data can be applied to develop optimization
strategies and new concepts to improve DPF performance.
Because of the special geometry of DPF channels, in which the ratio of channel length to
channel open width is in the range of 100 to 130, one dimensional model is suitable to
simulate the flow and temperature distribution in DPF channels. In the one dimensional
model, most of the quantities like flow velocity and ash layer thickness only have the
variation in the channel length direction. The only exception is that in the passive
regeneration model the species concentration has a two dimensional distribution inside
the porous media region. Due to the nature of one dimension problem, the computation
cost of solving the problems is quite low. In most of the cases, the model computation
can be finished in 30 minutes.
Through the simulations and analysis mentioned above, the main conclusions are listed as
following.
6.1 DPF Study Summaries
For the modeling of soot and ash effects on DPF performance, porous media filtration,
cake layer formation and flow distribution are considered to understand the complex
physical process. And the model is applied to analyze the depth filtration, mass
distribution and cake layer effects.on DPF pressure drop.
1, Depth filtration, during which the particles penetrate into the substrate wall, can cause
the DPF pressure drop have an exponential-like increase. Depth filtration is accounting
for the initial rapid pressure drop increase of clean DPF during soot loading. Cake
filtration, during which the particles deposit on the substrate wall to form the cake layer,
linearly increases the DPF pressure drop. And it explains why DPF pressure drop
119
increase linearly with soot loading after initial pressure jump. Generally speaking, the
depth filtration should be avoided to optimize DPF pressure drop.
2, For mass distribution between substrate wall slabs, it is found that the uniform mass
distribution between slabs has the lowest pressure drop. Mathematically, this arises from
the relation between DPF pressure drop and deposited mass inside wall is a concave
function. Since the practical mass distribution between slabs exponentially decreases in
the depth direction, if possible, it would be beneficial to adjust the porous media
parameters to achieve more uniform mass distribution between substrate wall slabs to
minimize the DPF pressure drop.
3, Certain porous media, like fibrous porous media, consists of several layers and each
layer's property can be independently controlled. If the top layer is selected and all the
layers have the same porosity, from layer 2 to layer N the layer pore size decreasing in
the depth direction is the optimal arrangement. According to the simulation results, with
significant amount of loading the optimal arrangement can reduce the filter pressure drop
by 15% compared with the worst arrangement.
4, During the soot and ash loading process, the formed ash cake layer acts like membrane,
which helps to improve the filtration efficiency and block the soot particles penetrate into
substrate wall. In this point of view, the formed ash cake layer helps avoid the depth
filtration and reduce DPF pressure drop. This is the reason that under certain soot loading
level the ash aged DPF has lower pressure drop than no ash loaded DPF.
At given amount of ash deposit, the effects of ash spatial distribution inside DPF are
investigated through DPF performance model. The ash radial distribution, axial
distribution, and ash end plug length are discussed in this analysis.
1, the ash radial distribution has minor effect on DPF pressure drop. In the range of
normal substrate and ash layer permeability, which is usually from 10-1 m2 to 10-14 m2
the DPF pressure drop change caused ash radial distribution is less than 3%.
2, The ash axial distribution inside DPF inlet channels has small effect on DPF pressure
drop. In the normal ash layer thickness of 100 micron, the radical changes in cake layer
profile only introduces a 2% difference in terms of DPF pressure drop.
3, The ash end plug length has relatively large effect on DPF performance. For example,
at 20g/L ash load, the ash distributed as end plug or as cake layer could introduce a 20%
difference in terms of DPF pressure drop. However, the optimal distribution pattern
depends on the ash permeability and wall permeability. At known ash/wall permeability,
the optimal distribution can be determined according to the sensitivity map developed in
this study.
From the ash transport observations in optical experiment, it is found that ash particles
begin to detach from substrate wall with elevated flow rate. From the post-term analysis
of ash distribution inside DPF channel, it is safe to conclude that ash particles transport
120
inside DPF channels. The exhaust gas flowing through DPF moves some of the deposited
ash particles to the rear part of the channel.
A one dimensional transport model is built to help visualize the ash transport inside DPF.
Based on the analysis of experimental observations, the flow shear stress is assumed to be
the governing force to move the ash particles. At each position, if the flow shear stress is
larger than the critical detach force, the particle leaves its original position and begins
transport. If the particle moves, its new redeposit position will be the position where flow
shear stress equals particle critical redeposit stress. The predicted ash distribution has a
good agreement with experiment results. The transport model provides useful
information to understand ash transport inside DPF.
For the ash aging effects on DPF passive regeneration, following conclusions can be
made from the study.
1, From model simulation and experiment measure, it is found that ash aging has negative
effects on DPF catalyst activity. In other words, the ash aged catalyst has decreased
ability in N02 formation and lower passive regeneration rate.
2, DPF catalyst deactivation mechanism with ash aging is surface masking or fouling.
With increasing ash load level, a portion of catalyst surface may be covered by ash
particle, which could also block the micro-pores in the wash coat. This blocking may
cause the catalyst deposited in that pore is inaccessible to catalytic reaction. This
understanding is supported by Focused Ion Beam observation and model simulation.
3, The Monte-Carlo method is used to study the ash masking effects on catalyst surface.
It is found that ash particles could cover 26% of the catalyst surface, which means 26%
reduction in catalytic activity.
4, A passive regeneration model is built to understand the flow, diffusion, and chemical
reaction inside DPF. The NO 2 is generated in the catalyzed region- wash coat and it
diffuses back to soot cake layer and is consumed to oxidize the carbon. No chemical
reaction happens in ash cake layer region and it just acts like a diffusion barrier.
5, For NO 2 generated in the downstream of DPF without soot deposit, NO 2 downstream
concentration is governed by NO 2 formation kinetics at the temperature lower than 400'C.
For the temperature above 400 0C, the downstream NO 2 concentration is limited by NONO 2 equilibrium.
6, From the model, it is found that the ash aged DPF has reduced regeneration rate than
the no ash loaded DPF. At the soot loading of 3 g/L, with or without ash loading of 15
g/L, the passive regeneration rate can have a 30% difference.
6.2 Possible Applications of Modeling Understandings
121
6.2.1 Ash Membrane
The basic concept of this strategy is using the ash cake layer of minimum thickness to
avoid the depth filtration. As fewer particles deposited inside substrate wall, a lower DPF
pressure drop can be achieved. Since slightly ash aged DPF has lower pressure drop
compared with new filter, a DPF should be loaded with suitable amount of ash before
using in vehicle. The detailed procedures are shown below.
1.
Load the clean DPF with soot until it transits to cake layer filtration. If possible,
the loaded soot should be pure carbon and nothing remains after regeneration.
2. Continue load the DPF with a suitable amount of ash
3. Conduct a complete regeneration
After these steps, an ash cake layer should form on the substrate and nothing deposits in
the substrate wall. In DPF with active regeneration, the approach should be beneficial to
reduce DPF pressure drop. For DPF with passive regeneration, the loaded ash layer may
cover the catalyst and affect the catalyst performance. One possible way to avoid this
problem is do the ash loading first and then do the catalyst coating.
6.2.2 Sensitivity Map
This approach is based on the study in the ash end plug effects on DPF performance. To
implement this idea, the ash and substrate wall permeability should be measured through
carefully designed experiments since its property can be easily disturbed. Once this
information is available, the DPF's position in the sensitivity map can be determined.
Thus the optimal distribution pattern, deposited as ash end plug or cake layer, will be
provided by the sensitivity map. Certain strategies like increasing flow rate after
regeneration can be used to make the ash distributed close to optimal pattern.
122
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130
Appendix 1
This section shows the dimensionless form of Eq. (2.1) to Eq. (2.5) and how to reduce the
dimensionless system of equations into one equation. At the same time, an approximate
analytical solution is introduced and the quick expression to calculate DPF pressure drop
is presented.
1.1Dimensionless system of equations
Introducing dimensionless quantities as follows:
I z
= -ui -;
=z;
Leff
= 4LWu.
Uin
k
4
P
;
(Al-1)
in
(A1-2)
Lef k,
With i = 1 for the inlet channel and i= 2 for the outlet channel leads to the dimensionless
system, with the mass balance in dimensionless form:
dffii
bk 2
dz
b102
-l
--iw (Al-3)
W
d2
(A1-4)
Momentum balance in dimensionless form:
dP
dT2
- +A1 -
dz
d
d
I dz
b2
k'I+-k 2u=0
bl,2
+ AV +A02=0
dz
(Al-5)
(A1-6)
Darcy equation in dimensionless form (quadratic form is neglected here):
AP=B1fi
(A1-7)
The terms are defined as following:
131
k . 4Lff Re
bsI, bk
"~'bk
Re=
77
(A1-8)
A2
=4F kK
bks,
s, k,
ks s,
B =1
s, k,
k, SW
2
Multiplying (A 1-4) by
b2
, adding this product to (A 1-3) and integrating from 0 to Z
results in:
2
2+bk
2
2
0 2=b
(A1-9)
Subtract (A 1-6) from (A 1-5), and substituting (A 1-7) and (A 1-9) into the expression
results in:
d 2fi2
d 2
+
B, blo
2A,2
b di2
B, b1 d
di
,di
A2
+
B,
+
A2b2
B b
=0
(A 1-10)
Eq. (A 1-10) is used in the numerical simulation, which is easier to solve than the system
of governing equations.
1.2Approximate analytical solution
If the second term in Eq. (A 1-10) drops out, the equation is changed into:
d 22,
d 2
2A, bk di 2
B, b|,d
A2
B,
+ -)2
bo
+
A2 bk
0
(A 1-11)
Eq. (A 1-11) is the ordinary differential equation has the following form
y"+Ey'+Hy+G = 0
The analytical solution for this ODE is
132
x(-4E2-4H-E)
x(
y=kle2
1+H
1-e2
H
And k =
E2-4H-E)
k2e2
+
e2
e2
_
(A 1-12)
2
SE -4H-E)
1
1 E2-4H-E)
G
H
2
IE -4H-E)
k =
H
-k-
19
The pressure drop across the diesel particulate filter is
b/
=1
1
4
(A1
APDPF
L
2k
g1
d
Jo
(e
+BU,(^=0)-P
-
1)+ k1 (e92 -10+
g2
G ]+ B, -(k1g, + k 2 92)
P
H_
And the terms used in the equation above are:
g 1 =-(
g 2 =(
2
2
E 2-4H - E)
E 2 -4H-
E)
133
Appendix 2
Derivation of Eq. (3.12)
The one dimensional DPF model extended the classical model considering the clean
and/or soot-loaded channel to a model incorporating the ash cake layer and end-plug. The
following section presents the approach taken to include the ash end-plug and variable
ash cake layer thickness in the one dimensional DPF model. The extended model requires
a new derivation of the classical equations as given below.
The acronyms and the nomenclature of the corresponding equations are kept similar to
[21] to allow a quick comparison of the extensions in the model equations, which now
incorporate ash layer variance in the axial direction.
Mass balance:
Inlet channel:
db
dz
--
4 bu,.
(A 2-1)
Outlet channel:
d(u2)b2 = 4bkuw
dz
(A 2-2)
Momentum balance
Introducing the friction factors to express the shear stresses leads to the momentum
balances. F = 28.454
Inlet channel:
p
d(b,2u2)
dz
dz
-
=
d
dz
12
-Fu,
((A 2-3)
Outlet channel:
p
d____
dz
bf =
dP 2
bk-
dz
F7u2
(A 2-4)
Darcy Equation
134
Pressure drop of substrate, soot layer and ash layer
(k,
P - P,=
s'a)U"
s
k,
+ Aps + A S, )u
P(pA,
+
k,
(A 2-5)
,
Since the shooting method does not work in most of cases, the solution proceeds by
solving the transient equation of incompressible flow inside the DPF channel. The mass
balance and Darcy equation do not change. The time derivative term needs to be added to
the momentum balance equation to describe how the flow evolves to steady state.
Momentum balance in transient problem
Inlet channel:
p d(b u2)
pdbu
b_2
±
o
b,
dt
__dP
Fu
b,
dz
b,
,
I
lo
dz
2
2(A 2-7)
Outlet channel:
d(u2 )
dt+ p
dt
d(ut4)
dz
=
dP
F_
__u
d
dz
7 2
(A 2-8)
b
Introducing dimensionless quantities as follows:
=
4LeU
zu
in
Leff
P- P
Pol
* =llUinbkS1
4Lejj k,
P
=
_
;
(A 2-9)
bkUin
(A 2-10)
(A 2-11)
t
Lef / U~
With i = 1 for the inlet channel and i = 2 for the outlet channel leads to the dimensionless
system, with the mass balance in dimensionless form:
db
d162
d2i
d2
1
= -b
2
fi
(A 2-12)
(A 2-13)
=
Multiplying (A 2-13) by b2
,
adding this product to (A 2-12) and integrating from 0 to 2
results in:
135
bI(2
2
)+bk26 2 (2)= b,0( = 0)2
6(
(A 2-14)
Momentum balance in dimensionless form:
dIg
d
+
A3 (b, 6
2b,
d
dP
di2
A- dz
2+
bk2
A
A 2fi± + 2~db
b 0 di
b
+k
Gi
Adb
22 2
2z
+
2
b2
di
-
(A 2-16)
=0
2
(A 2-15)
Darcy equation in dimensionless form:
APA= B1
(A 2-17)
w+ /modUw
Subtract (A 2-16) from (A 2-15), and substituting (A 2-14) and (A 2-17) into the
expression results in:
A 3(L2
!±Ju2u
d(fi2 )
b2
A
b
) di
_-d
d
B du2
d 2
d
dQ2
+2
2m
m
d2
±Arbk
+ 14 ~i1i~2A
-1
-fi2AAI bk di
d2
-A
A
2(1+
2 +A 2
2A (A-b2Q
5
k
2
(A 2-18)
-
db0
The dimensionless parameters are defined from Eq.(3.13) to Eq.(3.19).
The boundary conditions are defined in Eq.(3.20) and Eq.(3.21).
The initial condition is shown at Eq.(3.22).
136
Appendix 3
Data from NIST-JANAF Thermochemical Tables
Temperature
LogioKf
02
NO
K
100
200
250
298.15
300
350
400
450
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
NO 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-6.460
-2.931
-8.218
-5.172
-5.074
-2.828
-1.143
-.8320
-.7840
-.2100
-.0860
-.2430
-.5870
-.0630
-.6330
-.2750
-.9720
-.7120
-.4870
-.2900
-.1160
-.9620
-.8240
-.6990
-0.874
-1.863
-0.103
-.9800
-.9440
-.125
-.517
-.046
-.672
-.114
-.717
-.420
-.188
-.003
-.851
-.724
-.615
-.522
-.441
-.370
-.307
-.251
-.201
-.155
137