Effect of Heat and Mass Transfer Coefficients on thePerformance of Automotive Catalytic Converters

Tariq ShamimDepartment of Mechanical EngineeringThe University of Michigan-Dearborn

Dearborn, MI 48128-1491, USA

Full Length Article

Corresponding Author

T. ShamimAssistant Professor

Department of Mechanical EngineeringThe University of Michigan-Dearborn

Dearborn, MI 48128-1491

Phone: (313) 593-0913Fax : (313) 593-3851

email: shamim@umich.edu

1

Effect of Heat and Mass Transfer Coefficients on the Performance of

Automotive Catalytic Converters

Tariq Shamim

Department of Mechanical Engineering

The University of Michigan-Dearborn

Dearborn, MI 48128-1491, USA

Abstract

This paper numerically investigates the role of heat and mass transfer

coefficients on the performance of automotive catalytic converters, which are

employed to reduce engine exhaust emissions. The pollutant conversion performance

of a converter is influenced by a number of physical and chemical processes that take

place in gaseous and solid phases as the exhaust gases flow through the catalyst. A

quantitative predictive understanding of these complex catalyst processes involving

flow dynamics, heterogeneous surface reactions, and heat and mass transport

mechanisms is important in improving the converter design. The role of convective

transport phenomena becomes important at high temperature when the mass transfer

becomes rate limiting to an increasing extent. The objective of the present study is to

elucidate the influence of convective heat and mass transfer mechanisms. The

mathematical model considers the conservation of mass, momentum and energy in

both gaseous and solid phases. In addition to the heterogeneous surface reactions, the

2

model also takes into account the adsorption/desorption of oxygen in the catalyst

during non-stoichiometric composition of air-fuel mixtures. The governing equations

are solved by an implicit scheme using a successive line under relaxation method.

The converter performance under both the steady state and the transient conditions is

analyzed.

Key Words

engine emissions, engine exhaust after-treatment, heat and mass transfer, numerical

simulations.

Nomenclature

Cgj gas phase concentration of species j, mol/m3

Csj surface concentration of species j, mol/m3

cpg specific heat of gas, J/kg·K

cps specific heat of substrate, J/kg·K

Dh hydraulic diameter, m

Dj diffusion coefficient of species j, m2/s

Ga geometric surface area, m2/m3

∆Hk heat of reaction of species k, J/mol

hg heat transfer coefficient between flow and substrate, J/m2·s·K

h∞ heat transfer coefficient between substrate and atmosphere, J/m2·s·K

kmj mass transfer coefficient for species j, m/s

L catalyst length, m

Nu Nusselt number

Pr Prandtl number

3

Rk reaction rate of kth reaction, mol/m2·s

Re Reynolds number

Sc Schmidt number

Sext external surface to volume area ratio, m2/m3

t time, s

T∞ ambient temperature, K

Tg gas temperature, K

Ts substrate temperature, K

vg gas flow velocity, m/s

z coordinate along catalyst axis, m

Greek symbols

ε void volume fraction

λg thermal conductivity of gas, J/m·s·K

λs thermal conductivity of substrate, J/m·s·K

ρg gas density, kg/m3

ρs substrate density, kg/m3

1. Introduction

Emissions from engines are major sources of urban air pollution. The engine

exhaust gases contain oxides of nitrogen (NOx), carbon monoxide (CO), and partially

burned or unburned hydrocarbons (HC). These pollutants have hazardous effects on

environment and living beings. They may cause acid rain, smog, and several

respiratory diseases. Accordingly, they are being subjected to stringent regulations

4

worldwide. In gasoline engine applications, these pollutants can be removed from the

exhaust gases by employing catalytic converters.

Catalytic converters have been used in automobiles for several years and

various types of them are available. They can reduce engine emissions by more than

90%. However, due to progressively stricter emission regulations, the catalytic

converter design and performance need to be continuously improved. The design

improvement efforts require broadening of fundamental understanding of various

physiochemical processes that occur in a catalytic converter. The performance of a

catalyst depends greatly on the heterogeneous chemical reactions between the exhaust

gas and the monolith surface. The effect of these surface reactions has been studied

by many investigators [1]. In addition to chemical reactions, the catalyst performance

is strongly influenced by the transport mechanisms of mass and heat transfer from the

exhaust gases to the catalyst surface. Especially at higher temperatures, the mass

transfer process becomes rate-limiting to an increasing extent [2]. Hence, a correct

description of the mass transfer processes is important in catalyst models.

Most studies modeled the convective heat and mass transfer processes by

using the simplified one-dimensional film model. In the film model, the

dimensionless Nusselt (Nu) and Sherwood (Sh) numbers describe the heat and mass

transfer rates. Without being too much sophisticated, the film model is a good

compromise to obtain a reasonable prediction of the converter efficiency [3].

However, many uncertainties remain about the estimate of Nu and Sh numbers [4].

Some studies [e.g., 5] compute Nu and Sh numbers assuming the flow in monolith

channels is fully developed laminar. Other studies [e.g., 6] include the effect of

developing laminar flow at the channel inlet in the calculation of Nu and Sh numbers.

The effect of initial turbulence in the channel flow has also been proposed to be

5

included in the analysis of transport mechanism [2]. The ignition of reactions inside

the monolith has also been reported to influence the transfer processes [7].

The heat and mass transfer coefficients in monolithic structure were

experimentally determined by Votruba et al. [8]. They found no influence of inlet

effect on the mass transfer coefficient. Their values of Nu number are similar to that

of a recent study by Shayler et al. [9]. Their proposed mass transfer expression gives

values of Sh number approximately three times lower than that predicted by the

Hawthorn [6]’s expression. The mass transfer coefficients proposed by Ullah et al.

[10] are also lower than those of Hawthorn [6]. Ullah et al. proposed a new mass

transfer correlation based on experimental measurements. They reported the increase

in the mass transfer coefficients with an increase of cell density. They also found the

flow disturbance at the monolith inlet to influence the mass transfer process. A much

higher range of Nu and Sh numbers inside a monolith reactor was determined by

Hayes and Kolaczkowski [7]. In their numerical work, they found that at steady state

conditions, the correct value of Nu and Sh number in fully developed region for an

adiabatic cylindrical system is in the range 3.0–4.5. For other geometry, such as

square or triangular ducts, the value may be lower. For sharp transients, they found

that the values of Nu and Sh numbers might exhibit discontinuities. They suspected

incorrect analysis methodology for the substantial underprediction of Nu and Sh

numbers reported in the literature.

Holmgren and Andersson [2], in their experimental study, found that the

values of Sh number to be higher than that predicted by laminar flow calculations.

Their measurements for square monolith channels predicted Sh numbers in the range

3.7–7. They ascribed the higher values of Sh numbers to the turbulence effects. Even

though the Reynolds (Re) numbers in the monolith channel are generally below 600, a

6

certain degree of turbulence is present in the channel. The channel turbulence is

partly created by the presence of turbulence in the entering flow, turbulence generated

by monolith walls at the entrance, and the surface roughness of channels. The

enhancement of the heat and mass transfer processes as a result of the presence of

surface roughness has been documented by several other studies [e.g., 11]. Holmgren

and Andersson concluded that a Sh number below 2 is highly unreasonable as it

means that the film thickness in the film model for mass transfer is greater than half

the channel diameter. Hatton et al. [12] found that the bulk conversion in the catalyst

at high temperatures is not purely mass controlled. They suggested inclusion of a

temperature dependent term into the Sh relationship. In a numerical heat transfer

study, Day et al. [13] reported that the Nu number varies in the range 2.8–8 for a

triangular channel. The value was found to remain close to 3 for most of the channel

length. They also determined that the angle of incidence of the inlet flow to the front

face of a monolith has no net effect on the warm-up of the substrate for an equivalent

mass flow rate.

A critical review of the past studies show that there are contradicting reports

on the values of Nu and Sh numbers in a monolith catalyst. A wide range of the

values of these dimensionless numbers has been used in the past studies. However,

due to differences in the operating conditions and modeling approaches, it is difficult

to assess the effect of these numbers on the catalyst performance. The objective of

the present study is to systematically investigate the effects of heat and mass transfer

coefficients on the catalyst performance. This is done by varying only Nu and Sh

numbers and keeping operating conditions and modeling approach consistent. This

investigation will elucidate the effect of Nu and Sh numbers on the catalyst

performance. The improved understanding of catalyst performance is essential in

7

designing catalysts that can meet the future stringent emission regulations. In

addition to their applications in catalyst modeling, the results can be applied to

general cases of reacting flows in small tube configurations.

2. Mathematical Formulation

Figure 1 shows schematic of a catalytic converter. The details of mathematical

modeling of various phenomena in three-way catalysts are given elsewhere [14]. The

governing conservation equations are listed below:

The gas phase energy equation:

)()( sgagg

gg

Pg TTGhz

Tv

tT

cg

−−=∂

∂+

∂∂

ερ (1)

The gas phase species equation:

)()( js

jga

jm

jg

g

jg CCGk

zC

vt

C−−=

∂∂

+∂

∂ε (2)

The surface energy equation:

knss

n

ks

ka

sextsgags

ss

Pss

HCCTRG

TTShTTGhzT

tT

c

speciesreaction

∆⋅⋅⋅⋅⋅⋅⋅+

−−−+∂∂

−=∂

∂−

�=

∞∞

),,,(

)()()1()1(

1

1

2

2

λερε (3)

The surface species equation:

),,,()()1( 1 speciesNsss

ja

js

jga

jm

js CCTRGCCGkt

C⋅⋅⋅⋅⋅⋅−−=

∂∂

−ε (4)

where the superscript j varies from 1 to 7 representing, respectively, the following gas

and surface species: CO, NO, NH3, O2, C3H6, H2 and C3H8. The conservation

equation for the surface oxygen storage mechanism can be represented by Eq. (4)

excluding the convective mass transport term. The heat and mass transfer coefficients

(hg and jmk ) in the above equations are calculated from

8

h

gg D

Nuh

λ= (5)

h

jjm D

DShk = (6)

Values of Nu and Sh numbers are obtained from the correlations with Re, Pr and Sc

numbers. In the present study, the model validation was performed by using the

following forms of correlations:

n

zLPrRecNu ��

���

�= (7)

andn

zLScRecSh ��

���

�= (8)

The values of constants c and n used in the model validation part of this study were

based on proprietary information. The typical values of Nu and Sh numbers using the

selected constants are shown in Fig. 2. These values of Nu and Sh numbers yield

good agreement between model results and experimental measurements as described

in the next section.

The governing equations were discretized by using a non-uniform grid and

employing the control volume approach and the central implicit difference scheme in

the spatial direction. Since more chemical reactions take place near the inlet, smaller

grid spacing is used near the inlet and larger spacing near the exit. The equations

were solved by using a standard tri-diagonal matrix algorithm (TDMA) with a

successive line under-relaxation scheme. The surface chemical reactions are modeled

by using a 13-step reaction mechanism. The model also includes an additional 9-step

chemistry to model the oxygen storage capacity of the substrate wash-coat material. A

detailed description of the model, various mechanisms, solution procedure, initial and

boundary conditions are given by Shamim et al. [14].

9

3. Results and discussion

The numerical model was validated using the experimental measurements at

both steady and transient conditions. An excellent agreement (within 5%) between

the model results and the experimental measurements was found [14]. The effect of

heat and mass transfer coefficients was investigated by considering the converter

performance under transient conditions in a 4.6L 2V Lincoln Town car as it was

driven during the FTP cycle. The converter was a palladium-based catalyst, with a

length of 8 cm, cross-sectional area of 86.0254 cm2, cell density of 62 cells/cm2, and

wall thickness of 0.1905 mm. The boundary conditions for the model were obtained

from the experimental measurements, which included the mass flow rates of CO, HC,

NOx and the total gases at the catalyst inlet during the FTP. The measurements were

made at an interval of 1 second; therefore, there were 1372 measured data. The air-

fuel ratio of engine's fresh charge was calculated based on the measured air flow and

fuel supply rates. The ambient temperature for the measurements and simulation was

297 K.

3.1 Effect of Nusselt number

The effect of Nusselt number on the catalyst conversion performance during

the Federal Test Procedure (FTP) was investigated by simulating the catalyst

performance using a constant value of Nu number of 2.89 and comparing it with that

obtained by using a variable Nu number as calculated from Eq. (7). For this

comparison, the Sh number was calculated from Eq. (8). Figure 3 shows the results of

this comparison of constant and variable values of Nu numbers during the FTP. The

results depict that the cumulative emissions are slightly higher for variable Nu

number. Since the average values of Nu number calculated from Eq. (7) is higher

10

than 2.89, the results indicate that an increase of Nu number has a negative effect on

the catalyst pollutant conversion performance. Figure 3 shows that CO emissions

(5% higher than that for constant Nu number) are relatively more influenced than HC

(3.7% higher) and NO (0.8% higher) emissions. During the cold start period, the Nu

number dependence of catalyst performance is negligibly small.

To further investigate the effect of Nu number, a parametric study with

constant value of Nu number ranging from 1 to 10 was conducted. The value of Sh

number for this case also was calculated according to Eq. (8). Figure 4 shows the

cumulative CO, HC, and NO emissions during the FTP for different values of Nu

number. As in the above case, Nu number is shown to have some influence on the

pollutant conversion performance during the legislated cycle. Figure 4a plots the

cumulative CO emission, which is found to be relatively less influenced. The results

show that low Nu numbers produce relatively higher CO emissions during the initial

part of the FTP (first 200 seconds, which represents the cold start conditions).

Compared to Nu number of 10, the CO emission is 7.4% higher for Nu number of

unity. However, beyond 200 seconds, the higher Nu number does not produce low

CO emission. For the whole FTP cycle, Nu number of unity has the lowest CO

emissions. The CO emissions increase with an increase of Nu number. At Nu

number of 10, the emissions are roughly 7.7% higher than that for Nu number of 1.

HC emissions are found to have relatively stronger influence of Nu number

during the cold start conditions, as shown in the inset of Fig. 4b. During the first 200

seconds, the HC emissions are 23% higher for Nu number of unity compared to that

for Nu number of 10. During the entire FTP cycle, however, the Nu number

dependence of HC emissions is much smaller (approximately 3% difference between

values of Nu numbers of unity and 10). For Nu number ranging from 1 to 4, there is

11

no clear pattern of increasing or decreasing effect of Nu number on the catalyst HC

conversion performance. The NO emission results, plotted in Fig. 4c, show that NO

emission is lowest for Nu number of 1 during the first 200 seconds (approximately 7%

lower than that for other Nu numbers). During this cold start period, the other Nu

number results do not show any Nu number dependence. During the entire FTP cycle,

there is also no clear pattern of increasing or decreasing effect of Nu number on the

catalyst NO conversion performance. There is appreciable difference between the

results of Nu numbers of 3 and 4. The NO emission drops by 5% when Nu number is

changed from 3 to 4.

3.1.1 Oxygen Storage Capacity Effect

The effect of oxygen storage capacity (OSC) was investigated by simulating

the catalyst performance without OSC and then comparing it with the OSC case.

Figure 5 shows the cumulative CO, HC, and NO emissions at the exit of a non-

oxygen storage catalyst during the FTP for different Nu numbers. The results show

no significant influence of oxygen storage on Nu number dependence of catalyst

pollutant conversion efficiency. The CO emission pattern is similar to the OSC case –

at low Nu numbers, the CO emissions are higher during the initial part of the FTP and

are lower during the entire FTP cycle. Compared to Nu number of 1, the CO

emissions for Nu number of 10 are 5.4% higher. The Nu number dependence of HC

emission for non-OSC case is also small. However, in this case, there is more clear

decreasing effect of Nu number on HC emissions. The NO emissions, on the other

hand, do not show a clear pattern of increasing or decreasing effect of Nu number.

For different Nu numbers, NO emissions are within 3.5%.

12

3.2 Effect of Sherwood Number

The mass transfer effect on the catalyst conversion performance during the

FTP was investigated by simulating the catalyst performance by using a constant

value of Sh number of 2.89 and comparing it with that obtained by using a variable Sh

number as calculated from Eq. (8). For this comparison, the Nu number was

calculated from Eq. (7). Figure 6 shows the results of this comparison of constant and

variable values of Sh numbers during the FTP. As expected, the results show the Sh

number has much greater influence on the catalyst’s pollutant conversion

performance. The cumulative emissions are significantly lower for variable Sh

number (with the average value higher than 2.89). The CO and HC emissions are

respectively 26.3% and 20.3% lower than that for Sh number of 2.89. The effect of

Sh number on NO emissions, however, is relatively low (approximately 2.7%

difference between the two cases). Similar to the case of Nu number, the Sh number

dependence of CO and HC emissions during the cold start is negligibly small. NO

emissions, on the other hand, show Sh number dependence at much earlier stages of

the FTP. The results clearly show the importance of accurate modeling of Sh number

in determining the catalyst conversion performance.

The effect of Sh number was further investigated by conducting a parametric

study with constant values of Sh numbers ranging from 1 to 10. The value of Nu

number for this case also was calculated according to Eq. (7). Figure 7 shows the

cumulative CO, HC, and NO emissions during the FTP for different values of Sh

number. As expected, the results show a significant influence of Sh number (i.e.,

mass transfer phenomenon) on the catalyst conversion performance. Among the three

pollutants, CO depicts the strongest dependence on Sh number. The CO conversion

performance increases with an increase in Sh number. The cumulative CO emission

13

decreases by roughly 73% when Sh number is increased from a value of 1 to 10. A

strong influence of Sh number is shown even for values of Sh numbers from 2 to 4.

For this range of Sh number, typically used in determining the automotive catalyst

performance, the CO emission may vary by as much as 37%. This result clearly

underscores the importance of correct modeling of mass transfer phenomenon. The

figure shows that Sh number dependence is relatively stronger at low Sh numbers.

The pattern of Sh number dependence is found to be similar during the entire FTP.

The difference between the results of each Sh number becomes large at the later part

of the FTP.

The HC emissions also show strong dependence on Sh number as depicted in

Fig. 7b. The HC conversion performance increases with an increase in Sh number.

The results show a decrease of HC emissions by 75% when Sh number is changed

from a value of 1 to 10. Similar to the case of CO conversion, the Sh number

dependence is stronger at low Sh numbers. The effect of Sh number is also strong for

the range of Sh numbers from 2 to 4, as the emission decreases by 48%. The pattern

of Sh number dependence during the entire FTP is similar to that of the CO case.

Contrary to the cases of CO and HC conversion, the catalyst NO conversion

performance decreases with an increase of Sh number (see Fig. 7c). The cumulative

NO emission increases by 20% when Sh number is increased from a value of 1 to 10.

And there is a maximum 3.3% difference in the NO emissions for the Sh number

range of 2 to 4. The dependence of NO conversion performance on the mass transfer

phenomenon is relatively not as strong as in the cases of CO and HC. For NO also,

the Sh number dependence is stronger at low Sh number.

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3.2.1 Oxygen Storage Capacity Effect

The coupled effect of mass transfer phenomenon and the OSC was investigated by

simulating the catalyst performance without OSC and then comparing it with the OSC

case of the previous section. Figure 8 shows the cumulative CO, HC, and NO

emissions at the exit of a non-oxygen storage catalyst during the FTP for different Sh

numbers. The results show no significant effect of OSC on CO and HC emissions.

Similar to the OSC case, the emissions of both of these pollutants decrease with an

increase of Sh number. The OSC, however, is found to have a strange effect on NO

emissions. It changes the pattern of NO emissions for some Sh numbers. For the

OSC case, the slope of cumulative NO emissions during the FTP is small, indicating

small amounts of NO production at the later stage of FTP. However for the non-OSC

case, for some Sh numbers (especially for 10), the emission slope becomes steeper,

which indicates a higher production of NO at the later stage of FTP. For Sh number

of 1, the slope is relatively flat. Other than Sh number of 1, the NO emissions

increase with an increase of Sh number. The Sh number dependence of NO emissions

in the non-OSC case is much stronger (the cumulative NO emission increases by 86%

when Sh number is increased from a value of 2 to 10).

4. Conclusions

• The catalyst performance is influenced by both heat and mass transfer

phenomena, with mass transfer playing more substantial role. The influence of

these phenomena is relatively higher at low Nusselt / Sherwood numbers.

• With an increase of Nusselt number (i.e., heat transfer coefficient) CO emissions

increase, HC emissions slightly decrease. NO emissions show no clear pattern of

15

increasing or decreasing effect of Nu number. The increase of Sherwood number,

on the other hand, decreases CO and HC and increases NO emissions.

• The Nu number dependence of emissions during the cold start period may be

different from that during the warm up stage. For example, in contrast to the

warm-up period, the increase of Nu number has a decreasing effect on CO

emissions during the cold start period.

• The oxygen storage capacity (OSC) generally has no significant influence on the

Nu/Sh number dependence of catalyst conversion performance. However, the

OSC decreases the Sh number dependence of NO emissions.

Acknowledgments

The financial supports from the Chemical Engineering Department of the Ford

Scientific Research Laboratory, Office of Sponsored Research and the Center for

Engineering Education and Practice (CEEP) of the University of Michigan - Dearborn

are greatly appreciated.

References

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Science, 2000, 55, 1707-1716.

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Figure Captions

Figure 1 Schematic of a three-way catalytic converter

Figure 2 Values of Nu and Sh numbers along the catalytic converter length

Figure 3 Effect of Nu number on catalyst performance. Comparison of

cumulative emissions during the FTP for constant and variable Nu

numbers: (a) CO emissions; (b) HC emissions; (c) NO emissions.

Figure 4 Effect of Nu number on catalyst performance. Comparison of

cumulative emissions during the FTP for different Nu numbers: (a) CO

emissions; (b) HC emissions; (c) NO emissions.

Figure 5 Effect of Nu number on catalyst performance. Comparison of

cumulative emissions during the FTP for different Nu numbers without

oxygen storage capacity: (a) CO emissions; (b) HC emissions; (c) NO

emissions.

Figure 6 Effect of Sh number on catalyst performance. Comparison of

cumulative emissions during the FTP for constant and variable Sh

numbers: (a) CO emissions; (b) HC emissions; (c) NO emissions.

Figure 7 Effect of Sh number on catalyst performance. Comparison of

cumulative emissions during the FTP for different Sh numbers: (a) CO

emissions; (b) HC emissions; (c) NO emissions.

Figure 8 Effect of Sh number on catalyst performance. Comparison of

cumulative emissions during the FTP for constant and variable Sh

numbers without oxygen storage capacity: (a) CO emissions; (b) HC

emissions; (c) NO emissions.

19

L a Exhaust gases Exhaust gases from engine to tailpipe b

Inlet cone Catalyst Outlet cone Cell/channel

Side view of catalyst assembly Front view of catalyst brick

Fig. 1

20

Fig. 2

21

Fig. 3 (a)

22

Fig. 3 (b)

23

Fig. 3 (c)

24

Fig. 4 (a)

25

Fig. 4 (b)

26

Fig. 4 (c)

27

Fig. 5 (a)

Fig. 5 (b)

28

29

Fig. 5 (c)

Fig. 6 (a)

30

Fig. 6 (b)

31

Fig. 6 (c)

32

Fig. 7 (a)

33

Fig. 7 (b)

34

Fig. 7 (c)

35

Fig. 8 (a)

36

Fig. 8 (b)

37

38

Fig. 8 (c)