characterization and analysis of ceria-coated gasoline ...ardous particulate matter emissions from...

Characterization and Analysis of Ceria-Coated GasolineParticulate Filter

Harikesh Arunachalama, Gabriele Pozzatob, Mark A. Hoffmanc, Simona Onoria,∗

aDepartment of Energy Resources Engineering, Stanford University, Stanford, California 94305, USAbDipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy

cDepartment of Mechanical Engineering, Auburn University, Auburn, Alabama 36849, USA

Abstract

Gasoline particulate filters (GPFs) are practically adoptable devices to mitigate haz-

ardous particulate matter emissions from vehicles using gasoline direct ignition (GDI)

engines. This paper describes the soot accumulation and regeneration experiments con-

ducted on a ceria-coated GPF installed downstream of a three-way catalytic converter

in a vehicle operating a GDI engine. Using the geometric design parameters of the

coated GPF, the total volume of cordierite and the total trapping volume of exhaust gas

in the GPF were calculated. The measured pre-GPF air-fuel ratio was used to determine

the volume fraction of the exhaust gas constituents. Oxygen density and the specific

heat of the exhaust gas were obtained as a function of temperature using the computed

volume fractions. Finally, the amount of soot mass oxidized during a regeneration

event was evaluated using the measured parts per million levels of pre- and post-GPF

CO2 gas. These parameters are essential to characterize the dynamic performance of

a GPF. Data acquired from experiments, and the aforementioned parameters serve as a

foundation for the development of mathematical models for virtual sensor deployment

and assessment of GPF performance across different initial soot loading and operating

temperature conditions.

Keywords: gasoline direct injection, gasoline particulate filter, catalytic washcoat,

experimental characterization

∗Corresponding authorEmail address: [email protected] (Simona Onori)

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 28 May 2018 doi:10.20944/preprints201805.0397.v1

© 2018 by the author(s). Distributed under a Creative Commons CC BY license.

http://dx.doi.org/10.20944/preprints201805.0397.v1

http://creativecommons.org/licenses/by/4.0/

Nomenclature

λ air/fuel ratio normalized by the stoichio-

metric air/fuel ratio, [−]

φwall average porosity of the wall in the coated

GPF channels, [−]

ρO2density of oxygen, [kg/m3]

CO2,in pre-GPF ppm levels of CO2, [−]

CO2,out post-GPF ppm levels of CO2, [−]

Cp,gas specific heat capacity of the exhaust gas,

[J/(kgK)]

Cp,i specific heat capacity of exhaust gas con-

stituent species i, [J/(kgK)]

D coated GPF substrate diameter, [m]

hchannel width of each channel, [m]


2




hplug width of each plug, [m]

hwall thickness of the wall, [m]

lwall length of the coated GPF substrate, [m]

lplug length of each plug in the channels of the

coated GPF, [m]

mc,exp experimentally determined soot mass, [kg]

mc,exp,ini the value of mc,exp prior to the beginning

of a regeneration event, [kg]

mc,exp,end the value of mc,exp at the end of a regener-

ation event, [kg]

mc,init initial mass of soot prior to regeneration,

[kg]

mO2 mass of oxygen, [kg]

mg exhaust gas mass flow rate, [kg/s]

MC carbon molar mass, 12× 10−3 [kg/mol]

MCO2carbon dioxide molar mass,

44× 10−3 [kg/mol]

MO2oxygen molar mass, 32× 10−3 [kg/mol]

nC number of moles of carbon, [−]

nO2 number of moles of oxygen, [−]

ntotal total moles of the products of the combus-

tion reaction, [mol]

Nch total number of channels in the GPF, [−]

Ncross total number of channels across the semi-

circular GPF section, [−]

ppm parts per million

R ideal gas constant, 8.314 [J/(molK)]

tf end time of a regeneration event, [s]

tm time when the pre-GPF air-fuel ratio first

reaches its maximum value, [s]

ts start time of a regeneration event, [s]

Tgas temperature of the exhaust gas con-

stituents, [K]

Tinlet measured exhaust gas temperature at the

inlet of the GPF, [K]

Vcord total volume of cordierite in the GPF

Vexh filter trapping volume

Yi volume fraction of exhaust gas constituent

i, [−]

3



1. Introduction

Rapid urbanization and industrialization in recent decades has been achieved through

excessive consumption of fossil-fuel based energy resources. These advancements

come at the cost of environmental degradation resulting from various factors of pollu-

tion [1]. Different nations have called for innovative solutions to mitigate the negative

impact of economic development on climate change. Policies enforced in the trans-

portation sector involve improved fuel quality, promoting sustainable transportation,

and alternate sources of propulsion [2].

A notable advancement in engine technology to meet current and future regulation

targets is the transition from port fuel injection (PFI) systems to gasoline direct injec-

tion (GDI) systems [3]. In PFI engines, fuel is sprayed into the intake ports where

it mixes with the incoming air, whereas in GDI engines, fuel is sprayed directly into

the engine cylinder where it atomizes, mixes with the incoming air, and evaporates.

GDI engines offer more flexibility and accuracy in terms of fuel injection quantity and

provide thermodynamic benefits from evaporative charge cooling [4].

However, under certain operating modes, GDI engines suffer from limited fuel-air

mixing in the combustion chamber. As a result, hazardous particulate matter (PM)

are released into the atmosphere [5]. Experimental studies [4] have revealed that GDI

engines emit greater quantities of PM than PFI engines. PM emissions pose serious

health concerns such as decreased respiratory function and irregular heart beat [6].

Addressing the release of non-volatile PM presents an urgent technological and social

concern. Acknowledging the need to mitigate these hazardous emissions, increasingly

stringent regulations have been imposed across the world [7, 8, 9, 10].

Two approaches to mitigate PM emissions exist today: a) minimize PM forma-

tion in the combustion chamber, and b) oxidize particulates in the exhaust system [11].

Post-combustion PM elimination methodologies include: increasing the exhaust mani-

fold wall temperatures to support soot oxidation, and the use of aftertreatment devices

such as PM filters. Automotive manufacturers have recognized gasoline particulate fil-

ters (GPFs) as a promising and practically adoptable PM emission control device for

the exhaust system [12].

4



Particulate filter (PF) technology has been successfully implemented to mitigate

exhaust gas emissions in diesel vehicles through diesel particulate filters (DPFs) [13].

In comparison, GPF technology is relatively new and many research challenges remain

to be addressed. While the geometric structures of DPFs and GPFs are similar, there

are characteristic differences in the operating conditions and PM size and morphology

between the gasoline and diesel cases [14, 15]. These dissimilarities make it difficult

to apply DPF knowledge directly to GDI engines without making suitable adjustments.

The varying behavioral characteristics also elucidate the need for characterization tools

designed specifically for GPFs.

Different studies have experimentally evaluated the performance of GPFs in miti-

gating PM emissions in GDI engine operated vehicles, both as stand-alone devices [14,

16] as well as in conjunction with a three-way catalytic converter (TWC) [17, 18].

Lambert et. al. [19, 20] analyzed the accumulation of ash in ceramic wall-flow GPFs

located downstream of a TWC as a function of the vehicle mileage. Another study [21]

evaluated the filtration efficiency and PM mitigation performance of GPFs as a function

of the ambient temperature for the FTP-75 and US06 driving cycles.

Despite these developments, experimental investigations of exhaust gas behavior

in GPFs have not been sufficiently explored. A critical challenge in characterizing

GPF dynamics is that the filtration and regeneration mechanisms for small particu-

lates dispersed within the wall pores rather than caked atop the porous wall are not

well understood. Boger et. al. [22] conducted experiments to evaluate the amount of

soot oxidized in uncoated GPFs during a regeneration event. However, no such stud-

ies have been reported in literature for catalyzed GPFs which offer a comparatively

enhanced performance in terms of: a) filtration efficiency [23], b) reduction in NOx

emissions [24], and c) soot oxidation capability [24].

Regeneration events require a lean air-fuel mixture with significantly higher O2

concentration in the exhaust gas compared to nominal operating conditions. In sce-

narios where the GPF is installed downstream of a TWC, a device which requires

stoichiometric operating conditions for optimal performance, the conflicting needs of

the two devices can create non-optimal operating scenarios which hamper fuel econ-

omy. Therefore, experimental characterization and analysis of exhaust transport in

5



GPFs during regeneration is required to: a) monitor GPF internal temperature and pre-

vent thermal stresses, and b) assess the frequency of conducting regeneration events to

oxidize the accumulated soot and relieve the increasing back pressure on the engine.

One of the novel contributions of this work is a quantitative assessment of the ther-

mal and soot oxidation dynamics in a ceria washcoated GPF through experiments. This

experimental campaign not only enables the evaluation of parameters that are vital to

characterize GPF dynamics, but also serves as a foundation for the development of

mathematical models which can virtually sense GPF behavior under diverse operating

conditions. This aspect of research is crucial, given that the costs and calibration efforts

associated with the installation of real sensors in GPFs would be infeasible for practical

applications.

This paper is structured as follows: Section 2 presents a overview of GPFs and

Section 3 summarizes the experimental studies undertaken to understand the transport

dynamics in a ceria coated GPF during nominal operation and regeneration events. Sec-

tion 4 elaborates upon the approach to determine critical parameters that characterize

GPF dynamic transport, using geometric information, experimental data, and thermo-

dynamic principles. Finally, Section 5 summarizes the contributions of this work.

2. Gasoline Particulate Filters

GPFs are emissions aftertreatment devices that are installed in the tailpipe of GDI

operating gasoline vehicles to mitigate particulate emissions. They were first com-

mercially introduced by Diamler in their Mercedez-Benz S500 luxury sedan vehicle

segment in early 2014 [25]. GPF substrates are generally composed of a porous three-

dimensional structure [26] and are made of ceramic materials or metallic fibers. They

have been synthesized in a variety of shapes ranging from circular to oval cross sec-

tion [27].

GPFs consist of a monolithic structure with axially parallel channels which are

alternatively plugged at each end. As the exhaust gas enters the inlet channel and

is forced to pass through the porous walls, soot particulates are trapped within the

channel walls. Over time, this accumulation of soot increases the engine back pressure,

6



Frontal View

Plugs

(b)

Inlet Outlet

Wall-flowmonolith

configuration

Channels

(a)

Brick

Housing

Figure 1: (a) Side view of the sectioned coated GPF, and (b) axially parallel channels which are alternativelyplugged at each end with cordierite. A two-dimensional view of an inlet channel, porous wall, and an outletchannel of the GPF is shown here.

which can negatively impact engine performance and fuel economy. To minimize this

negative impact, the soot trapped in the GPF must be periodically removed. This is

accomplished via regeneration, i.e. oxidation of soot at elevated temperatures in the

presence of oxygen [28].

The structure and internal design of the coated GPF used in the experimental cam-

paign of this work is presented in Fig. 1. The washcoat material is primarily composed

of ceria (CeO2). Precious metals are loaded within the cerium to provide catalytic

reaction benefits, while the cerium provides the scaffolding for the precious metals and

oxygen storage ability that enhance soot oxidation reactions inside the GPF.

3. Experimental Characterization of a Ceria-Coated GPF

Experimental work, data acquisition, and data analysis associated with the soot

accumulation and soot regeneration stages were conducted at the Chassis Dynamome-

ter laboratory located at the Clemson University International Center for Automotive

Research.1

1The authors of this manuscript were affiliated with the Department of Automotive Engineering, ClemsonUniversity, Greenville, SC 29607, USA, when the experimental work and model development studies wereundertaken.

7



Experimental data sets are developed with different initial soot loadings and tem-

peratures at the onset of regeneration. For each data set, multiple regeneration events

are performed in a sequential manner to gradually decrease the overall amount of soot

accumulated inside the coated GPF through oxidation. Temperature measurements

were obtained by installing K-type thermocouples in the GPF channel from the rear

of the filter. The spatially diverse locations of the sensors spanned the axial and radial

directions from the inlet to the outlet of the coated GPF. The pre- and post-GPF ppm

levels of CO and CO2 gases were measured by simultaneously passing the respective

gas streams through a dual channel Fourier Transform Infrared Spectroscopy (FTIR)

analyzer with equivalent sample line lengths and sample flow rates.

Prior to regeneration, the engine is switched to lean operation, producing a precip-

itous decrease in CO2 pre-GPF. Because of the presence of a TWC upstream of the

GPF, the decline in CO2 concentration is gradually observed, instead of a step change

as seen in the measured exhaust gas mass flow rate, mg . Due to an increase in the

amount of O2 inside the GPF compared to nominal operation, the post-GPF CO2 lev-

els increase beyond the inlet, indicating regeneration. During the onset of regeneration,

the air-fuel ratio λ, measured using a wide range lambda sensor mounted upstream of

the GPF, is greater than the stoichiometric value of 1. When the regeneration event is

terminated, the post-TWC air-fuel ratio returns to its stoichiometric value.

The layout of different thermocouples installed in the coated GPF is shown in

Fig. 2. Sensor locations 2, 3, and 4 represent the GPF internal temperatures along

the flow centerline of the front-plane, rear-plane, and mid-plane, respectively. Prior

to regeneration, soot accumulation experiments were performed with the coated GPF

installed downstream of a TWC on a vehicle operating at a constant engine load for

extended periods of time. Based on the engine operating conditions and mg , the back-

pressure developing across the GPF (measured using a differential pressure sensor) and

soot mass accumulation were determined. Accumulation experiments were specifically

designed to produce different initial soot loading densities within the coated GPF.

The GPF inlet temperature at the onset of each successive regeneration event was

increased to enhance the soot oxidation reaction kinetics despite the decreasing GPF

carbon concentration after each successive regeneration event. Note that utilizing a

8



𝑇𝑇2

𝑇𝑇3

𝑇𝑇4

Exhaust Flow1.5” from front face

1.5” from rear face

Mid bed

Inlet Outlet

FP MP RP

Front Plane (FP)

Mid Plane (MP)

Rear Plane (RP)

Engine SideExhaust

Flow

𝑇𝑇𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝑇𝑇4Exhaust Flow

GPF

Thermocouples

𝑇𝑇2 𝑇𝑇3

Figure 2: Schematic representation of the location of different thermocouples to measure the internal GPFtemperature.

conservative inlet temperature at the onset of the first regeneration minimizes the risk

of overheating the GPF during soot oxidation. For every experimental regeneration

event, it is possible to determine the initial and final soot mass inside the coated GPF

from the pre- and post-GPF CO2 ppm measurements. This is outlined in Section 4.4.

4. GPF Dynamics Charaterization Parameters

4.1. Calculation of Vcord and Vexh

An isometric view of the coated GPF with alternating channels and plugs is shown

in Fig. 3. The GPF has an equal number of channels and plugs, and every channel

and plug have the same width. Vcord is the total volume of cordierite in the GPF and

Vexh is the exhaust gas trapping volume inside the GPF. The wall thickness, hwall,

is obtained by assuming the coated GPF to have a cylindrical shape with a circular

cross-section. This facilitates the calculation of Ncross, the total number of channels

across the frontal semi-circular view of the sectioned GPF. The geometric properties of

the GPF are summarized in Table 1. Assuming the GPF is composed of two identical

9



𝑫/𝟐

𝑫

𝟖𝟎 𝒑𝒍𝒖𝒈𝒔

(a)

𝐶ℎ𝑎𝑛𝑛𝑒𝑙

ℎ𝑤𝑎𝑙𝑙

ℎ𝑐ℎ𝑎𝑛𝑛𝑒𝑙

One channel unit

𝑃𝑙𝑢𝑔

ℎ𝑤𝑎𝑙𝑙

ℎ𝑝𝑙𝑢𝑔 = ℎ𝑐ℎ𝑎𝑛𝑛𝑒𝑙

One plug unit

(c)

𝑃𝑙𝑢𝑔


𝑃𝑙𝑢𝑔


𝑃𝑙𝑢𝑔


𝑫

(b)

Figure 3: (a) Isometric view showing the front and sectioned interior of a coated GPF. The cross-sectionshown here is assumed to be semi-circular, and the frontal view represents the maximum number of channelsfrom top to bottom. Alternating channels and plugs span the entire frontal view, as shown in (b). All channelsand plugs have a thickness of (hchannel + hwall). (c) represents the cross-section of a single channel anda single plug.

semi-cylinders, Nch is expressed in terms of Ncross as:

Nch = 2 ·{Ncross ·

Ncross2·

0.5× π4D

2

D × D2

}⇒ Ncross =

√4×Nch

π≈ 80

(1)

The substrate diameter, D, is expressed in terms of Ncross and (hchannel + hwall)

as:

D = Ncross · (hchannel + hwall)

⇒ hwall =D

Ncross− hchannel = 0.215 [mm].

(2)

Figure 4 (a) represents a single inlet/outlet channel pair sectioned in the axial di-

rection. Figure 4 (b) illustrates a three dimensional view of a single inlet channel. Note

that the outlet channel is a mirror image of the inlet channel. The walls have a porosity

fraction of φwall, such that the volume fraction of the cordierite in the wall is equal to

10



Geometric parameter ValueSubstrate diameter, D 118 [mm]

Substrate length, lwall 127 [mm]

Plug length, lplug 5 [mm]

Width of inlet channel, hchannel 1.26 [mm]

Total number of channels, Nch 5085Average porosity of the wall, φwall 0.625 [−]

Substrate volume 1.39 × 10−3 [m3]

Particulate filter density, ρGPF 1100 [kg/m3]

Table 1: Geometric properties of the coated GPF used in the experimental campaign of this work.

(1− φwall). Vexh is then determined as:

Vexh = Nch ·{

(lwall − lplug) · h2channel + φwall · lwall · h2wall

+ 2 · φwall · lwall · hwall · hchannel}

= 1.222× 10−3 [m3]

(3)

Similarly, Vcord is equal to the sum of the volume of all the cordierite plugs and the

sum of the volume of cordierite in all the porous walls:

Vcord = Nch ·{lplug · h2plug + (1− φwall) · lwall · h2wall

+ 2 · (1− φwall) · lwall · hwall · hchannel}

= 0.1828× 10−3 [m3]

(4)

The sum of Vexh and Vcord is 1.4048 ×10−3 [m3], a value that is approximately equal

to the volume encompassed by the exterior geometric dimensions of the coated GPF

substrate.

11



(a) (b)

ℎ𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤

ℎ𝑐𝑐𝑐𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐𝑤𝑤

Outlet channel

Inlet channel

Wall

Wall

𝑙𝑙𝑝𝑝𝑤𝑤𝑝𝑝𝑝𝑝

𝑙𝑙𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤

ℎ𝑝𝑝𝑤𝑤𝑝𝑝𝑝𝑝

𝑃𝑃𝑙𝑙𝑃𝑃𝑃𝑃


𝐶𝐶ℎ𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑙𝑙


ℎ𝑐𝑐𝑐𝑤𝑤𝑐𝑐𝑐𝑐𝑐𝑐𝑤𝑤

𝑙𝑙𝑝𝑝𝑤𝑤𝑝𝑝𝑝𝑝𝑙𝑙𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤

ℎ𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤

Figure 4: (a) Two-dimensional view of an inlet channel, porous wall, and an outlet channel of the coatedGPF, and (b) three-dimensional view of the inlet channel incorporating the cordierite plug at the downstreamend.

4.2. Calculation of the volume fraction of the exhaust gas constituents

The volume fraction of species i in the exhaust gas is the ratio of the volume Vi that

it occupies and the total volume of all the exhaust gas species:

Yi =Vi∑j Vj

(5)

If the exhaust gas constituents follow ideal gas behavior, they satisfy the ideal gas

equation [29]:

P · Vi = ni ·R · Tgas, (6)

where ni represents the number of moles of exhaust gas constituent i, P and Tgas

represent the pressure and temperature of the exhaust gas, and R is the universal gas

constant. The ideal gas equation satisfied by the exhaust gas is:

P ·∑j

Vj =∑j

nj ·R · Tgas (7)

Using (6) and (7), Yi is expressed in terms of the total number of moles of the exhaust

gas constituents, ntotal:

Yi =ni

ntotal(8)

Under nominal operating conditions, the volume fraction of oxygen, YO2, is set

12



to zero by assuming near stoichiometric combustion of gasoline and a properly func-

tioning TWC upstream of the GPF. To initiate a regeneration event within the GPF, the

engine is forced to operate under lean conditions (λ > 1). As a result, the concentration

of oxygen inside the GPF increases and initiates the regeneration reactions.

As the internal GPF temperature increases, the enhanced reaction rates lead to an

accelerated oxidation of the trapped soot. YO2is computed using λ measurements and

the kinetics of the following combustion reaction [30]:

CaHb + λ(a+ b

4

)(O2 + 3.773N2)→

aCO2 + b2H2O + λ · 3.773 ·

(a+ b

4

)N2 + (λ− 1)

(a+ b

4

)O2 (9)

The total number of moles of combustion products in the above equation is:

ntotal = a+b

2+ λ · 3.773 ·

(a+

b

4

)+ (λ− 1)

(a+

b

4

)(10)

Considering CaHb = C8H18 (octane), Yi for each constituent gas species is deter-

mined using the ratio of the moles of that particular species:

YN2= λ ·

3.773×(a+ b

4

)ntotal

, YO2=

(λ− 1) ·(a+ b

4

)ntotal

,

YCO2=

a

ntotal, and YH2O =

(b2

)ntotal

(11)

Figure 5 presents the volume fraction of each exhaust gas constituent during the

regeneration event. When the fuel-cut event occurs, the volume fraction of O2 in the

exhaust gas is set to that of atmospheric air, 0.209 [31], and the regeneration event

begins. Due to the ceria’s oxygen storage capability, the regeneration event may be

elongated beyond the time when YO2drops to 0 at the GPF inlet.

13



Regeneration Event

Regeneration Event

(a) (b)

Figure 5: (a) Volume fraction of O2 and CO2 in the exhaust gas, and (b) Volume fraction of N2 and H2Oin the exhaust gas, during the course of the regeneration event.

(a) (b)

Regeneration Event

Regeneration Event

Figure 6: (a) Exhaust gas temperature at the GPF inlet, and (b) variation in O2 gas density with time as afunction of the exhaust gas GPF inlet temperature.

4.3. Calculation of ρO2and Cp,gas

ρO2and Cp,gas are exhaust gas properties that are dependent on the species con-

centration. ρO2 is determined as a function of Tinlet using the ideal gas equation:

PO2· VO2

= nO2·R · Tinlet (12)

The mass of oxygen trapped inside the coated GPF, mO2, is mathematically expressed

as ρO2· YO2

· Vexh. Converting VO2and nO2

in terms of mass and density terms, the

14



Regeneration Event

Regeneration Event

(a) (b)

Figure 7: (a) Pre- and post-GPF air-fuel ratio, and (b) variation in the specific heat capacity of the exhaustgas, over the course of the regeneration event.

above equation is reformulated as:

PO2·(mO2

ρO2

)=

(mO2

MO2

)·R · Tinlet (13)

The density of oxygen, ρO2, is then expressed as:

ρO2=PO2·MO2

R · Tinlet(14)

ρO2is evaluated using the exhaust gas temperature at the GPF inlet. Exhaust gas

pressure at this location is assumed to be equal to atmospheric pressure. Figure 6

(a) presents the exhaust gas temperature profile at the GPF inlet during a regenera-

tion event. Corresponding to this temperature profile, the dynamic variation of ρO2 is

presented in Fig. 6 (b).

Cp,gas is determined as a function of Tinlet using the volume fraction of each con-

stituent gas species (N2, O2, CO2, and H2O):

Cp,gas = YN2 · Cp,N2(Tinlet) + YO2 · Cp,O2(Tinlet)

+ YCO2· Cp,CO2

(Tinlet) + YH2O · Cp,H2O(Tinlet),(15)

15



Observation Window 1

Observation Window 2

X:162.6Y: 1.498e+05

X:161.8Y: 1.542e+05

X:316.4Y: 1.312e+05

X:315.6Y: 1.303e+05

(a)

(c)

(b)

Figure 8: (a) Raw measurements of pre and post-GPF CO2 ppm levels with the observation windows high-lighted, (b) magnified view of observation window 1, and (c) magnified view of observation window 2.

where Cp,N2(Tinlet), Cp,O2

(Tinlet), Cp,CO2(Tinlet), and Cp,H2O(Tinlet) are specific

heat capacities of the individual exhaust gas constituents. Their values as a function of

temperature are provided in the NIST-JANAF tables [32].

Figure 7 illustrates a representative variation in exhaust gas heat capacity during a

regeneration event. The decrease in the overall specific heat capacity is due to a de-

crease in the volume fraction of triatomic molecules, CO2 andH2O, whose more com-

plex molecular structures have a greater number of vibrational and rotational modes to

absorb energy than the simpler, diatomic molecular structures of N2 and O2.

4.4. Calculation of the soot mass oxidized, mc,exp, during regeneration

The experimental measurements of CO2 ppm levels are processed to account for

time delays associated with exhaust gas transport through the GPF and the FTIR ana-

lyzer. The following sequence of steps are implemented before determining the amount

of soot oxidized during a regeneration event:

1. Temporally shift the post-GPF CO2 ppm data to align with the pre-GPF CO2

ppm data. This shift eliminates the transport delay associated with exhaust gas

flow through the GPF.

16



(a) (b)

Figure 9: (a) Pre and post-GPF CO2 ppm levels before shifting (original data), and (b) CO2 ppm levelmeasurements after shifting the post-GPF CO2 ppm by 0.8 s.

2. Temporally shift pre- and post-GPF CO2 ppm to correlate the measured data

with the onset of a regeneration event. This shift eliminates the transport delay

associated with exhaust gas flow through transport lines to the FTIR analyzer.

Since the transport lines for both pre- and post-GPF ppm measurements are of

the same length and both analyzers use the same flow rate, both pre and post-GPF

CO2 measured data are shifted by the same amount. After employing this shift, the

FTIR species concentration data more accurately aligns with the mass flow and lambda

signals.

Using the raw measured CO2 ppm data, two time windows were observed to un-

derstand the magnitude of the time shift required. This is illustrated in Fig. 8. During

nominal engine operation, the pre- and post-GPF CO2 ppm measurements must be

nearly equal. The time instant at which the pre and post-GPF CO2 ppm levels reached

a peak/trough were analyzed. The post-GPF measurements achieved their correspond-

ing peak/trough value with a 0.8 s time delay with respect to their pre-GPF counter-

parts. Hence, this value was chosen to perform the time shift in step 1. The CO2 ppm

levels after this implementation are shown in Fig. 9.

To perform step 2, the start and end time of the regeneration event must be first

identified. The start time, ts, is chosen as the first time instance when the post-GPF

CO2 ppm level, CO2,out, exceeds the pre-GPFCO2 ppm level, CO2,in. The end time,

17



X:16.6Y: 1.832

X:16.6Y: 1.116e+05

X:18.4Y: 1.176e+05

X:18.4Y: 1.116e+05

X:31.6Y: 1.498e+05

X:31.6Y: 1.542e+05

Start of Regeneration

End of Regeneration

(a) (b)

Figure 10: (a) Approach to determine the start and end time of a regeneration event, and (b) pre-GPF CO2

ppm measurements with respect to the pre-GPF air-fuel ratio after a shift of 1.8 seconds to the left.

tf , is chosen as the first time instance when CO2,in exceeds CO2,out during the rise

in ppm levels. As shown in Fig. 10 (a), ts is equal to 18.4 s and tf is equal to 31.6 s.

Time tm is chosen as the instant when the pre-GPF air-fuel ratio curve first reaches its

maximum measured value. As shown in Fig. 10 (b), tm = 16.6 s.

Both pre- and post-GPF CO2 ppm data are shifted by the same amount such that

the start time of regeneration matches time tm. In this case, the pre- and post-GPF ppm

measurements are shifted by (ts − tm), or 1.8 s. With this time shift employed, YO2 is

equal to 0.209 as soon as the regeneration event begins.

It is assumed that no soot is oxidized during nominal engine operation, when the

post TWC λ is at the stoichiometric value of 1. During the regeneration event, mc,exp,

which represents the amount of soot oxidized, is calculated using the expression:

mc,exp,end = mc,exp,ini

+

∫ tf

ts

(CO2,out − CO2,in

)· 10−6 × mg ×

(MC

MCO2

)· dt

(16)

Once the pre- and post-GPF CO2 ppm levels are shifted with respect to the pre-GPF

λ, ts and tf become 16.6 s and 29.8 s, respectively. The experimental data presented

in this paper have been measured in time steps of ∆t = 0.2 s. Equation (16) can then

18



X: 0Y: 0

X: 16.6Y: 0

X: 23.2Y: 0.09 [𝑔𝑔]

X: 29.8Y: 0.24 [𝑔𝑔]

X: 50Y: 0.24 [𝑔𝑔]

Figure 11: The amount of soot oxidized as a function of time during the regeneration event illustrated inFig. 10 (a).

be expressed in discrete time as:

mc,exp,end = mc,exp,ini

+

M∑i=1

(CO2,out(i)− CO2,in(i)

)· 10−6 × mg(i)×

(MC

MCO2

)·∆t,

(17)

whereM = (tf−ts)/∆t = 66. Then,mc,exp at any time step (j+1) can be expressed

in terms of mc,exp at time step j:

mc,exp(j + 1) = mc,exp(j)

+

[(CO2,out(j)− CO2,in(j)

)· 10−6 × mg(j)×

(MC

MCO2

)·∆t

] (18)

The experimental data set presented in Fig. 10 (a) is 50 s long. The following consid-

erations have been made:

1. From time t = 0 s to time t = ts, it is assumed that there is no soot oxidation

(mc,exp = mc,exp,ini = 0).

2. From time t = ts to time t = tf , soot oxidation occurs due to regeneration, and

mc,exp is calculated at every time instant using equation (18).

19



3. From time t = tf to time t = 50 s, it is assumed that there is no soot oxidation

(mc,exp = mc,exp,end).

The amount of soot oxidized, mc,exp, for the experimental data presented in Fig. 10 (a)

is schematically represented in Fig. 11. The total amount of soot oxidized during this

regeneration event is equal to 0.24 [g].

5. Conclusions

Experimental characterization and analysis of vehicle aftertreatment devices such

as GPFs is essential to understand the different mechanisms that influence mass trans-

port, heat transport, and reaction kinetics of the exhaust gas constituents. This paper

summarized the experimental campaign undertaken on a vehicle operating a GDI en-

gine with a ceria-coated GPF installed downstream of a TWC.

The dynamic performance of the coated GPF is characterized by: a) geometric

parameters such as Vexh and Vcord, b) volume fraction of the exhaust gas constituents,

Yi, c) oxygen gas density, ρO2 and the specific heat of the exhaust gas, Cp,gas, and d)

the amount of soot mass oxidized during a regeneration event, mc,exp.

The overall trapping volume of the exhaust gas, Vexh, and the total volume of

cordierite, Vcord, were calculated based on the knowledge of the coated GPF design

parameters. The volume fraction of the exhaust gas constituent species were deter-

mined from the measured pre-GPF air-fuel ratio and the internal combustion reaction.

ρO2and Cp,gas were obtained from the volume fraction data and the use of the NIST-

JANAF thermochemical tables.

mc,exp was evaluated from the pre- and post-GPF CO2 ppm measurements. Data

pre-processing was performed to account for time delays associated with exhaust gas

transport through the GPF and a dual channel FTIR analyzer that measured the ppm

levels of CO and CO2 gases simultaneously.

The contributions of this paper serve as a foundation for the development of math-

ematical modeling tools that can: a) predict GPF transport dynamics during regenera-

tion events for different initial soot loading and temperature operating conditions, and

20



b) facilitate the optimization of GPF design for different geometric configurations and

washcoat materials.

6. Acknowledgements

The authors gratefully acknowledge the support of Fiat Chrysler Automobiles (FCA)

US LLC for granting permission to utilize experimental data from their research col-

laboration toward this effort. Responsibility for the contents of this paper lies with the

authors. Funding for this research work was in part supported by NSF Career Award

CMMI 1653836.

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